4_analyses_robust

Robustness Analyses

Helper

source("0_helpers.R")

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opts_chunk$set(warning = FALSE)

Load data

birthorder = readRDS("data/alldata_birthorder.rds")

Data preparations

# For analyses we want to clean the dataset and get rid of all uninteresting data
birthorder = birthorder %>%
  filter(!is.na(pidlink)) %>% # no individuals who are only known from the pregnancy file
  filter(is.na(lifebirths) | lifebirths == 2) %>% # remove 7 and 2 individuals who are known as stillbirth or miscarriage but still have PID
  select(-lifebirths) %>%
  filter(!is.na(mother_pidlink)) %>%
  select(-father_pidlink) %>%
  filter(is.na(any_multiple_birth) | any_multiple_birth != 1) %>% # remove families with twins/triplets/..
  filter(!is.na(birthorder_naive)) %>%
  select(-starts_with("age_"), -wave, -any_multiple_birth, -multiple_birth) %>%
  mutate(money_spent_smoking_log = if_else(is.na(money_spent_smoking_log) & ever_smoked == 0, 0, money_spent_smoking_log),
         amount = if_else(is.na(amount) & ever_smoked == 0, 0, amount),
         amount_still_smokers = if_else(is.na(amount_still_smokers) &  still_smoking == 0, 0, amount_still_smokers),
         birthyear = lubridate::year(birthdate))

# recode Factor Variable as Dummy Variable
birthorder = left_join(birthorder,
                                birthorder %>%
                                  filter(!is.na(Category)) %>%
                                  mutate(var = 1) %>%
                                  select(pidlink, Category, var) %>%
                                  spread(Category, var, fill = 0, sep = "_"), by = "pidlink") %>%
  select(-Category)

# recode Factor Variable as Dummy Variable
birthorder = left_join(birthorder,
                                birthorder %>%
                                  filter(!is.na(Sector)) %>%
                                  mutate(var = 1) %>%
                                  select(pidlink, Sector, var) %>%
                                  spread(Sector, var, fill = 0, sep = "_"), by = "pidlink") %>%
  select(-Sector)


### Variables
birthorder = birthorder %>%
  mutate(
    # center variables that are used for analysis
  g_factor_2015_old = scale(g_factor_2015_old),
  g_factor_2015_young = scale(g_factor_2015_young),
  g_factor_2007_old = scale(g_factor_2007_old),
  g_factor_2007_young = scale(g_factor_2007_young),
  raven_2015_old = scale(raven_2015_old),
  math_2015_old = scale(math_2015_old),
  count_backwards = scale(count_backwards),
  raven_2015_young = scale(raven_2015_young),
  math_2015_young = scale(math_2015_young),
  words_remembered_avg = scale(words_remembered_avg),
  words_immediate = scale(words_immediate),
  words_delayed = scale(words_delayed),
  adaptive_numbering = scale(adaptive_numbering),
  raven_2007_old = scale(raven_2007_old),
  math_2007_old = scale(math_2007_old),
  raven_2007_young = scale(raven_2007_young),
  math_2007_young = scale(math_2007_young),
  riskA = scale(riskA),
  riskB = scale(riskB),
  years_of_education_z = scale(years_of_education),
  Total_score_highest_z = scale(Total_score_highest),
  wage_last_month_z = scale(wage_last_month_log),
  wage_last_year_z = scale(wage_last_year_log),
  big5_ext = scale(big5_ext),
  big5_con = scale(big5_con),
  big5_agree = scale(big5_agree),
  big5_open = scale(big5_open),
  big5_neu = scale(big5_neu),
  attended_school = as.integer(attended_school),
  attended_school = ifelse(attended_school == 1, 0,
                           ifelse(attended_school == 2, 1, NA)))

### Birthorder and Sibling Count
birthorder = birthorder %>% 
  mutate(
# birthorder as factors with levels of 1, 2, 3, 4, 5,
    birthorder_naive_factor = as.character(birthorder_naive),
    birthorder_naive_factor = ifelse(birthorder_naive > 5, NA,
                                            birthorder_naive_factor),
    birthorder_naive_factor = factor(birthorder_naive_factor, 
                                            levels = c("1","2","3","4","5")),
    sibling_count_naive_factor = as.character(sibling_count_naive),
    sibling_count_naive_factor = ifelse(sibling_count_naive > 5, NA,
                                               sibling_count_naive_factor),
    sibling_count_naive_factor = factor(sibling_count_naive_factor, 
                                               levels = c("2","3","4","5")),

    birthorder_uterus_alive_factor = as.character(birthorder_uterus_alive),
    birthorder_uterus_alive_factor = ifelse(birthorder_uterus_alive > 5, NA,
                                            birthorder_uterus_alive_factor),
    birthorder_uterus_alive_factor = factor(birthorder_uterus_alive_factor, 
                                            levels = c("1","2","3","4","5")),
    sibling_count_uterus_alive_factor = as.character(sibling_count_uterus_alive),
    sibling_count_uterus_alive_factor = ifelse(sibling_count_uterus_alive > 5, NA,
                                               sibling_count_uterus_alive_factor),
    sibling_count_uterus_alive_factor = factor(sibling_count_uterus_alive_factor, 
                                               levels = c("2","3","4","5")),
    birthorder_uterus_preg_factor = as.character(birthorder_uterus_preg),
    birthorder_uterus_preg_factor = ifelse(birthorder_uterus_preg > 5, NA,
                                           birthorder_uterus_preg_factor),
    birthorder_uterus_preg_factor = factor(birthorder_uterus_preg_factor,
                                           levels = c("1","2","3","4","5")),
    sibling_count_uterus_preg_factor = as.character(sibling_count_uterus_preg),
    sibling_count_uterus_preg_factor = ifelse(sibling_count_uterus_preg > 5, NA,
                                              sibling_count_uterus_preg_factor),
    sibling_count_uterus_preg_factor = factor(sibling_count_uterus_preg_factor, 
                                              levels = c("2","3","4","5")),
    birthorder_genes_factor = as.character(birthorder_genes),
    birthorder_genes_factor = ifelse(birthorder_genes >5 , NA, birthorder_genes_factor),
    birthorder_genes_factor = factor(birthorder_genes_factor, 
                                     levels = c("1","2","3","4","5")),
    sibling_count_genes_factor = as.character(sibling_count_genes),
    sibling_count_genes_factor = ifelse(sibling_count_genes >5 , NA,
                                        sibling_count_genes_factor),
    sibling_count_genes_factor = factor(sibling_count_genes_factor, 
                                        levels = c("2","3","4","5")),
    # interaction birthorder * siblingcout for each birthorder
    count_birthorder_naive =
      factor(str_replace(as.character(interaction(birthorder_naive_factor,                                                              sibling_count_naive_factor)),
                        "\\.", "/"),
                                           levels =   c("1/2","2/2", "1/3",  "2/3",
                                                        "3/3", "1/4", "2/4", "3/4", "4/4",
                                                        "1/5", "2/5", "3/5", "4/5",
                                                        "5/5")),
    count_birthorder_uterus_alive =
      factor(str_replace(as.character(interaction(birthorder_uterus_alive_factor,                                                              sibling_count_uterus_alive_factor)),
                        "\\.", "/"),
                                           levels =   c("1/2","2/2", "1/3",  "2/3",
                                                        "3/3", "1/4", "2/4", "3/4", "4/4",
                                                        "1/5", "2/5", "3/5", "4/5", "5/5")),
    count_birthorder_uterus_preg =
      factor(str_replace(as.character(interaction(birthorder_uterus_preg_factor,                                                              sibling_count_uterus_preg_factor)), 
                         "\\.", "/"),
                                           levels =   c("1/2","2/2", "1/3",  "2/3",
                                                        "3/3", "1/4", "2/4", "3/4", "4/4",
                                                        "1/5", "2/5", "3/5", "4/5", "5/5")),
    count_birthorder_genes =
      factor(str_replace(as.character(interaction(birthorder_genes_factor,                                                              sibling_count_genes_factor)), "\\.", "/"),
                                           levels =   c("1/2","2/2", "1/3",  "2/3",
                                                        "3/3", "1/4", "2/4", "3/4", "4/4",
                                                        "1/5", "2/5", "3/5", "4/5", "5/5")))

birthorder <- birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive)

Intelligence

g-factor 2015 old

birthorder <- birthorder %>% mutate(outcome = g_factor_2015_old)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3231	0.2601	-1.242	6662	0.2143	-1.053	0.407
fixed	NA	poly(age, 3, raw = TRUE)1	0.08335	0.02685	3.104	6645	0.001918	0.007973	0.1587
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002898	0.0008524	-3.4	6621	0.0006773	-0.005291	-0.0005057
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002128	0.000008432	2.524	6572	0.01164	-0.000002389	0.00004495
fixed	NA	male	0.04163	0.02121	1.963	6015	0.04975	-0.01791	0.1012
fixed	NA	sibling_count3	0.02483	0.0347	0.7154	4807	0.4744	-0.07259	0.1222
fixed	NA	sibling_count4	-0.01283	0.03626	-0.3539	4537	0.7234	-0.1146	0.08896
fixed	NA	sibling_count5	-0.01726	0.03807	-0.4535	4267	0.6502	-0.1241	0.08959
ran_pars	mother_pidlink	sd__(Intercept)	0.6049	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7309	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3259	0.2608	-1.25	6691	0.2115	-1.058	0.4061
fixed	NA	birth_order	0.001529	0.01018	0.1502	5182	0.8806	-0.02705	0.03011
fixed	NA	poly(age, 3, raw = TRUE)1	0.0834	0.02686	3.105	6647	0.001908	0.008012	0.1588
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0029	0.0008526	-3.402	6622	0.000673	-0.005294	-0.0005072
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002132	0.000008436	2.527	6574	0.01154	-0.000002365	0.000045
fixed	NA	male	0.0416	0.02122	1.961	6013	0.04994	-0.01795	0.1012
fixed	NA	sibling_count3	0.02434	0.03485	0.6984	4893	0.4849	-0.07349	0.1222
fixed	NA	sibling_count4	-0.01404	0.03714	-0.3779	4905	0.7055	-0.1183	0.09022
fixed	NA	sibling_count5	-0.01924	0.04029	-0.4775	5009	0.633	-0.1323	0.09385
ran_pars	mother_pidlink	sd__(Intercept)	0.6048	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.731	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.333	0.2625	-1.268	6734	0.2048	-1.07	0.404
fixed	NA	poly(age, 3, raw = TRUE)1	0.08388	0.02704	3.102	6712	0.001929	0.007981	0.1598
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002912	0.0008597	-3.387	6701	0.0007101	-0.005325	-0.0004988
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002139	0.000008516	2.512	6669	0.01202	-0.00000251	0.0000453
fixed	NA	male	0.04166	0.02122	1.963	6012	0.04965	-0.0179	0.1012
fixed	NA	sibling_count3	0.02627	0.0352	0.7465	5034	0.4554	-0.07252	0.1251
fixed	NA	sibling_count4	-0.006379	0.03752	-0.17	5058	0.865	-0.1117	0.09895
fixed	NA	sibling_count5	-0.02046	0.04046	-0.5057	5105	0.6131	-0.1341	0.09312
fixed	NA	birth_order_nonlinear2	0.009127	0.02447	0.3729	5243	0.7092	-0.05957	0.07782
fixed	NA	birth_order_nonlinear3	-0.004058	0.03093	-0.1312	4875	0.8956	-0.09087	0.08275
fixed	NA	birth_order_nonlinear4	-0.02644	0.04008	-0.6596	4745	0.5095	-0.1389	0.08606
fixed	NA	birth_order_nonlinear5	0.06311	0.05779	1.092	4467	0.2749	-0.09912	0.2253
ran_pars	mother_pidlink	sd__(Intercept)	0.604	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7315	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2996	0.2631	-1.138	6739	0.255	-1.038	0.4391
fixed	NA	poly(age, 3, raw = TRUE)1	0.0817	0.02706	3.02	6713	0.002541	0.005751	0.1577
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002829	0.0008605	-3.287	6706	0.001018	-0.005244	-0.000413
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002046	0.000008528	2.399	6678	0.01647	-0.00000348	0.0000444
fixed	NA	male	0.0421	0.02122	1.984	6001	0.04734	-0.01747	0.1017
fixed	NA	count_birth_order2/2	-0.03765	0.04216	-0.893	5516	0.3719	-0.156	0.0807
fixed	NA	count_birth_order1/3	0.02004	0.04291	0.467	6695	0.6405	-0.1004	0.1405
fixed	NA	count_birth_order2/3	0.01348	0.0474	0.2845	6859	0.776	-0.1196	0.1465
fixed	NA	count_birth_order3/3	-0.0111	0.05256	-0.2113	6890	0.8327	-0.1586	0.1364
fixed	NA	count_birth_order1/4	-0.0239	0.0487	-0.4908	6857	0.6236	-0.1606	0.1128
fixed	NA	count_birth_order2/4	0.01282	0.05089	0.252	6892	0.801	-0.13	0.1557
fixed	NA	count_birth_order3/4	-0.03739	0.05447	-0.6864	6874	0.4925	-0.1903	0.1155
fixed	NA	count_birth_order4/4	-0.07971	0.05726	-1.392	6838	0.164	-0.2405	0.08103
fixed	NA	count_birth_order1/5	-0.105	0.05422	-1.937	6897	0.05276	-0.2572	0.04716
fixed	NA	count_birth_order2/5	-0.006955	0.05671	-0.1226	6874	0.9024	-0.1661	0.1522
fixed	NA	count_birth_order3/5	-0.01149	0.05812	-0.1977	6834	0.8433	-0.1746	0.1517
fixed	NA	count_birth_order4/5	-0.02821	0.0612	-0.461	6754	0.6448	-0.2	0.1436
fixed	NA	count_birth_order5/5	0.02817	0.06237	0.4517	6733	0.6515	-0.1469	0.2033
ran_pars	mother_pidlink	sd__(Intercept)	0.6045	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7312	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	18410	18479	-9195	18390	NA	NA	NA
11	18412	18487	-9195	18390	0.02267	1	0.8803
14	18416	18512	-9194	18388	2.301	3	0.5122
20	18421	18558	-9191	18381	6.438	6	0.3759

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7436	0.4688	-1.586	4282	0.1128	-2.06	0.5723
fixed	NA	poly(age, 3, raw = TRUE)1	0.1332	0.05476	2.433	4293	0.01503	-0.0205	0.2869
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004198	0.00202	-2.078	4310	0.03772	-0.009868	0.001472
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000361	0.00002369	1.524	4328	0.1276	-0.0000304	0.0001026
fixed	NA	male	-0.04436	0.02496	-1.777	3982	0.07558	-0.1144	0.0257
fixed	NA	sibling_count3	0.00115	0.03716	0.03096	3165	0.9753	-0.1032	0.1055
fixed	NA	sibling_count4	-0.07358	0.04065	-1.81	2931	0.07039	-0.1877	0.04053
fixed	NA	sibling_count5	-0.1475	0.04672	-3.157	2769	0.00161	-0.2786	-0.01636
ran_pars	mother_pidlink	sd__(Intercept)	0.5194	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7004	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7611	0.4694	-1.621	4285	0.105	-2.079	0.5565
fixed	NA	birth_order	0.009772	0.01292	0.7564	3821	0.4495	-0.02649	0.04603
fixed	NA	poly(age, 3, raw = TRUE)1	0.1337	0.05476	2.441	4293	0.01469	-0.02005	0.2874
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004221	0.00202	-2.089	4308	0.03674	-0.009892	0.00145
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003656	0.0000237	1.543	4326	0.123	-0.00002996	0.0001031
fixed	NA	male	-0.04473	0.02496	-1.792	3982	0.07323	-0.1148	0.02534
fixed	NA	sibling_count3	-0.003487	0.03766	-0.0926	3220	0.9262	-0.1092	0.1022
fixed	NA	sibling_count4	-0.08445	0.04311	-1.959	3117	0.05024	-0.2055	0.03658
fixed	NA	sibling_count5	-0.1654	0.05239	-3.158	3206	0.001605	-0.3125	-0.01837
ran_pars	mother_pidlink	sd__(Intercept)	0.5191	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7006	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8081	0.4706	-1.717	4305	0.08599	-2.129	0.5127
fixed	NA	poly(age, 3, raw = TRUE)1	0.1386	0.05489	2.525	4309	0.01161	-0.01548	0.2927
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004396	0.002024	-2.171	4321	0.02996	-0.01008	0.001287
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003844	0.00002374	1.619	4335	0.1054	-0.00002819	0.0001051
fixed	NA	male	-0.04387	0.02497	-1.757	3975	0.07899	-0.1139	0.02622
fixed	NA	sibling_count3	-0.003513	0.0381	-0.0922	3317	0.9265	-0.1105	0.1034
fixed	NA	sibling_count4	-0.07787	0.04362	-1.785	3204	0.07437	-0.2003	0.04459
fixed	NA	sibling_count5	-0.1555	0.05312	-2.928	3301	0.003439	-0.3046	-0.006406
fixed	NA	birth_order_nonlinear2	0.05449	0.02872	1.898	3157	0.05783	-0.02611	0.1351
fixed	NA	birth_order_nonlinear3	0.02076	0.0368	0.564	3324	0.5728	-0.08254	0.124
fixed	NA	birth_order_nonlinear4	0.01169	0.04992	0.2342	3501	0.8149	-0.1284	0.1518
fixed	NA	birth_order_nonlinear5	0.04547	0.07653	0.5942	3272	0.5524	-0.1693	0.2603
ran_pars	mother_pidlink	sd__(Intercept)	0.5195	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7004	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8021	0.471	-1.703	4302	0.08866	-2.124	0.5201
fixed	NA	poly(age, 3, raw = TRUE)1	0.1375	0.05493	2.503	4303	0.01236	-0.01671	0.2917
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004338	0.002026	-2.141	4315	0.03234	-0.01003	0.00135
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003759	0.00002376	1.582	4329	0.1138	-0.00002912	0.0001043
fixed	NA	male	-0.04431	0.025	-1.773	3970	0.07637	-0.1145	0.02586
fixed	NA	count_birth_order2/2	0.05411	0.04991	1.084	3498	0.2784	-0.08599	0.1942
fixed	NA	count_birth_order1/3	-0.004653	0.04659	-0.09986	4345	0.9205	-0.1354	0.1261
fixed	NA	count_birth_order2/3	0.04349	0.05027	0.8651	4411	0.387	-0.09761	0.1846
fixed	NA	count_birth_order3/3	0.0296	0.05593	0.5291	4401	0.5967	-0.1274	0.1866
fixed	NA	count_birth_order1/4	-0.09954	0.0569	-1.749	4406	0.08032	-0.2593	0.06019
fixed	NA	count_birth_order2/4	-0.01884	0.05842	-0.3224	4405	0.7471	-0.1828	0.1451
fixed	NA	count_birth_order3/4	-0.06075	0.06096	-0.9965	4362	0.3191	-0.2319	0.1104
fixed	NA	count_birth_order4/4	-0.03633	0.06357	-0.5715	4349	0.5677	-0.2148	0.1421
fixed	NA	count_birth_order1/5	-0.1058	0.07594	-1.393	4382	0.1638	-0.3189	0.1074
fixed	NA	count_birth_order2/5	-0.08542	0.08138	-1.05	4240	0.2939	-0.3138	0.143
fixed	NA	count_birth_order3/5	-0.1551	0.07613	-2.037	4265	0.04168	-0.3688	0.0586
fixed	NA	count_birth_order4/5	-0.1873	0.07361	-2.545	4321	0.01097	-0.3939	0.01931
fixed	NA	count_birth_order5/5	-0.1121	0.07545	-1.485	4290	0.1375	-0.3239	0.09971
ran_pars	mother_pidlink	sd__(Intercept)	0.5185	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7014	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11166	11230	-5573	11146	NA	NA	NA
11	11167	11238	-5573	11145	0.5738	1	0.4488
14	11170	11260	-5571	11142	3.264	3	0.3527
20	11180	11308	-5570	11140	1.949	6	0.9243

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7435	0.4819	-1.543	3975	0.123	-2.096	0.6092
fixed	NA	poly(age, 3, raw = TRUE)1	0.1331	0.05632	2.363	3985	0.0182	-0.02504	0.2912
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004244	0.002078	-2.042	4000	0.0412	-0.01008	0.00159
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003669	0.00002437	1.505	4018	0.1323	-0.00003173	0.0001051
fixed	NA	male	-0.03882	0.02587	-1.501	3697	0.1334	-0.1114	0.03378
fixed	NA	sibling_count3	0.007909	0.03991	0.1982	3012	0.8429	-0.1041	0.1199
fixed	NA	sibling_count4	-0.03952	0.04268	-0.9261	2835	0.3544	-0.1593	0.08027
fixed	NA	sibling_count5	-0.07459	0.04593	-1.624	2669	0.1045	-0.2035	0.05433
ran_pars	mother_pidlink	sd__(Intercept)	0.515	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7004	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7403	0.4825	-1.534	3976	0.125	-2.095	0.6139
fixed	NA	birth_order	-0.001929	0.01298	-0.1485	3632	0.8819	-0.03837	0.03452
fixed	NA	poly(age, 3, raw = TRUE)1	0.133	0.05633	2.361	3983	0.01826	-0.02511	0.2911
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004241	0.002079	-2.04	3998	0.04137	-0.01008	0.001593
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003661	0.00002438	1.502	4015	0.1332	-0.00003182	0.000105
fixed	NA	male	-0.03877	0.02587	-1.499	3696	0.134	-0.1114	0.03385
fixed	NA	sibling_count3	0.00883	0.04039	0.2186	3052	0.827	-0.1046	0.1222
fixed	NA	sibling_count4	-0.03746	0.04489	-0.8346	2976	0.404	-0.1635	0.08854
fixed	NA	sibling_count5	-0.07133	0.0509	-1.401	3002	0.1612	-0.2142	0.07155
ran_pars	mother_pidlink	sd__(Intercept)	0.515	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7005	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8051	0.4835	-1.665	3998	0.09595	-2.162	0.552
fixed	NA	poly(age, 3, raw = TRUE)1	0.1381	0.05643	2.446	4000	0.01447	-0.02035	0.2965
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004421	0.002082	-2.123	4012	0.03378	-0.01027	0.001423
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003854	0.00002441	1.579	4025	0.1145	-0.00002999	0.0001071
fixed	NA	male	-0.03757	0.02586	-1.453	3689	0.1464	-0.1102	0.03503
fixed	NA	sibling_count3	0.009672	0.04084	0.2368	3135	0.8128	-0.105	0.1243
fixed	NA	sibling_count4	-0.02811	0.04538	-0.6194	3053	0.5357	-0.1555	0.09927
fixed	NA	sibling_count5	-0.06211	0.05131	-1.211	3056	0.2262	-0.2062	0.08192
fixed	NA	birth_order_nonlinear2	0.05758	0.02997	1.921	2997	0.05477	-0.02654	0.1417
fixed	NA	birth_order_nonlinear3	-0.007206	0.03803	-0.1895	3146	0.8497	-0.114	0.09955
fixed	NA	birth_order_nonlinear4	-0.03213	0.05075	-0.633	3290	0.5268	-0.1746	0.1103
fixed	NA	birth_order_nonlinear5	0.02177	0.07352	0.296	3090	0.7672	-0.1846	0.2281
ran_pars	mother_pidlink	sd__(Intercept)	0.5157	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6998	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8036	0.4838	-1.661	3994	0.09682	-2.162	0.5546
fixed	NA	poly(age, 3, raw = TRUE)1	0.1364	0.05645	2.416	3994	0.01575	-0.02209	0.2948
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004347	0.002083	-2.087	4006	0.03695	-0.01019	0.0015
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003753	0.00002443	1.536	4019	0.1245	-0.00003104	0.0001061
fixed	NA	male	-0.0392	0.02588	-1.515	3682	0.1298	-0.1118	0.03343
fixed	NA	count_birth_order2/2	0.09254	0.05464	1.694	3313	0.09045	-0.06085	0.2459
fixed	NA	count_birth_order1/3	0.04149	0.05028	0.8251	4041	0.4094	-0.09965	0.1826
fixed	NA	count_birth_order2/3	0.03037	0.05388	0.5636	4094	0.573	-0.1209	0.1816
fixed	NA	count_birth_order3/3	0.04362	0.0603	0.7233	4085	0.4695	-0.1257	0.2129
fixed	NA	count_birth_order1/4	-0.06879	0.05946	-1.157	4089	0.2474	-0.2357	0.09812
fixed	NA	count_birth_order2/4	0.09198	0.06038	1.524	4095	0.1277	-0.07749	0.2615
fixed	NA	count_birth_order3/4	-0.0285	0.06509	-0.4379	4036	0.6615	-0.2112	0.1542
fixed	NA	count_birth_order4/4	-0.03212	0.06728	-0.4775	4038	0.633	-0.221	0.1567
fixed	NA	count_birth_order1/5	0.01199	0.06973	0.172	4095	0.8635	-0.1837	0.2077
fixed	NA	count_birth_order2/5	-0.008682	0.07461	-0.1164	3996	0.9074	-0.2181	0.2008
fixed	NA	count_birth_order3/5	-0.09928	0.07207	-1.378	3999	0.1684	-0.3016	0.103
fixed	NA	count_birth_order4/5	-0.1043	0.07462	-1.397	3954	0.1625	-0.3137	0.1052
fixed	NA	count_birth_order5/5	-0.03106	0.07443	-0.4173	3966	0.6765	-0.24	0.1779
ran_pars	mother_pidlink	sd__(Intercept)	0.5155	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6997	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	10355	10418	-5167	10335	NA	NA	NA
11	10357	10426	-5167	10335	0.02194	1	0.8823
14	10357	10446	-5165	10329	5.805	3	0.1215
20	10362	10488	-5161	10322	7.515	6	0.2758

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8161	0.471	-1.733	4271	0.0832	-2.138	0.5059
fixed	NA	poly(age, 3, raw = TRUE)1	0.1401	0.05508	2.543	4282	0.01103	-0.01455	0.2947
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00443	0.002035	-2.177	4297	0.02952	-0.01014	0.001281
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003822	0.00002391	1.599	4314	0.1099	-0.00002888	0.0001053
fixed	NA	male	-0.04486	0.0249	-1.802	3983	0.07169	-0.1148	0.02504
fixed	NA	sibling_count3	0.01733	0.03647	0.4751	3184	0.6347	-0.08506	0.1197
fixed	NA	sibling_count4	-0.05818	0.0401	-1.451	2969	0.1469	-0.1707	0.05438
fixed	NA	sibling_count5	-0.12	0.04769	-2.517	2735	0.01191	-0.2539	0.01386
ran_pars	mother_pidlink	sd__(Intercept)	0.5138	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6993	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8377	0.4716	-1.776	4274	0.07574	-2.161	0.486
fixed	NA	birth_order	0.01203	0.01302	0.9236	3791	0.3557	-0.02453	0.04858
fixed	NA	poly(age, 3, raw = TRUE)1	0.1406	0.05509	2.553	4281	0.01071	-0.01399	0.2953
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004458	0.002035	-2.191	4296	0.02852	-0.01017	0.001254
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000388	0.00002391	1.622	4312	0.1048	-0.00002833	0.0001059
fixed	NA	male	-0.0452	0.0249	-1.815	3982	0.06959	-0.1151	0.0247
fixed	NA	sibling_count3	0.01158	0.037	0.3131	3235	0.7542	-0.09227	0.1154
fixed	NA	sibling_count4	-0.07149	0.04261	-1.678	3167	0.09347	-0.1911	0.04811
fixed	NA	sibling_count5	-0.1411	0.05289	-2.669	3122	0.007658	-0.2896	0.007326
ran_pars	mother_pidlink	sd__(Intercept)	0.5135	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6995	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8837	0.4727	-1.87	4294	0.0616	-2.211	0.4431
fixed	NA	poly(age, 3, raw = TRUE)1	0.1457	0.05521	2.638	4297	0.008361	-0.009313	0.3006
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004635	0.002039	-2.273	4308	0.02305	-0.01036	0.001088
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004069	0.00002395	1.699	4320	0.0894	-0.00002654	0.0001079
fixed	NA	male	-0.04487	0.0249	-1.802	3974	0.07164	-0.1148	0.02503
fixed	NA	sibling_count3	0.01272	0.03746	0.3396	3336	0.7342	-0.09242	0.1179
fixed	NA	sibling_count4	-0.06832	0.04313	-1.584	3256	0.1133	-0.1894	0.05274
fixed	NA	sibling_count5	-0.127	0.05379	-2.36	3231	0.01831	-0.278	0.02403
fixed	NA	birth_order_nonlinear2	0.0573	0.02844	2.015	3154	0.04403	-0.02254	0.1371
fixed	NA	birth_order_nonlinear3	0.02371	0.03653	0.6491	3309	0.5163	-0.07883	0.1263
fixed	NA	birth_order_nonlinear4	0.03831	0.05064	0.7565	3465	0.4494	-0.1038	0.1805
fixed	NA	birth_order_nonlinear5	0.01316	0.0818	0.1609	3321	0.8722	-0.2164	0.2428
ran_pars	mother_pidlink	sd__(Intercept)	0.5141	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6991	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8808	0.4732	-1.861	4291	0.06274	-2.209	0.4474
fixed	NA	poly(age, 3, raw = TRUE)1	0.1448	0.05525	2.621	4291	0.008791	-0.01026	0.2999
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00459	0.002041	-2.249	4301	0.02455	-0.01032	0.001138
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004	0.00002398	1.668	4314	0.09534	-0.0000273	0.0001073
fixed	NA	male	-0.04527	0.02493	-1.816	3968	0.06945	-0.1152	0.02471
fixed	NA	count_birth_order2/2	0.06104	0.04831	1.264	3438	0.2065	-0.07456	0.1966
fixed	NA	count_birth_order1/3	0.01191	0.0458	0.26	4336	0.7949	-0.1167	0.1405
fixed	NA	count_birth_order2/3	0.06666	0.04995	1.334	4402	0.1821	-0.07356	0.2069
fixed	NA	count_birth_order3/3	0.04796	0.05471	0.8766	4385	0.3807	-0.1056	0.2015
fixed	NA	count_birth_order1/4	-0.08141	0.05677	-1.434	4400	0.1516	-0.2408	0.07794
fixed	NA	count_birth_order2/4	-0.01152	0.05804	-0.1985	4385	0.8427	-0.1745	0.1514
fixed	NA	count_birth_order3/4	-0.04143	0.06011	-0.6893	4345	0.4907	-0.2102	0.1273
fixed	NA	count_birth_order4/4	-0.007317	0.06337	-0.1155	4311	0.9081	-0.1852	0.1706
fixed	NA	count_birth_order1/5	-0.08094	0.07556	-1.071	4385	0.2841	-0.293	0.1312
fixed	NA	count_birth_order2/5	-0.05516	0.08349	-0.6606	4206	0.5089	-0.2895	0.1792
fixed	NA	count_birth_order3/5	-0.1308	0.07923	-1.651	4234	0.09876	-0.3532	0.09157
fixed	NA	count_birth_order4/5	-0.1222	0.07667	-1.594	4293	0.111	-0.3374	0.09301
fixed	NA	count_birth_order5/5	-0.1139	0.0803	-1.419	4253	0.156	-0.3394	0.1115
ran_pars	mother_pidlink	sd__(Intercept)	0.5133	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7001	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11095	11159	-5538	11075	NA	NA	NA
11	11096	11167	-5537	11074	0.8553	1	0.3551
14	11099	11189	-5535	11071	3.32	3	0.3449
20	11110	11238	-5535	11070	1.346	6	0.969

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

g-factor 2015 young

birthorder <- birthorder %>% mutate(outcome = g_factor_2015_young)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.083	0.1238	-24.9	7824	8.961e-132	-3.431	-2.736
fixed	NA	poly(age, 3, raw = TRUE)1	0.4532	0.023	19.7	7997	1.928e-84	0.3886	0.5177
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01822	0.001326	-13.75	8131	1.605e-42	-0.02195	-0.0145
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002241	0.00002419	9.264	8079	2.486e-20	0.0001562	0.000292
fixed	NA	male	-0.008124	0.01933	-0.4203	7346	0.6743	-0.06238	0.04613
fixed	NA	sibling_count3	-0.03141	0.02829	-1.11	5286	0.267	-0.1108	0.04801
fixed	NA	sibling_count4	-0.1015	0.0319	-3.182	4857	0.001474	-0.1911	-0.01195
fixed	NA	sibling_count5	-0.08078	0.03625	-2.229	4457	0.02589	-0.1825	0.02097
ran_pars	mother_pidlink	sd__(Intercept)	0.5378	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7408	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.081	0.127	-24.26	7931	1.93e-125	-3.437	-2.724
fixed	NA	birth_order	-0.0009582	0.01068	-0.08975	7577	0.9285	-0.03093	0.02901
fixed	NA	poly(age, 3, raw = TRUE)1	0.453	0.02306	19.65	8004	5.891e-84	0.3883	0.5178
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01822	0.001327	-13.74	8129	1.855e-42	-0.02194	-0.0145
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002241	0.00002419	9.261	8080	2.549e-20	0.0001562	0.000292
fixed	NA	male	-0.008111	0.01933	-0.4196	7346	0.6748	-0.06237	0.04615
fixed	NA	sibling_count3	-0.03085	0.02896	-1.066	5404	0.2867	-0.1121	0.05043
fixed	NA	sibling_count4	-0.1002	0.03514	-2.851	5264	0.004371	-0.1988	-0.001556
fixed	NA	sibling_count5	-0.07865	0.04336	-1.814	5243	0.06976	-0.2004	0.04307
ran_pars	mother_pidlink	sd__(Intercept)	0.5378	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7409	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.093	0.1257	-24.61	7926	6.766e-129	-3.446	-2.74
fixed	NA	poly(age, 3, raw = TRUE)1	0.4541	0.02309	19.67	8015	3.81e-84	0.3893	0.5189
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01827	0.001328	-13.76	8128	1.326e-42	-0.022	-0.01454
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002247	0.00002421	9.282	8074	2.109e-20	0.0001567	0.0002926
fixed	NA	male	-0.008347	0.01933	-0.4318	7344	0.6659	-0.06262	0.04592
fixed	NA	sibling_count3	-0.03815	0.02941	-1.297	5626	0.1946	-0.1207	0.0444
fixed	NA	sibling_count4	-0.1032	0.0358	-2.881	5522	0.003977	-0.2036	-0.002654
fixed	NA	sibling_count5	-0.07188	0.04397	-1.635	5375	0.1021	-0.1953	0.05154
fixed	NA	birth_order_nonlinear2	0.01223	0.02244	0.5448	5828	0.5859	-0.05077	0.07523
fixed	NA	birth_order_nonlinear3	0.02639	0.02963	0.8907	6575	0.3731	-0.05679	0.1096
fixed	NA	birth_order_nonlinear4	-0.02156	0.0402	-0.5363	6807	0.5918	-0.1344	0.09128
fixed	NA	birth_order_nonlinear5	-0.02575	0.05839	-0.441	6915	0.6592	-0.1897	0.1382
ran_pars	mother_pidlink	sd__(Intercept)	0.538	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7408	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.097	0.1266	-24.47	7944	1.478e-127	-3.452	-2.742
fixed	NA	poly(age, 3, raw = TRUE)1	0.4554	0.02313	19.69	8020	2.404e-84	0.3905	0.5203
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01835	0.001329	-13.8	8122	7.39e-43	-0.02208	-0.01462
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002261	0.00002422	9.333	8068	1.309e-20	0.0001581	0.0002941
fixed	NA	male	-0.008984	0.01933	-0.4647	7340	0.6422	-0.06326	0.04529
fixed	NA	count_birth_order2/2	0.007872	0.03522	0.2235	6133	0.8232	-0.091	0.1067
fixed	NA	count_birth_order1/3	-0.05798	0.03658	-1.585	7989	0.113	-0.1607	0.04471
fixed	NA	count_birth_order2/3	-0.03211	0.03721	-0.8631	8067	0.3881	-0.1366	0.07233
fixed	NA	count_birth_order3/3	0.02493	0.04208	0.5925	8124	0.5536	-0.09319	0.143
fixed	NA	count_birth_order1/4	-0.09505	0.05004	-1.899	8115	0.05754	-0.2355	0.04542
fixed	NA	count_birth_order2/4	-0.06273	0.04741	-1.323	8113	0.1859	-0.1958	0.07036
fixed	NA	count_birth_order3/4	-0.1402	0.0446	-3.144	8124	0.00167	-0.2654	-0.01504
fixed	NA	count_birth_order4/4	-0.08802	0.04859	-1.812	8099	0.07009	-0.2244	0.04837
fixed	NA	count_birth_order1/5	-0.01007	0.06774	-0.1487	7742	0.8818	-0.2002	0.1801
fixed	NA	count_birth_order2/5	-0.09053	0.06435	-1.407	7831	0.1595	-0.2711	0.09009
fixed	NA	count_birth_order3/5	-0.005519	0.05823	-0.09479	7995	0.9245	-0.169	0.1579
fixed	NA	count_birth_order4/5	-0.1444	0.05474	-2.639	8082	0.008339	-0.2981	0.009217
fixed	NA	count_birth_order5/5	-0.0987	0.05428	-1.818	8106	0.06903	-0.2511	0.05366
ran_pars	mother_pidlink	sd__(Intercept)	0.538	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7406	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	21276	21346	-10628	21256	NA	NA	NA
11	21278	21355	-10628	21256	0.008064	1	0.9284
14	21282	21380	-10627	21254	2.199	3	0.5321
20	21284	21424	-10622	21244	10.01	6	0.1242

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.627	0.1999	-18.15	6250	9.36e-72	-4.188	-3.066
fixed	NA	poly(age, 3, raw = TRUE)1	0.5706	0.04194	13.61	6240	1.451e-41	0.4529	0.6884
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02578	0.002715	-9.497	6284	3.006e-21	-0.0334	-0.01816
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003777	0.00005446	6.935	6329	4.452e-12	0.0002248	0.0005306
fixed	NA	male	-0.02086	0.02012	-1.037	6918	0.2999	-0.07734	0.03562
fixed	NA	sibling_count3	-0.0516	0.0273	-1.89	4730	0.05883	-0.1282	0.02504
fixed	NA	sibling_count4	-0.1156	0.0336	-3.44	4168	0.0005881	-0.2099	-0.02126
fixed	NA	sibling_count5	-0.23	0.04319	-5.327	3806	0.0000001059	-0.3513	-0.1088
ran_pars	mother_pidlink	sd__(Intercept)	0.5172	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7472	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.613	0.203	-17.8	6425	3.321e-69	-4.183	-3.043
fixed	NA	birth_order	-0.004797	0.01238	-0.3876	7182	0.6983	-0.03954	0.02994
fixed	NA	poly(age, 3, raw = TRUE)1	0.5696	0.04202	13.56	6265	2.81e-41	0.4517	0.6876
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02574	0.002716	-9.477	6285	3.625e-21	-0.03337	-0.01812
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003773	0.00005448	6.925	6327	4.804e-12	0.0002243	0.0005302
fixed	NA	male	-0.02076	0.02012	-1.032	6919	0.3022	-0.07725	0.03572
fixed	NA	sibling_count3	-0.04839	0.02853	-1.696	4844	0.08993	-0.1285	0.0317
fixed	NA	sibling_count4	-0.1084	0.03833	-2.829	4626	0.004691	-0.216	-0.0008389
fixed	NA	sibling_count5	-0.2182	0.05292	-4.123	4691	0.00003807	-0.3667	-0.06963
ran_pars	mother_pidlink	sd__(Intercept)	0.5171	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7473	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.628	0.2016	-18	6374	1.117e-70	-4.194	-3.062
fixed	NA	poly(age, 3, raw = TRUE)1	0.5702	0.04203	13.57	6269	2.428e-41	0.4522	0.6882
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02575	0.002717	-9.479	6286	3.566e-21	-0.03338	-0.01813
fixed	NA	poly(age, 3, raw = TRUE)3	0.000377	0.00005449	6.918	6328	5.024e-12	0.000224	0.0005299
fixed	NA	male	-0.02136	0.02013	-1.061	6919	0.2887	-0.07786	0.03514
fixed	NA	sibling_count3	-0.0557	0.0292	-1.907	5130	0.05653	-0.1377	0.02627
fixed	NA	sibling_count4	-0.1139	0.03924	-2.904	4858	0.003706	-0.2241	-0.003786
fixed	NA	sibling_count5	-0.1914	0.05551	-3.448	4961	0.0005684	-0.3472	-0.03561
fixed	NA	birth_order_nonlinear2	0.009611	0.02281	0.4213	5364	0.6736	-0.05443	0.07365
fixed	NA	birth_order_nonlinear3	0.01457	0.03256	0.4476	6241	0.6544	-0.07681	0.106
fixed	NA	birth_order_nonlinear4	-0.01329	0.04644	-0.2862	6606	0.7748	-0.1437	0.1171
fixed	NA	birth_order_nonlinear5	-0.1016	0.07323	-1.388	6513	0.1652	-0.3072	0.1039
ran_pars	mother_pidlink	sd__(Intercept)	0.5169	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7475	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.639	0.2023	-17.99	6396	1.16e-70	-4.207	-3.072
fixed	NA	poly(age, 3, raw = TRUE)1	0.5723	0.04209	13.6	6276	1.621e-41	0.4541	0.6904
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02591	0.00272	-9.523	6287	2.34e-21	-0.03354	-0.01827
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003804	0.00005456	6.972	6324	3.445e-12	0.0002272	0.0005335
fixed	NA	male	-0.02073	0.02013	-1.03	6905	0.3033	-0.07724	0.03579
fixed	NA	count_birth_order2/2	0.02002	0.03173	0.631	5817	0.5281	-0.06905	0.1091
fixed	NA	count_birth_order1/3	-0.05851	0.03768	-1.553	7465	0.1206	-0.1643	0.04727
fixed	NA	count_birth_order2/3	-0.05422	0.03619	-1.498	7477	0.1342	-0.1558	0.04738
fixed	NA	count_birth_order3/3	-0.01434	0.0396	-0.3621	7506	0.7173	-0.1255	0.09681
fixed	NA	count_birth_order1/4	-0.06173	0.05925	-1.042	7365	0.2975	-0.2281	0.1046
fixed	NA	count_birth_order2/4	-0.09877	0.05204	-1.898	7489	0.05775	-0.2448	0.04731
fixed	NA	count_birth_order3/4	-0.1626	0.04964	-3.275	7490	0.001061	-0.3019	-0.02324
fixed	NA	count_birth_order4/4	-0.09257	0.04919	-1.882	7510	0.0599	-0.2307	0.04552
fixed	NA	count_birth_order1/5	-0.195	0.1027	-1.898	6363	0.0577	-0.4832	0.09333
fixed	NA	count_birth_order2/5	-0.1403	0.09161	-1.531	6767	0.1258	-0.3974	0.1169
fixed	NA	count_birth_order3/5	-0.09425	0.07768	-1.213	7189	0.225	-0.3123	0.1238
fixed	NA	count_birth_order4/5	-0.2587	0.06447	-4.012	7496	0.00006081	-0.4396	-0.07769
fixed	NA	count_birth_order5/5	-0.2905	0.06257	-4.642	7510	0.000003505	-0.4661	-0.1148
ran_pars	mother_pidlink	sd__(Intercept)	0.517	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7473	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	19620	19690	-9800	19600	NA	NA	NA
11	19622	19698	-9800	19600	0.1506	1	0.6979
14	19626	19723	-9799	19598	2.709	3	0.4387
20	19630	19768	-9795	19590	7.688	6	0.2619

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.666	0.2047	-17.91	5929	7.22e-70	-4.241	-3.091
fixed	NA	poly(age, 3, raw = TRUE)1	0.581	0.0431	13.48	5907	7.969e-41	0.46	0.702
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02675	0.002797	-9.563	5944	1.629e-21	-0.0346	-0.0189
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004002	0.00005625	7.115	5980	1.247e-12	0.0002423	0.0005581
fixed	NA	male	-0.02033	0.02061	-0.9865	6546	0.3239	-0.07818	0.03752
fixed	NA	sibling_count3	-0.02948	0.02861	-1.03	4669	0.3029	-0.1098	0.05084
fixed	NA	sibling_count4	-0.07251	0.03375	-2.148	4252	0.03175	-0.1672	0.02223
fixed	NA	sibling_count5	-0.08763	0.03965	-2.21	3957	0.02715	-0.1989	0.02367
ran_pars	mother_pidlink	sd__(Intercept)	0.5228	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7443	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.62	0.2077	-17.43	6080	2.026e-66	-4.203	-3.037
fixed	NA	birth_order	-0.01575	0.01201	-1.311	6894	0.1898	-0.04948	0.01797
fixed	NA	poly(age, 3, raw = TRUE)1	0.5775	0.04318	13.38	5929	3.217e-40	0.4563	0.6987
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02661	0.002799	-9.507	5944	2.777e-21	-0.03447	-0.01875
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003983	0.00005627	7.078	5978	1.636e-12	0.0002403	0.0005562
fixed	NA	male	-0.01994	0.02061	-0.9675	6548	0.3333	-0.0778	0.03792
fixed	NA	sibling_count3	-0.0196	0.02958	-0.6627	4780	0.5076	-0.1026	0.06343
fixed	NA	sibling_count4	-0.05019	0.03779	-1.328	4668	0.1842	-0.1563	0.05589
fixed	NA	sibling_count5	-0.05252	0.04783	-1.098	4743	0.2722	-0.1868	0.08172
ran_pars	mother_pidlink	sd__(Intercept)	0.5223	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7445	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.644	0.2064	-17.65	6037	4.893e-68	-4.224	-3.065
fixed	NA	poly(age, 3, raw = TRUE)1	0.5779	0.0432	13.38	5933	3.099e-40	0.4566	0.6991
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0266	0.0028	-9.5	5946	2.979e-21	-0.03446	-0.01874
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003975	0.00005629	7.062	5980	1.829e-12	0.0002395	0.0005555
fixed	NA	male	-0.02051	0.02061	-0.9948	6546	0.3199	-0.07837	0.03736
fixed	NA	sibling_count3	-0.02767	0.03024	-0.9153	5034	0.3601	-0.1125	0.0572
fixed	NA	sibling_count4	-0.05929	0.03869	-1.533	4893	0.1254	-0.1679	0.04931
fixed	NA	sibling_count5	-0.03552	0.04908	-0.7236	4898	0.4693	-0.1733	0.1023
fixed	NA	birth_order_nonlinear2	-0.003182	0.02367	-0.1344	5065	0.8931	-0.06961	0.06325
fixed	NA	birth_order_nonlinear3	-0.003502	0.03252	-0.1077	6018	0.9142	-0.0948	0.08779
fixed	NA	birth_order_nonlinear4	-0.03829	0.0452	-0.847	6358	0.397	-0.1652	0.08859
fixed	NA	birth_order_nonlinear5	-0.139	0.06737	-2.062	6301	0.03921	-0.3281	0.05016
ran_pars	mother_pidlink	sd__(Intercept)	0.5222	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7446	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.655	0.2073	-17.63	6053	7.171e-68	-4.237	-3.073
fixed	NA	poly(age, 3, raw = TRUE)1	0.5806	0.04327	13.42	5939	1.821e-40	0.4591	0.702
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02681	0.002804	-9.559	5946	1.689e-21	-0.03468	-0.01894
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004023	0.00005638	7.136	5975	1.076e-12	0.000244	0.0005606
fixed	NA	male	-0.01985	0.02062	-0.9629	6535	0.3357	-0.07773	0.03802
fixed	NA	count_birth_order2/2	-0.002972	0.03461	-0.08587	5441	0.9316	-0.1001	0.09417
fixed	NA	count_birth_order1/3	-0.03706	0.03898	-0.9505	7118	0.3419	-0.1465	0.07237
fixed	NA	count_birth_order2/3	-0.03475	0.03807	-0.9128	7133	0.3614	-0.1416	0.07212
fixed	NA	count_birth_order3/3	-0.01403	0.04172	-0.3362	7149	0.7368	-0.1311	0.1031
fixed	NA	count_birth_order1/4	-0.08157	0.05792	-1.408	7056	0.1591	-0.2441	0.08101
fixed	NA	count_birth_order2/4	-0.05563	0.052	-1.07	7115	0.2847	-0.2016	0.09033
fixed	NA	count_birth_order3/4	-0.1043	0.04975	-2.096	7128	0.03614	-0.2439	0.03539
fixed	NA	count_birth_order4/4	-0.04947	0.05034	-0.9829	7153	0.3257	-0.1908	0.09182
fixed	NA	count_birth_order1/5	0.07996	0.08392	0.9528	6471	0.3407	-0.1556	0.3155
fixed	NA	count_birth_order2/5	-0.03529	0.07519	-0.4693	6782	0.6389	-0.2464	0.1758
fixed	NA	count_birth_order3/5	-0.006645	0.06755	-0.09837	6939	0.9216	-0.1963	0.183
fixed	NA	count_birth_order4/5	-0.1521	0.06228	-2.443	7054	0.01459	-0.327	0.02268
fixed	NA	count_birth_order5/5	-0.1769	0.06004	-2.947	7144	0.00322	-0.3454	-0.008396
ran_pars	mother_pidlink	sd__(Intercept)	0.5225	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7443	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	18703	18772	-9342	18683	NA	NA	NA
11	18703	18779	-9341	18681	1.722	1	0.1895
14	18706	18803	-9339	18678	2.938	3	0.4013
20	18711	18848	-9335	18671	7.677	6	0.2627

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.602	0.2007	-17.95	6146	3.013e-70	-4.166	-3.039
fixed	NA	poly(age, 3, raw = TRUE)1	0.565	0.0421	13.42	6145	1.65e-40	0.4469	0.6832
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02542	0.002722	-9.337	6197	1.35e-20	-0.03306	-0.01778
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003703	0.00005457	6.785	6249	0.00000000001265	0.0002171	0.0005235
fixed	NA	male	-0.02573	0.02023	-1.272	6788	0.2034	-0.08252	0.03105
fixed	NA	sibling_count3	-0.044	0.02736	-1.608	4649	0.1078	-0.1208	0.0328
fixed	NA	sibling_count4	-0.1002	0.03395	-2.951	4083	0.003184	-0.1955	-0.004893
fixed	NA	sibling_count5	-0.2183	0.04499	-4.852	3743	0.000001274	-0.3446	-0.09199
ran_pars	mother_pidlink	sd__(Intercept)	0.5175	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7437	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.592	0.204	-17.61	6317	8.329e-68	-4.165	-3.02
fixed	NA	birth_order	-0.003464	0.01251	-0.2769	7002	0.7818	-0.03857	0.03164
fixed	NA	poly(age, 3, raw = TRUE)1	0.5643	0.04218	13.38	6171	2.999e-40	0.4459	0.6827
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02539	0.002724	-9.32	6197	1.588e-20	-0.03304	-0.01774
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003699	0.00005459	6.776	6246	0.00000000001349	0.0002167	0.0005232
fixed	NA	male	-0.02567	0.02023	-1.269	6789	0.2045	-0.08247	0.03112
fixed	NA	sibling_count3	-0.0417	0.02859	-1.458	4767	0.1448	-0.122	0.03856
fixed	NA	sibling_count4	-0.09507	0.03867	-2.459	4555	0.01398	-0.2036	0.01347
fixed	NA	sibling_count5	-0.2099	0.05425	-3.868	4573	0.000111	-0.3622	-0.05759
ran_pars	mother_pidlink	sd__(Intercept)	0.5175	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7438	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.603	0.2025	-17.79	6270	3.98e-69	-4.171	-3.034
fixed	NA	poly(age, 3, raw = TRUE)1	0.5644	0.0422	13.38	6176	3.054e-40	0.446	0.6829
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02538	0.002725	-9.312	6200	1.703e-20	-0.03303	-0.01773
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003693	0.00005461	6.763	6248	0.00000000001478	0.000216	0.0005226
fixed	NA	male	-0.026	0.02024	-1.285	6788	0.199	-0.08281	0.03081
fixed	NA	sibling_count3	-0.04394	0.02925	-1.502	5047	0.1331	-0.1261	0.03817
fixed	NA	sibling_count4	-0.09961	0.03959	-2.516	4794	0.0119	-0.2107	0.01152
fixed	NA	sibling_count5	-0.188	0.05722	-3.286	4832	0.001022	-0.3486	-0.02742
fixed	NA	birth_order_nonlinear2	0.01017	0.02277	0.4466	5267	0.6552	-0.05374	0.07408
fixed	NA	birth_order_nonlinear3	0.0002027	0.0327	0.006198	6080	0.9951	-0.09158	0.09198
fixed	NA	birth_order_nonlinear4	0.002949	0.04722	0.06245	6395	0.9502	-0.1296	0.1355
fixed	NA	birth_order_nonlinear5	-0.08493	0.07715	-1.101	6452	0.271	-0.3015	0.1316
ran_pars	mother_pidlink	sd__(Intercept)	0.517	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7441	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.607	0.2031	-17.76	6289	7.159e-69	-4.177	-3.037
fixed	NA	poly(age, 3, raw = TRUE)1	0.565	0.04225	13.37	6181	3.153e-40	0.4464	0.6836
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02543	0.002729	-9.32	6199	1.581e-20	-0.03309	-0.01777
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003706	0.00005467	6.778	6243	0.0000000000133	0.0002171	0.000524
fixed	NA	male	-0.02521	0.02024	-1.245	6778	0.213	-0.08203	0.03161
fixed	NA	count_birth_order2/2	0.0168	0.03136	0.5358	5661	0.5921	-0.07123	0.1048
fixed	NA	count_birth_order1/3	-0.04745	0.03781	-1.255	7329	0.2095	-0.1536	0.05869
fixed	NA	count_birth_order2/3	-0.0408	0.03627	-1.125	7338	0.2607	-0.1426	0.06101
fixed	NA	count_birth_order3/3	-0.02223	0.03973	-0.5595	7368	0.5759	-0.1338	0.0893
fixed	NA	count_birth_order1/4	-0.06359	0.05955	-1.068	7242	0.2857	-0.2307	0.1036
fixed	NA	count_birth_order2/4	-0.08109	0.05266	-1.54	7347	0.1236	-0.2289	0.06673
fixed	NA	count_birth_order3/4	-0.1601	0.04996	-3.205	7353	0.001358	-0.3003	-0.01987
fixed	NA	count_birth_order4/4	-0.06132	0.04983	-1.231	7371	0.2185	-0.2012	0.07855
fixed	NA	count_birth_order1/5	-0.1793	0.1026	-1.748	6417	0.08056	-0.4672	0.1087
fixed	NA	count_birth_order2/5	-0.1509	0.09813	-1.537	6543	0.1242	-0.4263	0.1246
fixed	NA	count_birth_order3/5	-0.09533	0.07971	-1.196	7119	0.2317	-0.3191	0.1284
fixed	NA	count_birth_order4/5	-0.2489	0.06774	-3.674	7353	0.0002405	-0.439	-0.05872
fixed	NA	count_birth_order5/5	-0.2723	0.06622	-4.112	7371	0.00003971	-0.4582	-0.0864
ran_pars	mother_pidlink	sd__(Intercept)	0.5169	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7441	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	19207	19276	-9594	19187	NA	NA	NA
11	19209	19285	-9593	19187	0.07694	1	0.7815
14	19213	19310	-9593	19185	1.686	3	0.6402
20	19218	19356	-9589	19178	6.998	6	0.3211

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

g-factor 2007 old

birthorder <- birthorder %>% mutate(outcome = g_factor_2007_old)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.042	2.574	-1.182	3255	0.2375	-10.27	4.185
fixed	NA	poly(age, 3, raw = TRUE)1	0.3752	0.2695	1.392	3256	0.1639	-0.3812	1.132
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01334	0.009287	-1.436	3258	0.151	-0.03941	0.01273
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001442	0.0001053	1.369	3259	0.171	-0.0001514	0.0004399
fixed	NA	male	0.1155	0.0318	3.632	3001	0.000286	0.02623	0.2048
fixed	NA	sibling_count3	-0.01357	0.0549	-0.2471	2386	0.8048	-0.1677	0.1405
fixed	NA	sibling_count4	-0.1226	0.05373	-2.281	2289	0.02262	-0.2734	0.02824
fixed	NA	sibling_count5	-0.02873	0.05463	-0.5258	2145	0.5991	-0.1821	0.1246
ran_pars	mother_pidlink	sd__(Intercept)	0.5363	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7785	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.887	2.575	-1.121	3254	0.2623	-10.11	4.341
fixed	NA	birth_order	-0.02725	0.01454	-1.873	2890	0.06113	-0.06807	0.01358
fixed	NA	poly(age, 3, raw = TRUE)1	0.3639	0.2694	1.351	3255	0.1769	-0.3924	1.12
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01297	0.009286	-1.397	3257	0.1627	-0.03903	0.0131
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001401	0.0001053	1.33	3258	0.1837	-0.0001556	0.0004357
fixed	NA	male	0.1156	0.03178	3.637	2998	0.0002808	0.02637	0.2048
fixed	NA	sibling_count3	-0.001359	0.05528	-0.02458	2419	0.9804	-0.1565	0.1538
fixed	NA	sibling_count4	-0.09776	0.05534	-1.767	2425	0.07741	-0.2531	0.05757
fixed	NA	sibling_count5	0.01099	0.0586	0.1876	2449	0.8512	-0.1535	0.1755
ran_pars	mother_pidlink	sd__(Intercept)	0.5373	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7776	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.677	2.576	-1.039	3252	0.2987	-9.908	4.554
fixed	NA	poly(age, 3, raw = TRUE)1	0.3442	0.2696	1.277	3253	0.2018	-0.4126	1.101
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01239	0.009291	-1.334	3254	0.1824	-0.03847	0.01369
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001349	0.0001054	1.281	3255	0.2004	-0.0001608	0.0004307
fixed	NA	male	0.1165	0.03178	3.665	2998	0.0002513	0.02727	0.2057
fixed	NA	sibling_count3	0.009002	0.05621	0.1602	2509	0.8728	-0.1488	0.1668
fixed	NA	sibling_count4	-0.09129	0.05612	-1.627	2512	0.1039	-0.2488	0.06623
fixed	NA	sibling_count5	-0.004278	0.05906	-0.07243	2491	0.9423	-0.17	0.1615
fixed	NA	birth_order_nonlinear2	-0.09063	0.03864	-2.345	2486	0.01908	-0.1991	0.01784
fixed	NA	birth_order_nonlinear3	-0.1202	0.0446	-2.696	2472	0.007066	-0.2454	0.004953
fixed	NA	birth_order_nonlinear4	-0.1009	0.0553	-1.825	2637	0.06811	-0.2561	0.0543
fixed	NA	birth_order_nonlinear5	-0.01561	0.07873	-0.1983	2622	0.8428	-0.2366	0.2054
ran_pars	mother_pidlink	sd__(Intercept)	0.5356	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7778	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.973	2.578	-1.153	3246	0.2489	-10.21	4.263
fixed	NA	poly(age, 3, raw = TRUE)1	0.375	0.2698	1.39	3247	0.1646	-0.3822	1.132
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01341	0.009297	-1.442	3248	0.1494	-0.0395	0.01269
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001459	0.0001054	1.384	3249	0.1664	-0.00015	0.0004419
fixed	NA	male	0.1144	0.0318	3.596	2995	0.0003285	0.02509	0.2036
fixed	NA	count_birth_order2/2	-0.1172	0.0734	-1.597	2569	0.1105	-0.3232	0.08884
fixed	NA	count_birth_order1/3	-0.02158	0.074	-0.2916	3227	0.7706	-0.2293	0.1861
fixed	NA	count_birth_order2/3	-0.05197	0.07895	-0.6582	3249	0.5104	-0.2736	0.1696
fixed	NA	count_birth_order3/3	-0.1374	0.07922	-1.734	3248	0.08293	-0.3598	0.08497
fixed	NA	count_birth_order1/4	-0.07658	0.07624	-1.004	3244	0.3153	-0.2906	0.1374
fixed	NA	count_birth_order2/4	-0.1582	0.07938	-1.993	3248	0.04634	-0.381	0.06461
fixed	NA	count_birth_order3/4	-0.3096	0.08162	-3.794	3235	0.0001511	-0.5388	-0.08054
fixed	NA	count_birth_order4/4	-0.1979	0.08237	-2.402	3248	0.01635	-0.4291	0.03335
fixed	NA	count_birth_order1/5	-0.03977	0.08352	-0.4761	3244	0.634	-0.2742	0.1947
fixed	NA	count_birth_order2/5	-0.1867	0.08495	-2.198	3235	0.02805	-0.4251	0.05178
fixed	NA	count_birth_order3/5	-0.02341	0.08385	-0.2793	3224	0.7801	-0.2588	0.2119
fixed	NA	count_birth_order4/5	-0.1285	0.0857	-1.499	3208	0.1339	-0.3691	0.1121
fixed	NA	count_birth_order5/5	-0.0269	0.0875	-0.3075	3232	0.7585	-0.2725	0.2187
ran_pars	mother_pidlink	sd__(Intercept)	0.5328	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7788	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	8787	8848	-4383	8767	NA	NA	NA
11	8785	8852	-4382	8763	3.511	1	0.06095
14	8784	8870	-4378	8756	6.802	3	0.07848
20	8787	8909	-4374	8747	8.975	6	0.175

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.049	4.157	-0.9739	2238	0.3302	-15.72	7.621
fixed	NA	poly(age, 3, raw = TRUE)1	0.4708	0.4346	1.083	2235	0.2788	-0.7492	1.691
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01623	0.01493	-1.087	2230	0.277	-0.05814	0.02567
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001811	0.0001685	1.074	2226	0.2828	-0.0002921	0.0006542
fixed	NA	male	0.01779	0.03242	0.5488	2355	0.5832	-0.07322	0.1088
fixed	NA	sibling_count3	0.006539	0.05033	0.1299	1780	0.8967	-0.1348	0.1478
fixed	NA	sibling_count4	-0.1089	0.05217	-2.088	1700	0.03693	-0.2554	0.0375
fixed	NA	sibling_count5	-0.1734	0.05708	-3.038	1644	0.00242	-0.3336	-0.01317
ran_pars	mother_pidlink	sd__(Intercept)	0.4654	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7075	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.21	4.159	-1.012	2239	0.3115	-15.88	7.464
fixed	NA	birth_order	0.01819	0.01657	1.098	2445	0.2725	-0.02833	0.06471
fixed	NA	poly(age, 3, raw = TRUE)1	0.4854	0.4348	1.116	2234	0.2643	-0.735	1.706
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01677	0.01493	-1.123	2230	0.2617	-0.05869	0.02516
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001877	0.0001686	1.113	2225	0.2657	-0.0002856	0.000661
fixed	NA	male	0.01756	0.03242	0.5416	2354	0.5882	-0.07344	0.1086
fixed	NA	sibling_count3	-0.001135	0.05083	-0.02234	1800	0.9822	-0.1438	0.1415
fixed	NA	sibling_count4	-0.1285	0.05514	-2.33	1770	0.0199	-0.2833	0.02628
fixed	NA	sibling_count5	-0.2059	0.06431	-3.202	1859	0.001389	-0.3864	-0.02539
ran_pars	mother_pidlink	sd__(Intercept)	0.4662	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.707	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.218	4.163	-1.013	2236	0.311	-15.9	7.467
fixed	NA	poly(age, 3, raw = TRUE)1	0.4896	0.4352	1.125	2231	0.2608	-0.7321	1.711
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01692	0.01495	-1.132	2226	0.2578	-0.05889	0.02504
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001896	0.0001688	1.124	2221	0.2613	-0.0002842	0.0006634
fixed	NA	male	0.01723	0.03244	0.5311	2350	0.5954	-0.07383	0.1083
fixed	NA	sibling_count3	-0.003582	0.05136	-0.06974	1849	0.9444	-0.1478	0.1406
fixed	NA	sibling_count4	-0.1342	0.05588	-2.401	1823	0.01645	-0.291	0.02269
fixed	NA	sibling_count5	-0.2109	0.06508	-3.241	1895	0.001212	-0.3936	-0.02824
fixed	NA	birth_order_nonlinear2	-0.009857	0.03808	-0.2589	1861	0.7958	-0.1168	0.09704
fixed	NA	birth_order_nonlinear3	0.04096	0.0471	0.8695	2055	0.3847	-0.09127	0.1732
fixed	NA	birth_order_nonlinear4	0.06328	0.06293	1.006	2292	0.3147	-0.1134	0.2399
fixed	NA	birth_order_nonlinear5	0.05697	0.09433	0.6039	2201	0.546	-0.2078	0.3218
ran_pars	mother_pidlink	sd__(Intercept)	0.4665	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7073	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.419	4.161	-1.062	2226	0.2883	-16.1	7.26
fixed	NA	poly(age, 3, raw = TRUE)1	0.5147	0.435	1.183	2221	0.2368	-0.7063	1.736
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01783	0.01494	-1.193	2216	0.2328	-0.05977	0.02411
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002004	0.0001687	1.188	2212	0.235	-0.0002731	0.000674
fixed	NA	male	0.01741	0.03247	0.536	2346	0.592	-0.07375	0.1086
fixed	NA	count_birth_order2/2	-0.08644	0.06784	-1.274	1862	0.2028	-0.2769	0.104
fixed	NA	count_birth_order1/3	-0.05432	0.06349	-0.8555	2492	0.3923	-0.2325	0.1239
fixed	NA	count_birth_order2/3	0.01796	0.06945	0.2586	2526	0.796	-0.177	0.2129
fixed	NA	count_birth_order3/3	-0.02227	0.07689	-0.2897	2524	0.7721	-0.2381	0.1936
fixed	NA	count_birth_order1/4	-0.16	0.07415	-2.157	2520	0.03109	-0.3681	0.04819
fixed	NA	count_birth_order2/4	-0.1696	0.07555	-2.245	2526	0.02486	-0.3817	0.04246
fixed	NA	count_birth_order3/4	-0.1822	0.07645	-2.383	2515	0.01724	-0.3968	0.03241
fixed	NA	count_birth_order4/4	-0.02882	0.08303	-0.3471	2519	0.7285	-0.2619	0.2042
fixed	NA	count_birth_order1/5	-0.2606	0.09569	-2.723	2523	0.006511	-0.5292	0.008027
fixed	NA	count_birth_order2/5	-0.3084	0.09884	-3.12	2490	0.001829	-0.5859	-0.03095
fixed	NA	count_birth_order3/5	-0.04529	0.08998	-0.5034	2488	0.6147	-0.2979	0.2073
fixed	NA	count_birth_order4/5	-0.2563	0.08942	-2.867	2500	0.004184	-0.5073	-0.005324
fixed	NA	count_birth_order5/5	-0.1791	0.09358	-1.913	2501	0.0558	-0.4418	0.08362
ran_pars	mother_pidlink	sd__(Intercept)	0.4688	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.705	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	6301	6359	-3140	6281	NA	NA	NA
11	6302	6366	-3140	6280	1.205	1	0.2722
14	6307	6388	-3139	6279	0.817	3	0.8454
20	6307	6424	-3133	6267	11.91	6	0.06407

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.864	4.382	-0.4254	2052	0.6706	-14.16	10.44
fixed	NA	poly(age, 3, raw = TRUE)1	0.2282	0.4587	0.4975	2049	0.6189	-1.059	1.516
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007366	0.01577	-0.467	2046	0.6406	-0.05164	0.03691
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007476	0.0001783	0.4193	2042	0.675	-0.0004256	0.0005752
fixed	NA	male	0.02406	0.03385	0.7108	2135	0.4773	-0.07095	0.1191
fixed	NA	sibling_count3	-0.03132	0.05529	-0.5664	1666	0.5712	-0.1865	0.1239
fixed	NA	sibling_count4	-0.07875	0.05618	-1.402	1607	0.1612	-0.2365	0.07895
fixed	NA	sibling_count5	-0.1307	0.0586	-2.231	1564	0.02585	-0.2952	0.03378
ran_pars	mother_pidlink	sd__(Intercept)	0.459	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7071	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.865	4.386	-0.4251	2051	0.6708	-14.18	10.45
fixed	NA	birth_order	0.00004857	0.01671	0.002906	2242	0.9977	-0.04687	0.04697
fixed	NA	poly(age, 3, raw = TRUE)1	0.2282	0.459	0.4972	2047	0.6191	-1.06	1.517
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007368	0.01579	-0.4667	2044	0.6408	-0.05168	0.03694
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007478	0.0001784	0.4191	2040	0.6752	-0.0004261	0.0005757
fixed	NA	male	0.02406	0.03385	0.7106	2134	0.4774	-0.07097	0.1191
fixed	NA	sibling_count3	-0.03134	0.05579	-0.5617	1679	0.5744	-0.1879	0.1253
fixed	NA	sibling_count4	-0.0788	0.05857	-1.345	1652	0.1787	-0.2432	0.08562
fixed	NA	sibling_count5	-0.1308	0.06441	-2.031	1713	0.04246	-0.3116	0.05002
ran_pars	mother_pidlink	sd__(Intercept)	0.4591	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7073	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.762	4.39	-0.4014	2050	0.6882	-14.09	10.56
fixed	NA	poly(age, 3, raw = TRUE)1	0.2178	0.4595	0.474	2046	0.6355	-1.072	1.508
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007016	0.0158	-0.4439	2043	0.6571	-0.05138	0.03734
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007091	0.0001786	0.397	2038	0.6914	-0.0004305	0.0005723
fixed	NA	male	0.02363	0.03388	0.6975	2133	0.4855	-0.07148	0.1187
fixed	NA	sibling_count3	-0.02587	0.05638	-0.4589	1724	0.6463	-0.1841	0.1324
fixed	NA	sibling_count4	-0.0723	0.0592	-1.221	1695	0.2221	-0.2385	0.09387
fixed	NA	sibling_count5	-0.1346	0.06485	-2.076	1734	0.03804	-0.3167	0.04741
fixed	NA	birth_order_nonlinear2	-0.005863	0.04001	-0.1465	1752	0.8835	-0.1182	0.1064
fixed	NA	birth_order_nonlinear3	-0.02504	0.04885	-0.5126	1911	0.6083	-0.1622	0.1121
fixed	NA	birth_order_nonlinear4	-0.008092	0.06495	-0.1246	2070	0.9009	-0.1904	0.1742
fixed	NA	birth_order_nonlinear5	0.05145	0.09334	0.5512	2039	0.5816	-0.2106	0.3135
ran_pars	mother_pidlink	sd__(Intercept)	0.4581	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7083	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.114	4.402	-0.4803	2044	0.6311	-14.47	10.24
fixed	NA	poly(age, 3, raw = TRUE)1	0.2561	0.4606	0.556	2040	0.5783	-1.037	1.549
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008386	0.01584	-0.5294	2036	0.5966	-0.05285	0.03608
fixed	NA	poly(age, 3, raw = TRUE)3	0.000087	0.000179	0.486	2032	0.627	-0.0004155	0.0005895
fixed	NA	male	0.02347	0.03395	0.6913	2128	0.4894	-0.07183	0.1188
fixed	NA	count_birth_order2/2	-0.005311	0.07669	-0.06925	1724	0.9448	-0.2206	0.21
fixed	NA	count_birth_order1/3	-0.06219	0.07036	-0.8838	2273	0.3769	-0.2597	0.1353
fixed	NA	count_birth_order2/3	0.01898	0.0764	0.2485	2298	0.8038	-0.1955	0.2334
fixed	NA	count_birth_order3/3	-0.0448	0.08294	-0.5401	2297	0.5892	-0.2776	0.188
fixed	NA	count_birth_order1/4	-0.03733	0.0782	-0.4774	2289	0.6331	-0.2568	0.1822
fixed	NA	count_birth_order2/4	-0.1113	0.07891	-1.41	2298	0.1586	-0.3328	0.1102
fixed	NA	count_birth_order3/4	-0.1624	0.08312	-1.953	2284	0.05089	-0.3957	0.07095
fixed	NA	count_birth_order4/4	-0.006416	0.09156	-0.07008	2286	0.9441	-0.2634	0.2506
fixed	NA	count_birth_order1/5	-0.1064	0.08996	-1.183	2298	0.2371	-0.3589	0.1461
fixed	NA	count_birth_order2/5	-0.1828	0.09325	-1.961	2287	0.05004	-0.4446	0.07893
fixed	NA	count_birth_order3/5	-0.07218	0.0928	-0.7778	2263	0.4368	-0.3327	0.1883
fixed	NA	count_birth_order4/5	-0.2232	0.09322	-2.395	2263	0.01672	-0.4849	0.03844
fixed	NA	count_birth_order5/5	-0.08344	0.09662	-0.8637	2275	0.3879	-0.3546	0.1878
ran_pars	mother_pidlink	sd__(Intercept)	0.4591	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7074	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	5719	5776	-2849	5699	NA	NA	NA
11	5721	5784	-2849	5699	0.000007659	1	0.9978
14	5726	5806	-2849	5698	0.7646	3	0.8579
20	5730	5845	-2845	5690	7.578	6	0.2707

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.229	4.172	-1.493	2253	0.1355	-17.94	5.481
fixed	NA	poly(age, 3, raw = TRUE)1	0.6964	0.4359	1.598	2250	0.1103	-0.5272	1.92
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02388	0.01496	-1.596	2247	0.1107	-0.06588	0.01813
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002652	0.0001688	1.571	2243	0.1164	-0.0002088	0.0007391
fixed	NA	male	0.01166	0.03243	0.3595	2366	0.7192	-0.07938	0.1027
fixed	NA	sibling_count3	0.0124	0.04975	0.2493	1791	0.8031	-0.1272	0.152
fixed	NA	sibling_count4	-0.07298	0.05175	-1.41	1720	0.1586	-0.2182	0.07227
fixed	NA	sibling_count5	-0.1414	0.05802	-2.436	1622	0.01495	-0.3042	0.02152
ran_pars	mother_pidlink	sd__(Intercept)	0.4702	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7075	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.391	4.173	-1.532	2254	0.1258	-18.1	5.323
fixed	NA	birth_order	0.02125	0.01668	1.274	2440	0.2029	-0.02558	0.06807
fixed	NA	poly(age, 3, raw = TRUE)1	0.7102	0.436	1.629	2250	0.1034	-0.5135	1.934
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02438	0.01497	-1.629	2247	0.1034	-0.06639	0.01763
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002715	0.0001689	1.608	2243	0.108	-0.0002025	0.0007456
fixed	NA	male	0.01127	0.03243	0.3475	2365	0.7282	-0.07976	0.1023
fixed	NA	sibling_count3	0.003248	0.05026	0.06462	1809	0.9485	-0.1378	0.1443
fixed	NA	sibling_count4	-0.09601	0.05482	-1.752	1796	0.08002	-0.2499	0.05786
fixed	NA	sibling_count5	-0.1777	0.06465	-2.748	1823	0.006051	-0.3592	0.003803
ran_pars	mother_pidlink	sd__(Intercept)	0.4705	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7072	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.414	4.176	-1.536	2248	0.1247	-18.14	5.308
fixed	NA	poly(age, 3, raw = TRUE)1	0.717	0.4363	1.643	2244	0.1005	-0.5078	1.942
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02464	0.01498	-1.645	2241	0.1001	-0.06669	0.01741
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002748	0.000169	1.626	2237	0.1042	-0.0001997	0.0007492
fixed	NA	male	0.01085	0.03245	0.3344	2363	0.7381	-0.08025	0.102
fixed	NA	sibling_count3	-0.002607	0.05085	-0.05127	1864	0.9591	-0.1453	0.1401
fixed	NA	sibling_count4	-0.09985	0.05554	-1.798	1848	0.07239	-0.2558	0.05606
fixed	NA	sibling_count5	-0.1857	0.0655	-2.835	1869	0.004634	-0.3695	-0.00182
fixed	NA	birth_order_nonlinear2	-0.01148	0.03779	-0.3037	1864	0.7614	-0.1176	0.0946
fixed	NA	birth_order_nonlinear3	0.058	0.04677	1.24	2054	0.2151	-0.07328	0.1893
fixed	NA	birth_order_nonlinear4	0.0477	0.06321	0.7547	2298	0.4505	-0.1297	0.2251
fixed	NA	birth_order_nonlinear5	0.09578	0.1002	0.9556	2168	0.3394	-0.1856	0.3771
ran_pars	mother_pidlink	sd__(Intercept)	0.4709	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7073	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.366	4.173	-1.526	2237	0.1273	-18.08	5.347
fixed	NA	poly(age, 3, raw = TRUE)1	0.717	0.436	1.645	2233	0.1002	-0.5068	1.941
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02474	0.01497	-1.653	2230	0.09846	-0.06675	0.01727
fixed	NA	poly(age, 3, raw = TRUE)3	0.000277	0.0001689	1.64	2226	0.1011	-0.0001971	0.0007511
fixed	NA	male	0.01205	0.03248	0.3709	2356	0.7107	-0.07913	0.1032
fixed	NA	count_birth_order2/2	-0.0718	0.0659	-1.089	1888	0.2761	-0.2568	0.1132
fixed	NA	count_birth_order1/3	-0.04571	0.0628	-0.7279	2500	0.4667	-0.222	0.1306
fixed	NA	count_birth_order2/3	0.03087	0.06934	0.4452	2535	0.6562	-0.1638	0.2255
fixed	NA	count_birth_order3/3	-0.01001	0.07506	-0.1334	2531	0.8939	-0.2207	0.2007
fixed	NA	count_birth_order1/4	-0.1066	0.074	-1.441	2530	0.1497	-0.3143	0.1011
fixed	NA	count_birth_order2/4	-0.1273	0.07535	-1.689	2531	0.09131	-0.3388	0.08424
fixed	NA	count_birth_order3/4	-0.1199	0.07649	-1.567	2521	0.1173	-0.3346	0.09486
fixed	NA	count_birth_order4/4	-0.0405	0.08201	-0.4938	2530	0.6215	-0.2707	0.1897
fixed	NA	count_birth_order1/5	-0.2444	0.09518	-2.568	2531	0.0103	-0.5116	0.02279
fixed	NA	count_birth_order2/5	-0.3341	0.1005	-3.323	2493	0.0009026	-0.6164	-0.0519
fixed	NA	count_birth_order3/5	0.01908	0.09128	0.2091	2497	0.8344	-0.2371	0.2753
fixed	NA	count_birth_order4/5	-0.2035	0.09196	-2.213	2502	0.02699	-0.4617	0.05464
fixed	NA	count_birth_order5/5	-0.1077	0.09939	-1.083	2491	0.2788	-0.3867	0.1713
ran_pars	mother_pidlink	sd__(Intercept)	0.474	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7045	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	6332	6390	-3156	6312	NA	NA	NA
11	6332	6396	-3155	6310	1.626	1	0.2023
14	6337	6419	-3154	6309	1.335	3	0.7207
20	6336	6453	-3148	6296	12.39	6	0.05381

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

g-factor 2007 young

birthorder <- birthorder %>% mutate(outcome = g_factor_2007_young)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.324	0.5196	-14.1	4623	3.293e-44	-8.783	-5.866
fixed	NA	poly(age, 3, raw = TRUE)1	0.8042	0.06916	11.63	4758	7.745e-31	0.6101	0.9984
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02602	0.002968	-8.766	4905	2.507e-18	-0.03435	-0.01769
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002514	0.0000416	6.042	4961	0.000000001634	0.0001346	0.0003681
fixed	NA	male	-0.0007239	0.02439	-0.02969	4521	0.9763	-0.06918	0.06773
fixed	NA	sibling_count3	-0.01199	0.03865	-0.3102	3499	0.7564	-0.1205	0.0965
fixed	NA	sibling_count4	-0.149	0.03954	-3.768	3309	0.0001672	-0.26	-0.03801
fixed	NA	sibling_count5	-0.1275	0.04271	-2.984	3095	0.002865	-0.2474	-0.00757
ran_pars	mother_pidlink	sd__(Intercept)	0.5178	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7313	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.402	0.5202	-14.23	4621	5.464e-45	-8.862	-5.941
fixed	NA	birth_order	0.03096	0.01203	2.574	4570	0.01007	-0.002797	0.06472
fixed	NA	poly(age, 3, raw = TRUE)1	0.8073	0.06914	11.68	4755	4.49e-31	0.6132	1.001
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02608	0.002966	-8.791	4903	2.02e-18	-0.0344	-0.01775
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002518	0.00004158	6.056	4960	0.000000001499	0.0001351	0.0003685
fixed	NA	male	-0.001843	0.02438	-0.07559	4523	0.9397	-0.07028	0.06659
fixed	NA	sibling_count3	-0.02616	0.03901	-0.6708	3533	0.5024	-0.1357	0.08333
fixed	NA	sibling_count4	-0.1809	0.0414	-4.369	3474	0.00001282	-0.2971	-0.06468
fixed	NA	sibling_count5	-0.1817	0.04758	-3.818	3438	0.0001369	-0.3152	-0.0481
ran_pars	mother_pidlink	sd__(Intercept)	0.5166	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7313	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.436	0.5197	-14.31	4629	1.775e-45	-8.895	-5.977
fixed	NA	poly(age, 3, raw = TRUE)1	0.8136	0.0691	11.77	4756	1.444e-31	0.6197	1.008
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02634	0.002964	-8.884	4901	8.913e-19	-0.03466	-0.01801
fixed	NA	poly(age, 3, raw = TRUE)3	0.000255	0.00004154	6.139	4957	0.0000000008979	0.0001384	0.0003716
fixed	NA	male	-0.001712	0.02436	-0.07031	4520	0.944	-0.07008	0.06666
fixed	NA	sibling_count3	-0.01184	0.03936	-0.3008	3628	0.7636	-0.1223	0.09863
fixed	NA	sibling_count4	-0.173	0.04183	-4.136	3584	0.0000361	-0.2904	-0.0556
fixed	NA	sibling_count5	-0.1748	0.04788	-3.651	3466	0.0002648	-0.3092	-0.04042
fixed	NA	birth_order_nonlinear2	0.08672	0.02855	3.038	3512	0.002401	0.006587	0.1668
fixed	NA	birth_order_nonlinear3	-0.005976	0.03524	-0.1696	3790	0.8654	-0.1049	0.09296
fixed	NA	birth_order_nonlinear4	0.1429	0.04709	3.034	4106	0.002429	0.01069	0.2751
fixed	NA	birth_order_nonlinear5	0.1438	0.06739	2.134	4326	0.03291	-0.04536	0.333
ran_pars	mother_pidlink	sd__(Intercept)	0.5155	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7308	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.43	0.5203	-14.28	4624	2.692e-45	-8.89	-5.969
fixed	NA	poly(age, 3, raw = TRUE)1	0.8131	0.06915	11.76	4749	1.751e-31	0.6189	1.007
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02631	0.002966	-8.869	4894	1.018e-18	-0.03463	-0.01798
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002546	0.00004157	6.126	4951	0.0000000009724	0.000138	0.0003713
fixed	NA	male	-0.00201	0.02439	-0.08244	4520	0.9343	-0.07047	0.06645
fixed	NA	count_birth_order2/2	0.07828	0.05326	1.47	3614	0.1417	-0.07121	0.2278
fixed	NA	count_birth_order1/3	-0.01815	0.04764	-0.3809	4857	0.7033	-0.1519	0.1156
fixed	NA	count_birth_order2/3	0.08603	0.05245	1.64	4951	0.101	-0.06119	0.2332
fixed	NA	count_birth_order3/3	-0.03171	0.05884	-0.5389	4943	0.59	-0.1969	0.1335
fixed	NA	count_birth_order1/4	-0.186	0.05426	-3.428	4940	0.0006124	-0.3383	-0.03371
fixed	NA	count_birth_order2/4	-0.0982	0.05542	-1.772	4952	0.07645	-0.2538	0.05736
fixed	NA	count_birth_order3/4	-0.1839	0.05789	-3.178	4922	0.001494	-0.3464	-0.02145
fixed	NA	count_birth_order4/4	0.001654	0.06316	0.02619	4903	0.9791	-0.1756	0.1789
fixed	NA	count_birth_order1/5	-0.1567	0.06592	-2.376	4943	0.01752	-0.3417	0.02838
fixed	NA	count_birth_order2/5	-0.09442	0.06949	-1.359	4853	0.1743	-0.2895	0.1006
fixed	NA	count_birth_order3/5	-0.1626	0.06617	-2.458	4848	0.01401	-0.3484	0.0231
fixed	NA	count_birth_order4/5	-0.07784	0.06944	-1.121	4820	0.2623	-0.2728	0.1171
fixed	NA	count_birth_order5/5	-0.03441	0.06756	-0.5094	4919	0.6105	-0.224	0.1552
ran_pars	mother_pidlink	sd__(Intercept)	0.5145	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7318	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12822	12887	-6401	12802	NA	NA	NA
11	12818	12889	-6398	12796	6.635	1	0.009998
14	12810	12901	-6391	12782	13.72	3	0.003312
20	12820	12950	-6390	12780	1.632	6	0.9502

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.328	1.241	-5.1	3363	0.0000003579	-9.81	-2.845
fixed	NA	poly(age, 3, raw = TRUE)1	0.639	0.1897	3.368	3342	0.0007666	0.1064	1.172
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01717	0.009434	-1.82	3326	0.06879	-0.04365	0.009308
fixed	NA	poly(age, 3, raw = TRUE)3	0.000104	0.0001526	0.6816	3314	0.4955	-0.0003244	0.0005325
fixed	NA	male	-0.03967	0.02524	-1.572	4096	0.116	-0.1105	0.03117
fixed	NA	sibling_count3	-0.0009547	0.03506	-0.02723	3129	0.9783	-0.09938	0.09747
fixed	NA	sibling_count4	-0.1098	0.03972	-2.764	2845	0.00575	-0.2213	0.001717
fixed	NA	sibling_count5	-0.183	0.04801	-3.811	2737	0.0001413	-0.3178	-0.04822
ran_pars	mother_pidlink	sd__(Intercept)	0.5065	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7103	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.51	1.244	-5.233	3370	0.000000177	-10	-3.018
fixed	NA	birth_order	0.02758	0.01385	1.992	4280	0.04648	-0.01129	0.06646
fixed	NA	poly(age, 3, raw = TRUE)1	0.6595	0.19	3.471	3343	0.0005256	0.1261	1.193
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01813	0.009446	-1.919	3325	0.05501	-0.04465	0.008384
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001192	0.0001528	0.7801	3313	0.4354	-0.0003098	0.0005482
fixed	NA	male	-0.04046	0.02524	-1.603	4099	0.109	-0.1113	0.03038
fixed	NA	sibling_count3	-0.01434	0.03568	-0.4019	3177	0.6878	-0.1145	0.08581
fixed	NA	sibling_count4	-0.1424	0.04293	-3.316	3063	0.0009224	-0.2629	-0.02187
fixed	NA	sibling_count5	-0.2388	0.05555	-4.299	3155	0.0000177	-0.3947	-0.08287
ran_pars	mother_pidlink	sd__(Intercept)	0.5052	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7107	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.548	1.244	-5.262	3374	0.0000001512	-10.04	-3.055
fixed	NA	poly(age, 3, raw = TRUE)1	0.6687	0.1902	3.516	3348	0.000444	0.1348	1.203
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01858	0.009455	-1.965	3331	0.04946	-0.04512	0.007958
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001263	0.000153	0.8259	3320	0.4089	-0.0003031	0.0005557
fixed	NA	male	-0.04067	0.02525	-1.611	4097	0.1073	-0.1115	0.03021
fixed	NA	sibling_count3	-0.007151	0.03623	-0.1974	3294	0.8436	-0.1089	0.09456
fixed	NA	sibling_count4	-0.1343	0.04367	-3.075	3159	0.002122	-0.2569	-0.01171
fixed	NA	sibling_count5	-0.2444	0.05724	-4.271	3232	0.00002006	-0.4051	-0.08376
fixed	NA	birth_order_nonlinear2	0.04433	0.02868	1.546	2993	0.1222	-0.03616	0.1248
fixed	NA	birth_order_nonlinear3	0.02522	0.03858	0.6539	3589	0.5132	-0.08306	0.1335
fixed	NA	birth_order_nonlinear4	0.08059	0.05323	1.514	3993	0.1301	-0.06881	0.23
fixed	NA	birth_order_nonlinear5	0.1653	0.08324	1.986	3964	0.04713	-0.06837	0.3989
ran_pars	mother_pidlink	sd__(Intercept)	0.5046	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7111	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.542	1.245	-5.253	3372	0.0000001586	-10.04	-3.046
fixed	NA	poly(age, 3, raw = TRUE)1	0.6681	0.1903	3.51	3346	0.0004542	0.1338	1.202
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01856	0.009462	-1.961	3329	0.04995	-0.04512	0.008004
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001262	0.0001531	0.8243	3317	0.4098	-0.0003035	0.0005559
fixed	NA	male	-0.04045	0.02528	-1.6	4091	0.1096	-0.1114	0.03051
fixed	NA	count_birth_order2/2	0.03333	0.04609	0.7233	3275	0.4696	-0.09604	0.1627
fixed	NA	count_birth_order1/3	-0.03346	0.04428	-0.7557	4369	0.4499	-0.1577	0.09083
fixed	NA	count_birth_order2/3	0.06004	0.04812	1.248	4420	0.2121	-0.07502	0.1951
fixed	NA	count_birth_order3/3	0.0239	0.05367	0.4453	4420	0.6561	-0.1267	0.1745
fixed	NA	count_birth_order1/4	-0.1253	0.05955	-2.104	4422	0.03541	-0.2925	0.04185
fixed	NA	count_birth_order2/4	-0.1411	0.05944	-2.374	4382	0.01762	-0.308	0.02572
fixed	NA	count_birth_order3/4	-0.1075	0.06195	-1.735	4290	0.08282	-0.2814	0.06642
fixed	NA	count_birth_order4/4	-0.0287	0.06155	-0.4663	4419	0.641	-0.2015	0.1441
fixed	NA	count_birth_order1/5	-0.1659	0.08989	-1.845	4342	0.06507	-0.4182	0.08645
fixed	NA	count_birth_order2/5	-0.1693	0.09476	-1.786	4084	0.0741	-0.4353	0.09671
fixed	NA	count_birth_order3/5	-0.2539	0.08351	-3.041	4194	0.002373	-0.4883	-0.01954
fixed	NA	count_birth_order4/5	-0.2206	0.07848	-2.811	4295	0.004959	-0.4409	-0.0003212
fixed	NA	count_birth_order5/5	-0.08879	0.07603	-1.168	4407	0.2429	-0.3022	0.1246
ran_pars	mother_pidlink	sd__(Intercept)	0.5053	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7109	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11231	11295	-5606	11211	NA	NA	NA
11	11229	11299	-5604	11207	3.971	1	0.04628
14	11233	11323	-5603	11205	2.088	3	0.5544
20	11241	11369	-5600	11201	4.469	6	0.6135

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.168	1.273	-4.846	3077	0.000001323	-9.741	-2.595
fixed	NA	poly(age, 3, raw = TRUE)1	0.6238	0.1948	3.203	3055	0.001374	0.07712	1.171
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01682	0.009694	-1.735	3040	0.08282	-0.04403	0.01039
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001046	0.000157	0.6661	3027	0.5054	-0.0003362	0.0005453
fixed	NA	male	-0.03772	0.02602	-1.45	3792	0.1472	-0.1108	0.03532
fixed	NA	sibling_count3	-0.02109	0.03765	-0.5602	2973	0.5754	-0.1268	0.08459
fixed	NA	sibling_count4	-0.08749	0.04106	-2.131	2746	0.03319	-0.2027	0.02776
fixed	NA	sibling_count5	-0.1585	0.04644	-3.413	2690	0.0006516	-0.2889	-0.02815
ran_pars	mother_pidlink	sd__(Intercept)	0.5117	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7037	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.331	1.276	-4.962	3084	0.0000007361	-9.912	-2.749
fixed	NA	birth_order	0.02546	0.01379	1.846	4030	0.06496	-0.01326	0.06418
fixed	NA	poly(age, 3, raw = TRUE)1	0.6421	0.195	3.292	3057	0.001005	0.09466	1.19
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01768	0.009706	-1.822	3040	0.06857	-0.04493	0.009562
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001185	0.0001572	0.7535	3027	0.4512	-0.0003228	0.0005597
fixed	NA	male	-0.03847	0.02602	-1.478	3795	0.1395	-0.1115	0.03458
fixed	NA	sibling_count3	-0.03373	0.03824	-0.8819	3005	0.3779	-0.1411	0.07362
fixed	NA	sibling_count4	-0.1159	0.04382	-2.645	2917	0.008213	-0.2389	0.007101
fixed	NA	sibling_count5	-0.2061	0.05308	-3.883	2997	0.0001056	-0.3551	-0.05709
ran_pars	mother_pidlink	sd__(Intercept)	0.5105	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7041	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.391	1.275	-5.011	3084	0.0000005722	-9.97	-2.811
fixed	NA	poly(age, 3, raw = TRUE)1	0.6528	0.1951	3.346	3057	0.0008285	0.1052	1.2
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0182	0.009708	-1.875	3040	0.06088	-0.04545	0.009048
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001266	0.0001572	0.8051	3028	0.4208	-0.0003148	0.000568
fixed	NA	male	-0.03784	0.02602	-1.454	3789	0.1459	-0.1109	0.03519
fixed	NA	sibling_count3	-0.02436	0.03878	-0.6281	3104	0.53	-0.1332	0.08451
fixed	NA	sibling_count4	-0.1044	0.04446	-2.348	3010	0.01894	-0.2292	0.02041
fixed	NA	sibling_count5	-0.2034	0.05402	-3.765	3019	0.0001696	-0.3551	-0.05176
fixed	NA	birth_order_nonlinear2	0.0732	0.02976	2.46	2812	0.01396	-0.01033	0.1567
fixed	NA	birth_order_nonlinear3	0.009629	0.03919	0.2457	3372	0.8059	-0.1004	0.1196
fixed	NA	birth_order_nonlinear4	0.07597	0.05328	1.426	3667	0.154	-0.07358	0.2255
fixed	NA	birth_order_nonlinear5	0.1518	0.07995	1.898	3844	0.05773	-0.07266	0.3762
ran_pars	mother_pidlink	sd__(Intercept)	0.5108	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7035	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.391	1.274	-5.015	3073	0.0000005613	-9.968	-2.814
fixed	NA	poly(age, 3, raw = TRUE)1	0.6531	0.195	3.35	3048	0.0008193	0.1058	1.2
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01827	0.009703	-1.883	3031	0.05977	-0.04551	0.008964
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001289	0.0001572	0.8201	3019	0.4122	-0.0003123	0.00057
fixed	NA	male	-0.03926	0.02602	-1.509	3780	0.1314	-0.1123	0.03378
fixed	NA	count_birth_order2/2	0.08644	0.05025	1.72	3010	0.08548	-0.05461	0.2275
fixed	NA	count_birth_order1/3	-0.04782	0.04758	-1.005	4085	0.3149	-0.1814	0.08574
fixed	NA	count_birth_order2/3	0.06277	0.05105	1.23	4128	0.2189	-0.08053	0.2061
fixed	NA	count_birth_order3/3	0.02804	0.05732	0.4891	4124	0.6248	-0.1329	0.189
fixed	NA	count_birth_order1/4	-0.09395	0.05961	-1.576	4129	0.1151	-0.2613	0.07338
fixed	NA	count_birth_order2/4	-0.06605	0.06009	-1.099	4099	0.2718	-0.2347	0.1026
fixed	NA	count_birth_order3/4	-0.1119	0.06309	-1.774	4013	0.0761	-0.289	0.06515
fixed	NA	count_birth_order4/4	0.03027	0.06473	0.4677	4121	0.64	-0.1514	0.212
fixed	NA	count_birth_order1/5	-0.07302	0.08077	-0.904	4075	0.366	-0.2998	0.1537
fixed	NA	count_birth_order2/5	-0.1053	0.08165	-1.29	3971	0.1971	-0.3346	0.1239
fixed	NA	count_birth_order3/5	-0.2344	0.07788	-3.009	3952	0.002635	-0.453	-0.01575
fixed	NA	count_birth_order4/5	-0.2159	0.07831	-2.757	3923	0.005858	-0.4357	0.003906
fixed	NA	count_birth_order5/5	-0.05716	0.07509	-0.7612	4117	0.4466	-0.268	0.1536
ran_pars	mother_pidlink	sd__(Intercept)	0.5131	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7019	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	10463	10526	-5221	10443	NA	NA	NA
11	10462	10531	-5220	10440	3.413	1	0.0647
14	10461	10550	-5217	10433	6.292	3	0.09825
20	10465	10591	-5212	10425	8.753	6	0.188

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.829	1.258	-4.634	3264	0.000003724	-9.36	-2.298
fixed	NA	poly(age, 3, raw = TRUE)1	0.56	0.1923	2.912	3243	0.003611	0.02026	1.1
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01319	0.009558	-1.38	3229	0.1677	-0.04002	0.01364
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003789	0.0001546	0.2451	3217	0.8064	-0.0003961	0.0004719
fixed	NA	male	-0.04295	0.02561	-1.677	4000	0.09358	-0.1148	0.02893
fixed	NA	sibling_count3	0.01545	0.0354	0.4364	3066	0.6626	-0.08393	0.1148
fixed	NA	sibling_count4	-0.09473	0.04028	-2.352	2790	0.01876	-0.2078	0.01835
fixed	NA	sibling_count5	-0.1953	0.05039	-3.875	2713	0.0001089	-0.3367	-0.05383
ran_pars	mother_pidlink	sd__(Intercept)	0.5188	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.713	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.028	1.261	-4.779	3271	0.00000184	-9.569	-2.487
fixed	NA	birth_order	0.02919	0.01417	2.061	4172	0.03941	-0.01057	0.06895
fixed	NA	poly(age, 3, raw = TRUE)1	0.5828	0.1926	3.026	3243	0.002495	0.04223	1.123
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01427	0.009571	-1.491	3226	0.1362	-0.04113	0.0126
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005509	0.0001548	0.3559	3215	0.7219	-0.0003795	0.0004896
fixed	NA	male	-0.04357	0.0256	-1.702	4001	0.0889	-0.1154	0.0283
fixed	NA	sibling_count3	0.00164	0.03601	0.04555	3112	0.9637	-0.09945	0.1027
fixed	NA	sibling_count4	-0.1295	0.04365	-2.967	3013	0.003032	-0.252	-0.006979
fixed	NA	sibling_count5	-0.2529	0.0576	-4.391	3096	0.00001166	-0.4146	-0.09125
ran_pars	mother_pidlink	sd__(Intercept)	0.5178	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7132	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.023	1.263	-4.77	3276	0.000001918	-9.567	-2.479
fixed	NA	poly(age, 3, raw = TRUE)1	0.5852	0.1929	3.034	3249	0.002433	0.04376	1.127
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01436	0.009586	-1.498	3232	0.1342	-0.04127	0.01255
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005626	0.000155	0.3629	3221	0.7167	-0.0003789	0.0004915
fixed	NA	male	-0.04382	0.02562	-1.711	3998	0.08724	-0.1157	0.02809
fixed	NA	sibling_count3	0.001778	0.03659	0.04861	3227	0.9612	-0.1009	0.1045
fixed	NA	sibling_count4	-0.1253	0.04444	-2.821	3113	0.004825	-0.2501	-0.0006004
fixed	NA	sibling_count5	-0.2469	0.05971	-4.135	3179	0.00003646	-0.4145	-0.07928
fixed	NA	birth_order_nonlinear2	0.04764	0.02886	1.651	2904	0.09895	-0.03338	0.1287
fixed	NA	birth_order_nonlinear3	0.05963	0.03912	1.524	3454	0.1275	-0.05018	0.1694
fixed	NA	birth_order_nonlinear4	0.07538	0.05463	1.38	3879	0.1677	-0.07796	0.2287
fixed	NA	birth_order_nonlinear5	0.1165	0.08926	1.305	3927	0.1921	-0.1341	0.367
ran_pars	mother_pidlink	sd__(Intercept)	0.5175	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7137	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.022	1.263	-4.767	3274	0.000001953	-9.569	-2.476
fixed	NA	poly(age, 3, raw = TRUE)1	0.5849	0.193	3.03	3248	0.002465	0.04303	1.127
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01432	0.009593	-1.493	3230	0.1355	-0.04125	0.01261
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005547	0.0001552	0.3575	3218	0.7207	-0.0003801	0.000491
fixed	NA	male	-0.04315	0.02566	-1.682	3994	0.09265	-0.1152	0.02886
fixed	NA	count_birth_order2/2	0.03616	0.04536	0.7973	3146	0.4254	-0.09116	0.1635
fixed	NA	count_birth_order1/3	-0.02526	0.04458	-0.5665	4304	0.5711	-0.1504	0.09989
fixed	NA	count_birth_order2/3	0.08174	0.04901	1.668	4355	0.09543	-0.05584	0.2193
fixed	NA	count_birth_order3/3	0.05704	0.0542	1.052	4353	0.2927	-0.0951	0.2092
fixed	NA	count_birth_order1/4	-0.1136	0.06091	-1.865	4357	0.06225	-0.2846	0.05738
fixed	NA	count_birth_order2/4	-0.1328	0.06033	-2.201	4317	0.02778	-0.3021	0.03655
fixed	NA	count_birth_order3/4	-0.06945	0.06258	-1.11	4208	0.2672	-0.2451	0.1062
fixed	NA	count_birth_order4/4	-0.0207	0.06221	-0.3327	4355	0.7394	-0.1953	0.1539
fixed	NA	count_birth_order1/5	-0.1693	0.09198	-1.84	4291	0.06581	-0.4275	0.08893
fixed	NA	count_birth_order2/5	-0.2048	0.1015	-2.017	3964	0.04375	-0.4898	0.0802
fixed	NA	count_birth_order3/5	-0.1832	0.08841	-2.072	4117	0.03835	-0.4313	0.06501
fixed	NA	count_birth_order4/5	-0.2445	0.08348	-2.929	4198	0.003423	-0.4788	-0.01015
fixed	NA	count_birth_order5/5	-0.1409	0.08145	-1.73	4340	0.08375	-0.3695	0.08774
ran_pars	mother_pidlink	sd__(Intercept)	0.5178	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7136	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11157	11221	-5569	11137	NA	NA	NA
11	11155	11225	-5567	11133	4.252	1	0.0392
14	11161	11250	-5566	11133	0.5888	3	0.899
20	11167	11295	-5564	11127	5.03	6	0.54

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Raven 2015 old

birthorder <- birthorder %>% mutate(outcome = raven_2015_old)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.4153	0.1856	-2.237	7051	0.02529	-0.9363	0.1057
fixed	NA	poly(age, 3, raw = TRUE)1	0.07945	0.01789	4.441	6992	0.000009113	0.02923	0.1297
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002707	0.0005245	-5.161	6891	0.0000002526	-0.004179	-0.001235
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001973	0.000004771	4.136	6792	0.00003577	0.000006341	0.00003313
fixed	NA	male	0.148	0.02101	7.044	6696	2.054e-12	0.08903	0.207
fixed	NA	sibling_count3	0.02843	0.0322	0.8828	4908	0.3774	-0.06196	0.1188
fixed	NA	sibling_count4	-0.009102	0.03344	-0.2722	4522	0.7855	-0.103	0.08477
fixed	NA	sibling_count5	0.02765	0.0351	0.7878	4153	0.4308	-0.07087	0.1262
ran_pars	mother_pidlink	sd__(Intercept)	0.4717	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7857	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.4193	0.1857	-2.258	7039	0.02401	-0.9406	0.1021
fixed	NA	birth_order	0.006446	0.01027	0.6279	5656	0.5301	-0.02237	0.03527
fixed	NA	poly(age, 3, raw = TRUE)1	0.07888	0.01792	4.403	7005	0.00001083	0.02859	0.1292
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002691	0.0005251	-5.125	6900	0.000000306	-0.004165	-0.001217
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001963	0.000004774	4.111	6797	0.00003979	0.000006228	0.00003303
fixed	NA	male	0.1479	0.02102	7.035	6693	2.184e-12	0.08886	0.2068
fixed	NA	sibling_count3	0.02628	0.03238	0.8114	5017	0.4172	-0.06462	0.1172
fixed	NA	sibling_count4	-0.01424	0.03443	-0.4137	4974	0.6791	-0.1109	0.0824
fixed	NA	sibling_count5	0.01925	0.03757	0.5123	5064	0.6085	-0.08621	0.1247
ran_pars	mother_pidlink	sd__(Intercept)	0.4717	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7858	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.4077	0.1861	-2.191	7046	0.02851	-0.93	0.1147
fixed	NA	poly(age, 3, raw = TRUE)1	0.07889	0.01793	4.401	6990	0.00001093	0.02858	0.1292
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002684	0.0005257	-5.105	6872	0.0000003399	-0.004159	-0.001208
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000195	0.000004783	4.077	6753	0.00004613	0.000006074	0.00003292
fixed	NA	male	0.148	0.02101	7.046	6692	2.033e-12	0.08906	0.207
fixed	NA	sibling_count3	0.02062	0.03277	0.6292	5198	0.5292	-0.07136	0.1126
fixed	NA	sibling_count4	-0.009991	0.03485	-0.2866	5171	0.7744	-0.1078	0.08784
fixed	NA	sibling_count5	0.01146	0.0378	0.3032	5200	0.7617	-0.09465	0.1176
fixed	NA	birth_order_nonlinear2	-0.01535	0.02437	-0.63	5626	0.5287	-0.08375	0.05304
fixed	NA	birth_order_nonlinear3	0.03391	0.03121	1.087	5409	0.2773	-0.05369	0.1215
fixed	NA	birth_order_nonlinear4	-0.04011	0.04063	-0.9872	5323	0.3236	-0.1542	0.07394
fixed	NA	birth_order_nonlinear5	0.09271	0.05926	1.565	5082	0.1177	-0.07362	0.259
ran_pars	mother_pidlink	sd__(Intercept)	0.4708	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.786	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3852	0.1864	-2.066	7043	0.03884	-0.9085	0.1381
fixed	NA	poly(age, 3, raw = TRUE)1	0.07885	0.01793	4.399	6985	0.00001106	0.02853	0.1292
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002669	0.0005257	-5.078	6865	0.0000003922	-0.004145	-0.001194
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001926	0.000004784	4.027	6742	0.0000571	0.000005836	0.00003269
fixed	NA	male	0.1483	0.02102	7.057	6684	1.875e-12	0.08931	0.2073
fixed	NA	count_birth_order2/2	-0.08728	0.04168	-2.094	5752	0.03628	-0.2043	0.0297
fixed	NA	count_birth_order1/3	-0.00209	0.0411	-0.05085	7026	0.9594	-0.1175	0.1133
fixed	NA	count_birth_order2/3	-0.02197	0.04564	-0.4814	7116	0.6303	-0.1501	0.1061
fixed	NA	count_birth_order3/3	0.0221	0.05101	0.4333	7133	0.6648	-0.1211	0.1653
fixed	NA	count_birth_order1/4	-0.06028	0.04657	-1.294	7115	0.1956	-0.191	0.07044
fixed	NA	count_birth_order2/4	-0.01072	0.04913	-0.2181	7135	0.8273	-0.1486	0.1272
fixed	NA	count_birth_order3/4	-0.01018	0.05312	-0.1917	7119	0.848	-0.1593	0.1389
fixed	NA	count_birth_order4/4	-0.08644	0.05594	-1.545	7096	0.1224	-0.2435	0.0706
fixed	NA	count_birth_order1/5	-0.06351	0.05287	-1.201	7136	0.2297	-0.2119	0.0849
fixed	NA	count_birth_order2/5	-0.00108	0.05527	-0.01954	7118	0.9844	-0.1562	0.1541
fixed	NA	count_birth_order3/5	0.03526	0.05691	0.6196	7090	0.5356	-0.1245	0.195
fixed	NA	count_birth_order4/5	-0.04227	0.06011	-0.7032	7037	0.4819	-0.211	0.1265
fixed	NA	count_birth_order5/5	0.07895	0.06157	1.282	7012	0.1998	-0.09389	0.2518
ran_pars	mother_pidlink	sd__(Intercept)	0.471	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7859	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	18847	18916	-9414	18827	NA	NA	NA
11	18849	18924	-9413	18827	0.3945	1	0.5299
14	18849	18945	-9410	18821	6.299	3	0.09794
20	18854	18991	-9407	18814	6.616	6	0.3578

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1652	0.4595	0.3595	4468	0.7192	-1.125	1.455
fixed	NA	poly(age, 3, raw = TRUE)1	0.003894	0.05367	0.07255	4478	0.9422	-0.1468	0.1545
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007124	0.00198	0.3599	4488	0.719	-0.004845	0.006269
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002249	0.00002321	-0.9689	4496	0.3327	-0.00008765	0.00004267
fixed	NA	male	0.07522	0.02458	3.061	4284	0.002223	0.006232	0.1442
fixed	NA	sibling_count3	0.02922	0.03501	0.8345	3224	0.4041	-0.06907	0.1275
fixed	NA	sibling_count4	-0.03855	0.03799	-1.015	2900	0.3103	-0.1452	0.06808
fixed	NA	sibling_count5	-0.08842	0.04375	-2.021	2657	0.04335	-0.2112	0.03437
ran_pars	mother_pidlink	sd__(Intercept)	0.4123	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7366	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1444	0.46	0.3139	4468	0.7536	-1.147	1.436
fixed	NA	birth_order	0.01205	0.0128	0.9417	4011	0.3464	-0.02387	0.04797
fixed	NA	poly(age, 3, raw = TRUE)1	0.004529	0.05367	0.08438	4477	0.9328	-0.1461	0.1552
fixed	NA	poly(age, 3, raw = TRUE)2	0.0006787	0.00198	0.3428	4486	0.7318	-0.004879	0.006237
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002185	0.00002322	-0.9408	4494	0.3469	-0.00008704	0.00004334
fixed	NA	male	0.07476	0.02458	3.041	4282	0.002372	0.005754	0.1438
fixed	NA	sibling_count3	0.02358	0.03552	0.6639	3282	0.5068	-0.07613	0.1233
fixed	NA	sibling_count4	-0.05155	0.04042	-1.275	3112	0.2023	-0.165	0.0619
fixed	NA	sibling_count5	-0.1101	0.04942	-2.227	3144	0.026	-0.2488	0.02865
ran_pars	mother_pidlink	sd__(Intercept)	0.4123	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7367	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.08316	0.4608	0.1805	4478	0.8568	-1.21	1.377
fixed	NA	poly(age, 3, raw = TRUE)1	0.01147	0.05376	0.2133	4484	0.8311	-0.1394	0.1624
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004311	0.001983	0.2174	4491	0.8279	-0.005135	0.005997
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001917	0.00002325	-0.8244	4497	0.4097	-0.00008444	0.0000461
fixed	NA	male	0.07541	0.02459	3.067	4281	0.002177	0.006387	0.1444
fixed	NA	sibling_count3	0.0153	0.03598	0.4251	3394	0.6708	-0.0857	0.1163
fixed	NA	sibling_count4	-0.05404	0.04092	-1.321	3207	0.1868	-0.1689	0.06083
fixed	NA	sibling_count5	-0.09206	0.05014	-1.836	3242	0.06644	-0.2328	0.04869
fixed	NA	birth_order_nonlinear2	0.05441	0.0287	1.896	3384	0.05805	-0.02615	0.135
fixed	NA	birth_order_nonlinear3	0.06348	0.03675	1.727	3588	0.08419	-0.03968	0.1666
fixed	NA	birth_order_nonlinear4	0.02236	0.04959	0.4509	3779	0.6521	-0.1168	0.1616
fixed	NA	birth_order_nonlinear5	-0.02694	0.07696	-0.3501	3571	0.7263	-0.243	0.1891
ran_pars	mother_pidlink	sd__(Intercept)	0.4106	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7372	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.08871	0.4612	0.1924	4473	0.8475	-1.206	1.383
fixed	NA	poly(age, 3, raw = TRUE)1	0.0111	0.0538	0.2063	4477	0.8366	-0.1399	0.1621
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004685	0.001984	0.2361	4484	0.8134	-0.005102	0.006039
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001987	0.00002327	-0.8538	4490	0.3933	-0.0000852	0.00004546
fixed	NA	male	0.07578	0.02461	3.079	4275	0.00209	0.006695	0.1449
fixed	NA	count_birth_order2/2	0.0315	0.04953	0.636	3674	0.5248	-0.1075	0.1705
fixed	NA	count_birth_order1/3	-0.01303	0.04503	-0.2893	4466	0.7724	-0.1394	0.1134
fixed	NA	count_birth_order2/3	0.0853	0.04888	1.745	4501	0.08106	-0.05192	0.2225
fixed	NA	count_birth_order3/3	0.0798	0.05455	1.463	4493	0.1435	-0.07332	0.2329
fixed	NA	count_birth_order1/4	-0.06294	0.05485	-1.147	4497	0.2512	-0.2169	0.09103
fixed	NA	count_birth_order2/4	-0.02508	0.05663	-0.4429	4497	0.6578	-0.184	0.1339
fixed	NA	count_birth_order3/4	0.004614	0.05957	0.07745	4463	0.9383	-0.1626	0.1718
fixed	NA	count_birth_order4/4	-0.01753	0.06194	-0.283	4459	0.7772	-0.1914	0.1563
fixed	NA	count_birth_order1/5	-0.0476	0.07444	-0.6395	4484	0.5225	-0.2565	0.1613
fixed	NA	count_birth_order2/5	-0.04182	0.07935	-0.527	4399	0.5983	-0.2646	0.1809
fixed	NA	count_birth_order3/5	-0.05883	0.07456	-0.789	4408	0.4302	-0.2681	0.1505
fixed	NA	count_birth_order4/5	-0.1101	0.072	-1.529	4438	0.1262	-0.3122	0.09199
fixed	NA	count_birth_order5/5	-0.128	0.07442	-1.721	4410	0.08539	-0.3369	0.08085
ran_pars	mother_pidlink	sd__(Intercept)	0.41	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7379	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11211	11276	-5596	11191	NA	NA	NA
11	11213	11283	-5595	11191	0.8885	1	0.3459
14	11214	11304	-5593	11186	4.8	3	0.187
20	11223	11352	-5592	11183	2.476	6	0.8712

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3212	0.4696	0.684	4155	0.494	-0.9971	1.64
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01712	0.0549	-0.3118	4164	0.7552	-0.1712	0.137
fixed	NA	poly(age, 3, raw = TRUE)2	0.001505	0.002025	0.7428	4173	0.4576	-0.004181	0.00719
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000321	0.00002375	-1.351	4180	0.1766	-0.00009877	0.00003457
fixed	NA	male	0.08135	0.02535	3.209	3990	0.001342	0.01019	0.1525
fixed	NA	sibling_count3	0.03156	0.03734	0.8452	3051	0.3981	-0.07325	0.1364
fixed	NA	sibling_count4	-0.01131	0.03961	-0.2857	2793	0.7751	-0.1225	0.09986
fixed	NA	sibling_count5	-0.01969	0.04263	-0.4619	2555	0.6442	-0.1394	0.09997
ran_pars	mother_pidlink	sd__(Intercept)	0.3934	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7378	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.304	0.4701	0.6466	4155	0.5179	-1.016	1.624
fixed	NA	birth_order	0.01035	0.01277	0.8108	3824	0.4175	-0.02549	0.0462
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01666	0.0549	-0.3035	4163	0.7615	-0.1708	0.1374
fixed	NA	poly(age, 3, raw = TRUE)2	0.00148	0.002026	0.7304	4171	0.4652	-0.004207	0.007166
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000316	0.00002376	-1.33	4178	0.1836	-0.00009829	0.0000351
fixed	NA	male	0.08109	0.02535	3.198	3990	0.001393	0.009921	0.1523
fixed	NA	sibling_count3	0.02674	0.0378	0.7074	3093	0.4794	-0.07938	0.1329
fixed	NA	sibling_count4	-0.02204	0.04176	-0.5277	2954	0.5977	-0.1392	0.09517
fixed	NA	sibling_count5	-0.03686	0.0476	-0.7744	2936	0.4387	-0.1705	0.09674
ran_pars	mother_pidlink	sd__(Intercept)	0.393	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.738	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.2365	0.4707	0.5024	4164	0.6154	-1.085	1.558
fixed	NA	poly(age, 3, raw = TRUE)1	-0.009492	0.05497	-0.1727	4168	0.8629	-0.1638	0.1448
fixed	NA	poly(age, 3, raw = TRUE)2	0.00122	0.002028	0.6014	4174	0.5476	-0.004473	0.006912
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002875	0.00002378	-1.209	4179	0.2268	-0.00009551	0.00003801
fixed	NA	male	0.08186	0.02535	3.23	3985	0.00125	0.01071	0.153
fixed	NA	sibling_count3	0.0179	0.03829	0.4675	3190	0.6401	-0.08957	0.1254
fixed	NA	sibling_count4	-0.02621	0.04227	-0.62	3041	0.5353	-0.1449	0.09245
fixed	NA	sibling_count5	-0.02217	0.04805	-0.4613	2990	0.6446	-0.157	0.1127
fixed	NA	birth_order_nonlinear2	0.06266	0.0298	2.103	3193	0.03556	-0.02099	0.1463
fixed	NA	birth_order_nonlinear3	0.06276	0.03782	1.659	3399	0.09713	-0.0434	0.1689
fixed	NA	birth_order_nonlinear4	0.02567	0.0502	0.5113	3562	0.6092	-0.1152	0.1666
fixed	NA	birth_order_nonlinear5	-0.03084	0.07318	-0.4215	3413	0.6734	-0.2363	0.1746
ran_pars	mother_pidlink	sd__(Intercept)	0.3932	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7376	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.267	0.4712	0.5668	4158	0.5709	-1.056	1.59
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01214	0.055	-0.2208	4161	0.8253	-0.1665	0.1422
fixed	NA	poly(age, 3, raw = TRUE)2	0.001334	0.002029	0.6575	4168	0.5109	-0.004362	0.007031
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003027	0.0000238	-1.272	4173	0.2035	-0.00009709	0.00003654
fixed	NA	male	0.08133	0.02537	3.206	3977	0.001356	0.01012	0.1525
fixed	NA	count_birth_order2/2	0.02836	0.05401	0.5251	3462	0.5995	-0.1232	0.18
fixed	NA	count_birth_order1/3	-0.005132	0.0483	-0.1063	4152	0.9154	-0.1407	0.1304
fixed	NA	count_birth_order2/3	0.06901	0.05212	1.324	4180	0.1856	-0.07729	0.2153
fixed	NA	count_birth_order3/3	0.09276	0.0586	1.583	4172	0.1135	-0.07172	0.2572
fixed	NA	count_birth_order1/4	-0.07718	0.05692	-1.356	4175	0.1752	-0.2369	0.08259
fixed	NA	count_birth_order2/4	0.03891	0.05812	0.6695	4179	0.5032	-0.1242	0.2021
fixed	NA	count_birth_order3/4	0.0434	0.06328	0.6859	4140	0.4928	-0.1342	0.221
fixed	NA	count_birth_order4/4	0.01112	0.06527	0.1704	4144	0.8647	-0.1721	0.1943
fixed	NA	count_birth_order1/5	0.02681	0.06769	0.396	4180	0.6921	-0.1632	0.2168
fixed	NA	count_birth_order2/5	0.04688	0.07265	0.6452	4124	0.5188	-0.1571	0.2508
fixed	NA	count_birth_order3/5	-0.03177	0.07038	-0.4514	4119	0.6517	-0.2293	0.1658
fixed	NA	count_birth_order4/5	-0.03833	0.0728	-0.5265	4089	0.5986	-0.2427	0.166
fixed	NA	count_birth_order5/5	-0.06641	0.07258	-0.915	4097	0.3602	-0.2701	0.1373
ran_pars	mother_pidlink	sd__(Intercept)	0.394	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7374	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	10350	10413	-5165	10330	NA	NA	NA
11	10351	10421	-5165	10329	0.6594	1	0.4168
14	10351	10440	-5162	10323	5.737	3	0.1251
20	10359	10486	-5159	10319	4.508	6	0.6083

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1919	0.4629	0.4145	4454	0.6785	-1.108	1.491
fixed	NA	poly(age, 3, raw = TRUE)1	0.002144	0.05414	0.03959	4463	0.9684	-0.1498	0.1541
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007434	0.002	0.3717	4472	0.7101	-0.00487	0.006357
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002273	0.00002349	-0.9674	4480	0.3334	-0.00008867	0.00004322
fixed	NA	male	0.07125	0.02459	2.897	4279	0.003787	0.002212	0.1403
fixed	NA	sibling_count3	0.02066	0.03446	0.5995	3229	0.5489	-0.07606	0.1174
fixed	NA	sibling_count4	-0.03106	0.03762	-0.8254	2914	0.4092	-0.1367	0.07456
fixed	NA	sibling_count5	-0.0859	0.04475	-1.92	2597	0.05502	-0.2115	0.03972
ran_pars	mother_pidlink	sd__(Intercept)	0.4078	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7369	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1688	0.4635	0.3643	4455	0.7157	-1.132	1.47
fixed	NA	birth_order	0.01354	0.01294	1.046	3978	0.2955	-0.02279	0.04987
fixed	NA	poly(age, 3, raw = TRUE)1	0.002806	0.05415	0.05183	4462	0.9587	-0.1492	0.1548
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007076	0.002	0.3538	4471	0.7235	-0.004907	0.006322
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002203	0.0000235	-0.9375	4478	0.3486	-0.000088	0.00004394
fixed	NA	male	0.07082	0.0246	2.879	4277	0.004006	0.001777	0.1399
fixed	NA	sibling_count3	0.01432	0.03499	0.4092	3282	0.6824	-0.08389	0.1125
fixed	NA	sibling_count4	-0.0456	0.04011	-1.137	3137	0.2557	-0.1582	0.06699
fixed	NA	sibling_count5	-0.1092	0.04997	-2.185	3031	0.02899	-0.2494	0.0311
ran_pars	mother_pidlink	sd__(Intercept)	0.4079	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7369	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.09842	0.4641	0.2121	4464	0.8321	-1.204	1.401
fixed	NA	poly(age, 3, raw = TRUE)1	0.0104	0.05422	0.1918	4469	0.8479	-0.1418	0.1626
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004386	0.002002	0.2191	4475	0.8266	-0.005182	0.006059
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001915	0.00002352	-0.8141	4480	0.4156	-0.00008517	0.00004688
fixed	NA	male	0.07164	0.0246	2.913	4274	0.003602	0.002598	0.1407
fixed	NA	sibling_count3	0.009576	0.03546	0.2701	3398	0.7871	-0.08995	0.1091
fixed	NA	sibling_count4	-0.04664	0.04063	-1.148	3234	0.2511	-0.1607	0.0674
fixed	NA	sibling_count5	-0.08504	0.05087	-1.672	3140	0.09465	-0.2278	0.05774
fixed	NA	birth_order_nonlinear2	0.06891	0.0285	2.417	3379	0.01568	-0.0111	0.1489
fixed	NA	birth_order_nonlinear3	0.05499	0.03656	1.504	3560	0.1326	-0.04763	0.1576
fixed	NA	birth_order_nonlinear4	0.03758	0.05054	0.7436	3747	0.4572	-0.1043	0.1795
fixed	NA	birth_order_nonlinear5	-0.04573	0.08241	-0.5549	3627	0.579	-0.277	0.1856
ran_pars	mother_pidlink	sd__(Intercept)	0.4065	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7372	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1026	0.4645	0.2208	4458	0.8252	-1.201	1.406
fixed	NA	poly(age, 3, raw = TRUE)1	0.01011	0.05425	0.1864	4462	0.8521	-0.1422	0.1624
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004652	0.002004	0.2322	4468	0.8164	-0.00516	0.00609
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001964	0.00002354	-0.834	4474	0.4043	-0.00008572	0.00004645
fixed	NA	male	0.0719	0.02462	2.921	4268	0.003513	0.002794	0.141
fixed	NA	count_birth_order2/2	0.05321	0.0481	1.106	3623	0.2686	-0.08179	0.1882
fixed	NA	count_birth_order1/3	-0.01115	0.04436	-0.2515	4451	0.8015	-0.1357	0.1134
fixed	NA	count_birth_order2/3	0.09775	0.04872	2.006	4486	0.0449	-0.03902	0.2345
fixed	NA	count_birth_order3/3	0.05654	0.05345	1.058	4473	0.2902	-0.0935	0.2066
fixed	NA	count_birth_order1/4	-0.05762	0.05495	-1.049	4484	0.2944	-0.2119	0.09662
fixed	NA	count_birth_order2/4	-0.001019	0.05656	-0.01801	4476	0.9856	-0.1598	0.1578
fixed	NA	count_birth_order3/4	0.01591	0.0589	0.2702	4445	0.787	-0.1494	0.1812
fixed	NA	count_birth_order4/4	0.002424	0.06205	0.03907	4428	0.9688	-0.1717	0.1766
fixed	NA	count_birth_order1/5	-0.03924	0.07434	-0.5279	4476	0.5976	-0.2479	0.1694
fixed	NA	count_birth_order2/5	-0.03639	0.08185	-0.4446	4374	0.6566	-0.2662	0.1934
fixed	NA	count_birth_order3/5	-0.053	0.07775	-0.6817	4384	0.4955	-0.2712	0.1652
fixed	NA	count_birth_order4/5	-0.08061	0.07537	-1.07	4413	0.2849	-0.2922	0.1309
fixed	NA	count_birth_order5/5	-0.1373	0.07948	-1.727	4383	0.0842	-0.3604	0.08582
ran_pars	mother_pidlink	sd__(Intercept)	0.4056	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.738	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11153	11217	-5567	11133	NA	NA	NA
11	11154	11225	-5566	11132	1.096	1	0.2951
14	11154	11243	-5563	11126	6.396	3	0.09386
20	11164	11292	-5562	11124	2.068	6	0.9133

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Numeracy 2015 old

birthorder <- birthorder %>% mutate(outcome = math_2015_old)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1434	0.2829	0.507	7090	0.6121	-0.6507	0.9376
fixed	NA	poly(age, 3, raw = TRUE)1	0.03262	0.02914	1.119	7094	0.263	-0.04919	0.1144
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001464	0.000923	-1.587	7093	0.1127	-0.004055	0.001126
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001303	0.000009115	1.43	7085	0.1528	-0.00001255	0.00003862
fixed	NA	male	-0.1109	0.02366	-4.687	6802	0.000002823	-0.1773	-0.04448
fixed	NA	sibling_count3	0.02993	0.03547	0.8437	4996	0.3989	-0.06964	0.1295
fixed	NA	sibling_count4	-0.05079	0.03669	-1.384	4565	0.1663	-0.1538	0.05219
fixed	NA	sibling_count5	-0.02016	0.0384	-0.5251	4141	0.5995	-0.128	0.08762
ran_pars	mother_pidlink	sd__(Intercept)	0.4687	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9013	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1297	0.2833	0.4579	7093	0.647	-0.6656	0.9251
fixed	NA	birth_order	0.01012	0.01162	0.8706	5810	0.384	-0.0225	0.04273
fixed	NA	poly(age, 3, raw = TRUE)1	0.03262	0.02914	1.119	7093	0.2631	-0.04919	0.1144
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001471	0.0009231	-1.593	7092	0.1111	-0.004062	0.00112
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000132	0.000009117	1.448	7084	0.1478	-0.00001239	0.00003879
fixed	NA	male	-0.1111	0.02366	-4.697	6801	0.000002695	-0.1775	-0.04471
fixed	NA	sibling_count3	0.02648	0.03569	0.7421	5107	0.4581	-0.07369	0.1267
fixed	NA	sibling_count4	-0.05896	0.03787	-1.557	5033	0.1195	-0.1653	0.04733
fixed	NA	sibling_count5	-0.03345	0.04132	-0.8096	5084	0.4182	-0.1495	0.08254
ran_pars	mother_pidlink	sd__(Intercept)	0.4683	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9016	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1785	0.2849	0.6265	7095	0.531	-0.6213	0.9784
fixed	NA	poly(age, 3, raw = TRUE)1	0.02929	0.02929	0.9999	7096	0.3174	-0.05293	0.1115
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001352	0.0009288	-1.456	7097	0.1456	-0.003959	0.001255
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001193	0.000009182	1.299	7095	0.1941	-0.00001385	0.0000377
fixed	NA	male	-0.1111	0.02366	-4.696	6798	0.000002711	-0.1775	-0.04469
fixed	NA	sibling_count3	0.02668	0.03616	0.7376	5291	0.4608	-0.07484	0.1282
fixed	NA	sibling_count4	-0.05799	0.03839	-1.511	5238	0.131	-0.1658	0.04977
fixed	NA	sibling_count5	-0.04003	0.04162	-0.9616	5229	0.3363	-0.1569	0.07681
fixed	NA	birth_order_nonlinear2	-0.01975	0.02777	-0.7111	5850	0.4771	-0.0977	0.05821
fixed	NA	birth_order_nonlinear3	0.01226	0.03543	0.3459	5621	0.7294	-0.08721	0.1117
fixed	NA	birth_order_nonlinear4	0.01825	0.04599	0.3969	5528	0.6915	-0.1108	0.1474
fixed	NA	birth_order_nonlinear5	0.07661	0.06708	1.142	5305	0.2535	-0.1117	0.2649
ran_pars	mother_pidlink	sd__(Intercept)	0.4678	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9019	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1745	0.2856	0.6108	7090	0.5413	-0.6273	0.9762
fixed	NA	poly(age, 3, raw = TRUE)1	0.02899	0.02931	0.989	7091	0.3227	-0.05329	0.1113
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001338	0.0009298	-1.44	7091	0.15	-0.003948	0.001271
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001176	0.000009195	1.279	7090	0.201	-0.00001405	0.00003757
fixed	NA	male	-0.1106	0.02367	-4.671	6790	0.000003055	-0.177	-0.04413
fixed	NA	count_birth_order2/2	-0.004851	0.04751	-0.1021	5942	0.9187	-0.1382	0.1285
fixed	NA	count_birth_order1/3	0.04678	0.04599	1.017	7020	0.3091	-0.08232	0.1759
fixed	NA	count_birth_order2/3	0.009359	0.05116	0.1829	7076	0.8548	-0.1342	0.153
fixed	NA	count_birth_order3/3	0.01759	0.05729	0.307	7088	0.7588	-0.1432	0.1784
fixed	NA	count_birth_order1/4	-0.05097	0.05213	-0.9777	7078	0.3283	-0.1973	0.09537
fixed	NA	count_birth_order2/4	-0.06209	0.05497	-1.13	7090	0.2587	-0.2164	0.09221
fixed	NA	count_birth_order3/4	-0.03653	0.05945	-0.6145	7080	0.5389	-0.2034	0.1303
fixed	NA	count_birth_order4/4	-0.05719	0.06261	-0.9135	7061	0.361	-0.233	0.1186
fixed	NA	count_birth_order1/5	-0.05291	0.05914	-0.8945	7089	0.3711	-0.2189	0.1131
fixed	NA	count_birth_order2/5	-0.08266	0.06194	-1.334	7075	0.1821	-0.2565	0.09121
fixed	NA	count_birth_order3/5	0.007637	0.06371	0.1199	7056	0.9046	-0.1712	0.1865
fixed	NA	count_birth_order4/5	0.01128	0.06732	0.1675	7019	0.8669	-0.1777	0.2003
fixed	NA	count_birth_order5/5	0.04267	0.06897	0.6187	6998	0.5361	-0.1509	0.2363
ran_pars	mother_pidlink	sd__(Intercept)	0.4682	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.902	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	20269	20338	-10125	20249	NA	NA	NA
11	20271	20346	-10124	20249	0.7595	1	0.3835
14	20275	20371	-10123	20247	1.755	3	0.6249
20	20285	20422	-10123	20245	1.911	6	0.9277

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.245	0.5633	-0.4349	4496	0.6636	-1.826	1.336
fixed	NA	poly(age, 3, raw = TRUE)1	0.07656	0.06578	1.164	4502	0.2445	-0.1081	0.2612
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002516	0.002426	-1.037	4507	0.2997	-0.009324	0.004293
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002232	0.00002843	0.785	4510	0.4325	-0.00005749	0.0001021
fixed	NA	male	-0.18	0.03021	-5.959	4381	0.000000002737	-0.2649	-0.09523
fixed	NA	sibling_count3	0.01108	0.04228	0.2621	3364	0.7932	-0.1076	0.1298
fixed	NA	sibling_count4	-0.0854	0.04575	-1.867	3018	0.06205	-0.2138	0.04302
fixed	NA	sibling_count5	-0.1326	0.05257	-2.523	2748	0.01169	-0.2802	0.01493
ran_pars	mother_pidlink	sd__(Intercept)	0.4446	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9278	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2722	0.5639	-0.4826	4496	0.6294	-1.855	1.311
fixed	NA	birth_order	0.01604	0.01578	1.017	4123	0.3093	-0.02824	0.06033
fixed	NA	poly(age, 3, raw = TRUE)1	0.07742	0.06578	1.177	4501	0.2393	-0.1072	0.2621
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002563	0.002426	-1.056	4506	0.2909	-0.009372	0.004247
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000232	0.00002845	0.8156	4509	0.4148	-0.00005665	0.000103
fixed	NA	male	-0.1807	0.03022	-5.979	4380	0.000000002426	-0.2655	-0.09585
fixed	NA	sibling_count3	0.003624	0.04291	0.08448	3421	0.9327	-0.1168	0.1241
fixed	NA	sibling_count4	-0.1025	0.04875	-2.103	3229	0.03554	-0.2394	0.03432
fixed	NA	sibling_count5	-0.1612	0.05961	-2.705	3234	0.006873	-0.3286	0.006103
ran_pars	mother_pidlink	sd__(Intercept)	0.4442	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.928	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2693	0.5649	-0.4766	4499	0.6337	-1.855	1.317
fixed	NA	poly(age, 3, raw = TRUE)1	0.07898	0.0659	1.199	4502	0.2307	-0.106	0.264
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002617	0.00243	-1.077	4505	0.2816	-0.009438	0.004204
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002375	0.00002849	0.8338	4507	0.4045	-0.00005621	0.0001037
fixed	NA	male	-0.1804	0.03024	-5.965	4377	0.000000002633	-0.2652	-0.09549
fixed	NA	sibling_count3	-0.003152	0.04353	-0.07241	3528	0.9423	-0.1253	0.119
fixed	NA	sibling_count4	-0.1027	0.04943	-2.078	3321	0.0378	-0.2415	0.03605
fixed	NA	sibling_count5	-0.1596	0.06058	-2.635	3325	0.008445	-0.3297	0.0104
fixed	NA	birth_order_nonlinear2	0.01484	0.03555	0.4174	3574	0.6764	-0.08496	0.1146
fixed	NA	birth_order_nonlinear3	0.06235	0.04546	1.372	3772	0.1702	-0.06525	0.19
fixed	NA	birth_order_nonlinear4	0.01672	0.06126	0.2729	3946	0.785	-0.1552	0.1887
fixed	NA	birth_order_nonlinear5	0.06174	0.09519	0.6486	3779	0.5167	-0.2055	0.329
ran_pars	mother_pidlink	sd__(Intercept)	0.4437	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9284	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2688	0.5653	-0.4755	4493	0.6345	-1.856	1.318
fixed	NA	poly(age, 3, raw = TRUE)1	0.07764	0.06593	1.178	4496	0.239	-0.1074	0.2627
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002554	0.002431	-1.051	4499	0.2935	-0.00938	0.004271
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002289	0.00002851	0.8031	4501	0.422	-0.00005713	0.0001029
fixed	NA	male	-0.1798	0.03026	-5.941	4370	0.000000003045	-0.2647	-0.09485
fixed	NA	count_birth_order2/2	0.03824	0.06123	0.6246	3805	0.5322	-0.1336	0.2101
fixed	NA	count_birth_order1/3	0.006112	0.05503	0.1111	4482	0.9116	-0.1483	0.1606
fixed	NA	count_birth_order2/3	0.02754	0.05983	0.4604	4501	0.6452	-0.1404	0.1955
fixed	NA	count_birth_order3/3	0.05204	0.06684	0.7787	4495	0.4362	-0.1356	0.2397
fixed	NA	count_birth_order1/4	-0.09395	0.0671	-1.4	4498	0.1615	-0.2823	0.0944
fixed	NA	count_birth_order2/4	-0.1263	0.06936	-1.82	4499	0.06876	-0.321	0.06843
fixed	NA	count_birth_order3/4	-0.03124	0.07305	-0.4277	4476	0.6689	-0.2363	0.1738
fixed	NA	count_birth_order4/4	-0.02205	0.07596	-0.2902	4474	0.7717	-0.2353	0.1912
fixed	NA	count_birth_order1/5	-0.1231	0.09123	-1.349	4492	0.1774	-0.3792	0.133
fixed	NA	count_birth_order2/5	-0.1036	0.09742	-1.063	4441	0.2876	-0.3771	0.1699
fixed	NA	count_birth_order3/5	-0.05967	0.09153	-0.652	4444	0.5145	-0.3166	0.1973
fixed	NA	count_birth_order4/5	-0.2167	0.08834	-2.453	4460	0.0142	-0.4647	0.03127
fixed	NA	count_birth_order5/5	-0.09149	0.09136	-1.001	4441	0.3166	-0.3479	0.165
ran_pars	mother_pidlink	sd__(Intercept)	0.4432	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.929	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	13037	13101	-6509	13017	NA	NA	NA
11	13038	13109	-6508	13016	1.037	1	0.3086
14	13043	13133	-6507	13015	1.053	3	0.7884
20	13052	13180	-6506	13012	3.242	6	0.778

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3124	0.5809	-0.5378	4175	0.5907	-1.943	1.318
fixed	NA	poly(age, 3, raw = TRUE)1	0.08482	0.06788	1.25	4181	0.2115	-0.1057	0.2754
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002853	0.002504	-1.139	4186	0.2546	-0.009882	0.004176
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002625	0.00002936	0.8941	4189	0.3713	-0.00005616	0.0001087
fixed	NA	male	-0.1795	0.03141	-5.716	4065	0.00000001172	-0.2677	-0.09135
fixed	NA	sibling_count3	0.02764	0.04572	0.6045	3205	0.5455	-0.1007	0.156
fixed	NA	sibling_count4	-0.07076	0.04843	-1.461	2948	0.1441	-0.2067	0.06519
fixed	NA	sibling_count5	-0.08049	0.05206	-1.546	2701	0.1222	-0.2266	0.06564
ran_pars	mother_pidlink	sd__(Intercept)	0.4434	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9298	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3139	0.5815	-0.5398	4174	0.5893	-1.946	1.318
fixed	NA	birth_order	0.0009025	0.01584	0.05696	3912	0.9546	-0.04357	0.04538
fixed	NA	poly(age, 3, raw = TRUE)1	0.08486	0.0679	1.25	4180	0.2114	-0.1057	0.2755
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002855	0.002505	-1.14	4184	0.2544	-0.009886	0.004176
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002629	0.00002937	0.8952	4187	0.3707	-0.00005615	0.0001087
fixed	NA	male	-0.1795	0.03142	-5.715	4064	0.00000001174	-0.2677	-0.09136
fixed	NA	sibling_count3	0.02722	0.04631	0.5878	3245	0.5567	-0.1028	0.1572
fixed	NA	sibling_count4	-0.07169	0.05111	-1.403	3102	0.1608	-0.2152	0.07178
fixed	NA	sibling_count5	-0.08197	0.05825	-1.407	3071	0.1595	-0.2455	0.08155
ran_pars	mother_pidlink	sd__(Intercept)	0.4433	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.93	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3432	0.5824	-0.5893	4178	0.5557	-1.978	1.292
fixed	NA	poly(age, 3, raw = TRUE)1	0.08818	0.068	1.297	4181	0.1948	-0.1027	0.279
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002974	0.002508	-1.186	4184	0.2358	-0.01002	0.004067
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002758	0.00002941	0.9376	4186	0.3485	-0.00005498	0.0001101
fixed	NA	male	-0.1794	0.03142	-5.71	4060	0.00000001211	-0.2676	-0.09122
fixed	NA	sibling_count3	0.01714	0.04695	0.3651	3336	0.715	-0.1147	0.1489
fixed	NA	sibling_count4	-0.07655	0.0518	-1.478	3185	0.1395	-0.222	0.06885
fixed	NA	sibling_count5	-0.07804	0.05886	-1.326	3120	0.185	-0.2433	0.08718
fixed	NA	birth_order_nonlinear2	0.007457	0.03712	0.2009	3372	0.8408	-0.09675	0.1117
fixed	NA	birth_order_nonlinear3	0.04764	0.04706	1.012	3566	0.3114	-0.08446	0.1797
fixed	NA	birth_order_nonlinear4	-0.01793	0.06241	-0.2873	3709	0.7739	-0.1931	0.1572
fixed	NA	birth_order_nonlinear5	-0.03863	0.09104	-0.4243	3591	0.6714	-0.2942	0.2169
ran_pars	mother_pidlink	sd__(Intercept)	0.444	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9299	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3502	0.5828	-0.6008	4172	0.548	-1.986	1.286
fixed	NA	poly(age, 3, raw = TRUE)1	0.08616	0.06802	1.267	4174	0.2054	-0.1048	0.2771
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002888	0.00251	-1.151	4178	0.2499	-0.009933	0.004157
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002645	0.00002943	0.8987	4180	0.3689	-0.00005616	0.0001091
fixed	NA	male	-0.1812	0.03144	-5.763	4053	0.000000008881	-0.2695	-0.09295
fixed	NA	count_birth_order2/2	0.07487	0.06719	1.114	3587	0.2652	-0.1137	0.2635
fixed	NA	count_birth_order1/3	0.06736	0.05962	1.13	4164	0.2587	-0.1	0.2347
fixed	NA	count_birth_order2/3	0.0078	0.0644	0.1211	4180	0.9036	-0.173	0.1886
fixed	NA	count_birth_order3/3	0.08895	0.07246	1.227	4175	0.2197	-0.1145	0.2924
fixed	NA	count_birth_order1/4	-0.09565	0.0703	-1.361	4177	0.1737	-0.293	0.1017
fixed	NA	count_birth_order2/4	-0.03206	0.07184	-0.4462	4180	0.6555	-0.2337	0.1696
fixed	NA	count_birth_order3/4	-0.02432	0.07831	-0.3106	4155	0.7561	-0.2441	0.1955
fixed	NA	count_birth_order4/4	-0.007524	0.08077	-0.09315	4156	0.9258	-0.2343	0.2192
fixed	NA	count_birth_order1/5	0.006059	0.08367	0.07241	4180	0.9423	-0.2288	0.2409
fixed	NA	count_birth_order2/5	-0.06487	0.08993	-0.7213	4146	0.4708	-0.3173	0.1876
fixed	NA	count_birth_order3/5	0.01195	0.08712	0.1371	4141	0.8909	-0.2326	0.2565
fixed	NA	count_birth_order4/5	-0.1584	0.09015	-1.757	4119	0.07903	-0.4115	0.09468
fixed	NA	count_birth_order5/5	-0.09581	0.08987	-1.066	4123	0.2865	-0.3481	0.1565
ran_pars	mother_pidlink	sd__(Intercept)	0.4436	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9301	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12125	12188	-6052	12105	NA	NA	NA
11	12127	12197	-6052	12105	0.003311	1	0.9541
14	12131	12220	-6052	12103	1.742	3	0.6276
20	12137	12264	-6049	12097	5.854	6	0.4397

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.416	0.5686	-0.7316	4479	0.4645	-2.012	1.18
fixed	NA	poly(age, 3, raw = TRUE)1	0.09561	0.06648	1.438	4485	0.1505	-0.091	0.2822
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003242	0.002455	-1.321	4490	0.1867	-0.01013	0.003649
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003082	0.00002883	1.069	4493	0.2851	-0.00005011	0.0001118
fixed	NA	male	-0.1756	0.03027	-5.802	4364	0.000000007033	-0.2606	-0.09066
fixed	NA	sibling_count3	0.01526	0.04177	0.3653	3358	0.7149	-0.102	0.1325
fixed	NA	sibling_count4	-0.0601	0.04552	-1.32	3026	0.1868	-0.1879	0.06767
fixed	NA	sibling_count5	-0.1183	0.05401	-2.19	2686	0.02858	-0.2699	0.03331
ran_pars	mother_pidlink	sd__(Intercept)	0.4493	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9259	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.4442	0.5692	-0.7804	4479	0.4352	-2.042	1.154
fixed	NA	birth_order	0.01691	0.01597	1.058	4084	0.2899	-0.02793	0.06174
fixed	NA	poly(age, 3, raw = TRUE)1	0.09643	0.06649	1.45	4484	0.147	-0.09019	0.2831
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003288	0.002455	-1.339	4489	0.1806	-0.01018	0.003604
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003171	0.00002884	1.099	4492	0.2717	-0.00004926	0.0001127
fixed	NA	male	-0.1762	0.03028	-5.819	4362	0.000000006345	-0.2612	-0.0912
fixed	NA	sibling_count3	0.007398	0.04243	0.1744	3410	0.8616	-0.1117	0.1265
fixed	NA	sibling_count4	-0.07811	0.04859	-1.607	3246	0.1081	-0.2145	0.05829
fixed	NA	sibling_count5	-0.1472	0.06049	-2.432	3120	0.01505	-0.317	0.02266
ran_pars	mother_pidlink	sd__(Intercept)	0.4491	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.926	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.432	0.5701	-0.7577	4482	0.4487	-2.032	1.168
fixed	NA	poly(age, 3, raw = TRUE)1	0.09753	0.06659	1.465	4485	0.1431	-0.0894	0.2845
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003326	0.002459	-1.353	4488	0.1763	-0.01023	0.003577
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003209	0.00002888	1.111	4490	0.2665	-0.00004897	0.0001132
fixed	NA	male	-0.1758	0.03029	-5.805	4358	0.000000006895	-0.2609	-0.09081
fixed	NA	sibling_count3	-0.000006417	0.04307	-0.000149	3523	0.9999	-0.1209	0.1209
fixed	NA	sibling_count4	-0.08365	0.0493	-1.697	3342	0.08983	-0.222	0.05473
fixed	NA	sibling_count5	-0.1455	0.06168	-2.358	3224	0.01841	-0.3186	0.02767
fixed	NA	birth_order_nonlinear2	0.002265	0.03533	0.06411	3557	0.9489	-0.0969	0.1014
fixed	NA	birth_order_nonlinear3	0.06415	0.04526	1.417	3730	0.1564	-0.06289	0.1912
fixed	NA	birth_order_nonlinear4	0.0386	0.06249	0.6177	3905	0.5368	-0.1368	0.214
fixed	NA	birth_order_nonlinear5	0.02918	0.102	0.2862	3814	0.7748	-0.257	0.3154
ran_pars	mother_pidlink	sd__(Intercept)	0.4493	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9262	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.4268	0.5705	-0.7481	4476	0.4545	-2.028	1.175
fixed	NA	poly(age, 3, raw = TRUE)1	0.0961	0.06663	1.442	4478	0.1493	-0.09094	0.2831
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00326	0.002461	-1.325	4482	0.1852	-0.01017	0.003647
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003118	0.0000289	1.079	4484	0.2807	-0.00004995	0.0001123
fixed	NA	male	-0.1759	0.03031	-5.802	4351	0.000000007003	-0.261	-0.0908
fixed	NA	count_birth_order2/2	0.01494	0.05951	0.251	3756	0.8018	-0.1521	0.182
fixed	NA	count_birth_order1/3	0.006263	0.05435	0.1152	4464	0.9083	-0.1463	0.1588
fixed	NA	count_birth_order2/3	0.009709	0.05978	0.1624	4486	0.871	-0.1581	0.1775
fixed	NA	count_birth_order3/3	0.06011	0.06564	0.9157	4477	0.3599	-0.1241	0.2444
fixed	NA	count_birth_order1/4	-0.08948	0.06739	-1.328	4485	0.1843	-0.2787	0.0997
fixed	NA	count_birth_order2/4	-0.1179	0.06945	-1.697	4480	0.08976	-0.3128	0.07709
fixed	NA	count_birth_order3/4	0.002842	0.07238	0.03927	4458	0.9687	-0.2003	0.206
fixed	NA	count_birth_order4/4	0.006872	0.07627	0.0901	4446	0.9282	-0.2072	0.221
fixed	NA	count_birth_order1/5	-0.1059	0.09127	-1.16	4480	0.246	-0.3621	0.1503
fixed	NA	count_birth_order2/5	-0.07683	0.1007	-0.7631	4416	0.4454	-0.3595	0.2058
fixed	NA	count_birth_order3/5	-0.09122	0.09563	-0.9539	4419	0.3402	-0.3597	0.1772
fixed	NA	count_birth_order4/5	-0.1786	0.09266	-1.928	4437	0.05395	-0.4387	0.08148
fixed	NA	count_birth_order5/5	-0.1131	0.09776	-1.157	4416	0.2474	-0.3875	0.1613
ran_pars	mother_pidlink	sd__(Intercept)	0.4486	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9269	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12991	13055	-6485	12971	NA	NA	NA
11	12992	13062	-6485	12970	1.123	1	0.2894
14	12997	13086	-6484	12969	1.185	3	0.7566
20	13006	13134	-6483	12966	2.819	6	0.8312

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Raven 2015 young

birthorder <- birthorder %>% mutate(outcome = raven_2015_young)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.822	0.1249	-22.6	7834	1.451e-109	-3.172	-2.471
fixed	NA	poly(age, 3, raw = TRUE)1	0.4021	0.02318	17.35	8001	3.445e-66	0.337	0.4671
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01567	0.001335	-11.74	8131	1.449e-31	-0.01942	-0.01192
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001864	0.00002434	7.66	8084	2.069e-14	0.0001181	0.0002547
fixed	NA	male	0.04525	0.01952	2.319	7411	0.02044	-0.009532	0.1
fixed	NA	sibling_count3	-0.03604	0.02829	-1.274	5234	0.2027	-0.1155	0.04337
fixed	NA	sibling_count4	-0.09036	0.03188	-2.835	4779	0.004606	-0.1798	-0.0008817
fixed	NA	sibling_count5	-0.07959	0.03619	-2.199	4357	0.0279	-0.1812	0.02199
ran_pars	mother_pidlink	sd__(Intercept)	0.5239	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.755	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.811	0.1281	-21.95	7938	9.899e-104	-3.17	-2.451
fixed	NA	birth_order	-0.004207	0.01077	-0.3905	7575	0.6962	-0.03445	0.02604
fixed	NA	poly(age, 3, raw = TRUE)1	0.4014	0.02324	17.27	8007	1.187e-65	0.3362	0.4667
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01565	0.001336	-11.72	8129	1.818e-31	-0.0194	-0.0119
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001863	0.00002434	7.653	8085	2.183e-14	0.000118	0.0002546
fixed	NA	male	0.0453	0.01952	2.321	7410	0.0203	-0.009479	0.1001
fixed	NA	sibling_count3	-0.03363	0.02896	-1.161	5354	0.2456	-0.1149	0.04767
fixed	NA	sibling_count4	-0.08459	0.03513	-2.408	5192	0.01608	-0.1832	0.01402
fixed	NA	sibling_count5	-0.07027	0.04335	-1.621	5149	0.1051	-0.192	0.05143
ran_pars	mother_pidlink	sd__(Intercept)	0.5239	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.755	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.824	0.1267	-22.29	7934	9.056e-107	-3.18	-2.469
fixed	NA	poly(age, 3, raw = TRUE)1	0.4024	0.02327	17.29	8018	8.72e-66	0.337	0.4677
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0157	0.001337	-11.74	8128	1.425e-31	-0.01945	-0.01194
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001868	0.00002435	7.671	8079	1.899e-14	0.0001185	0.0002552
fixed	NA	male	0.04507	0.01952	2.309	7408	0.02099	-0.009729	0.09986
fixed	NA	sibling_count3	-0.03865	0.02943	-1.313	5582	0.1891	-0.1213	0.04395
fixed	NA	sibling_count4	-0.08783	0.03582	-2.452	5455	0.01423	-0.1884	0.01271
fixed	NA	sibling_count5	-0.06417	0.04397	-1.459	5278	0.1445	-0.1876	0.05926
fixed	NA	birth_order_nonlinear2	0.006981	0.02273	0.3072	5825	0.7587	-0.05681	0.07077
fixed	NA	birth_order_nonlinear3	0.01078	0.02997	0.3599	6579	0.719	-0.07334	0.09491
fixed	NA	birth_order_nonlinear4	-0.01946	0.04063	-0.4788	6819	0.6321	-0.1335	0.0946
fixed	NA	birth_order_nonlinear5	-0.04141	0.05901	-0.7017	6939	0.4829	-0.2071	0.1242
ran_pars	mother_pidlink	sd__(Intercept)	0.5241	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.755	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.827	0.1276	-22.16	7951	1.214e-105	-3.185	-2.469
fixed	NA	poly(age, 3, raw = TRUE)1	0.4038	0.0233	17.33	8023	4.361e-66	0.3384	0.4692
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01579	0.001338	-11.8	8122	7.326e-32	-0.01954	-0.01203
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001884	0.00002437	7.733	8073	1.178e-14	0.00012	0.0002568
fixed	NA	male	0.04432	0.01952	2.271	7402	0.02318	-0.01046	0.0991
fixed	NA	count_birth_order2/2	-0.004487	0.03564	-0.1259	6126	0.8998	-0.1045	0.09554
fixed	NA	count_birth_order1/3	-0.06921	0.03678	-1.882	8000	0.05991	-0.1725	0.03404
fixed	NA	count_birth_order2/3	-0.0402	0.03743	-1.074	8073	0.2828	-0.1453	0.06486
fixed	NA	count_birth_order3/3	0.02043	0.04235	0.4825	8124	0.6295	-0.09845	0.1393
fixed	NA	count_birth_order1/4	-0.07409	0.05038	-1.471	8115	0.1414	-0.2155	0.06734
fixed	NA	count_birth_order2/4	-0.04536	0.04774	-0.9502	8113	0.342	-0.1794	0.08865
fixed	NA	count_birth_order3/4	-0.1553	0.04489	-3.459	8124	0.0005452	-0.2813	-0.02926
fixed	NA	count_birth_order4/4	-0.07482	0.04893	-1.529	8097	0.1263	-0.2122	0.06253
fixed	NA	count_birth_order1/5	0.002788	0.06832	0.04081	7756	0.9674	-0.189	0.1946
fixed	NA	count_birth_order2/5	-0.09213	0.06488	-1.42	7840	0.1557	-0.2742	0.08999
fixed	NA	count_birth_order3/5	-0.02168	0.05868	-0.3695	7996	0.7118	-0.1864	0.143
fixed	NA	count_birth_order4/5	-0.1349	0.05514	-2.448	8081	0.0144	-0.2897	0.01982
fixed	NA	count_birth_order5/5	-0.109	0.05466	-1.994	8104	0.04617	-0.2624	0.04443
ran_pars	mother_pidlink	sd__(Intercept)	0.5244	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7544	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	21385	21455	-10683	21365	NA	NA	NA
11	21387	21464	-10682	21365	0.1526	1	0.6961
14	21392	21490	-10682	21364	1.06	3	0.7867
20	21390	21531	-10675	21350	13.4	6	0.03716

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.19	0.2021	-15.78	6316	4.42e-55	-3.758	-2.623
fixed	NA	poly(age, 3, raw = TRUE)1	0.4824	0.04241	11.37	6310	1.11e-29	0.3633	0.6014
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02082	0.002745	-7.583	6356	3.851e-14	-0.02852	-0.01311
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002915	0.00005507	5.294	6401	0.0000001238	0.0001369	0.0004461
fixed	NA	male	0.03392	0.02031	1.67	6991	0.09498	-0.0231	0.09093
fixed	NA	sibling_count3	-0.05851	0.02723	-2.149	4661	0.03172	-0.135	0.01793
fixed	NA	sibling_count4	-0.1176	0.03346	-3.515	4059	0.0004438	-0.2116	-0.02371
fixed	NA	sibling_count5	-0.2155	0.04296	-5.015	3671	0.0000005553	-0.3361	-0.09486
ran_pars	mother_pidlink	sd__(Intercept)	0.4977	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7635	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.173	0.2052	-15.46	6483	5.531e-53	-3.749	-2.597
fixed	NA	birth_order	-0.006215	0.01248	-0.4979	7191	0.6186	-0.04125	0.02882
fixed	NA	poly(age, 3, raw = TRUE)1	0.4811	0.04249	11.32	6334	1.97e-29	0.3618	0.6004
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02077	0.002747	-7.561	6356	4.563e-14	-0.02848	-0.01306
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002909	0.00005508	5.281	6399	0.0000001327	0.0001363	0.0004455
fixed	NA	male	0.03404	0.02031	1.676	6993	0.09385	-0.02298	0.09106
fixed	NA	sibling_count3	-0.05439	0.02847	-1.911	4774	0.05611	-0.1343	0.02552
fixed	NA	sibling_count4	-0.1084	0.03822	-2.838	4515	0.004565	-0.2157	-0.001169
fixed	NA	sibling_count5	-0.2002	0.05277	-3.794	4559	0.0001504	-0.3483	-0.05206
ran_pars	mother_pidlink	sd__(Intercept)	0.4976	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7636	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.185	0.2038	-15.63	6435	4.515e-54	-3.757	-2.613
fixed	NA	poly(age, 3, raw = TRUE)1	0.4815	0.04251	11.33	6338	1.847e-29	0.3622	0.6008
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02077	0.002747	-7.56	6358	4.604e-14	-0.02848	-0.01306
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002906	0.00005509	5.274	6400	0.0000001379	0.0001359	0.0004452
fixed	NA	male	0.03356	0.02032	1.652	6993	0.09866	-0.02348	0.0906
fixed	NA	sibling_count3	-0.06243	0.02915	-2.141	5068	0.03229	-0.1443	0.01941
fixed	NA	sibling_count4	-0.1148	0.03914	-2.932	4746	0.003386	-0.2246	-0.004885
fixed	NA	sibling_count5	-0.1774	0.05539	-3.203	4806	0.001367	-0.3329	-0.02196
fixed	NA	birth_order_nonlinear2	0.001136	0.02312	0.04915	5355	0.9608	-0.06377	0.06604
fixed	NA	birth_order_nonlinear3	0.01465	0.03293	0.4449	6251	0.6564	-0.07778	0.1071
fixed	NA	birth_order_nonlinear4	-0.02001	0.04693	-0.4264	6636	0.6698	-0.1517	0.1117
fixed	NA	birth_order_nonlinear5	-0.1004	0.07401	-1.357	6569	0.175	-0.3081	0.1073
ran_pars	mother_pidlink	sd__(Intercept)	0.4972	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7639	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.195	0.2044	-15.63	6452	4.265e-54	-3.769	-2.621
fixed	NA	poly(age, 3, raw = TRUE)1	0.4837	0.04254	11.37	6342	1.155e-29	0.3643	0.6031
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02094	0.00275	-7.614	6355	3.038e-14	-0.02866	-0.01322
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002943	0.00005514	5.336	6393	0.00000009803	0.0001395	0.000449
fixed	NA	male	0.03408	0.02032	1.678	6977	0.09346	-0.02295	0.09111
fixed	NA	count_birth_order2/2	0.005046	0.03211	0.1571	5808	0.8751	-0.08509	0.09518
fixed	NA	count_birth_order1/3	-0.07786	0.03788	-2.056	7470	0.03986	-0.1842	0.02847
fixed	NA	count_birth_order2/3	-0.07189	0.03638	-1.976	7482	0.04821	-0.174	0.03024
fixed	NA	count_birth_order3/3	-0.011	0.03982	-0.2761	7507	0.7825	-0.1228	0.1008
fixed	NA	count_birth_order1/4	-0.04491	0.0597	-0.7523	7375	0.4519	-0.2125	0.1227
fixed	NA	count_birth_order2/4	-0.09627	0.05238	-1.838	7489	0.06612	-0.2433	0.05077
fixed	NA	count_birth_order3/4	-0.187	0.04996	-3.743	7489	0.0001831	-0.3273	-0.04677
fixed	NA	count_birth_order4/4	-0.1058	0.04949	-2.137	7510	0.03261	-0.2447	0.03315
fixed	NA	count_birth_order1/5	-0.1948	0.1038	-1.877	6429	0.0606	-0.4861	0.09655
fixed	NA	count_birth_order2/5	-0.1427	0.09249	-1.543	6810	0.1228	-0.4024	0.1169
fixed	NA	count_birth_order3/5	-0.08111	0.07832	-1.036	7206	0.3004	-0.301	0.1387
fixed	NA	count_birth_order4/5	-0.2496	0.06489	-3.846	7495	0.0001211	-0.4317	-0.06741
fixed	NA	count_birth_order5/5	-0.2774	0.06294	-4.407	7510	0.00001064	-0.4541	-0.1007
ran_pars	mother_pidlink	sd__(Intercept)	0.498	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7631	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	19714	19783	-9847	19694	NA	NA	NA
11	19715	19792	-9847	19693	0.2484	1	0.6182
14	19719	19816	-9846	19691	2.358	3	0.5015
20	19720	19858	-9840	19680	11.06	6	0.08663

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.236	0.207	-15.63	5981	5.156e-54	-3.817	-2.655
fixed	NA	poly(age, 3, raw = TRUE)1	0.4936	0.04358	11.33	5963	1.942e-29	0.3713	0.6159
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02181	0.002828	-7.711	6002	1.455e-14	-0.02975	-0.01387
fixed	NA	poly(age, 3, raw = TRUE)3	0.000314	0.00005687	5.521	6038	0.00000003512	0.0001543	0.0004736
fixed	NA	male	0.0372	0.02081	1.788	6607	0.07384	-0.02121	0.09561
fixed	NA	sibling_count3	-0.04103	0.02859	-1.435	4602	0.1513	-0.1213	0.03922
fixed	NA	sibling_count4	-0.07103	0.03369	-2.109	4157	0.03504	-0.1656	0.02353
fixed	NA	sibling_count5	-0.08426	0.03954	-2.131	3839	0.03315	-0.1953	0.02673
ran_pars	mother_pidlink	sd__(Intercept)	0.5057	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.76	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.183	0.2099	-15.16	6126	5.295e-51	-3.772	-2.594
fixed	NA	birth_order	-0.01834	0.01212	-1.513	6902	0.1302	-0.05235	0.01567
fixed	NA	poly(age, 3, raw = TRUE)1	0.4896	0.04366	11.21	5984	6.801e-29	0.367	0.6121
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02165	0.00283	-7.649	6002	2.349e-14	-0.02959	-0.0137
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003117	0.00005689	5.478	6036	0.00000004464	0.000152	0.0004714
fixed	NA	male	0.03765	0.02081	1.809	6610	0.07044	-0.02076	0.09606
fixed	NA	sibling_count3	-0.0296	0.02956	-1.001	4714	0.3168	-0.1126	0.05338
fixed	NA	sibling_count4	-0.0452	0.03775	-1.197	4574	0.2313	-0.1512	0.06078
fixed	NA	sibling_count5	-0.04361	0.04778	-0.9126	4631	0.3615	-0.1777	0.09052
ran_pars	mother_pidlink	sd__(Intercept)	0.5051	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7602	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.207	0.2087	-15.37	6086	2.571e-52	-3.793	-2.622
fixed	NA	poly(age, 3, raw = TRUE)1	0.4899	0.04368	11.22	5989	6.65e-29	0.3673	0.6125
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02164	0.002831	-7.644	6005	2.433e-14	-0.02959	-0.0137
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003113	0.00005692	5.468	6038	0.00000004722	0.0001515	0.000471
fixed	NA	male	0.03721	0.02081	1.788	6609	0.07384	-0.02121	0.09564
fixed	NA	sibling_count3	-0.03506	0.03023	-1.16	4976	0.2462	-0.1199	0.0498
fixed	NA	sibling_count4	-0.05354	0.03867	-1.385	4802	0.1662	-0.1621	0.055
fixed	NA	sibling_count5	-0.03095	0.04906	-0.6308	4777	0.5282	-0.1687	0.1068
fixed	NA	birth_order_nonlinear2	-0.01075	0.02398	-0.4481	5054	0.6541	-0.07806	0.05657
fixed	NA	birth_order_nonlinear3	-0.01769	0.03288	-0.538	6027	0.5906	-0.11	0.07461
fixed	NA	birth_order_nonlinear4	-0.04186	0.04566	-0.9167	6379	0.3593	-0.17	0.08632
fixed	NA	birth_order_nonlinear5	-0.1356	0.06807	-1.991	6336	0.04647	-0.3266	0.05552
ran_pars	mother_pidlink	sd__(Intercept)	0.5049	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7604	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.22	0.2096	-15.36	6100	2.669e-52	-3.808	-2.631
fixed	NA	poly(age, 3, raw = TRUE)1	0.4937	0.04374	11.29	5994	3.06e-29	0.3709	0.6164
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02193	0.002835	-7.734	6003	1.211e-14	-0.02989	-0.01397
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003176	0.00005699	5.573	6033	0.00000002611	0.0001577	0.0004776
fixed	NA	male	0.03796	0.02082	1.824	6597	0.06827	-0.02047	0.09639
fixed	NA	count_birth_order2/2	-0.01805	0.03503	-0.5153	5430	0.6063	-0.1164	0.08028
fixed	NA	count_birth_order1/3	-0.06167	0.03921	-1.573	7122	0.1158	-0.1717	0.0484
fixed	NA	count_birth_order2/3	-0.05229	0.0383	-1.365	7136	0.1722	-0.1598	0.05522
fixed	NA	count_birth_order3/3	-0.02024	0.04198	-0.4821	7150	0.6297	-0.1381	0.09761
fixed	NA	count_birth_order1/4	-0.052	0.05836	-0.891	7062	0.373	-0.2158	0.1118
fixed	NA	count_birth_order2/4	-0.05039	0.05238	-0.962	7116	0.3361	-0.1974	0.09663
fixed	NA	count_birth_order3/4	-0.1357	0.0501	-2.709	7127	0.006758	-0.2764	0.004895
fixed	NA	count_birth_order4/4	-0.05579	0.05067	-1.101	7152	0.2709	-0.198	0.08643
fixed	NA	count_birth_order1/5	0.08461	0.08474	0.9984	6510	0.3181	-0.1533	0.3225
fixed	NA	count_birth_order2/5	-0.03531	0.07586	-0.4655	6802	0.6416	-0.2482	0.1776
fixed	NA	count_birth_order3/5	-0.03455	0.06811	-0.5073	6948	0.612	-0.2257	0.1566
fixed	NA	count_birth_order4/5	-0.1467	0.06276	-2.338	7056	0.01942	-0.3229	0.02944
fixed	NA	count_birth_order5/5	-0.1714	0.06045	-2.835	7143	0.004597	-0.341	-0.001684
ran_pars	mother_pidlink	sd__(Intercept)	0.5055	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7599	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	18797	18866	-9389	18777	NA	NA	NA
11	18797	18872	-9387	18775	2.293	1	0.1299
14	18801	18897	-9386	18773	1.75	3	0.6258
20	18804	18941	-9382	18764	9.378	6	0.1534

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.181	0.2033	-15.65	6211	3.641e-54	-3.751	-2.61
fixed	NA	poly(age, 3, raw = TRUE)1	0.4799	0.04263	11.26	6214	4.035e-29	0.3603	0.5996
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0207	0.002756	-7.508	6268	6.824e-14	-0.02843	-0.01296
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002895	0.00005525	5.241	6320	0.0000001652	0.0001345	0.0004446
fixed	NA	male	0.02833	0.02045	1.385	6861	0.166	-0.02907	0.08573
fixed	NA	sibling_count3	-0.0465	0.02731	-1.703	4573	0.08869	-0.1232	0.03016
fixed	NA	sibling_count4	-0.09864	0.03383	-2.915	3966	0.003572	-0.1936	-0.003666
fixed	NA	sibling_count5	-0.2016	0.04479	-4.502	3600	0.000006955	-0.3273	-0.0759
ran_pars	mother_pidlink	sd__(Intercept)	0.4979	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7613	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.164	0.2065	-15.32	6375	4.637e-52	-3.743	-2.584
fixed	NA	birth_order	-0.005982	0.01263	-0.4735	7010	0.6359	-0.04145	0.02948
fixed	NA	poly(age, 3, raw = TRUE)1	0.4786	0.04272	11.21	6239	7.226e-29	0.3587	0.5986
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02065	0.002759	-7.485	6268	8.133e-14	-0.02839	-0.0129
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002889	0.00005527	5.227	6317	0.0000001777	0.0001338	0.000444
fixed	NA	male	0.02843	0.02045	1.39	6862	0.1645	-0.02898	0.08584
fixed	NA	sibling_count3	-0.04256	0.02855	-1.491	4691	0.1361	-0.1227	0.03758
fixed	NA	sibling_count4	-0.08986	0.03859	-2.329	4438	0.01992	-0.1982	0.01845
fixed	NA	sibling_count5	-0.1872	0.05414	-3.458	4433	0.0005493	-0.3392	-0.03524
ran_pars	mother_pidlink	sd__(Intercept)	0.4978	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7614	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.174	0.205	-15.48	6330	4.172e-53	-3.75	-2.599
fixed	NA	poly(age, 3, raw = TRUE)1	0.4787	0.04273	11.2	6244	7.443e-29	0.3588	0.5987
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02064	0.002759	-7.478	6271	8.577e-14	-0.02838	-0.01289
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002884	0.00005529	5.216	6319	0.0000001887	0.0001332	0.0004436
fixed	NA	male	0.02822	0.02046	1.379	6861	0.1679	-0.02921	0.08565
fixed	NA	sibling_count3	-0.0454	0.02923	-1.553	4980	0.1204	-0.1275	0.03665
fixed	NA	sibling_count4	-0.09354	0.03953	-2.366	4679	0.01802	-0.2045	0.01743
fixed	NA	sibling_count5	-0.1703	0.05714	-2.98	4668	0.002896	-0.3307	-0.009892
fixed	NA	birth_order_nonlinear2	0.003025	0.02311	0.1309	5256	0.8959	-0.06184	0.06789
fixed	NA	birth_order_nonlinear3	-0.002564	0.03312	-0.07743	6087	0.9383	-0.09553	0.09041
fixed	NA	birth_order_nonlinear4	-0.01117	0.04779	-0.2337	6424	0.8152	-0.1453	0.123
fixed	NA	birth_order_nonlinear5	-0.07969	0.07807	-1.021	6509	0.3074	-0.2988	0.1395
ran_pars	mother_pidlink	sd__(Intercept)	0.4975	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7617	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.174	0.2056	-15.44	6344	7.73e-53	-3.751	-2.597
fixed	NA	poly(age, 3, raw = TRUE)1	0.479	0.04277	11.2	6245	7.531e-29	0.359	0.5991
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02067	0.002762	-7.485	6265	8.126e-14	-0.02842	-0.01292
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002893	0.00005533	5.229	6309	0.0000001757	0.000134	0.0004446
fixed	NA	male	0.02905	0.02046	1.42	6848	0.1556	-0.02837	0.08647
fixed	NA	count_birth_order2/2	0.0009753	0.03179	0.03068	5649	0.9755	-0.08825	0.0902
fixed	NA	count_birth_order1/3	-0.06278	0.03805	-1.65	7333	0.09903	-0.1696	0.04404
fixed	NA	count_birth_order2/3	-0.05251	0.0365	-1.439	7343	0.1503	-0.155	0.04994
fixed	NA	count_birth_order3/3	-0.0171	0.04001	-0.4274	7369	0.6691	-0.1294	0.0952
fixed	NA	count_birth_order1/4	-0.04273	0.06007	-0.7113	7251	0.4769	-0.2113	0.1259
fixed	NA	count_birth_order2/4	-0.07004	0.05307	-1.32	7347	0.187	-0.219	0.07894
fixed	NA	count_birth_order3/4	-0.1841	0.05035	-3.656	7352	0.000258	-0.3254	-0.04274
fixed	NA	count_birth_order4/4	-0.07312	0.05019	-1.457	7370	0.1452	-0.214	0.06777
fixed	NA	count_birth_order1/5	-0.1874	0.1038	-1.806	6471	0.07096	-0.4786	0.1039
fixed	NA	count_birth_order2/5	-0.1367	0.09923	-1.377	6587	0.1685	-0.4152	0.1419
fixed	NA	count_birth_order3/5	-0.07523	0.08045	-0.9351	7132	0.3498	-0.3011	0.1506
fixed	NA	count_birth_order4/5	-0.2492	0.06826	-3.651	7352	0.0002628	-0.4409	-0.05763
fixed	NA	count_birth_order5/5	-0.2523	0.06671	-3.783	7370	0.0001564	-0.4396	-0.06508
ran_pars	mother_pidlink	sd__(Intercept)	0.4979	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7611	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	19316	19385	-9648	19296	NA	NA	NA
11	19318	19394	-9648	19296	0.2247	1	0.6355
14	19323	19420	-9647	19295	0.9323	3	0.8176
20	19324	19462	-9642	19284	10.87	6	0.09248

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Numeracy 2015 young

birthorder <- birthorder %>% mutate(outcome = math_2015_young)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.4	0.1332	-18.01	7928	3.943e-71	-2.774	-2.026
fixed	NA	poly(age, 3, raw = TRUE)1	0.3891	0.02467	15.77	8038	3.269e-55	0.3198	0.4583
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01698	0.001415	-12	8129	6.933e-33	-0.02095	-0.01301
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002247	0.00002571	8.739	8114	2.817e-18	0.0001525	0.0002969
fixed	NA	male	-0.1652	0.02089	-7.909	7770	2.954e-15	-0.2238	-0.1066
fixed	NA	sibling_count3	-0.003366	0.02911	-0.1156	5422	0.908	-0.08509	0.07836
fixed	NA	sibling_count4	-0.08741	0.03267	-2.676	4870	0.007485	-0.1791	0.004294
fixed	NA	sibling_count5	-0.04743	0.03694	-1.284	4352	0.1991	-0.1511	0.05625
ran_pars	mother_pidlink	sd__(Intercept)	0.4677	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.842	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.421	0.1364	-17.75	8003	3.445e-69	-2.804	-2.039
fixed	NA	birth_order	0.008505	0.01153	0.7378	7693	0.4607	-0.02386	0.04087
fixed	NA	poly(age, 3, raw = TRUE)1	0.3904	0.02473	15.78	8043	2.692e-55	0.3209	0.4598
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01702	0.001416	-12.02	8127	5.579e-33	-0.02099	-0.01304
fixed	NA	poly(age, 3, raw = TRUE)3	0.000225	0.00002572	8.751	8115	2.539e-18	0.0001529	0.0002972
fixed	NA	male	-0.1653	0.02089	-7.913	7769	2.852e-15	-0.2239	-0.1067
fixed	NA	sibling_count3	-0.008157	0.02983	-0.2734	5545	0.7845	-0.0919	0.07558
fixed	NA	sibling_count4	-0.09879	0.03613	-2.734	5289	0.006273	-0.2002	0.002629
fixed	NA	sibling_count5	-0.06581	0.04455	-1.477	5147	0.1397	-0.1909	0.05925
ran_pars	mother_pidlink	sd__(Intercept)	0.4678	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.842	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.421	0.135	-17.94	7999	1.354e-70	-2.8	-2.042
fixed	NA	poly(age, 3, raw = TRUE)1	0.391	0.02475	15.8	8050	2.125e-55	0.3216	0.4605
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01705	0.001417	-12.03	8126	4.687e-33	-0.02102	-0.01307
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002254	0.00002572	8.762	8110	2.305e-18	0.0001532	0.0002976
fixed	NA	male	-0.1654	0.02089	-7.918	7767	2.758e-15	-0.224	-0.1068
fixed	NA	sibling_count3	-0.01839	0.03036	-0.6057	5783	0.5448	-0.1036	0.06683
fixed	NA	sibling_count4	-0.09876	0.0369	-2.676	5558	0.007466	-0.2023	0.004824
fixed	NA	sibling_count5	-0.06099	0.04522	-1.349	5253	0.1774	-0.1879	0.06594
fixed	NA	birth_order_nonlinear2	0.02107	0.02464	0.8551	6177	0.3925	-0.0481	0.09024
fixed	NA	birth_order_nonlinear3	0.05765	0.03232	1.784	6882	0.07448	-0.03306	0.1484
fixed	NA	birth_order_nonlinear4	-0.02123	0.04373	-0.4854	7121	0.6274	-0.144	0.1015
fixed	NA	birth_order_nonlinear5	0.03537	0.06344	0.5575	7266	0.5772	-0.1427	0.2135
ran_pars	mother_pidlink	sd__(Intercept)	0.4678	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8419	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.43	0.1359	-17.88	8008	3.81e-70	-2.811	-2.048
fixed	NA	poly(age, 3, raw = TRUE)1	0.3913	0.02479	15.78	8052	2.772e-55	0.3217	0.4609
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01706	0.001419	-12.02	8120	5.027e-33	-0.02105	-0.01308
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002257	0.00002575	8.766	8104	2.231e-18	0.0001534	0.000298
fixed	NA	male	-0.1654	0.0209	-7.913	7766	2.867e-15	-0.2241	-0.1067
fixed	NA	count_birth_order2/2	0.04371	0.0386	1.132	6418	0.2575	-0.06464	0.1521
fixed	NA	count_birth_order1/3	0.002918	0.03881	0.0752	8063	0.9401	-0.106	0.1119
fixed	NA	count_birth_order2/3	0.00944	0.03955	0.2387	8102	0.8114	-0.1016	0.1205
fixed	NA	count_birth_order3/3	0.02532	0.04488	0.5641	8124	0.5727	-0.1007	0.1513
fixed	NA	count_birth_order1/4	-0.1027	0.05345	-1.922	8120	0.0547	-0.2527	0.04733
fixed	NA	count_birth_order2/4	-0.0895	0.05066	-1.767	8116	0.07732	-0.2317	0.0527
fixed	NA	count_birth_order3/4	-0.03057	0.04757	-0.6427	8124	0.5205	-0.1641	0.103
fixed	NA	count_birth_order4/4	-0.08469	0.05197	-1.63	8099	0.1032	-0.2306	0.06119
fixed	NA	count_birth_order1/5	-0.03692	0.07295	-0.5061	7916	0.6128	-0.2417	0.1679
fixed	NA	count_birth_order2/5	-0.04579	0.06922	-0.6615	7954	0.5083	-0.2401	0.1485
fixed	NA	count_birth_order3/5	0.04616	0.06247	0.7389	8041	0.46	-0.1292	0.2215
fixed	NA	count_birth_order4/5	-0.1104	0.05859	-1.885	8091	0.0595	-0.2749	0.05404
fixed	NA	count_birth_order5/5	-0.01793	0.05804	-0.3089	8102	0.7574	-0.1809	0.145
ran_pars	mother_pidlink	sd__(Intercept)	0.4669	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8425	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	22322	22392	-11151	22302	NA	NA	NA
11	22323	22400	-11151	22301	0.5443	1	0.4607
14	22325	22423	-11148	22297	4.614	3	0.2023
20	22334	22474	-11147	22294	2.804	6	0.833

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.178	0.2178	-14.59	6607	1.729e-47	-3.789	-2.567
fixed	NA	poly(age, 3, raw = TRUE)1	0.5555	0.04571	12.15	6610	1.238e-33	0.4272	0.6838
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02776	0.002957	-9.387	6654	8.318e-21	-0.03606	-0.01946
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004428	0.00005931	7.465	6693	9.354e-14	0.0002763	0.0006093
fixed	NA	male	-0.1763	0.0218	-8.086	7201	7.175e-16	-0.2375	-0.1151
fixed	NA	sibling_count3	-0.004145	0.0285	-0.1454	4801	0.8844	-0.08415	0.07586
fixed	NA	sibling_count4	-0.05481	0.03489	-1.571	4121	0.1162	-0.1527	0.04312
fixed	NA	sibling_count5	-0.1574	0.04468	-3.524	3678	0.0004304	-0.2829	-0.03203
ran_pars	mother_pidlink	sd__(Intercept)	0.4742	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8419	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.178	0.2209	-14.38	6738	3.105e-46	-3.798	-2.558
fixed	NA	birth_order	0.00003101	0.01338	0.002317	7263	0.9982	-0.03754	0.0376
fixed	NA	poly(age, 3, raw = TRUE)1	0.5555	0.04579	12.13	6628	1.59e-33	0.427	0.684
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02776	0.002959	-9.381	6653	8.801e-21	-0.03606	-0.01945
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004428	0.00005933	7.463	6691	9.52e-14	0.0002762	0.0006093
fixed	NA	male	-0.1763	0.0218	-8.085	7201	7.23e-16	-0.2375	-0.1151
fixed	NA	sibling_count3	-0.004165	0.02981	-0.1397	4910	0.8889	-0.08784	0.07951
fixed	NA	sibling_count4	-0.05486	0.03995	-1.373	4563	0.1698	-0.167	0.05729
fixed	NA	sibling_count5	-0.1575	0.05518	-2.855	4552	0.004328	-0.3124	-0.002626
ran_pars	mother_pidlink	sd__(Intercept)	0.4743	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.842	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.195	0.2194	-14.56	6698	2.729e-47	-3.811	-2.579
fixed	NA	poly(age, 3, raw = TRUE)1	0.5565	0.04579	12.15	6629	1.279e-33	0.4279	0.685
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02779	0.002959	-9.39	6652	8.084e-21	-0.0361	-0.01948
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004429	0.00005933	7.464	6689	9.455e-14	0.0002763	0.0006094
fixed	NA	male	-0.1768	0.02181	-8.109	7200	5.973e-16	-0.238	-0.1156
fixed	NA	sibling_count3	-0.00574	0.03058	-0.1877	5204	0.8511	-0.09158	0.0801
fixed	NA	sibling_count4	-0.05628	0.04098	-1.373	4786	0.1697	-0.1713	0.05875
fixed	NA	sibling_count5	-0.1323	0.05799	-2.281	4738	0.02261	-0.295	0.03052
fixed	NA	birth_order_nonlinear2	0.02838	0.02504	1.133	5588	0.2572	-0.04192	0.09867
fixed	NA	birth_order_nonlinear3	0.004336	0.0355	0.1221	6444	0.9028	-0.09531	0.104
fixed	NA	birth_order_nonlinear4	0.01114	0.05049	0.2207	6825	0.8254	-0.1306	0.1529
fixed	NA	birth_order_nonlinear5	-0.06758	0.07964	-0.8487	6816	0.3961	-0.2911	0.156
ran_pars	mother_pidlink	sd__(Intercept)	0.474	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8421	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.208	0.2202	-14.57	6716	2.403e-47	-3.826	-2.59
fixed	NA	poly(age, 3, raw = TRUE)1	0.5573	0.04586	12.15	6638	1.29e-33	0.4285	0.686
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02785	0.002964	-9.396	6657	7.606e-21	-0.03617	-0.01953
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004442	0.00005942	7.475	6690	8.673e-14	0.0002774	0.000611
fixed	NA	male	-0.176	0.02182	-8.069	7191	8.238e-16	-0.2373	-0.1148
fixed	NA	count_birth_order2/2	0.05523	0.03473	1.59	6001	0.1118	-0.04225	0.1527
fixed	NA	count_birth_order1/3	0.03204	0.04035	0.794	7484	0.4272	-0.08124	0.1453
fixed	NA	count_birth_order2/3	0.0281	0.03877	0.7248	7495	0.4686	-0.08074	0.1369
fixed	NA	count_birth_order3/3	-0.0193	0.04248	-0.4543	7509	0.6496	-0.1386	0.09995
fixed	NA	count_birth_order1/4	-0.07964	0.06391	-1.246	7422	0.2128	-0.259	0.09976
fixed	NA	count_birth_order2/4	-0.06614	0.05597	-1.182	7495	0.2374	-0.2232	0.09097
fixed	NA	count_birth_order3/4	-0.009582	0.05339	-0.1795	7492	0.8576	-0.1594	0.1403
fixed	NA	count_birth_order4/4	-0.007008	0.05282	-0.1327	7509	0.8945	-0.1553	0.1413
fixed	NA	count_birth_order1/5	-0.07898	0.1118	-0.7063	6753	0.48	-0.3929	0.2349
fixed	NA	count_birth_order2/5	-0.06533	0.09944	-0.657	7025	0.5112	-0.3445	0.2138
fixed	NA	count_birth_order3/5	-0.07808	0.08398	-0.9297	7301	0.3525	-0.3138	0.1577
fixed	NA	count_birth_order4/5	-0.1593	0.06933	-2.298	7497	0.0216	-0.3539	0.0353
fixed	NA	count_birth_order5/5	-0.191	0.06718	-2.843	7509	0.004485	-0.3796	-0.002399
ran_pars	mother_pidlink	sd__(Intercept)	0.4732	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8425	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	20687	20756	-10333	20667	NA	NA	NA
11	20689	20765	-10333	20667	0.000003839	1	0.9984
14	20692	20789	-10332	20664	2.596	3	0.4581
20	20699	20837	-10329	20659	5.37	6	0.4972

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.174	0.2233	-14.21	6328	3.799e-45	-3.801	-2.547
fixed	NA	poly(age, 3, raw = TRUE)1	0.5569	0.04701	11.85	6323	4.888e-32	0.425	0.6889
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02805	0.00305	-9.198	6361	4.867e-20	-0.03662	-0.01949
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004512	0.00006132	7.357	6392	2.11e-13	0.000279	0.0006233
fixed	NA	male	-0.1854	0.02234	-8.298	6863	1.263e-16	-0.2481	-0.1227
fixed	NA	sibling_count3	0.02048	0.02977	0.6879	4765	0.4915	-0.06308	0.104
fixed	NA	sibling_count4	-0.04367	0.03496	-1.249	4248	0.2116	-0.1418	0.05445
fixed	NA	sibling_count5	-0.05311	0.04092	-1.298	3862	0.1944	-0.168	0.06175
ran_pars	mother_pidlink	sd__(Intercept)	0.4666	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8447	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.166	0.2263	-13.99	6434	7.553e-44	-3.801	-2.531
fixed	NA	birth_order	-0.002726	0.01298	-0.21	6980	0.8337	-0.03916	0.03371
fixed	NA	poly(age, 3, raw = TRUE)1	0.5564	0.0471	11.81	6337	7.184e-32	0.4242	0.6886
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02803	0.003052	-9.183	6359	5.577e-20	-0.0366	-0.01946
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004508	0.00006135	7.348	6388	2.255e-13	0.0002786	0.000623
fixed	NA	male	-0.1853	0.02234	-8.294	6863	1.305e-16	-0.248	-0.1226
fixed	NA	sibling_count3	0.02215	0.03081	0.7188	4873	0.4723	-0.06435	0.1086
fixed	NA	sibling_count4	-0.03989	0.03931	-1.015	4649	0.3102	-0.1502	0.07044
fixed	NA	sibling_count5	-0.04716	0.04976	-0.9478	4639	0.3433	-0.1868	0.09251
ran_pars	mother_pidlink	sd__(Intercept)	0.4665	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8448	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.179	0.2249	-14.13	6401	1.1e-44	-3.811	-2.548
fixed	NA	poly(age, 3, raw = TRUE)1	0.5565	0.04711	11.81	6337	7.175e-32	0.4243	0.6887
fixed	NA	poly(age, 3, raw = TRUE)2	-0.028	0.003053	-9.171	6358	6.204e-20	-0.03657	-0.01943
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004496	0.00006136	7.328	6387	2.625e-13	0.0002774	0.0006219
fixed	NA	male	-0.1858	0.02234	-8.319	6860	1.065e-16	-0.2486	-0.1231
fixed	NA	sibling_count3	0.01029	0.03157	0.3258	5132	0.7446	-0.07834	0.09891
fixed	NA	sibling_count4	-0.04726	0.04033	-1.172	4865	0.2412	-0.1605	0.06593
fixed	NA	sibling_count5	-0.02709	0.05114	-0.5298	4745	0.5963	-0.1706	0.1164
fixed	NA	birth_order_nonlinear2	0.01691	0.02603	0.6497	5343	0.5159	-0.05616	0.08998
fixed	NA	birth_order_nonlinear3	0.03612	0.03547	1.018	6257	0.3085	-0.06344	0.1357
fixed	NA	birth_order_nonlinear4	-0.01534	0.04913	-0.3123	6586	0.7549	-0.1532	0.1226
fixed	NA	birth_order_nonlinear5	-0.0896	0.07324	-1.223	6585	0.2213	-0.2952	0.116
ran_pars	mother_pidlink	sd__(Intercept)	0.4669	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8446	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.183	0.2258	-14.1	6412	1.851e-44	-3.817	-2.549
fixed	NA	poly(age, 3, raw = TRUE)1	0.5551	0.04717	11.77	6344	1.226e-31	0.4227	0.6875
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0279	0.003057	-9.127	6359	9.329e-20	-0.03648	-0.01932
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004476	0.00006144	7.285	6385	3.595e-13	0.0002752	0.0006201
fixed	NA	male	-0.1857	0.02234	-8.313	6852	1.114e-16	-0.2485	-0.123
fixed	NA	count_birth_order2/2	0.04363	0.03794	1.15	5669	0.2502	-0.06287	0.1501
fixed	NA	count_birth_order1/3	0.05878	0.04169	1.41	7136	0.1586	-0.05824	0.1758
fixed	NA	count_birth_order2/3	0.03572	0.04074	0.8769	7145	0.3806	-0.07863	0.1501
fixed	NA	count_birth_order3/3	0.009043	0.04469	0.2023	7152	0.8397	-0.1164	0.1345
fixed	NA	count_birth_order1/4	-0.1252	0.06235	-2.008	7101	0.04471	-0.3002	0.04984
fixed	NA	count_birth_order2/4	-0.05209	0.0559	-0.932	7130	0.3514	-0.209	0.1048
fixed	NA	count_birth_order3/4	0.04482	0.05346	0.8385	7135	0.4018	-0.1052	0.1949
fixed	NA	count_birth_order4/4	-0.01274	0.05398	-0.2361	7152	0.8134	-0.1643	0.1388
fixed	NA	count_birth_order1/5	0.04844	0.09105	0.532	6757	0.5947	-0.2071	0.304
fixed	NA	count_birth_order2/5	-0.02286	0.08131	-0.2812	6938	0.7786	-0.2511	0.2054
fixed	NA	count_birth_order3/5	0.07511	0.0729	1.03	7024	0.3029	-0.1295	0.2797
fixed	NA	count_birth_order4/5	-0.09412	0.06707	-1.403	7088	0.1605	-0.2824	0.09414
fixed	NA	count_birth_order5/5	-0.1082	0.06446	-1.678	7144	0.09332	-0.2891	0.07275
ran_pars	mother_pidlink	sd__(Intercept)	0.4662	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8446	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	19703	19772	-9842	19683	NA	NA	NA
11	19705	19781	-9842	19683	0.04432	1	0.8333
14	19707	19804	-9840	19679	3.843	3	0.2789
20	19708	19846	-9834	19668	10.89	6	0.09197

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.122	0.2188	-14.27	6490	1.692e-45	-3.736	-2.508
fixed	NA	poly(age, 3, raw = TRUE)1	0.5431	0.04589	11.84	6500	5.471e-32	0.4143	0.6719
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02684	0.002966	-9.049	6550	1.878e-19	-0.03517	-0.01851
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004225	0.00005944	7.107	6595	1.308e-12	0.0002556	0.0005893
fixed	NA	male	-0.1756	0.02193	-8.008	7062	1.353e-15	-0.2371	-0.114
fixed	NA	sibling_count3	-0.01287	0.02857	-0.4505	4708	0.6523	-0.09307	0.06733
fixed	NA	sibling_count4	-0.05807	0.03526	-1.647	4028	0.09969	-0.1571	0.04092
fixed	NA	sibling_count5	-0.1585	0.04656	-3.404	3607	0.0006713	-0.2892	-0.0278
ran_pars	mother_pidlink	sd__(Intercept)	0.4762	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8379	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.133	0.2221	-14.11	6618	1.495e-44	-3.757	-2.51
fixed	NA	birth_order	0.004036	0.01354	0.2981	7086	0.7656	-0.03397	0.04204
fixed	NA	poly(age, 3, raw = TRUE)1	0.5439	0.04597	11.83	6518	5.738e-32	0.4149	0.673
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02687	0.002968	-9.053	6548	1.805e-19	-0.03521	-0.01854
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004229	0.00005946	7.112	6591	1.264e-12	0.000256	0.0005898
fixed	NA	male	-0.1757	0.02193	-8.01	7061	1.333e-15	-0.2372	-0.1141
fixed	NA	sibling_count3	-0.01549	0.02989	-0.5181	4823	0.6044	-0.09938	0.06841
fixed	NA	sibling_count4	-0.0639	0.04033	-1.584	4491	0.1132	-0.1771	0.0493
fixed	NA	sibling_count5	-0.1681	0.05657	-2.971	4429	0.002986	-0.3269	-0.009269
ran_pars	mother_pidlink	sd__(Intercept)	0.4763	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8379	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.139	0.2205	-14.23	6583	2.613e-45	-3.758	-2.52
fixed	NA	poly(age, 3, raw = TRUE)1	0.5441	0.04599	11.83	6522	5.62e-32	0.415	0.6732
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02686	0.002969	-9.048	6551	1.893e-19	-0.0352	-0.01853
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004223	0.00005947	7.1	6593	1.375e-12	0.0002553	0.0005892
fixed	NA	male	-0.1761	0.02194	-8.027	7061	1.159e-15	-0.2377	-0.1145
fixed	NA	sibling_count3	-0.01427	0.03064	-0.4656	5112	0.6415	-0.1003	0.07174
fixed	NA	sibling_count4	-0.07048	0.04136	-1.704	4720	0.08845	-0.1866	0.04562
fixed	NA	sibling_count5	-0.1424	0.05976	-2.383	4601	0.01722	-0.3101	0.02536
fixed	NA	birth_order_nonlinear2	0.02454	0.025	0.9815	5482	0.3264	-0.04564	0.09472
fixed	NA	birth_order_nonlinear3	0.003256	0.03568	0.09124	6279	0.9273	-0.09691	0.1034
fixed	NA	birth_order_nonlinear4	0.04629	0.05139	0.9007	6619	0.3678	-0.09796	0.1905
fixed	NA	birth_order_nonlinear5	-0.07451	0.08389	-0.8881	6742	0.3745	-0.31	0.161
ran_pars	mother_pidlink	sd__(Intercept)	0.4754	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8383	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.156	0.2212	-14.27	6599	1.694e-45	-3.777	-2.535
fixed	NA	poly(age, 3, raw = TRUE)1	0.5455	0.04605	11.85	6529	4.744e-32	0.4163	0.6748
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02696	0.002973	-9.069	6553	1.558e-19	-0.03531	-0.01862
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004244	0.00005955	7.126	6592	1.143e-12	0.0002572	0.0005915
fixed	NA	male	-0.1758	0.02194	-8.01	7055	1.336e-15	-0.2373	-0.1142
fixed	NA	count_birth_order2/2	0.05559	0.03435	1.619	5844	0.1056	-0.04082	0.152
fixed	NA	count_birth_order1/3	0.02666	0.0405	0.6583	7346	0.5104	-0.08703	0.1404
fixed	NA	count_birth_order2/3	0.01778	0.03886	0.4576	7355	0.6473	-0.0913	0.1269
fixed	NA	count_birth_order3/3	-0.02945	0.04264	-0.6907	7370	0.4898	-0.1491	0.09023
fixed	NA	count_birth_order1/4	-0.09389	0.06423	-1.462	7293	0.1438	-0.2742	0.08641
fixed	NA	count_birth_order2/4	-0.08455	0.05666	-1.492	7354	0.1357	-0.2436	0.0745
fixed	NA	count_birth_order3/4	-0.01305	0.05374	-0.2428	7355	0.8082	-0.1639	0.1378
fixed	NA	count_birth_order4/4	0.009224	0.05353	0.1723	7369	0.8632	-0.141	0.1595
fixed	NA	count_birth_order1/5	-0.05048	0.1116	-0.4524	6739	0.651	-0.3637	0.2627
fixed	NA	count_birth_order2/5	-0.1133	0.1066	-1.062	6816	0.2883	-0.4126	0.1861
fixed	NA	count_birth_order3/5	-0.104	0.08614	-1.207	7205	0.2274	-0.3458	0.1378
fixed	NA	count_birth_order4/5	-0.1239	0.07287	-1.701	7355	0.08904	-0.3285	0.08062
fixed	NA	count_birth_order5/5	-0.2064	0.07115	-2.901	7369	0.003727	-0.4061	-0.006708
ran_pars	mother_pidlink	sd__(Intercept)	0.4745	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8387	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	20260	20329	-10120	20240	NA	NA	NA
11	20262	20338	-10120	20240	0.08875	1	0.7658
14	20265	20361	-10118	20237	3.264	3	0.3527
20	20271	20409	-10115	20231	5.983	6	0.4251

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Raven 2007 old

birthorder <- birthorder %>% mutate(outcome = raven_2007_old)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
             data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.827	2.562	-0.7131	3259	0.4759	-9.017	5.364
fixed	NA	poly(age, 3, raw = TRUE)1	0.234	0.2682	0.8728	3260	0.3828	-0.5187	0.9868
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008346	0.009243	-0.903	3261	0.3666	-0.03429	0.0176
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008858	0.0001049	0.8447	3262	0.3984	-0.0002058	0.000383
fixed	NA	male	0.1557	0.03189	4.883	3085	0.000001098	0.0662	0.2452
fixed	NA	sibling_count3	-0.02541	0.0538	-0.4724	2391	0.6367	-0.1764	0.1256
fixed	NA	sibling_count4	-0.1124	0.05256	-2.139	2281	0.03253	-0.26	0.0351
fixed	NA	sibling_count5	-0.02315	0.05334	-0.434	2116	0.6643	-0.1729	0.1266
ran_pars	mother_pidlink	sd__(Intercept)	0.4768	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8043	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.655	2.562	-0.646	3259	0.5183	-8.847	5.537
fixed	NA	birth_order	-0.02899	0.01461	-1.984	2924	0.04735	-0.07001	0.01203
fixed	NA	poly(age, 3, raw = TRUE)1	0.2209	0.2681	0.824	3259	0.41	-0.5317	0.9736
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007904	0.009242	-0.8552	3260	0.3925	-0.03385	0.01804
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000836	0.0001049	0.7973	3261	0.4253	-0.0002107	0.0003779
fixed	NA	male	0.1559	0.03187	4.891	3082	0.000001052	0.06644	0.2454
fixed	NA	sibling_count3	-0.01234	0.05419	-0.2277	2426	0.8199	-0.1644	0.1398
fixed	NA	sibling_count4	-0.08595	0.05422	-1.585	2424	0.113	-0.2381	0.06624
fixed	NA	sibling_count5	0.01907	0.05742	0.3322	2437	0.7398	-0.1421	0.1803
ran_pars	mother_pidlink	sd__(Intercept)	0.4775	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8035	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.464	2.563	-0.5714	3256	0.5678	-8.659	5.73
fixed	NA	poly(age, 3, raw = TRUE)1	0.2027	0.2683	0.7557	3256	0.4499	-0.5503	0.9558
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007374	0.009247	-0.7974	3257	0.4253	-0.03333	0.01858
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007892	0.0001049	0.7522	3258	0.452	-0.0002156	0.0003734
fixed	NA	male	0.1567	0.03186	4.918	3081	0.0000009198	0.06727	0.2462
fixed	NA	sibling_count3	-0.00198	0.05517	-0.03589	2518	0.9714	-0.1568	0.1529
fixed	NA	sibling_count4	-0.07838	0.05506	-1.424	2517	0.1547	-0.2329	0.07617
fixed	NA	sibling_count5	0.004062	0.05791	0.07014	2482	0.9441	-0.1585	0.1666
fixed	NA	birth_order_nonlinear2	-0.09006	0.03904	-2.307	2552	0.02113	-0.1996	0.01952
fixed	NA	birth_order_nonlinear3	-0.1224	0.04504	-2.718	2536	0.006606	-0.2489	0.003996
fixed	NA	birth_order_nonlinear4	-0.1101	0.05575	-1.975	2700	0.04837	-0.2666	0.04639
fixed	NA	birth_order_nonlinear5	-0.01848	0.0794	-0.2328	2696	0.8159	-0.2414	0.2044
ran_pars	mother_pidlink	sd__(Intercept)	0.4764	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8035	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.778	2.564	-0.6935	3250	0.4881	-8.976	5.42
fixed	NA	poly(age, 3, raw = TRUE)1	0.2353	0.2684	0.8766	3251	0.3808	-0.5181	0.9887
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008449	0.009251	-0.9133	3251	0.3612	-0.03442	0.01752
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009063	0.000105	0.8635	3252	0.3879	-0.000204	0.0003852
fixed	NA	male	0.1548	0.03188	4.856	3078	0.000001258	0.06532	0.2443
fixed	NA	count_birth_order2/2	-0.1113	0.0741	-1.502	2605	0.1333	-0.3193	0.09671
fixed	NA	count_birth_order1/3	-0.02558	0.07353	-0.348	3236	0.7279	-0.232	0.1808
fixed	NA	count_birth_order2/3	-0.07059	0.0786	-0.8981	3252	0.3692	-0.2912	0.15
fixed	NA	count_birth_order3/3	-0.1446	0.07885	-1.834	3252	0.06671	-0.366	0.0767
fixed	NA	count_birth_order1/4	-0.04806	0.07578	-0.6342	3249	0.526	-0.2608	0.1646
fixed	NA	count_birth_order2/4	-0.1356	0.07907	-1.715	3251	0.08638	-0.3576	0.08632
fixed	NA	count_birth_order3/4	-0.311	0.0813	-3.825	3242	0.0001331	-0.5392	-0.08278
fixed	NA	count_birth_order4/4	-0.2024	0.08206	-2.467	3251	0.01369	-0.4327	0.02794
fixed	NA	count_birth_order1/5	-0.05145	0.08312	-0.619	3248	0.536	-0.2848	0.1819
fixed	NA	count_birth_order2/5	-0.174	0.08473	-2.054	3240	0.04009	-0.4118	0.06384
fixed	NA	count_birth_order3/5	-0.004018	0.08368	-0.04801	3232	0.9617	-0.2389	0.2309
fixed	NA	count_birth_order4/5	-0.1149	0.08558	-1.343	3218	0.1795	-0.3552	0.1253
fixed	NA	count_birth_order5/5	-0.01877	0.08729	-0.215	3237	0.8298	-0.2638	0.2263
ran_pars	mother_pidlink	sd__(Intercept)	0.4728	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8045	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	8769	8830	-4374	8749	NA	NA	NA
11	8767	8834	-4372	8745	3.941	1	0.04712
14	8766	8851	-4369	8738	6.58	3	0.08656
20	8768	8889	-4364	8728	10.6	6	0.1017

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.945	4.169	-0.7063	2326	0.4801	-14.65	8.759
fixed	NA	poly(age, 3, raw = TRUE)1	0.3379	0.436	0.775	2324	0.4384	-0.8859	1.562
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01145	0.01498	-0.7649	2322	0.4444	-0.05349	0.03058
fixed	NA	poly(age, 3, raw = TRUE)3	0.000127	0.0001691	0.7509	2319	0.4528	-0.0003476	0.0006016
fixed	NA	male	0.05754	0.03241	1.775	2434	0.07597	-0.03344	0.1485
fixed	NA	sibling_count3	-0.003758	0.04882	-0.07698	1772	0.9386	-0.1408	0.1333
fixed	NA	sibling_count4	-0.1099	0.05052	-2.176	1670	0.0297	-0.2517	0.03189
fixed	NA	sibling_count5	-0.1784	0.05512	-3.236	1590	0.001235	-0.3331	-0.02367
ran_pars	mother_pidlink	sd__(Intercept)	0.393	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.735	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.078	4.172	-0.7378	2325	0.4607	-14.79	8.632
fixed	NA	birth_order	0.01523	0.01653	0.9214	2463	0.3569	-0.03117	0.06162
fixed	NA	poly(age, 3, raw = TRUE)1	0.35	0.4361	0.8026	2322	0.4223	-0.8742	1.574
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0119	0.01498	-0.7944	2320	0.4271	-0.05396	0.03015
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001326	0.0001692	0.7835	2318	0.4334	-0.0003423	0.0006074
fixed	NA	male	0.05732	0.03241	1.769	2432	0.0771	-0.03366	0.1483
fixed	NA	sibling_count3	-0.01016	0.04932	-0.206	1794	0.8368	-0.1486	0.1283
fixed	NA	sibling_count4	-0.126	0.05348	-2.357	1746	0.01855	-0.2761	0.02409
fixed	NA	sibling_count5	-0.2053	0.06237	-3.291	1823	0.001016	-0.3803	-0.03021
ran_pars	mother_pidlink	sd__(Intercept)	0.3942	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7345	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.107	4.175	-0.7441	2321	0.4569	-14.83	8.614
fixed	NA	poly(age, 3, raw = TRUE)1	0.3557	0.4366	0.8148	2318	0.4153	-0.8698	1.581
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01211	0.015	-0.8072	2315	0.4196	-0.05421	0.02999
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001349	0.0001694	0.7968	2313	0.4256	-0.0003404	0.0006103
fixed	NA	male	0.05711	0.03243	1.761	2429	0.07836	-0.03393	0.1482
fixed	NA	sibling_count3	-0.01447	0.04989	-0.2901	1848	0.7718	-0.1545	0.1256
fixed	NA	sibling_count4	-0.1275	0.05425	-2.351	1802	0.01883	-0.2798	0.02474
fixed	NA	sibling_count5	-0.2101	0.06315	-3.328	1859	0.0008926	-0.3874	-0.03288
fixed	NA	birth_order_nonlinear2	-0.004541	0.0385	-0.118	1917	0.9061	-0.1126	0.1035
fixed	NA	birth_order_nonlinear3	0.04573	0.04747	0.9633	2103	0.3355	-0.08752	0.179
fixed	NA	birth_order_nonlinear4	0.0251	0.06298	0.3986	2334	0.6902	-0.1517	0.2019
fixed	NA	birth_order_nonlinear5	0.07403	0.09469	0.7818	2261	0.4344	-0.1918	0.3398
ran_pars	mother_pidlink	sd__(Intercept)	0.3942	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7349	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.288	4.175	-0.7875	2313	0.4311	-15.01	8.431
fixed	NA	poly(age, 3, raw = TRUE)1	0.3785	0.4365	0.867	2311	0.386	-0.8468	1.604
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01294	0.015	-0.8629	2308	0.3883	-0.05504	0.02915
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001449	0.0001693	0.8559	2306	0.3921	-0.0003304	0.0006202
fixed	NA	male	0.05816	0.03247	1.791	2425	0.07341	-0.03299	0.1493
fixed	NA	count_birth_order2/2	-0.06829	0.06869	-0.9942	1905	0.3203	-0.2611	0.1245
fixed	NA	count_birth_order1/3	-0.05431	0.06277	-0.8652	2510	0.387	-0.2305	0.1219
fixed	NA	count_birth_order2/3	0.01655	0.0688	0.2406	2531	0.8099	-0.1766	0.2097
fixed	NA	count_birth_order3/3	-0.03883	0.07639	-0.5083	2528	0.6113	-0.2533	0.1756
fixed	NA	count_birth_order1/4	-0.1429	0.07346	-1.945	2526	0.05193	-0.3491	0.06335
fixed	NA	count_birth_order2/4	-0.1636	0.07503	-2.181	2530	0.0293	-0.3742	0.04699
fixed	NA	count_birth_order3/4	-0.1546	0.07604	-2.034	2521	0.04209	-0.3681	0.05881
fixed	NA	count_birth_order4/4	-0.06506	0.08254	-0.7882	2525	0.4307	-0.2968	0.1666
fixed	NA	count_birth_order1/5	-0.2747	0.09467	-2.901	2529	0.003749	-0.5404	-0.008918
fixed	NA	count_birth_order2/5	-0.2925	0.09802	-2.984	2507	0.002871	-0.5677	-0.01736
fixed	NA	count_birth_order3/5	-0.03308	0.08964	-0.369	2502	0.7122	-0.2847	0.2185
fixed	NA	count_birth_order4/5	-0.278	0.08875	-3.133	2511	0.001751	-0.5272	-0.02892
fixed	NA	count_birth_order5/5	-0.1568	0.09316	-1.683	2511	0.09251	-0.4183	0.1047
ran_pars	mother_pidlink	sd__(Intercept)	0.3962	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7332	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	6270	6328	-3125	6250	NA	NA	NA
11	6271	6335	-3125	6249	0.8474	1	0.3573
14	6276	6358	-3124	6248	0.7468	3	0.8621
20	6278	6395	-3119	6238	10.65	6	0.09966

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.121	4.391	-0.2553	2134	0.7985	-13.45	11.2
fixed	NA	poly(age, 3, raw = TRUE)1	0.1369	0.4597	0.2979	2133	0.7658	-1.153	1.427
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004125	0.01581	-0.261	2132	0.7941	-0.0485	0.04025
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003911	0.0001787	0.2189	2130	0.8268	-0.0004625	0.0005407
fixed	NA	male	0.06037	0.03382	1.785	2210	0.07441	-0.03457	0.1553
fixed	NA	sibling_count3	-0.04486	0.0536	-0.8369	1671	0.4028	-0.1953	0.1056
fixed	NA	sibling_count4	-0.08056	0.0544	-1.481	1594	0.1388	-0.2333	0.07214
fixed	NA	sibling_count5	-0.1482	0.05662	-2.617	1537	0.008945	-0.3071	0.01073
ran_pars	mother_pidlink	sd__(Intercept)	0.3838	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7351	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.091	4.396	-0.2481	2134	0.8041	-13.43	11.25
fixed	NA	birth_order	-0.002983	0.01665	-0.1792	2260	0.8578	-0.04971	0.04375
fixed	NA	poly(age, 3, raw = TRUE)1	0.1341	0.46	0.2915	2133	0.7707	-1.157	1.425
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004023	0.01582	-0.2543	2131	0.7993	-0.04844	0.04039
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003786	0.0001789	0.2117	2129	0.8324	-0.0004642	0.0005399
fixed	NA	male	0.06033	0.03383	1.783	2209	0.07469	-0.03464	0.1553
fixed	NA	sibling_count3	-0.04355	0.05411	-0.8049	1685	0.421	-0.1954	0.1083
fixed	NA	sibling_count4	-0.07766	0.05677	-1.368	1645	0.1715	-0.237	0.0817
fixed	NA	sibling_count5	-0.1435	0.06243	-2.298	1699	0.02167	-0.3187	0.03177
ran_pars	mother_pidlink	sd__(Intercept)	0.3837	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7353	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1	4.399	-0.2274	2131	0.8202	-13.35	11.35
fixed	NA	poly(age, 3, raw = TRUE)1	0.1247	0.4605	0.2708	2129	0.7865	-1.168	1.417
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003704	0.01584	-0.2339	2127	0.8151	-0.04816	0.04075
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003432	0.000179	0.1917	2125	0.848	-0.0004682	0.0005369
fixed	NA	male	0.05993	0.03386	1.77	2207	0.07685	-0.03511	0.155
fixed	NA	sibling_count3	-0.04035	0.05475	-0.7369	1734	0.4613	-0.194	0.1133
fixed	NA	sibling_count4	-0.07136	0.05745	-1.242	1692	0.2143	-0.2326	0.0899
fixed	NA	sibling_count5	-0.1478	0.0629	-2.35	1720	0.01889	-0.3244	0.02875
fixed	NA	birth_order_nonlinear2	-0.01205	0.04037	-0.2986	1812	0.7653	-0.1254	0.1013
fixed	NA	birth_order_nonlinear3	-0.02193	0.04916	-0.4461	1968	0.6555	-0.1599	0.1161
fixed	NA	birth_order_nonlinear4	-0.02862	0.06498	-0.4405	2117	0.6596	-0.211	0.1538
fixed	NA	birth_order_nonlinear5	0.0424	0.09357	0.4532	2096	0.6505	-0.2203	0.3051
ran_pars	mother_pidlink	sd__(Intercept)	0.3834	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7359	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.186	4.409	-0.2691	2124	0.7879	-13.56	11.19
fixed	NA	poly(age, 3, raw = TRUE)1	0.1455	0.4615	0.3153	2122	0.7526	-1.15	1.441
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004506	0.01587	-0.2839	2120	0.7765	-0.04905	0.04004
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004434	0.0001794	0.2472	2118	0.8048	-0.0004592	0.0005479
fixed	NA	male	0.06036	0.03392	1.78	2202	0.07529	-0.03485	0.1556
fixed	NA	count_birth_order2/2	0.01977	0.07753	0.255	1772	0.7988	-0.1979	0.2374
fixed	NA	count_birth_order1/3	-0.05247	0.0695	-0.7549	2288	0.4504	-0.2476	0.1426
fixed	NA	count_birth_order2/3	0.007776	0.07558	0.1029	2302	0.9181	-0.2044	0.2199
fixed	NA	count_birth_order3/3	-0.06859	0.08225	-0.834	2301	0.4044	-0.2995	0.1623
fixed	NA	count_birth_order1/4	-0.01434	0.07735	-0.1854	2297	0.8529	-0.2315	0.2028
fixed	NA	count_birth_order2/4	-0.1156	0.07821	-1.478	2302	0.1396	-0.3351	0.104
fixed	NA	count_birth_order3/4	-0.1448	0.08259	-1.753	2291	0.07979	-0.3766	0.08708
fixed	NA	count_birth_order4/4	-0.01648	0.09095	-0.1812	2293	0.8562	-0.2718	0.2388
fixed	NA	count_birth_order1/5	-0.128	0.08888	-1.441	2302	0.1498	-0.3775	0.1214
fixed	NA	count_birth_order2/5	-0.1972	0.09233	-2.136	2296	0.03276	-0.4564	0.06194
fixed	NA	count_birth_order3/5	-0.04265	0.09233	-0.462	2278	0.6441	-0.3018	0.2165
fixed	NA	count_birth_order4/5	-0.2416	0.09246	-2.613	2278	0.009025	-0.5012	0.01791
fixed	NA	count_birth_order5/5	-0.09316	0.09606	-0.9698	2285	0.3322	-0.3628	0.1765
ran_pars	mother_pidlink	sd__(Intercept)	0.384	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7351	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	5688	5745	-2834	5668	NA	NA	NA
11	5690	5753	-2834	5668	0.03242	1	0.8571
14	5695	5776	-2834	5667	0.7083	3	0.8713
20	5699	5814	-2829	5659	8.526	6	0.202

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.359	4.191	-1.279	2335	0.2011	-17.12	6.406
fixed	NA	poly(age, 3, raw = TRUE)1	0.588	0.438	1.342	2334	0.1796	-0.6414	1.817
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01994	0.01504	-1.326	2333	0.185	-0.06214	0.02227
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002205	0.0001697	1.3	2330	0.1938	-0.0002557	0.0006967
fixed	NA	male	0.05559	0.03248	1.711	2441	0.08715	-0.03559	0.1468
fixed	NA	sibling_count3	-0.002478	0.04838	-0.05122	1784	0.9592	-0.1383	0.1333
fixed	NA	sibling_count4	-0.08207	0.05026	-1.633	1691	0.1027	-0.2232	0.05901
fixed	NA	sibling_count5	-0.1536	0.05614	-2.736	1565	0.006295	-0.3112	0.004005
ran_pars	mother_pidlink	sd__(Intercept)	0.4022	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.735	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.508	4.192	-1.314	2335	0.1891	-17.28	6.26
fixed	NA	birth_order	0.01995	0.01668	1.196	2458	0.2317	-0.02686	0.06677
fixed	NA	poly(age, 3, raw = TRUE)1	0.6008	0.438	1.372	2333	0.1703	-0.6287	1.83
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02041	0.01504	-1.357	2331	0.1749	-0.06262	0.0218
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002264	0.0001697	1.334	2329	0.1822	-0.0002499	0.0007028
fixed	NA	male	0.0552	0.03248	1.7	2440	0.08934	-0.03597	0.1464
fixed	NA	sibling_count3	-0.011	0.04891	-0.2249	1804	0.8221	-0.1483	0.1263
fixed	NA	sibling_count4	-0.1034	0.05333	-1.938	1772	0.05277	-0.253	0.04634
fixed	NA	sibling_count5	-0.1873	0.0628	-2.982	1785	0.002906	-0.3635	-0.01097
ran_pars	mother_pidlink	sd__(Intercept)	0.4031	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7345	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.571	4.194	-1.328	2330	0.1842	-17.35	6.203
fixed	NA	poly(age, 3, raw = TRUE)1	0.6117	0.4383	1.396	2328	0.1629	-0.6186	1.842
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02081	0.01505	-1.383	2326	0.1668	-0.06305	0.02143
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002312	0.0001698	1.362	2324	0.1734	-0.0002454	0.0007079
fixed	NA	male	0.05476	0.03249	1.685	2437	0.09208	-0.03645	0.146
fixed	NA	sibling_count3	-0.02073	0.04953	-0.4186	1863	0.6756	-0.1598	0.1183
fixed	NA	sibling_count4	-0.1062	0.05409	-1.963	1827	0.04977	-0.258	0.04564
fixed	NA	sibling_count5	-0.195	0.06367	-3.063	1831	0.002223	-0.3737	-0.0163
fixed	NA	birth_order_nonlinear2	-0.01028	0.03825	-0.2688	1916	0.7881	-0.1177	0.09709
fixed	NA	birth_order_nonlinear3	0.07328	0.0472	1.553	2099	0.1206	-0.0592	0.2058
fixed	NA	birth_order_nonlinear4	0.01959	0.06336	0.3092	2337	0.7572	-0.1583	0.1974
fixed	NA	birth_order_nonlinear5	0.1004	0.1008	0.9956	2234	0.3195	-0.1827	0.3834
ran_pars	mother_pidlink	sd__(Intercept)	0.4038	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7343	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.506	4.192	-1.313	2320	0.1892	-17.27	6.262
fixed	NA	poly(age, 3, raw = TRUE)1	0.6092	0.4381	1.391	2318	0.1645	-0.6205	1.839
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02082	0.01504	-1.384	2316	0.1665	-0.06304	0.0214
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002324	0.0001697	1.369	2314	0.1711	-0.000244	0.0007088
fixed	NA	male	0.05624	0.03253	1.729	2431	0.08394	-0.03507	0.1475
fixed	NA	count_birth_order2/2	-0.0546	0.06678	-0.8176	1928	0.4137	-0.242	0.1328
fixed	NA	count_birth_order1/3	-0.04933	0.06221	-0.793	2518	0.4278	-0.2239	0.1253
fixed	NA	count_birth_order2/3	0.01169	0.06885	0.1697	2539	0.8652	-0.1816	0.205
fixed	NA	count_birth_order3/3	-0.01606	0.07471	-0.215	2535	0.8298	-0.2258	0.1937
fixed	NA	count_birth_order1/4	-0.1051	0.07346	-1.43	2535	0.1528	-0.3113	0.1011
fixed	NA	count_birth_order2/4	-0.132	0.07501	-1.76	2536	0.07857	-0.3425	0.07855
fixed	NA	count_birth_order3/4	-0.1016	0.07622	-1.333	2528	0.1828	-0.3155	0.1124
fixed	NA	count_birth_order4/4	-0.06905	0.08164	-0.8458	2535	0.3977	-0.2982	0.1601
fixed	NA	count_birth_order1/5	-0.2639	0.09434	-2.797	2537	0.005193	-0.5287	0.0009223
fixed	NA	count_birth_order2/5	-0.3259	0.09988	-3.263	2511	0.001117	-0.6063	-0.04555
fixed	NA	count_birth_order3/5	0.03848	0.09108	0.4224	2510	0.6727	-0.2172	0.2941
fixed	NA	count_birth_order4/5	-0.235	0.09142	-2.57	2514	0.01022	-0.4916	0.02165
fixed	NA	count_birth_order5/5	-0.1072	0.0992	-1.081	2506	0.28	-0.3856	0.1713
ran_pars	mother_pidlink	sd__(Intercept)	0.4064	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7321	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	6312	6370	-3146	6292	NA	NA	NA
11	6312	6376	-3145	6290	1.432	1	0.2314
14	6316	6398	-3144	6288	2.444	3	0.4855
20	6316	6433	-3138	6276	11.6	6	0.07141

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Numeracy 2007 old

birthorder <- birthorder %>% mutate(outcome = math_2007_old)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
             data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.457	2.732	-1.632	3255	0.1028	-12.13	3.211
fixed	NA	poly(age, 3, raw = TRUE)1	0.5424	0.2859	1.897	3256	0.05791	-0.2602	1.345
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01929	0.009854	-1.958	3258	0.05034	-0.04695	0.008368
fixed	NA	poly(age, 3, raw = TRUE)3	0.000212	0.0001118	1.897	3259	0.05788	-0.0001017	0.0005258
fixed	NA	male	-0.1061	0.03366	-3.153	2996	0.001633	-0.2006	-0.01164
fixed	NA	sibling_count3	0.03597	0.05849	0.615	2429	0.5386	-0.1282	0.2002
fixed	NA	sibling_count4	-0.1177	0.05726	-2.055	2339	0.03994	-0.2784	0.04304
fixed	NA	sibling_count5	-0.05071	0.05826	-0.8704	2204	0.3842	-0.2142	0.1128
ran_pars	mother_pidlink	sd__(Intercept)	0.584	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8178	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.468	2.734	-1.634	3255	0.1023	-12.14	3.206
fixed	NA	birth_order	0.001952	0.0154	0.1268	2906	0.8991	-0.04128	0.04519
fixed	NA	poly(age, 3, raw = TRUE)1	0.5432	0.286	1.899	3256	0.05768	-0.2598	1.346
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01932	0.009858	-1.959	3257	0.05014	-0.04699	0.008355
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002123	0.0001118	1.899	3258	0.05766	-0.0001015	0.0005262
fixed	NA	male	-0.1061	0.03367	-3.152	2995	0.001636	-0.2007	-0.01163
fixed	NA	sibling_count3	0.03511	0.0589	0.596	2461	0.5512	-0.1302	0.2005
fixed	NA	sibling_count4	-0.1195	0.05896	-2.026	2468	0.04284	-0.285	0.04603
fixed	NA	sibling_count5	-0.05356	0.06243	-0.8578	2494	0.3911	-0.2288	0.1217
ran_pars	mother_pidlink	sd__(Intercept)	0.5838	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8181	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.267	2.737	-1.559	3252	0.119	-11.95	3.415
fixed	NA	poly(age, 3, raw = TRUE)1	0.524	0.2864	1.83	3253	0.0674	-0.2799	1.328
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0187	0.009869	-1.895	3254	0.05818	-0.04641	0.009001
fixed	NA	poly(age, 3, raw = TRUE)3	0.000206	0.0001119	1.841	3255	0.06577	-0.0001082	0.0005202
fixed	NA	male	-0.1053	0.03369	-3.127	2995	0.001783	-0.1999	-0.01078
fixed	NA	sibling_count3	0.04889	0.05991	0.8161	2546	0.4145	-0.1193	0.2171
fixed	NA	sibling_count4	-0.1145	0.05981	-1.914	2550	0.05573	-0.2824	0.05341
fixed	NA	sibling_count5	-0.05681	0.06295	-0.9026	2533	0.3668	-0.2335	0.1199
fixed	NA	birth_order_nonlinear2	-0.01554	0.0409	-0.38	2512	0.704	-0.1304	0.09927
fixed	NA	birth_order_nonlinear3	-0.05006	0.04721	-1.06	2500	0.289	-0.1826	0.08245
fixed	NA	birth_order_nonlinear4	0.02073	0.05856	0.3539	2658	0.7234	-0.1436	0.1851
fixed	NA	birth_order_nonlinear5	0.04748	0.08337	0.5695	2642	0.5691	-0.1865	0.2815
ran_pars	mother_pidlink	sd__(Intercept)	0.5821	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8192	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.415	2.741	-1.611	3246	0.1073	-12.11	3.279
fixed	NA	poly(age, 3, raw = TRUE)1	0.5414	0.2868	1.887	3247	0.05918	-0.2638	1.347
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01927	0.009884	-1.95	3248	0.05131	-0.04702	0.008475
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002121	0.0001121	1.892	3249	0.05855	-0.0001025	0.0005268
fixed	NA	male	-0.1066	0.03373	-3.161	2985	0.001588	-0.2013	-0.01194
fixed	NA	count_birth_order2/2	-0.0757	0.07771	-0.9742	2592	0.3301	-0.2938	0.1424
fixed	NA	count_birth_order1/3	0.004212	0.07872	0.05351	3226	0.9573	-0.2168	0.2252
fixed	NA	count_birth_order2/3	0.04847	0.08393	0.5775	3249	0.5636	-0.1871	0.2841
fixed	NA	count_birth_order3/3	-0.04386	0.08423	-0.5207	3247	0.6026	-0.2803	0.1926
fixed	NA	count_birth_order1/4	-0.1728	0.08107	-2.132	3244	0.03308	-0.4004	0.05472
fixed	NA	count_birth_order2/4	-0.1319	0.08437	-1.564	3248	0.118	-0.3688	0.1049
fixed	NA	count_birth_order3/4	-0.2138	0.08672	-2.466	3235	0.01373	-0.4572	0.0296
fixed	NA	count_birth_order4/4	-0.08364	0.08755	-0.9553	3248	0.3395	-0.3294	0.1621
fixed	NA	count_birth_order1/5	-0.0523	0.08876	-0.5892	3245	0.5558	-0.3015	0.1969
fixed	NA	count_birth_order2/5	-0.1417	0.09026	-1.57	3235	0.1165	-0.3951	0.1116
fixed	NA	count_birth_order3/5	-0.08611	0.08907	-0.9668	3225	0.3337	-0.3361	0.1639
fixed	NA	count_birth_order4/5	-0.1041	0.09102	-1.144	3209	0.2528	-0.3596	0.1514
fixed	NA	count_birth_order5/5	-0.037	0.09297	-0.398	3233	0.6906	-0.298	0.224
ran_pars	mother_pidlink	sd__(Intercept)	0.5833	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8189	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	9173	9234	-4576	9153	NA	NA	NA
11	9175	9242	-4576	9153	0.01638	1	0.8982
14	9179	9264	-4575	9151	2.313	3	0.5101
20	9187	9309	-4573	9147	3.815	6	0.7017

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.68	4.853	-1.377	2238	0.1688	-20.3	6.943
fixed	NA	poly(age, 3, raw = TRUE)1	0.7869	0.5074	1.551	2234	0.1211	-0.6374	2.211
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0279	0.01743	-1.601	2229	0.1096	-0.07682	0.02102
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003159	0.0001968	1.606	2224	0.1085	-0.0002364	0.0008682
fixed	NA	male	-0.1556	0.03788	-4.108	2350	0.00004132	-0.2619	-0.04927
fixed	NA	sibling_count3	0.02745	0.0592	0.4636	1815	0.643	-0.1387	0.1936
fixed	NA	sibling_count4	-0.04673	0.06138	-0.7613	1741	0.4466	-0.219	0.1256
fixed	NA	sibling_count5	-0.1241	0.06718	-1.848	1690	0.0648	-0.3127	0.06444
ran_pars	mother_pidlink	sd__(Intercept)	0.5604	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.82	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.893	4.856	-1.419	2239	0.1559	-20.52	6.739
fixed	NA	birth_order	0.02361	0.01937	1.219	2449	0.2231	-0.03077	0.07799
fixed	NA	poly(age, 3, raw = TRUE)1	0.806	0.5076	1.588	2235	0.1125	-0.6189	2.231
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02859	0.01744	-1.64	2230	0.1012	-0.07754	0.02035
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003246	0.0001969	1.649	2225	0.09932	-0.000228	0.0008772
fixed	NA	male	-0.1559	0.03787	-4.117	2349	0.00003965	-0.2623	-0.04963
fixed	NA	sibling_count3	0.01752	0.05975	0.2933	1834	0.7693	-0.1502	0.1852
fixed	NA	sibling_count4	-0.07218	0.06483	-1.113	1809	0.2657	-0.2542	0.1098
fixed	NA	sibling_count5	-0.1664	0.07558	-2.201	1895	0.02785	-0.3785	0.0458
ran_pars	mother_pidlink	sd__(Intercept)	0.5601	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8201	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.836	4.856	-1.408	2233	0.1594	-20.47	6.795
fixed	NA	poly(age, 3, raw = TRUE)1	0.8049	0.5077	1.585	2228	0.113	-0.6202	2.23
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02857	0.01744	-1.639	2223	0.1014	-0.07753	0.02038
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003247	0.0001969	1.649	2218	0.09926	-0.000228	0.0008774
fixed	NA	male	-0.1564	0.03787	-4.131	2344	0.00003733	-0.2627	-0.05015
fixed	NA	sibling_count3	0.01956	0.06035	0.3241	1881	0.7459	-0.1498	0.189
fixed	NA	sibling_count4	-0.08656	0.06567	-1.318	1858	0.1876	-0.2709	0.09777
fixed	NA	sibling_count5	-0.1744	0.07646	-2.281	1930	0.02266	-0.389	0.04022
fixed	NA	birth_order_nonlinear2	-0.03023	0.04435	-0.6816	1880	0.4956	-0.1547	0.09426
fixed	NA	birth_order_nonlinear3	0.02447	0.0549	0.4456	2070	0.6559	-0.1297	0.1786
fixed	NA	birth_order_nonlinear4	0.1414	0.07344	1.925	2298	0.05431	-0.06475	0.3475
fixed	NA	birth_order_nonlinear5	0.02823	0.11	0.2566	2207	0.7975	-0.2806	0.3371
ran_pars	mother_pidlink	sd__(Intercept)	0.5617	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.819	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.779	4.858	-1.395	2225	0.1631	-20.42	6.859
fixed	NA	poly(age, 3, raw = TRUE)1	0.8018	0.5079	1.579	2220	0.1146	-0.6239	2.228
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02847	0.01745	-1.632	2215	0.1028	-0.07745	0.0205
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003237	0.000197	1.643	2210	0.1005	-0.0002292	0.0008766
fixed	NA	male	-0.1605	0.03794	-4.231	2341	0.0000242	-0.267	-0.05402
fixed	NA	count_birth_order2/2	-0.1024	0.07909	-1.295	1884	0.1954	-0.3244	0.1196
fixed	NA	count_birth_order1/3	-0.02307	0.07439	-0.3101	2491	0.7565	-0.2319	0.1857
fixed	NA	count_birth_order2/3	-0.02947	0.08131	-0.3624	2526	0.717	-0.2577	0.1988
fixed	NA	count_birth_order3/3	0.04417	0.08999	0.4909	2524	0.6236	-0.2084	0.2968
fixed	NA	count_birth_order1/4	-0.1308	0.08685	-1.507	2520	0.132	-0.3746	0.1129
fixed	NA	count_birth_order2/4	-0.0849	0.08843	-0.96	2526	0.3371	-0.3331	0.1633
fixed	NA	count_birth_order3/4	-0.1839	0.08946	-2.056	2515	0.03993	-0.435	0.06723
fixed	NA	count_birth_order4/4	0.09668	0.09717	0.995	2520	0.3198	-0.1761	0.3694
fixed	NA	count_birth_order1/5	-0.2013	0.112	-1.798	2523	0.07236	-0.5157	0.1131
fixed	NA	count_birth_order2/5	-0.2702	0.1156	-2.337	2490	0.0195	-0.5948	0.05431
fixed	NA	count_birth_order3/5	-0.05964	0.1052	-0.5667	2488	0.571	-0.3551	0.2358
fixed	NA	count_birth_order4/5	-0.1405	0.1046	-1.343	2501	0.1793	-0.4342	0.1531
fixed	NA	count_birth_order5/5	-0.1716	0.1095	-1.568	2502	0.1171	-0.4789	0.1357
ran_pars	mother_pidlink	sd__(Intercept)	0.5637	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8175	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	7102	7161	-3541	7082	NA	NA	NA
11	7103	7167	-3540	7081	1.49	1	0.2222
14	7105	7187	-3538	7077	4.061	3	0.255
20	7109	7226	-3535	7069	7.837	6	0.2503

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.237	5.137	-0.8248	2035	0.4096	-18.66	10.18
fixed	NA	poly(age, 3, raw = TRUE)1	0.5105	0.5377	0.9494	2031	0.3425	-0.9989	2.02
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01775	0.01849	-0.9601	2028	0.3371	-0.06966	0.03415
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001941	0.000209	0.929	2023	0.353	-0.0003925	0.0007808
fixed	NA	male	-0.1386	0.03971	-3.49	2117	0.0004922	-0.2501	-0.02714
fixed	NA	sibling_count3	0.0148	0.06556	0.2257	1686	0.8214	-0.1692	0.1988
fixed	NA	sibling_count4	-0.0346	0.06664	-0.5192	1633	0.6037	-0.2217	0.1525
fixed	NA	sibling_count5	-0.05863	0.06953	-0.8431	1594	0.3993	-0.2538	0.1366
ran_pars	mother_pidlink	sd__(Intercept)	0.565	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8196	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.408	5.142	-0.8573	2035	0.3914	-18.84	10.03
fixed	NA	birth_order	0.01701	0.01964	0.8665	2242	0.3863	-0.03811	0.07214
fixed	NA	poly(age, 3, raw = TRUE)1	0.5261	0.5381	0.9776	2031	0.3284	-0.9844	2.037
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01831	0.01851	-0.9896	2027	0.3225	-0.07026	0.03363
fixed	NA	poly(age, 3, raw = TRUE)3	0.000201	0.0002092	0.9612	2023	0.3366	-0.0003861	0.0007882
fixed	NA	male	-0.1384	0.03972	-3.484	2117	0.0005045	-0.2499	-0.02688
fixed	NA	sibling_count3	0.007267	0.06612	0.1099	1698	0.9125	-0.1783	0.1929
fixed	NA	sibling_count4	-0.05148	0.06943	-0.7414	1676	0.4585	-0.2464	0.1434
fixed	NA	sibling_count5	-0.08591	0.07632	-1.126	1735	0.2605	-0.3001	0.1283
ran_pars	mother_pidlink	sd__(Intercept)	0.5644	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.82	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.244	5.147	-0.8246	2034	0.4097	-18.69	10.2
fixed	NA	poly(age, 3, raw = TRUE)1	0.511	0.5387	0.9486	2029	0.3429	-1.001	2.023
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0178	0.01853	-0.9611	2025	0.3366	-0.06981	0.0342
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001955	0.0002094	0.9336	2021	0.3506	-0.0003923	0.0007833
fixed	NA	male	-0.1389	0.03975	-3.494	2116	0.0004862	-0.2505	-0.0273
fixed	NA	sibling_count3	0.01598	0.06678	0.2393	1740	0.8109	-0.1715	0.2034
fixed	NA	sibling_count4	-0.04317	0.07014	-0.6155	1715	0.5383	-0.24	0.1537
fixed	NA	sibling_count5	-0.09032	0.07682	-1.176	1754	0.2398	-0.3059	0.1253
fixed	NA	birth_order_nonlinear2	0.01225	0.0468	0.2617	1752	0.7936	-0.1191	0.1436
fixed	NA	birth_order_nonlinear3	-0.005	0.05721	-0.0874	1910	0.9304	-0.1656	0.1556
fixed	NA	birth_order_nonlinear4	0.05054	0.07616	0.6636	2066	0.507	-0.1632	0.2643
fixed	NA	birth_order_nonlinear5	0.1295	0.1094	1.184	2033	0.2367	-0.1777	0.4367
ran_pars	mother_pidlink	sd__(Intercept)	0.5629	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8213	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.548	5.163	-0.8809	2029	0.3785	-19.04	9.944
fixed	NA	poly(age, 3, raw = TRUE)1	0.545	0.5403	1.009	2024	0.3132	-0.9716	2.062
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01892	0.01858	-1.019	2020	0.3085	-0.07107	0.03323
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002077	0.00021	0.9891	2015	0.3227	-0.0003817	0.0007971
fixed	NA	male	-0.1424	0.03985	-3.572	2111	0.000362	-0.2542	-0.03049
fixed	NA	count_birth_order2/2	-0.08478	0.08974	-0.9448	1728	0.3449	-0.3367	0.1671
fixed	NA	count_birth_order1/3	-0.05764	0.08296	-0.6948	2270	0.4873	-0.2905	0.1752
fixed	NA	count_birth_order2/3	-0.004796	0.08998	-0.0533	2297	0.9575	-0.2574	0.2478
fixed	NA	count_birth_order3/3	0.04995	0.09765	0.5115	2297	0.6091	-0.2242	0.324
fixed	NA	count_birth_order1/4	-0.09664	0.09216	-1.049	2289	0.2944	-0.3553	0.162
fixed	NA	count_birth_order2/4	-0.02682	0.09293	-0.2886	2298	0.7729	-0.2877	0.234
fixed	NA	count_birth_order3/4	-0.1537	0.09779	-1.571	2284	0.1162	-0.4282	0.1208
fixed	NA	count_birth_order4/4	0.0291	0.1077	0.2701	2286	0.7871	-0.2733	0.3315
fixed	NA	count_birth_order1/5	-0.09154	0.1059	-0.8641	2298	0.3876	-0.3889	0.2058
fixed	NA	count_birth_order2/5	-0.09581	0.1097	-0.8731	2287	0.3827	-0.4038	0.2122
fixed	NA	count_birth_order3/5	-0.1293	0.1091	-1.185	2262	0.2361	-0.4357	0.177
fixed	NA	count_birth_order4/5	-0.1377	0.1096	-1.256	2262	0.2092	-0.4454	0.17
fixed	NA	count_birth_order5/5	0.0006132	0.1136	0.005396	2274	0.9957	-0.3184	0.3196
ran_pars	mother_pidlink	sd__(Intercept)	0.5643	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8207	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	6475	6532	-3227	6455	NA	NA	NA
11	6476	6539	-3227	6454	0.7542	1	0.3852
14	6481	6561	-3226	6453	1.056	3	0.7876
20	6488	6602	-3224	6448	5.283	6	0.508

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.26	4.863	-1.493	2257	0.1356	-20.91	6.392
fixed	NA	poly(age, 3, raw = TRUE)1	0.8473	0.5081	1.668	2254	0.09555	-0.579	2.274
fixed	NA	poly(age, 3, raw = TRUE)2	-0.03	0.01744	-1.72	2250	0.08562	-0.07896	0.01897
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003393	0.0001968	1.724	2246	0.08483	-0.0002131	0.0008918
fixed	NA	male	-0.171	0.03782	-4.52	2366	0.000006482	-0.2771	-0.06479
fixed	NA	sibling_count3	0.04392	0.05817	0.7551	1815	0.4503	-0.1194	0.2072
fixed	NA	sibling_count4	-0.002439	0.06051	-0.0403	1746	0.9679	-0.1723	0.1674
fixed	NA	sibling_count5	-0.08814	0.06787	-1.299	1652	0.1943	-0.2786	0.1024
ran_pars	mother_pidlink	sd__(Intercept)	0.5551	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8223	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.419	4.866	-1.525	2257	0.1275	-21.08	6.239
fixed	NA	birth_order	0.02083	0.01946	1.07	2443	0.2845	-0.03379	0.07546
fixed	NA	poly(age, 3, raw = TRUE)1	0.861	0.5083	1.694	2253	0.09045	-0.5659	2.288
fixed	NA	poly(age, 3, raw = TRUE)2	-0.03049	0.01745	-1.747	2249	0.0807	-0.07948	0.01849
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003456	0.0001969	1.755	2246	0.07939	-0.0002071	0.0008983
fixed	NA	male	-0.1714	0.03782	-4.531	2366	0.000006159	-0.2775	-0.06521
fixed	NA	sibling_count3	0.03496	0.05876	0.5949	1832	0.552	-0.13	0.1999
fixed	NA	sibling_count4	-0.02503	0.06408	-0.3906	1820	0.6961	-0.2049	0.1548
fixed	NA	sibling_count5	-0.1237	0.07558	-1.637	1847	0.1017	-0.3359	0.08841
ran_pars	mother_pidlink	sd__(Intercept)	0.5545	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8226	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.26	4.869	-1.491	2253	0.1361	-20.93	6.406
fixed	NA	poly(age, 3, raw = TRUE)1	0.8481	0.5087	1.667	2249	0.09563	-0.5799	2.276
fixed	NA	poly(age, 3, raw = TRUE)2	-0.03006	0.01746	-1.721	2245	0.08531	-0.07908	0.01896
fixed	NA	poly(age, 3, raw = TRUE)3	0.000341	0.0001971	1.73	2242	0.08372	-0.0002122	0.0008941
fixed	NA	male	-0.1718	0.03785	-4.538	2365	0.000005949	-0.278	-0.06553
fixed	NA	sibling_count3	0.04227	0.05942	0.7113	1885	0.477	-0.1245	0.2091
fixed	NA	sibling_count4	-0.02761	0.06492	-0.4253	1871	0.6707	-0.2098	0.1546
fixed	NA	sibling_count5	-0.1347	0.07655	-1.76	1892	0.07856	-0.3496	0.08015
fixed	NA	birth_order_nonlinear2	-0.01548	0.04403	-0.3515	1881	0.7252	-0.1391	0.1081
fixed	NA	birth_order_nonlinear3	-0.002459	0.05451	-0.04511	2068	0.964	-0.1555	0.1505
fixed	NA	birth_order_nonlinear4	0.1047	0.07371	1.42	2305	0.1557	-0.1022	0.3116
fixed	NA	birth_order_nonlinear5	0.106	0.1168	0.9069	2177	0.3646	-0.222	0.4339
ran_pars	mother_pidlink	sd__(Intercept)	0.5549	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8226	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.118	4.874	-1.46	2248	0.1443	-20.8	6.564
fixed	NA	poly(age, 3, raw = TRUE)1	0.8378	0.5093	1.645	2244	0.1001	-0.5917	2.267
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02978	0.01748	-1.703	2241	0.08867	-0.07885	0.0193
fixed	NA	poly(age, 3, raw = TRUE)3	0.0003385	0.0001973	1.716	2237	0.08633	-0.0002153	0.0008922
fixed	NA	male	-0.1732	0.03795	-4.564	2361	0.000005264	-0.2797	-0.06669
fixed	NA	count_birth_order2/2	-0.08601	0.07696	-1.118	1909	0.2639	-0.302	0.13
fixed	NA	count_birth_order1/3	-0.003876	0.0734	-0.0528	2501	0.9579	-0.2099	0.2021
fixed	NA	count_birth_order2/3	0.03461	0.08104	0.4271	2535	0.6694	-0.1929	0.2621
fixed	NA	count_birth_order3/3	0.01203	0.08771	0.1371	2531	0.8909	-0.2342	0.2582
fixed	NA	count_birth_order1/4	-0.05514	0.08648	-0.6376	2530	0.5238	-0.2979	0.1876
fixed	NA	count_birth_order2/4	-0.02637	0.08806	-0.2995	2531	0.7646	-0.2735	0.2208
fixed	NA	count_birth_order3/4	-0.1175	0.08939	-1.314	2522	0.1889	-0.3684	0.1334
fixed	NA	count_birth_order4/4	0.07005	0.09583	0.731	2530	0.4649	-0.199	0.3391
fixed	NA	count_birth_order1/5	-0.1812	0.1112	-1.629	2531	0.1033	-0.4935	0.131
fixed	NA	count_birth_order2/5	-0.2549	0.1175	-2.17	2495	0.03012	-0.5847	0.07487
fixed	NA	count_birth_order3/5	-0.05634	0.1067	-0.5283	2499	0.5974	-0.3557	0.243
fixed	NA	count_birth_order4/5	-0.08139	0.1075	-0.7574	2503	0.4489	-0.383	0.2202
fixed	NA	count_birth_order5/5	-0.05191	0.1161	-0.447	2493	0.6549	-0.3779	0.2741
ran_pars	mother_pidlink	sd__(Intercept)	0.5565	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.822	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	7120	7179	-3550	7100	NA	NA	NA
11	7121	7185	-3550	7099	1.15	1	0.2835
14	7125	7207	-3548	7097	2.16	3	0.5399
20	7132	7249	-3546	7092	4.957	6	0.5494

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Raven 2007 young

birthorder <- birthorder %>% mutate(outcome = raven_2007_young)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
             data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.433	0.5236	-12.29	4641	3.614e-34	-7.903	-4.964
fixed	NA	poly(age, 3, raw = TRUE)1	0.694	0.06965	9.964	4767	3.686e-23	0.4985	0.8895
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02187	0.002986	-7.324	4905	2.791e-13	-0.03025	-0.01349
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002023	0.00004179	4.84	4962	0.000001339	0.00008496	0.0003196
fixed	NA	male	0.05122	0.02458	2.083	4575	0.03727	-0.01779	0.1202
fixed	NA	sibling_count3	-0.02576	0.03857	-0.6679	3484	0.5042	-0.134	0.0825
fixed	NA	sibling_count4	-0.1318	0.03942	-3.343	3281	0.0008389	-0.2424	-0.02112
fixed	NA	sibling_count5	-0.1461	0.04256	-3.432	3053	0.0006071	-0.2655	-0.0266
ran_pars	mother_pidlink	sd__(Intercept)	0.4987	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7462	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.505	0.5243	-12.41	4639	8.419e-35	-7.977	-5.034
fixed	NA	birth_order	0.02885	0.01212	2.379	4571	0.01738	-0.005183	0.06288
fixed	NA	poly(age, 3, raw = TRUE)1	0.697	0.06964	10.01	4764	2.366e-23	0.5015	0.8924
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02194	0.002984	-7.35	4903	2.311e-13	-0.03031	-0.01356
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002029	0.00004177	4.856	4961	0.000001235	0.00008559	0.0003201
fixed	NA	male	0.05018	0.02458	2.042	4577	0.04125	-0.01882	0.1192
fixed	NA	sibling_count3	-0.03891	0.03893	-0.9996	3518	0.3176	-0.1482	0.07036
fixed	NA	sibling_count4	-0.1614	0.04131	-3.907	3450	0.00009519	-0.2773	-0.04544
fixed	NA	sibling_count5	-0.1963	0.04747	-4.136	3402	0.00003623	-0.3295	-0.06307
ran_pars	mother_pidlink	sd__(Intercept)	0.4973	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7465	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.542	0.5234	-12.5	4646	2.81e-35	-8.011	-5.073
fixed	NA	poly(age, 3, raw = TRUE)1	0.7033	0.06956	10.11	4764	8.509e-24	0.5081	0.8986
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02219	0.002981	-7.445	4901	1.138e-13	-0.03056	-0.01383
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002061	0.00004172	4.939	4958	0.0000008103	0.00008896	0.0003232
fixed	NA	male	0.05027	0.02454	2.048	4572	0.04058	-0.01862	0.1192
fixed	NA	sibling_count3	-0.02031	0.03928	-0.517	3616	0.6052	-0.1306	0.08996
fixed	NA	sibling_count4	-0.1473	0.04174	-3.528	3565	0.0004234	-0.2644	-0.03011
fixed	NA	sibling_count5	-0.193	0.04777	-4.041	3429	0.0000543	-0.3271	-0.05896
fixed	NA	birth_order_nonlinear2	0.08362	0.02887	2.897	3533	0.003792	0.002595	0.1646
fixed	NA	birth_order_nonlinear3	-0.02977	0.03561	-0.8362	3807	0.4031	-0.1297	0.07017
fixed	NA	birth_order_nonlinear4	0.1277	0.04753	2.686	4128	0.00725	-0.005731	0.2611
fixed	NA	birth_order_nonlinear5	0.1784	0.06796	2.625	4355	0.008702	-0.01239	0.3691
ran_pars	mother_pidlink	sd__(Intercept)	0.4969	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7452	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.531	0.524	-12.46	4640	4.283e-35	-8.002	-5.06
fixed	NA	poly(age, 3, raw = TRUE)1	0.7027	0.0696	10.1	4757	9.917e-24	0.5073	0.898
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02216	0.002983	-7.43	4894	1.277e-13	-0.03053	-0.01379
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002055	0.00004175	4.924	4952	0.0000008769	0.00008836	0.0003227
fixed	NA	male	0.04974	0.02457	2.025	4569	0.04297	-0.01923	0.1187
fixed	NA	count_birth_order2/2	0.0618	0.05382	1.148	3631	0.2509	-0.08927	0.2129
fixed	NA	count_birth_order1/3	-0.03876	0.04778	-0.8111	4867	0.4173	-0.1729	0.09537
fixed	NA	count_birth_order2/3	0.07324	0.05267	1.391	4952	0.1644	-0.07459	0.2211
fixed	NA	count_birth_order3/3	-0.05428	0.05912	-0.9181	4943	0.3586	-0.2202	0.1117
fixed	NA	count_birth_order1/4	-0.1691	0.05447	-3.105	4942	0.001911	-0.322	-0.01625
fixed	NA	count_birth_order2/4	-0.08263	0.05566	-1.484	4952	0.1377	-0.2389	0.07362
fixed	NA	count_birth_order3/4	-0.1807	0.05818	-3.105	4923	0.001911	-0.344	-0.01736
fixed	NA	count_birth_order4/4	0.01402	0.0635	0.2208	4903	0.8252	-0.1642	0.1923
fixed	NA	count_birth_order1/5	-0.1613	0.06624	-2.436	4944	0.0149	-0.3473	0.0246
fixed	NA	count_birth_order2/5	-0.1047	0.06989	-1.498	4859	0.1342	-0.3009	0.09148
fixed	NA	count_birth_order3/5	-0.2337	0.06655	-3.512	4853	0.0004491	-0.4205	-0.0469
fixed	NA	count_birth_order4/5	-0.1226	0.06986	-1.755	4828	0.07933	-0.3187	0.07349
fixed	NA	count_birth_order5/5	-0.02349	0.06791	-0.3459	4919	0.7294	-0.2141	0.1671
ran_pars	mother_pidlink	sd__(Intercept)	0.4965	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7458	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12870	12935	-6425	12850	NA	NA	NA
11	12866	12938	-6422	12844	5.668	1	0.01727
14	12854	12945	-6413	12826	17.76	3	0.0004918
20	12864	12994	-6412	12824	2.581	6	0.8593

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.65	1.263	-4.474	3433	0.000007923	-9.195	-2.105
fixed	NA	poly(age, 3, raw = TRUE)1	0.5643	0.1931	2.922	3413	0.003503	0.02217	1.107
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01493	0.009604	-1.555	3398	0.1201	-0.04189	0.01203
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008698	0.0001554	0.5597	3385	0.5757	-0.0003492	0.0005232
fixed	NA	male	0.01296	0.0256	0.5061	4143	0.6128	-0.0589	0.08482
fixed	NA	sibling_count3	-0.01646	0.03515	-0.4682	3081	0.6397	-0.1151	0.08222
fixed	NA	sibling_count4	-0.1213	0.03977	-3.051	2771	0.002303	-0.233	-0.009699
fixed	NA	sibling_count5	-0.1898	0.04805	-3.95	2653	0.00008025	-0.3247	-0.05491
ran_pars	mother_pidlink	sd__(Intercept)	0.4866	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7318	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.806	1.266	-4.584	3439	0.000004713	-9.361	-2.251
fixed	NA	birth_order	0.02364	0.01404	1.684	4282	0.0922	-0.01576	0.06304
fixed	NA	poly(age, 3, raw = TRUE)1	0.582	0.1935	3.008	3413	0.002647	0.03893	1.125
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01576	0.009618	-1.638	3396	0.1014	-0.04276	0.01124
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001001	0.0001556	0.6429	3384	0.5203	-0.0003368	0.0005369
fixed	NA	male	0.0123	0.0256	0.4805	4145	0.6309	-0.05956	0.08417
fixed	NA	sibling_count3	-0.02788	0.03578	-0.7792	3130	0.4359	-0.1283	0.07256
fixed	NA	sibling_count4	-0.1492	0.04304	-3.466	2994	0.0005361	-0.27	-0.02835
fixed	NA	sibling_count5	-0.2374	0.05571	-4.261	3083	0.00002091	-0.3938	-0.08102
ran_pars	mother_pidlink	sd__(Intercept)	0.4853	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7323	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.85	1.266	-4.62	3439	0.000003988	-9.405	-2.295
fixed	NA	poly(age, 3, raw = TRUE)1	0.5909	0.1936	3.052	3413	0.002288	0.04749	1.134
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01618	0.009624	-1.682	3397	0.09274	-0.0432	0.01083
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001066	0.0001557	0.6847	3385	0.4936	-0.0003305	0.0005437
fixed	NA	male	0.01195	0.02561	0.4667	4141	0.6407	-0.05994	0.08384
fixed	NA	sibling_count3	-0.0216	0.03637	-0.5939	3252	0.5526	-0.1237	0.08049
fixed	NA	sibling_count4	-0.141	0.0438	-3.219	3092	0.001301	-0.2639	-0.01803
fixed	NA	sibling_count5	-0.2377	0.05743	-4.138	3154	0.00003592	-0.3989	-0.07645
fixed	NA	birth_order_nonlinear2	0.04965	0.02924	1.698	2986	0.08955	-0.03241	0.1317
fixed	NA	birth_order_nonlinear3	0.02137	0.03923	0.5447	3590	0.586	-0.08875	0.1315
fixed	NA	birth_order_nonlinear4	0.0674	0.05402	1.248	4007	0.2122	-0.08424	0.2191
fixed	NA	birth_order_nonlinear5	0.1342	0.0845	1.588	3990	0.1123	-0.103	0.3714
ran_pars	mother_pidlink	sd__(Intercept)	0.4856	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7322	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.846	1.267	-4.614	3436	0.000004091	-9.402	-2.289
fixed	NA	poly(age, 3, raw = TRUE)1	0.591	0.1937	3.052	3411	0.002294	0.04736	1.135
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01619	0.009628	-1.682	3394	0.09269	-0.04322	0.01083
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001071	0.0001558	0.6872	3382	0.492	-0.0003302	0.0005443
fixed	NA	male	0.01191	0.02564	0.4647	4135	0.6422	-0.06005	0.08388
fixed	NA	count_birth_order2/2	0.02876	0.04692	0.6131	3275	0.5398	-0.1029	0.1605
fixed	NA	count_birth_order1/3	-0.05858	0.04469	-1.311	4375	0.19	-0.184	0.06687
fixed	NA	count_birth_order2/3	0.05075	0.04865	1.043	4420	0.2969	-0.08581	0.1873
fixed	NA	count_birth_order3/3	0.01289	0.05426	0.2375	4420	0.8122	-0.1394	0.1652
fixed	NA	count_birth_order1/4	-0.1245	0.0602	-2.069	4422	0.03862	-0.2935	0.04444
fixed	NA	count_birth_order2/4	-0.1546	0.06015	-2.571	4384	0.01018	-0.3235	0.01421
fixed	NA	count_birth_order3/4	-0.1275	0.06275	-2.031	4296	0.04229	-0.3036	0.04868
fixed	NA	count_birth_order4/4	-0.04852	0.06224	-0.7796	4419	0.4357	-0.2232	0.1262
fixed	NA	count_birth_order1/5	-0.172	0.09099	-1.89	4351	0.05884	-0.4274	0.08346
fixed	NA	count_birth_order2/5	-0.1145	0.0961	-1.192	4111	0.2335	-0.3843	0.1553
fixed	NA	count_birth_order3/5	-0.2707	0.08464	-3.198	4209	0.001394	-0.5082	-0.03309
fixed	NA	count_birth_order4/5	-0.2367	0.07949	-2.978	4303	0.002919	-0.4598	-0.01358
fixed	NA	count_birth_order5/5	-0.1166	0.0769	-1.516	4408	0.1295	-0.3325	0.09926
ran_pars	mother_pidlink	sd__(Intercept)	0.4864	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7317	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11327	11391	-5653	11307	NA	NA	NA
11	11326	11397	-5652	11304	2.841	1	0.0919
14	11330	11420	-5651	11302	2.208	3	0.5303
20	11335	11463	-5648	11295	6.6	6	0.3595

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.436	1.292	-4.209	3112	0.00002636	-9.062	-1.811
fixed	NA	poly(age, 3, raw = TRUE)1	0.5392	0.1977	2.728	3090	0.006404	-0.01558	1.094
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01401	0.009838	-1.424	3075	0.1546	-0.04162	0.01361
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007685	0.0001594	0.4823	3061	0.6297	-0.0003705	0.0005242
fixed	NA	male	0.01933	0.02634	0.734	3820	0.463	-0.0546	0.09326
fixed	NA	sibling_count3	-0.03298	0.03778	-0.8727	2926	0.3829	-0.139	0.07309
fixed	NA	sibling_count4	-0.08832	0.04117	-2.145	2682	0.03203	-0.2039	0.02725
fixed	NA	sibling_count5	-0.1704	0.04656	-3.66	2620	0.0002569	-0.3011	-0.03973
ran_pars	mother_pidlink	sd__(Intercept)	0.4984	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7204	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.57	1.295	-4.302	3117	0.00001746	-9.205	-1.935
fixed	NA	birth_order	0.02101	0.01395	1.506	4030	0.1321	-0.01814	0.06015
fixed	NA	poly(age, 3, raw = TRUE)1	0.5543	0.1979	2.8	3090	0.005137	-0.001326	1.11
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01472	0.009851	-1.494	3073	0.1352	-0.04237	0.01293
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008831	0.0001596	0.5534	3060	0.58	-0.0003596	0.0005362
fixed	NA	male	0.01874	0.02634	0.7115	3822	0.4768	-0.0552	0.09268
fixed	NA	sibling_count3	-0.04337	0.03839	-1.13	2958	0.2587	-0.1511	0.0644
fixed	NA	sibling_count4	-0.1117	0.04397	-2.54	2857	0.01113	-0.2351	0.01173
fixed	NA	sibling_count5	-0.2096	0.05329	-3.932	2935	0.00008604	-0.3591	-0.05997
ran_pars	mother_pidlink	sd__(Intercept)	0.4971	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.721	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.649	1.293	-4.368	3110	0.00001295	-9.28	-2.019
fixed	NA	poly(age, 3, raw = TRUE)1	0.5672	0.1978	2.867	3084	0.004175	0.01181	1.123
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01536	0.009847	-1.56	3066	0.1189	-0.043	0.01228
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009846	0.0001595	0.6173	3054	0.5371	-0.0003492	0.0005462
fixed	NA	male	0.01948	0.02632	0.7401	3813	0.4593	-0.05441	0.09338
fixed	NA	sibling_count3	-0.03149	0.03895	-0.8084	3060	0.4189	-0.1408	0.07785
fixed	NA	sibling_count4	-0.09791	0.04465	-2.193	2953	0.02838	-0.2232	0.02741
fixed	NA	sibling_count5	-0.2075	0.05424	-3.825	2953	0.0001333	-0.3598	-0.05523
fixed	NA	birth_order_nonlinear2	0.07433	0.0302	2.461	2789	0.01391	-0.01045	0.1591
fixed	NA	birth_order_nonlinear3	-0.01017	0.03971	-0.2562	3361	0.7978	-0.1216	0.1013
fixed	NA	birth_order_nonlinear4	0.06452	0.05393	1.196	3667	0.2316	-0.08687	0.2159
fixed	NA	birth_order_nonlinear5	0.1475	0.08088	1.824	3852	0.0682	-0.07949	0.3746
ran_pars	mother_pidlink	sd__(Intercept)	0.4988	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7194	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.638	1.292	-4.364	3097	0.00001321	-9.265	-2.011
fixed	NA	poly(age, 3, raw = TRUE)1	0.5661	0.1977	2.863	3072	0.004218	0.01116	1.121
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01537	0.009839	-1.562	3055	0.1183	-0.04299	0.01225
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009993	0.0001594	0.6271	3042	0.5307	-0.0003474	0.0005473
fixed	NA	male	0.0172	0.02632	0.6536	3803	0.5134	-0.05668	0.09108
fixed	NA	count_birth_order2/2	0.08626	0.05096	1.693	2992	0.0906	-0.05678	0.2293
fixed	NA	count_birth_order1/3	-0.06631	0.04797	-1.382	4087	0.1669	-0.201	0.06834
fixed	NA	count_birth_order2/3	0.058	0.05152	1.126	4128	0.2603	-0.08662	0.2026
fixed	NA	count_birth_order3/3	0.0198	0.05786	0.3422	4124	0.7323	-0.1426	0.1822
fixed	NA	count_birth_order1/4	-0.0688	0.06015	-1.144	4129	0.2528	-0.2377	0.1001
fixed	NA	count_birth_order2/4	-0.06173	0.06068	-1.017	4099	0.3091	-0.2321	0.1086
fixed	NA	count_birth_order3/4	-0.1235	0.06374	-1.937	4014	0.05277	-0.3024	0.05544
fixed	NA	count_birth_order4/4	0.003209	0.06534	0.04911	4121	0.9608	-0.1802	0.1866
fixed	NA	count_birth_order1/5	-0.0709	0.08158	-0.869	4078	0.3849	-0.2999	0.1581
fixed	NA	count_birth_order2/5	-0.1033	0.08253	-1.251	3976	0.2109	-0.3349	0.1284
fixed	NA	count_birth_order3/5	-0.3042	0.07872	-3.864	3956	0.0001135	-0.5251	-0.08318
fixed	NA	count_birth_order4/5	-0.1991	0.07917	-2.514	3927	0.01196	-0.4213	0.02316
fixed	NA	count_birth_order5/5	-0.06404	0.07581	-0.8448	4117	0.3983	-0.2768	0.1488
ran_pars	mother_pidlink	sd__(Intercept)	0.5015	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7174	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	10541	10604	-5260	10521	NA	NA	NA
11	10540	10610	-5259	10518	2.272	1	0.1317
14	10538	10626	-5255	10510	8.47	3	0.03723
20	10539	10666	-5250	10499	10.41	6	0.1084

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.019	1.28	-3.92	3334	0.00009048	-8.613	-1.425
fixed	NA	poly(age, 3, raw = TRUE)1	0.4672	0.1958	2.386	3314	0.01707	-0.08233	1.017
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01011	0.009731	-1.039	3300	0.2987	-0.03743	0.0172
fixed	NA	poly(age, 3, raw = TRUE)3	0.000008366	0.0001574	0.05315	3288	0.9576	-0.0004335	0.0004502
fixed	NA	male	0.009549	0.02598	0.3676	4048	0.7132	-0.06337	0.08247
fixed	NA	sibling_count3	-0.009593	0.03549	-0.2703	3018	0.7869	-0.1092	0.09002
fixed	NA	sibling_count4	-0.1137	0.04033	-2.819	2716	0.004858	-0.2269	-0.0004671
fixed	NA	sibling_count5	-0.1938	0.05042	-3.843	2631	0.0001242	-0.3353	-0.05225
ran_pars	mother_pidlink	sd__(Intercept)	0.4991	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7345	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.19	1.284	-4.041	3340	0.00005431	-8.795	-1.585
fixed	NA	birth_order	0.02514	0.01436	1.751	4174	0.08004	-0.01516	0.06544
fixed	NA	poly(age, 3, raw = TRUE)1	0.4869	0.1961	2.483	3314	0.01307	-0.06351	1.037
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01105	0.009746	-1.134	3297	0.257	-0.03841	0.01631
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000233	0.0001576	0.1478	3286	0.8825	-0.0004192	0.0004658
fixed	NA	male	0.009023	0.02598	0.3474	4049	0.7283	-0.06389	0.08194
fixed	NA	sibling_count3	-0.02143	0.03611	-0.5934	3065	0.553	-0.1228	0.07994
fixed	NA	sibling_count4	-0.1435	0.04375	-3.279	2945	0.001053	-0.2663	-0.02065
fixed	NA	sibling_count5	-0.2432	0.05775	-4.211	3025	0.00002617	-0.4053	-0.08108
ran_pars	mother_pidlink	sd__(Intercept)	0.4982	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7348	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.19	1.285	-4.039	3343	0.00005495	-8.797	-1.583
fixed	NA	poly(age, 3, raw = TRUE)1	0.4888	0.1963	2.49	3318	0.01283	-0.0623	1.04
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01111	0.009758	-1.139	3301	0.2548	-0.03851	0.01628
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002383	0.0001578	0.151	3290	0.88	-0.0004192	0.0004669
fixed	NA	male	0.008719	0.02599	0.3355	4045	0.7373	-0.06423	0.08167
fixed	NA	sibling_count3	-0.0222	0.03671	-0.6047	3185	0.5454	-0.1252	0.08085
fixed	NA	sibling_count4	-0.1393	0.04456	-3.125	3047	0.001793	-0.2644	-0.01418
fixed	NA	sibling_count5	-0.2314	0.05989	-3.863	3099	0.0001142	-0.3995	-0.06326
fixed	NA	birth_order_nonlinear2	0.05207	0.02943	1.769	2900	0.07694	-0.03054	0.1347
fixed	NA	birth_order_nonlinear3	0.05619	0.03979	1.412	3457	0.158	-0.05551	0.1679
fixed	NA	birth_order_nonlinear4	0.06141	0.05545	1.107	3895	0.2682	-0.09425	0.2171
fixed	NA	birth_order_nonlinear5	0.08254	0.09058	0.9112	3956	0.3622	-0.1717	0.3368
ran_pars	mother_pidlink	sd__(Intercept)	0.4982	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.735	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.182	1.286	-4.03	3344	0.00005698	-8.791	-1.573
fixed	NA	poly(age, 3, raw = TRUE)1	0.4879	0.1965	2.483	3319	0.01307	-0.06363	1.039
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01104	0.009765	-1.13	3302	0.2585	-0.03845	0.01638
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002227	0.0001579	0.141	3289	0.8879	-0.0004211	0.0004656
fixed	NA	male	0.008893	0.02602	0.3418	4043	0.7325	-0.06415	0.08194
fixed	NA	count_birth_order2/2	0.02821	0.0462	0.6107	3150	0.5414	-0.1015	0.1579
fixed	NA	count_birth_order1/3	-0.06192	0.04499	-1.376	4311	0.1688	-0.1882	0.06438
fixed	NA	count_birth_order2/3	0.06353	0.04955	1.282	4355	0.1999	-0.07557	0.2026
fixed	NA	count_birth_order3/3	0.03548	0.0548	0.6474	4352	0.5174	-0.1184	0.1893
fixed	NA	count_birth_order1/4	-0.1107	0.06157	-1.798	4357	0.07218	-0.2836	0.06211
fixed	NA	count_birth_order2/4	-0.1568	0.06104	-2.569	4319	0.01024	-0.3282	0.01455
fixed	NA	count_birth_order3/4	-0.1015	0.06339	-1.601	4215	0.1094	-0.2795	0.07642
fixed	NA	count_birth_order4/4	-0.05428	0.0629	-0.8629	4355	0.3882	-0.2308	0.1223
fixed	NA	count_birth_order1/5	-0.1947	0.0931	-2.092	4298	0.03653	-0.4561	0.06661
fixed	NA	count_birth_order2/5	-0.133	0.103	-1.291	3995	0.1967	-0.4222	0.1561
fixed	NA	count_birth_order3/5	-0.1812	0.08961	-2.022	4135	0.04322	-0.4328	0.07033
fixed	NA	count_birth_order4/5	-0.2449	0.08457	-2.895	4209	0.003806	-0.4822	-0.007477
fixed	NA	count_birth_order5/5	-0.1625	0.08238	-1.972	4342	0.04862	-0.3937	0.06875
ran_pars	mother_pidlink	sd__(Intercept)	0.498	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.735	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11250	11314	-5615	11230	NA	NA	NA
11	11249	11320	-5614	11227	3.071	1	0.0797
14	11254	11344	-5613	11226	1.156	3	0.7635
20	11260	11387	-5610	11220	6.436	6	0.3761

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Numeracy 2007 young

birthorder <- birthorder %>% mutate(outcome = math_2007_young)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
             data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.423	0.5453	-11.78	4640	1.427e-31	-7.953	-4.892
fixed	NA	poly(age, 3, raw = TRUE)1	0.7323	0.07259	10.09	4769	1.075e-23	0.5285	0.936
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02495	0.003115	-8.009	4908	1.428e-15	-0.03369	-0.0162
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002604	0.00004366	5.964	4961	0.000000002627	0.0001379	0.000383
fixed	NA	male	-0.1132	0.02559	-4.422	4543	0.000009986	-0.185	-0.04134
fixed	NA	sibling_count3	0.02256	0.04057	0.5561	3558	0.5782	-0.09132	0.1364
fixed	NA	sibling_count4	-0.1283	0.0415	-3.092	3372	0.002001	-0.2448	-0.01184
fixed	NA	sibling_count5	-0.03847	0.04484	-0.858	3163	0.3909	-0.1643	0.08738
ran_pars	mother_pidlink	sd__(Intercept)	0.5439	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7672	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.482	0.5461	-11.87	4638	4.842e-32	-8.015	-4.95
fixed	NA	birth_order	0.02427	0.01262	1.923	4590	0.05455	-0.01116	0.05971
fixed	NA	poly(age, 3, raw = TRUE)1	0.7345	0.07258	10.12	4765	7.749e-24	0.5308	0.9383
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02499	0.003114	-8.025	4906	1.256e-15	-0.03373	-0.01625
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002607	0.00004365	5.973	4960	0.000000002494	0.0001382	0.0003833
fixed	NA	male	-0.1141	0.02559	-4.457	4541	0.000008494	-0.1859	-0.04223
fixed	NA	sibling_count3	0.01144	0.04097	0.2793	3591	0.78	-0.1036	0.1265
fixed	NA	sibling_count4	-0.1534	0.04349	-3.527	3534	0.0004258	-0.2754	-0.0313
fixed	NA	sibling_count5	-0.08097	0.04998	-1.62	3500	0.1053	-0.2213	0.05932
ran_pars	mother_pidlink	sd__(Intercept)	0.5439	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7669	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.496	0.5459	-11.9	4644	3.519e-32	-8.028	-4.963
fixed	NA	poly(age, 3, raw = TRUE)1	0.738	0.0726	10.17	4766	4.918e-24	0.5343	0.9418
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02513	0.003115	-8.07	4904	8.794e-16	-0.03388	-0.01639
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002625	0.00004366	6.014	4957	0.000000001941	0.00014	0.0003851
fixed	NA	male	-0.1139	0.02559	-4.452	4537	0.000008716	-0.1857	-0.04209
fixed	NA	sibling_count3	0.01112	0.04138	0.2686	3681	0.7882	-0.105	0.1273
fixed	NA	sibling_count4	-0.1614	0.04398	-3.671	3639	0.0002451	-0.2849	-0.03799
fixed	NA	sibling_count5	-0.06866	0.05035	-1.364	3525	0.1728	-0.21	0.07267
fixed	NA	birth_order_nonlinear2	0.06097	0.02998	2.034	3565	0.04206	-0.02318	0.1451
fixed	NA	birth_order_nonlinear3	0.04911	0.03702	1.327	3836	0.1847	-0.0548	0.153
fixed	NA	birth_order_nonlinear4	0.1212	0.04946	2.451	4141	0.0143	-0.01763	0.2601
fixed	NA	birth_order_nonlinear5	0.01766	0.07079	0.2494	4353	0.803	-0.181	0.2164
ran_pars	mother_pidlink	sd__(Intercept)	0.5436	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7669	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-6.501	0.5465	-11.9	4638	3.67e-32	-8.035	-4.967
fixed	NA	poly(age, 3, raw = TRUE)1	0.7377	0.07263	10.16	4759	5.415e-24	0.5338	0.9416
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02513	0.003116	-8.063	4897	9.26e-16	-0.03387	-0.01638
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002626	0.00004368	6.013	4951	0.000000001956	0.00014	0.0003852
fixed	NA	male	-0.1135	0.02561	-4.432	4535	0.000009555	-0.1854	-0.04162
fixed	NA	count_birth_order2/2	0.08511	0.05591	1.522	3665	0.128	-0.07183	0.2421
fixed	NA	count_birth_order1/3	0.0339	0.05006	0.677	4860	0.4984	-0.1066	0.1744
fixed	NA	count_birth_order2/3	0.08199	0.0551	1.488	4951	0.1368	-0.07269	0.2367
fixed	NA	count_birth_order3/3	0.02926	0.06181	0.4733	4944	0.636	-0.1443	0.2028
fixed	NA	count_birth_order1/4	-0.1495	0.05701	-2.622	4940	0.008778	-0.3095	0.01057
fixed	NA	count_birth_order2/4	-0.09275	0.05822	-1.593	4953	0.1112	-0.2562	0.07068
fixed	NA	count_birth_order3/4	-0.1192	0.06081	-1.96	4924	0.05005	-0.2899	0.05151
fixed	NA	count_birth_order4/4	-0.02441	0.06635	-0.3679	4905	0.713	-0.2107	0.1618
fixed	NA	count_birth_order1/5	-0.08821	0.06926	-1.274	4944	0.2029	-0.2826	0.1062
fixed	NA	count_birth_order2/5	-0.03633	0.07299	-0.4977	4857	0.6187	-0.2412	0.1686
fixed	NA	count_birth_order3/5	0.05753	0.0695	0.8278	4853	0.4078	-0.1376	0.2526
fixed	NA	count_birth_order4/5	0.04828	0.07294	0.662	4826	0.508	-0.1565	0.253
fixed	NA	count_birth_order5/5	-0.04089	0.07097	-0.5761	4921	0.5646	-0.2401	0.1583
ran_pars	mother_pidlink	sd__(Intercept)	0.5431	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7675	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	13303	13368	-6641	13283	NA	NA	NA
11	13301	13373	-6640	13279	3.703	1	0.05433
14	13302	13394	-6637	13274	4.61	3	0.2027
20	13311	13441	-6636	13271	3.332	6	0.7661

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.27	1.314	-4.011	3342	0.0000617	-8.958	-1.582
fixed	NA	poly(age, 3, raw = TRUE)1	0.5413	0.2009	2.695	3321	0.007082	-0.02258	1.105
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01476	0.009989	-1.477	3306	0.1397	-0.0428	0.01328
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009009	0.0001616	0.5575	3293	0.5773	-0.0003636	0.0005437
fixed	NA	male	-0.1385	0.02677	-5.176	4079	0.0000002376	-0.2137	-0.06341
fixed	NA	sibling_count3	0.03331	0.03738	0.891	3159	0.373	-0.07163	0.1382
fixed	NA	sibling_count4	-0.04248	0.04237	-1.002	2887	0.3162	-0.1614	0.07647
fixed	NA	sibling_count5	-0.09838	0.05123	-1.92	2783	0.05491	-0.2422	0.04543
ran_pars	mother_pidlink	sd__(Intercept)	0.5494	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7482	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.445	1.317	-4.134	3347	0.00003651	-9.142	-1.748
fixed	NA	birth_order	0.02649	0.0147	1.802	4281	0.07155	-0.01477	0.06775
fixed	NA	poly(age, 3, raw = TRUE)1	0.561	0.2012	2.789	3319	0.005318	-0.003632	1.126
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01568	0.01	-1.568	3302	0.117	-0.04375	0.01239
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001047	0.0001618	0.6471	3290	0.5176	-0.0003494	0.0005588
fixed	NA	male	-0.1393	0.02676	-5.204	4079	0.0000002042	-0.2144	-0.06416
fixed	NA	sibling_count3	0.02042	0.03805	0.5367	3205	0.5915	-0.08638	0.1272
fixed	NA	sibling_count4	-0.07386	0.0458	-1.613	3103	0.1069	-0.2024	0.0547
fixed	NA	sibling_count5	-0.1521	0.05925	-2.567	3195	0.01031	-0.3184	0.01423
ran_pars	mother_pidlink	sd__(Intercept)	0.5489	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7482	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.451	1.318	-4.136	3352	0.00003619	-9.15	-1.751
fixed	NA	poly(age, 3, raw = TRUE)1	0.567	0.2014	2.815	3326	0.004901	0.001682	1.132
fixed	NA	poly(age, 3, raw = TRUE)2	-0.016	0.01001	-1.598	3309	0.1101	-0.04411	0.0121
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001103	0.000162	0.6807	3297	0.4961	-0.0003444	0.000565
fixed	NA	male	-0.1391	0.02678	-5.194	4079	0.0000002154	-0.2143	-0.06394
fixed	NA	sibling_count3	0.02657	0.03863	0.688	3320	0.4915	-0.08185	0.135
fixed	NA	sibling_count4	-0.06915	0.04657	-1.485	3196	0.1376	-0.1999	0.06156
fixed	NA	sibling_count5	-0.1674	0.06102	-2.744	3274	0.006111	-0.3387	0.003875
fixed	NA	birth_order_nonlinear2	0.01502	0.03035	0.495	3005	0.6206	-0.07017	0.1002
fixed	NA	birth_order_nonlinear3	0.02673	0.04087	0.654	3595	0.5132	-0.088	0.1415
fixed	NA	birth_order_nonlinear4	0.08087	0.05644	1.433	3990	0.152	-0.07758	0.2393
fixed	NA	birth_order_nonlinear5	0.1731	0.08827	1.962	3956	0.04988	-0.07462	0.4209
ran_pars	mother_pidlink	sd__(Intercept)	0.5476	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7491	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.445	1.32	-4.126	3359	0.00003786	-9.149	-1.74
fixed	NA	poly(age, 3, raw = TRUE)1	0.5654	0.2017	2.803	3333	0.005094	-0.0008416	1.132
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01592	0.01003	-1.588	3316	0.1124	-0.04407	0.01223
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001091	0.0001622	0.6726	3304	0.5012	-0.0003463	0.0005645
fixed	NA	male	-0.1383	0.02683	-5.156	4077	0.0000002645	-0.2136	-0.06302
fixed	NA	count_birth_order2/2	0.0294	0.04884	0.602	3287	0.5472	-0.1077	0.1665
fixed	NA	count_birth_order1/3	0.03419	0.04708	0.7262	4367	0.4678	-0.09797	0.1664
fixed	NA	count_birth_order2/3	0.05688	0.05113	1.112	4420	0.266	-0.08665	0.2004
fixed	NA	count_birth_order3/3	0.03759	0.05703	0.6592	4420	0.5098	-0.1225	0.1977
fixed	NA	count_birth_order1/4	-0.07872	0.06328	-1.244	4422	0.2136	-0.2564	0.09892
fixed	NA	count_birth_order2/4	-0.06051	0.06314	-0.9582	4382	0.338	-0.2378	0.1167
fixed	NA	count_birth_order3/4	-0.02095	0.06578	-0.3185	4290	0.7501	-0.2056	0.1637
fixed	NA	count_birth_order4/4	0.02731	0.06541	0.4176	4420	0.6763	-0.1563	0.2109
fixed	NA	count_birth_order1/5	-0.09907	0.09546	-1.038	4340	0.2994	-0.367	0.1689
fixed	NA	count_birth_order2/5	-0.226	0.1006	-2.247	4079	0.02468	-0.5083	0.0563
fixed	NA	count_birth_order3/5	-0.1136	0.08865	-1.282	4191	0.2	-0.3624	0.1352
fixed	NA	count_birth_order4/5	-0.1012	0.08334	-1.214	4294	0.2249	-0.3351	0.1328
fixed	NA	count_birth_order5/5	0.008885	0.08078	0.11	4407	0.9124	-0.2179	0.2356
ran_pars	mother_pidlink	sd__(Intercept)	0.547	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7499	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11768	11832	-5874	11748	NA	NA	NA
11	11767	11837	-5872	11745	3.254	1	0.07124
14	11771	11861	-5872	11743	1.351	3	0.717
20	11781	11909	-5871	11741	2.092	6	0.911

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.346	1.357	-3.94	3131	0.00008318	-9.154	-1.537
fixed	NA	poly(age, 3, raw = TRUE)1	0.5626	0.2076	2.71	3110	0.006771	-0.02021	1.145
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01623	0.01033	-1.57	3095	0.1165	-0.04523	0.01278
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001208	0.0001674	0.7217	3082	0.4705	-0.000349	0.0005906
fixed	NA	male	-0.1475	0.02773	-5.317	3815	0.0000001116	-0.2253	-0.06961
fixed	NA	sibling_count3	0.01327	0.04009	0.3311	3023	0.7406	-0.09927	0.1258
fixed	NA	sibling_count4	-0.05222	0.04372	-1.194	2801	0.2324	-0.175	0.0705
fixed	NA	sibling_count5	-0.07084	0.04945	-1.433	2745	0.1521	-0.2096	0.06797
ran_pars	mother_pidlink	sd__(Intercept)	0.5436	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7507	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.512	1.36	-4.054	3135	0.00005157	-9.329	-1.696
fixed	NA	birth_order	0.02608	0.0147	1.774	4037	0.07607	-0.01518	0.06734
fixed	NA	poly(age, 3, raw = TRUE)1	0.5813	0.2079	2.797	3109	0.005195	-0.00215	1.165
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01711	0.01034	-1.654	3092	0.09818	-0.04615	0.01192
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001351	0.0001675	0.8062	3080	0.4202	-0.0003352	0.0006053
fixed	NA	male	-0.1482	0.02773	-5.345	3815	0.00000009593	-0.226	-0.07037
fixed	NA	sibling_count3	0.0003254	0.04074	0.007986	3056	0.9936	-0.114	0.1147
fixed	NA	sibling_count4	-0.08131	0.04668	-1.742	2970	0.08165	-0.2123	0.04973
fixed	NA	sibling_count5	-0.1196	0.05655	-2.114	3047	0.03456	-0.2783	0.03917
ran_pars	mother_pidlink	sd__(Intercept)	0.5432	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7506	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.504	1.361	-4.045	3140	0.00005347	-9.324	-1.685
fixed	NA	poly(age, 3, raw = TRUE)1	0.583	0.2081	2.801	3115	0.005123	-0.001217	1.167
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01718	0.01036	-1.659	3098	0.0973	-0.04625	0.01189
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001359	0.0001678	0.81	3086	0.418	-0.000335	0.0006068
fixed	NA	male	-0.1482	0.02775	-5.339	3813	0.0000000987	-0.2261	-0.07027
fixed	NA	sibling_count3	0.0004552	0.04133	0.01101	3152	0.9912	-0.1156	0.1165
fixed	NA	sibling_count4	-0.07924	0.04738	-1.672	3060	0.09459	-0.2122	0.05377
fixed	NA	sibling_count5	-0.1162	0.05757	-2.018	3068	0.04368	-0.2778	0.04543
fixed	NA	birth_order_nonlinear2	0.04271	0.03175	1.345	2872	0.1786	-0.04641	0.1318
fixed	NA	birth_order_nonlinear3	0.0513	0.0418	1.227	3413	0.2199	-0.06605	0.1686
fixed	NA	birth_order_nonlinear4	0.07387	0.05683	1.3	3696	0.1937	-0.08565	0.2334
fixed	NA	birth_order_nonlinear5	0.1039	0.08527	1.219	3863	0.2231	-0.1354	0.3433
ran_pars	mother_pidlink	sd__(Intercept)	0.5426	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7513	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.535	1.361	-4.067	3139	0.00004877	-9.355	-1.715
fixed	NA	poly(age, 3, raw = TRUE)1	0.587	0.2082	2.819	3115	0.004847	0.002501	1.171
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01738	0.01036	-1.678	3099	0.09354	-0.04647	0.0117
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001395	0.0001678	0.8311	3087	0.406	-0.0003316	0.0006106
fixed	NA	male	-0.1471	0.02777	-5.297	3810	0.0000001245	-0.225	-0.06914
fixed	NA	count_birth_order2/2	0.05386	0.05366	1.004	3068	0.3156	-0.09677	0.2045
fixed	NA	count_birth_order1/3	0.01198	0.05073	0.2362	4089	0.8133	-0.1304	0.1544
fixed	NA	count_birth_order2/3	0.04961	0.05445	0.9111	4128	0.3623	-0.1032	0.2024
fixed	NA	count_birth_order3/3	0.03463	0.06114	0.5664	4124	0.5711	-0.137	0.2062
fixed	NA	count_birth_order1/4	-0.112	0.06357	-1.761	4129	0.07826	-0.2904	0.06648
fixed	NA	count_birth_order2/4	-0.05171	0.0641	-0.8068	4102	0.4198	-0.2316	0.1282
fixed	NA	count_birth_order3/4	-0.04066	0.0673	-0.6041	4022	0.5458	-0.2296	0.1483
fixed	NA	count_birth_order4/4	0.07804	0.06904	1.13	4122	0.2584	-0.1158	0.2718
fixed	NA	count_birth_order1/5	-0.05507	0.08616	-0.6392	4080	0.5227	-0.2969	0.1868
fixed	NA	count_birth_order2/5	-0.06749	0.08712	-0.7747	3984	0.4385	-0.312	0.1771
fixed	NA	count_birth_order3/5	0.01181	0.0831	0.1422	3966	0.8869	-0.2214	0.2451
fixed	NA	count_birth_order4/5	-0.1652	0.08356	-1.977	3939	0.04814	-0.3997	0.06938
fixed	NA	count_birth_order5/5	-0.01713	0.08009	-0.2139	4118	0.8307	-0.242	0.2077
ran_pars	mother_pidlink	sd__(Intercept)	0.5424	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7512	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	10989	11052	-5485	10969	NA	NA	NA
11	10988	11058	-5483	10966	3.154	1	0.07572
14	10994	11082	-5483	10966	0.3642	3	0.9475
20	10998	11125	-5479	10958	7.449	6	0.2813

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.242	1.327	-3.952	3280	0.00007928	-8.966	-1.518
fixed	NA	poly(age, 3, raw = TRUE)1	0.5305	0.2028	2.616	3260	0.008937	-0.03873	1.1
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01401	0.01008	-1.39	3245	0.1648	-0.0423	0.01429
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007446	0.000163	0.4567	3233	0.6479	-0.0003832	0.0005321
fixed	NA	male	-0.1405	0.02702	-5.199	4002	0.0000002102	-0.2164	-0.06464
fixed	NA	sibling_count3	0.06438	0.03744	1.719	3104	0.08564	-0.04072	0.1695
fixed	NA	sibling_count4	-0.01646	0.04261	-0.3864	2836	0.6992	-0.1361	0.1031
fixed	NA	sibling_count5	-0.123	0.0533	-2.308	2761	0.02107	-0.2726	0.02659
ran_pars	mother_pidlink	sd__(Intercept)	0.5523	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7505	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.43	1.33	-4.081	3285	0.00004586	-9.164	-1.695
fixed	NA	birth_order	0.02734	0.01495	1.828	4178	0.06759	-0.01464	0.06931
fixed	NA	poly(age, 3, raw = TRUE)1	0.552	0.2031	2.718	3258	0.006606	-0.01812	1.122
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01502	0.01009	-1.488	3241	0.1368	-0.04336	0.01331
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009068	0.0001633	0.5555	3230	0.5786	-0.0003676	0.000549
fixed	NA	male	-0.1411	0.02702	-5.221	4002	0.0000001865	-0.2169	-0.06524
fixed	NA	sibling_count3	0.05143	0.03809	1.35	3148	0.1771	-0.05549	0.1584
fixed	NA	sibling_count4	-0.04907	0.04618	-1.063	3054	0.2881	-0.1787	0.08055
fixed	NA	sibling_count5	-0.1771	0.06093	-2.906	3137	0.003685	-0.3481	-0.00604
ran_pars	mother_pidlink	sd__(Intercept)	0.5517	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7505	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.412	1.332	-4.064	3290	0.00004943	-9.15	-1.674
fixed	NA	poly(age, 3, raw = TRUE)1	0.5542	0.2034	2.724	3264	0.006485	-0.01691	1.125
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01515	0.01011	-1.498	3247	0.1342	-0.04353	0.01323
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009293	0.0001635	0.5683	3236	0.5699	-0.0003661	0.000552
fixed	NA	male	-0.1411	0.02704	-5.218	4000	0.0000001896	-0.217	-0.0652
fixed	NA	sibling_count3	0.05318	0.03869	1.374	3261	0.1694	-0.05544	0.1618
fixed	NA	sibling_count4	-0.04646	0.047	-0.9885	3152	0.323	-0.1784	0.08548
fixed	NA	sibling_count5	-0.1868	0.06315	-2.959	3220	0.003111	-0.3641	-0.009586
fixed	NA	birth_order_nonlinear2	0.01922	0.03043	0.6316	2936	0.5277	-0.06621	0.1046
fixed	NA	birth_order_nonlinear3	0.0465	0.04127	1.127	3477	0.2599	-0.06935	0.1623
fixed	NA	birth_order_nonlinear4	0.07684	0.05765	1.333	3890	0.1826	-0.08498	0.2387
fixed	NA	birth_order_nonlinear5	0.1511	0.0942	1.604	3934	0.1089	-0.1134	0.4155
ran_pars	mother_pidlink	sd__(Intercept)	0.5511	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7512	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.423	1.333	-4.069	3290	0.00004824	-9.164	-1.682
fixed	NA	poly(age, 3, raw = TRUE)1	0.5548	0.2036	2.724	3265	0.006475	-0.01681	1.126
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01518	0.01012	-1.5	3247	0.1338	-0.04358	0.01323
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009353	0.0001637	0.5715	3235	0.5677	-0.0003659	0.0005529
fixed	NA	male	-0.1395	0.02708	-5.15	3998	0.0000002728	-0.2155	-0.06345
fixed	NA	count_birth_order2/2	0.0389	0.04784	0.8132	3175	0.4162	-0.09539	0.1732
fixed	NA	count_birth_order1/3	0.06461	0.0471	1.372	4305	0.1702	-0.06759	0.1968
fixed	NA	count_birth_order2/3	0.09009	0.05176	1.74	4355	0.08184	-0.0552	0.2354
fixed	NA	count_birth_order3/3	0.08117	0.05723	1.418	4353	0.1562	-0.07949	0.2418
fixed	NA	count_birth_order1/4	-0.0743	0.06432	-1.155	4357	0.2481	-0.2548	0.1063
fixed	NA	count_birth_order2/4	-0.03049	0.0637	-0.4787	4318	0.6322	-0.2093	0.1483
fixed	NA	count_birth_order3/4	0.02953	0.06606	0.447	4212	0.6549	-0.1559	0.215
fixed	NA	count_birth_order4/4	0.06093	0.0657	0.9274	4356	0.3538	-0.1235	0.2453
fixed	NA	count_birth_order1/5	-0.05863	0.09712	-0.6037	4292	0.5461	-0.3312	0.214
fixed	NA	count_birth_order2/5	-0.2847	0.1072	-2.657	3971	0.007918	-0.5855	0.01609
fixed	NA	count_birth_order3/5	-0.1085	0.09332	-1.163	4122	0.2449	-0.3705	0.1534
fixed	NA	count_birth_order4/5	-0.151	0.08812	-1.714	4201	0.08667	-0.3984	0.09636
fixed	NA	count_birth_order5/5	-0.03391	0.086	-0.3942	4341	0.6934	-0.2753	0.2075
ran_pars	mother_pidlink	sd__(Intercept)	0.5511	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7512	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11635	11698	-5807	11615	NA	NA	NA
11	11633	11704	-5806	11611	3.348	1	0.06728
14	11639	11728	-5805	11611	0.3631	3	0.9478
20	11646	11773	-5803	11606	5.416	6	0.4916

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Counting backwards

birthorder <- birthorder %>% mutate(outcome = count_backwards)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7392	0.1991	-3.714	6789	0.000206	-1.298	-0.1804
fixed	NA	poly(age, 3, raw = TRUE)1	0.09312	0.01916	4.86	6683	0.000001198	0.03934	0.1469
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003023	0.0005607	-5.392	6539	0.00000007214	-0.004597	-0.001449
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000272	0.000005094	5.339	6410	0.0000000965	0.0000129	0.0000415
fixed	NA	male	0.03845	0.02283	1.684	6721	0.09216	-0.02563	0.1025
fixed	NA	sibling_count3	-0.002074	0.034	-0.06101	4888	0.9514	-0.09751	0.09336
fixed	NA	sibling_count4	0.02362	0.03528	0.6695	4440	0.5032	-0.0754	0.1226
fixed	NA	sibling_count5	0.004105	0.03678	0.1116	4000	0.9111	-0.09913	0.1073
ran_pars	mother_pidlink	sd__(Intercept)	0.4316	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.871	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7214	0.1991	-3.624	6779	0.0002922	-1.28	-0.1626
fixed	NA	birth_order	-0.03413	0.01121	-3.043	5683	0.002351	-0.06561	-0.002648
fixed	NA	poly(age, 3, raw = TRUE)1	0.0962	0.01918	5.016	6708	0.0000005408	0.04237	0.15
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003105	0.0005612	-5.533	6556	0.00000003262	-0.00468	-0.00153
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002773	0.000005095	5.442	6423	0.00000005465	0.00001343	0.00004203
fixed	NA	male	0.03942	0.02281	1.728	6713	0.08403	-0.02461	0.1035
fixed	NA	sibling_count3	0.009728	0.03422	0.2843	4998	0.7762	-0.08632	0.1058
fixed	NA	sibling_count4	0.05173	0.03647	1.418	4924	0.1561	-0.05064	0.1541
fixed	NA	sibling_count5	0.04923	0.03966	1.241	4958	0.2146	-0.0621	0.1606
ran_pars	mother_pidlink	sd__(Intercept)	0.4337	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8695	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7553	0.1995	-3.786	6792	0.0001546	-1.315	-0.1953
fixed	NA	poly(age, 3, raw = TRUE)1	0.09605	0.01919	5.005	6692	0.0000005729	0.04218	0.1499
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003095	0.0005617	-5.51	6530	0.00000003725	-0.004672	-0.001518
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002759	0.000005103	5.407	6383	0.00000006636	0.00001327	0.00004192
fixed	NA	male	0.0395	0.02281	1.731	6711	0.08346	-0.02454	0.1035
fixed	NA	sibling_count3	0.01763	0.03468	0.5083	5186	0.6113	-0.07972	0.115
fixed	NA	sibling_count4	0.0575	0.03699	1.555	5134	0.1201	-0.04633	0.1613
fixed	NA	sibling_count5	0.04835	0.03996	1.21	5102	0.2263	-0.06382	0.1605
fixed	NA	birth_order_nonlinear2	-0.03516	0.02673	-1.315	5658	0.1885	-0.1102	0.03988
fixed	NA	birth_order_nonlinear3	-0.1045	0.03421	-3.056	5479	0.002257	-0.2006	-0.008503
fixed	NA	birth_order_nonlinear4	-0.09262	0.04459	-2.077	5422	0.03782	-0.2178	0.03253
fixed	NA	birth_order_nonlinear5	-0.09832	0.06457	-1.523	5225	0.1279	-0.2796	0.08294
ran_pars	mother_pidlink	sd__(Intercept)	0.4331	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8698	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7543	0.1998	-3.774	6793	0.0001617	-1.315	-0.1933
fixed	NA	poly(age, 3, raw = TRUE)1	0.09604	0.01919	5.005	6691	0.0000005728	0.04218	0.1499
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003087	0.0005617	-5.496	6527	0.00000004033	-0.004663	-0.00151
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002746	0.000005103	5.381	6377	0.00000007683	0.00001313	0.00004178
fixed	NA	male	0.04028	0.02281	1.766	6701	0.07749	-0.02376	0.1043
fixed	NA	count_birth_order2/2	-0.04647	0.04579	-1.015	5745	0.3102	-0.175	0.08206
fixed	NA	count_birth_order1/3	0.03489	0.04414	0.7904	6927	0.4293	-0.08902	0.1588
fixed	NA	count_birth_order2/3	-0.0248	0.04917	-0.5045	6980	0.6139	-0.1628	0.1132
fixed	NA	count_birth_order3/3	-0.132	0.05508	-2.397	6985	0.01656	-0.2866	0.0226
fixed	NA	count_birth_order1/4	0.07574	0.05051	1.499	6981	0.1338	-0.06606	0.2175
fixed	NA	count_birth_order2/4	-0.001802	0.053	-0.03399	6989	0.9729	-0.1506	0.147
fixed	NA	count_birth_order3/4	-0.07465	0.05727	-1.303	6978	0.1925	-0.2354	0.08611
fixed	NA	count_birth_order4/4	-0.022	0.06047	-0.3639	6960	0.7159	-0.1917	0.1477
fixed	NA	count_birth_order1/5	-0.04515	0.05674	-0.7957	6988	0.4262	-0.2044	0.1141
fixed	NA	count_birth_order2/5	0.05356	0.05969	0.8973	6971	0.3696	-0.114	0.2211
fixed	NA	count_birth_order3/5	0.02089	0.06146	0.3399	6951	0.7339	-0.1516	0.1934
fixed	NA	count_birth_order4/5	-0.07004	0.06499	-1.078	6915	0.2812	-0.2525	0.1124
fixed	NA	count_birth_order5/5	-0.05243	0.06614	-0.7927	6904	0.428	-0.2381	0.1332
ran_pars	mother_pidlink	sd__(Intercept)	0.4338	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8693	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	19384	19453	-9682	19364	NA	NA	NA
11	19377	19453	-9678	19355	9.247	1	0.002359
14	19381	19477	-9677	19353	2.051	3	0.5618
20	19384	19521	-9672	19344	9.481	6	0.1483

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.723	0.4969	-3.467	4434	0.0005318	-3.117	-0.3278
fixed	NA	poly(age, 3, raw = TRUE)1	0.2051	0.05798	3.538	4440	0.0004076	0.04237	0.3679
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006628	0.002137	-3.102	4445	0.001934	-0.01263	-0.0006305
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006633	0.00002503	2.649	4448	0.00809	-0.000003944	0.0001366
fixed	NA	male	-0.006547	0.0267	-0.2452	4306	0.8063	-0.0815	0.06841
fixed	NA	sibling_count3	-0.007674	0.03723	-0.2061	3153	0.8367	-0.1122	0.09684
fixed	NA	sibling_count4	-0.0271	0.04045	-0.67	2772	0.5029	-0.1406	0.08644
fixed	NA	sibling_count5	-0.0746	0.04619	-1.615	2502	0.1064	-0.2043	0.05506
ran_pars	mother_pidlink	sd__(Intercept)	0.3812	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8173	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.709	0.4975	-3.435	4433	0.0005984	-3.105	-0.3123
fixed	NA	birth_order	-0.008166	0.01393	-0.586	3998	0.5579	-0.04728	0.03095
fixed	NA	poly(age, 3, raw = TRUE)1	0.2047	0.05799	3.53	4438	0.0004204	0.0419	0.3675
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006604	0.002137	-3.09	4443	0.002015	-0.0126	-0.0006044
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006587	0.00002505	2.63	4446	0.008571	-0.000004438	0.0001362
fixed	NA	male	-0.006218	0.02671	-0.2328	4304	0.8159	-0.08119	0.06875
fixed	NA	sibling_count3	-0.003895	0.0378	-0.103	3214	0.9179	-0.11	0.1022
fixed	NA	sibling_count4	-0.01835	0.04314	-0.4253	2995	0.6707	-0.1394	0.1027
fixed	NA	sibling_count5	-0.06005	0.05247	-1.144	3011	0.2525	-0.2073	0.08724
ran_pars	mother_pidlink	sd__(Intercept)	0.3821	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.817	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.722	0.4979	-3.458	4436	0.0005496	-3.12	-0.3241
fixed	NA	poly(age, 3, raw = TRUE)1	0.204	0.05805	3.515	4439	0.0004447	0.04108	0.367
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006583	0.002139	-3.077	4443	0.002101	-0.01259	-0.0005785
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006572	0.00002507	2.622	4445	0.008782	-0.000004648	0.0001361
fixed	NA	male	-0.005921	0.0267	-0.2217	4298	0.8246	-0.08088	0.06904
fixed	NA	sibling_count3	0.009106	0.03835	0.2375	3333	0.8123	-0.09853	0.1167
fixed	NA	sibling_count4	-0.008766	0.04375	-0.2004	3098	0.8412	-0.1316	0.114
fixed	NA	sibling_count5	-0.05973	0.05332	-1.12	3110	0.2627	-0.2094	0.08995
fixed	NA	birth_order_nonlinear2	0.02484	0.03148	0.7891	3389	0.4301	-0.06352	0.1132
fixed	NA	birth_order_nonlinear3	-0.0727	0.04012	-1.812	3598	0.07004	-0.1853	0.03991
fixed	NA	birth_order_nonlinear4	0.0009335	0.05412	0.01725	3786	0.9862	-0.151	0.1529
fixed	NA	birth_order_nonlinear5	0.01743	0.08369	0.2083	3617	0.835	-0.2175	0.2524
ran_pars	mother_pidlink	sd__(Intercept)	0.3834	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8163	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.725	0.4981	-3.463	4430	0.0005388	-3.123	-0.3269
fixed	NA	poly(age, 3, raw = TRUE)1	0.2031	0.05807	3.498	4432	0.0004726	0.04015	0.3661
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00655	0.00214	-3.061	4436	0.002221	-0.01256	-0.000543
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000653	0.00002508	2.604	4438	0.009257	-0.000005104	0.0001357
fixed	NA	male	-0.007608	0.02672	-0.2847	4291	0.7759	-0.08261	0.06739
fixed	NA	count_birth_order2/2	0.06025	0.05431	1.109	3647	0.2674	-0.0922	0.2127
fixed	NA	count_birth_order1/3	0.04044	0.04845	0.8346	4417	0.404	-0.09557	0.1764
fixed	NA	count_birth_order2/3	0.005604	0.05278	0.1062	4439	0.9154	-0.1425	0.1537
fixed	NA	count_birth_order3/3	-0.03423	0.05885	-0.5815	4432	0.5609	-0.1994	0.131
fixed	NA	count_birth_order1/4	-0.03384	0.05957	-0.5682	4436	0.57	-0.2011	0.1334
fixed	NA	count_birth_order2/4	0.08197	0.06152	1.332	4436	0.1828	-0.09072	0.2547
fixed	NA	count_birth_order3/4	-0.07529	0.06448	-1.168	4412	0.243	-0.2563	0.1057
fixed	NA	count_birth_order4/4	-0.004362	0.06717	-0.06494	4404	0.9482	-0.1929	0.1842
fixed	NA	count_birth_order1/5	0.01059	0.08027	0.1319	4427	0.8951	-0.2147	0.2359
fixed	NA	count_birth_order2/5	-0.0757	0.0861	-0.8793	4373	0.3793	-0.3174	0.166
fixed	NA	count_birth_order3/5	-0.1512	0.08077	-1.872	4370	0.06127	-0.3779	0.07552
fixed	NA	count_birth_order4/5	-0.03478	0.07775	-0.4474	4393	0.6546	-0.253	0.1835
fixed	NA	count_birth_order5/5	-0.03065	0.08022	-0.3821	4371	0.7024	-0.2558	0.1945
ran_pars	mother_pidlink	sd__(Intercept)	0.383	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8165	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11689	11753	-5835	11669	NA	NA	NA
11	11691	11761	-5834	11669	0.3407	1	0.5594
14	11691	11781	-5832	11663	5.603	3	0.1326
20	11698	11826	-5829	11658	5.166	6	0.5227

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.672	0.5143	-3.251	4112	0.001158	-3.116	-0.2285
fixed	NA	poly(age, 3, raw = TRUE)1	0.2008	0.06007	3.343	4117	0.0008354	0.03221	0.3694
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006501	0.002214	-2.936	4123	0.003344	-0.01272	-0.0002855
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006511	0.00002594	2.51	4126	0.01213	-0.000007718	0.0001379
fixed	NA	male	-0.002898	0.02786	-0.104	3986	0.9172	-0.08111	0.07532
fixed	NA	sibling_count3	-0.03883	0.04046	-0.9596	3017	0.3373	-0.1524	0.07476
fixed	NA	sibling_count4	-0.01039	0.04301	-0.2416	2746	0.8091	-0.1311	0.1103
fixed	NA	sibling_count5	-0.07237	0.04605	-1.572	2485	0.1162	-0.2016	0.0569
ran_pars	mother_pidlink	sd__(Intercept)	0.3864	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.82	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.643	0.5148	-3.191	4110	0.00143	-3.088	-0.1975
fixed	NA	birth_order	-0.01829	0.01405	-1.302	3793	0.1929	-0.05772	0.02114
fixed	NA	poly(age, 3, raw = TRUE)1	0.2	0.06006	3.33	4116	0.0008748	0.03144	0.3686
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006456	0.002214	-2.916	4121	0.003569	-0.01267	-0.0002404
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006421	0.00002595	2.474	4124	0.01339	-0.000008632	0.0001371
fixed	NA	male	-0.002367	0.02786	-0.08495	3983	0.9323	-0.08057	0.07584
fixed	NA	sibling_count3	-0.0303	0.041	-0.739	3058	0.4599	-0.1454	0.0848
fixed	NA	sibling_count4	0.008544	0.04542	0.1881	2912	0.8508	-0.119	0.136
fixed	NA	sibling_count5	-0.04233	0.05155	-0.821	2873	0.4117	-0.187	0.1024
ran_pars	mother_pidlink	sd__(Intercept)	0.3883	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8191	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.648	0.5152	-3.199	4114	0.001387	-3.094	-0.2022
fixed	NA	poly(age, 3, raw = TRUE)1	0.1975	0.06011	3.287	4117	0.001022	0.02883	0.3663
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006367	0.002216	-2.873	4121	0.004081	-0.01259	-0.0001472
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006325	0.00002596	2.436	4123	0.01489	-0.000009631	0.0001361
fixed	NA	male	-0.001729	0.02785	-0.06206	3978	0.9505	-0.07991	0.07646
fixed	NA	sibling_count3	-0.0167	0.04155	-0.4019	3160	0.6878	-0.1333	0.09994
fixed	NA	sibling_count4	0.02424	0.04601	0.5268	3006	0.5983	-0.1049	0.1534
fixed	NA	sibling_count5	-0.04462	0.05203	-0.8576	2929	0.3912	-0.1907	0.1014
fixed	NA	birth_order_nonlinear2	0.006307	0.03295	0.1914	3211	0.8482	-0.08619	0.0988
fixed	NA	birth_order_nonlinear3	-0.0971	0.04164	-2.332	3409	0.01978	-0.214	0.0198
fixed	NA	birth_order_nonlinear4	-0.06401	0.0554	-1.155	3557	0.248	-0.2195	0.0915
fixed	NA	birth_order_nonlinear5	0.03111	0.08057	0.3861	3421	0.6995	-0.1951	0.2573
ran_pars	mother_pidlink	sd__(Intercept)	0.3886	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8186	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.699	0.5152	-3.297	4107	0.0009849	-3.145	-0.2525
fixed	NA	poly(age, 3, raw = TRUE)1	0.2	0.06009	3.327	4110	0.0008841	0.03127	0.3686
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006461	0.002215	-2.916	4114	0.003561	-0.01268	-0.0002421
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006434	0.00002597	2.478	4117	0.01326	-0.000008549	0.0001372
fixed	NA	male	-0.003124	0.02785	-0.1122	3965	0.9107	-0.08129	0.07504
fixed	NA	count_birth_order2/2	0.1048	0.05963	1.758	3436	0.07879	-0.06254	0.2722
fixed	NA	count_birth_order1/3	0.04469	0.05273	0.8475	4099	0.3968	-0.1033	0.1927
fixed	NA	count_birth_order2/3	-0.03942	0.05694	-0.6923	4118	0.4888	-0.1992	0.1204
fixed	NA	count_birth_order3/3	-0.04743	0.06392	-0.742	4111	0.4581	-0.2269	0.132
fixed	NA	count_birth_order1/4	0.07906	0.06266	1.262	4115	0.2071	-0.09682	0.2549
fixed	NA	count_birth_order2/4	0.1188	0.06378	1.862	4118	0.06263	-0.06026	0.2978
fixed	NA	count_birth_order3/4	-0.09997	0.06932	-1.442	4088	0.1493	-0.2945	0.0946
fixed	NA	count_birth_order4/4	-0.05328	0.07163	-0.7438	4086	0.457	-0.2544	0.1478
fixed	NA	count_birth_order1/5	-0.01956	0.07394	-0.2645	4118	0.7914	-0.2271	0.188
fixed	NA	count_birth_order2/5	-0.07445	0.07938	-0.9379	4079	0.3483	-0.2973	0.1484
fixed	NA	count_birth_order3/5	-0.08677	0.07702	-1.127	4070	0.26	-0.303	0.1294
fixed	NA	count_birth_order4/5	-0.01681	0.07992	-0.2104	4043	0.8334	-0.2412	0.2075
fixed	NA	count_birth_order5/5	0.02023	0.0795	0.2545	4046	0.7991	-0.2029	0.2434
ran_pars	mother_pidlink	sd__(Intercept)	0.3926	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8164	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	10890	10953	-5435	10870	NA	NA	NA
11	10890	10960	-5434	10868	1.69	1	0.1937
14	10890	10978	-5431	10862	6.354	3	0.09561
20	10891	11018	-5426	10851	10.89	6	0.09181

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.806	0.4996	-3.615	4423	0.0003036	-3.209	-0.4037
fixed	NA	poly(age, 3, raw = TRUE)1	0.212	0.05838	3.631	4428	0.000286	0.04808	0.3758
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006831	0.002155	-3.171	4433	0.001532	-0.01288	-0.0007832
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006775	0.00002529	2.679	4436	0.007417	-0.000003245	0.0001387
fixed	NA	male	-0.003468	0.02666	-0.1301	4304	0.8965	-0.0783	0.07137
fixed	NA	sibling_count3	0.02394	0.03657	0.6547	3158	0.5127	-0.07872	0.1266
fixed	NA	sibling_count4	-0.01511	0.03993	-0.3784	2796	0.7051	-0.1272	0.09697
fixed	NA	sibling_count5	-0.02829	0.0471	-0.6006	2438	0.5481	-0.1605	0.1039
ran_pars	mother_pidlink	sd__(Intercept)	0.3744	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8164	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.784	0.5002	-3.567	4422	0.0003648	-3.188	-0.3802
fixed	NA	birth_order	-0.01327	0.01407	-0.9433	3979	0.3456	-0.05276	0.02622
fixed	NA	poly(age, 3, raw = TRUE)1	0.2113	0.05839	3.619	4427	0.0002989	0.04741	0.3752
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006794	0.002155	-3.153	4431	0.001628	-0.01284	-0.0007451
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006705	0.0000253	2.65	4434	0.008086	-0.000003982	0.0001381
fixed	NA	male	-0.00305	0.02666	-0.1144	4300	0.9089	-0.07789	0.07179
fixed	NA	sibling_count3	0.0301	0.03716	0.8101	3214	0.418	-0.07421	0.1344
fixed	NA	sibling_count4	-0.0009211	0.04269	-0.02157	3032	0.9828	-0.1208	0.1189
fixed	NA	sibling_count5	-0.005691	0.05287	-0.1076	2892	0.9143	-0.1541	0.1427
ran_pars	mother_pidlink	sd__(Intercept)	0.376	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8158	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.787	0.5006	-3.569	4424	0.0003622	-3.192	-0.3814
fixed	NA	poly(age, 3, raw = TRUE)1	0.2092	0.05844	3.58	4427	0.0003477	0.04516	0.3733
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006723	0.002157	-3.117	4430	0.00184	-0.01278	-0.0006681
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006633	0.00002532	2.619	4432	0.008841	-0.000004754	0.0001374
fixed	NA	male	-0.003809	0.02666	-0.1429	4293	0.8864	-0.07864	0.07102
fixed	NA	sibling_count3	0.04375	0.03773	1.16	3336	0.2463	-0.06216	0.1497
fixed	NA	sibling_count4	0.004315	0.04332	0.09961	3136	0.9207	-0.1173	0.1259
fixed	NA	sibling_count5	-0.006141	0.05392	-0.1139	2999	0.9093	-0.1575	0.1452
fixed	NA	birth_order_nonlinear2	0.01023	0.0312	0.3278	3393	0.7431	-0.07736	0.09782
fixed	NA	birth_order_nonlinear3	-0.08294	0.03988	-2.08	3581	0.03761	-0.1949	0.029
fixed	NA	birth_order_nonlinear4	0.006899	0.05504	0.1253	3766	0.9003	-0.1476	0.1614
fixed	NA	birth_order_nonlinear5	-0.02859	0.08942	-0.3197	3693	0.7492	-0.2796	0.2224
ran_pars	mother_pidlink	sd__(Intercept)	0.3773	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.815	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.789	0.5009	-3.571	4418	0.000359	-3.195	-0.3828
fixed	NA	poly(age, 3, raw = TRUE)1	0.2077	0.05847	3.552	4421	0.0003864	0.04356	0.3718
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006655	0.002158	-3.084	4424	0.002056	-0.01271	-0.0005975
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006538	0.00002534	2.58	4426	0.009902	-0.000005744	0.0001365
fixed	NA	male	-0.004814	0.02667	-0.1805	4286	0.8568	-0.07968	0.07006
fixed	NA	count_birth_order2/2	0.05052	0.05269	0.9587	3606	0.3378	-0.09739	0.1984
fixed	NA	count_birth_order1/3	0.06193	0.04767	1.299	4404	0.194	-0.07189	0.1958
fixed	NA	count_birth_order2/3	0.03904	0.05254	0.7431	4427	0.4575	-0.1084	0.1865
fixed	NA	count_birth_order3/3	0.003967	0.05765	0.06881	4417	0.9451	-0.1579	0.1658
fixed	NA	count_birth_order1/4	0.01146	0.0596	0.1923	4426	0.8475	-0.1558	0.1788
fixed	NA	count_birth_order2/4	0.05606	0.06117	0.9165	4420	0.3595	-0.1156	0.2278
fixed	NA	count_birth_order3/4	-0.07676	0.06355	-1.208	4396	0.2272	-0.2552	0.1016
fixed	NA	count_birth_order4/4	0.01228	0.06721	0.1827	4382	0.8551	-0.1764	0.2009
fixed	NA	count_birth_order1/5	0.07351	0.07983	0.9209	4421	0.3572	-0.1506	0.2976
fixed	NA	count_birth_order2/5	-0.03273	0.08845	-0.37	4355	0.7114	-0.281	0.2155
fixed	NA	count_birth_order3/5	-0.1296	0.08443	-1.535	4351	0.1247	-0.3667	0.1074
fixed	NA	count_birth_order4/5	0.03266	0.08106	0.4029	4375	0.687	-0.1949	0.2602
fixed	NA	count_birth_order5/5	-0.02134	0.08554	-0.2495	4354	0.803	-0.2615	0.2188
ran_pars	mother_pidlink	sd__(Intercept)	0.3771	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8153	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11621	11685	-5800	11601	NA	NA	NA
11	11622	11692	-5800	11600	0.884	1	0.3471
14	11623	11712	-5797	11595	5.114	3	0.1636
20	11631	11759	-5795	11591	3.846	6	0.6974

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Immediate word recall

birthorder <- birthorder %>% mutate(outcome = words_immediate)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.04395	0.1917	0.2292	6960	0.8187	-0.4942	0.5821
fixed	NA	poly(age, 3, raw = TRUE)1	0.04144	0.01846	2.244	6864	0.02483	-0.01039	0.09326
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001579	0.0005406	-2.92	6729	0.003513	-0.003096	-0.000061
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001075	0.000004915	2.187	6610	0.02874	-0.000003045	0.00002455
fixed	NA	male	-0.08657	0.0219	-3.953	6853	0.00007805	-0.148	-0.02509
fixed	NA	sibling_count3	0.02118	0.03276	0.6466	4982	0.5179	-0.07077	0.1131
fixed	NA	sibling_count4	0.01727	0.03395	0.5087	4558	0.611	-0.07803	0.1126
fixed	NA	sibling_count5	-0.01697	0.03553	-0.4778	4111	0.6328	-0.1167	0.08275
ran_pars	mother_pidlink	sd__(Intercept)	0.4299	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8404	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.04735	0.1918	0.2469	6947	0.805	-0.4911	0.5858
fixed	NA	birth_order	-0.006297	0.01078	-0.5841	5827	0.5592	-0.03656	0.02397
fixed	NA	poly(age, 3, raw = TRUE)1	0.04201	0.01849	2.272	6882	0.02311	-0.009889	0.0939
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001594	0.0005413	-2.945	6739	0.003244	-0.003113	-0.0000745
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001085	0.000004918	2.206	6616	0.02739	-0.000002954	0.00002466
fixed	NA	male	-0.08641	0.0219	-3.945	6851	0.00008066	-0.1479	-0.02492
fixed	NA	sibling_count3	0.02332	0.03296	0.7075	5096	0.4793	-0.06921	0.1159
fixed	NA	sibling_count4	0.02237	0.03505	0.6381	5040	0.5234	-0.07603	0.1208
fixed	NA	sibling_count5	-0.00868	0.03826	-0.2269	5080	0.8205	-0.1161	0.09871
ran_pars	mother_pidlink	sd__(Intercept)	0.4299	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8404	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.0379	0.1923	0.1971	6960	0.8437	-0.5018	0.5776
fixed	NA	poly(age, 3, raw = TRUE)1	0.0421	0.0185	2.276	6867	0.0229	-0.009833	0.09404
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001596	0.0005419	-2.945	6714	0.003245	-0.003117	-0.00007453
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001086	0.000004927	2.204	6577	0.02754	-0.00000297	0.00002469
fixed	NA	male	-0.08641	0.02191	-3.944	6849	0.00008098	-0.1479	-0.02491
fixed	NA	sibling_count3	0.02687	0.03341	0.8044	5287	0.4212	-0.0669	0.1206
fixed	NA	sibling_count4	0.02511	0.03554	0.7064	5249	0.4799	-0.07466	0.1249
fixed	NA	sibling_count5	-0.007966	0.03855	-0.2066	5227	0.8363	-0.1162	0.1002
fixed	NA	birth_order_nonlinear2	-0.001198	0.02559	-0.04681	5785	0.9627	-0.07303	0.07063
fixed	NA	birth_order_nonlinear3	-0.02758	0.03281	-0.8407	5610	0.4006	-0.1197	0.06452
fixed	NA	birth_order_nonlinear4	-0.01404	0.04285	-0.3276	5551	0.7432	-0.1343	0.1063
fixed	NA	birth_order_nonlinear5	-0.01168	0.06223	-0.1876	5345	0.8512	-0.1864	0.163
ran_pars	mother_pidlink	sd__(Intercept)	0.4295	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8408	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.03058	0.1927	0.1587	6959	0.8739	-0.5102	0.5714
fixed	NA	poly(age, 3, raw = TRUE)1	0.04236	0.0185	2.289	6862	0.02211	-0.009586	0.0943
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001606	0.000542	-2.964	6705	0.003052	-0.003128	-0.00008481
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001098	0.000004928	2.227	6564	0.02595	-0.000002856	0.00002481
fixed	NA	male	-0.08653	0.02192	-3.948	6842	0.00007951	-0.1481	-0.02501
fixed	NA	count_birth_order2/2	0.0149	0.04371	0.3408	5856	0.7332	-0.1078	0.1376
fixed	NA	count_birth_order1/3	0.03031	0.0424	0.7148	7068	0.4748	-0.08872	0.1493
fixed	NA	count_birth_order2/3	0.0312	0.04732	0.6592	7127	0.5098	-0.1016	0.164
fixed	NA	count_birth_order3/3	0.01083	0.05295	0.2045	7136	0.8379	-0.1378	0.1595
fixed	NA	count_birth_order1/4	0.003951	0.04836	0.0817	7127	0.9349	-0.1318	0.1397
fixed	NA	count_birth_order2/4	0.05633	0.05075	1.11	7138	0.267	-0.08611	0.1988
fixed	NA	count_birth_order3/4	0.004922	0.05507	0.08938	7128	0.9288	-0.1497	0.1595
fixed	NA	count_birth_order4/4	0.02358	0.05833	0.4042	7108	0.6861	-0.1402	0.1873
fixed	NA	count_birth_order1/5	0.05911	0.05476	1.079	7137	0.2805	-0.09461	0.2128
fixed	NA	count_birth_order2/5	-0.05904	0.05742	-1.028	7123	0.3039	-0.2202	0.1021
fixed	NA	count_birth_order3/5	-0.03787	0.05903	-0.6415	7104	0.5212	-0.2036	0.1278
fixed	NA	count_birth_order4/5	-0.02387	0.06248	-0.382	7066	0.7025	-0.1993	0.1515
fixed	NA	count_birth_order5/5	-0.0147	0.06385	-0.2302	7052	0.8179	-0.1939	0.1645
ran_pars	mother_pidlink	sd__(Intercept)	0.429	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8411	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	19361	19430	-9670	19341	NA	NA	NA
11	19363	19438	-9670	19341	0.3416	1	0.5589
14	19368	19464	-9670	19340	0.4585	3	0.9279
20	19376	19513	-9668	19336	4.406	6	0.6219

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3288	0.4976	0.6608	4502	0.5088	-1.068	1.726
fixed	NA	poly(age, 3, raw = TRUE)1	0.005066	0.05809	0.08722	4505	0.9305	-0.158	0.1681
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0000285	0.002141	-0.01331	4507	0.9894	-0.006039	0.005982
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003809	0.00002509	-0.1518	4507	0.8794	-0.00007424	0.00006662
fixed	NA	male	-0.1418	0.02676	-5.301	4424	0.000000121	-0.2169	-0.06672
fixed	NA	sibling_count3	0.03656	0.03684	0.9923	3311	0.3211	-0.06686	0.14
fixed	NA	sibling_count4	-0.08719	0.03984	-2.188	2907	0.02872	-0.199	0.02465
fixed	NA	sibling_count5	-0.1082	0.04556	-2.374	2596	0.01765	-0.2361	0.01971
ran_pars	mother_pidlink	sd__(Intercept)	0.3383	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8393	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3524	0.4982	0.7074	4501	0.4794	-1.046	1.751
fixed	NA	birth_order	-0.01366	0.01402	-0.9748	4148	0.3297	-0.05301	0.02568
fixed	NA	poly(age, 3, raw = TRUE)1	0.004233	0.0581	0.07286	4504	0.9419	-0.1588	0.1673
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001682	0.002142	0.007852	4506	0.9937	-0.005995	0.006029
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004621	0.00002511	-0.1841	4506	0.854	-0.00007509	0.00006585
fixed	NA	male	-0.1414	0.02676	-5.283	4422	0.0000001334	-0.2165	-0.06625
fixed	NA	sibling_count3	0.04283	0.03741	1.145	3372	0.2523	-0.06217	0.1478
fixed	NA	sibling_count4	-0.0727	0.04253	-1.709	3135	0.08749	-0.1921	0.04669
fixed	NA	sibling_count5	-0.08396	0.0519	-1.618	3112	0.1059	-0.2297	0.06174
ran_pars	mother_pidlink	sd__(Intercept)	0.3388	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8391	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3302	0.4988	0.6619	4501	0.5081	-1.07	1.73
fixed	NA	poly(age, 3, raw = TRUE)1	0.005404	0.05817	0.0929	4502	0.926	-0.1579	0.1687
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002355	0.002144	-0.01098	4503	0.9912	-0.006043	0.005996
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004222	0.00002513	-0.168	4503	0.8666	-0.00007477	0.00006633
fixed	NA	male	-0.1411	0.02677	-5.271	4418	0.0000001418	-0.2163	-0.06597
fixed	NA	sibling_count3	0.03586	0.03798	0.9441	3490	0.3452	-0.07076	0.1425
fixed	NA	sibling_count4	-0.07382	0.04316	-1.71	3237	0.08729	-0.195	0.04733
fixed	NA	sibling_count5	-0.08279	0.05278	-1.568	3206	0.1169	-0.231	0.06538
fixed	NA	birth_order_nonlinear2	-0.01819	0.03171	-0.5736	3587	0.5663	-0.1072	0.07081
fixed	NA	birth_order_nonlinear3	0.003378	0.04045	0.08351	3801	0.9335	-0.1102	0.1169
fixed	NA	birth_order_nonlinear4	-0.06973	0.05442	-1.281	3984	0.2001	-0.2225	0.08303
fixed	NA	birth_order_nonlinear5	-0.06116	0.08469	-0.7222	3838	0.4702	-0.2989	0.1766
ran_pars	mother_pidlink	sd__(Intercept)	0.3392	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8391	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3367	0.4992	0.6745	4495	0.5001	-1.065	1.738
fixed	NA	poly(age, 3, raw = TRUE)1	0.005142	0.05822	0.08833	4496	0.9296	-0.1583	0.1686
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002064	0.002146	-0.009616	4497	0.9923	-0.006045	0.006004
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004154	0.00002516	-0.1651	4497	0.8689	-0.00007477	0.00006647
fixed	NA	male	-0.1405	0.0268	-5.242	4412	0.0000001659	-0.2157	-0.06526
fixed	NA	count_birth_order2/2	-0.02885	0.05451	-0.5292	3803	0.5967	-0.1818	0.1242
fixed	NA	count_birth_order1/3	0.03917	0.04843	0.8089	4484	0.4186	-0.09676	0.1751
fixed	NA	count_birth_order2/3	0.02527	0.05285	0.4781	4497	0.6326	-0.1231	0.1736
fixed	NA	count_birth_order3/3	0.006197	0.05903	0.105	4491	0.9164	-0.1595	0.1719
fixed	NA	count_birth_order1/4	-0.09156	0.05942	-1.541	4494	0.1234	-0.2583	0.07522
fixed	NA	count_birth_order2/4	-0.1156	0.06128	-1.886	4496	0.05938	-0.2876	0.05646
fixed	NA	count_birth_order3/4	-0.04838	0.06465	-0.7484	4479	0.4543	-0.2298	0.1331
fixed	NA	count_birth_order4/4	-0.1291	0.06724	-1.921	4475	0.05485	-0.3179	0.05961
fixed	NA	count_birth_order1/5	-0.1032	0.08074	-1.278	4490	0.2012	-0.3299	0.1234
fixed	NA	count_birth_order2/5	-0.0768	0.08614	-0.8916	4459	0.3727	-0.3186	0.165
fixed	NA	count_birth_order3/5	-0.06275	0.08069	-0.7777	4456	0.4368	-0.2892	0.1637
fixed	NA	count_birth_order4/5	-0.1806	0.0777	-2.325	4467	0.02014	-0.3987	0.03748
fixed	NA	count_birth_order5/5	-0.1476	0.08078	-1.827	4450	0.06781	-0.3743	0.07919
ran_pars	mother_pidlink	sd__(Intercept)	0.3383	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8399	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11889	11953	-5935	11869	NA	NA	NA
11	11890	11961	-5934	11868	0.9504	1	0.3296
14	11895	11985	-5933	11867	1.325	3	0.7232
20	11905	12034	-5933	11865	1.494	6	0.9599

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4567	0.5104	0.8949	4176	0.3709	-0.9759	1.889
fixed	NA	poly(age, 3, raw = TRUE)1	-0.009468	0.05963	-0.1588	4179	0.8738	-0.1768	0.1579
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004898	0.002199	0.2227	4182	0.8237	-0.005682	0.006662
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001023	0.00002577	-0.3971	4183	0.6913	-0.00008258	0.00006211
fixed	NA	male	-0.1367	0.02765	-4.944	4092	0.000000797	-0.2143	-0.05909
fixed	NA	sibling_count3	0.03155	0.03975	0.7937	3150	0.4274	-0.08004	0.1431
fixed	NA	sibling_count4	-0.06652	0.04207	-1.581	2868	0.1139	-0.1846	0.05157
fixed	NA	sibling_count5	-0.04892	0.04517	-1.083	2575	0.2788	-0.1757	0.07787
ran_pars	mother_pidlink	sd__(Intercept)	0.3464	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8322	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4924	0.5108	0.9639	4174	0.3351	-0.9415	1.926
fixed	NA	birth_order	-0.02118	0.01399	-1.514	3917	0.1302	-0.06045	0.01809
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01057	0.05962	-0.1772	4178	0.8594	-0.1779	0.1568
fixed	NA	poly(age, 3, raw = TRUE)2	0.0005504	0.002199	0.2503	4181	0.8023	-0.005622	0.006723
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001137	0.00002578	-0.4411	4182	0.6592	-0.00008373	0.00006099
fixed	NA	male	-0.1363	0.02765	-4.928	4091	0.0000008635	-0.2139	-0.05865
fixed	NA	sibling_count3	0.04126	0.04026	1.025	3193	0.3056	-0.07177	0.1543
fixed	NA	sibling_count4	-0.04482	0.04444	-1.008	3035	0.3133	-0.1696	0.07994
fixed	NA	sibling_count5	-0.01422	0.05065	-0.2809	2967	0.7788	-0.1564	0.1279
ran_pars	mother_pidlink	sd__(Intercept)	0.3468	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8319	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4382	0.5113	0.8569	4175	0.3915	-0.9972	1.873
fixed	NA	poly(age, 3, raw = TRUE)1	-0.007412	0.05969	-0.1242	4177	0.9012	-0.175	0.1601
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004352	0.002201	0.1977	4179	0.8433	-0.005744	0.006614
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000101	0.0000258	-0.3915	4179	0.6955	-0.00008253	0.00006233
fixed	NA	male	-0.136	0.02766	-4.918	4087	0.0000009066	-0.2137	-0.0584
fixed	NA	sibling_count3	0.03449	0.04084	0.8446	3292	0.3984	-0.08015	0.1491
fixed	NA	sibling_count4	-0.0512	0.04505	-1.136	3124	0.2559	-0.1777	0.07526
fixed	NA	sibling_count5	-0.006314	0.05116	-0.1234	3020	0.9018	-0.1499	0.1373
fixed	NA	birth_order_nonlinear2	-0.001131	0.03283	-0.03445	3370	0.9725	-0.09328	0.09102
fixed	NA	birth_order_nonlinear3	-0.01076	0.04158	-0.2587	3579	0.7959	-0.1275	0.106
fixed	NA	birth_order_nonlinear4	-0.05773	0.05512	-1.047	3728	0.295	-0.2125	0.09699
fixed	NA	birth_order_nonlinear5	-0.1495	0.08072	-1.852	3605	0.06414	-0.3761	0.07711
ran_pars	mother_pidlink	sd__(Intercept)	0.3473	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8319	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4422	0.5119	0.8638	4169	0.3877	-0.9948	1.879
fixed	NA	poly(age, 3, raw = TRUE)1	-0.008889	0.05974	-0.1488	4171	0.8817	-0.1766	0.1588
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004942	0.002203	0.2243	4173	0.8225	-0.005691	0.006679
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001083	0.00002583	-0.4191	4173	0.6752	-0.00008335	0.00006169
fixed	NA	male	-0.1364	0.02769	-4.928	4080	0.0000008658	-0.2142	-0.05872
fixed	NA	count_birth_order2/2	0.0214	0.05936	0.3605	3566	0.7185	-0.1452	0.188
fixed	NA	count_birth_order1/3	0.05195	0.05221	0.9949	4161	0.3198	-0.09462	0.1985
fixed	NA	count_birth_order2/3	0.03827	0.05659	0.6762	4173	0.4989	-0.1206	0.1971
fixed	NA	count_birth_order3/3	0.01518	0.06364	0.2386	4167	0.8114	-0.1635	0.1938
fixed	NA	count_birth_order1/4	-0.06525	0.06198	-1.053	4170	0.2925	-0.2392	0.1087
fixed	NA	count_birth_order2/4	-0.05804	0.06282	-0.924	4173	0.3556	-0.2344	0.1183
fixed	NA	count_birth_order3/4	-0.03496	0.06891	-0.5074	4152	0.6119	-0.2284	0.1585
fixed	NA	count_birth_order4/4	-0.06964	0.07108	-0.9797	4152	0.3273	-0.2692	0.1299
fixed	NA	count_birth_order1/5	0.03193	0.07369	0.4334	4173	0.6648	-0.1749	0.2388
fixed	NA	count_birth_order2/5	0.001311	0.07884	0.01663	4150	0.9867	-0.22	0.2226
fixed	NA	count_birth_order3/5	-0.009253	0.07655	-0.1209	4143	0.9038	-0.2241	0.2056
fixed	NA	count_birth_order4/5	-0.09757	0.07925	-1.231	4124	0.2183	-0.32	0.1249
fixed	NA	count_birth_order5/5	-0.149	0.07939	-1.876	4122	0.06067	-0.3718	0.07388
ran_pars	mother_pidlink	sd__(Intercept)	0.3473	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8324	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11002	11065	-5491	10982	NA	NA	NA
11	11002	11071	-5490	10980	2.294	1	0.1299
14	11006	11095	-5489	10978	1.804	3	0.614
20	11016	11143	-5488	10976	1.574	6	0.9544

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.382	0.5014	0.7617	4487	0.4463	-1.026	1.79
fixed	NA	poly(age, 3, raw = TRUE)1	-0.002567	0.05861	-0.0438	4490	0.9651	-0.1671	0.162
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003015	0.002164	0.1393	4492	0.8892	-0.005772	0.006375
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000008284	0.0000254	-0.3261	4492	0.7444	-0.00007959	0.00006302
fixed	NA	male	-0.131	0.02676	-4.895	4408	0.000001017	-0.2061	-0.05589
fixed	NA	sibling_count3	0.01628	0.03633	0.448	3294	0.6542	-0.08571	0.1183
fixed	NA	sibling_count4	-0.08339	0.03951	-2.11	2908	0.03491	-0.1943	0.02753
fixed	NA	sibling_count5	-0.1064	0.04665	-2.282	2514	0.02259	-0.2374	0.02451
ran_pars	mother_pidlink	sd__(Intercept)	0.3393	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8372	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4022	0.502	0.8012	4486	0.4231	-1.007	1.811
fixed	NA	birth_order	-0.01191	0.01418	-0.8402	4114	0.4008	-0.05171	0.02788
fixed	NA	poly(age, 3, raw = TRUE)1	-0.003238	0.05862	-0.05524	4489	0.9559	-0.1678	0.1613
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003388	0.002164	0.1565	4491	0.8756	-0.005736	0.006414
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000008964	0.00002542	-0.3527	4491	0.7243	-0.00008031	0.00006238
fixed	NA	male	-0.1307	0.02677	-4.883	4406	0.000001082	-0.2058	-0.05557
fixed	NA	sibling_count3	0.02174	0.03691	0.589	3352	0.5559	-0.08188	0.1254
fixed	NA	sibling_count4	-0.0708	0.04226	-1.675	3148	0.09399	-0.1894	0.04783
fixed	NA	sibling_count5	-0.08626	0.05247	-1.644	2976	0.1003	-0.2335	0.06102
ran_pars	mother_pidlink	sd__(Intercept)	0.3395	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8372	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3786	0.5026	0.7534	4486	0.4513	-1.032	1.789
fixed	NA	poly(age, 3, raw = TRUE)1	-0.001463	0.05869	-0.02493	4487	0.9801	-0.1662	0.1633
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002766	0.002167	0.1277	4488	0.8984	-0.005805	0.006358
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000008318	0.00002544	-0.327	4488	0.7437	-0.00007974	0.0000631
fixed	NA	male	-0.1301	0.02677	-4.861	4401	0.000001209	-0.2053	-0.05499
fixed	NA	sibling_count3	0.01266	0.03751	0.3374	3474	0.7359	-0.09264	0.118
fixed	NA	sibling_count4	-0.07595	0.0429	-1.77	3251	0.07676	-0.1964	0.04447
fixed	NA	sibling_count5	-0.08292	0.05354	-1.549	3081	0.1215	-0.2332	0.06737
fixed	NA	birth_order_nonlinear2	-0.02296	0.03146	-0.7298	3568	0.4656	-0.1113	0.06535
fixed	NA	birth_order_nonlinear3	0.01392	0.04024	0.346	3760	0.7294	-0.09902	0.1269
fixed	NA	birth_order_nonlinear4	-0.05674	0.05549	-1.023	3947	0.3066	-0.2125	0.09902
fixed	NA	birth_order_nonlinear5	-0.08854	0.09055	-0.9778	3882	0.3282	-0.3427	0.1656
ran_pars	mother_pidlink	sd__(Intercept)	0.3409	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8368	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3787	0.503	0.7529	4480	0.4515	-1.033	1.791
fixed	NA	poly(age, 3, raw = TRUE)1	-0.001063	0.05874	-0.0181	4481	0.9856	-0.166	0.1638
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002579	0.002169	0.1189	4482	0.9053	-0.00583	0.006345
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000008047	0.00002547	-0.316	4482	0.752	-0.00007954	0.00006344
fixed	NA	male	-0.1298	0.0268	-4.842	4395	0.000001332	-0.205	-0.05453
fixed	NA	count_birth_order2/2	-0.03177	0.05298	-0.5996	3754	0.5488	-0.1805	0.117
fixed	NA	count_birth_order1/3	0.00818	0.04777	0.1712	4467	0.864	-0.1259	0.1423
fixed	NA	count_birth_order2/3	-0.003009	0.05274	-0.05706	4482	0.9545	-0.1511	0.145
fixed	NA	count_birth_order3/3	0.01269	0.05789	0.2192	4474	0.8265	-0.1498	0.1752
fixed	NA	count_birth_order1/4	-0.07253	0.05958	-1.217	4481	0.2236	-0.2398	0.09472
fixed	NA	count_birth_order2/4	-0.1148	0.06107	-1.879	4479	0.06025	-0.2862	0.05665
fixed	NA	count_birth_order3/4	-0.05902	0.06386	-0.9243	4460	0.3554	-0.2383	0.1202
fixed	NA	count_birth_order4/4	-0.1354	0.06754	-2.004	4451	0.04511	-0.3249	0.05422
fixed	NA	count_birth_order1/5	-0.1097	0.08044	-1.363	4479	0.1729	-0.3355	0.1161
fixed	NA	count_birth_order2/5	-0.09573	0.08861	-1.08	4439	0.28	-0.3445	0.153
fixed	NA	count_birth_order3/5	-0.05593	0.08442	-0.6626	4434	0.5076	-0.2929	0.181
fixed	NA	count_birth_order4/5	-0.1428	0.08132	-1.756	4448	0.07909	-0.3711	0.08543
fixed	NA	count_birth_order5/5	-0.1742	0.08632	-2.018	4431	0.04363	-0.4165	0.06809
ran_pars	mother_pidlink	sd__(Intercept)	0.3402	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8376	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11833	11897	-5907	11813	NA	NA	NA
11	11835	11905	-5906	11813	0.7062	1	0.4007
14	11839	11928	-5905	11811	1.968	3	0.5792
20	11850	11978	-5905	11810	0.4314	6	0.9986

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Delayed word recall

birthorder <- birthorder %>% mutate(outcome = words_delayed)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1677	0.1929	0.8695	6924	0.3846	-0.3737	0.709
fixed	NA	poly(age, 3, raw = TRUE)1	0.03045	0.01856	1.64	6814	0.101	-0.02166	0.08255
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001281	0.0005433	-2.358	6667	0.01842	-0.002806	0.0002442
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000719	0.000004938	1.456	6541	0.1454	-0.000006671	0.00002105
fixed	NA	male	-0.07999	0.02212	-3.617	6905	0.0003002	-0.1421	-0.01791
fixed	NA	sibling_count3	0.04555	0.03279	1.389	5003	0.1648	-0.04648	0.1376
fixed	NA	sibling_count4	0.02904	0.03394	0.8554	4558	0.3923	-0.06624	0.1243
fixed	NA	sibling_count5	-0.00268	0.03548	-0.07554	4089	0.9398	-0.1023	0.09691
ran_pars	mother_pidlink	sd__(Intercept)	0.4083	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8571	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1646	0.1929	0.8529	6911	0.3938	-0.377	0.7062
fixed	NA	birth_order	0.006134	0.01092	0.5618	5892	0.5743	-0.02451	0.03678
fixed	NA	poly(age, 3, raw = TRUE)1	0.02988	0.01859	1.608	6834	0.108	-0.0223	0.08207
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001266	0.000544	-2.327	6679	0.01998	-0.002793	0.000261
fixed	NA	poly(age, 3, raw = TRUE)3	0.000007093	0.000004941	1.435	6547	0.1512	-0.000006777	0.00002096
fixed	NA	male	-0.08016	0.02212	-3.624	6903	0.0002924	-0.1422	-0.01807
fixed	NA	sibling_count3	0.04344	0.033	1.316	5121	0.1881	-0.04919	0.1361
fixed	NA	sibling_count4	0.02405	0.03509	0.6854	5052	0.4931	-0.07444	0.1225
fixed	NA	sibling_count5	-0.01078	0.0383	-0.2815	5080	0.7783	-0.1183	0.09673
ran_pars	mother_pidlink	sd__(Intercept)	0.4083	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8572	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.156	0.1934	0.8064	6926	0.4201	-0.3869	0.6988
fixed	NA	poly(age, 3, raw = TRUE)1	0.03053	0.0186	1.641	6820	0.1008	-0.02169	0.08275
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001286	0.0005446	-2.361	6654	0.01824	-0.002814	0.0002427
fixed	NA	poly(age, 3, raw = TRUE)3	0.000007278	0.000004949	1.471	6510	0.1414	-0.000006614	0.00002117
fixed	NA	male	-0.08019	0.02212	-3.625	6900	0.000291	-0.1423	-0.0181
fixed	NA	sibling_count3	0.04936	0.03346	1.475	5316	0.1402	-0.04456	0.1433
fixed	NA	sibling_count4	0.03168	0.03559	0.8901	5267	0.3735	-0.06823	0.1316
fixed	NA	sibling_count5	-0.00781	0.0386	-0.2023	5233	0.8397	-0.1162	0.1005
fixed	NA	birth_order_nonlinear2	0.02941	0.02591	1.135	5840	0.2564	-0.04332	0.1021
fixed	NA	birth_order_nonlinear3	-0.00886	0.03324	-0.2666	5688	0.7898	-0.1022	0.08444
fixed	NA	birth_order_nonlinear4	0.01245	0.04341	0.2867	5640	0.7744	-0.1094	0.1343
fixed	NA	birth_order_nonlinear5	0.05994	0.06307	0.9503	5447	0.342	-0.1171	0.237
ran_pars	mother_pidlink	sd__(Intercept)	0.4081	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8573	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1607	0.1938	0.8292	6927	0.407	-0.3833	0.7048
fixed	NA	poly(age, 3, raw = TRUE)1	0.03059	0.01861	1.644	6817	0.1003	-0.02164	0.08282
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001282	0.0005447	-2.353	6649	0.01867	-0.002811	0.0002475
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000719	0.000004951	1.452	6501	0.1465	-0.000006708	0.00002109
fixed	NA	male	-0.07979	0.02213	-3.606	6891	0.0003134	-0.1419	-0.01767
fixed	NA	count_birth_order2/2	0.00907	0.04424	0.205	5888	0.8376	-0.1151	0.1333
fixed	NA	count_birth_order1/3	0.06095	0.04269	1.428	7081	0.1534	-0.05888	0.1808
fixed	NA	count_birth_order2/3	0.04536	0.04767	0.9516	7129	0.3414	-0.08844	0.1792
fixed	NA	count_birth_order3/3	0.02921	0.05336	0.5474	7136	0.5841	-0.1206	0.179
fixed	NA	count_birth_order1/4	0.0005352	0.04871	0.01099	7129	0.9912	-0.1362	0.1373
fixed	NA	count_birth_order2/4	0.09781	0.05113	1.913	7138	0.05577	-0.0457	0.2413
fixed	NA	count_birth_order3/4	0.01087	0.05551	0.1958	7130	0.8447	-0.1449	0.1667
fixed	NA	count_birth_order4/4	0.01601	0.05882	0.2722	7113	0.7855	-0.1491	0.1811
fixed	NA	count_birth_order1/5	-0.04564	0.05519	-0.8269	7137	0.4083	-0.2006	0.1093
fixed	NA	count_birth_order2/5	0.02042	0.05788	0.3528	7125	0.7243	-0.1421	0.1829
fixed	NA	count_birth_order3/5	-0.01535	0.05952	-0.2579	7109	0.7965	-0.1824	0.1517
fixed	NA	count_birth_order4/5	0.02189	0.06302	0.3473	7077	0.7284	-0.155	0.1988
fixed	NA	count_birth_order5/5	0.04514	0.06441	0.7008	7065	0.4834	-0.1357	0.2259
ran_pars	mother_pidlink	sd__(Intercept)	0.4088	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8572	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	19471	19540	-9726	19451	NA	NA	NA
11	19473	19549	-9725	19451	0.3159	1	0.5741
14	19477	19573	-9724	19449	2.245	3	0.5232
20	19485	19623	-9723	19445	3.571	6	0.7345

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6686	0.5126	1.304	4500	0.1921	-0.7702	2.108
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03466	0.05984	-0.5792	4504	0.5625	-0.2026	0.1333
fixed	NA	poly(age, 3, raw = TRUE)2	0.00142	0.002206	0.6438	4506	0.5198	-0.004772	0.007612
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000226	0.00002585	-0.8744	4507	0.3819	-0.00009516	0.00004996
fixed	NA	male	-0.1245	0.02755	-4.518	4415	0.000006407	-0.2018	-0.04713
fixed	NA	sibling_count3	0.02766	0.03805	0.7269	3326	0.4673	-0.07916	0.1345
fixed	NA	sibling_count4	-0.03875	0.04118	-0.9412	2935	0.3467	-0.1543	0.07683
fixed	NA	sibling_count5	-0.05762	0.04711	-1.223	2635	0.2214	-0.1898	0.07462
ran_pars	mother_pidlink	sd__(Intercept)	0.3611	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.86	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6651	0.5133	1.296	4499	0.1951	-0.7757	2.106
fixed	NA	birth_order	0.002077	0.01443	0.144	4145	0.8855	-0.03841	0.04257
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03453	0.05985	-0.577	4503	0.564	-0.2025	0.1335
fixed	NA	poly(age, 3, raw = TRUE)2	0.001413	0.002206	0.6405	4505	0.5219	-0.00478	0.007607
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002248	0.00002587	-0.8691	4506	0.3848	-0.00009509	0.00005013
fixed	NA	male	-0.1245	0.02755	-4.519	4414	0.000006366	-0.2019	-0.04718
fixed	NA	sibling_count3	0.02671	0.03863	0.6914	3387	0.4894	-0.08173	0.1352
fixed	NA	sibling_count4	-0.04096	0.04394	-0.9323	3159	0.3513	-0.1643	0.08237
fixed	NA	sibling_count5	-0.0613	0.05362	-1.143	3143	0.253	-0.2118	0.08922
ran_pars	mother_pidlink	sd__(Intercept)	0.3611	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8601	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6623	0.5138	1.289	4500	0.1975	-0.7799	2.104
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03482	0.05992	-0.5812	4502	0.5612	-0.203	0.1334
fixed	NA	poly(age, 3, raw = TRUE)2	0.001424	0.002209	0.6447	4503	0.5191	-0.004776	0.007624
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000226	0.00002589	-0.8731	4503	0.3826	-0.00009528	0.00005007
fixed	NA	male	-0.1238	0.02756	-4.493	4411	0.000007201	-0.2012	-0.04647
fixed	NA	sibling_count3	0.03289	0.0392	0.8391	3502	0.4015	-0.07715	0.1429
fixed	NA	sibling_count4	-0.02709	0.04456	-0.608	3257	0.5432	-0.1522	0.09798
fixed	NA	sibling_count5	-0.06611	0.0545	-1.213	3234	0.2252	-0.2191	0.08686
fixed	NA	birth_order_nonlinear2	0.02273	0.0326	0.6972	3589	0.4858	-0.06878	0.1142
fixed	NA	birth_order_nonlinear3	-0.02193	0.0416	-0.5272	3798	0.5981	-0.1387	0.09485
fixed	NA	birth_order_nonlinear4	-0.02637	0.05598	-0.4711	3978	0.6376	-0.1835	0.1308
fixed	NA	birth_order_nonlinear5	0.1112	0.0871	1.276	3829	0.2019	-0.1333	0.3557
ran_pars	mother_pidlink	sd__(Intercept)	0.3602	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8604	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6748	0.514	1.313	4494	0.1894	-0.7682	2.118
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03349	0.05995	-0.5586	4495	0.5765	-0.2018	0.1348
fixed	NA	poly(age, 3, raw = TRUE)2	0.001357	0.00221	0.6141	4497	0.5392	-0.004847	0.007561
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002158	0.00002591	-0.8329	4497	0.405	-0.00009431	0.00005115
fixed	NA	male	-0.1235	0.02758	-4.478	4405	0.000007728	-0.2009	-0.04609
fixed	NA	count_birth_order2/2	-0.04003	0.05604	-0.7142	3808	0.4751	-0.1973	0.1173
fixed	NA	count_birth_order1/3	0.01968	0.04988	0.3946	4483	0.6932	-0.1203	0.1597
fixed	NA	count_birth_order2/3	0.03583	0.05443	0.6583	4497	0.5104	-0.117	0.1886
fixed	NA	count_birth_order3/3	-0.02706	0.06078	-0.4452	4491	0.6562	-0.1977	0.1436
fixed	NA	count_birth_order1/4	-0.09086	0.0612	-1.485	4494	0.1377	-0.2626	0.08093
fixed	NA	count_birth_order2/4	0.01249	0.06311	0.1979	4495	0.8431	-0.1647	0.1896
fixed	NA	count_birth_order3/4	-0.06358	0.06656	-0.9552	4477	0.3395	-0.2504	0.1233
fixed	NA	count_birth_order4/4	-0.06842	0.06923	-0.9883	4474	0.323	-0.2628	0.1259
fixed	NA	count_birth_order1/5	-0.132	0.08314	-1.588	4489	0.1124	-0.3654	0.1014
fixed	NA	count_birth_order2/5	-0.03475	0.08868	-0.3919	4455	0.6952	-0.2837	0.2142
fixed	NA	count_birth_order3/5	-0.08159	0.08307	-0.9822	4453	0.3261	-0.3148	0.1516
fixed	NA	count_birth_order4/5	-0.1201	0.07999	-1.501	4465	0.1335	-0.3446	0.1045
fixed	NA	count_birth_order5/5	0.02451	0.08316	0.2948	4448	0.7682	-0.2089	0.2579
ran_pars	mother_pidlink	sd__(Intercept)	0.3594	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.861	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12158	12222	-6069	12138	NA	NA	NA
11	12160	12230	-6069	12138	0.02078	1	0.8854
14	12162	12252	-6067	12134	3.517	3	0.3185
20	12171	12299	-6065	12131	3.434	6	0.7527

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.695	0.5289	1.314	4175	0.1889	-0.7896	2.18
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0338	0.0618	-0.5469	4179	0.5845	-0.2073	0.1397
fixed	NA	poly(age, 3, raw = TRUE)2	0.001282	0.002279	0.5627	4182	0.5737	-0.005115	0.007679
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002026	0.00002671	-0.7584	4183	0.4483	-0.00009523	0.00005472
fixed	NA	male	-0.1249	0.02866	-4.36	4093	0.00001334	-0.2054	-0.0445
fixed	NA	sibling_count3	0.01693	0.04122	0.4107	3177	0.6813	-0.09877	0.1326
fixed	NA	sibling_count4	-0.04111	0.04362	-0.9424	2900	0.3461	-0.1636	0.08134
fixed	NA	sibling_count5	-0.0009798	0.04684	-0.02092	2611	0.9833	-0.1325	0.1305
ran_pars	mother_pidlink	sd__(Intercept)	0.3614	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8616	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.7063	0.5295	1.334	4174	0.1823	-0.7801	2.193
fixed	NA	birth_order	-0.006704	0.0145	-0.4624	3924	0.6438	-0.04741	0.034
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03414	0.06181	-0.5524	4178	0.5807	-0.2076	0.1394
fixed	NA	poly(age, 3, raw = TRUE)2	0.001301	0.002279	0.5709	4181	0.5681	-0.005097	0.0077
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002061	0.00002672	-0.7714	4182	0.4405	-0.00009563	0.0000544
fixed	NA	male	-0.1248	0.02866	-4.354	4092	0.00001368	-0.2052	-0.04434
fixed	NA	sibling_count3	0.02	0.04176	0.4791	3219	0.6319	-0.0972	0.1372
fixed	NA	sibling_count4	-0.03424	0.04609	-0.7428	3064	0.4576	-0.1636	0.09514
fixed	NA	sibling_count5	0.01	0.05252	0.1905	2998	0.849	-0.1374	0.1574
ran_pars	mother_pidlink	sd__(Intercept)	0.3614	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8617	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6616	0.53	1.248	4175	0.212	-0.826	2.149
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03172	0.06186	-0.5128	4177	0.6081	-0.2054	0.1419
fixed	NA	poly(age, 3, raw = TRUE)2	0.001213	0.002281	0.5319	4179	0.5948	-0.005191	0.007617
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001965	0.00002674	-0.7348	4179	0.4625	-0.00009472	0.00005542
fixed	NA	male	-0.1238	0.02866	-4.321	4088	0.00001594	-0.2043	-0.04338
fixed	NA	sibling_count3	0.02245	0.04234	0.5303	3315	0.596	-0.0964	0.1413
fixed	NA	sibling_count4	-0.02571	0.04671	-0.5505	3151	0.582	-0.1568	0.1054
fixed	NA	sibling_count5	0.01751	0.05305	0.33	3050	0.7414	-0.1314	0.1664
fixed	NA	birth_order_nonlinear2	0.04513	0.03401	1.327	3391	0.1846	-0.05034	0.1406
fixed	NA	birth_order_nonlinear3	-0.02175	0.04309	-0.5047	3594	0.6138	-0.1427	0.0992
fixed	NA	birth_order_nonlinear4	-0.03946	0.05712	-0.6909	3739	0.4897	-0.1998	0.1209
fixed	NA	birth_order_nonlinear5	0.004556	0.08364	0.05447	3619	0.9566	-0.2302	0.2393
ran_pars	mother_pidlink	sd__(Intercept)	0.3617	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8615	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6742	0.5305	1.271	4169	0.2038	-0.815	2.163
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03249	0.06191	-0.5248	4171	0.5998	-0.2063	0.1413
fixed	NA	poly(age, 3, raw = TRUE)2	0.001232	0.002283	0.5396	4173	0.5895	-0.005178	0.007642
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001973	0.00002677	-0.737	4173	0.4612	-0.00009488	0.00005542
fixed	NA	male	-0.1236	0.02869	-4.309	4082	0.00001678	-0.2042	-0.0431
fixed	NA	count_birth_order2/2	0.03116	0.0615	0.5067	3585	0.6124	-0.1415	0.2038
fixed	NA	count_birth_order1/3	0.04129	0.05411	0.763	4161	0.4455	-0.1106	0.1932
fixed	NA	count_birth_order2/3	0.04748	0.05864	0.8096	4173	0.4182	-0.1171	0.2121
fixed	NA	count_birth_order3/3	-0.029	0.06595	-0.4398	4167	0.6601	-0.2141	0.1561
fixed	NA	count_birth_order1/4	-0.08659	0.06423	-1.348	4170	0.1777	-0.2669	0.09371
fixed	NA	count_birth_order2/4	0.04596	0.0651	0.706	4173	0.4802	-0.1368	0.2287
fixed	NA	count_birth_order3/4	-0.02934	0.07141	-0.4108	4153	0.6812	-0.2298	0.1711
fixed	NA	count_birth_order4/4	-0.05257	0.07366	-0.7137	4153	0.4755	-0.2593	0.1542
fixed	NA	count_birth_order1/5	0.02131	0.07636	0.2791	4173	0.7802	-0.193	0.2357
fixed	NA	count_birth_order2/5	0.05541	0.0817	0.6782	4150	0.4977	-0.1739	0.2848
fixed	NA	count_birth_order3/5	0.001603	0.07932	0.02021	4143	0.9839	-0.2211	0.2243
fixed	NA	count_birth_order4/5	-0.04752	0.08212	-0.5786	4125	0.5629	-0.278	0.183
fixed	NA	count_birth_order5/5	0.01724	0.08227	0.2095	4124	0.834	-0.2137	0.2482
ran_pars	mother_pidlink	sd__(Intercept)	0.3612	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8621	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11302	11365	-5641	11282	NA	NA	NA
11	11303	11373	-5641	11281	0.2141	1	0.6436
14	11306	11395	-5639	11278	3.506	3	0.32
20	11315	11442	-5638	11275	2.747	6	0.8399

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.5915	0.5148	1.149	4485	0.2506	-0.8534	2.036
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02534	0.06017	-0.4211	4489	0.6737	-0.1942	0.1436
fixed	NA	poly(age, 3, raw = TRUE)2	0.00102	0.002221	0.4591	4491	0.6462	-0.005215	0.007255
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001703	0.00002608	-0.6529	4492	0.5139	-0.00009024	0.00005618
fixed	NA	male	-0.1205	0.02746	-4.386	4400	0.00001179	-0.1976	-0.04337
fixed	NA	sibling_count3	0.02893	0.03739	0.7738	3307	0.4391	-0.07602	0.1339
fixed	NA	sibling_count4	-0.02826	0.04069	-0.6945	2932	0.4874	-0.1425	0.08595
fixed	NA	sibling_count5	-0.04755	0.04806	-0.9894	2549	0.3226	-0.1825	0.08736
ran_pars	mother_pidlink	sd__(Intercept)	0.3599	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8553	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.5921	0.5154	1.149	4484	0.2507	-0.8546	2.039
fixed	NA	birth_order	-0.0003708	0.01454	-0.0255	4110	0.9797	-0.04118	0.04044
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02536	0.06018	-0.4214	4488	0.6735	-0.1943	0.1436
fixed	NA	poly(age, 3, raw = TRUE)2	0.001021	0.002222	0.4595	4490	0.6459	-0.005216	0.007258
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001705	0.0000261	-0.6533	4491	0.5136	-0.00009031	0.00005621
fixed	NA	male	-0.1205	0.02747	-4.385	4399	0.00001186	-0.1976	-0.04335
fixed	NA	sibling_count3	0.02911	0.03799	0.7662	3364	0.4436	-0.07753	0.1357
fixed	NA	sibling_count4	-0.02787	0.0435	-0.6406	3169	0.5218	-0.15	0.09424
fixed	NA	sibling_count5	-0.04692	0.05402	-0.8686	3005	0.3851	-0.1986	0.1047
ran_pars	mother_pidlink	sd__(Intercept)	0.3598	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8555	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.5839	0.516	1.132	4485	0.2578	-0.8645	2.032
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02524	0.06026	-0.4189	4487	0.6753	-0.1944	0.1439
fixed	NA	poly(age, 3, raw = TRUE)2	0.001018	0.002225	0.4574	4488	0.6474	-0.005227	0.007263
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001704	0.00002613	-0.6522	4488	0.5143	-0.00009037	0.0000563
fixed	NA	male	-0.1204	0.02748	-4.38	4395	0.00001212	-0.1975	-0.04324
fixed	NA	sibling_count3	0.03159	0.03858	0.8188	3485	0.4129	-0.07671	0.1399
fixed	NA	sibling_count4	-0.01926	0.04413	-0.4365	3269	0.6625	-0.1431	0.1046
fixed	NA	sibling_count5	-0.04748	0.05509	-0.8618	3107	0.3888	-0.2021	0.1072
fixed	NA	birth_order_nonlinear2	0.01925	0.03225	0.5968	3569	0.5506	-0.07128	0.1098
fixed	NA	birth_order_nonlinear3	-0.008693	0.04126	-0.2107	3758	0.8331	-0.1245	0.1071
fixed	NA	birth_order_nonlinear4	-0.02725	0.05691	-0.4788	3941	0.6321	-0.187	0.1325
fixed	NA	birth_order_nonlinear5	0.05811	0.09287	0.6257	3874	0.5315	-0.2026	0.3188
ran_pars	mother_pidlink	sd__(Intercept)	0.359	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8559	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.59	0.5164	1.142	4479	0.2533	-0.8596	2.04
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02401	0.06031	-0.3982	4480	0.6905	-0.1933	0.1453
fixed	NA	poly(age, 3, raw = TRUE)2	0.0009604	0.002227	0.4313	4482	0.6662	-0.00529	0.00721
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001621	0.00002615	-0.6199	4482	0.5354	-0.00008961	0.00005719
fixed	NA	male	-0.1201	0.0275	-4.368	4389	0.00001284	-0.1973	-0.04293
fixed	NA	count_birth_order2/2	-0.02305	0.05432	-0.4244	3758	0.6713	-0.1755	0.1294
fixed	NA	count_birth_order1/3	0.01817	0.04906	0.3704	4466	0.7111	-0.1195	0.1559
fixed	NA	count_birth_order2/3	0.03697	0.05415	0.6827	4482	0.4948	-0.115	0.189
fixed	NA	count_birth_order3/3	0.005794	0.05943	0.0975	4474	0.9223	-0.161	0.1726
fixed	NA	count_birth_order1/4	-0.04966	0.06118	-0.8117	4481	0.417	-0.2214	0.1221
fixed	NA	count_birth_order2/4	0.01482	0.06269	0.2364	4479	0.8132	-0.1612	0.1908
fixed	NA	count_birth_order3/4	-0.05328	0.06555	-0.8128	4459	0.4164	-0.2373	0.1307
fixed	NA	count_birth_order4/4	-0.064	0.06932	-0.9232	4450	0.356	-0.2586	0.1306
fixed	NA	count_birth_order1/5	-0.1075	0.08258	-1.301	4479	0.1932	-0.3393	0.1243
fixed	NA	count_birth_order2/5	-0.0238	0.09094	-0.2616	4435	0.7936	-0.2791	0.2315
fixed	NA	count_birth_order3/5	-0.0411	0.08664	-0.4743	4431	0.6353	-0.2843	0.2021
fixed	NA	count_birth_order4/5	-0.08323	0.08347	-0.9971	4446	0.3188	-0.3175	0.1511
fixed	NA	count_birth_order5/5	-0.003306	0.0886	-0.03732	4428	0.9702	-0.252	0.2454
ran_pars	mother_pidlink	sd__(Intercept)	0.3584	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8566	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12070	12135	-6025	12050	NA	NA	NA
11	12072	12143	-6025	12050	0.0006531	1	0.9796
14	12077	12167	-6025	12049	1.409	3	0.7035
20	12087	12216	-6024	12047	1.689	6	0.9459

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Adaptive Numbering

birthorder <- birthorder %>% mutate(outcome = adaptive_numbering)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01499	0.1951	-0.07684	7025	0.9388	-0.5626	0.5327
fixed	NA	poly(age, 3, raw = TRUE)1	0.02448	0.0188	1.302	6960	0.193	-0.0283	0.07726
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000663	0.0005511	-1.203	6857	0.229	-0.00221	0.000884
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001357	0.000005014	0.02706	6761	0.9784	-0.00001394	0.00001421
fixed	NA	male	0.06532	0.0221	2.955	6727	0.003133	0.00328	0.1274
fixed	NA	sibling_count3	0.02239	0.03372	0.6639	4990	0.5068	-0.07227	0.117
fixed	NA	sibling_count4	-0.02749	0.03503	-0.7849	4608	0.4325	-0.1258	0.07082
fixed	NA	sibling_count5	-0.001222	0.03672	-0.03328	4217	0.9735	-0.1043	0.1019
ran_pars	mother_pidlink	sd__(Intercept)	0.4861	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8295	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.0223	0.1952	-0.1143	7013	0.909	-0.5703	0.5257
fixed	NA	birth_order	0.01183	0.01081	1.095	5728	0.2738	-0.01851	0.04218
fixed	NA	poly(age, 3, raw = TRUE)1	0.02345	0.01883	1.246	6973	0.2129	-0.02939	0.07629
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006348	0.0005517	-1.151	6865	0.25	-0.002183	0.0009139
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000004854	0.000005017	-0.009675	6766	0.9923	-0.00001413	0.00001403
fixed	NA	male	0.06503	0.0221	2.942	6725	0.003271	0.002985	0.1271
fixed	NA	sibling_count3	0.01844	0.03391	0.5437	5097	0.5867	-0.07675	0.1136
fixed	NA	sibling_count4	-0.03695	0.03608	-1.024	5060	0.3057	-0.1382	0.06431
fixed	NA	sibling_count5	-0.01672	0.03936	-0.4247	5128	0.671	-0.1272	0.09376
ran_pars	mother_pidlink	sd__(Intercept)	0.486	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8295	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.02965	0.1956	-0.1515	7021	0.8796	-0.5788	0.5195
fixed	NA	poly(age, 3, raw = TRUE)1	0.02454	0.01884	1.303	6960	0.1927	-0.02834	0.07743
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006724	0.0005524	-1.217	6840	0.2236	-0.002223	0.0008783
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000003378	0.000005026	0.06721	6728	0.9464	-0.00001377	0.00001445
fixed	NA	male	0.06497	0.0221	2.939	6722	0.0033	0.002926	0.127
fixed	NA	sibling_count3	0.01795	0.03434	0.5227	5273	0.6012	-0.07844	0.1143
fixed	NA	sibling_count4	-0.03119	0.03654	-0.8534	5253	0.3935	-0.1338	0.07139
fixed	NA	sibling_count5	-0.01372	0.03963	-0.3461	5262	0.7293	-0.125	0.09753
fixed	NA	birth_order_nonlinear2	0.03908	0.02567	1.523	5696	0.1279	-0.03296	0.1111
fixed	NA	birth_order_nonlinear3	0.03266	0.03286	0.9939	5484	0.3203	-0.05958	0.1249
fixed	NA	birth_order_nonlinear4	0.006277	0.04289	0.1463	5402	0.8837	-0.1141	0.1267
fixed	NA	birth_order_nonlinear5	0.07373	0.06223	1.185	5187	0.2361	-0.1009	0.2484
ran_pars	mother_pidlink	sd__(Intercept)	0.4859	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8296	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.009529	0.196	-0.04861	7018	0.9612	-0.5598	0.5407
fixed	NA	poly(age, 3, raw = TRUE)1	0.02437	0.01884	1.293	6954	0.1959	-0.02852	0.07727
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006619	0.0005525	-1.198	6832	0.231	-0.002213	0.0008891
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001967	0.000005028	0.03913	6716	0.9688	-0.00001392	0.00001431
fixed	NA	male	0.06467	0.02211	2.925	6715	0.00346	0.002602	0.1267
fixed	NA	count_birth_order2/2	-0.0156	0.04384	-0.3559	5813	0.7219	-0.1387	0.1075
fixed	NA	count_birth_order1/3	-0.0183	0.04312	-0.4243	7029	0.6713	-0.1393	0.1027
fixed	NA	count_birth_order2/3	0.05471	0.04804	1.139	7111	0.2549	-0.08015	0.1896
fixed	NA	count_birth_order3/3	0.04092	0.05364	0.7627	7124	0.4456	-0.1097	0.1915
fixed	NA	count_birth_order1/4	-0.05459	0.04907	-1.112	7110	0.266	-0.1923	0.08316
fixed	NA	count_birth_order2/4	-0.02086	0.05156	-0.4046	7126	0.6858	-0.1656	0.1239
fixed	NA	count_birth_order3/4	-0.0000896	0.05581	-0.001605	7112	0.9987	-0.1568	0.1566
fixed	NA	count_birth_order4/4	-0.04707	0.05903	-0.7973	7088	0.4253	-0.2128	0.1186
fixed	NA	count_birth_order1/5	-0.05021	0.05549	-0.9049	7127	0.3655	-0.206	0.1055
fixed	NA	count_birth_order2/5	0.05359	0.05826	0.9199	7108	0.3576	-0.1099	0.2171
fixed	NA	count_birth_order3/5	-0.03637	0.05973	-0.609	7084	0.5426	-0.204	0.1313
fixed	NA	count_birth_order4/5	-0.02435	0.06318	-0.3854	7034	0.6999	-0.2017	0.153
fixed	NA	count_birth_order5/5	0.0399	0.06455	0.6181	7019	0.5365	-0.1413	0.2211
ran_pars	mother_pidlink	sd__(Intercept)	0.4855	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8299	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	19524	19592	-9752	19504	NA	NA	NA
11	19525	19600	-9751	19503	1.199	1	0.2734
14	19528	19624	-9750	19500	2.353	3	0.5024
20	19536	19674	-9748	19496	4.032	6	0.6724

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.182	0.4781	-2.473	4466	0.01344	-2.524	0.1598
fixed	NA	poly(age, 3, raw = TRUE)1	0.1757	0.05583	3.146	4473	0.001665	0.01894	0.3324
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006345	0.002059	-3.082	4481	0.002067	-0.01212	-0.0005664
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007153	0.00002413	2.964	4487	0.003054	0.000003785	0.0001393
fixed	NA	male	0.0121	0.02561	0.4723	4311	0.6368	-0.0598	0.08399
fixed	NA	sibling_count3	-0.02085	0.03623	-0.5755	3265	0.565	-0.1225	0.08084
fixed	NA	sibling_count4	-0.07205	0.03934	-1.832	2928	0.06713	-0.1825	0.03838
fixed	NA	sibling_count5	-0.08284	0.04512	-1.836	2679	0.06645	-0.2095	0.04381
ran_pars	mother_pidlink	sd__(Intercept)	0.4106	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7731	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.22	0.4786	-2.55	4466	0.01081	-2.564	0.123
fixed	NA	birth_order	0.02172	0.01335	1.627	4049	0.1038	-0.01576	0.05919
fixed	NA	poly(age, 3, raw = TRUE)1	0.1769	0.05583	3.169	4472	0.00154	0.02021	0.3336
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006412	0.002059	-3.114	4480	0.001856	-0.01219	-0.0006326
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007275	0.00002414	3.014	4486	0.002595	0.000004989	0.0001405
fixed	NA	male	0.0114	0.02561	0.445	4310	0.6564	-0.0605	0.08329
fixed	NA	sibling_count3	-0.03091	0.03674	-0.8411	3324	0.4004	-0.134	0.07224
fixed	NA	sibling_count4	-0.09541	0.04187	-2.279	3140	0.02276	-0.2129	0.02213
fixed	NA	sibling_count5	-0.1218	0.05108	-2.385	3167	0.01714	-0.2652	0.02156
ran_pars	mother_pidlink	sd__(Intercept)	0.4105	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.773	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.214	0.4794	-2.532	4472	0.01136	-2.56	0.1316
fixed	NA	poly(age, 3, raw = TRUE)1	0.178	0.05592	3.184	4476	0.001465	0.02106	0.335
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00645	0.002062	-3.128	4482	0.001772	-0.01224	-0.0006617
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007314	0.00002417	3.026	4486	0.002495	0.000005286	0.000141
fixed	NA	male	0.01198	0.02562	0.4676	4307	0.6401	-0.05995	0.08391
fixed	NA	sibling_count3	-0.03056	0.03725	-0.8204	3436	0.412	-0.1351	0.07401
fixed	NA	sibling_count4	-0.08822	0.04243	-2.079	3237	0.03771	-0.2073	0.0309
fixed	NA	sibling_count5	-0.1215	0.05187	-2.341	3263	0.01927	-0.2671	0.02415
fixed	NA	birth_order_nonlinear2	0.03861	0.03	1.287	3449	0.1981	-0.0456	0.1228
fixed	NA	birth_order_nonlinear3	0.04295	0.03837	1.119	3641	0.263	-0.06475	0.1507
fixed	NA	birth_order_nonlinear4	0.03676	0.05169	0.7111	3832	0.477	-0.1083	0.1819
fixed	NA	birth_order_nonlinear5	0.1317	0.08026	1.641	3641	0.1009	-0.09359	0.357
ran_pars	mother_pidlink	sd__(Intercept)	0.4103	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7732	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.207	0.4796	-2.517	4466	0.01187	-2.553	0.1391
fixed	NA	poly(age, 3, raw = TRUE)1	0.177	0.05594	3.164	4470	0.001565	0.01999	0.334
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006382	0.002063	-3.094	4475	0.00199	-0.01217	-0.000591
fixed	NA	poly(age, 3, raw = TRUE)3	0.000072	0.00002419	2.976	4480	0.002934	0.000004093	0.0001399
fixed	NA	male	0.01172	0.02564	0.457	4301	0.6477	-0.06026	0.0837
fixed	NA	count_birth_order2/2	0.02482	0.05171	0.48	3721	0.6312	-0.1203	0.17
fixed	NA	count_birth_order1/3	-0.05179	0.04673	-1.108	4459	0.2678	-0.183	0.07939
fixed	NA	count_birth_order2/3	0.01877	0.05089	0.3687	4488	0.7124	-0.1241	0.1616
fixed	NA	count_birth_order3/3	0.01967	0.05676	0.3466	4480	0.7289	-0.1396	0.179
fixed	NA	count_birth_order1/4	-0.1177	0.05721	-2.056	4484	0.0398	-0.2782	0.04295
fixed	NA	count_birth_order2/4	-0.05827	0.05897	-0.9881	4485	0.3231	-0.2238	0.1073
fixed	NA	count_birth_order3/4	-0.02992	0.06212	-0.4817	4455	0.63	-0.2043	0.1444
fixed	NA	count_birth_order4/4	-0.03523	0.0645	-0.5462	4451	0.5849	-0.2163	0.1458
fixed	NA	count_birth_order1/5	-0.02122	0.07753	-0.2737	4472	0.7844	-0.2388	0.1964
fixed	NA	count_birth_order2/5	-0.107	0.08253	-1.296	4405	0.1951	-0.3386	0.1247
fixed	NA	count_birth_order3/5	-0.1429	0.07731	-1.848	4408	0.06469	-0.3599	0.07415
fixed	NA	count_birth_order4/5	-0.12	0.0745	-1.611	4436	0.1073	-0.3291	0.08911
fixed	NA	count_birth_order5/5	0.003717	0.07739	0.04803	4409	0.9617	-0.2135	0.221
ran_pars	mother_pidlink	sd__(Intercept)	0.409	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.774	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11521	11585	-5750	11501	NA	NA	NA
11	11520	11590	-5749	11498	2.651	1	0.1035
14	11525	11614	-5748	11497	1.301	3	0.7289
20	11532	11660	-5746	11492	4.642	6	0.5904

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.383	0.4926	-2.809	4138	0.004999	-2.766	-0.0007621
fixed	NA	poly(age, 3, raw = TRUE)1	0.1984	0.05757	3.446	4145	0.0005748	0.03678	0.36
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007227	0.002124	-3.403	4154	0.0006723	-0.01319	-0.001266
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008183	0.0000249	3.286	4161	0.001024	0.00001193	0.0001517
fixed	NA	male	0.01785	0.02658	0.6716	3981	0.5019	-0.05677	0.09248
fixed	NA	sibling_count3	-0.0001382	0.03925	-0.003522	3118	0.9972	-0.1103	0.11
fixed	NA	sibling_count4	-0.04659	0.04173	-1.117	2881	0.2643	-0.1637	0.07054
fixed	NA	sibling_count5	-0.03438	0.04491	-0.7656	2646	0.444	-0.1604	0.09167
ran_pars	mother_pidlink	sd__(Intercept)	0.4227	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7681	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.41	0.493	-2.859	4137	0.004269	-2.794	-0.02569
fixed	NA	birth_order	0.01565	0.0134	1.168	3829	0.2429	-0.02196	0.05326
fixed	NA	poly(age, 3, raw = TRUE)1	0.1991	0.05757	3.458	4144	0.0005498	0.03747	0.3607
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007265	0.002124	-3.421	4152	0.0006303	-0.01323	-0.001304
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008259	0.00002491	3.316	4159	0.000922	0.00001267	0.0001525
fixed	NA	male	0.01752	0.02658	0.6589	3980	0.51	-0.05711	0.09214
fixed	NA	sibling_count3	-0.007381	0.03974	-0.1857	3160	0.8527	-0.1189	0.1042
fixed	NA	sibling_count4	-0.06285	0.04399	-1.429	3036	0.1531	-0.1863	0.06062
fixed	NA	sibling_count5	-0.06031	0.05009	-1.204	3012	0.2287	-0.2009	0.0803
ran_pars	mother_pidlink	sd__(Intercept)	0.4228	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7681	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.401	0.4936	-2.837	4146	0.00457	-2.786	-0.01499
fixed	NA	poly(age, 3, raw = TRUE)1	0.1987	0.05763	3.448	4149	0.0005709	0.03692	0.3605
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007248	0.002126	-3.409	4156	0.0006572	-0.01322	-0.001281
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008235	0.00002493	3.303	4161	0.0009632	0.00001237	0.0001523
fixed	NA	male	0.01819	0.02658	0.6843	3978	0.4938	-0.05643	0.0928
fixed	NA	sibling_count3	-0.002283	0.04022	-0.05675	3255	0.9547	-0.1152	0.1106
fixed	NA	sibling_count4	-0.04588	0.0445	-1.031	3123	0.3027	-0.1708	0.07905
fixed	NA	sibling_count5	-0.06299	0.05053	-1.247	3067	0.2126	-0.2048	0.07885
fixed	NA	birth_order_nonlinear2	0.04216	0.0312	1.351	3253	0.1767	-0.04542	0.1297
fixed	NA	birth_order_nonlinear3	0.009415	0.03961	0.2377	3433	0.8121	-0.1018	0.1206
fixed	NA	birth_order_nonlinear4	-0.009049	0.0526	-0.172	3587	0.8634	-0.1567	0.1386
fixed	NA	birth_order_nonlinear5	0.1786	0.07685	2.324	3426	0.02021	-0.03715	0.3943
ran_pars	mother_pidlink	sd__(Intercept)	0.4218	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7681	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.375	0.4938	-2.785	4140	0.005379	-2.761	0.01094
fixed	NA	poly(age, 3, raw = TRUE)1	0.1959	0.05764	3.399	4143	0.0006828	0.03412	0.3577
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007127	0.002127	-3.352	4149	0.0008103	-0.0131	-0.001158
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008071	0.00002494	3.236	4155	0.00122	0.00001071	0.0001507
fixed	NA	male	0.01721	0.02659	0.6471	3971	0.5176	-0.05744	0.09185
fixed	NA	count_birth_order2/2	0.0283	0.0565	0.5009	3506	0.6165	-0.1303	0.1869
fixed	NA	count_birth_order1/3	-0.01313	0.05059	-0.2595	4138	0.7952	-0.1552	0.1289
fixed	NA	count_birth_order2/3	0.02001	0.0547	0.3658	4165	0.7145	-0.1335	0.1735
fixed	NA	count_birth_order3/3	0.03772	0.06139	0.6144	4157	0.539	-0.1346	0.21
fixed	NA	count_birth_order1/4	-0.1026	0.05995	-1.711	4161	0.0871	-0.2709	0.06569
fixed	NA	count_birth_order2/4	0.02987	0.06093	0.4902	4165	0.624	-0.1412	0.2009
fixed	NA	count_birth_order3/4	-0.007508	0.06648	-0.1129	4127	0.9101	-0.1941	0.1791
fixed	NA	count_birth_order4/4	-0.06705	0.06848	-0.9791	4131	0.3276	-0.2593	0.1252
fixed	NA	count_birth_order1/5	0.02117	0.07115	0.2976	4164	0.766	-0.1785	0.2209
fixed	NA	count_birth_order2/5	-0.03984	0.07592	-0.5247	4114	0.5998	-0.2529	0.1733
fixed	NA	count_birth_order3/5	-0.1577	0.07368	-2.141	4107	0.03235	-0.3646	0.0491
fixed	NA	count_birth_order4/5	-0.06692	0.07622	-0.878	4080	0.38	-0.2809	0.147
fixed	NA	count_birth_order5/5	0.1091	0.07635	1.429	4081	0.1532	-0.1052	0.3234
ran_pars	mother_pidlink	sd__(Intercept)	0.4217	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.768	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	10703	10766	-5341	10683	NA	NA	NA
11	10703	10773	-5341	10681	1.367	1	0.2424
14	10703	10792	-5338	10675	6.199	3	0.1023
20	10707	10834	-5333	10667	8.046	6	0.2348

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.192	0.4812	-2.477	4446	0.0133	-2.542	0.159
fixed	NA	poly(age, 3, raw = TRUE)1	0.1748	0.05627	3.107	4454	0.001901	0.01689	0.3328
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006236	0.002078	-3.001	4462	0.002704	-0.01207	-0.0004034
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006911	0.00002441	2.832	4469	0.004652	0.0000006001	0.0001376
fixed	NA	male	0.006333	0.02558	0.2476	4282	0.8045	-0.06547	0.07814
fixed	NA	sibling_count3	-0.006151	0.03575	-0.172	3243	0.8634	-0.1065	0.09421
fixed	NA	sibling_count4	-0.07407	0.03906	-1.897	2926	0.05798	-0.1837	0.03556
fixed	NA	sibling_count5	-0.06387	0.04631	-1.379	2607	0.1679	-0.1939	0.06611
ran_pars	mother_pidlink	sd__(Intercept)	0.4172	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7676	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.241	0.4816	-2.577	4447	0.01001	-2.593	0.1109
fixed	NA	birth_order	0.02818	0.01347	2.093	3996	0.03643	-0.009618	0.06599
fixed	NA	poly(age, 3, raw = TRUE)1	0.1764	0.05625	3.136	4453	0.001726	0.01848	0.3343
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006318	0.002077	-3.041	4461	0.00237	-0.01215	-0.0004866
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007065	0.00002441	2.894	4468	0.003817	0.000002133	0.0001392
fixed	NA	male	0.005651	0.02557	0.221	4281	0.8251	-0.06613	0.07743
fixed	NA	sibling_count3	-0.01925	0.03628	-0.5306	3298	0.5957	-0.1211	0.0826
fixed	NA	sibling_count4	-0.1043	0.04163	-2.506	3151	0.01228	-0.2211	0.01255
fixed	NA	sibling_count5	-0.1123	0.05174	-2.17	3042	0.03009	-0.2575	0.03297
ran_pars	mother_pidlink	sd__(Intercept)	0.4169	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7674	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.227	0.4824	-2.543	4454	0.01101	-2.581	0.1272
fixed	NA	poly(age, 3, raw = TRUE)1	0.1771	0.05635	3.143	4458	0.001685	0.01891	0.3352
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006342	0.002081	-3.048	4464	0.002317	-0.01218	-0.0005015
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007089	0.00002444	2.9	4469	0.003744	0.000002284	0.0001395
fixed	NA	male	0.005679	0.02558	0.222	4277	0.8243	-0.06613	0.07749
fixed	NA	sibling_count3	-0.01592	0.03681	-0.4325	3415	0.6654	-0.1192	0.0874
fixed	NA	sibling_count4	-0.09735	0.04219	-2.307	3249	0.02109	-0.2158	0.02108
fixed	NA	sibling_count5	-0.1101	0.05271	-2.089	3150	0.03676	-0.2581	0.03783
fixed	NA	birth_order_nonlinear2	0.05219	0.02968	1.758	3404	0.07878	-0.03113	0.1355
fixed	NA	birth_order_nonlinear3	0.0451	0.03806	1.185	3580	0.236	-0.06172	0.1519
fixed	NA	birth_order_nonlinear4	0.07206	0.05257	1.371	3766	0.1705	-0.0755	0.2196
fixed	NA	birth_order_nonlinear5	0.1491	0.08566	1.74	3659	0.08196	-0.09141	0.3895
ran_pars	mother_pidlink	sd__(Intercept)	0.4166	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7677	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.219	0.4826	-2.525	4448	0.01161	-2.573	0.1362
fixed	NA	poly(age, 3, raw = TRUE)1	0.1761	0.05637	3.124	4452	0.001799	0.01784	0.3343
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006281	0.002082	-3.017	4458	0.002566	-0.01212	-0.0004375
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006991	0.00002446	2.859	4463	0.004276	0.00000126	0.0001386
fixed	NA	male	0.00549	0.0256	0.2145	4271	0.8302	-0.06637	0.07735
fixed	NA	count_birth_order2/2	0.03835	0.05012	0.7653	3646	0.4442	-0.1023	0.179
fixed	NA	count_birth_order1/3	-0.03473	0.04605	-0.7542	4441	0.4508	-0.164	0.09454
fixed	NA	count_birth_order2/3	0.04904	0.05071	0.9671	4474	0.3336	-0.0933	0.1914
fixed	NA	count_birth_order3/3	0.02911	0.05558	0.5237	4462	0.6005	-0.1269	0.1851
fixed	NA	count_birth_order1/4	-0.1317	0.05728	-2.3	4472	0.02149	-0.2925	0.02904
fixed	NA	count_birth_order2/4	-0.04869	0.05866	-0.83	4466	0.4066	-0.2134	0.116
fixed	NA	count_birth_order3/4	-0.03818	0.06126	-0.6233	4433	0.5331	-0.2101	0.1338
fixed	NA	count_birth_order4/4	-0.008645	0.06466	-0.1337	4419	0.8937	-0.1901	0.1729
fixed	NA	count_birth_order1/5	-0.01297	0.07718	-0.168	4464	0.8666	-0.2296	0.2037
fixed	NA	count_birth_order2/5	-0.103	0.08474	-1.216	4373	0.224	-0.3409	0.1348
fixed	NA	count_birth_order3/5	-0.1175	0.08073	-1.455	4375	0.1458	-0.3441	0.1092
fixed	NA	count_birth_order4/5	-0.07706	0.07783	-0.9902	4409	0.3221	-0.2955	0.1414
fixed	NA	count_birth_order5/5	0.03252	0.08254	0.394	4377	0.6936	-0.1992	0.2642
ran_pars	mother_pidlink	sd__(Intercept)	0.4152	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7685	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11457	11522	-5719	11437	NA	NA	NA
11	11455	11526	-5717	11433	4.387	1	0.03622
14	11460	11549	-5716	11432	1.37	3	0.7125
20	11467	11595	-5714	11427	4.496	6	0.6099

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Personality

Extraversion

birthorder <- birthorder %>% mutate(outcome = big5_ext)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.476	0.2004	2.375	6635	0.01759	-0.08663	1.039
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02873	0.01923	-1.494	6434	0.1352	-0.08272	0.02525
fixed	NA	poly(age, 3, raw = TRUE)2	0.0008189	0.0005611	1.459	6220	0.1445	-0.0007561	0.002394
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000008385	0.000005087	-1.648	6062	0.09933	-0.00002266	0.000005894
fixed	NA	male	-0.2425	0.02352	-10.31	7104	9.543e-25	-0.3085	-0.1764
fixed	NA	sibling_count3	0.006154	0.03316	0.1856	5038	0.8528	-0.08694	0.09924
fixed	NA	sibling_count4	-0.0243	0.03408	-0.713	4415	0.4759	-0.12	0.07136
fixed	NA	sibling_count5	-0.03191	0.03531	-0.9037	3753	0.3662	-0.131	0.06721
ran_pars	mother_pidlink	sd__(Intercept)	0.215	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9699	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4758	0.2005	2.373	6626	0.01765	-0.08693	1.038
fixed	NA	birth_order	0.0004919	0.01182	0.0416	6238	0.9668	-0.0327	0.03368
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02878	0.01927	-1.494	6462	0.1354	-0.08287	0.02531
fixed	NA	poly(age, 3, raw = TRUE)2	0.0008201	0.0005619	1.459	6235	0.1445	-0.0007572	0.002397
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000008392	0.000005091	-1.649	6070	0.09929	-0.00002268	0.000005897
fixed	NA	male	-0.2425	0.02352	-10.31	7102	9.67e-25	-0.3085	-0.1764
fixed	NA	sibling_count3	0.005976	0.03344	0.1787	5174	0.8582	-0.08789	0.09984
fixed	NA	sibling_count4	-0.02471	0.03549	-0.6962	4993	0.4863	-0.1243	0.07492
fixed	NA	sibling_count5	-0.03257	0.03873	-0.8409	4912	0.4005	-0.1413	0.07616
ran_pars	mother_pidlink	sd__(Intercept)	0.2149	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.97	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4474	0.201	2.226	6653	0.02608	-0.1169	1.012
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02775	0.01928	-1.439	6451	0.1501	-0.08186	0.02636
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007794	0.0005623	1.386	6215	0.1658	-0.0007989	0.002358
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000007944	0.000005096	-1.559	6039	0.119	-0.00002225	0.00000636
fixed	NA	male	-0.2425	0.02352	-10.31	7098	9.31e-25	-0.3085	-0.1765
fixed	NA	sibling_count3	0.01114	0.03401	0.3277	5397	0.7431	-0.08431	0.1066
fixed	NA	sibling_count4	-0.01998	0.03613	-0.5532	5249	0.5802	-0.1214	0.08143
fixed	NA	sibling_count5	-0.01999	0.03914	-0.5107	5099	0.6096	-0.1299	0.08988
fixed	NA	birth_order_nonlinear2	0.0591	0.02811	2.103	6066	0.03554	-0.0198	0.138
fixed	NA	birth_order_nonlinear3	-0.006697	0.03608	-0.1856	6075	0.8527	-0.108	0.09457
fixed	NA	birth_order_nonlinear4	0.01674	0.04711	0.3554	6112	0.7223	-0.1155	0.149
fixed	NA	birth_order_nonlinear5	-0.02431	0.06859	-0.3544	6026	0.7231	-0.2168	0.1682
ran_pars	mother_pidlink	sd__(Intercept)	0.2171	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9693	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4498	0.2014	2.233	6660	0.02559	-0.1157	1.015
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02739	0.01928	-1.421	6448	0.1554	-0.08151	0.02672
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007745	0.0005623	1.377	6209	0.1684	-0.0008038	0.002353
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000794	0.000005096	-1.558	6030	0.1192	-0.00002224	0.000006364
fixed	NA	male	-0.2422	0.02352	-10.29	7092	1.113e-24	-0.3082	-0.1761
fixed	NA	count_birth_order2/2	0.03729	0.04798	0.7771	5968	0.4371	-0.09741	0.172
fixed	NA	count_birth_order1/3	0.004145	0.04484	0.09244	7122	0.9263	-0.1217	0.13
fixed	NA	count_birth_order2/3	0.05518	0.05016	1.1	7127	0.2713	-0.08563	0.196
fixed	NA	count_birth_order3/3	0.003678	0.05627	0.06535	7129	0.9479	-0.1543	0.1616
fixed	NA	count_birth_order1/4	-0.03432	0.05125	-0.6697	7128	0.5031	-0.1782	0.1095
fixed	NA	count_birth_order2/4	0.0945	0.05391	1.753	7128	0.07963	-0.05682	0.2458
fixed	NA	count_birth_order3/4	-0.06735	0.05861	-1.149	7129	0.2506	-0.2319	0.09719
fixed	NA	count_birth_order4/4	-0.05733	0.06212	-0.9228	7128	0.3561	-0.2317	0.117
fixed	NA	count_birth_order1/5	-0.0448	0.05819	-0.7699	7129	0.4414	-0.2081	0.1185
fixed	NA	count_birth_order2/5	-0.02115	0.06125	-0.3453	7128	0.7299	-0.1931	0.1508
fixed	NA	count_birth_order3/5	-0.006252	0.06288	-0.09941	7127	0.9208	-0.1828	0.1703
fixed	NA	count_birth_order4/5	0.04315	0.06666	0.6473	7126	0.5175	-0.144	0.2303
fixed	NA	count_birth_order5/5	-0.05223	0.06815	-0.7663	7125	0.4435	-0.2435	0.1391
ran_pars	mother_pidlink	sd__(Intercept)	0.2158	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9696	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	20193	20262	-10087	20173	NA	NA	NA
11	20195	20271	-10087	20173	0.001739	1	0.9667
14	20195	20292	-10084	20167	5.786	3	0.1225
20	20202	20339	-10081	20162	5.763	6	0.4502

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.292	0.5584	2.313	4493	0.02078	-0.276	2.859
fixed	NA	poly(age, 3, raw = TRUE)1	-0.115	0.06514	-1.766	4486	0.07745	-0.2979	0.0678
fixed	NA	poly(age, 3, raw = TRUE)2	0.003916	0.002399	1.632	4477	0.1027	-0.002818	0.01065
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004165	0.0000281	-1.482	4468	0.1383	-0.0001205	0.00003722
fixed	NA	male	-0.2914	0.03016	-9.661	4492	7.18e-22	-0.3761	-0.2067
fixed	NA	sibling_count3	-0.0332	0.0402	-0.826	3343	0.4089	-0.146	0.07963
fixed	NA	sibling_count4	-0.08768	0.04314	-2.033	2819	0.04219	-0.2088	0.0334
fixed	NA	sibling_count5	-0.08574	0.04897	-1.751	2384	0.08008	-0.2232	0.05171
ran_pars	mother_pidlink	sd__(Intercept)	0.1635	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.998	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.24	0.5589	2.219	4492	0.02652	-0.3285	2.809
fixed	NA	birth_order	0.03075	0.01593	1.93	4268	0.05362	-0.01396	0.07545
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1131	0.06512	-1.737	4485	0.08237	-0.296	0.06965
fixed	NA	poly(age, 3, raw = TRUE)2	0.003808	0.002399	1.587	4476	0.1125	-0.002926	0.01054
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003976	0.0000281	-1.415	4468	0.1572	-0.0001186	0.00003913
fixed	NA	male	-0.2925	0.03016	-9.697	4491	5.098e-22	-0.3771	-0.2078
fixed	NA	sibling_count3	-0.04723	0.04084	-1.156	3406	0.2476	-0.1619	0.0674
fixed	NA	sibling_count4	-0.1198	0.04621	-2.592	3069	0.0096	-0.2495	0.009959
fixed	NA	sibling_count5	-0.1394	0.0563	-2.477	2936	0.01331	-0.2975	0.0186
ran_pars	mother_pidlink	sd__(Intercept)	0.163	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9978	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.282	0.5593	2.292	4486	0.02195	-0.288	2.852
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1146	0.06518	-1.759	4478	0.07871	-0.2976	0.06833
fixed	NA	poly(age, 3, raw = TRUE)2	0.003862	0.002401	1.608	4469	0.1078	-0.002878	0.0106
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004034	0.00002813	-1.434	4461	0.1516	-0.0001193	0.00003861
fixed	NA	male	-0.2923	0.03017	-9.689	4488	5.485e-22	-0.377	-0.2076
fixed	NA	sibling_count3	-0.03841	0.04154	-0.9247	3535	0.3552	-0.155	0.0782
fixed	NA	sibling_count4	-0.11	0.04697	-2.341	3178	0.01927	-0.2418	0.02187
fixed	NA	sibling_count5	-0.1473	0.05733	-2.569	3021	0.01026	-0.3082	0.01367
fixed	NA	birth_order_nonlinear2	0.03432	0.03642	0.9424	3737	0.3461	-0.0679	0.1365
fixed	NA	birth_order_nonlinear3	0.02303	0.04628	0.4976	3985	0.6188	-0.1069	0.1529
fixed	NA	birth_order_nonlinear4	0.08706	0.06198	1.405	4177	0.1602	-0.08693	0.261
fixed	NA	birth_order_nonlinear5	0.2078	0.09666	2.15	4091	0.03165	-0.06356	0.4791
ran_pars	mother_pidlink	sd__(Intercept)	0.1628	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.998	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.277	0.5596	2.283	4481	0.02248	-0.2933	2.848
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1141	0.06522	-1.75	4474	0.08016	-0.2972	0.06893
fixed	NA	poly(age, 3, raw = TRUE)2	0.003865	0.002403	1.609	4465	0.1078	-0.002879	0.01061
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004064	0.00002815	-1.444	4457	0.1489	-0.0001197	0.00003838
fixed	NA	male	-0.2915	0.03019	-9.654	4482	7.724e-22	-0.3762	-0.2067
fixed	NA	count_birth_order2/2	0.02172	0.06239	0.3482	3846	0.7277	-0.1534	0.1969
fixed	NA	count_birth_order1/3	-0.08163	0.05423	-1.505	4489	0.1323	-0.2339	0.0706
fixed	NA	count_birth_order2/3	0.03728	0.05929	0.6288	4490	0.5295	-0.1291	0.2037
fixed	NA	count_birth_order3/3	-0.008793	0.06633	-0.1326	4488	0.8945	-0.195	0.1774
fixed	NA	count_birth_order1/4	-0.0623	0.06653	-0.9363	4487	0.3492	-0.2491	0.1245
fixed	NA	count_birth_order2/4	-0.1188	0.06881	-1.727	4490	0.08423	-0.312	0.07431
fixed	NA	count_birth_order3/4	-0.1042	0.07274	-1.432	4487	0.1522	-0.3084	0.1
fixed	NA	count_birth_order4/4	-0.03789	0.07557	-0.5014	4486	0.6161	-0.25	0.1742
fixed	NA	count_birth_order1/5	-0.1243	0.09059	-1.372	4490	0.1701	-0.3786	0.13
fixed	NA	count_birth_order2/5	-0.1651	0.09681	-1.705	4490	0.08818	-0.4369	0.1066
fixed	NA	count_birth_order3/5	-0.1305	0.09073	-1.438	4487	0.1504	-0.3852	0.1242
fixed	NA	count_birth_order4/5	-0.05037	0.08735	-0.5766	4486	0.5642	-0.2956	0.1948
fixed	NA	count_birth_order5/5	0.0559	0.09088	0.6151	4482	0.5385	-0.1992	0.311
ran_pars	mother_pidlink	sd__(Intercept)	0.1654	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9978	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12906	12970	-6443	12886	NA	NA	NA
11	12904	12974	-6441	12882	3.733	1	0.05336
14	12908	12998	-6440	12880	1.947	3	0.5834
20	12916	13044	-6438	12876	3.902	6	0.6899

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.255	0.5773	2.175	4173	0.02971	-0.3651	2.876
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1126	0.0674	-1.67	4168	0.09495	-0.3018	0.07662
fixed	NA	poly(age, 3, raw = TRUE)2	0.003895	0.002483	1.568	4161	0.1169	-0.003077	0.01087
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004159	0.00002909	-1.43	4154	0.1529	-0.0001232	0.00004006
fixed	NA	male	-0.2858	0.03143	-9.094	4165	1.445e-19	-0.374	-0.1976
fixed	NA	sibling_count3	-0.03749	0.04377	-0.8564	3182	0.3918	-0.1604	0.08538
fixed	NA	sibling_count4	-0.08365	0.0461	-1.815	2829	0.0697	-0.2131	0.04575
fixed	NA	sibling_count5	-0.1098	0.04914	-2.235	2436	0.02551	-0.2478	0.02811
ran_pars	mother_pidlink	sd__(Intercept)	0.1888	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9972	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.222	0.5779	2.114	4173	0.03454	-0.4002	2.844
fixed	NA	birth_order	0.02041	0.01599	1.277	4018	0.2018	-0.02447	0.06529
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1114	0.0674	-1.653	4168	0.09832	-0.3006	0.07776
fixed	NA	poly(age, 3, raw = TRUE)2	0.003829	0.002484	1.541	4161	0.1233	-0.003144	0.0108
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000404	0.0000291	-1.388	4154	0.1651	-0.0001221	0.00004129
fixed	NA	male	-0.2862	0.03143	-9.108	4163	1.27e-19	-0.3745	-0.198
fixed	NA	sibling_count3	-0.04677	0.04438	-1.054	3225	0.292	-0.1713	0.07779
fixed	NA	sibling_count4	-0.1043	0.04885	-2.135	3009	0.03288	-0.2414	0.03285
fixed	NA	sibling_count5	-0.1428	0.05552	-2.572	2863	0.01016	-0.2987	0.01305
ran_pars	mother_pidlink	sd__(Intercept)	0.1906	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9968	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.241	0.5779	2.147	4167	0.03184	-0.3814	2.863
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1116	0.06742	-1.656	4162	0.09786	-0.3009	0.07763
fixed	NA	poly(age, 3, raw = TRUE)2	0.003839	0.002485	1.545	4154	0.1224	-0.003136	0.01081
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004056	0.00002911	-1.393	4148	0.1636	-0.0001223	0.00004115
fixed	NA	male	-0.2856	0.03143	-9.089	4160	1.51e-19	-0.3738	-0.1974
fixed	NA	sibling_count3	-0.0449	0.04507	-0.9963	3332	0.3192	-0.1714	0.08161
fixed	NA	sibling_count4	-0.08676	0.04958	-1.75	3105	0.08021	-0.2259	0.0524
fixed	NA	sibling_count5	-0.1508	0.05611	-2.688	2908	0.007232	-0.3083	0.006687
fixed	NA	birth_order_nonlinear2	0.0264	0.03794	0.6958	3506	0.4866	-0.0801	0.1329
fixed	NA	birth_order_nonlinear3	0.03279	0.04785	0.6853	3753	0.4932	-0.1015	0.1671
fixed	NA	birth_order_nonlinear4	-0.01721	0.0632	-0.2722	3906	0.7854	-0.1946	0.1602
fixed	NA	birth_order_nonlinear5	0.2182	0.09272	2.353	3840	0.01867	-0.04209	0.4784
ran_pars	mother_pidlink	sd__(Intercept)	0.1888	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9969	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.238	0.5785	2.14	4161	0.03241	-0.3858	2.862
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1109	0.06747	-1.643	4156	0.1004	-0.3003	0.07852
fixed	NA	poly(age, 3, raw = TRUE)2	0.003821	0.002487	1.536	4149	0.1245	-0.00316	0.0108
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004046	0.00002914	-1.389	4142	0.165	-0.0001223	0.00004133
fixed	NA	male	-0.2856	0.03145	-9.08	4154	1.639e-19	-0.3739	-0.1973
fixed	NA	count_birth_order2/2	0.01054	0.06836	0.1541	3607	0.8775	-0.1813	0.2024
fixed	NA	count_birth_order1/3	-0.08448	0.05893	-1.433	4166	0.1518	-0.2499	0.08095
fixed	NA	count_birth_order2/3	0.01745	0.06393	0.273	4167	0.7849	-0.162	0.1969
fixed	NA	count_birth_order3/3	-0.01086	0.07201	-0.1508	4165	0.8801	-0.213	0.1913
fixed	NA	count_birth_order1/4	-0.05595	0.06996	-0.7997	4165	0.4239	-0.2523	0.1404
fixed	NA	count_birth_order2/4	-0.07123	0.07123	-1	4167	0.3173	-0.2712	0.1287
fixed	NA	count_birth_order3/4	-0.07095	0.07817	-0.9077	4164	0.3641	-0.2904	0.1485
fixed	NA	count_birth_order4/4	-0.145	0.08051	-1.801	4163	0.07183	-0.371	0.08103
fixed	NA	count_birth_order1/5	-0.1363	0.08325	-1.637	4166	0.1016	-0.37	0.09737
fixed	NA	count_birth_order2/5	-0.2032	0.08926	-2.277	4167	0.02285	-0.4538	0.04733
fixed	NA	count_birth_order3/5	-0.1196	0.08672	-1.38	4165	0.1678	-0.3631	0.1238
fixed	NA	count_birth_order4/5	-0.1273	0.08986	-1.417	4160	0.1566	-0.3796	0.1249
fixed	NA	count_birth_order5/5	0.06195	0.09005	0.688	4157	0.4915	-0.1908	0.3147
ran_pars	mother_pidlink	sd__(Intercept)	0.1876	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9974	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12011	12074	-5995	11991	NA	NA	NA
11	12011	12081	-5995	11989	1.63	1	0.2017
14	12012	12101	-5992	11984	4.952	3	0.1753
20	12021	12147	-5990	11981	3.454	6	0.75

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.114	0.5627	1.98	4478	0.04782	-0.4656	2.693
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09265	0.06572	-1.41	4470	0.1587	-0.2771	0.09182
fixed	NA	poly(age, 3, raw = TRUE)2	0.003106	0.002424	1.281	4460	0.2002	-0.003698	0.00991
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003262	0.00002844	-1.147	4451	0.2515	-0.0001125	0.00004721
fixed	NA	male	-0.2954	0.03018	-9.79	4478	2.077e-22	-0.3801	-0.2107
fixed	NA	sibling_count3	-0.04275	0.03959	-1.08	3310	0.2804	-0.1539	0.06839
fixed	NA	sibling_count4	-0.07902	0.04273	-1.849	2802	0.06454	-0.199	0.04093
fixed	NA	sibling_count5	-0.1128	0.04997	-2.257	2255	0.0241	-0.253	0.02748
ran_pars	mother_pidlink	sd__(Intercept)	0.1587	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9969	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.055	0.563	1.874	4476	0.06097	-0.5252	2.636
fixed	NA	birth_order	0.03612	0.01612	2.241	4241	0.02507	-0.009119	0.08136
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09067	0.06569	-1.38	4469	0.1676	-0.2751	0.09373
fixed	NA	poly(age, 3, raw = TRUE)2	0.002988	0.002423	1.233	4459	0.2176	-0.003815	0.009791
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003051	0.00002844	-1.073	4450	0.2834	-0.0001104	0.00004933
fixed	NA	male	-0.2964	0.03017	-9.827	4477	1.46e-22	-0.3811	-0.2117
fixed	NA	sibling_count3	-0.05915	0.04025	-1.47	3369	0.1418	-0.1721	0.05383
fixed	NA	sibling_count4	-0.1166	0.04588	-2.541	3065	0.01111	-0.2454	0.01222
fixed	NA	sibling_count5	-0.1729	0.0567	-3.05	2755	0.002311	-0.3321	-0.01377
ran_pars	mother_pidlink	sd__(Intercept)	0.1587	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9965	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.098	0.5634	1.949	4470	0.0513	-0.4831	2.68
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0916	0.06575	-1.393	4462	0.1637	-0.2762	0.09298
fixed	NA	poly(age, 3, raw = TRUE)2	0.003021	0.002426	1.245	4452	0.2131	-0.003788	0.009829
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003084	0.00002847	-1.083	4443	0.2787	-0.0001108	0.00004907
fixed	NA	male	-0.2969	0.03018	-9.839	4474	1.301e-22	-0.3816	-0.2122
fixed	NA	sibling_count3	-0.05314	0.04098	-1.297	3506	0.1948	-0.1682	0.0619
fixed	NA	sibling_count4	-0.1177	0.04665	-2.523	3176	0.01169	-0.2486	0.01326
fixed	NA	sibling_count5	-0.1727	0.05794	-2.981	2847	0.002898	-0.3354	-0.01008
fixed	NA	birth_order_nonlinear2	0.03917	0.03616	1.083	3727	0.2788	-0.06233	0.1407
fixed	NA	birth_order_nonlinear3	0.04696	0.04609	1.019	3948	0.3083	-0.08241	0.1763
fixed	NA	birth_order_nonlinear4	0.1435	0.06325	2.268	4157	0.02336	-0.03407	0.321
fixed	NA	birth_order_nonlinear5	0.1306	0.1033	1.265	4141	0.2061	-0.1593	0.4206
ran_pars	mother_pidlink	sd__(Intercept)	0.1578	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9968	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.098	0.5639	1.948	4464	0.05153	-0.4846	2.681
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09102	0.06581	-1.383	4458	0.1667	-0.2758	0.09371
fixed	NA	poly(age, 3, raw = TRUE)2	0.003015	0.002428	1.242	4448	0.2144	-0.0038	0.00983
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003096	0.0000285	-1.087	4439	0.2772	-0.000111	0.00004902
fixed	NA	male	-0.2964	0.0302	-9.813	4468	1.673e-22	-0.3812	-0.2116
fixed	NA	count_birth_order2/2	0.01571	0.06073	0.2586	3815	0.7959	-0.1548	0.1862
fixed	NA	count_birth_order1/3	-0.08884	0.05349	-1.661	4474	0.0968	-0.239	0.06131
fixed	NA	count_birth_order2/3	0.009791	0.05918	0.1654	4475	0.8686	-0.1563	0.1759
fixed	NA	count_birth_order3/3	-0.004587	0.06508	-0.07048	4472	0.9438	-0.1873	0.1781
fixed	NA	count_birth_order1/4	-0.1022	0.06675	-1.531	4473	0.1259	-0.2895	0.0852
fixed	NA	count_birth_order2/4	-0.1114	0.0686	-1.624	4475	0.1045	-0.3039	0.08117
fixed	NA	count_birth_order3/4	-0.08587	0.07189	-1.195	4472	0.2323	-0.2877	0.1159
fixed	NA	count_birth_order4/4	0.02402	0.07595	0.3163	4470	0.7518	-0.1892	0.2372
fixed	NA	count_birth_order1/5	-0.1552	0.09022	-1.721	4474	0.08539	-0.4085	0.09802
fixed	NA	count_birth_order2/5	-0.1484	0.09962	-1.49	4475	0.1364	-0.428	0.1312
fixed	NA	count_birth_order3/5	-0.1456	0.09496	-1.533	4472	0.1253	-0.4122	0.121
fixed	NA	count_birth_order4/5	-0.04816	0.09145	-0.5266	4472	0.5985	-0.3048	0.2085
fixed	NA	count_birth_order5/5	-0.05059	0.09714	-0.5208	4469	0.6025	-0.3233	0.2221
ran_pars	mother_pidlink	sd__(Intercept)	0.1587	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9972	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12846	12910	-6413	12826	NA	NA	NA
11	12843	12914	-6411	12821	5.03	1	0.02491
14	12848	12938	-6410	12820	0.9274	3	0.8188
20	12859	12987	-6409	12819	1.677	6	0.9469

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Neuroticism

birthorder <- birthorder %>% mutate(outcome = big5_neu)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4764	0.1993	2.39	6737	0.01687	-0.0831	1.036
fixed	NA	poly(age, 3, raw = TRUE)1	-0.006945	0.01915	-0.3627	6567	0.7169	-0.0607	0.04681
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002754	0.0005593	-0.4924	6372	0.6224	-0.001845	0.001295
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003654	0.000005075	0.7201	6220	0.4715	-0.00001059	0.0000179
fixed	NA	male	-0.2908	0.0232	-12.53	7047	1.18e-35	-0.3559	-0.2257
fixed	NA	sibling_count3	-0.009614	0.03327	-0.2889	5006	0.7726	-0.103	0.08379
fixed	NA	sibling_count4	-0.002416	0.03429	-0.07046	4453	0.9438	-0.09868	0.09385
fixed	NA	sibling_count5	-0.04077	0.03566	-1.143	3873	0.2529	-0.1409	0.05932
ran_pars	mother_pidlink	sd__(Intercept)	0.3044	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9355	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4816	0.1994	2.416	6726	0.01574	-0.07803	1.041
fixed	NA	birth_order	-0.01358	0.01159	-1.172	6101	0.2411	-0.0461	0.01894
fixed	NA	poly(age, 3, raw = TRUE)1	-0.005613	0.01918	-0.2926	6593	0.7698	-0.05946	0.04823
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003095	0.0005601	-0.5526	6387	0.5806	-0.001882	0.001263
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003875	0.000005079	0.763	6228	0.4455	-0.00001038	0.00001813
fixed	NA	male	-0.2904	0.02321	-12.51	7046	1.475e-35	-0.3556	-0.2253
fixed	NA	sibling_count3	-0.004777	0.03353	-0.1425	5137	0.8867	-0.09889	0.08933
fixed	NA	sibling_count4	0.008855	0.03561	0.2486	5002	0.8036	-0.09111	0.1088
fixed	NA	sibling_count5	-0.02262	0.03887	-0.5818	4971	0.5607	-0.1317	0.0865
ran_pars	mother_pidlink	sd__(Intercept)	0.3041	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9355	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4589	0.1999	2.295	6748	0.02174	-0.1023	1.02
fixed	NA	poly(age, 3, raw = TRUE)1	-0.00526	0.01919	-0.2741	6579	0.784	-0.05914	0.04862
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003274	0.0005605	-0.5841	6363	0.5592	-0.001901	0.001246
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000041	0.000005085	0.8063	6192	0.4201	-0.00001017	0.00001837
fixed	NA	male	-0.2905	0.02321	-12.52	7043	1.459e-35	-0.3556	-0.2253
fixed	NA	sibling_count3	-0.007908	0.03405	-0.2322	5353	0.8164	-0.1035	0.08769
fixed	NA	sibling_count4	0.005984	0.0362	0.1653	5246	0.8687	-0.09563	0.1076
fixed	NA	sibling_count5	-0.01713	0.03925	-0.4365	5148	0.6625	-0.1273	0.09303
fixed	NA	birth_order_nonlinear2	0.00793	0.02753	0.288	5981	0.7734	-0.06936	0.08522
fixed	NA	birth_order_nonlinear3	-0.00762	0.03534	-0.2156	5930	0.8293	-0.1068	0.09157
fixed	NA	birth_order_nonlinear4	-0.03616	0.04615	-0.7835	5932	0.4334	-0.1657	0.09339
fixed	NA	birth_order_nonlinear5	-0.09561	0.06715	-1.424	5807	0.1546	-0.2841	0.09289
ran_pars	mother_pidlink	sd__(Intercept)	0.3036	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9358	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4578	0.2004	2.285	6751	0.02236	-0.1047	1.02
fixed	NA	poly(age, 3, raw = TRUE)1	-0.005241	0.0192	-0.273	6575	0.7849	-0.05914	0.04865
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003285	0.0005607	-0.5859	6354	0.558	-0.001902	0.001245
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004111	0.000005086	0.8082	6180	0.419	-0.00001017	0.00001839
fixed	NA	male	-0.2906	0.02322	-12.51	7036	1.515e-35	-0.3558	-0.2254
fixed	NA	count_birth_order2/2	0.01125	0.04701	0.2393	5937	0.8109	-0.1207	0.1432
fixed	NA	count_birth_order1/3	-0.0001867	0.04439	-0.004206	7110	0.9966	-0.1248	0.1244
fixed	NA	count_birth_order2/3	-0.008199	0.04964	-0.1651	7125	0.8688	-0.1476	0.1312
fixed	NA	count_birth_order3/3	-0.01451	0.05566	-0.2607	7128	0.7943	-0.1707	0.1417
fixed	NA	count_birth_order1/4	-0.01966	0.05071	-0.3876	7126	0.6983	-0.162	0.1227
fixed	NA	count_birth_order2/4	0.02814	0.05334	0.5275	7128	0.5979	-0.1216	0.1779
fixed	NA	count_birth_order3/4	0.01074	0.05797	0.1852	7127	0.8531	-0.152	0.1735
fixed	NA	count_birth_order4/4	-0.01446	0.06142	-0.2355	7122	0.8139	-0.1869	0.158
fixed	NA	count_birth_order1/5	0.01169	0.05755	0.2031	7128	0.8391	-0.1499	0.1732
fixed	NA	count_birth_order2/5	-0.01379	0.06056	-0.2277	7123	0.8199	-0.1838	0.1562
fixed	NA	count_birth_order3/5	-0.03657	0.06217	-0.5882	7119	0.5564	-0.2111	0.1379
fixed	NA	count_birth_order4/5	-0.06921	0.06589	-1.05	7110	0.2936	-0.2542	0.1157
fixed	NA	count_birth_order5/5	-0.1119	0.06736	-1.661	7106	0.09673	-0.301	0.07718
ran_pars	mother_pidlink	sd__(Intercept)	0.3027	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9364	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	20030	20099	-10005	20010	NA	NA	NA
11	20031	20107	-10005	20009	1.376	1	0.2407
14	20036	20132	-10004	20008	1.405	3	0.7043
20	20046	20184	-10003	20006	1.255	6	0.9741

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.772	0.5401	-1.429	4500	0.153	-2.288	0.7442
fixed	NA	poly(age, 3, raw = TRUE)1	0.1448	0.06302	2.297	4497	0.02166	-0.03214	0.3217
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006181	0.002322	-2.662	4492	0.007793	-0.0127	0.0003365
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007284	0.0000272	2.678	4487	0.007428	-0.000003503	0.0001492
fixed	NA	male	-0.2789	0.02913	-9.575	4471	1.642e-21	-0.3607	-0.1971
fixed	NA	sibling_count3	0.01973	0.03929	0.5021	3297	0.6157	-0.09056	0.13
fixed	NA	sibling_count4	0.02189	0.0423	0.5175	2818	0.6048	-0.09684	0.1406
fixed	NA	sibling_count5	0.07225	0.04815	1.5	2435	0.1336	-0.06292	0.2074
ran_pars	mother_pidlink	sd__(Intercept)	0.258	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9439	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7391	0.5407	-1.367	4498	0.1717	-2.257	0.7787
fixed	NA	birth_order	-0.01964	0.01533	-1.281	4211	0.2002	-0.06268	0.02339
fixed	NA	poly(age, 3, raw = TRUE)1	0.1436	0.06302	2.278	4496	0.02275	-0.03332	0.3205
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006114	0.002322	-2.633	4491	0.008494	-0.01263	0.0004043
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007166	0.00002721	2.633	4486	0.008481	-0.000004723	0.000148
fixed	NA	male	-0.2782	0.02913	-9.551	4470	2.053e-21	-0.36	-0.1965
fixed	NA	sibling_count3	0.02871	0.0399	0.7195	3362	0.4719	-0.0833	0.1407
fixed	NA	sibling_count4	0.0425	0.04525	0.9393	3062	0.3476	-0.08451	0.1695
fixed	NA	sibling_count5	0.1068	0.05517	1.935	2979	0.05307	-0.0481	0.2616
ran_pars	mother_pidlink	sd__(Intercept)	0.2574	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.944	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.802	0.5405	-1.484	4494	0.138	-2.319	0.7154
fixed	NA	poly(age, 3, raw = TRUE)1	0.1487	0.06301	2.36	4491	0.01832	-0.02817	0.3256
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006297	0.002322	-2.712	4486	0.006713	-0.01281	0.0002206
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007357	0.0000272	2.704	4481	0.006867	-0.00000279	0.0001499
fixed	NA	male	-0.2775	0.02911	-9.532	4467	2.461e-21	-0.3592	-0.1958
fixed	NA	sibling_count3	0.003462	0.04052	0.08544	3492	0.9319	-0.1103	0.1172
fixed	NA	sibling_count4	0.03207	0.04591	0.6985	3173	0.4849	-0.0968	0.1609
fixed	NA	sibling_count5	0.1202	0.05608	2.143	3073	0.03215	-0.03721	0.2776
fixed	NA	birth_order_nonlinear2	-0.01941	0.03488	-0.5564	3660	0.578	-0.1173	0.07849
fixed	NA	birth_order_nonlinear3	0.07233	0.0444	1.629	3899	0.1034	-0.05229	0.1969
fixed	NA	birth_order_nonlinear4	-0.1266	0.05955	-2.127	4094	0.03351	-0.2938	0.04052
fixed	NA	birth_order_nonlinear5	-0.1761	0.09279	-1.898	3980	0.0578	-0.4366	0.08437
ran_pars	mother_pidlink	sd__(Intercept)	0.2574	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.943	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8205	0.5404	-1.518	4488	0.129	-2.337	0.6963
fixed	NA	poly(age, 3, raw = TRUE)1	0.151	0.063	2.396	4486	0.0166	-0.02587	0.3278
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006352	0.002321	-2.736	4481	0.006236	-0.01287	0.000164
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000739	0.0000272	2.717	4476	0.006621	-0.00000246	0.0001503
fixed	NA	male	-0.2777	0.0291	-9.54	4459	2.277e-21	-0.3594	-0.196
fixed	NA	count_birth_order2/2	-0.03788	0.05976	-0.6339	3814	0.5262	-0.2056	0.1299
fixed	NA	count_birth_order1/3	-0.04035	0.05236	-0.7706	4486	0.441	-0.1873	0.1066
fixed	NA	count_birth_order2/3	0.0175	0.05722	0.3057	4490	0.7598	-0.1431	0.1781
fixed	NA	count_birth_order3/3	0.08657	0.06399	1.353	4487	0.1762	-0.09306	0.2662
fixed	NA	count_birth_order1/4	0.04223	0.06424	0.6574	4487	0.511	-0.1381	0.2226
fixed	NA	count_birth_order2/4	0.04556	0.06641	0.6861	4490	0.4927	-0.1408	0.232
fixed	NA	count_birth_order3/4	0.0414	0.07016	0.59	4482	0.5552	-0.1555	0.2383
fixed	NA	count_birth_order4/4	-0.1137	0.07288	-1.56	4480	0.1188	-0.3183	0.09089
fixed	NA	count_birth_order1/5	0.205	0.08742	2.345	4489	0.01907	-0.0404	0.4504
fixed	NA	count_birth_order2/5	-0.1068	0.09339	-1.144	4481	0.2529	-0.3689	0.1553
fixed	NA	count_birth_order3/5	0.2462	0.0875	2.814	4476	0.004913	0.0006185	0.4918
fixed	NA	count_birth_order4/5	0.004021	0.08424	0.04773	4477	0.9619	-0.2324	0.2405
fixed	NA	count_birth_order5/5	-0.06247	0.08762	-0.7129	4469	0.4759	-0.3084	0.1835
ran_pars	mother_pidlink	sd__(Intercept)	0.259	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.942	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12601	12665	-6290	12581	NA	NA	NA
11	12601	12672	-6290	12579	1.645	1	0.1996
14	12595	12685	-6284	12567	12.18	3	0.006797
20	12596	12724	-6278	12556	11.23	6	0.08139

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.064	0.5549	-1.918	4177	0.05516	-2.622	0.4933
fixed	NA	poly(age, 3, raw = TRUE)1	0.1824	0.0648	2.815	4174	0.0049	0.0005176	0.3643
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007538	0.002388	-3.156	4170	0.001609	-0.01424	-0.0008341
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008825	0.00002798	3.154	4165	0.00162	0.000009715	0.0001668
fixed	NA	male	-0.3028	0.03018	-10.03	4149	1.982e-23	-0.3875	-0.2181
fixed	NA	sibling_count3	0.000532	0.04237	0.01256	3145	0.99	-0.1184	0.1195
fixed	NA	sibling_count4	0.002049	0.0447	0.04585	2809	0.9634	-0.1234	0.1275
fixed	NA	sibling_count5	-0.03458	0.04774	-0.7244	2443	0.4689	-0.1686	0.09943
ran_pars	mother_pidlink	sd__(Intercept)	0.2497	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9434	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.035	0.5555	-1.863	4176	0.06258	-2.594	0.5246
fixed	NA	birth_order	-0.01807	0.01533	-1.179	3985	0.2385	-0.06109	0.02495
fixed	NA	poly(age, 3, raw = TRUE)1	0.1815	0.0648	2.8	4173	0.005133	-0.0004529	0.3634
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007482	0.002389	-3.132	4169	0.001746	-0.01419	-0.0007773
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008723	0.00002799	3.117	4165	0.001842	0.000008663	0.0001658
fixed	NA	male	-0.3024	0.03018	-10.02	4148	2.269e-23	-0.3871	-0.2177
fixed	NA	sibling_count3	0.008793	0.04294	0.2048	3190	0.8377	-0.1117	0.1293
fixed	NA	sibling_count4	0.02037	0.04731	0.4305	2987	0.6669	-0.1124	0.1532
fixed	NA	sibling_count5	-0.005312	0.05381	-0.09872	2865	0.9214	-0.1564	0.1457
ran_pars	mother_pidlink	sd__(Intercept)	0.2487	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9437	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.099	0.5551	-1.98	4171	0.04777	-2.657	0.4591
fixed	NA	poly(age, 3, raw = TRUE)1	0.1871	0.06476	2.888	4169	0.003894	0.005257	0.3689
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007687	0.002387	-3.22	4164	0.001292	-0.01439	-0.0009859
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008946	0.00002797	3.198	4159	0.001392	0.00001095	0.000168
fixed	NA	male	-0.3027	0.03014	-10.04	4144	1.816e-23	-0.3873	-0.2181
fixed	NA	sibling_count3	-0.01704	0.04356	-0.3911	3296	0.6957	-0.1393	0.1052
fixed	NA	sibling_count4	-0.002756	0.04797	-0.05745	3083	0.9542	-0.1374	0.1319
fixed	NA	sibling_count5	0.006124	0.05433	0.1127	2915	0.9103	-0.1464	0.1586
fixed	NA	birth_order_nonlinear2	-0.01769	0.03621	-0.4886	3448	0.6252	-0.1193	0.08396
fixed	NA	birth_order_nonlinear3	0.07904	0.04572	1.729	3689	0.08396	-0.04931	0.2074
fixed	NA	birth_order_nonlinear4	-0.05703	0.06045	-0.9435	3847	0.3455	-0.2267	0.1127
fixed	NA	birth_order_nonlinear5	-0.2522	0.08864	-2.846	3761	0.004457	-0.5011	-0.003418
ran_pars	mother_pidlink	sd__(Intercept)	0.2513	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9417	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.073	0.5554	-1.932	4165	0.05337	-2.632	0.4858
fixed	NA	poly(age, 3, raw = TRUE)1	0.1835	0.06479	2.832	4163	0.004652	0.001599	0.3653
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007532	0.002388	-3.154	4158	0.001624	-0.01424	-0.000828
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000874	0.00002799	3.122	4153	0.001806	0.000008829	0.000166
fixed	NA	male	-0.304	0.03016	-10.08	4139	1.29e-23	-0.3887	-0.2193
fixed	NA	count_birth_order2/2	-0.01504	0.06528	-0.2304	3580	0.8178	-0.1983	0.1682
fixed	NA	count_birth_order1/3	-0.02606	0.05658	-0.4606	4164	0.6451	-0.1849	0.1328
fixed	NA	count_birth_order2/3	-0.03837	0.06136	-0.6253	4167	0.5318	-0.2106	0.1339
fixed	NA	count_birth_order3/3	0.08944	0.06909	1.295	4164	0.1955	-0.1045	0.2834
fixed	NA	count_birth_order1/4	-0.05097	0.06716	-0.7588	4165	0.448	-0.2395	0.1376
fixed	NA	count_birth_order2/4	-0.00024	0.06836	-0.003511	4167	0.9972	-0.1921	0.1917
fixed	NA	count_birth_order3/4	0.1025	0.07499	1.367	4160	0.1716	-0.108	0.313
fixed	NA	count_birth_order4/4	-0.03813	0.07724	-0.4936	4159	0.6216	-0.2549	0.1787
fixed	NA	count_birth_order1/5	0.1186	0.07992	1.484	4167	0.1378	-0.1057	0.343
fixed	NA	count_birth_order2/5	-0.03846	0.08565	-0.449	4164	0.6535	-0.2789	0.202
fixed	NA	count_birth_order3/5	0.0095	0.0832	0.1142	4160	0.9091	-0.224	0.243
fixed	NA	count_birth_order4/5	-0.07809	0.08619	-0.9059	4151	0.365	-0.32	0.1639
fixed	NA	count_birth_order5/5	-0.2462	0.08636	-2.851	4147	0.004375	-0.4887	-0.003826
ran_pars	mother_pidlink	sd__(Intercept)	0.2471	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9428	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11678	11741	-5829	11658	NA	NA	NA
11	11679	11748	-5828	11657	1.394	1	0.2378
14	11671	11759	-5821	11643	13.85	3	0.003115
20	11677	11804	-5819	11637	5.612	6	0.468

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.9207	0.5436	-1.694	4484	0.09038	-2.447	0.6052
fixed	NA	poly(age, 3, raw = TRUE)1	0.1625	0.06351	2.558	4480	0.01055	-0.0158	0.3407
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006881	0.002343	-2.937	4474	0.003335	-0.01346	-0.0003037
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008168	0.0000275	2.97	4468	0.002991	0.00000449	0.0001589
fixed	NA	male	-0.2813	0.02911	-9.664	4461	7.035e-22	-0.3631	-0.1996
fixed	NA	sibling_count3	0.02414	0.0386	0.6253	3261	0.5318	-0.08423	0.1325
fixed	NA	sibling_count4	0.02711	0.04178	0.6489	2789	0.5165	-0.09016	0.1444
fixed	NA	sibling_count5	0.063	0.04901	1.285	2296	0.1988	-0.07458	0.2006
ran_pars	mother_pidlink	sd__(Intercept)	0.2432	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9447	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8966	0.5442	-1.647	4483	0.09954	-2.424	0.6311
fixed	NA	birth_order	-0.0148	0.01551	-0.9544	4187	0.3399	-0.05834	0.02873
fixed	NA	poly(age, 3, raw = TRUE)1	0.1617	0.06351	2.545	4479	0.01095	-0.01661	0.34
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006834	0.002344	-2.916	4473	0.003563	-0.01341	-0.0002554
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008083	0.00002751	2.938	4467	0.003321	0.000003602	0.0001581
fixed	NA	male	-0.2809	0.02912	-9.649	4460	8.13e-22	-0.3627	-0.1992
fixed	NA	sibling_count3	0.03089	0.03924	0.7871	3323	0.4313	-0.07927	0.141
fixed	NA	sibling_count4	0.04257	0.04481	0.9501	3049	0.3421	-0.0832	0.1683
fixed	NA	sibling_count5	0.08778	0.05546	1.583	2789	0.1136	-0.0679	0.2435
ran_pars	mother_pidlink	sd__(Intercept)	0.2424	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9449	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.9606	0.5441	-1.765	4477	0.07755	-2.488	0.5667
fixed	NA	poly(age, 3, raw = TRUE)1	0.1673	0.06352	2.634	4473	0.008464	-0.01098	0.3456
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007035	0.002344	-3.002	4467	0.0027	-0.01361	-0.0004562
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008295	0.00002751	3.016	4461	0.00258	0.000005735	0.0001602
fixed	NA	male	-0.2791	0.0291	-9.591	4457	1.407e-21	-0.3608	-0.1974
fixed	NA	sibling_count3	0.007852	0.03989	0.1969	3462	0.8439	-0.1041	0.1198
fixed	NA	sibling_count4	0.03562	0.04548	0.7832	3163	0.4335	-0.09204	0.1633
fixed	NA	sibling_count5	0.102	0.05658	1.803	2890	0.07154	-0.05683	0.2608
fixed	NA	birth_order_nonlinear2	-0.01212	0.03465	-0.3497	3650	0.7266	-0.1094	0.08515
fixed	NA	birth_order_nonlinear3	0.06997	0.04421	1.583	3867	0.1136	-0.05414	0.1941
fixed	NA	birth_order_nonlinear4	-0.1202	0.06077	-1.978	4077	0.04798	-0.2908	0.05037
fixed	NA	birth_order_nonlinear5	-0.1434	0.09921	-1.446	4044	0.1483	-0.4219	0.1351
ran_pars	mother_pidlink	sd__(Intercept)	0.241	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9444	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.9636	0.5441	-1.771	4472	0.07661	-2.491	0.5636
fixed	NA	poly(age, 3, raw = TRUE)1	0.1681	0.06352	2.647	4468	0.008147	-0.01016	0.3464
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007048	0.002344	-3.007	4462	0.002649	-0.01363	-0.0004697
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008295	0.00002751	3.015	4457	0.002585	0.000005721	0.0001602
fixed	NA	male	-0.2786	0.0291	-9.573	4450	1.676e-21	-0.3603	-0.1969
fixed	NA	count_birth_order2/2	-0.03536	0.05818	-0.6078	3774	0.5434	-0.1987	0.128
fixed	NA	count_birth_order1/3	-0.03386	0.0516	-0.6561	4471	0.5118	-0.1787	0.111
fixed	NA	count_birth_order2/3	0.02379	0.05707	0.4168	4475	0.6768	-0.1364	0.184
fixed	NA	count_birth_order3/3	0.08574	0.06273	1.367	4471	0.1718	-0.09035	0.2618
fixed	NA	count_birth_order1/4	0.03541	0.06439	0.5499	4473	0.5824	-0.1453	0.2162
fixed	NA	count_birth_order2/4	0.05524	0.06615	0.8351	4475	0.4037	-0.1304	0.2409
fixed	NA	count_birth_order3/4	0.06876	0.06929	0.9923	4467	0.3211	-0.1257	0.2632
fixed	NA	count_birth_order4/4	-0.125	0.0732	-1.707	4464	0.08782	-0.3304	0.08049
fixed	NA	count_birth_order1/5	0.1799	0.08702	2.067	4475	0.0388	-0.06441	0.4241
fixed	NA	count_birth_order2/5	-0.1064	0.09603	-1.108	4468	0.2679	-0.376	0.1632
fixed	NA	count_birth_order3/5	0.1785	0.09152	1.95	4462	0.05125	-0.07845	0.4354
fixed	NA	count_birth_order4/5	0.02266	0.08813	0.2571	4464	0.7971	-0.2247	0.2701
fixed	NA	count_birth_order5/5	-0.04992	0.09361	-0.5333	4458	0.5939	-0.3127	0.2128
ran_pars	mother_pidlink	sd__(Intercept)	0.2413	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.944	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12533	12597	-6256	12513	NA	NA	NA
11	12534	12604	-6256	12512	0.9136	1	0.3392
14	12530	12619	-6251	12502	10.13	3	0.01746
20	12533	12661	-6246	12493	9.021	6	0.1724

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Conscientiousness

birthorder <- birthorder %>% mutate(outcome = big5_con)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.47	0.1995	-7.367	6662	1.949e-13	-2.029	-0.9097
fixed	NA	poly(age, 3, raw = TRUE)1	0.08787	0.01915	4.588	6467	0.000004563	0.03411	0.1416
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001427	0.0005591	-2.553	6253	0.01071	-0.002997	0.0001421
fixed	NA	poly(age, 3, raw = TRUE)3	0.000007095	0.000005071	1.399	6090	0.1618	-0.000007139	0.00002133
fixed	NA	male	0.03101	0.02331	1.33	7074	0.1834	-0.03442	0.09645
fixed	NA	sibling_count3	-0.01205	0.03315	-0.3634	4930	0.7163	-0.1051	0.08101
fixed	NA	sibling_count4	-0.0115	0.03412	-0.337	4334	0.7361	-0.1073	0.08428
fixed	NA	sibling_count5	-0.003066	0.03542	-0.08656	3711	0.931	-0.1025	0.09637
ran_pars	mother_pidlink	sd__(Intercept)	0.2647	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9501	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.458	0.1995	-7.312	6654	2.943e-13	-2.018	-0.8985
fixed	NA	birth_order	-0.03218	0.01167	-2.758	6109	0.005835	-0.06494	0.0005733
fixed	NA	poly(age, 3, raw = TRUE)1	0.09109	0.01918	4.748	6500	0.000002095	0.03724	0.1449
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001509	0.0005598	-2.696	6273	0.007042	-0.00308	0.00006229
fixed	NA	poly(age, 3, raw = TRUE)3	0.000007626	0.000005074	1.503	6103	0.1329	-0.000006616	0.00002187
fixed	NA	male	0.03193	0.0233	1.37	7070	0.1706	-0.03348	0.09734
fixed	NA	sibling_count3	-0.0005436	0.03342	-0.01627	5064	0.987	-0.09434	0.09326
fixed	NA	sibling_count4	0.01531	0.03548	0.4315	4906	0.6661	-0.08429	0.1149
fixed	NA	sibling_count5	0.04002	0.03873	1.033	4853	0.3015	-0.0687	0.1487
ran_pars	mother_pidlink	sd__(Intercept)	0.2673	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.949	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.471	0.2	-7.355	6680	2.145e-13	-2.033	-0.9096
fixed	NA	poly(age, 3, raw = TRUE)1	0.09023	0.01919	4.701	6486	0.000002641	0.03635	0.1441
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001482	0.0005602	-2.645	6249	0.008185	-0.003054	0.00009066
fixed	NA	poly(age, 3, raw = TRUE)3	0.000007368	0.000005079	1.451	6067	0.1469	-0.00000689	0.00002163
fixed	NA	male	0.03195	0.0233	1.371	7067	0.1704	-0.03346	0.09736
fixed	NA	sibling_count3	-0.005349	0.03396	-0.1575	5290	0.8749	-0.1007	0.08998
fixed	NA	sibling_count4	0.005625	0.03609	0.1559	5162	0.8762	-0.09568	0.1069
fixed	NA	sibling_count5	0.03633	0.03912	0.9286	5039	0.3531	-0.07348	0.1461
fixed	NA	birth_order_nonlinear2	-0.06284	0.02774	-2.266	5961	0.0235	-0.1407	0.01501
fixed	NA	birth_order_nonlinear3	-0.05089	0.0356	-1.43	5936	0.1529	-0.1508	0.04903
fixed	NA	birth_order_nonlinear4	-0.07589	0.04649	-1.632	5955	0.1026	-0.2064	0.05461
fixed	NA	birth_order_nonlinear5	-0.1737	0.06767	-2.567	5842	0.01028	-0.3637	0.01623
ran_pars	mother_pidlink	sd__(Intercept)	0.2675	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9489	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.448	0.2004	-7.223	6686	5.669e-13	-2.01	-0.885
fixed	NA	poly(age, 3, raw = TRUE)1	0.09029	0.01919	4.704	6484	0.000002602	0.03641	0.1442
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001478	0.0005602	-2.638	6244	0.008357	-0.00305	0.00009461
fixed	NA	poly(age, 3, raw = TRUE)3	0.000007284	0.00000508	1.434	6059	0.1516	-0.000006974	0.00002154
fixed	NA	male	0.03158	0.02331	1.355	7060	0.1755	-0.03385	0.09701
fixed	NA	count_birth_order2/2	-0.1321	0.04734	-2.791	5893	0.005273	-0.265	0.0007633
fixed	NA	count_birth_order1/3	-0.06049	0.04449	-1.36	7116	0.174	-0.1854	0.0644
fixed	NA	count_birth_order2/3	-0.05489	0.04977	-1.103	7126	0.27	-0.1946	0.0848
fixed	NA	count_birth_order3/3	-0.07674	0.05581	-1.375	7129	0.1692	-0.2334	0.07992
fixed	NA	count_birth_order1/4	-0.03788	0.05084	-0.7452	7127	0.4562	-0.1806	0.1048
fixed	NA	count_birth_order2/4	-0.08253	0.05347	-1.543	7128	0.1228	-0.2326	0.06757
fixed	NA	count_birth_order3/4	-0.03697	0.05813	-0.6359	7128	0.5249	-0.2001	0.1262
fixed	NA	count_birth_order4/4	-0.1067	0.0616	-1.732	7125	0.08339	-0.2796	0.06625
fixed	NA	count_birth_order1/5	0.02716	0.05771	0.4706	7129	0.638	-0.1348	0.1892
fixed	NA	count_birth_order2/5	-0.03752	0.06073	-0.6178	7125	0.5367	-0.208	0.133
fixed	NA	count_birth_order3/5	-0.08859	0.06235	-1.421	7123	0.1554	-0.2636	0.08644
fixed	NA	count_birth_order4/5	-0.0528	0.06609	-0.7988	7118	0.4244	-0.2383	0.1327
fixed	NA	count_birth_order5/5	-0.1635	0.06757	-2.42	7115	0.01556	-0.3532	0.02618
ran_pars	mother_pidlink	sd__(Intercept)	0.2666	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9492	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	20080	20149	-10030	20060	NA	NA	NA
11	20075	20150	-10026	20053	7.597	1	0.005845
14	20078	20174	-10025	20050	2.76	3	0.4301
20	20084	20222	-10022	20044	5.739	6	0.4531

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.099	0.5525	-1.989	4498	0.04672	-2.65	0.4518
fixed	NA	poly(age, 3, raw = TRUE)1	0.04192	0.06446	0.6504	4494	0.5155	-0.139	0.2229
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002302	0.002375	0.09693	4487	0.9228	-0.006435	0.006896
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000977	0.00002781	-0.3513	4481	0.7254	-0.00008784	0.0000683
fixed	NA	male	0.04417	0.02981	1.482	4477	0.1385	-0.0395	0.1279
fixed	NA	sibling_count3	-0.02662	0.04006	-0.6644	3248	0.5065	-0.1391	0.08583
fixed	NA	sibling_count4	-0.04555	0.04309	-1.057	2744	0.2905	-0.1665	0.07539
fixed	NA	sibling_count5	-0.0141	0.04901	-0.2876	2343	0.7736	-0.1517	0.1235
ran_pars	mother_pidlink	sd__(Intercept)	0.2378	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.972	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.033	0.5528	-1.868	4497	0.0618	-2.584	0.519
fixed	NA	birth_order	-0.03961	0.01569	-2.524	4208	0.01165	-0.08366	0.004447
fixed	NA	poly(age, 3, raw = TRUE)1	0.03953	0.06443	0.6135	4493	0.5396	-0.1413	0.2204
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003663	0.002374	0.1543	4488	0.8774	-0.006297	0.00703
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001217	0.00002781	-0.4376	4481	0.6617	-0.00009025	0.0000659
fixed	NA	male	0.0454	0.0298	1.524	4475	0.1276	-0.03823	0.129
fixed	NA	sibling_count3	-0.008487	0.04069	-0.2086	3316	0.8348	-0.1227	0.1057
fixed	NA	sibling_count4	-0.004046	0.04612	-0.08773	2999	0.9301	-0.1335	0.1254
fixed	NA	sibling_count5	0.05526	0.05622	0.9828	2902	0.3258	-0.1026	0.2131
ran_pars	mother_pidlink	sd__(Intercept)	0.2421	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9704	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.077	0.5532	-1.947	4492	0.05163	-2.63	0.4759
fixed	NA	poly(age, 3, raw = TRUE)1	0.0406	0.06449	0.6296	4488	0.529	-0.1404	0.2216
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003283	0.002376	0.1382	4481	0.8901	-0.006341	0.006998
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001179	0.00002784	-0.4236	4475	0.6719	-0.00008993	0.00006635
fixed	NA	male	0.04547	0.02981	1.525	4472	0.1272	-0.0382	0.1291
fixed	NA	sibling_count3	-0.0181	0.04137	-0.4374	3448	0.6618	-0.1342	0.09802
fixed	NA	sibling_count4	-0.01065	0.04685	-0.2274	3108	0.8201	-0.1421	0.1208
fixed	NA	sibling_count5	0.05809	0.05721	1.015	2992	0.31	-0.1025	0.2187
fixed	NA	birth_order_nonlinear2	-0.05233	0.03578	-1.462	3633	0.1437	-0.1528	0.04811
fixed	NA	birth_order_nonlinear3	-0.03777	0.04553	-0.8295	3886	0.4069	-0.1656	0.09003
fixed	NA	birth_order_nonlinear4	-0.1355	0.06104	-2.22	4092	0.02645	-0.3069	0.03581
fixed	NA	birth_order_nonlinear5	-0.2042	0.09514	-2.147	3979	0.03189	-0.4713	0.06284
ran_pars	mother_pidlink	sd__(Intercept)	0.2405	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9709	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.062	0.5533	-1.919	4486	0.05501	-2.615	0.4912
fixed	NA	poly(age, 3, raw = TRUE)1	0.04168	0.0645	0.6462	4483	0.5182	-0.1394	0.2227
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002473	0.002377	0.104	4476	0.9171	-0.006424	0.006918
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001032	0.00002785	-0.3706	4470	0.7109	-0.00008849	0.00006785
fixed	NA	male	0.04612	0.02982	1.547	4466	0.122	-0.03758	0.1298
fixed	NA	count_birth_order2/2	-0.1015	0.06133	-1.654	3783	0.09812	-0.2736	0.07069
fixed	NA	count_birth_order1/3	-0.005411	0.05361	-0.1009	4487	0.9196	-0.1559	0.1451
fixed	NA	count_birth_order2/3	-0.1003	0.0586	-1.712	4490	0.08705	-0.2648	0.06419
fixed	NA	count_birth_order3/3	-0.1107	0.06554	-1.69	4487	0.09116	-0.2947	0.07323
fixed	NA	count_birth_order1/4	-0.06003	0.06578	-0.9126	4487	0.3615	-0.2447	0.1246
fixed	NA	count_birth_order2/4	-0.06124	0.06801	-0.9005	4490	0.3679	-0.2521	0.1297
fixed	NA	count_birth_order3/4	-0.02798	0.07186	-0.3893	4484	0.6971	-0.2297	0.1737
fixed	NA	count_birth_order4/4	-0.1808	0.07465	-2.422	4482	0.01546	-0.3904	0.02873
fixed	NA	count_birth_order1/5	-0.09531	0.08953	-1.064	4490	0.2872	-0.3466	0.156
fixed	NA	count_birth_order2/5	0.09181	0.09565	0.9598	4484	0.3372	-0.1767	0.3603
fixed	NA	count_birth_order3/5	0.02478	0.08963	0.2765	4479	0.7822	-0.2268	0.2764
fixed	NA	count_birth_order4/5	-0.06633	0.08629	-0.7687	4480	0.4421	-0.3085	0.1759
fixed	NA	count_birth_order5/5	-0.1617	0.08976	-1.802	4472	0.07164	-0.4137	0.09023
ran_pars	mother_pidlink	sd__(Intercept)	0.239	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9711	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12806	12870	-6393	12786	NA	NA	NA
11	12801	12872	-6390	12779	6.362	1	0.01166
14	12805	12895	-6389	12777	1.86	3	0.602
20	12810	12939	-6385	12770	7.234	6	0.2998

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.313	0.5685	-2.309	4175	0.02097	-2.909	0.283
fixed	NA	poly(age, 3, raw = TRUE)1	0.07063	0.06638	1.064	4171	0.2874	-0.1157	0.257
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0008233	0.002446	-0.3366	4164	0.7365	-0.00769	0.006043
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002617	0.00002865	0.09135	4157	0.9272	-0.00007781	0.00008305
fixed	NA	male	0.03828	0.03094	1.237	4158	0.216	-0.04856	0.1251
fixed	NA	sibling_count3	-0.07058	0.04322	-1.633	3127	0.1026	-0.1919	0.05075
fixed	NA	sibling_count4	-0.06824	0.04555	-1.498	2774	0.1342	-0.1961	0.05962
fixed	NA	sibling_count5	-0.06113	0.0486	-1.258	2387	0.2086	-0.1975	0.07528
ran_pars	mother_pidlink	sd__(Intercept)	0.2159	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.976	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.254	0.5688	-2.204	4174	0.02755	-2.851	0.3428
fixed	NA	birth_order	-0.03564	0.01572	-2.268	3996	0.0234	-0.07977	0.008477
fixed	NA	poly(age, 3, raw = TRUE)1	0.06867	0.06635	1.035	4170	0.3008	-0.1176	0.2549
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007097	0.002446	-0.2902	4164	0.7717	-0.007574	0.006155
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000005678	0.00002865	0.01981	4158	0.9842	-0.00007987	0.000081
fixed	NA	male	0.03898	0.03092	1.261	4156	0.2075	-0.04781	0.1258
fixed	NA	sibling_count3	-0.05432	0.04381	-1.24	3174	0.215	-0.1773	0.06864
fixed	NA	sibling_count4	-0.03216	0.04825	-0.6665	2959	0.5051	-0.1676	0.1033
fixed	NA	sibling_count5	-0.003572	0.05485	-0.06511	2822	0.9481	-0.1575	0.1504
ran_pars	mother_pidlink	sd__(Intercept)	0.2197	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9746	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.263	0.5692	-2.219	4169	0.02655	-2.861	0.3347
fixed	NA	poly(age, 3, raw = TRUE)1	0.0667	0.0664	1.004	4164	0.3152	-0.1197	0.2531
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006384	0.002447	-0.2609	4158	0.7942	-0.007508	0.006231
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000002049	0.00002867	-0.007144	4152	0.9943	-0.00008069	0.00008028
fixed	NA	male	0.03836	0.03093	1.24	4154	0.215	-0.04847	0.1252
fixed	NA	sibling_count3	-0.05133	0.04449	-1.154	3286	0.2487	-0.1762	0.07355
fixed	NA	sibling_count4	-0.03892	0.04896	-0.7949	3060	0.4267	-0.1764	0.09852
fixed	NA	sibling_count5	-0.006557	0.05543	-0.1183	2870	0.9058	-0.1622	0.149
fixed	NA	birth_order_nonlinear2	-0.065	0.03728	-1.744	3457	0.08128	-0.1696	0.03963
fixed	NA	birth_order_nonlinear3	-0.08652	0.04703	-1.84	3710	0.06589	-0.2185	0.04549
fixed	NA	birth_order_nonlinear4	-0.06627	0.06214	-1.066	3871	0.2863	-0.2407	0.1082
fixed	NA	birth_order_nonlinear5	-0.1763	0.09115	-1.934	3795	0.05321	-0.4321	0.07959
ran_pars	mother_pidlink	sd__(Intercept)	0.2164	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9755	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.266	0.5697	-2.222	4163	0.02637	-2.865	0.3336
fixed	NA	poly(age, 3, raw = TRUE)1	0.0677	0.06646	1.019	4159	0.3084	-0.1188	0.2542
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00069	0.002449	-0.2817	4153	0.7782	-0.007566	0.006186
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000005663	0.0000287	0.01973	4146	0.9843	-0.00008	0.00008114
fixed	NA	male	0.03937	0.03096	1.271	4147	0.2036	-0.04754	0.1263
fixed	NA	count_birth_order2/2	-0.07457	0.06716	-1.11	3572	0.2669	-0.2631	0.114
fixed	NA	count_birth_order1/3	-0.04803	0.05804	-0.8275	4165	0.408	-0.2109	0.1149
fixed	NA	count_birth_order2/3	-0.1054	0.06295	-1.675	4167	0.094	-0.2821	0.07126
fixed	NA	count_birth_order3/3	-0.1743	0.07089	-2.459	4164	0.01396	-0.3733	0.02466
fixed	NA	count_birth_order1/4	-0.045	0.06889	-0.6533	4165	0.5136	-0.2384	0.1484
fixed	NA	count_birth_order2/4	-0.09229	0.07014	-1.316	4167	0.1883	-0.2892	0.1046
fixed	NA	count_birth_order3/4	-0.09046	0.07696	-1.175	4162	0.2399	-0.3065	0.1256
fixed	NA	count_birth_order4/4	-0.1669	0.07926	-2.106	4161	0.0353	-0.3894	0.0556
fixed	NA	count_birth_order1/5	-0.03418	0.08198	-0.4169	4166	0.6768	-0.2643	0.1959
fixed	NA	count_birth_order2/5	-0.1247	0.08789	-1.419	4166	0.1559	-0.3714	0.122
fixed	NA	count_birth_order3/5	-0.09217	0.08538	-1.08	4163	0.2804	-0.3318	0.1475
fixed	NA	count_birth_order4/5	0.001339	0.08846	0.01514	4156	0.9879	-0.247	0.2497
fixed	NA	count_birth_order5/5	-0.1854	0.08864	-2.092	4152	0.03648	-0.4343	0.06337
ran_pars	mother_pidlink	sd__(Intercept)	0.2177	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9756	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11881	11945	-5931	11861	NA	NA	NA
11	11878	11948	-5928	11856	5.14	1	0.02338
14	11883	11971	-5927	11855	1.673	3	0.643
20	11891	12018	-5926	11851	3.155	6	0.7892

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7774	0.5576	-1.394	4483	0.1634	-2.343	0.7879
fixed	NA	poly(age, 3, raw = TRUE)1	0.006837	0.06514	0.105	4478	0.9164	-0.176	0.1897
fixed	NA	poly(age, 3, raw = TRUE)2	0.001469	0.002403	0.611	4471	0.5412	-0.005278	0.008215
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002355	0.0000282	-0.8349	4464	0.4038	-0.0001027	0.00005562
fixed	NA	male	0.04058	0.02987	1.358	4464	0.1744	-0.04327	0.1244
fixed	NA	sibling_count3	-0.06404	0.03953	-1.62	3211	0.1053	-0.175	0.04691
fixed	NA	sibling_count4	-0.05905	0.04275	-1.381	2720	0.1673	-0.1791	0.06096
fixed	NA	sibling_count5	0.006905	0.05013	0.1378	2213	0.8904	-0.1338	0.1476
ran_pars	mother_pidlink	sd__(Intercept)	0.2339	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9728	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7228	0.558	-1.295	4482	0.1953	-2.289	0.8437
fixed	NA	birth_order	-0.03318	0.01591	-2.085	4177	0.0371	-0.07785	0.01148
fixed	NA	poly(age, 3, raw = TRUE)1	0.005	0.06513	0.07678	4477	0.9388	-0.1778	0.1878
fixed	NA	poly(age, 3, raw = TRUE)2	0.001576	0.002403	0.6557	4471	0.512	-0.00517	0.008321
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002547	0.00002821	-0.903	4464	0.3666	-0.0001047	0.00005371
fixed	NA	male	0.04138	0.02986	1.386	4461	0.1659	-0.04244	0.1252
fixed	NA	sibling_count3	-0.04889	0.04019	-1.216	3275	0.2239	-0.1617	0.06393
fixed	NA	sibling_count4	-0.02443	0.04588	-0.5325	2990	0.5944	-0.1532	0.1044
fixed	NA	sibling_count5	0.06233	0.05678	1.098	2718	0.2724	-0.09704	0.2217
ran_pars	mother_pidlink	sd__(Intercept)	0.2381	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9714	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7631	0.5585	-1.366	4476	0.1719	-2.331	0.8045
fixed	NA	poly(age, 3, raw = TRUE)1	0.006244	0.06519	0.09579	4471	0.9237	-0.1767	0.1892
fixed	NA	poly(age, 3, raw = TRUE)2	0.001532	0.002405	0.6371	4464	0.5241	-0.005219	0.008284
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002504	0.00002823	-0.8868	4458	0.3752	-0.0001043	0.00005421
fixed	NA	male	0.04204	0.02988	1.407	4458	0.1594	-0.04182	0.1259
fixed	NA	sibling_count3	-0.05789	0.04089	-1.416	3415	0.1569	-0.1727	0.05689
fixed	NA	sibling_count4	-0.02594	0.04662	-0.5565	3102	0.5779	-0.1568	0.1049
fixed	NA	sibling_count5	0.06232	0.05798	1.075	2816	0.2826	-0.1004	0.2251
fixed	NA	birth_order_nonlinear2	-0.04423	0.0356	-1.242	3616	0.2142	-0.1442	0.0557
fixed	NA	birth_order_nonlinear3	-0.02929	0.04542	-0.6448	3843	0.5191	-0.1568	0.09821
fixed	NA	birth_order_nonlinear4	-0.1381	0.06241	-2.212	4064	0.02701	-0.3133	0.03713
fixed	NA	birth_order_nonlinear5	-0.1351	0.1019	-1.325	4032	0.1851	-0.4211	0.151
ran_pars	mother_pidlink	sd__(Intercept)	0.2369	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9719	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7424	0.5583	-1.33	4471	0.1837	-2.31	0.8249
fixed	NA	poly(age, 3, raw = TRUE)1	0.006954	0.06518	0.1067	4466	0.915	-0.176	0.1899
fixed	NA	poly(age, 3, raw = TRUE)2	0.001458	0.002405	0.6061	4460	0.5445	-0.005293	0.008208
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002354	0.00002823	-0.8338	4453	0.4044	-0.0001028	0.0000557
fixed	NA	male	0.0423	0.02987	1.416	4452	0.1569	-0.04155	0.1261
fixed	NA	count_birth_order2/2	-0.09533	0.05977	-1.595	3740	0.1108	-0.2631	0.07245
fixed	NA	count_birth_order1/3	-0.03278	0.05295	-0.619	4471	0.5359	-0.1814	0.1159
fixed	NA	count_birth_order2/3	-0.1422	0.05857	-2.427	4475	0.01525	-0.3066	0.02224
fixed	NA	count_birth_order3/3	-0.1568	0.06438	-2.436	4471	0.01491	-0.3375	0.02392
fixed	NA	count_birth_order1/4	-0.1093	0.06608	-1.655	4473	0.09804	-0.2948	0.07614
fixed	NA	count_birth_order2/4	-0.03314	0.06789	-0.4881	4475	0.6255	-0.2237	0.1574
fixed	NA	count_birth_order3/4	-0.02125	0.07111	-0.2989	4467	0.7651	-0.2209	0.1784
fixed	NA	count_birth_order4/4	-0.2189	0.07512	-2.914	4464	0.003591	-0.4298	-0.008005
fixed	NA	count_birth_order1/5	-0.09137	0.0893	-1.023	4475	0.3063	-0.342	0.1593
fixed	NA	count_birth_order2/5	0.0628	0.09856	0.6372	4469	0.524	-0.2139	0.3395
fixed	NA	count_birth_order3/5	0.04785	0.09394	0.5094	4464	0.6105	-0.2158	0.3115
fixed	NA	count_birth_order4/5	-0.03201	0.09046	-0.3539	4464	0.7234	-0.2859	0.2219
fixed	NA	count_birth_order5/5	-0.08909	0.09607	-0.9272	4459	0.3538	-0.3588	0.1806
ran_pars	mother_pidlink	sd__(Intercept)	0.2364	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9715	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12762	12826	-6371	12742	NA	NA	NA
11	12760	12830	-6369	12738	4.342	1	0.03719
14	12764	12854	-6368	12736	1.716	3	0.6335
20	12765	12894	-6363	12725	10.69	6	0.09841

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Agreeableness

birthorder <- birthorder %>% mutate(outcome = big5_agree)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.6396	0.2026	-3.157	6657	0.0016	-1.208	-0.07095
fixed	NA	poly(age, 3, raw = TRUE)1	0.03037	0.01945	1.562	6461	0.1184	-0.02423	0.08497
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000251	0.0005678	-0.442	6245	0.6585	-0.001845	0.001343
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001566	0.00000515	-0.3042	6082	0.761	-0.00001602	0.00001289
fixed	NA	male	0.08125	0.02368	3.431	7076	0.0006058	0.01477	0.1477
fixed	NA	sibling_count3	-0.02006	0.03366	-0.5959	4930	0.5513	-0.1145	0.07442
fixed	NA	sibling_count4	0.02959	0.03464	0.8544	4330	0.3929	-0.06763	0.1268
fixed	NA	sibling_count5	0.005736	0.03595	0.1595	3704	0.8733	-0.09519	0.1067
ran_pars	mother_pidlink	sd__(Intercept)	0.265	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9662	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.6382	0.2026	-3.149	6646	0.001643	-1.207	-0.06939
fixed	NA	birth_order	-0.004159	0.01187	-0.3504	6119	0.726	-0.03747	0.02916
fixed	NA	poly(age, 3, raw = TRUE)1	0.03079	0.01949	1.58	6489	0.1141	-0.02391	0.0855
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002616	0.0005686	-0.4601	6261	0.6455	-0.001858	0.001335
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001497	0.000005154	-0.2905	6090	0.7715	-0.00001596	0.00001297
fixed	NA	male	0.08137	0.02369	3.435	7074	0.0005957	0.01488	0.1479
fixed	NA	sibling_count3	-0.01856	0.03393	-0.5471	5066	0.5844	-0.1138	0.07668
fixed	NA	sibling_count4	0.03307	0.03603	0.9178	4904	0.3588	-0.06807	0.1342
fixed	NA	sibling_count5	0.01131	0.03932	0.2876	4847	0.7736	-0.09907	0.1217
ran_pars	mother_pidlink	sd__(Intercept)	0.2652	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9663	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.6372	0.2032	-3.136	6674	0.001721	-1.208	-0.06682
fixed	NA	poly(age, 3, raw = TRUE)1	0.03043	0.0195	1.561	6477	0.1187	-0.0243	0.08516
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002432	0.000569	-0.4274	6239	0.6691	-0.00184	0.001354
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000173	0.000005159	-0.3352	6056	0.7375	-0.00001621	0.00001275
fixed	NA	male	0.08145	0.02368	3.439	7070	0.0005871	0.01497	0.1479
fixed	NA	sibling_count3	-0.006306	0.03449	-0.1829	5292	0.8549	-0.1031	0.0905
fixed	NA	sibling_count4	0.0369	0.03665	1.007	5161	0.314	-0.06597	0.1398
fixed	NA	sibling_count5	0.009944	0.03972	0.2503	5035	0.8023	-0.1015	0.1214
fixed	NA	birth_order_nonlinear2	-0.01421	0.02821	-0.5037	5966	0.6145	-0.09338	0.06497
fixed	NA	birth_order_nonlinear3	-0.06549	0.0362	-1.809	5946	0.07049	-0.1671	0.03613
fixed	NA	birth_order_nonlinear4	0.02726	0.04728	0.5766	5967	0.5643	-0.1055	0.16
fixed	NA	birth_order_nonlinear5	0.008859	0.06881	0.1287	5857	0.8976	-0.1843	0.202
ran_pars	mother_pidlink	sd__(Intercept)	0.2661	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9659	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.6303	0.2037	-3.095	6681	0.001978	-1.202	-0.05859
fixed	NA	poly(age, 3, raw = TRUE)1	0.03066	0.0195	1.572	6477	0.116	-0.02409	0.08541
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002451	0.0005692	-0.4306	6235	0.6668	-0.001843	0.001353
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001756	0.000005161	-0.3403	6049	0.7337	-0.00001624	0.00001273
fixed	NA	male	0.08157	0.02369	3.443	7062	0.000579	0.01506	0.1481
fixed	NA	count_birth_order2/2	-0.04349	0.04814	-0.9035	5891	0.3663	-0.1786	0.09163
fixed	NA	count_birth_order1/3	-0.0283	0.04522	-0.6258	7116	0.5315	-0.1552	0.09864
fixed	NA	count_birth_order2/3	0.002456	0.05058	0.04856	7126	0.9613	-0.1395	0.1444
fixed	NA	count_birth_order3/3	-0.1075	0.05672	-1.895	7129	0.05807	-0.2667	0.05171
fixed	NA	count_birth_order1/4	-0.002901	0.05167	-0.05614	7127	0.9552	-0.1479	0.1421
fixed	NA	count_birth_order2/4	0.0132	0.05435	0.2429	7128	0.8081	-0.1394	0.1658
fixed	NA	count_birth_order3/4	-0.03154	0.05909	-0.5337	7128	0.5935	-0.1974	0.1343
fixed	NA	count_birth_order4/4	0.09117	0.06261	1.456	7125	0.1454	-0.08459	0.2669
fixed	NA	count_birth_order1/5	0.03404	0.05866	0.5804	7129	0.5617	-0.1306	0.1987
fixed	NA	count_birth_order2/5	-0.04159	0.06173	-0.6738	7125	0.5005	-0.2149	0.1317
fixed	NA	count_birth_order3/5	-0.04275	0.06338	-0.6745	7123	0.5	-0.2207	0.1352
fixed	NA	count_birth_order4/5	-0.01951	0.06718	-0.2904	7118	0.7715	-0.2081	0.1691
fixed	NA	count_birth_order5/5	0.007504	0.06868	0.1093	7116	0.913	-0.1853	0.2003
ran_pars	mother_pidlink	sd__(Intercept)	0.2671	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9658	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	20306	20374	-10143	20286	NA	NA	NA
11	20308	20383	-10143	20286	0.1222	1	0.7266
14	20309	20405	-10140	20281	4.63	3	0.201
20	20317	20454	-10138	20277	4.042	6	0.671

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.5	0.5476	-2.739	4500	0.00619	-3.037	0.03735
fixed	NA	poly(age, 3, raw = TRUE)1	0.1335	0.06391	2.089	4500	0.03676	-0.04588	0.3129
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004014	0.002355	-1.704	4498	0.08838	-0.01062	0.002597
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004243	0.00002759	1.538	4494	0.1241	-0.00003501	0.0001199
fixed	NA	male	0.06132	0.0295	2.078	4451	0.03772	-0.0215	0.1441
fixed	NA	sibling_count3	-0.04346	0.04011	-1.084	3284	0.2786	-0.156	0.06912
fixed	NA	sibling_count4	-0.05491	0.04325	-1.27	2832	0.2044	-0.1763	0.0665
fixed	NA	sibling_count5	0.003817	0.04932	0.07739	2478	0.9383	-0.1346	0.1423
ran_pars	mother_pidlink	sd__(Intercept)	0.3084	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9439	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.5	0.5483	-2.736	4499	0.006243	-3.039	0.03894
fixed	NA	birth_order	0.0002383	0.0155	0.01537	4179	0.9877	-0.04327	0.04375
fixed	NA	poly(age, 3, raw = TRUE)1	0.1335	0.06392	2.089	4499	0.03678	-0.04591	0.3129
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004014	0.002356	-1.704	4497	0.08845	-0.01063	0.002598
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004244	0.00002761	1.537	4494	0.1243	-0.00003505	0.0001199
fixed	NA	male	0.06132	0.02951	2.078	4450	0.03779	-0.02152	0.1442
fixed	NA	sibling_count3	-0.04357	0.04073	-1.07	3348	0.2848	-0.1579	0.07077
fixed	NA	sibling_count4	-0.05516	0.04624	-1.193	3071	0.233	-0.185	0.07463
fixed	NA	sibling_count5	0.003396	0.05639	0.06022	3013	0.952	-0.1549	0.1617
ran_pars	mother_pidlink	sd__(Intercept)	0.3083	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.944	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.441	0.5487	-2.626	4496	0.008657	-2.982	0.09909
fixed	NA	poly(age, 3, raw = TRUE)1	0.1283	0.06398	2.006	4495	0.04497	-0.05128	0.3079
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003825	0.002358	-1.622	4492	0.1048	-0.01044	0.002793
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004036	0.00002763	1.461	4489	0.1441	-0.00003719	0.0001179
fixed	NA	male	0.06081	0.02952	2.06	4447	0.03942	-0.02204	0.1437
fixed	NA	sibling_count3	-0.03525	0.04137	-0.852	3473	0.3943	-0.1514	0.08088
fixed	NA	sibling_count4	-0.04977	0.04693	-1.061	3176	0.289	-0.1815	0.08197
fixed	NA	sibling_count5	-0.01692	0.05735	-0.295	3105	0.768	-0.1779	0.1441
fixed	NA	birth_order_nonlinear2	-0.04439	0.03521	-1.261	3616	0.2075	-0.1432	0.05445
fixed	NA	birth_order_nonlinear3	-0.03947	0.04486	-0.8798	3847	0.379	-0.1654	0.08646
fixed	NA	birth_order_nonlinear4	0.0003313	0.06023	0.005502	4043	0.9956	-0.1687	0.1694
fixed	NA	birth_order_nonlinear5	0.1025	0.0938	1.092	3913	0.2748	-0.1608	0.3657
ran_pars	mother_pidlink	sd__(Intercept)	0.3076	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9441	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.441	0.5491	-2.624	4490	0.00872	-2.982	0.1005
fixed	NA	poly(age, 3, raw = TRUE)1	0.1278	0.06402	1.996	4489	0.04596	-0.0519	0.3075
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003799	0.00236	-1.61	4487	0.1075	-0.01042	0.002825
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003998	0.00002765	1.446	4484	0.1483	-0.00003764	0.0001176
fixed	NA	male	0.06115	0.02954	2.07	4440	0.03851	-0.02177	0.1441
fixed	NA	count_birth_order2/2	-0.03908	0.06043	-0.6467	3794	0.5179	-0.2087	0.1306
fixed	NA	count_birth_order1/3	-0.03174	0.05322	-0.5964	4483	0.551	-0.1811	0.1177
fixed	NA	count_birth_order2/3	-0.05728	0.05814	-0.9852	4490	0.3246	-0.2205	0.1059
fixed	NA	count_birth_order3/3	-0.1057	0.065	-1.627	4486	0.1039	-0.2882	0.07672
fixed	NA	count_birth_order1/4	-0.07014	0.06529	-1.074	4487	0.2828	-0.2534	0.1131
fixed	NA	count_birth_order2/4	-0.1093	0.06747	-1.62	4490	0.1054	-0.2987	0.08011
fixed	NA	count_birth_order3/4	-0.06472	0.07125	-0.9083	4478	0.3637	-0.2647	0.1353
fixed	NA	count_birth_order4/4	-0.01905	0.07401	-0.2574	4476	0.7969	-0.2268	0.1887
fixed	NA	count_birth_order1/5	0.03532	0.08881	0.3977	4487	0.6909	-0.214	0.2846
fixed	NA	count_birth_order2/5	-0.1062	0.09483	-1.12	4471	0.2627	-0.3724	0.16
fixed	NA	count_birth_order3/5	-0.02283	0.08884	-0.257	4466	0.7972	-0.2722	0.2265
fixed	NA	count_birth_order4/5	-0.05543	0.08553	-0.6481	4471	0.517	-0.2955	0.1847
fixed	NA	count_birth_order5/5	0.08677	0.08895	0.9754	4459	0.3294	-0.1629	0.3365
ran_pars	mother_pidlink	sd__(Intercept)	0.3084	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9443	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12726	12790	-6353	12706	NA	NA	NA
11	12728	12798	-6353	12706	0.0002465	1	0.9875
14	12730	12819	-6351	12702	3.899	3	0.2726
20	12739	12868	-6350	12699	2.374	6	0.8823

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.622	0.5615	-2.889	4176	0.003883	-3.198	-0.04611
fixed	NA	poly(age, 3, raw = TRUE)1	0.1442	0.06558	2.199	4177	0.02793	-0.03988	0.3283
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004261	0.002417	-1.763	4176	0.07801	-0.01105	0.002524
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000436	0.00002833	1.539	4174	0.1238	-0.00003591	0.0001231
fixed	NA	male	0.08473	0.03048	2.78	4121	0.005467	-0.000836	0.1703
fixed	NA	sibling_count3	-0.05352	0.04327	-1.237	3135	0.2162	-0.175	0.06794
fixed	NA	sibling_count4	-0.02786	0.04574	-0.6092	2825	0.5424	-0.1562	0.1005
fixed	NA	sibling_count5	-0.03858	0.04896	-0.788	2496	0.4308	-0.176	0.09884
ran_pars	mother_pidlink	sd__(Intercept)	0.3201	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9354	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.617	0.5621	-2.876	4175	0.00405	-3.194	-0.03868
fixed	NA	birth_order	-0.003374	0.01545	-0.2184	3947	0.8271	-0.04674	0.04
fixed	NA	poly(age, 3, raw = TRUE)1	0.144	0.06559	2.196	4176	0.02816	-0.04009	0.3281
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004251	0.002418	-1.758	4175	0.0788	-0.01104	0.002536
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004342	0.00002834	1.532	4173	0.1256	-0.00003614	0.000123
fixed	NA	male	0.0848	0.03049	2.782	4120	0.005435	-0.000777	0.1704
fixed	NA	sibling_count3	-0.05198	0.04385	-1.185	3180	0.2359	-0.1751	0.0711
fixed	NA	sibling_count4	-0.02442	0.04837	-0.5049	2999	0.6136	-0.1602	0.1114
fixed	NA	sibling_count5	-0.03308	0.05505	-0.601	2905	0.5479	-0.1876	0.1214
ran_pars	mother_pidlink	sd__(Intercept)	0.3202	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9355	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.576	0.5626	-2.802	4173	0.005098	-3.156	0.002685
fixed	NA	poly(age, 3, raw = TRUE)1	0.1403	0.06565	2.137	4173	0.03266	-0.04399	0.3246
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004115	0.00242	-1.7	4171	0.08916	-0.01091	0.002679
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004192	0.00002837	1.478	4169	0.1395	-0.0000377	0.0001215
fixed	NA	male	0.08421	0.0305	2.761	4117	0.00578	-0.001391	0.1698
fixed	NA	sibling_count3	-0.04483	0.0445	-1.007	3284	0.3138	-0.1697	0.08009
fixed	NA	sibling_count4	-0.02207	0.04906	-0.4498	3093	0.6529	-0.1598	0.1157
fixed	NA	sibling_count5	-0.04252	0.05563	-0.7643	2957	0.4447	-0.1987	0.1136
fixed	NA	birth_order_nonlinear2	-0.03947	0.03643	-1.083	3405	0.2787	-0.1417	0.06279
fixed	NA	birth_order_nonlinear3	-0.04091	0.04606	-0.8882	3630	0.3745	-0.1702	0.08839
fixed	NA	birth_order_nonlinear4	0.001996	0.06097	0.03275	3786	0.9739	-0.1691	0.1731
fixed	NA	birth_order_nonlinear5	0.03051	0.08934	0.3415	3681	0.7328	-0.2203	0.2813
ran_pars	mother_pidlink	sd__(Intercept)	0.3202	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9356	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.573	0.5631	-2.793	4167	0.005245	-3.154	0.00786
fixed	NA	poly(age, 3, raw = TRUE)1	0.141	0.0657	2.146	4167	0.03197	-0.04346	0.3254
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004139	0.002423	-1.709	4165	0.08759	-0.01094	0.002661
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004225	0.00002839	1.488	4163	0.1369	-0.00003746	0.000122
fixed	NA	male	0.0846	0.03053	2.771	4111	0.005608	-0.001091	0.1703
fixed	NA	count_birth_order2/2	-0.0697	0.06574	-1.06	3567	0.2891	-0.2542	0.1148
fixed	NA	count_birth_order1/3	-0.0591	0.05739	-1.03	4160	0.3032	-0.2202	0.102
fixed	NA	count_birth_order2/3	-0.06768	0.0622	-1.088	4167	0.2767	-0.2423	0.1069
fixed	NA	count_birth_order3/3	-0.1278	0.07001	-1.825	4163	0.06804	-0.3243	0.06873
fixed	NA	count_birth_order1/4	-0.05625	0.06811	-0.8259	4164	0.4089	-0.2474	0.1349
fixed	NA	count_birth_order2/4	-0.05083	0.0693	-0.7335	4167	0.4633	-0.2454	0.1437
fixed	NA	count_birth_order3/4	-0.0794	0.07597	-1.045	4154	0.296	-0.2926	0.1338
fixed	NA	count_birth_order4/4	-0.01828	0.07824	-0.2336	4154	0.8153	-0.2379	0.2013
fixed	NA	count_birth_order1/5	-0.03751	0.08102	-0.463	4167	0.6434	-0.2649	0.1899
fixed	NA	count_birth_order2/5	-0.1608	0.08677	-1.854	4156	0.06386	-0.4044	0.08273
fixed	NA	count_birth_order3/5	-0.03499	0.08427	-0.4153	4150	0.678	-0.2715	0.2015
fixed	NA	count_birth_order4/5	-0.06664	0.08727	-0.7636	4136	0.4452	-0.3116	0.1783
fixed	NA	count_birth_order5/5	-0.02222	0.08743	-0.2541	4133	0.7994	-0.2676	0.2232
ran_pars	mother_pidlink	sd__(Intercept)	0.3189	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9364	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11776	11840	-5878	11756	NA	NA	NA
11	11778	11848	-5878	11756	0.04759	1	0.8273
14	11782	11871	-5877	11754	1.988	3	0.5749
20	11791	11918	-5876	11751	2.845	6	0.8281

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.265	0.5515	-2.294	4485	0.02184	-2.813	0.2829
fixed	NA	poly(age, 3, raw = TRUE)1	0.1056	0.06445	1.638	4484	0.1015	-0.07534	0.2865
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002981	0.002378	-1.254	4482	0.21	-0.009657	0.003694
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003057	0.00002791	1.095	4479	0.2734	-0.00004778	0.0001089
fixed	NA	male	0.05885	0.0295	1.995	4438	0.04612	-0.02396	0.1417
fixed	NA	sibling_count3	-0.04899	0.03949	-1.24	3251	0.2149	-0.1598	0.06187
fixed	NA	sibling_count4	-0.06476	0.04283	-1.512	2812	0.1307	-0.185	0.05548
fixed	NA	sibling_count5	0.04328	0.05038	0.8591	2364	0.3904	-0.09814	0.1847
ran_pars	mother_pidlink	sd__(Intercept)	0.3054	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9423	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.27	0.5522	-2.3	4484	0.02151	-2.82	0.2801
fixed	NA	birth_order	0.002858	0.01568	0.1823	4145	0.8553	-0.04114	0.04686
fixed	NA	poly(age, 3, raw = TRUE)1	0.1057	0.06446	1.64	4483	0.1011	-0.07522	0.2867
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00299	0.002379	-1.257	4481	0.2088	-0.009668	0.003688
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003074	0.00002793	1.1	4478	0.2712	-0.00004767	0.0001091
fixed	NA	male	0.05877	0.02951	1.992	4436	0.04644	-0.02405	0.1416
fixed	NA	sibling_count3	-0.05029	0.04014	-1.253	3311	0.2103	-0.163	0.06238
fixed	NA	sibling_count4	-0.06776	0.04589	-1.477	3066	0.1399	-0.1966	0.06106
fixed	NA	sibling_count5	0.03847	0.05687	0.6765	2845	0.4988	-0.1212	0.1981
ran_pars	mother_pidlink	sd__(Intercept)	0.3053	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9425	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.208	0.5525	-2.187	4481	0.02878	-2.759	0.3425
fixed	NA	poly(age, 3, raw = TRUE)1	0.1001	0.06451	1.552	4479	0.1208	-0.08099	0.2812
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002788	0.002381	-1.171	4476	0.2417	-0.00947	0.003895
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002854	0.00002795	1.021	4473	0.3073	-0.00004991	0.000107
fixed	NA	male	0.05776	0.02951	1.957	4433	0.05036	-0.02507	0.1406
fixed	NA	sibling_count3	-0.03926	0.0408	-0.9621	3442	0.336	-0.1538	0.07528
fixed	NA	sibling_count4	-0.05917	0.04659	-1.27	3172	0.2041	-0.1899	0.0716
fixed	NA	sibling_count5	0.01592	0.05803	0.2743	2945	0.7839	-0.147	0.1788
fixed	NA	birth_order_nonlinear2	-0.02834	0.03494	-0.8112	3594	0.4173	-0.1264	0.06973
fixed	NA	birth_order_nonlinear3	-0.04639	0.04463	-1.04	3803	0.2986	-0.1717	0.07888
fixed	NA	birth_order_nonlinear4	0.01135	0.06141	0.1849	4009	0.8533	-0.161	0.1837
fixed	NA	birth_order_nonlinear5	0.1509	0.1002	1.505	3960	0.1324	-0.1305	0.4322
ran_pars	mother_pidlink	sd__(Intercept)	0.305	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9424	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.203	0.5529	-2.175	4475	0.02967	-2.755	0.3494
fixed	NA	poly(age, 3, raw = TRUE)1	0.09945	0.06455	1.541	4474	0.1235	-0.08176	0.2807
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002762	0.002382	-1.159	4471	0.2463	-0.00945	0.003925
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002825	0.00002797	1.01	4468	0.3126	-0.00005027	0.0001068
fixed	NA	male	0.05823	0.02953	1.972	4426	0.04867	-0.02466	0.1411
fixed	NA	count_birth_order2/2	-0.03221	0.05875	-0.5482	3745	0.5836	-0.1971	0.1327
fixed	NA	count_birth_order1/3	-0.03496	0.05246	-0.6665	4467	0.5051	-0.1822	0.1123
fixed	NA	count_birth_order2/3	-0.05099	0.05799	-0.8793	4475	0.3793	-0.2138	0.1118
fixed	NA	count_birth_order3/3	-0.1223	0.06371	-1.919	4469	0.05505	-0.3011	0.05657
fixed	NA	count_birth_order1/4	-0.088	0.06544	-1.345	4473	0.1787	-0.2717	0.09568
fixed	NA	count_birth_order2/4	-0.1098	0.06719	-1.634	4474	0.1023	-0.2984	0.0788
fixed	NA	count_birth_order3/4	-0.07642	0.07034	-1.086	4461	0.2774	-0.2739	0.121
fixed	NA	count_birth_order4/4	-0.01713	0.0743	-0.2306	4456	0.8176	-0.2257	0.1914
fixed	NA	count_birth_order1/5	0.0415	0.0884	0.4695	4474	0.6388	-0.2066	0.2896
fixed	NA	count_birth_order2/5	-0.02249	0.09749	-0.2307	4455	0.8176	-0.2962	0.2512
fixed	NA	count_birth_order3/5	-0.001968	0.0929	-0.02118	4448	0.9831	-0.2627	0.2588
fixed	NA	count_birth_order4/5	-0.02361	0.08947	-0.264	4454	0.7918	-0.2747	0.2275
fixed	NA	count_birth_order5/5	0.1649	0.095	1.736	4443	0.0827	-0.1018	0.4316
ran_pars	mother_pidlink	sd__(Intercept)	0.3058	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9426	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12662	12726	-6321	12642	NA	NA	NA
11	12664	12734	-6321	12642	0.03329	1	0.8552
14	12665	12755	-6319	12637	4.585	3	0.2048
20	12675	12803	-6318	12635	2.189	6	0.9015

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Openness

birthorder <- birthorder %>% mutate(outcome = big5_open)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1884	0.1972	0.9556	6706	0.3393	-0.3651	0.7419
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01562	0.01894	-0.8246	6526	0.4097	-0.06878	0.03754
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004604	0.000553	0.8325	6323	0.4051	-0.001092	0.002013
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000005537	0.000005017	-1.104	6167	0.2697	-0.00001962	0.000008545
fixed	NA	male	0.1661	0.023	7.222	7062	5.643e-13	0.1016	0.2307
fixed	NA	sibling_count3	-0.02065	0.03284	-0.6287	4991	0.5296	-0.1128	0.07154
fixed	NA	sibling_count4	-0.05262	0.03382	-1.556	4419	0.1199	-0.1476	0.04233
fixed	NA	sibling_count5	-0.01423	0.03514	-0.4048	3819	0.6856	-0.1129	0.08442
ran_pars	mother_pidlink	sd__(Intercept)	0.2814	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9325	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1939	0.1972	0.983	6695	0.3257	-0.3598	0.7475
fixed	NA	birth_order	-0.0152	0.0115	-1.322	6118	0.1862	-0.04749	0.01708
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0141	0.01897	-0.7432	6554	0.4574	-0.06736	0.03916
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004218	0.0005538	0.7617	6339	0.4463	-0.001133	0.001976
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000005287	0.000005021	-1.053	6176	0.2924	-0.00001938	0.000008806
fixed	NA	male	0.1666	0.023	7.242	7060	4.905e-13	0.102	0.2311
fixed	NA	sibling_count3	-0.01521	0.0331	-0.4594	5121	0.646	-0.1081	0.07771
fixed	NA	sibling_count4	-0.03998	0.03516	-1.137	4975	0.2555	-0.1387	0.0587
fixed	NA	sibling_count5	0.006125	0.03837	0.1596	4933	0.8732	-0.1016	0.1138
ran_pars	mother_pidlink	sd__(Intercept)	0.2824	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9322	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1783	0.1978	0.9016	6719	0.3673	-0.3768	0.7335
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01421	0.01898	-0.7484	6540	0.4543	-0.06749	0.03908
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004305	0.0005542	0.7768	6315	0.4373	-0.001125	0.001986
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000005414	0.000005026	-1.077	6140	0.2814	-0.00001952	0.000008694
fixed	NA	male	0.1666	0.023	7.245	7057	4.794e-13	0.1021	0.2312
fixed	NA	sibling_count3	-0.004773	0.03363	-0.1419	5340	0.8871	-0.09917	0.08963
fixed	NA	sibling_count4	-0.03468	0.03574	-0.9704	5223	0.3319	-0.135	0.06565
fixed	NA	sibling_count5	0.005849	0.03875	0.151	5113	0.88	-0.1029	0.1146
fixed	NA	birth_order_nonlinear2	-0.01603	0.02733	-0.5864	5985	0.5577	-0.09276	0.0607
fixed	NA	birth_order_nonlinear3	-0.0772	0.03508	-2.201	5947	0.0278	-0.1757	0.02128
fixed	NA	birth_order_nonlinear4	-0.02083	0.04582	-0.4546	5958	0.6494	-0.1494	0.1078
fixed	NA	birth_order_nonlinear5	-0.02959	0.06668	-0.4438	5840	0.6572	-0.2168	0.1576
ran_pars	mother_pidlink	sd__(Intercept)	0.2822	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9322	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.201	0.1981	1.015	6724	0.3103	-0.3551	0.7572
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0141	0.01898	-0.7431	6537	0.4574	-0.06738	0.03917
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004332	0.0005541	0.7818	6309	0.4344	-0.001122	0.001988
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000005479	0.000005025	-1.09	6130	0.2756	-0.00001958	0.000008626
fixed	NA	male	0.1664	0.023	7.233	7051	5.225e-13	0.1018	0.231
fixed	NA	count_birth_order2/2	-0.08506	0.04665	-1.824	5931	0.06828	-0.216	0.04588
fixed	NA	count_birth_order1/3	-0.05985	0.04394	-1.362	7113	0.1732	-0.1832	0.06349
fixed	NA	count_birth_order2/3	-0.02781	0.04914	-0.5659	7125	0.5714	-0.1658	0.1101
fixed	NA	count_birth_order3/3	-0.07335	0.0551	-1.331	7128	0.1832	-0.228	0.08133
fixed	NA	count_birth_order1/4	-0.07601	0.0502	-1.514	7126	0.1301	-0.2169	0.06491
fixed	NA	count_birth_order2/4	-0.01537	0.0528	-0.291	7128	0.7711	-0.1636	0.1329
fixed	NA	count_birth_order3/4	-0.1879	0.0574	-3.273	7128	0.00107	-0.349	-0.02673
fixed	NA	count_birth_order4/4	-0.08668	0.06082	-1.425	7124	0.1542	-0.2574	0.08405
fixed	NA	count_birth_order1/5	-0.005622	0.05698	-0.09866	7128	0.9214	-0.1656	0.1543
fixed	NA	count_birth_order2/5	-0.07134	0.05996	-1.19	7124	0.2342	-0.2397	0.09698
fixed	NA	count_birth_order3/5	-0.08237	0.06156	-1.338	7121	0.1809	-0.2552	0.09043
fixed	NA	count_birth_order4/5	-0.03452	0.06525	-0.5291	7115	0.5967	-0.2177	0.1486
fixed	NA	count_birth_order5/5	-0.04936	0.06671	-0.74	7111	0.4593	-0.2366	0.1379
ran_pars	mother_pidlink	sd__(Intercept)	0.2805	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9326	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	19896	19965	-9938	19876	NA	NA	NA
11	19896	19972	-9937	19874	1.746	1	0.1864
14	19899	19995	-9936	19871	3.169	3	0.3663
20	19903	20041	-9932	19863	7.754	6	0.2567

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.131	0.5097	-2.218	4499	0.02658	-2.561	0.3
fixed	NA	poly(age, 3, raw = TRUE)1	0.1491	0.05948	2.507	4500	0.01222	-0.01785	0.3161
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00554	0.002192	-2.528	4498	0.01152	-0.01169	0.0006123
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006508	0.00002568	2.535	4496	0.01129	-0.000006995	0.0001372
fixed	NA	male	0.1181	0.02745	4.304	4448	0.00001717	0.04108	0.1952
fixed	NA	sibling_count3	-0.09546	0.03738	-2.553	3304	0.01071	-0.2004	0.009483
fixed	NA	sibling_count4	-0.0851	0.04034	-2.11	2863	0.03496	-0.1983	0.02812
fixed	NA	sibling_count5	-0.1082	0.04601	-2.352	2517	0.01874	-0.2374	0.02092
ran_pars	mother_pidlink	sd__(Intercept)	0.2964	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8755	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.157	0.5102	-2.268	4499	0.02337	-2.589	0.275
fixed	NA	birth_order	0.01578	0.01441	1.095	4179	0.2737	-0.02468	0.05624
fixed	NA	poly(age, 3, raw = TRUE)1	0.15	0.05948	2.522	4499	0.01169	-0.01693	0.317
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005592	0.002192	-2.551	4498	0.01078	-0.01175	0.0005614
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006602	0.00002569	2.57	4495	0.01021	-0.000006098	0.0001381
fixed	NA	male	0.1176	0.02745	4.284	4447	0.00001873	0.04055	0.1947
fixed	NA	sibling_count3	-0.1027	0.03796	-2.706	3367	0.006852	-0.2092	0.003849
fixed	NA	sibling_count4	-0.1018	0.0431	-2.361	3098	0.01828	-0.2227	0.01922
fixed	NA	sibling_count5	-0.1361	0.05256	-2.589	3046	0.00967	-0.2836	0.01146
ran_pars	mother_pidlink	sd__(Intercept)	0.2957	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8757	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.124	0.5107	-2.201	4496	0.02779	-2.558	0.3096
fixed	NA	poly(age, 3, raw = TRUE)1	0.148	0.05955	2.486	4495	0.01296	-0.01912	0.3152
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005521	0.002195	-2.516	4493	0.01191	-0.01168	0.0006393
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006527	0.00002572	2.538	4491	0.01118	-0.000006915	0.0001375
fixed	NA	male	0.1174	0.02746	4.274	4443	0.00001961	0.04028	0.1945
fixed	NA	sibling_count3	-0.09381	0.03857	-2.432	3488	0.01505	-0.2021	0.01445
fixed	NA	sibling_count4	-0.09743	0.04376	-2.226	3200	0.02606	-0.2203	0.02541
fixed	NA	sibling_count5	-0.1417	0.05348	-2.65	3136	0.008091	-0.2918	0.008401
fixed	NA	birth_order_nonlinear2	0.01459	0.03273	0.4457	3623	0.6558	-0.07728	0.1064
fixed	NA	birth_order_nonlinear3	-0.007921	0.04171	-0.1899	3848	0.8494	-0.125	0.1092
fixed	NA	birth_order_nonlinear4	0.06769	0.056	1.209	4040	0.2268	-0.0895	0.2249
fixed	NA	birth_order_nonlinear5	0.1049	0.0872	1.203	3908	0.229	-0.1399	0.3497
ran_pars	mother_pidlink	sd__(Intercept)	0.2965	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8756	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.119	0.5109	-2.19	4490	0.02855	-2.553	0.3151
fixed	NA	poly(age, 3, raw = TRUE)1	0.1483	0.05957	2.489	4490	0.01285	-0.01895	0.3155
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005511	0.002196	-2.51	4488	0.01211	-0.01167	0.0006524
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006492	0.00002573	2.523	4485	0.01167	-0.00000731	0.0001372
fixed	NA	male	0.1182	0.02748	4.301	4436	0.00001739	0.04105	0.1953
fixed	NA	count_birth_order2/2	-0.01883	0.05617	-0.3353	3805	0.7374	-0.1765	0.1388
fixed	NA	count_birth_order1/3	-0.1352	0.04953	-2.73	4482	0.006358	-0.2742	0.003814
fixed	NA	count_birth_order2/3	-0.07522	0.0541	-1.39	4490	0.1645	-0.2271	0.07665
fixed	NA	count_birth_order3/3	-0.07505	0.06047	-1.241	4486	0.2146	-0.2448	0.0947
fixed	NA	count_birth_order1/4	-0.07112	0.06076	-1.171	4487	0.2418	-0.2417	0.09943
fixed	NA	count_birth_order2/4	-0.1272	0.06278	-2.025	4489	0.04288	-0.3034	0.04907
fixed	NA	count_birth_order3/4	-0.1429	0.06629	-2.155	4477	0.03119	-0.3289	0.0432
fixed	NA	count_birth_order4/4	-0.024	0.06885	-0.3485	4475	0.7275	-0.2173	0.1693
fixed	NA	count_birth_order1/5	-0.1653	0.08263	-2	4487	0.04552	-0.3972	0.06666
fixed	NA	count_birth_order2/5	-0.04699	0.08822	-0.5327	4469	0.5943	-0.2946	0.2006
fixed	NA	count_birth_order3/5	-0.1978	0.08265	-2.394	4464	0.01671	-0.4298	0.03415
fixed	NA	count_birth_order4/5	-0.1109	0.07957	-1.394	4470	0.1634	-0.3343	0.1124
fixed	NA	count_birth_order5/5	-0.04873	0.08275	-0.5889	4457	0.556	-0.281	0.1836
ran_pars	mother_pidlink	sd__(Intercept)	0.2966	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8757	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12078	12142	-6029	12058	NA	NA	NA
11	12078	12149	-6028	12056	1.202	1	0.273
14	12083	12172	-6027	12055	1.724	3	0.6316
20	12090	12218	-6025	12050	4.844	6	0.5639

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.319	0.5255	-2.509	4175	0.01214	-2.794	0.1566
fixed	NA	poly(age, 3, raw = TRUE)1	0.1718	0.06139	2.798	4177	0.005168	-0.0005629	0.3441
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006328	0.002263	-2.796	4177	0.005196	-0.01268	0.00002468
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007372	0.00002652	2.78	4175	0.005459	-0.0000007143	0.0001482
fixed	NA	male	0.118	0.02852	4.139	4114	0.00003561	0.03798	0.1981
fixed	NA	sibling_count3	-0.1239	0.0406	-3.052	3147	0.002291	-0.2379	-0.009953
fixed	NA	sibling_count4	-0.09755	0.04293	-2.272	2846	0.02316	-0.2181	0.02297
fixed	NA	sibling_count5	-0.1168	0.04598	-2.541	2527	0.01112	-0.2459	0.01224
ran_pars	mother_pidlink	sd__(Intercept)	0.3139	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.871	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.356	0.526	-2.578	4174	0.00998	-2.832	0.1206
fixed	NA	birth_order	0.02246	0.01444	1.555	3942	0.1201	-0.01809	0.063
fixed	NA	poly(age, 3, raw = TRUE)1	0.1729	0.06138	2.817	4176	0.00487	0.0006121	0.3452
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006394	0.002263	-2.825	4176	0.004747	-0.01275	-0.00004116
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007495	0.00002653	2.826	4175	0.004742	0.0000004923	0.0001494
fixed	NA	male	0.1176	0.02852	4.122	4113	0.00003828	0.0375	0.1976
fixed	NA	sibling_count3	-0.1342	0.04113	-3.263	3191	0.001113	-0.2496	-0.01876
fixed	NA	sibling_count4	-0.1205	0.04538	-2.654	3016	0.007985	-0.2479	0.006923
fixed	NA	sibling_count5	-0.1534	0.05165	-2.971	2929	0.002994	-0.2984	-0.008461
ran_pars	mother_pidlink	sd__(Intercept)	0.3134	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.871	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.303	0.5263	-2.476	4173	0.01331	-2.78	0.174
fixed	NA	poly(age, 3, raw = TRUE)1	0.17	0.06142	2.767	4173	0.005678	-0.002444	0.3424
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00629	0.002264	-2.778	4172	0.005499	-0.01265	0.00006647
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007387	0.00002654	2.784	4171	0.005402	-0.0000006244	0.0001484
fixed	NA	male	0.117	0.02851	4.104	4108	0.00004133	0.03699	0.1971
fixed	NA	sibling_count3	-0.1232	0.04174	-2.952	3291	0.003177	-0.2404	-0.00606
fixed	NA	sibling_count4	-0.1266	0.04603	-2.75	3108	0.005997	-0.2558	0.002632
fixed	NA	sibling_count5	-0.153	0.0522	-2.931	2981	0.003409	-0.2995	-0.006448
fixed	NA	birth_order_nonlinear2	0.008347	0.034	0.2455	3400	0.8061	-0.08709	0.1038
fixed	NA	birth_order_nonlinear3	-0.005034	0.04301	-0.117	3618	0.9068	-0.1258	0.1157
fixed	NA	birth_order_nonlinear4	0.1464	0.05694	2.571	3773	0.01018	-0.01344	0.3062
fixed	NA	birth_order_nonlinear5	0.04786	0.08343	0.5736	3662	0.5662	-0.1863	0.282
ran_pars	mother_pidlink	sd__(Intercept)	0.3163	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8698	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.299	0.5268	-2.465	4167	0.01373	-2.778	0.18
fixed	NA	poly(age, 3, raw = TRUE)1	0.171	0.06147	2.782	4167	0.005421	-0.001519	0.3436
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006321	0.002267	-2.789	4166	0.005311	-0.01268	0.0000409
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007416	0.00002657	2.791	4165	0.005271	-0.0000004136	0.0001487
fixed	NA	male	0.1169	0.02854	4.096	4103	0.00004291	0.03678	0.197
fixed	NA	count_birth_order2/2	-0.03659	0.06139	-0.596	3572	0.5512	-0.2089	0.1357
fixed	NA	count_birth_order1/3	-0.1578	0.0537	-2.939	4159	0.003307	-0.3086	-0.007106
fixed	NA	count_birth_order2/3	-0.1268	0.0582	-2.179	4167	0.02942	-0.2901	0.03658
fixed	NA	count_birth_order3/3	-0.1099	0.06548	-1.679	4162	0.0933	-0.2937	0.07389
fixed	NA	count_birth_order1/4	-0.1356	0.06373	-2.128	4164	0.03343	-0.3145	0.0433
fixed	NA	count_birth_order2/4	-0.1061	0.06483	-1.637	4167	0.1017	-0.2881	0.07584
fixed	NA	count_birth_order3/4	-0.1999	0.07105	-2.813	4152	0.004928	-0.3993	-0.0004374
fixed	NA	count_birth_order4/4	0.01211	0.07317	0.1655	4152	0.8686	-0.1933	0.2175
fixed	NA	count_birth_order1/5	-0.1726	0.07579	-2.278	4167	0.0228	-0.3854	0.04012
fixed	NA	count_birth_order2/5	-0.1605	0.08116	-1.977	4153	0.04809	-0.3883	0.06735
fixed	NA	count_birth_order3/5	-0.1581	0.07881	-2.006	4147	0.04497	-0.3793	0.06316
fixed	NA	count_birth_order4/5	-0.03308	0.08161	-0.4053	4132	0.6853	-0.2622	0.196
fixed	NA	count_birth_order5/5	-0.1204	0.08176	-1.473	4129	0.1408	-0.3499	0.1091
ran_pars	mother_pidlink	sd__(Intercept)	0.3143	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8709	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11224	11287	-5602	11204	NA	NA	NA
11	11223	11293	-5601	11201	2.422	1	0.1197
14	11224	11313	-5598	11196	5.18	3	0.1591
20	11234	11360	-5597	11194	2.394	6	0.8801

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.9088	0.5145	-1.766	4484	0.07742	-2.353	0.5355
fixed	NA	poly(age, 3, raw = TRUE)1	0.1233	0.06013	2.051	4485	0.04037	-0.04549	0.2921
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004581	0.002219	-2.064	4484	0.03905	-0.01081	0.001648
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005373	0.00002605	2.062	4482	0.03924	-0.0000194	0.0001269
fixed	NA	male	0.1072	0.0275	3.897	4425	0.00009896	0.02997	0.1843
fixed	NA	sibling_count3	-0.1071	0.03702	-2.894	3298	0.003829	-0.2111	-0.003218
fixed	NA	sibling_count4	-0.08615	0.0402	-2.143	2886	0.03219	-0.199	0.02669
fixed	NA	sibling_count5	-0.09137	0.04734	-1.93	2463	0.05372	-0.2243	0.04152
ran_pars	mother_pidlink	sd__(Intercept)	0.3117	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8708	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.9437	0.515	-1.832	4483	0.06697	-2.389	0.502
fixed	NA	birth_order	0.02102	0.01459	1.44	4142	0.1498	-0.01994	0.06197
fixed	NA	poly(age, 3, raw = TRUE)1	0.1244	0.06013	2.069	4484	0.03857	-0.04436	0.2932
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004646	0.002219	-2.093	4483	0.03639	-0.01088	0.001584
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005491	0.00002606	2.107	4482	0.03518	-0.00001824	0.0001281
fixed	NA	male	0.1066	0.0275	3.877	4425	0.0001073	0.02942	0.1838
fixed	NA	sibling_count3	-0.1168	0.03761	-3.105	3355	0.00192	-0.2223	-0.0112
fixed	NA	sibling_count4	-0.1083	0.04302	-2.517	3130	0.01188	-0.229	0.01247
fixed	NA	sibling_count5	-0.1268	0.05334	-2.378	2932	0.01747	-0.2766	0.02289
ran_pars	mother_pidlink	sd__(Intercept)	0.3105	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8711	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.894	0.5156	-1.734	4481	0.08298	-2.341	0.5532
fixed	NA	poly(age, 3, raw = TRUE)1	0.1216	0.0602	2.02	4481	0.04341	-0.04736	0.2906
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004547	0.002222	-2.046	4479	0.04078	-0.01078	0.00169
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005387	0.00002609	2.065	4477	0.03896	-0.00001935	0.0001271
fixed	NA	male	0.1058	0.02751	3.847	4420	0.000121	0.02862	0.1831
fixed	NA	sibling_count3	-0.1088	0.03823	-2.847	3479	0.004444	-0.2161	-0.001516
fixed	NA	sibling_count4	-0.1085	0.04368	-2.485	3231	0.01301	-0.2312	0.01408
fixed	NA	sibling_count5	-0.1343	0.05444	-2.467	3031	0.01367	-0.2871	0.0185
fixed	NA	birth_order_nonlinear2	0.007869	0.03248	0.2423	3606	0.8086	-0.08329	0.09903
fixed	NA	birth_order_nonlinear3	0.005863	0.04151	0.1413	3802	0.8877	-0.1107	0.1224
fixed	NA	birth_order_nonlinear4	0.09932	0.05715	1.738	3998	0.08231	-0.0611	0.2597
fixed	NA	birth_order_nonlinear5	0.1052	0.09327	1.128	3943	0.2596	-0.1566	0.367
ran_pars	mother_pidlink	sd__(Intercept)	0.3111	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.871	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8907	0.5158	-1.727	4475	0.08428	-2.339	0.5572
fixed	NA	poly(age, 3, raw = TRUE)1	0.1228	0.06023	2.039	4475	0.04148	-0.04624	0.2919
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004588	0.002223	-2.064	4474	0.03909	-0.01083	0.001652
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005429	0.0000261	2.08	4472	0.03758	-0.00001898	0.0001276
fixed	NA	male	0.1056	0.02752	3.837	4414	0.0001265	0.02834	0.1829
fixed	NA	count_birth_order2/2	-0.03167	0.05463	-0.5797	3768	0.5621	-0.185	0.1217
fixed	NA	count_birth_order1/3	-0.1362	0.04895	-2.781	4465	0.005437	-0.2736	0.00126
fixed	NA	count_birth_order2/3	-0.1206	0.05409	-2.229	4475	0.02585	-0.2724	0.03126
fixed	NA	count_birth_order3/3	-0.0812	0.05941	-1.367	4469	0.1718	-0.248	0.08558
fixed	NA	count_birth_order1/4	-0.1032	0.06105	-1.691	4474	0.09091	-0.2746	0.06814
fixed	NA	count_birth_order2/4	-0.1124	0.06268	-1.793	4473	0.07303	-0.2883	0.06355
fixed	NA	count_birth_order3/4	-0.1396	0.0656	-2.128	4458	0.03341	-0.3237	0.04455
fixed	NA	count_birth_order4/4	-0.02487	0.06928	-0.3589	4452	0.7197	-0.2193	0.1696
fixed	NA	count_birth_order1/5	-0.1981	0.08246	-2.402	4474	0.01633	-0.4296	0.03336
fixed	NA	count_birth_order2/5	-0.02959	0.0909	-0.3255	4448	0.7448	-0.2847	0.2256
fixed	NA	count_birth_order3/5	-0.1846	0.08661	-2.132	4442	0.03307	-0.4278	0.05848
fixed	NA	count_birth_order4/5	-0.04553	0.08342	-0.5458	4450	0.5852	-0.2797	0.1886
fixed	NA	count_birth_order5/5	-0.04235	0.08857	-0.4781	4437	0.6326	-0.291	0.2063
ran_pars	mother_pidlink	sd__(Intercept)	0.3107	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8713	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	12039	12103	-6009	12019	NA	NA	NA
11	12039	12109	-6008	12017	2.08	1	0.1492
14	12043	12133	-6007	12015	1.788	3	0.6175
20	12051	12179	-6005	12011	4.148	6	0.6566

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Risk preference

Risk A

birthorder <- birthorder %>% mutate(outcome = riskA)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.328	0.2089	6.359	5932	0.0000000002183	0.7418	1.914
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1122	0.02005	-5.597	5752	0.00000002285	-0.1685	-0.05593
fixed	NA	poly(age, 3, raw = TRUE)2	0.002981	0.0005856	5.092	5540	0.0000003665	0.001338	0.004625
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000239	0.000005321	-4.492	5353	0.000007215	-0.00003884	-0.000008965
fixed	NA	male	-0.2211	0.02451	-9.021	6279	2.438e-19	-0.2898	-0.1523
fixed	NA	sibling_count3	0.006697	0.03481	0.1924	4709	0.8475	-0.09103	0.1044
fixed	NA	sibling_count4	0.009771	0.03576	0.2733	4222	0.7846	-0.0906	0.1101
fixed	NA	sibling_count5	-0.0009568	0.03714	-0.02577	3641	0.9794	-0.1052	0.1033
ran_pars	mother_pidlink	sd__(Intercept)	0.2677	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9415	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.322	0.2089	6.33	5921	0.0000000002638	0.736	1.909
fixed	NA	birth_order	0.0139	0.0123	1.13	5589	0.2586	-0.02063	0.04842
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1135	0.02008	-5.652	5778	0.00000001659	-0.1699	-0.05714
fixed	NA	poly(age, 3, raw = TRUE)2	0.003014	0.0005863	5.141	5554	0.0000002819	0.001369	0.00466
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002411	0.000005325	-4.528	5361	0.000006076	-0.00003906	-0.000009165
fixed	NA	male	-0.2214	0.02451	-9.036	6277	2.134e-19	-0.2902	-0.1526
fixed	NA	sibling_count3	0.001551	0.03511	0.04416	4819	0.9648	-0.09702	0.1001
fixed	NA	sibling_count4	-0.001851	0.03721	-0.04974	4687	0.9603	-0.1063	0.1026
fixed	NA	sibling_count5	-0.02006	0.04081	-0.4916	4625	0.623	-0.1346	0.0945
ran_pars	mother_pidlink	sd__(Intercept)	0.2683	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9413	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.322	0.2095	6.312	5942	0.0000000002954	0.7342	1.91
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1126	0.02009	-5.605	5764	0.00000002175	-0.169	-0.05622
fixed	NA	poly(age, 3, raw = TRUE)2	0.002993	0.0005866	5.102	5532	0.000000347	0.001346	0.00464
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002396	0.000005329	-4.496	5329	0.000007067	-0.00003892	-0.000009002
fixed	NA	male	-0.2218	0.0245	-9.051	6274	1.852e-19	-0.2906	-0.153
fixed	NA	sibling_count3	0.003854	0.03571	0.1079	5007	0.9141	-0.09638	0.1041
fixed	NA	sibling_count4	0.01231	0.03783	0.3255	4890	0.7448	-0.09389	0.1185
fixed	NA	sibling_count5	-0.02412	0.04118	-0.5858	4765	0.558	-0.1397	0.09146
fixed	NA	birth_order_nonlinear2	0.02301	0.02931	0.785	5489	0.4325	-0.05927	0.1053
fixed	NA	birth_order_nonlinear3	0.02015	0.03743	0.5383	5415	0.5904	-0.08491	0.1252
fixed	NA	birth_order_nonlinear4	-0.02347	0.0493	-0.4762	5461	0.634	-0.1618	0.1149
fixed	NA	birth_order_nonlinear5	0.1614	0.07033	2.294	5340	0.02182	-0.03607	0.3588
ran_pars	mother_pidlink	sd__(Intercept)	0.2672	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9414	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.342	0.2097	6.402	5943	0.0000000001656	0.7537	1.931
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1137	0.02007	-5.665	5759	0.00000001542	-0.17	-0.05735
fixed	NA	poly(age, 3, raw = TRUE)2	0.003016	0.0005859	5.147	5524	0.000000274	0.001371	0.00466
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002408	0.000005323	-4.524	5317	0.000006186	-0.00003903	-0.000009142
fixed	NA	male	-0.2232	0.02448	-9.115	6268	1.042e-19	-0.2919	-0.1544
fixed	NA	count_birth_order2/2	0.006423	0.04974	0.1291	5441	0.8973	-0.1332	0.146
fixed	NA	count_birth_order1/3	-0.04722	0.04671	-1.011	6330	0.3121	-0.1783	0.08389
fixed	NA	count_birth_order2/3	0.03383	0.05272	0.6418	6336	0.5211	-0.1141	0.1818
fixed	NA	count_birth_order3/3	0.09029	0.05814	1.553	6336	0.1205	-0.0729	0.2535
fixed	NA	count_birth_order1/4	0.0577	0.05335	1.081	6336	0.2796	-0.09207	0.2075
fixed	NA	count_birth_order2/4	-0.01205	0.05597	-0.2154	6337	0.8295	-0.1691	0.145
fixed	NA	count_birth_order3/4	-0.08298	0.06069	-1.367	6335	0.1716	-0.2534	0.08739
fixed	NA	count_birth_order4/4	0.08942	0.06526	1.37	6330	0.1707	-0.09378	0.2726
fixed	NA	count_birth_order1/5	-0.02227	0.06135	-0.3629	6336	0.7167	-0.1945	0.1499
fixed	NA	count_birth_order2/5	0.05073	0.06339	0.8002	6333	0.4236	-0.1272	0.2287
fixed	NA	count_birth_order3/5	0.02637	0.06549	0.4026	6327	0.6872	-0.1575	0.2102
fixed	NA	count_birth_order4/5	-0.1776	0.06933	-2.562	6323	0.01042	-0.3722	0.01697
fixed	NA	count_birth_order5/5	0.1312	0.06982	1.88	6323	0.0602	-0.06475	0.3272
ran_pars	mother_pidlink	sd__(Intercept)	0.2652	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9408	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	17760	17827	-8870	17740	NA	NA	NA
11	17760	17835	-8869	17738	1.276	1	0.2586
14	17761	17856	-8867	17733	5.409	3	0.1442
20	17753	17888	-8856	17713	20.33	6	0.002418

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.028	0.5514	3.678	4061	0.0002378	0.4805	3.576
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1893	0.06434	-2.943	4059	0.003271	-0.3699	-0.008733
fixed	NA	poly(age, 3, raw = TRUE)2	0.005631	0.00237	2.376	4056	0.01756	-0.001022	0.01228
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005467	0.00002776	-1.969	4052	0.04902	-0.0001326	0.00002327
fixed	NA	male	-0.254	0.02984	-8.512	4031	2.37e-17	-0.3378	-0.1703
fixed	NA	sibling_count3	-0.01577	0.04021	-0.3922	3139	0.6949	-0.1286	0.09709
fixed	NA	sibling_count4	0.01271	0.04337	0.2931	2741	0.7695	-0.109	0.1344
fixed	NA	sibling_count5	0.0296	0.04917	0.602	2429	0.5472	-0.1084	0.1676
ran_pars	mother_pidlink	sd__(Intercept)	0.2636	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.916	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.015	0.5525	3.648	4060	0.000268	0.4644	3.566
fixed	NA	birth_order	0.006387	0.0157	0.4067	3833	0.6842	-0.03769	0.05047
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1887	0.06436	-2.931	4058	0.003396	-0.3693	-0.007987
fixed	NA	poly(age, 3, raw = TRUE)2	0.005599	0.002372	2.361	4055	0.01828	-0.001058	0.01226
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005417	0.00002779	-1.949	4052	0.05136	-0.0001322	0.00002385
fixed	NA	male	-0.2542	0.02985	-8.517	4030	2.28e-17	-0.338	-0.1704
fixed	NA	sibling_count3	-0.01881	0.0409	-0.4598	3194	0.6457	-0.1336	0.096
fixed	NA	sibling_count4	0.005779	0.0466	0.124	2965	0.9013	-0.125	0.1366
fixed	NA	sibling_count5	0.01818	0.05664	0.3209	2896	0.7483	-0.1408	0.1772
ran_pars	mother_pidlink	sd__(Intercept)	0.2637	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9161	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.002	0.5529	3.621	4055	0.0002971	0.4501	3.554
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1865	0.06444	-2.894	4053	0.003823	-0.3674	-0.005612
fixed	NA	poly(age, 3, raw = TRUE)2	0.005519	0.002375	2.324	4050	0.02016	-0.001147	0.01219
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005329	0.00002783	-1.915	4047	0.05557	-0.0001314	0.00002482
fixed	NA	male	-0.2541	0.02986	-8.51	4027	2.427e-17	-0.3379	-0.1703
fixed	NA	sibling_count3	-0.02659	0.04163	-0.6388	3298	0.523	-0.1435	0.09026
fixed	NA	sibling_count4	-0.000964	0.04731	-0.02038	3053	0.9837	-0.1338	0.1318
fixed	NA	sibling_count5	0.02667	0.05762	0.4628	2971	0.6435	-0.1351	0.1884
fixed	NA	birth_order_nonlinear2	0.01214	0.03597	0.3374	3431	0.7358	-0.08884	0.1131
fixed	NA	birth_order_nonlinear3	0.04638	0.04565	1.016	3592	0.3098	-0.08177	0.1745
fixed	NA	birth_order_nonlinear4	0.019	0.06061	0.3135	3725	0.7539	-0.1511	0.1891
fixed	NA	birth_order_nonlinear5	-0.04188	0.09446	-0.4434	3658	0.6575	-0.307	0.2233
ran_pars	mother_pidlink	sd__(Intercept)	0.2637	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9163	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.977	0.5528	3.575	4050	0.000354	0.4247	3.528
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1839	0.06443	-2.854	4048	0.004336	-0.3648	-0.003042
fixed	NA	poly(age, 3, raw = TRUE)2	0.005478	0.002374	2.307	4045	0.0211	-0.001187	0.01214
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005347	0.00002782	-1.922	4042	0.05471	-0.0001316	0.00002463
fixed	NA	male	-0.2538	0.02987	-8.495	4019	2.742e-17	-0.3376	-0.1699
fixed	NA	count_birth_order2/2	-0.0102	0.06112	-0.1669	3557	0.8674	-0.1818	0.1614
fixed	NA	count_birth_order1/3	-0.09999	0.05377	-1.86	4048	0.063	-0.2509	0.05094
fixed	NA	count_birth_order2/3	0.01397	0.05878	0.2376	4051	0.8122	-0.151	0.179
fixed	NA	count_birth_order3/3	0.08693	0.06491	1.339	4049	0.1805	-0.09526	0.2691
fixed	NA	count_birth_order1/4	0.05852	0.06668	0.8776	4050	0.3802	-0.1287	0.2457
fixed	NA	count_birth_order2/4	-0.01142	0.06792	-0.1681	4051	0.8665	-0.2021	0.1792
fixed	NA	count_birth_order3/4	-0.03839	0.0724	-0.5302	4042	0.596	-0.2416	0.1649
fixed	NA	count_birth_order4/4	0.01923	0.07359	0.2614	4042	0.7938	-0.1873	0.2258
fixed	NA	count_birth_order1/5	0.1145	0.09004	1.272	4050	0.2035	-0.1382	0.3673
fixed	NA	count_birth_order2/5	-0.01591	0.09641	-0.1651	4041	0.8689	-0.2865	0.2547
fixed	NA	count_birth_order3/5	0.0272	0.08955	0.3038	4035	0.7613	-0.2242	0.2786
fixed	NA	count_birth_order4/5	0.02233	0.08533	0.2617	4041	0.7936	-0.2172	0.2619
fixed	NA	count_birth_order5/5	-0.02365	0.08877	-0.2664	4033	0.7899	-0.2728	0.2255
ran_pars	mother_pidlink	sd__(Intercept)	0.2671	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9148	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11161	11224	-5570	11141	NA	NA	NA
11	11163	11232	-5570	11141	0.1654	1	0.6843
14	11167	11256	-5570	11139	1.346	3	0.7183
20	11169	11295	-5564	11129	10.56	6	0.1028

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.983	0.5677	3.493	3773	0.0004837	0.3892	3.576
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1863	0.06631	-2.81	3771	0.004976	-0.3725	-0.0002106
fixed	NA	poly(age, 3, raw = TRUE)2	0.005679	0.002444	2.324	3767	0.02019	-0.001181	0.01254
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005659	0.00002863	-1.976	3762	0.04819	-0.000137	0.00002378
fixed	NA	male	-0.2582	0.031	-8.328	3751	1.139e-16	-0.3452	-0.1712
fixed	NA	sibling_count3	-0.03455	0.04332	-0.7976	2967	0.4252	-0.1562	0.08705
fixed	NA	sibling_count4	-0.03858	0.04563	-0.8456	2663	0.3978	-0.1667	0.08949
fixed	NA	sibling_count5	0.02217	0.04852	0.4569	2366	0.6478	-0.114	0.1584
ran_pars	mother_pidlink	sd__(Intercept)	0.2248	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.926	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.95	0.5686	3.429	3772	0.0006123	0.3537	3.546
fixed	NA	birth_order	0.01603	0.01571	1.021	3630	0.3075	-0.02806	0.06012
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1847	0.06632	-2.785	3770	0.00538	-0.3709	0.001462
fixed	NA	poly(age, 3, raw = TRUE)2	0.005602	0.002445	2.291	3766	0.022	-0.001261	0.01247
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005538	0.00002866	-1.933	3763	0.05336	-0.0001358	0.00002506
fixed	NA	male	-0.2584	0.031	-8.335	3749	1.075e-16	-0.3454	-0.1714
fixed	NA	sibling_count3	-0.04213	0.04395	-0.9584	3003	0.3379	-0.1655	0.08125
fixed	NA	sibling_count4	-0.05529	0.04848	-1.141	2825	0.2542	-0.1914	0.08079
fixed	NA	sibling_count5	-0.0042	0.05498	-0.0764	2738	0.9391	-0.1585	0.1501
ran_pars	mother_pidlink	sd__(Intercept)	0.2251	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.926	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.94	0.5687	3.412	3767	0.0006512	0.3441	3.537
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1814	0.06635	-2.734	3765	0.006287	-0.3676	0.004848
fixed	NA	poly(age, 3, raw = TRUE)2	0.005473	0.002446	2.238	3761	0.02531	-0.001393	0.01234
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005388	0.00002866	-1.88	3757	0.06023	-0.0001343	0.00002658
fixed	NA	male	-0.2589	0.03099	-8.356	3746	8.994e-17	-0.3459	-0.172
fixed	NA	sibling_count3	-0.05967	0.04467	-1.336	3093	0.1818	-0.1851	0.06573
fixed	NA	sibling_count4	-0.07538	0.0492	-1.532	2910	0.1256	-0.2135	0.06272
fixed	NA	sibling_count5	0.005539	0.05553	0.09975	2788	0.9206	-0.1503	0.1614
fixed	NA	birth_order_nonlinear2	0.0166	0.03749	0.4427	3229	0.658	-0.08864	0.1218
fixed	NA	birth_order_nonlinear3	0.1088	0.04726	2.301	3413	0.02144	-0.02391	0.2414
fixed	NA	birth_order_nonlinear4	0.07073	0.06167	1.147	3527	0.2515	-0.1024	0.2438
fixed	NA	birth_order_nonlinear5	-0.08802	0.09004	-0.9776	3446	0.3284	-0.3408	0.1647
ran_pars	mother_pidlink	sd__(Intercept)	0.2269	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.925	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.922	0.569	3.378	3762	0.0007367	0.3251	3.519
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1786	0.06635	-2.691	3759	0.007158	-0.3648	0.007706
fixed	NA	poly(age, 3, raw = TRUE)2	0.005399	0.002446	2.207	3756	0.02737	-0.001468	0.01227
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005336	0.00002867	-1.861	3752	0.06278	-0.0001338	0.00002711
fixed	NA	male	-0.2588	0.03101	-8.345	3738	9.861e-17	-0.3458	-0.1717
fixed	NA	count_birth_order2/2	-0.02025	0.06678	-0.3033	3322	0.7617	-0.2077	0.1672
fixed	NA	count_birth_order1/3	-0.1425	0.05828	-2.446	3763	0.0145	-0.3061	0.02105
fixed	NA	count_birth_order2/3	0.002635	0.06296	0.04185	3764	0.9666	-0.1741	0.1794
fixed	NA	count_birth_order3/3	0.08658	0.07058	1.227	3762	0.22	-0.1115	0.2847
fixed	NA	count_birth_order1/4	-0.009103	0.06939	-0.1312	3763	0.8956	-0.2039	0.1857
fixed	NA	count_birth_order2/4	-0.1244	0.07015	-1.774	3764	0.0762	-0.3213	0.07249
fixed	NA	count_birth_order3/4	-0.0441	0.07739	-0.5698	3759	0.5688	-0.2613	0.1731
fixed	NA	count_birth_order4/4	0.007852	0.0779	0.1008	3759	0.9197	-0.2108	0.2265
fixed	NA	count_birth_order1/5	0.01982	0.08191	0.242	3764	0.8088	-0.2101	0.2497
fixed	NA	count_birth_order2/5	0.01078	0.08836	0.122	3762	0.9029	-0.2373	0.2588
fixed	NA	count_birth_order3/5	0.1027	0.08474	1.212	3759	0.2257	-0.1352	0.3405
fixed	NA	count_birth_order4/5	0.02752	0.08779	0.3135	3754	0.754	-0.2189	0.2739
fixed	NA	count_birth_order5/5	-0.09559	0.08723	-1.096	3750	0.2732	-0.3404	0.1493
ran_pars	mother_pidlink	sd__(Intercept)	0.2298	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9238	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	10376	10439	-5178	10356	NA	NA	NA
11	10377	10446	-5178	10355	1.043	1	0.3071
14	10376	10463	-5174	10348	7.323	3	0.06229
20	10378	10503	-5169	10338	9.6	6	0.1425

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.817	0.5575	3.259	4050	0.001127	0.252	3.382
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1648	0.06514	-2.529	4048	0.01147	-0.3476	0.0181
fixed	NA	poly(age, 3, raw = TRUE)2	0.004725	0.002404	1.966	4045	0.04942	-0.002023	0.01147
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004412	0.00002822	-1.564	4041	0.118	-0.0001233	0.00003509
fixed	NA	male	-0.26	0.02992	-8.692	4019	5.093e-18	-0.344	-0.1761
fixed	NA	sibling_count3	-0.01544	0.03971	-0.3887	3114	0.6975	-0.1269	0.09603
fixed	NA	sibling_count4	0.00454	0.04313	0.1053	2735	0.9162	-0.1165	0.1256
fixed	NA	sibling_count5	0.07114	0.05044	1.41	2338	0.1586	-0.07045	0.2127
ran_pars	mother_pidlink	sd__(Intercept)	0.2604	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9176	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.81	0.5585	3.241	4049	0.001201	0.2424	3.378
fixed	NA	birth_order	0.003336	0.01592	0.2096	3814	0.834	-0.04134	0.04801
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1644	0.06517	-2.523	4047	0.01167	-0.3474	0.01851
fixed	NA	poly(age, 3, raw = TRUE)2	0.004709	0.002405	1.958	4044	0.05032	-0.002043	0.01146
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004387	0.00002825	-1.553	4041	0.1205	-0.0001232	0.00003542
fixed	NA	male	-0.2601	0.02992	-8.693	4018	5.062e-18	-0.3441	-0.1761
fixed	NA	sibling_count3	-0.01704	0.04044	-0.4213	3165	0.6736	-0.1306	0.09649
fixed	NA	sibling_count4	0.0009267	0.04645	0.01995	2968	0.9841	-0.1295	0.1313
fixed	NA	sibling_count5	0.06544	0.0573	1.142	2766	0.2535	-0.0954	0.2263
ran_pars	mother_pidlink	sd__(Intercept)	0.2604	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9178	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.785	0.559	3.194	4044	0.001416	0.2161	3.354
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1612	0.06525	-2.47	4042	0.01353	-0.3444	0.02196
fixed	NA	poly(age, 3, raw = TRUE)2	0.00459	0.002408	1.906	4039	0.05674	-0.00217	0.01135
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004254	0.00002828	-1.504	4036	0.1326	-0.0001219	0.00003684
fixed	NA	male	-0.2594	0.02993	-8.668	4015	6.293e-18	-0.3435	-0.1754
fixed	NA	sibling_count3	-0.02581	0.0412	-0.6265	3275	0.531	-0.1415	0.08985
fixed	NA	sibling_count4	-0.008091	0.04717	-0.1715	3057	0.8638	-0.1405	0.1243
fixed	NA	sibling_count5	0.0776	0.0585	1.327	2851	0.1848	-0.08661	0.2418
fixed	NA	birth_order_nonlinear2	0.008103	0.0358	0.2263	3417	0.8209	-0.09239	0.1086
fixed	NA	birth_order_nonlinear3	0.0437	0.04543	0.9619	3561	0.3362	-0.08382	0.1712
fixed	NA	birth_order_nonlinear4	0.01622	0.06188	0.2621	3703	0.7933	-0.1575	0.1899
fixed	NA	birth_order_nonlinear5	-0.08965	0.1014	-0.8839	3697	0.3768	-0.3744	0.1951
ran_pars	mother_pidlink	sd__(Intercept)	0.2609	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9177	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.755	0.5588	3.14	4039	0.001701	0.1861	3.323
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1567	0.06522	-2.403	4037	0.01632	-0.3398	0.02637
fixed	NA	poly(age, 3, raw = TRUE)2	0.004469	0.002407	1.857	4034	0.06344	-0.002288	0.01123
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000417	0.00002826	-1.475	4031	0.1402	-0.000121	0.00003764
fixed	NA	male	-0.2594	0.02993	-8.669	4007	6.249e-18	-0.3434	-0.1754
fixed	NA	count_birth_order2/2	-0.03975	0.05965	-0.6664	3533	0.5052	-0.2072	0.1277
fixed	NA	count_birth_order1/3	-0.1107	0.05323	-2.081	4037	0.03752	-0.2602	0.03866
fixed	NA	count_birth_order2/3	-0.00592	0.05879	-0.1007	4040	0.9198	-0.171	0.1591
fixed	NA	count_birth_order3/3	0.09062	0.06354	1.426	4036	0.1539	-0.08773	0.269
fixed	NA	count_birth_order1/4	0.04216	0.06701	0.6292	4039	0.5293	-0.1459	0.2303
fixed	NA	count_birth_order2/4	0.006655	0.06813	0.09768	4039	0.9222	-0.1846	0.1979
fixed	NA	count_birth_order3/4	-0.07998	0.07193	-1.112	4029	0.2662	-0.2819	0.1219
fixed	NA	count_birth_order4/4	-0.01954	0.07381	-0.2647	4028	0.7913	-0.2267	0.1877
fixed	NA	count_birth_order1/5	0.1313	0.09025	1.455	4040	0.1459	-0.1221	0.3846
fixed	NA	count_birth_order2/5	0.01481	0.09951	0.1488	4030	0.8817	-0.2645	0.2941
fixed	NA	count_birth_order3/5	0.05974	0.09323	0.6407	4024	0.5217	-0.202	0.3214
fixed	NA	count_birth_order4/5	0.09232	0.08994	1.026	4029	0.3047	-0.1601	0.3448
fixed	NA	count_birth_order5/5	-0.029	0.09537	-0.3041	4022	0.7611	-0.2967	0.2387
ran_pars	mother_pidlink	sd__(Intercept)	0.2643	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.916	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11137	11200	-5558	11117	NA	NA	NA
11	11139	11208	-5558	11117	0.04383	1	0.8342
14	11142	11231	-5557	11114	2.104	3	0.5512
20	11142	11268	-5551	11102	12.71	6	0.04789

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Risk B

birthorder <- birthorder %>% mutate(outcome = riskB)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6854	0.2014	3.404	6324	0.000669	0.1202	1.251
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0475	0.0193	-2.461	6130	0.01387	-0.1017	0.006673
fixed	NA	poly(age, 3, raw = TRUE)2	0.001242	0.0005621	2.209	5915	0.02721	-0.0003361	0.00282
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001056	0.000005087	-2.075	5744	0.03804	-0.00002484	0.000003725
fixed	NA	male	-0.2056	0.02369	-8.679	6732	4.944e-18	-0.2721	-0.1391
fixed	NA	sibling_count3	-0.02283	0.03353	-0.6809	4779	0.4959	-0.117	0.07129
fixed	NA	sibling_count4	-0.005103	0.03461	-0.1474	4283	0.8828	-0.1023	0.09206
fixed	NA	sibling_count5	-0.02601	0.03576	-0.7275	3635	0.467	-0.1264	0.07436
ran_pars	mother_pidlink	sd__(Intercept)	0.2471	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9435	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6772	0.2014	3.362	6314	0.0007772	0.1119	1.243
fixed	NA	birth_order	0.02396	0.01188	2.017	5870	0.04378	-0.009391	0.05731
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04989	0.01933	-2.581	6157	0.009878	-0.1042	0.004372
fixed	NA	poly(age, 3, raw = TRUE)2	0.001303	0.0005629	2.314	5930	0.02068	-0.0002773	0.002883
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001096	0.000005091	-2.152	5752	0.03143	-0.00002525	0.000003334
fixed	NA	male	-0.2063	0.02368	-8.709	6729	3.796e-18	-0.2727	-0.1398
fixed	NA	sibling_count3	-0.03147	0.0338	-0.9311	4901	0.3518	-0.1264	0.06341
fixed	NA	sibling_count4	-0.02493	0.03598	-0.6929	4801	0.4884	-0.1259	0.07607
fixed	NA	sibling_count5	-0.05847	0.03921	-1.491	4715	0.136	-0.1685	0.0516
ran_pars	mother_pidlink	sd__(Intercept)	0.2482	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.943	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.7023	0.202	3.476	6338	0.0005126	0.1351	1.269
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04983	0.01934	-2.576	6144	0.01002	-0.1041	0.004473
fixed	NA	poly(age, 3, raw = TRUE)2	0.001303	0.0005634	2.312	5907	0.0208	-0.0002788	0.002884
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001097	0.000005097	-2.153	5719	0.03139	-0.00002528	0.000003336
fixed	NA	male	-0.2063	0.02369	-8.708	6727	3.836e-18	-0.2728	-0.1398
fixed	NA	sibling_count3	-0.03303	0.03436	-0.9614	5111	0.3364	-0.1295	0.06342
fixed	NA	sibling_count4	-0.02257	0.0366	-0.6166	5031	0.5375	-0.1253	0.08017
fixed	NA	sibling_count5	-0.06135	0.03959	-1.55	4884	0.1213	-0.1725	0.04979
fixed	NA	birth_order_nonlinear2	0.01745	0.0282	0.619	5718	0.536	-0.0617	0.09661
fixed	NA	birth_order_nonlinear3	0.05327	0.03634	1.466	5738	0.1427	-0.04873	0.1553
fixed	NA	birth_order_nonlinear4	0.04952	0.04752	1.042	5782	0.2975	-0.08388	0.1829
fixed	NA	birth_order_nonlinear5	0.1235	0.06842	1.806	5632	0.07105	-0.06852	0.3156
ran_pars	mother_pidlink	sd__(Intercept)	0.2471	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9434	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.7358	0.2022	3.638	6344	0.0002767	0.1681	1.304
fixed	NA	poly(age, 3, raw = TRUE)1	-0.05063	0.01933	-2.62	6144	0.008827	-0.1049	0.003624
fixed	NA	poly(age, 3, raw = TRUE)2	0.001323	0.0005628	2.35	5905	0.01879	-0.000257	0.002903
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001111	0.000005091	-2.181	5713	0.02919	-0.0000254	0.000003185
fixed	NA	male	-0.2065	0.02367	-8.726	6720	3.292e-18	-0.2729	-0.1401
fixed	NA	count_birth_order2/2	-0.04957	0.04813	-1.03	5643	0.3031	-0.1847	0.08554
fixed	NA	count_birth_order1/3	-0.1253	0.04511	-2.778	6752	0.005484	-0.252	0.001307
fixed	NA	count_birth_order2/3	0.002572	0.05029	0.05114	6759	0.9592	-0.1386	0.1437
fixed	NA	count_birth_order3/3	0.07243	0.05665	1.278	6761	0.2011	-0.08659	0.2314
fixed	NA	count_birth_order1/4	0.03681	0.05155	0.7141	6759	0.4752	-0.1079	0.1815
fixed	NA	count_birth_order2/4	-0.03557	0.05444	-0.6534	6761	0.5135	-0.1884	0.1172
fixed	NA	count_birth_order3/4	-0.1211	0.05978	-2.025	6760	0.04289	-0.2889	0.04674
fixed	NA	count_birth_order4/4	0.007753	0.06279	0.1235	6758	0.9017	-0.1685	0.184
fixed	NA	count_birth_order1/5	-0.13	0.05888	-2.209	6760	0.02724	-0.2953	0.03524
fixed	NA	count_birth_order2/5	-0.05497	0.06115	-0.899	6758	0.3687	-0.2266	0.1167
fixed	NA	count_birth_order3/5	0.0107	0.06276	0.1705	6757	0.8646	-0.1655	0.1869
fixed	NA	count_birth_order4/5	-0.04345	0.06722	-0.6464	6751	0.5181	-0.2322	0.1453
fixed	NA	count_birth_order5/5	0.038	0.06807	0.5582	6751	0.5767	-0.1531	0.2291
ran_pars	mother_pidlink	sd__(Intercept)	0.2474	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9422	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	18899	18967	-9439	18879	NA	NA	NA
11	18897	18972	-9437	18875	4.067	1	0.04373
14	18902	18998	-9437	18874	0.6018	3	0.896
20	18892	19029	-9426	18852	21.85	6	0.001288

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.277	0.5329	2.397	4261	0.01658	-0.2186	2.773
fixed	NA	poly(age, 3, raw = TRUE)1	-0.113	0.06212	-1.819	4256	0.06901	-0.2874	0.06139
fixed	NA	poly(age, 3, raw = TRUE)2	0.003652	0.002288	1.596	4249	0.1106	-0.002771	0.01007
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003752	0.0000268	-1.4	4244	0.1617	-0.0001128	0.00003772
fixed	NA	male	-0.2354	0.02876	-8.183	4262	3.623e-16	-0.3161	-0.1546
fixed	NA	sibling_count3	-0.07681	0.03814	-2.014	3189	0.04413	-0.1839	0.03026
fixed	NA	sibling_count4	-0.0239	0.04097	-0.5835	2703	0.5596	-0.1389	0.09109
fixed	NA	sibling_count5	-0.05159	0.04645	-1.11	2289	0.2669	-0.182	0.07881
ran_pars	mother_pidlink	sd__(Intercept)	0.1342	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9283	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.262	0.5335	2.367	4260	0.018	-0.235	2.76
fixed	NA	birth_order	0.009315	0.01523	0.6117	4054	0.5408	-0.03343	0.05206
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1125	0.06213	-1.811	4255	0.07021	-0.2869	0.06189
fixed	NA	poly(age, 3, raw = TRUE)2	0.003624	0.002289	1.583	4249	0.1134	-0.002801	0.01005
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003701	0.00002682	-1.38	4244	0.1676	-0.0001123	0.00003827
fixed	NA	male	-0.2357	0.02877	-8.193	4261	3.338e-16	-0.3165	-0.155
fixed	NA	sibling_count3	-0.08109	0.03879	-2.09	3247	0.03666	-0.19	0.0278
fixed	NA	sibling_count4	-0.03366	0.04399	-0.7652	2942	0.4442	-0.1572	0.08983
fixed	NA	sibling_count5	-0.06788	0.05358	-1.267	2819	0.2053	-0.2183	0.08253
ran_pars	mother_pidlink	sd__(Intercept)	0.1366	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9281	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.239	0.5338	2.32	4254	0.02037	-0.2598	2.737
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1096	0.06218	-1.763	4249	0.07796	-0.2842	0.06491
fixed	NA	poly(age, 3, raw = TRUE)2	0.003517	0.00229	1.536	4243	0.1247	-0.002912	0.009946
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003582	0.00002683	-1.335	4238	0.1819	-0.0001111	0.0000395
fixed	NA	male	-0.2352	0.02878	-8.172	4258	3.952e-16	-0.316	-0.1544
fixed	NA	sibling_count3	-0.08894	0.03946	-2.254	3370	0.02427	-0.1997	0.02183
fixed	NA	sibling_count4	-0.04037	0.04471	-0.9029	3045	0.3666	-0.1659	0.08513
fixed	NA	sibling_count5	-0.05315	0.0545	-0.9753	2892	0.3295	-0.2061	0.09983
fixed	NA	birth_order_nonlinear2	0.03623	0.03476	1.042	3565	0.2973	-0.06134	0.1338
fixed	NA	birth_order_nonlinear3	0.05454	0.04425	1.232	3800	0.2178	-0.06968	0.1788
fixed	NA	birth_order_nonlinear4	0.0318	0.05894	0.5394	3980	0.5896	-0.1337	0.1973
fixed	NA	birth_order_nonlinear5	-0.05454	0.09276	-0.5879	3908	0.5566	-0.3149	0.2058
ran_pars	mother_pidlink	sd__(Intercept)	0.1319	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9288	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.208	0.5335	2.265	4249	0.02358	-0.2893	2.706
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1068	0.06215	-1.719	4244	0.08568	-0.2813	0.06762
fixed	NA	poly(age, 3, raw = TRUE)2	0.003458	0.002289	1.511	4238	0.1309	-0.002968	0.009885
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003564	0.00002682	-1.329	4233	0.184	-0.0001109	0.00003966
fixed	NA	male	-0.2341	0.02877	-8.139	4252	5.195e-16	-0.3149	-0.1534
fixed	NA	count_birth_order2/2	0.02688	0.05921	0.4541	3652	0.6498	-0.1393	0.1931
fixed	NA	count_birth_order1/3	-0.1468	0.0516	-2.844	4254	0.00447	-0.2916	-0.001931
fixed	NA	count_birth_order2/3	-0.006226	0.05624	-0.1107	4254	0.9119	-0.1641	0.1516
fixed	NA	count_birth_order3/3	-0.003739	0.06312	-0.05924	4253	0.9528	-0.1809	0.1734
fixed	NA	count_birth_order1/4	0.01079	0.06345	0.17	4252	0.865	-0.1673	0.1889
fixed	NA	count_birth_order2/4	-0.02773	0.06572	-0.4219	4254	0.6731	-0.2122	0.1568
fixed	NA	count_birth_order3/4	-0.07186	0.0693	-1.037	4252	0.2998	-0.2664	0.1227
fixed	NA	count_birth_order4/4	0.02637	0.07157	0.3684	4251	0.7126	-0.1745	0.2273
fixed	NA	count_birth_order1/5	0.03834	0.08726	0.4393	4254	0.6605	-0.2066	0.2833
fixed	NA	count_birth_order2/5	-0.1342	0.09153	-1.467	4254	0.1426	-0.3912	0.1227
fixed	NA	count_birth_order3/5	0.06427	0.08583	0.7488	4252	0.454	-0.1766	0.3052
fixed	NA	count_birth_order4/5	-0.08061	0.08253	-0.9768	4251	0.3287	-0.3123	0.1511
fixed	NA	count_birth_order5/5	-0.1119	0.08703	-1.286	4248	0.1986	-0.3562	0.1324
ran_pars	mother_pidlink	sd__(Intercept)	0.1324	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.928	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11588	11651	-5784	11568	NA	NA	NA
11	11589	11659	-5784	11567	0.3712	1	0.5423
14	11593	11682	-5782	11565	2.509	3	0.4737
20	11593	11720	-5776	11553	11.94	6	0.06337

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.164	0.5493	2.12	3962	0.0341	-0.3776	2.706
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09927	0.06411	-1.549	3958	0.1216	-0.2792	0.08068
fixed	NA	poly(age, 3, raw = TRUE)2	0.003195	0.002362	1.353	3953	0.1763	-0.003436	0.009825
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003294	0.00002767	-1.191	3949	0.2339	-0.0001106	0.00004473
fixed	NA	male	-0.2337	0.02989	-7.819	3960	6.782e-15	-0.3176	-0.1498
fixed	NA	sibling_count3	-0.09083	0.04143	-2.192	3035	0.02844	-0.2071	0.02547
fixed	NA	sibling_count4	-0.04567	0.04367	-1.046	2694	0.2957	-0.1683	0.07691
fixed	NA	sibling_count5	-0.0509	0.04655	-1.093	2324	0.2743	-0.1816	0.07977
ran_pars	mother_pidlink	sd__(Intercept)	0.1607	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9259	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.149	0.5499	2.089	3961	0.03679	-0.395	2.692
fixed	NA	birth_order	0.009936	0.01523	0.6523	3815	0.5143	-0.03282	0.0527
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09881	0.06411	-1.541	3958	0.1234	-0.2788	0.08117
fixed	NA	poly(age, 3, raw = TRUE)2	0.003167	0.002363	1.34	3953	0.1802	-0.003465	0.009799
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003242	0.00002769	-1.171	3949	0.2416	-0.0001101	0.00004529
fixed	NA	male	-0.2339	0.02989	-7.824	3959	6.509e-15	-0.3178	-0.15
fixed	NA	sibling_count3	-0.09537	0.04202	-2.269	3074	0.02331	-0.2133	0.02259
fixed	NA	sibling_count4	-0.05566	0.0463	-1.202	2859	0.2295	-0.1856	0.07432
fixed	NA	sibling_count5	-0.06693	0.05269	-1.27	2739	0.2041	-0.2148	0.08096
ran_pars	mother_pidlink	sd__(Intercept)	0.1628	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9256	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.118	0.5501	2.033	3956	0.04211	-0.4258	2.663
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09541	0.06414	-1.487	3952	0.137	-0.2755	0.08465
fixed	NA	poly(age, 3, raw = TRUE)2	0.003041	0.002364	1.286	3947	0.1983	-0.003594	0.009676
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003103	0.0000277	-1.12	3943	0.2626	-0.0001088	0.00004671
fixed	NA	male	-0.2332	0.0299	-7.798	3957	7.978e-15	-0.3171	-0.1492
fixed	NA	sibling_count3	-0.1062	0.04268	-2.487	3175	0.01293	-0.226	0.01366
fixed	NA	sibling_count4	-0.06448	0.04696	-1.373	2943	0.1699	-0.1963	0.06735
fixed	NA	sibling_count5	-0.05467	0.05321	-1.027	2781	0.3043	-0.204	0.0947
fixed	NA	birth_order_nonlinear2	0.04518	0.03607	1.252	3343	0.2105	-0.05608	0.1464
fixed	NA	birth_order_nonlinear3	0.0698	0.04574	1.526	3580	0.1271	-0.0586	0.1982
fixed	NA	birth_order_nonlinear4	0.03272	0.06	0.5454	3735	0.5855	-0.1357	0.2011
fixed	NA	birth_order_nonlinear5	-0.0535	0.08864	-0.6035	3645	0.5462	-0.3023	0.1953
ran_pars	mother_pidlink	sd__(Intercept)	0.1568	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9265	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.109	0.5499	2.016	3950	0.04383	-0.4348	2.652
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09522	0.0641	-1.486	3947	0.1375	-0.2752	0.08471
fixed	NA	poly(age, 3, raw = TRUE)2	0.00307	0.002362	1.3	3942	0.1938	-0.003561	0.009701
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003175	0.00002768	-1.147	3937	0.2514	-0.0001095	0.00004595
fixed	NA	male	-0.2348	0.02989	-7.853	3950	5.188e-15	-0.3187	-0.1508
fixed	NA	count_birth_order2/2	0.04884	0.06475	0.7544	3412	0.4507	-0.1329	0.2306
fixed	NA	count_birth_order1/3	-0.1645	0.05586	-2.946	3953	0.003241	-0.3213	-0.007746
fixed	NA	count_birth_order2/3	-0.02636	0.06051	-0.4356	3954	0.6632	-0.1962	0.1435
fixed	NA	count_birth_order3/3	0.0319	0.06835	0.4667	3953	0.6407	-0.16	0.2238
fixed	NA	count_birth_order1/4	0.002842	0.06645	0.04277	3952	0.9659	-0.1837	0.1894
fixed	NA	count_birth_order2/4	-0.04257	0.06724	-0.6332	3954	0.5266	-0.2313	0.1462
fixed	NA	count_birth_order3/4	-0.1127	0.07465	-1.509	3952	0.1313	-0.3222	0.09687
fixed	NA	count_birth_order4/4	0.03027	0.07651	0.3956	3951	0.6924	-0.1845	0.245
fixed	NA	count_birth_order1/5	0.01054	0.07925	0.133	3953	0.8942	-0.2119	0.233
fixed	NA	count_birth_order2/5	-0.0534	0.0846	-0.6312	3954	0.528	-0.2909	0.1841
fixed	NA	count_birth_order3/5	0.05969	0.08283	0.7206	3952	0.4712	-0.1728	0.2922
fixed	NA	count_birth_order4/5	-0.1003	0.08434	-1.189	3950	0.2346	-0.337	0.1365
fixed	NA	count_birth_order5/5	-0.108	0.08585	-1.258	3945	0.2083	-0.349	0.1329
ran_pars	mother_pidlink	sd__(Intercept)	0.155	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.926	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	10789	10852	-5384	10769	NA	NA	NA
11	10790	10859	-5384	10768	0.4226	1	0.5156
14	10793	10881	-5382	10765	3.605	3	0.3074
20	10792	10917	-5376	10752	12.98	6	0.04339

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.151	0.5349	2.151	4247	0.03151	-0.3508	2.652
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0983	0.06246	-1.574	4242	0.1156	-0.2736	0.07702
fixed	NA	poly(age, 3, raw = TRUE)2	0.003034	0.002304	1.317	4237	0.188	-0.003434	0.009502
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002951	0.00002705	-1.091	4232	0.2753	-0.0001054	0.00004641
fixed	NA	male	-0.2306	0.02865	-8.05	4246	1.063e-15	-0.311	-0.1502
fixed	NA	sibling_count3	-0.04499	0.03751	-1.199	3155	0.2305	-0.1503	0.06032
fixed	NA	sibling_count4	-0.01041	0.04058	-0.2566	2687	0.7975	-0.1243	0.1035
fixed	NA	sibling_count5	0.005122	0.04744	0.108	2179	0.914	-0.128	0.1383
ran_pars	mother_pidlink	sd__(Intercept)	0.1631	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9178	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.137	0.5355	2.123	4246	0.03379	-0.3661	2.64
fixed	NA	birth_order	0.008813	0.01533	0.575	4019	0.5653	-0.03421	0.05184
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09791	0.06247	-1.567	4242	0.1171	-0.2733	0.07744
fixed	NA	poly(age, 3, raw = TRUE)2	0.00301	0.002305	1.306	4236	0.1917	-0.00346	0.009479
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002906	0.00002706	-1.074	4231	0.283	-0.000105	0.0000469
fixed	NA	male	-0.2309	0.02865	-8.058	4244	9.979e-16	-0.3113	-0.1505
fixed	NA	sibling_count3	-0.049	0.03817	-1.284	3210	0.1993	-0.1561	0.05814
fixed	NA	sibling_count4	-0.0196	0.04364	-0.4492	2937	0.6533	-0.1421	0.1029
fixed	NA	sibling_count5	-0.009626	0.05395	-0.1784	2660	0.8584	-0.1611	0.1418
ran_pars	mother_pidlink	sd__(Intercept)	0.1647	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9176	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.109	0.5358	2.069	4240	0.0386	-0.3953	2.612
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0946	0.06251	-1.513	4236	0.1303	-0.2701	0.08089
fixed	NA	poly(age, 3, raw = TRUE)2	0.002889	0.002307	1.252	4231	0.2105	-0.003586	0.009363
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002773	0.00002708	-1.024	4226	0.3058	-0.0001037	0.00004828
fixed	NA	male	-0.2299	0.02866	-8.02	4242	1.353e-15	-0.3104	-0.1494
fixed	NA	sibling_count3	-0.05602	0.03886	-1.442	3337	0.1495	-0.1651	0.05306
fixed	NA	sibling_count4	-0.0239	0.04436	-0.5389	3041	0.59	-0.1484	0.1006
fixed	NA	sibling_count5	0.005893	0.05508	0.107	2742	0.9148	-0.1487	0.1605
fixed	NA	birth_order_nonlinear2	0.03567	0.03429	1.04	3533	0.2983	-0.06058	0.1319
fixed	NA	birth_order_nonlinear3	0.05136	0.04374	1.174	3748	0.2404	-0.07142	0.1741
fixed	NA	birth_order_nonlinear4	0.02078	0.05996	0.3465	3939	0.729	-0.1475	0.1891
fixed	NA	birth_order_nonlinear5	-0.05124	0.09844	-0.5205	3930	0.6027	-0.3276	0.2251
ran_pars	mother_pidlink	sd__(Intercept)	0.1628	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.918	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.082	0.5356	2.021	4235	0.04339	-0.4212	2.585
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09134	0.06249	-1.462	4231	0.1439	-0.2667	0.08406
fixed	NA	poly(age, 3, raw = TRUE)2	0.00281	0.002305	1.219	4226	0.223	-0.003661	0.009281
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002729	0.00002707	-1.008	4221	0.3134	-0.0001033	0.00004869
fixed	NA	male	-0.2288	0.02865	-7.987	4235	1.773e-15	-0.3093	-0.1484
fixed	NA	count_birth_order2/2	0.006322	0.05726	0.1104	3613	0.9121	-0.1544	0.1671
fixed	NA	count_birth_order1/3	-0.1299	0.05063	-2.565	4237	0.01036	-0.272	0.01226
fixed	NA	count_birth_order2/3	0.02053	0.05597	0.3668	4239	0.7138	-0.1366	0.1777
fixed	NA	count_birth_order3/3	0.03731	0.06161	0.6056	4237	0.5448	-0.1356	0.2102
fixed	NA	count_birth_order1/4	0.02521	0.06337	0.3978	4238	0.6908	-0.1527	0.2031
fixed	NA	count_birth_order2/4	-0.009462	0.06525	-0.145	4239	0.8847	-0.1926	0.1737
fixed	NA	count_birth_order3/4	-0.06088	0.06805	-0.8947	4236	0.371	-0.2519	0.1301
fixed	NA	count_birth_order4/4	0.005436	0.0719	0.0756	4234	0.9397	-0.1964	0.2073
fixed	NA	count_birth_order1/5	0.09169	0.08652	1.06	4239	0.2893	-0.1512	0.3346
fixed	NA	count_birth_order2/5	-0.06964	0.09387	-0.7419	4238	0.4582	-0.3332	0.1939
fixed	NA	count_birth_order3/5	0.06613	0.08935	0.7402	4236	0.4592	-0.1847	0.3169
fixed	NA	count_birth_order4/5	-0.01503	0.08618	-0.1745	4235	0.8615	-0.2569	0.2269
fixed	NA	count_birth_order5/5	-0.05657	0.09245	-0.6118	4232	0.5407	-0.3161	0.203
ran_pars	mother_pidlink	sd__(Intercept)	0.1623	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9175	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	11494	11557	-5737	11474	NA	NA	NA
11	11495	11565	-5737	11473	0.3282	1	0.5667
14	11499	11588	-5736	11471	2.193	3	0.5333
20	11499	11626	-5730	11459	11.88	6	0.0647

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Educational Attainment

Years of Education - z-standardized

birthorder <- birthorder %>% mutate(outcome = years_of_education_z)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.464	0.1642	-21.09	7234	7.129e-96	-3.925	-3.003
fixed	NA	poly(age, 3, raw = TRUE)1	0.3301	0.01567	21.07	7194	1.22e-95	0.2861	0.374
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008606	0.000455	-18.91	7217	6.655e-78	-0.009883	-0.007329
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006344	0.000004092	15.5	7232	2.345e-53	0.00005196	0.00007493
fixed	NA	male	-0.016	0.01828	-0.8752	6039	0.3815	-0.0673	0.0353
fixed	NA	sibling_count3	0.06858	0.03289	2.085	5172	0.03711	-0.02374	0.1609
fixed	NA	sibling_count4	0.02168	0.03451	0.6282	4980	0.5299	-0.07519	0.1185
fixed	NA	sibling_count5	0.005908	0.03661	0.1613	4801	0.8718	-0.09687	0.1087
ran_pars	mother_pidlink	sd__(Intercept)	0.6653	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6199	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.446	0.1646	-20.94	7270	1.428e-94	-3.908	-2.984
fixed	NA	birth_order	-0.0135	0.0087	-1.551	5659	0.1209	-0.03792	0.01092
fixed	NA	poly(age, 3, raw = TRUE)1	0.3308	0.01567	21.11	7179	5.297e-96	0.2868	0.3748
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008635	0.0004553	-18.96	7209	2.631e-78	-0.009914	-0.007357
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006364	0.000004093	15.55	7227	1.215e-53	0.00005215	0.00007513
fixed	NA	male	-0.01579	0.01827	-0.8639	6034	0.3877	-0.06707	0.0355
fixed	NA	sibling_count3	0.07232	0.03298	2.193	5237	0.02837	-0.02026	0.1649
fixed	NA	sibling_count4	0.03143	0.03508	0.8958	5268	0.3704	-0.06705	0.1299
fixed	NA	sibling_count5	0.02279	0.03821	0.5966	5406	0.5508	-0.08446	0.13
ran_pars	mother_pidlink	sd__(Intercept)	0.6657	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6196	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.431	0.1645	-20.86	7246	7.049e-94	-3.893	-2.969
fixed	NA	poly(age, 3, raw = TRUE)1	0.3287	0.01567	20.97	7185	7.587e-95	0.2847	0.3727
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008538	0.0004558	-18.73	7223	1.719e-76	-0.009818	-0.007259
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006246	0.000004103	15.22	7251	1.547e-51	0.00005094	0.00007398
fixed	NA	male	-0.01519	0.01823	-0.8334	6017	0.4047	-0.06637	0.03599
fixed	NA	sibling_count3	0.0825	0.03321	2.484	5347	0.01302	-0.01072	0.1757
fixed	NA	sibling_count4	0.04427	0.03533	1.253	5385	0.2103	-0.05491	0.1435
fixed	NA	sibling_count5	0.0107	0.03834	0.2792	5479	0.7801	-0.09691	0.1183
fixed	NA	birth_order_nonlinear2	-0.06449	0.02051	-3.144	5341	0.001674	-0.1221	-0.006916
fixed	NA	birth_order_nonlinear3	-0.08792	0.026	-3.382	5125	0.0007246	-0.1609	-0.01495
fixed	NA	birth_order_nonlinear4	-0.07154	0.03388	-2.112	5069	0.03477	-0.1667	0.02356
fixed	NA	birth_order_nonlinear5	0.08977	0.04907	1.829	4784	0.0674	-0.04797	0.2275
ran_pars	mother_pidlink	sd__(Intercept)	0.6666	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6176	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-3.424	0.1648	-20.78	7240	3.585e-93	-3.886	-2.961
fixed	NA	poly(age, 3, raw = TRUE)1	0.3287	0.01568	20.96	7180	9.111e-95	0.2847	0.3727
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008534	0.000456	-18.71	7219	2.379e-76	-0.009814	-0.007254
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006239	0.000004106	15.19	7250	2.362e-51	0.00005086	0.00007392
fixed	NA	male	-0.01526	0.01824	-0.8368	6006	0.4027	-0.06645	0.03593
fixed	NA	count_birth_order2/2	-0.08721	0.03507	-2.486	5491	0.01293	-0.1857	0.01124
fixed	NA	count_birth_order1/3	0.07269	0.03884	1.872	6994	0.06131	-0.03633	0.1817
fixed	NA	count_birth_order2/3	0.01095	0.04268	0.2566	7314	0.7975	-0.1089	0.1308
fixed	NA	count_birth_order3/3	-0.01067	0.04684	-0.2279	7433	0.8197	-0.1422	0.1208
fixed	NA	count_birth_order1/4	0.02226	0.04328	0.5143	7252	0.607	-0.09923	0.1438
fixed	NA	count_birth_order2/4	-0.03591	0.04581	-0.7839	7387	0.4331	-0.1645	0.09267
fixed	NA	count_birth_order3/4	-0.02143	0.04878	-0.4394	7436	0.6604	-0.1584	0.1155
fixed	NA	count_birth_order4/4	-0.03057	0.05094	-0.6001	7429	0.5485	-0.1736	0.1124
fixed	NA	count_birth_order1/5	0.004056	0.04884	0.08305	7408	0.9338	-0.133	0.1411
fixed	NA	count_birth_order2/5	-0.02462	0.05108	-0.4819	7437	0.6299	-0.168	0.1188
fixed	NA	count_birth_order3/5	-0.1238	0.05165	-2.398	7433	0.01653	-0.2688	0.02115
fixed	NA	count_birth_order4/5	-0.07325	0.05469	-1.339	7374	0.1805	-0.2268	0.08026
fixed	NA	count_birth_order5/5	0.09118	0.05573	1.636	7370	0.1018	-0.06524	0.2476
ran_pars	mother_pidlink	sd__(Intercept)	0.6669	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6176	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	18711	18780	-9345	18691	NA	NA	NA
11	18710	18787	-9344	18688	2.406	1	0.1209
14	18693	18790	-9332	18665	23.78	3	0.00002772
20	18701	18840	-9331	18661	3.483	6	0.7462

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.236	0.3724	-19.43	4376	9.361e-81	-8.282	-6.191
fixed	NA	poly(age, 3, raw = TRUE)1	0.7719	0.04354	17.73	4384	5.778e-68	0.6497	0.8942
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02413	0.001609	-15	4403	1.225e-49	-0.02865	-0.01961
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002427	0.0000189	12.84	4428	4.355e-37	0.0001897	0.0002958
fixed	NA	male	-0.08201	0.01961	-4.183	4011	0.00002939	-0.137	-0.02698
fixed	NA	sibling_count3	0.0106	0.03091	0.343	3434	0.7316	-0.07615	0.09736
fixed	NA	sibling_count4	-0.0882	0.03392	-2.6	3258	0.009366	-0.1834	0.007025
fixed	NA	sibling_count5	-0.174	0.0395	-4.405	3145	0.00001091	-0.2849	-0.06314
ran_pars	mother_pidlink	sd__(Intercept)	0.4989	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5371	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.28	0.3728	-19.53	4384	1.672e-81	-8.326	-6.234
fixed	NA	birth_order	0.02178	0.01018	2.14	4070	0.03242	-0.006789	0.05034
fixed	NA	poly(age, 3, raw = TRUE)1	0.7732	0.04353	17.76	4383	3.246e-68	0.651	0.8954
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02418	0.001608	-15.04	4401	7.234e-50	-0.0287	-0.01967
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002438	0.0000189	12.9	4426	2.125e-37	0.0001907	0.0002968
fixed	NA	male	-0.08264	0.0196	-4.216	4011	0.00002539	-0.1377	-0.02762
fixed	NA	sibling_count3	-0.00009053	0.0313	-0.002893	3481	0.9977	-0.08794	0.08776
fixed	NA	sibling_count4	-0.1131	0.03586	-3.155	3418	0.001617	-0.2138	-0.01249
fixed	NA	sibling_count5	-0.2147	0.04382	-4.899	3521	0.000001006	-0.3377	-0.09167
ran_pars	mother_pidlink	sd__(Intercept)	0.4987	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5369	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.12	0.3736	-19.06	4415	7.194e-78	-8.168	-6.071
fixed	NA	poly(age, 3, raw = TRUE)1	0.7603	0.04361	17.43	4411	7.091e-66	0.6379	0.8827
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02373	0.001611	-14.74	4423	5.145e-48	-0.02825	-0.01921
fixed	NA	poly(age, 3, raw = TRUE)3	0.000239	0.00001891	12.64	4441	5.491e-36	0.0001859	0.0002921
fixed	NA	male	-0.08368	0.01957	-4.276	4005	0.00001951	-0.1386	-0.02874
fixed	NA	sibling_count3	0.002044	0.03157	0.06476	3570	0.9484	-0.08657	0.09066
fixed	NA	sibling_count4	-0.1153	0.03617	-3.188	3499	0.001445	-0.2168	-0.01378
fixed	NA	sibling_count5	-0.2389	0.04428	-5.395	3616	0.00000007273	-0.3632	-0.1146
fixed	NA	birth_order_nonlinear2	-0.05553	0.02208	-2.515	3297	0.01197	-0.1175	0.00646
fixed	NA	birth_order_nonlinear3	0.03104	0.02852	1.089	3512	0.2764	-0.04901	0.1111
fixed	NA	birth_order_nonlinear4	0.06363	0.0389	1.636	3698	0.1019	-0.04555	0.1728
fixed	NA	birth_order_nonlinear5	0.1591	0.06017	2.644	3376	0.008232	-0.009812	0.328
ran_pars	mother_pidlink	sd__(Intercept)	0.4988	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5357	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.118	0.3739	-19.04	4414	1.015e-77	-8.168	-6.068
fixed	NA	poly(age, 3, raw = TRUE)1	0.7593	0.04363	17.4	4405	1.196e-65	0.6368	0.8818
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0237	0.001612	-14.71	4417	7.629e-48	-0.02823	-0.01918
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002388	0.00001893	12.61	4435	7.403e-36	0.0001856	0.0002919
fixed	NA	male	-0.08366	0.01959	-4.27	4001	0.00002	-0.1387	-0.02866
fixed	NA	count_birth_order2/2	-0.03201	0.03837	-0.8343	3592	0.4041	-0.1397	0.07569
fixed	NA	count_birth_order1/3	0.02694	0.0376	0.7163	4546	0.4738	-0.07861	0.1325
fixed	NA	count_birth_order2/3	-0.06356	0.04041	-1.573	4655	0.1158	-0.177	0.04987
fixed	NA	count_birth_order3/3	0.02952	0.04463	0.6615	4661	0.5083	-0.09575	0.1548
fixed	NA	count_birth_order1/4	-0.1223	0.04558	-2.683	4645	0.007333	-0.2502	0.005674
fixed	NA	count_birth_order2/4	-0.1747	0.04642	-3.764	4665	0.0001695	-0.305	-0.0444
fixed	NA	count_birth_order3/4	-0.05508	0.0486	-1.133	4623	0.2571	-0.1915	0.08133
fixed	NA	count_birth_order4/4	-0.03078	0.05043	-0.6103	4618	0.5417	-0.1723	0.1108
fixed	NA	count_birth_order1/5	-0.2352	0.06134	-3.834	4644	0.000128	-0.4073	-0.06297
fixed	NA	count_birth_order2/5	-0.241	0.06472	-3.724	4489	0.0001986	-0.4227	-0.05933
fixed	NA	count_birth_order3/5	-0.2154	0.06039	-3.566	4545	0.0003655	-0.3849	-0.04587
fixed	NA	count_birth_order4/5	-0.1855	0.05906	-3.142	4587	0.001691	-0.3513	-0.01976
fixed	NA	count_birth_order5/5	-0.07281	0.06096	-1.194	4536	0.2324	-0.2439	0.0983
ran_pars	mother_pidlink	sd__(Intercept)	0.4984	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5362	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	9994	10058	-4987	9974	NA	NA	NA
11	9991	10062	-4984	9969	4.586	1	0.03224
14	9981	10071	-4976	9953	16.33	3	0.0009685
20	9989	10119	-4975	9949	3.115	6	0.7943

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.461	0.381	-19.58	4064	1.135e-81	-8.531	-6.392
fixed	NA	poly(age, 3, raw = TRUE)1	0.7966	0.0446	17.86	4071	9.208e-69	0.6714	0.9217
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02504	0.001649	-15.19	4092	1.018e-50	-0.02966	-0.02041
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002526	0.00001938	13.04	4120	4.317e-38	0.0001982	0.000307
fixed	NA	male	-0.07778	0.02023	-3.846	3720	0.0001223	-0.1346	-0.02101
fixed	NA	sibling_count3	0.0301	0.03313	0.9086	3273	0.3636	-0.06289	0.1231
fixed	NA	sibling_count4	-0.03826	0.03541	-1.08	3140	0.2801	-0.1377	0.06115
fixed	NA	sibling_count5	-0.09943	0.03854	-2.58	3026	0.009935	-0.2076	0.008762
ran_pars	mother_pidlink	sd__(Intercept)	0.4971	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5322	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.489	0.3814	-19.64	4067	4.221e-82	-8.559	-6.418
fixed	NA	birth_order	0.01576	0.01018	1.549	3855	0.1216	-0.01281	0.04433
fixed	NA	poly(age, 3, raw = TRUE)1	0.7969	0.04459	17.87	4070	7.591e-69	0.6718	0.9221
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02505	0.001648	-15.2	4090	8.609e-51	-0.02968	-0.02043
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002531	0.00001937	13.06	4118	3.102e-38	0.0001987	0.0003075
fixed	NA	male	-0.07808	0.02022	-3.861	3719	0.0001149	-0.1349	-0.02131
fixed	NA	sibling_count3	0.02236	0.0335	0.6676	3306	0.5045	-0.07167	0.1164
fixed	NA	sibling_count4	-0.05558	0.03713	-1.497	3257	0.1346	-0.1598	0.04866
fixed	NA	sibling_count5	-0.1268	0.0424	-2.991	3300	0.002805	-0.2458	-0.007782
ran_pars	mother_pidlink	sd__(Intercept)	0.4971	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.532	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.348	0.3826	-19.21	4104	8.7e-79	-8.422	-6.274
fixed	NA	poly(age, 3, raw = TRUE)1	0.7848	0.0447	17.56	4102	1.378e-66	0.6593	0.9103
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02463	0.001652	-14.91	4116	5.577e-49	-0.02926	-0.01999
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002485	0.00001941	12.8	4136	7.681e-37	0.000194	0.000303
fixed	NA	male	-0.07917	0.0202	-3.919	3714	0.00009067	-0.1359	-0.02246
fixed	NA	sibling_count3	0.02899	0.0338	0.8576	3381	0.3912	-0.06589	0.1239
fixed	NA	sibling_count4	-0.05305	0.03745	-1.416	3325	0.1567	-0.1582	0.05208
fixed	NA	sibling_count5	-0.1425	0.04267	-3.34	3354	0.0008465	-0.2623	-0.02275
fixed	NA	birth_order_nonlinear2	-0.04527	0.02298	-1.97	3116	0.04892	-0.1098	0.01923
fixed	NA	birth_order_nonlinear3	-0.001966	0.02937	-0.06694	3306	0.9466	-0.0844	0.08046
fixed	NA	birth_order_nonlinear4	0.05123	0.03947	1.298	3471	0.1944	-0.05956	0.162
fixed	NA	birth_order_nonlinear5	0.1288	0.05716	2.254	3230	0.02426	-0.0316	0.2893
ran_pars	mother_pidlink	sd__(Intercept)	0.4974	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5311	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.338	0.3831	-19.16	4104	2.067e-78	-8.413	-6.263
fixed	NA	poly(age, 3, raw = TRUE)1	0.7836	0.04473	17.52	4098	2.632e-66	0.658	0.9091
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02458	0.001653	-14.87	4113	9.562e-49	-0.02922	-0.01994
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002481	0.00001943	12.77	4133	1.201e-36	0.0001935	0.0003026
fixed	NA	male	-0.07969	0.02023	-3.94	3711	0.00008297	-0.1365	-0.02292
fixed	NA	count_birth_order2/2	-0.0407	0.04206	-0.9676	3409	0.3333	-0.1588	0.07737
fixed	NA	count_birth_order1/3	0.04937	0.04047	1.22	4235	0.2226	-0.06424	0.163
fixed	NA	count_birth_order2/3	-0.05495	0.04351	-1.263	4324	0.2067	-0.1771	0.0672
fixed	NA	count_birth_order3/3	0.04642	0.048	0.9671	4326	0.3335	-0.08831	0.1811
fixed	NA	count_birth_order1/4	-0.0827	0.0474	-1.745	4312	0.08112	-0.2158	0.05036
fixed	NA	count_birth_order2/4	-0.05819	0.04774	-1.219	4332	0.223	-0.1922	0.07582
fixed	NA	count_birth_order3/4	-0.06819	0.05154	-1.323	4273	0.1858	-0.2129	0.07647
fixed	NA	count_birth_order4/4	0.009902	0.0533	0.1858	4280	0.8526	-0.1397	0.1595
fixed	NA	count_birth_order1/5	-0.1378	0.05614	-2.454	4331	0.01415	-0.2954	0.0198
fixed	NA	count_birth_order2/5	-0.1687	0.05896	-2.862	4242	0.004229	-0.3342	-0.003246
fixed	NA	count_birth_order3/5	-0.1516	0.05762	-2.631	4242	0.00855	-0.3133	0.01016
fixed	NA	count_birth_order4/5	-0.103	0.05956	-1.729	4195	0.08386	-0.2702	0.0642
fixed	NA	count_birth_order5/5	-0.01275	0.0593	-0.215	4208	0.8298	-0.1792	0.1537
ran_pars	mother_pidlink	sd__(Intercept)	0.4966	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5316	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	9229	9293	-4605	9209	NA	NA	NA
11	9229	9299	-4604	9207	2.402	1	0.1212
14	9224	9314	-4598	9196	10.68	3	0.01362
20	9231	9359	-4596	9191	5.325	6	0.5028

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.211	0.3761	-19.17	4346	1.012e-78	-8.267	-6.155
fixed	NA	poly(age, 3, raw = TRUE)1	0.7701	0.04403	17.49	4353	3.069e-66	0.6465	0.8937
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02411	0.001629	-14.8	4371	2.25e-48	-0.02868	-0.01953
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002426	0.00001917	12.65	4396	4.612e-36	0.0001888	0.0002964
fixed	NA	male	-0.08855	0.01965	-4.507	3983	0.000006772	-0.1437	-0.0334
fixed	NA	sibling_count3	0.004782	0.03063	0.1561	3477	0.876	-0.0812	0.09076
fixed	NA	sibling_count4	-0.07132	0.03382	-2.109	3327	0.03505	-0.1663	0.02362
fixed	NA	sibling_count5	-0.1659	0.04076	-4.07	3144	0.00004825	-0.2803	-0.05147
ran_pars	mother_pidlink	sd__(Intercept)	0.5046	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5357	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.251	0.3766	-19.25	4355	2.351e-79	-8.308	-6.194
fixed	NA	birth_order	0.01979	0.01028	1.925	4008	0.0543	-0.009067	0.04864
fixed	NA	poly(age, 3, raw = TRUE)1	0.7713	0.04403	17.52	4354	1.88e-66	0.6477	0.8949
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02415	0.001629	-14.83	4371	1.438e-48	-0.02873	-0.01958
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002436	0.00001918	12.7	4395	2.498e-36	0.0001898	0.0002974
fixed	NA	male	-0.08892	0.01965	-4.526	3983	0.000006179	-0.1441	-0.03378
fixed	NA	sibling_count3	-0.005083	0.03104	-0.1637	3517	0.8699	-0.09222	0.08206
fixed	NA	sibling_count4	-0.09382	0.03577	-2.623	3490	0.008759	-0.1942	0.00659
fixed	NA	sibling_count5	-0.2016	0.04476	-4.503	3474	0.000006919	-0.3272	-0.07592
ran_pars	mother_pidlink	sd__(Intercept)	0.5042	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5357	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.088	0.3774	-18.78	4388	9.403e-76	-8.148	-6.029
fixed	NA	poly(age, 3, raw = TRUE)1	0.758	0.04411	17.19	4382	4.112e-64	0.6342	0.8818
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0237	0.001631	-14.53	4392	9.504e-47	-0.02828	-0.01912
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002388	0.00001919	12.45	4409	5.608e-35	0.000185	0.0002927
fixed	NA	male	-0.08975	0.01961	-4.576	3976	0.000004884	-0.1448	-0.0347
fixed	NA	sibling_count3	-0.003601	0.03133	-0.1149	3606	0.9085	-0.09155	0.08435
fixed	NA	sibling_count4	-0.09878	0.03609	-2.737	3569	0.006222	-0.2001	0.002511
fixed	NA	sibling_count5	-0.2281	0.04534	-5.031	3584	0.000000511	-0.3554	-0.1008
fixed	NA	birth_order_nonlinear2	-0.05814	0.02193	-2.651	3272	0.008053	-0.1197	0.003411
fixed	NA	birth_order_nonlinear3	0.02339	0.02839	0.8236	3475	0.4102	-0.05632	0.1031
fixed	NA	birth_order_nonlinear4	0.07316	0.03958	1.848	3628	0.06464	-0.03795	0.1843
fixed	NA	birth_order_nonlinear5	0.1492	0.06428	2.321	3359	0.02036	-0.03126	0.3296
ran_pars	mother_pidlink	sd__(Intercept)	0.5045	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5343	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-7.092	0.3777	-18.78	4386	1.025e-75	-8.153	-6.032
fixed	NA	poly(age, 3, raw = TRUE)1	0.7573	0.04413	17.16	4376	6.335e-64	0.6334	0.8812
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02368	0.001632	-14.51	4386	1.3e-46	-0.02826	-0.0191
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002387	0.0000192	12.43	4403	7.043e-35	0.0001848	0.0002926
fixed	NA	male	-0.08957	0.01963	-4.563	3969	0.000005199	-0.1447	-0.03447
fixed	NA	count_birth_order2/2	-0.02367	0.03719	-0.6364	3516	0.5245	-0.1281	0.08073
fixed	NA	count_birth_order1/3	0.02922	0.03725	0.7845	4537	0.4328	-0.07534	0.1338
fixed	NA	count_birth_order2/3	-0.06772	0.04039	-1.676	4648	0.09371	-0.1811	0.04566
fixed	NA	count_birth_order3/3	0.0106	0.04389	0.2416	4641	0.8091	-0.1126	0.1338
fixed	NA	count_birth_order1/4	-0.1006	0.04571	-2.201	4642	0.0278	-0.2289	0.02771
fixed	NA	count_birth_order2/4	-0.1596	0.0464	-3.439	4646	0.00059	-0.2898	-0.0293
fixed	NA	count_birth_order3/4	-0.04408	0.04822	-0.9142	4595	0.3607	-0.1794	0.09128
fixed	NA	count_birth_order4/4	0.001783	0.05062	0.03522	4572	0.9719	-0.1403	0.1439
fixed	NA	count_birth_order1/5	-0.2226	0.06176	-3.605	4639	0.0003153	-0.396	-0.04929
fixed	NA	count_birth_order2/5	-0.2492	0.06664	-3.739	4452	0.0001868	-0.4363	-0.06213
fixed	NA	count_birth_order3/5	-0.1838	0.06317	-2.909	4508	0.003646	-0.3611	-0.006428
fixed	NA	count_birth_order4/5	-0.1665	0.06175	-2.697	4554	0.007031	-0.3399	0.006819
fixed	NA	count_birth_order5/5	-0.06767	0.06494	-1.042	4480	0.2974	-0.2499	0.1146
ran_pars	mother_pidlink	sd__(Intercept)	0.5041	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5347	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	9979	10043	-4979	9959	NA	NA	NA
11	9977	10048	-4978	9955	3.712	1	0.05403
14	9966	10057	-4969	9938	16.72	3	0.0008055
20	9975	10104	-4967	9935	3.655	6	0.7233

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Elementary missed

birthorder <- birthorder %>% mutate(outcome = Elementary_missed)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)

## boundary (singular) fit: see ?isSingular

compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.06405	0.08209	-0.7802	4285	0.4353	-0.2945	0.1664
fixed	NA	poly(age, 3, raw = TRUE)1	0.008914	0.009546	0.9338	4285	0.3505	-0.01788	0.03571
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002855	0.0003483	-0.8198	4285	0.4124	-0.001263	0.0006922
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002916	0.000003985	0.7317	4285	0.4644	-0.00000827	0.0000141
fixed	NA	male	0.01113	0.004914	2.264	4285	0.02362	-0.002669	0.02492
fixed	NA	sibling_count3	-0.004754	0.006787	-0.7006	4285	0.4836	-0.0238	0.0143
fixed	NA	sibling_count4	0.002237	0.006986	0.3202	4285	0.7489	-0.01737	0.02185
fixed	NA	sibling_count5	0.0006969	0.007226	0.09644	4285	0.9232	-0.01959	0.02098
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1608	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.06261	0.08232	-0.7606	4284	0.4469	-0.2937	0.1685
fixed	NA	birth_order	-0.0005888	0.002461	-0.2392	4284	0.8109	-0.007497	0.00632
fixed	NA	poly(age, 3, raw = TRUE)1	0.008825	0.009555	0.9237	4284	0.3557	-0.01799	0.03565
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002818	0.0003487	-0.8083	4284	0.419	-0.001261	0.000697
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000287	0.00000399	0.7193	4284	0.472	-0.00000833	0.00001407
fixed	NA	male	0.01114	0.004915	2.266	4284	0.02349	-0.002658	0.02494
fixed	NA	sibling_count3	-0.004516	0.00686	-0.6582	4284	0.5104	-0.02377	0.01474
fixed	NA	sibling_count4	0.002809	0.007384	0.3803	4284	0.7037	-0.01792	0.02354
fixed	NA	sibling_count5	0.001613	0.008178	0.1972	4284	0.8437	-0.02134	0.02457
ran_pars	mother_pidlink	sd__(Intercept)	0.0000000003416	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1608	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.07008	0.08235	-0.851	4281	0.3948	-0.3012	0.1611
fixed	NA	poly(age, 3, raw = TRUE)1	0.009333	0.009563	0.976	4281	0.3291	-0.01751	0.03618
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002999	0.000349	-0.8595	4281	0.3901	-0.00128	0.0006797
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003062	0.000003993	0.7668	4281	0.4432	-0.000008146	0.00001427
fixed	NA	male	0.01123	0.004916	2.284	4281	0.0224	-0.00257	0.02503
fixed	NA	sibling_count3	-0.003716	0.006971	-0.533	4281	0.5941	-0.02328	0.01585
fixed	NA	sibling_count4	0.003706	0.007536	0.4918	4281	0.6229	-0.01745	0.02486
fixed	NA	sibling_count5	0.003001	0.008267	0.363	4281	0.7166	-0.02021	0.02621
fixed	NA	birth_order_nonlinear2	0.006739	0.005987	1.126	4281	0.2604	-0.01007	0.02354
fixed	NA	birth_order_nonlinear3	-0.004113	0.007625	-0.5394	4281	0.5897	-0.02552	0.01729
fixed	NA	birth_order_nonlinear4	-0.0003551	0.009867	-0.03599	4281	0.9713	-0.02805	0.02734
fixed	NA	birth_order_nonlinear5	-0.001871	0.01371	-0.1364	4281	0.8915	-0.04037	0.03663
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1608	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.07301	0.08244	-0.8856	4275	0.3759	-0.3044	0.1584
fixed	NA	poly(age, 3, raw = TRUE)1	0.00955	0.009567	0.9983	4275	0.3182	-0.0173	0.0364
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003061	0.0003491	-0.8767	4275	0.3807	-0.001286	0.000674
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003113	0.000003995	0.7792	4275	0.4359	-0.000008101	0.00001433
fixed	NA	male	0.0113	0.004918	2.298	4275	0.02158	-0.002501	0.02511
fixed	NA	count_birth_order2/2	0.008721	0.01044	0.8353	4275	0.4036	-0.02058	0.03803
fixed	NA	count_birth_order1/3	0.0009068	0.009166	0.09894	4275	0.9212	-0.02482	0.02664
fixed	NA	count_birth_order2/3	-0.003208	0.0102	-0.3147	4275	0.753	-0.03183	0.02541
fixed	NA	count_birth_order3/3	-0.005225	0.01175	-0.4447	4275	0.6566	-0.0382	0.02775
fixed	NA	count_birth_order1/4	0.006251	0.01083	0.5774	4275	0.5637	-0.02414	0.03664
fixed	NA	count_birth_order2/4	0.01993	0.01121	1.778	4275	0.07552	-0.01154	0.05141
fixed	NA	count_birth_order3/4	-0.01207	0.01212	-0.9959	4275	0.3193	-0.04608	0.02195
fixed	NA	count_birth_order4/4	0.00277	0.01256	0.2204	4275	0.8255	-0.0325	0.03804
fixed	NA	count_birth_order1/5	-0.006998	0.01248	-0.5606	4275	0.5751	-0.04204	0.02804
fixed	NA	count_birth_order2/5	0.008497	0.01338	0.6352	4275	0.5254	-0.02905	0.04605
fixed	NA	count_birth_order3/5	0.0122	0.01313	0.9291	4275	0.3529	-0.02465	0.04904
fixed	NA	count_birth_order4/5	0.004902	0.01388	0.3531	4275	0.724	-0.03407	0.04387
fixed	NA	count_birth_order5/5	0.001783	0.01328	0.1343	4275	0.8932	-0.0355	0.03907
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1608	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-3498	-3435	1759	-3518	NA	NA	NA
11	-3496	-3426	1759	-3518	0.05736	1	0.8107
14	-3493	-3404	1760	-3521	2.259	3	0.5204
20	-3486	-3359	1763	-3526	5.705	6	0.457

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1111	0.1254	-0.8862	3310	0.3756	-0.463	0.2408
fixed	NA	poly(age, 3, raw = TRUE)1	0.01595	0.01564	1.02	3310	0.3078	-0.02795	0.05985
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006233	0.0006197	-1.006	3310	0.3146	-0.002363	0.001116
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000807	0.000007777	1.038	3310	0.2995	-0.00001376	0.0000299
fixed	NA	male	0.009184	0.005331	1.723	3310	0.08506	-0.005782	0.02415
fixed	NA	sibling_count3	-0.003343	0.006687	-0.4999	3310	0.6172	-0.02211	0.01543
fixed	NA	sibling_count4	-0.004969	0.007465	-0.6656	3310	0.5057	-0.02592	0.01599
fixed	NA	sibling_count5	0.00186	0.00885	0.2101	3310	0.8336	-0.02298	0.0267
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1534	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1072	0.1255	-0.8541	3309	0.3931	-0.4595	0.2451
fixed	NA	birth_order	-0.002006	0.002908	-0.6898	3309	0.4904	-0.01017	0.006157
fixed	NA	poly(age, 3, raw = TRUE)1	0.01578	0.01564	1.009	3309	0.3131	-0.02813	0.05969
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006157	0.0006199	-0.9934	3309	0.3206	-0.002356	0.001124
fixed	NA	poly(age, 3, raw = TRUE)3	0.000007959	0.000007779	1.023	3309	0.3063	-0.00001388	0.0000298
fixed	NA	male	0.009237	0.005332	1.732	3309	0.08333	-0.005731	0.0242
fixed	NA	sibling_count3	-0.00242	0.00682	-0.3549	3309	0.7227	-0.02156	0.01672
fixed	NA	sibling_count4	-0.002807	0.008097	-0.3467	3309	0.7288	-0.02554	0.01992
fixed	NA	sibling_count5	0.005452	0.01027	0.5309	3309	0.5955	-0.02337	0.03428
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1534	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1143	0.1256	-0.91	3306	0.3629	-0.4669	0.2383
fixed	NA	poly(age, 3, raw = TRUE)1	0.01617	0.01566	1.033	3306	0.3018	-0.02778	0.06012
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006293	0.0006204	-1.014	3306	0.3105	-0.002371	0.001112
fixed	NA	poly(age, 3, raw = TRUE)3	0.000008099	0.000007786	1.04	3306	0.2983	-0.00001376	0.00002995
fixed	NA	male	0.009276	0.005335	1.739	3306	0.08221	-0.005701	0.02425
fixed	NA	sibling_count3	-0.002931	0.006964	-0.4209	3306	0.6738	-0.02248	0.01662
fixed	NA	sibling_count4	-0.002306	0.008264	-0.2791	3306	0.7802	-0.0255	0.02089
fixed	NA	sibling_count5	0.00733	0.01056	0.6944	3306	0.4875	-0.0223	0.03696
fixed	NA	birth_order_nonlinear2	0.003146	0.006416	0.4903	3306	0.6239	-0.01486	0.02116
fixed	NA	birth_order_nonlinear3	-0.001621	0.008373	-0.1936	3306	0.8465	-0.02512	0.02188
fixed	NA	birth_order_nonlinear4	-0.008807	0.01138	-0.7736	3306	0.4392	-0.04076	0.02315
fixed	NA	birth_order_nonlinear5	-0.01174	0.01842	-0.6372	3306	0.524	-0.06344	0.03997
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1535	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1164	0.1257	-0.9258	3300	0.3546	-0.4694	0.2365
fixed	NA	poly(age, 3, raw = TRUE)1	0.01672	0.01567	1.067	3300	0.286	-0.02727	0.06071
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006469	0.000621	-1.042	3300	0.2976	-0.00239	0.001096
fixed	NA	poly(age, 3, raw = TRUE)3	0.000008268	0.000007793	1.061	3300	0.2888	-0.00001361	0.00003014
fixed	NA	male	0.009474	0.00534	1.774	3300	0.07612	-0.005515	0.02446
fixed	NA	count_birth_order2/2	-0.006587	0.01038	-0.6348	3300	0.5256	-0.03572	0.02254
fixed	NA	count_birth_order1/3	-0.01279	0.009121	-1.402	3300	0.161	-0.03839	0.01281
fixed	NA	count_birth_order2/3	0.001834	0.009984	0.1837	3300	0.8543	-0.02619	0.02986
fixed	NA	count_birth_order3/3	-0.002196	0.01117	-0.1965	3300	0.8442	-0.03356	0.02917
fixed	NA	count_birth_order1/4	-0.0005371	0.01215	-0.0442	3300	0.9647	-0.03465	0.03357
fixed	NA	count_birth_order2/4	0.002783	0.01259	0.221	3300	0.8251	-0.03257	0.03813
fixed	NA	count_birth_order3/4	-0.01698	0.01326	-1.281	3300	0.2004	-0.05421	0.02024
fixed	NA	count_birth_order4/4	-0.01687	0.01311	-1.287	3300	0.1982	-0.05366	0.01992
fixed	NA	count_birth_order1/5	0.005217	0.01765	0.2955	3300	0.7676	-0.04434	0.05477
fixed	NA	count_birth_order2/5	-0.002252	0.01914	-0.1177	3300	0.9063	-0.05599	0.05148
fixed	NA	count_birth_order3/5	0.004141	0.0174	0.238	3300	0.8119	-0.0447	0.05298
fixed	NA	count_birth_order4/5	-0.0006506	0.01636	-0.03976	3300	0.9683	-0.04658	0.04528
fixed	NA	count_birth_order5/5	-0.007705	0.0168	-0.4586	3300	0.6465	-0.05486	0.03945
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1535	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-3012	-2951	1516	-3032	NA	NA	NA
11	-3011	-2944	1516	-3033	0.477	1	0.4898
14	-3006	-2920	1517	-3034	0.95	3	0.8133
20	-2998	-2876	1519	-3038	4.098	6	0.6634

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.09555	0.1279	-0.7468	3110	0.4552	-0.4547	0.2636
fixed	NA	poly(age, 3, raw = TRUE)1	0.01352	0.01596	0.8474	3110	0.3968	-0.03127	0.05832
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005147	0.0006321	-0.8142	3110	0.4156	-0.002289	0.00126
fixed	NA	poly(age, 3, raw = TRUE)3	0.000006592	0.000007924	0.8319	3110	0.4055	-0.00001565	0.00002883
fixed	NA	male	0.009673	0.005459	1.772	3110	0.07654	-0.005652	0.025
fixed	NA	sibling_count3	0.002693	0.00716	0.3761	3110	0.7069	-0.01741	0.02279
fixed	NA	sibling_count4	-0.005816	0.007732	-0.7522	3110	0.452	-0.02752	0.01589
fixed	NA	sibling_count5	-0.005405	0.008518	-0.6345	3110	0.5258	-0.02932	0.01851
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1522	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.09434	0.1281	-0.7367	3109	0.4614	-0.4538	0.2651
fixed	NA	birth_order	-0.0006958	0.00284	-0.245	3109	0.8065	-0.008668	0.007277
fixed	NA	poly(age, 3, raw = TRUE)1	0.01348	0.01596	0.8446	3109	0.3984	-0.03132	0.05829
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005127	0.0006323	-0.8109	3109	0.4175	-0.002288	0.001262
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000656	0.000007926	0.8277	3109	0.4079	-0.00001569	0.00002881
fixed	NA	male	0.009681	0.00546	1.773	3109	0.07633	-0.005646	0.02501
fixed	NA	sibling_count3	0.003021	0.007286	0.4147	3109	0.6784	-0.01743	0.02347
fixed	NA	sibling_count4	-0.005087	0.008286	-0.614	3109	0.5393	-0.02835	0.01817
fixed	NA	sibling_count5	-0.00425	0.009738	-0.4364	3109	0.6626	-0.03159	0.02309
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1522	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.09568	0.1281	-0.7469	3106	0.4552	-0.4553	0.2639
fixed	NA	poly(age, 3, raw = TRUE)1	0.01336	0.01597	0.8364	3106	0.403	-0.03147	0.05819
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005075	0.0006326	-0.8021	3106	0.4225	-0.002283	0.001268
fixed	NA	poly(age, 3, raw = TRUE)3	0.000006494	0.00000793	0.819	3106	0.4129	-0.00001577	0.00002875
fixed	NA	male	0.009854	0.005463	1.804	3106	0.0714	-0.005483	0.02519
fixed	NA	sibling_count3	0.003745	0.007435	0.5037	3106	0.6145	-0.01713	0.02462
fixed	NA	sibling_count4	-0.003304	0.00844	-0.3915	3106	0.6955	-0.027	0.02039
fixed	NA	sibling_count5	-0.004296	0.009915	-0.4333	3106	0.6648	-0.03213	0.02354
fixed	NA	birth_order_nonlinear2	0.003639	0.006613	0.5503	3106	0.5822	-0.01492	0.0222
fixed	NA	birth_order_nonlinear3	-0.004395	0.008476	-0.5185	3106	0.6041	-0.02819	0.0194
fixed	NA	birth_order_nonlinear4	-0.006257	0.01122	-0.5575	3106	0.5773	-0.03776	0.02525
fixed	NA	birth_order_nonlinear5	0.007926	0.01697	0.4672	3106	0.6404	-0.0397	0.05555
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1523	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.09762	0.1283	-0.7609	3100	0.4468	-0.4578	0.2625
fixed	NA	poly(age, 3, raw = TRUE)1	0.01386	0.01599	0.867	3100	0.386	-0.03102	0.05874
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005246	0.0006333	-0.8283	3100	0.4076	-0.002302	0.001253
fixed	NA	poly(age, 3, raw = TRUE)3	0.000006657	0.000007938	0.8387	3100	0.4017	-0.00001562	0.00002894
fixed	NA	male	0.01005	0.005472	1.838	3100	0.06623	-0.005305	0.02541
fixed	NA	count_birth_order2/2	-0.004029	0.01122	-0.359	3100	0.7196	-0.03553	0.02747
fixed	NA	count_birth_order1/3	-0.003772	0.009773	-0.386	3100	0.6995	-0.0312	0.02366
fixed	NA	count_birth_order2/3	0.007183	0.01061	0.6771	3100	0.4984	-0.02259	0.03696
fixed	NA	count_birth_order3/3	0.002688	0.01185	0.2267	3100	0.8207	-0.03059	0.03596
fixed	NA	count_birth_order1/4	0.0003133	0.01232	0.02542	3100	0.9797	-0.03428	0.0349
fixed	NA	count_birth_order2/4	0.001801	0.01243	0.1448	3100	0.8849	-0.03309	0.0367
fixed	NA	count_birth_order3/4	-0.02074	0.01384	-1.499	3100	0.1339	-0.05958	0.0181
fixed	NA	count_birth_order4/4	-0.01514	0.01345	-1.125	3100	0.2605	-0.0529	0.02262
fixed	NA	count_birth_order1/5	-0.01139	0.0153	-0.7442	3100	0.4568	-0.05435	0.03157
fixed	NA	count_birth_order2/5	-0.005266	0.01738	-0.3031	3100	0.7619	-0.05404	0.04351
fixed	NA	count_birth_order3/5	-0.008987	0.01591	-0.5649	3100	0.5722	-0.05364	0.03567
fixed	NA	count_birth_order4/5	-0.00826	0.01629	-0.5069	3100	0.6122	-0.054	0.03748
fixed	NA	count_birth_order5/5	0.001075	0.01594	0.06742	3100	0.9463	-0.04366	0.04581
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1523	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-2879	-2818	1449	-2899	NA	NA	NA
11	-2877	-2810	1449	-2899	0.06019	1	0.8062
14	-2872	-2788	1450	-2900	1.531	3	0.6751
20	-2863	-2742	1452	-2903	2.93	6	0.8175

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1276	0.1259	-1.014	3284	0.3108	-0.481	0.2258
fixed	NA	poly(age, 3, raw = TRUE)1	0.01847	0.0157	1.177	3284	0.2394	-0.02559	0.06254
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007421	0.0006219	-1.193	3284	0.2328	-0.002488	0.001004
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009978	0.000007806	1.278	3284	0.2013	-0.00001193	0.00003189
fixed	NA	male	0.005732	0.005374	1.067	3284	0.2862	-0.009352	0.02082
fixed	NA	sibling_count3	-0.001784	0.006659	-0.2678	3284	0.7888	-0.02048	0.01691
fixed	NA	sibling_count4	-0.007831	0.007468	-1.049	3284	0.2945	-0.02879	0.01313
fixed	NA	sibling_count5	0.001724	0.009164	0.1882	3284	0.8508	-0.024	0.02745
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1539	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1264	0.126	-1.003	3283	0.3161	-0.4801	0.2274
fixed	NA	birth_order	-0.000671	0.002963	-0.2265	3283	0.8208	-0.008987	0.007645
fixed	NA	poly(age, 3, raw = TRUE)1	0.01843	0.0157	1.174	3283	0.2407	-0.02565	0.0625
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00074	0.0006221	-1.19	3283	0.2343	-0.002486	0.001006
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009946	0.000007808	1.274	3283	0.2028	-0.00001197	0.00003186
fixed	NA	male	0.005745	0.005375	1.069	3283	0.2852	-0.009342	0.02083
fixed	NA	sibling_count3	-0.001483	0.006791	-0.2184	3283	0.8271	-0.02054	0.01758
fixed	NA	sibling_count4	-0.007111	0.008118	-0.8759	3283	0.3812	-0.0299	0.01568
fixed	NA	sibling_count5	0.002881	0.01049	0.2746	3283	0.7837	-0.02657	0.03233
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.154	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.135	0.1261	-1.07	3280	0.2845	-0.489	0.219
fixed	NA	poly(age, 3, raw = TRUE)1	0.01917	0.01572	1.22	3280	0.2226	-0.02495	0.06329
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007671	0.0006227	-1.232	3280	0.2181	-0.002515	0.0009807
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001024	0.000007815	1.31	3280	0.1903	-0.0000117	0.00003217
fixed	NA	male	0.005733	0.005377	1.066	3280	0.2864	-0.00936	0.02083
fixed	NA	sibling_count3	-0.002652	0.006939	-0.3822	3280	0.7024	-0.02213	0.01683
fixed	NA	sibling_count4	-0.007732	0.008295	-0.9321	3280	0.3513	-0.03102	0.01555
fixed	NA	sibling_count5	0.00662	0.01085	0.6103	3280	0.5417	-0.02383	0.03706
fixed	NA	birth_order_nonlinear2	0.004309	0.006425	0.6707	3280	0.5025	-0.01373	0.02234
fixed	NA	birth_order_nonlinear3	0.004283	0.008403	0.5098	3280	0.6103	-0.0193	0.02787
fixed	NA	birth_order_nonlinear4	-0.003198	0.01173	-0.2727	3280	0.7851	-0.03612	0.02972
fixed	NA	birth_order_nonlinear5	-0.01996	0.01966	-1.016	3280	0.3099	-0.07514	0.03522
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.154	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1376	0.1262	-1.09	3274	0.2758	-0.492	0.2168
fixed	NA	poly(age, 3, raw = TRUE)1	0.01976	0.01573	1.257	3274	0.209	-0.02439	0.06391
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007861	0.0006231	-1.262	3274	0.2072	-0.002535	0.000963
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001043	0.00000782	1.333	3274	0.1826	-0.00001153	0.00003238
fixed	NA	male	0.005953	0.005382	1.106	3274	0.2687	-0.009154	0.02106
fixed	NA	count_birth_order2/2	-0.004536	0.01013	-0.4477	3274	0.6544	-0.03298	0.02391
fixed	NA	count_birth_order1/3	-0.01268	0.009092	-1.395	3274	0.1632	-0.0382	0.01284
fixed	NA	count_birth_order2/3	0.003404	0.01012	0.3362	3274	0.7368	-0.02502	0.03182
fixed	NA	count_birth_order3/3	0.005291	0.01113	0.4752	3274	0.6347	-0.02597	0.03655
fixed	NA	count_birth_order1/4	-0.004382	0.01232	-0.3557	3274	0.7221	-0.03896	0.0302
fixed	NA	count_birth_order2/4	-0.001983	0.01271	-0.156	3274	0.876	-0.03766	0.03369
fixed	NA	count_birth_order3/4	-0.01713	0.01307	-1.311	3274	0.1899	-0.05382	0.01955
fixed	NA	count_birth_order4/4	-0.01591	0.01334	-1.193	3274	0.2331	-0.05336	0.02154
fixed	NA	count_birth_order1/5	0.005286	0.01779	0.2971	3274	0.7664	-0.04465	0.05522
fixed	NA	count_birth_order2/5	-0.0002005	0.02026	-0.009896	3274	0.9921	-0.05706	0.05666
fixed	NA	count_birth_order3/5	0.008486	0.01849	0.459	3274	0.6463	-0.04341	0.06038
fixed	NA	count_birth_order4/5	0.003727	0.01728	0.2156	3274	0.8293	-0.04479	0.05225
fixed	NA	count_birth_order5/5	-0.01646	0.01795	-0.917	3274	0.3592	-0.06683	0.03392
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.154	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-2966	-2905	1493	-2986	NA	NA	NA
11	-2964	-2897	1493	-2986	0.05144	1	0.8206
14	-2960	-2874	1494	-2988	1.997	3	0.573
20	-2952	-2830	1496	-2992	4.281	6	0.6387

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Elementary worked

birthorder <- birthorder %>% mutate(outcome = Elementary_worked)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.03812	0.09707	-0.3927	4266	0.6946	-0.3106	0.2344
fixed	NA	poly(age, 3, raw = TRUE)1	0.006604	0.01127	0.5861	4275	0.5578	-0.02503	0.03823
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002517	0.0004101	-0.6138	4281	0.5394	-0.001403	0.0008995
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003713	0.000004677	0.7938	4283	0.4274	-0.000009416	0.00001684
fixed	NA	male	0.02374	0.005877	4.041	4210	0.00005428	0.007249	0.04024
fixed	NA	sibling_count3	-0.008451	0.00834	-1.013	3393	0.311	-0.03186	0.01496
fixed	NA	sibling_count4	0.004285	0.008617	0.4972	3179	0.6191	-0.0199	0.02847
fixed	NA	sibling_count5	0.01206	0.008972	1.344	2833	0.1791	-0.01313	0.03724
ran_pars	mother_pidlink	sd__(Intercept)	0.06971	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1806	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.03277	0.09746	-0.3363	4280	0.7367	-0.3064	0.2408
fixed	NA	birth_order	-0.001798	0.002928	-0.6142	4026	0.5391	-0.01002	0.00642
fixed	NA	poly(age, 3, raw = TRUE)1	0.00624	0.01128	0.553	4280	0.5803	-0.02544	0.03792
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002378	0.0004108	-0.5789	4284	0.5627	-0.001391	0.0009152
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003548	0.000004685	0.7574	4285	0.4489	-0.000009603	0.0000167
fixed	NA	male	0.02377	0.005877	4.045	4209	0.00005335	0.007274	0.04027
fixed	NA	sibling_count3	-0.007728	0.008423	-0.9174	3443	0.359	-0.03137	0.01592
fixed	NA	sibling_count4	0.006035	0.009077	0.6649	3392	0.5062	-0.01944	0.03151
fixed	NA	sibling_count5	0.01488	0.01008	1.476	3264	0.14	-0.01342	0.04318
ran_pars	mother_pidlink	sd__(Intercept)	0.06967	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1806	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.03893	0.0975	-0.3993	4279	0.6897	-0.3126	0.2348
fixed	NA	poly(age, 3, raw = TRUE)1	0.006531	0.0113	0.578	4281	0.5633	-0.02518	0.03825
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002489	0.0004112	-0.6052	4283	0.5451	-0.001403	0.0009054
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003673	0.000004689	0.7833	4284	0.4335	-0.00000949	0.00001684
fixed	NA	male	0.02393	0.005877	4.072	4207	0.00004741	0.007436	0.04043
fixed	NA	sibling_count3	-0.005085	0.008542	-0.5953	3529	0.5517	-0.02906	0.01889
fixed	NA	sibling_count4	0.008949	0.009241	0.9684	3495	0.3329	-0.01699	0.03489
fixed	NA	sibling_count5	0.01533	0.01018	1.506	3291	0.1321	-0.01324	0.04391
fixed	NA	birth_order_nonlinear2	0.003991	0.007057	0.5655	3576	0.5717	-0.01582	0.0238
fixed	NA	birth_order_nonlinear3	-0.01552	0.009022	-1.72	3746	0.08549	-0.04084	0.009806
fixed	NA	birth_order_nonlinear4	-0.005023	0.01171	-0.4291	3881	0.6679	-0.03789	0.02784
fixed	NA	birth_order_nonlinear5	0.006543	0.0163	0.4014	3958	0.6882	-0.03922	0.0523
ran_pars	mother_pidlink	sd__(Intercept)	0.06925	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1807	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.0389	0.09764	-0.3984	4273	0.6904	-0.313	0.2352
fixed	NA	poly(age, 3, raw = TRUE)1	0.006551	0.01131	0.5794	4275	0.5624	-0.02519	0.03829
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002507	0.0004116	-0.6091	4277	0.5425	-0.001406	0.0009046
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003709	0.000004694	0.7902	4278	0.4294	-0.000009467	0.00001688
fixed	NA	male	0.02387	0.005882	4.058	4199	0.0000505	0.007355	0.04038
fixed	NA	count_birth_order2/2	0.003992	0.01233	0.3238	3700	0.7461	-0.03062	0.0386
fixed	NA	count_birth_order1/3	-0.004001	0.01101	-0.3633	4276	0.7164	-0.03491	0.02691
fixed	NA	count_birth_order2/3	0.0007906	0.01224	0.06459	4278	0.9485	-0.03357	0.03515
fixed	NA	count_birth_order3/3	-0.02583	0.0141	-1.833	4271	0.06694	-0.0654	0.01374
fixed	NA	count_birth_order1/4	0.001996	0.01299	0.1536	4278	0.8779	-0.03447	0.03846
fixed	NA	count_birth_order2/4	0.01665	0.01346	1.237	4273	0.2162	-0.02113	0.05442
fixed	NA	count_birth_order3/4	0.002168	0.01453	0.1492	4260	0.8814	-0.03863	0.04297
fixed	NA	count_birth_order4/4	0.0001625	0.01507	0.01079	4267	0.9914	-0.04213	0.04246
fixed	NA	count_birth_order1/5	0.02296	0.01499	1.532	4271	0.1256	-0.0191	0.06503
fixed	NA	count_birth_order2/5	0.009444	0.016	0.5902	4240	0.5551	-0.03547	0.05436
fixed	NA	count_birth_order3/5	-0.003822	0.01573	-0.243	4231	0.808	-0.04797	0.04033
fixed	NA	count_birth_order4/5	0.01533	0.01663	0.9216	4226	0.3568	-0.03136	0.06202
fixed	NA	count_birth_order5/5	0.02184	0.01592	1.372	4249	0.17	-0.02283	0.06652
ran_pars	mother_pidlink	sd__(Intercept)	0.06957	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1807	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-1925	-1861	972.5	-1945	NA	NA	NA
11	-1923	-1853	972.7	-1945	0.3781	1	0.5386
14	-1922	-1833	975	-1950	4.648	3	0.1994
20	-1912	-1785	976.2	-1952	2.449	6	0.8742

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1676	0.14	1.197	3302	0.2314	-0.2254	0.5605
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02047	0.01748	-1.171	3308	0.2417	-0.06954	0.0286
fixed	NA	poly(age, 3, raw = TRUE)2	0.0008317	0.0006936	1.199	3311	0.2306	-0.001115	0.002779
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001056	0.000008717	-1.211	3308	0.2259	-0.00003503	0.00001391
fixed	NA	male	0.02121	0.005949	3.566	3292	0.0003681	0.004513	0.03791
fixed	NA	sibling_count3	0.002832	0.007646	0.3704	2729	0.7111	-0.01863	0.0243
fixed	NA	sibling_count4	0.02947	0.008584	3.433	2525	0.0006058	0.005376	0.05357
fixed	NA	sibling_count5	0.02129	0.0102	2.087	2443	0.03699	-0.007345	0.04992
ran_pars	mother_pidlink	sd__(Intercept)	0.05795	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1618	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.166	0.1402	1.184	3303	0.2364	-0.2275	0.5595
fixed	NA	birth_order	0.0007245	0.003239	0.2237	3274	0.823	-0.008367	0.009816
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0204	0.01749	-1.166	3308	0.2435	-0.06948	0.02869
fixed	NA	poly(age, 3, raw = TRUE)2	0.0008289	0.0006938	1.195	3310	0.2323	-0.001119	0.002776
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001052	0.00000872	-1.207	3307	0.2277	-0.000035	0.00001396
fixed	NA	male	0.02119	0.00595	3.562	3291	0.0003733	0.004492	0.0379
fixed	NA	sibling_count3	0.002495	0.007793	0.3202	2759	0.7488	-0.01938	0.02437
fixed	NA	sibling_count4	0.02868	0.009288	3.088	2634	0.002038	0.002607	0.05475
fixed	NA	sibling_count5	0.01998	0.01177	1.697	2690	0.08974	-0.01306	0.05301
ran_pars	mother_pidlink	sd__(Intercept)	0.05791	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1618	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.169	0.1403	1.204	3302	0.2285	-0.2249	0.5628
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02081	0.01751	-1.189	3306	0.2346	-0.06995	0.02833
fixed	NA	poly(age, 3, raw = TRUE)2	0.0008468	0.0006945	1.219	3307	0.2229	-0.001103	0.002796
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001075	0.000008727	-1.232	3303	0.218	-0.00003525	0.00001374
fixed	NA	male	0.02141	0.005953	3.597	3289	0.000327	0.004701	0.03812
fixed	NA	sibling_count3	0.002689	0.007943	0.3385	2820	0.735	-0.01961	0.02498
fixed	NA	sibling_count4	0.03121	0.009465	3.298	2675	0.0009875	0.004645	0.05778
fixed	NA	sibling_count5	0.01828	0.01209	1.512	2692	0.1308	-0.01566	0.05222
fixed	NA	birth_order_nonlinear2	0.002557	0.007035	0.3635	2788	0.7163	-0.01719	0.0223
fixed	NA	birth_order_nonlinear3	0.0005794	0.009267	0.06252	3130	0.9502	-0.02543	0.02659
fixed	NA	birth_order_nonlinear4	-0.007226	0.01264	-0.5717	3213	0.5676	-0.04271	0.02826
fixed	NA	birth_order_nonlinear5	0.02259	0.02049	1.103	3245	0.2702	-0.03492	0.0801
ran_pars	mother_pidlink	sd__(Intercept)	0.05747	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.162	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.17	0.1405	1.21	3296	0.2263	-0.2244	0.5644
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02099	0.01753	-1.197	3300	0.2313	-0.07019	0.02821
fixed	NA	poly(age, 3, raw = TRUE)2	0.0008526	0.0006954	1.226	3301	0.2202	-0.001099	0.002805
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001082	0.000008738	-1.238	3297	0.2157	-0.00003535	0.00001371
fixed	NA	male	0.02143	0.00596	3.596	3283	0.0003278	0.004703	0.03816
fixed	NA	count_birth_order2/2	0.004241	0.01142	0.3715	2935	0.7103	-0.02781	0.03629
fixed	NA	count_birth_order1/3	0.003192	0.0102	0.3129	3300	0.7544	-0.02545	0.03183
fixed	NA	count_birth_order2/3	0.006016	0.01116	0.5392	3300	0.5898	-0.0253	0.03734
fixed	NA	count_birth_order3/3	0.003634	0.01248	0.2911	3298	0.771	-0.0314	0.03867
fixed	NA	count_birth_order1/4	0.039	0.01359	2.871	3300	0.00412	0.0008667	0.07714
fixed	NA	count_birth_order2/4	0.02755	0.01407	1.958	3294	0.05029	-0.01194	0.06704
fixed	NA	count_birth_order3/4	0.02907	0.01481	1.963	3288	0.04972	-0.01249	0.07063
fixed	NA	count_birth_order4/4	0.02626	0.01464	1.793	3298	0.07307	-0.01485	0.06736
fixed	NA	count_birth_order1/5	0.005416	0.01973	0.2745	3299	0.7838	-0.04998	0.06081
fixed	NA	count_birth_order2/5	0.03361	0.02137	1.573	3276	0.1158	-0.02636	0.09358
fixed	NA	count_birth_order3/5	0.02618	0.01943	1.347	3288	0.178	-0.02837	0.08072
fixed	NA	count_birth_order4/5	0.008786	0.01826	0.4811	3286	0.6305	-0.04248	0.06005
fixed	NA	count_birth_order5/5	0.04157	0.01876	2.215	3295	0.02682	-0.01111	0.09424
ran_pars	mother_pidlink	sd__(Intercept)	0.05722	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1622	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-2271	-2210	1146	-2291	NA	NA	NA
11	-2269	-2202	1146	-2291	0.05045	1	0.8223
14	-2265	-2180	1147	-2293	2.09	3	0.554
20	-2255	-2133	1148	-2295	1.907	6	0.928

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.09531	0.1437	0.6634	3108	0.5071	-0.308	0.4986
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01133	0.01793	-0.6318	3111	0.5276	-0.06166	0.039
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004759	0.0007107	0.6697	3109	0.5031	-0.001519	0.002471
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000006334	0.000008915	-0.7104	3101	0.4775	-0.00003136	0.00001869
fixed	NA	male	0.02382	0.006131	3.885	3105	0.0001043	0.006612	0.04103
fixed	NA	sibling_count3	-0.002972	0.008136	-0.3653	2565	0.7149	-0.02581	0.01987
fixed	NA	sibling_count4	0.02307	0.008802	2.62	2413	0.00884	-0.001644	0.04777
fixed	NA	sibling_count5	0.02403	0.009722	2.471	2185	0.01354	-0.003265	0.05132
ran_pars	mother_pidlink	sd__(Intercept)	0.04101	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1662	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.09804	0.1438	0.6818	3108	0.4954	-0.3056	0.5017
fixed	NA	birth_order	-0.001529	0.003188	-0.4796	3100	0.6315	-0.01048	0.007421
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01142	0.01793	-0.6368	3110	0.5243	-0.06176	0.03892
fixed	NA	poly(age, 3, raw = TRUE)2	0.00048	0.0007108	0.6753	3108	0.4995	-0.001515	0.002475
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000006398	0.000008917	-0.7175	3100	0.4731	-0.00003143	0.00001863
fixed	NA	male	0.02384	0.006132	3.887	3104	0.0001034	0.006625	0.04105
fixed	NA	sibling_count3	-0.002245	0.008277	-0.2713	2584	0.7862	-0.02548	0.02099
fixed	NA	sibling_count4	0.02468	0.009426	2.618	2480	0.008894	-0.00178	0.05114
fixed	NA	sibling_count5	0.02658	0.01109	2.398	2398	0.01656	-0.004535	0.0577
ran_pars	mother_pidlink	sd__(Intercept)	0.04116	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1662	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.09375	0.1439	0.6515	3106	0.5148	-0.3102	0.4977
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01133	0.01795	-0.6314	3107	0.5278	-0.06171	0.03905
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004761	0.0007113	0.6694	3104	0.5033	-0.001521	0.002473
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000006344	0.000008922	-0.711	3095	0.4772	-0.00003139	0.0000187
fixed	NA	male	0.024	0.006136	3.911	3101	0.00009392	0.006773	0.04122
fixed	NA	sibling_count3	-0.0009982	0.008439	-0.1183	2640	0.9058	-0.02469	0.02269
fixed	NA	sibling_count4	0.02583	0.009595	2.692	2520	0.007156	-0.001107	0.05276
fixed	NA	sibling_count5	0.02749	0.01128	2.436	2379	0.01494	-0.00419	0.05916
fixed	NA	birth_order_nonlinear2	0.004655	0.007363	0.6323	2663	0.5272	-0.01601	0.02532
fixed	NA	birth_order_nonlinear3	-0.008242	0.009483	-0.8691	2972	0.3848	-0.03486	0.01838
fixed	NA	birth_order_nonlinear4	-0.003501	0.01258	-0.2783	3049	0.7808	-0.03881	0.0318
fixed	NA	birth_order_nonlinear5	-0.001451	0.01903	-0.07624	3071	0.9392	-0.05486	0.05195
ran_pars	mother_pidlink	sd__(Intercept)	0.04085	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1663	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.09543	0.1441	0.6622	3100	0.5079	-0.3091	0.5
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0117	0.01797	-0.6514	3101	0.5148	-0.06213	0.03873
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004895	0.000712	0.6875	3097	0.4918	-0.001509	0.002488
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000649	0.000008931	-0.7267	3089	0.4675	-0.00003156	0.00001858
fixed	NA	male	0.02385	0.006146	3.88	3096	0.0001066	0.006594	0.0411
fixed	NA	count_birth_order2/2	0.009331	0.01252	0.7454	2762	0.4561	-0.02581	0.04447
fixed	NA	count_birth_order1/3	0.004077	0.01099	0.3711	3101	0.7106	-0.02676	0.03491
fixed	NA	count_birth_order2/3	-0.00007272	0.01192	-0.0061	3101	0.9951	-0.03353	0.03339
fixed	NA	count_birth_order3/3	-0.006943	0.01332	-0.5212	3100	0.6022	-0.04433	0.03045
fixed	NA	count_birth_order1/4	0.0228	0.01385	1.646	3101	0.09995	-0.01609	0.06168
fixed	NA	count_birth_order2/4	0.02987	0.01397	2.138	3101	0.03263	-0.009353	0.06908
fixed	NA	count_birth_order3/4	0.01873	0.01555	1.205	3097	0.2283	-0.0249	0.06237
fixed	NA	count_birth_order4/4	0.03272	0.01512	2.164	3100	0.03052	-0.009715	0.07515
fixed	NA	count_birth_order1/5	0.03131	0.0172	1.82	3101	0.06886	-0.01698	0.0796
fixed	NA	count_birth_order2/5	0.0482	0.01944	2.48	3095	0.0132	-0.006361	0.1028
fixed	NA	count_birth_order3/5	0.01967	0.01788	1.1	3099	0.2713	-0.03051	0.06985
fixed	NA	count_birth_order4/5	0.01146	0.0183	0.6262	3093	0.5312	-0.03991	0.06284
fixed	NA	count_birth_order5/5	0.02748	0.0179	1.535	3098	0.1249	-0.02277	0.07774
ran_pars	mother_pidlink	sd__(Intercept)	0.03987	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1666	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-2150	-2090	1085	-2170	NA	NA	NA
11	-2149	-2082	1085	-2171	0.2296	1	0.6319
14	-2144	-2060	1086	-2172	1.586	3	0.6625
20	-2135	-2014	1087	-2175	2.7	6	0.8454

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.156	0.14	1.114	3277	0.2654	-0.2371	0.5491
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01887	0.01748	-1.079	3283	0.2806	-0.06794	0.03021
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007754	0.0006935	1.118	3285	0.2636	-0.001171	0.002722
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000009944	0.000008715	-1.141	3282	0.254	-0.00003441	0.00001452
fixed	NA	male	0.02102	0.005973	3.519	3265	0.0004396	0.004251	0.03778
fixed	NA	sibling_count3	0.0004924	0.00758	0.06496	2707	0.9482	-0.02079	0.02177
fixed	NA	sibling_count4	0.02073	0.008548	2.425	2498	0.01537	-0.003263	0.04473
fixed	NA	sibling_count5	0.02588	0.01053	2.457	2355	0.01406	-0.003681	0.05544
ran_pars	mother_pidlink	sd__(Intercept)	0.05616	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1623	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1552	0.1402	1.107	3278	0.2684	-0.2384	0.5489
fixed	NA	birth_order	0.0003771	0.003285	0.1148	3236	0.9086	-0.008844	0.009598
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01884	0.01749	-1.077	3282	0.2815	-0.06792	0.03025
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007742	0.0006936	1.116	3284	0.2645	-0.001173	0.002721
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000009927	0.000008718	-1.139	3281	0.2549	-0.0000344	0.00001454
fixed	NA	male	0.02101	0.005974	3.517	3264	0.0004423	0.004242	0.03778
fixed	NA	sibling_count3	0.0003212	0.007725	0.04158	2733	0.9668	-0.02136	0.02201
fixed	NA	sibling_count4	0.02032	0.009268	2.193	2614	0.02843	-0.005695	0.04634
fixed	NA	sibling_count5	0.02522	0.01199	2.103	2594	0.03553	-0.008438	0.05888
ran_pars	mother_pidlink	sd__(Intercept)	0.05615	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1624	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1562	0.1404	1.112	3277	0.2661	-0.238	0.5504
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01903	0.01751	-1.087	3280	0.2773	-0.06819	0.03013
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007825	0.0006946	1.126	3281	0.26	-0.001167	0.002732
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001004	0.000008728	-1.15	3277	0.2503	-0.00003454	0.00001447
fixed	NA	male	0.02108	0.005978	3.527	3261	0.0004261	0.004304	0.03786
fixed	NA	sibling_count3	0.0006801	0.007883	0.08627	2791	0.9313	-0.02145	0.02281
fixed	NA	sibling_count4	0.02179	0.009461	2.303	2657	0.02133	-0.004764	0.04835
fixed	NA	sibling_count5	0.02467	0.01239	1.99	2600	0.0467	-0.01013	0.05946
fixed	NA	birth_order_nonlinear2	0.002625	0.007026	0.3736	2773	0.7087	-0.0171	0.02235
fixed	NA	birth_order_nonlinear3	-0.0005137	0.009271	-0.05541	3106	0.9558	-0.02654	0.02551
fixed	NA	birth_order_nonlinear4	-0.003143	0.01297	-0.2423	3173	0.8086	-0.03956	0.03327
fixed	NA	birth_order_nonlinear5	0.01182	0.0218	0.5421	3223	0.5878	-0.04937	0.073
ran_pars	mother_pidlink	sd__(Intercept)	0.05586	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1625	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1548	0.1406	1.101	3271	0.2709	-0.2399	0.5496
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01905	0.01753	-1.086	3274	0.2775	-0.06826	0.03017
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007824	0.0006954	1.125	3275	0.2606	-0.00117	0.002734
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001003	0.000008738	-1.148	3271	0.2509	-0.00003456	0.00001449
fixed	NA	male	0.02103	0.005987	3.512	3256	0.0004501	0.004223	0.03783
fixed	NA	count_birth_order2/2	0.007624	0.01112	0.6858	2900	0.4929	-0.02358	0.03883
fixed	NA	count_birth_order1/3	0.003736	0.01014	0.3685	3274	0.7125	-0.02472	0.03219
fixed	NA	count_birth_order2/3	0.002889	0.01128	0.2561	3273	0.7979	-0.02877	0.03455
fixed	NA	count_birth_order3/3	0.002055	0.0124	0.1657	3273	0.8684	-0.03275	0.03686
fixed	NA	count_birth_order1/4	0.02963	0.01373	2.158	3274	0.03097	-0.008906	0.06817
fixed	NA	count_birth_order2/4	0.02198	0.01415	1.553	3269	0.1205	-0.01775	0.06171
fixed	NA	count_birth_order3/4	0.02018	0.01454	1.387	3264	0.1654	-0.02065	0.06101
fixed	NA	count_birth_order4/4	0.02042	0.01486	1.374	3271	0.1695	-0.02128	0.06211
fixed	NA	count_birth_order1/5	0.01691	0.01982	0.8531	3272	0.3937	-0.03873	0.07255
fixed	NA	count_birth_order2/5	0.03535	0.02254	1.569	3249	0.1168	-0.02791	0.09861
fixed	NA	count_birth_order3/5	0.03142	0.02058	1.527	3262	0.1269	-0.02635	0.0892
fixed	NA	count_birth_order4/5	0.02316	0.01923	1.204	3259	0.2285	-0.03082	0.07714
fixed	NA	count_birth_order5/5	0.0383	0.01998	1.917	3269	0.05538	-0.01779	0.09439
ran_pars	mother_pidlink	sd__(Intercept)	0.05551	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1628	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-2255	-2194	1137	-2275	NA	NA	NA
11	-2253	-2186	1137	-2275	0.01335	1	0.908
14	-2247	-2162	1138	-2275	0.6087	3	0.8944
20	-2237	-2115	1138	-2277	1.169	6	0.9784

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Attended School

birthorder <- birthorder %>% mutate(outcome = attended_school)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.914	0.0215	42.51	7401	0	0.8536	0.9743
fixed	NA	poly(age, 3, raw = TRUE)1	0.007969	0.002044	3.898	7331	0.00009796	0.00223	0.01371
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000214	0.000059	-3.627	7243	0.0002885	-0.0003796	-0.00004839
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001249	0.0000005279	2.366	7172	0.01801	-0.0000002329	0.000002731
fixed	NA	male	0.005467	0.00257	2.127	7488	0.03347	-0.001748	0.01268
fixed	NA	sibling_count3	-0.0007012	0.003722	-0.1884	5946	0.8506	-0.01115	0.009747
fixed	NA	sibling_count4	-0.0009832	0.003837	-0.2562	5482	0.7978	-0.01175	0.009788
fixed	NA	sibling_count5	0.002998	0.004015	0.7467	5028	0.4553	-0.008272	0.01427
ran_pars	mother_pidlink	sd__(Intercept)	0.03849	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1057	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9131	0.0215	42.46	7394	0	0.8527	0.9734
fixed	NA	birth_order	0.002322	0.001279	1.815	6837	0.06962	-0.00127	0.005913
fixed	NA	poly(age, 3, raw = TRUE)1	0.00774	0.002048	3.779	7345	0.0001587	0.001991	0.01349
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000208	0.00005908	-3.521	7252	0.0004328	-0.0003739	-0.00004217
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001209	0.0000005283	2.289	7178	0.02209	-0.0000002735	0.000002692
fixed	NA	male	0.005399	0.00257	2.101	7486	0.03571	-0.001816	0.01261
fixed	NA	sibling_count3	-0.001528	0.00375	-0.4075	6054	0.6837	-0.01205	0.008997
fixed	NA	sibling_count4	-0.002894	0.003979	-0.7273	5939	0.4671	-0.01406	0.008275
fixed	NA	sibling_count5	-0.00006896	0.004356	-0.01583	5953	0.9874	-0.0123	0.01216
ran_pars	mother_pidlink	sd__(Intercept)	0.03851	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1057	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9116	0.02155	42.3	7407	0	0.8511	0.9721
fixed	NA	poly(age, 3, raw = TRUE)1	0.007886	0.002048	3.849	7339	0.0001194	0.002135	0.01364
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002142	0.00005911	-3.623	7239	0.0002928	-0.0003801	-0.00004826
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000128	0.0000005288	2.421	7158	0.01551	-0.0000002043	0.000002764
fixed	NA	male	0.005402	0.002569	2.102	7482	0.03555	-0.00181	0.01261
fixed	NA	sibling_count3	-0.001566	0.003806	-0.4114	6228	0.6808	-0.01225	0.009118
fixed	NA	sibling_count4	-0.002531	0.004042	-0.6262	6132	0.5312	-0.01388	0.008814
fixed	NA	sibling_count5	0.001566	0.004396	0.3562	6090	0.7217	-0.01077	0.01391
fixed	NA	birth_order_nonlinear2	0.01023	0.003037	3.368	6721	0.000761	0.001704	0.01875
fixed	NA	birth_order_nonlinear3	0.006807	0.003889	1.75	6680	0.08011	-0.004109	0.01772
fixed	NA	birth_order_nonlinear4	0.006857	0.00509	1.347	6691	0.178	-0.007432	0.02115
fixed	NA	birth_order_nonlinear5	0.00418	0.00747	0.5596	6609	0.5758	-0.01679	0.02515
ran_pars	mother_pidlink	sd__(Intercept)	0.03863	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1056	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9099	0.0216	42.12	7407	0	0.8493	0.9705
fixed	NA	poly(age, 3, raw = TRUE)1	0.007873	0.002049	3.842	7335	0.000123	0.002121	0.01363
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002143	0.00005913	-3.624	7234	0.0002926	-0.0003802	-0.00004828
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001284	0.0000005289	2.427	7150	0.01523	-0.0000002008	0.000002769
fixed	NA	male	0.005426	0.00257	2.111	7476	0.03479	-0.001789	0.01264
fixed	NA	count_birth_order2/2	0.01558	0.005183	3.005	6670	0.002663	0.001028	0.03013
fixed	NA	count_birth_order1/3	0.003308	0.004924	0.6718	7532	0.5017	-0.01051	0.01713
fixed	NA	count_birth_order2/3	0.007013	0.005508	1.273	7547	0.203	-0.008448	0.02247
fixed	NA	count_birth_order3/3	0.00626	0.006146	1.018	7552	0.3085	-0.01099	0.02351
fixed	NA	count_birth_order1/4	-0.001249	0.005578	-0.2239	7547	0.8228	-0.01691	0.01441
fixed	NA	count_birth_order2/4	0.008736	0.005935	1.472	7551	0.1411	-0.007925	0.0254
fixed	NA	count_birth_order3/4	0.007827	0.006441	1.215	7551	0.2243	-0.01025	0.02591
fixed	NA	count_birth_order4/4	0.007133	0.006763	1.055	7548	0.2916	-0.01185	0.02612
fixed	NA	count_birth_order1/5	0.003778	0.006386	0.5916	7552	0.5542	-0.01415	0.0217
fixed	NA	count_birth_order2/5	0.01494	0.00674	2.216	7549	0.02671	-0.003983	0.03386
fixed	NA	count_birth_order3/5	0.009701	0.006895	1.407	7546	0.1595	-0.009654	0.02906
fixed	NA	count_birth_order4/5	0.009395	0.007387	1.272	7535	0.2035	-0.01134	0.03013
fixed	NA	count_birth_order5/5	0.007711	0.007527	1.024	7533	0.3057	-0.01342	0.02884
ran_pars	mother_pidlink	sd__(Intercept)	0.03861	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1056	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-11631	-11562	5826	-11651	NA	NA	NA
11	-11633	-11557	5827	-11655	3.295	1	0.06949
14	-11635	-11538	5832	-11663	8.559	3	0.03576
20	-11626	-11487	5833	-11666	2.725	6	0.8425

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9676	0.03025	31.98	4744	2.082e-203	0.8827	1.053
fixed	NA	poly(age, 3, raw = TRUE)1	0.003197	0.00353	0.9058	4744	0.3651	-0.006711	0.01311
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001046	0.0001301	-0.8042	4744	0.4213	-0.0004698	0.0002605
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001122	0.000001525	0.7362	4744	0.4616	-0.000003157	0.000005402
fixed	NA	male	-0.001234	0.00163	-0.7572	4744	0.449	-0.00581	0.003341
fixed	NA	sibling_count3	-0.0004113	0.002153	-0.191	4744	0.8485	-0.006456	0.005634
fixed	NA	sibling_count4	-0.001407	0.002304	-0.6108	4744	0.5414	-0.007875	0.00506
fixed	NA	sibling_count5	-0.003486	0.002629	-1.326	4744	0.1848	-0.01086	0.003892
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.05611	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9655	0.03029	31.88	4743	3.321e-202	0.8805	1.051
fixed	NA	birth_order	0.001181	0.0008655	1.365	4743	0.1723	-0.001248	0.003611
fixed	NA	poly(age, 3, raw = TRUE)1	0.003281	0.00353	0.9293	4743	0.3528	-0.006629	0.01319
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001092	0.0001301	-0.8389	4743	0.4016	-0.0004744	0.0002561
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001199	0.000001525	0.7858	4743	0.432	-0.000003083	0.000005481
fixed	NA	male	-0.001269	0.00163	-0.7783	4743	0.4365	-0.005844	0.003307
fixed	NA	sibling_count3	-0.0009595	0.00219	-0.438	4743	0.6614	-0.007108	0.005189
fixed	NA	sibling_count4	-0.002635	0.002473	-1.065	4743	0.2868	-0.009577	0.004307
fixed	NA	sibling_count5	-0.005526	0.003023	-1.828	4743	0.06764	-0.01401	0.002961
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.05611	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9718	0.03028	32.09	4740	1.099e-204	0.8868	1.057
fixed	NA	poly(age, 3, raw = TRUE)1	0.002929	0.003529	0.8299	4740	0.4066	-0.006978	0.01284
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00009641	0.0001301	-0.741	4740	0.4587	-0.0004616	0.0002688
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001056	0.000001525	0.6924	4740	0.4887	-0.000003225	0.000005337
fixed	NA	male	-0.001339	0.001629	-0.822	4740	0.4111	-0.005911	0.003233
fixed	NA	sibling_count3	-0.001289	0.002227	-0.5787	4740	0.5628	-0.007541	0.004963
fixed	NA	sibling_count4	-0.00314	0.002512	-1.25	4740	0.2113	-0.01019	0.00391
fixed	NA	sibling_count5	-0.007082	0.003077	-2.302	4740	0.02139	-0.01572	0.001555
fixed	NA	birth_order_nonlinear2	-0.00492	0.001973	-2.493	4740	0.0127	-0.01046	0.0006195
fixed	NA	birth_order_nonlinear3	0.003382	0.002506	1.349	4740	0.1773	-0.003653	0.01042
fixed	NA	birth_order_nonlinear4	0.002613	0.003372	0.7749	4740	0.4385	-0.006852	0.01208
fixed	NA	birth_order_nonlinear5	0.007239	0.005303	1.365	4740	0.1723	-0.007647	0.02212
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.05605	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.971	0.03028	32.07	4734	2.425e-204	0.886	1.056
fixed	NA	poly(age, 3, raw = TRUE)1	0.002982	0.00353	0.8447	4734	0.3983	-0.006927	0.01289
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00009888	0.0001301	-0.7599	4734	0.4474	-0.0004641	0.0002664
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001092	0.000001526	0.7156	4734	0.4743	-0.000003191	0.000005374
fixed	NA	male	-0.001367	0.001629	-0.839	4734	0.4015	-0.00594	0.003206
fixed	NA	count_birth_order2/2	-0.003547	0.003364	-1.054	4734	0.2918	-0.01299	0.005897
fixed	NA	count_birth_order1/3	-0.0005839	0.002927	-0.1994	4734	0.8419	-0.008801	0.007634
fixed	NA	count_birth_order2/3	-0.004987	0.003191	-1.563	4734	0.1181	-0.01394	0.003969
fixed	NA	count_birth_order3/3	0.001052	0.003569	0.2947	4734	0.7682	-0.008966	0.01107
fixed	NA	count_birth_order1/4	-0.002343	0.003579	-0.6547	4734	0.5127	-0.01239	0.007703
fixed	NA	count_birth_order2/4	-0.005547	0.003702	-1.498	4734	0.1341	-0.01594	0.004845
fixed	NA	count_birth_order3/4	0.0005823	0.003921	0.1485	4734	0.8819	-0.01042	0.01159
fixed	NA	count_birth_order4/4	-0.003111	0.004073	-0.7638	4734	0.445	-0.01454	0.008321
fixed	NA	count_birth_order1/5	-0.006051	0.004891	-1.237	4734	0.2161	-0.01978	0.007678
fixed	NA	count_birth_order2/5	-0.02209	0.005256	-4.203	4734	0.00002679	-0.03685	-0.007339
fixed	NA	count_birth_order3/5	0.0003132	0.004874	0.06426	4734	0.9488	-0.01337	0.014
fixed	NA	count_birth_order4/5	0.0005421	0.004789	0.1132	4734	0.9099	-0.0129	0.01398
fixed	NA	count_birth_order5/5	0.0006309	0.004969	0.127	4734	0.899	-0.01332	0.01458
ran_pars	mother_pidlink	sd__(Intercept)	0.000000002298	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.05604	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-13878	-13813	6949	-13898	NA	NA	NA
11	-13878	-13807	6950	-13900	1.867	1	0.1719
14	-13884	-13794	6956	-13912	12.78	3	0.005144
20	-13881	-13751	6960	-13921	8.283	6	0.2181

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9581	0.03124	30.67	4383	2.929e-187	0.8704	1.046
fixed	NA	poly(age, 3, raw = TRUE)1	0.004337	0.003649	1.188	4362	0.2347	-0.005906	0.01458
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001472	0.0001345	-1.094	4336	0.2741	-0.0005249	0.0002305
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001606	0.000001577	1.018	4309	0.3087	-0.000002821	0.000006033
fixed	NA	male	-0.001817	0.001698	-1.071	4400	0.2844	-0.006582	0.002948
fixed	NA	sibling_count3	-0.0002619	0.002345	-0.1117	2586	0.9111	-0.006843	0.006319
fixed	NA	sibling_count4	-0.00004756	0.002458	-0.01935	2083	0.9846	-0.006948	0.006853
fixed	NA	sibling_count5	-0.002108	0.002627	-0.8025	1639	0.4224	-0.009481	0.005265
ran_pars	mother_pidlink	sd__(Intercept)	0.001143	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.05625	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9565	0.03128	30.58	4381	2.553e-186	0.8687	1.044
fixed	NA	birth_order	0.0009232	0.000866	1.066	4120	0.2865	-0.001508	0.003354
fixed	NA	poly(age, 3, raw = TRUE)1	0.004395	0.003649	1.204	4360	0.2286	-0.005849	0.01464
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001504	0.0001346	-1.117	4335	0.2639	-0.0005281	0.0002274
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001661	0.000001578	1.052	4309	0.2927	-0.000002769	0.00000609
fixed	NA	male	-0.001831	0.001698	-1.078	4399	0.2809	-0.006596	0.002935
fixed	NA	sibling_count3	-0.0006873	0.002378	-0.289	2634	0.7726	-0.007363	0.005989
fixed	NA	sibling_count4	-0.0009723	0.002607	-0.373	2291	0.7092	-0.00829	0.006345
fixed	NA	sibling_count5	-0.003582	0.002968	-1.207	2095	0.2277	-0.01191	0.00475
ran_pars	mother_pidlink	sd__(Intercept)	0.001379	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.05625	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9612	0.03127	30.74	4400	3.926e-188	0.8734	1.049
fixed	NA	poly(age, 3, raw = TRUE)1	0.004173	0.003649	1.144	4400	0.2528	-0.00607	0.01442
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001422	0.0001346	-1.057	4400	0.2908	-0.0005199	0.0002356
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001568	0.000001578	0.9941	4400	0.3202	-0.00000286	0.000005997
fixed	NA	male	-0.001912	0.001697	-1.127	4400	0.2597	-0.006675	0.00285
fixed	NA	sibling_count3	-0.001068	0.002416	-0.4419	4400	0.6586	-0.007849	0.005714
fixed	NA	sibling_count4	-0.001268	0.002645	-0.4793	4400	0.6318	-0.008693	0.006158
fixed	NA	sibling_count5	-0.004737	0.002999	-1.579	4400	0.1143	-0.01316	0.003682
fixed	NA	birth_order_nonlinear2	-0.004602	0.002059	-2.235	4400	0.02546	-0.01038	0.001178
fixed	NA	birth_order_nonlinear3	0.003053	0.002589	1.179	4400	0.2383	-0.004214	0.01032
fixed	NA	birth_order_nonlinear4	0.001132	0.003438	0.3293	4400	0.742	-0.008518	0.01078
fixed	NA	birth_order_nonlinear5	0.005537	0.005053	1.096	4400	0.2733	-0.008648	0.01972
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.05622	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9607	0.03129	30.7	4394	1.067e-187	0.8729	1.049
fixed	NA	poly(age, 3, raw = TRUE)1	0.004221	0.00365	1.156	4394	0.2476	-0.006026	0.01447
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001441	0.0001346	-1.071	4394	0.2844	-0.0005221	0.0002338
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001594	0.000001579	1.01	4394	0.3126	-0.000002837	0.000006026
fixed	NA	male	-0.001903	0.001698	-1.121	4394	0.2623	-0.006668	0.002862
fixed	NA	count_birth_order2/2	-0.004156	0.003696	-1.124	4394	0.261	-0.01453	0.00622
fixed	NA	count_birth_order1/3	-0.0004909	0.003182	-0.1543	4394	0.8774	-0.009424	0.008442
fixed	NA	count_birth_order2/3	-0.005566	0.003461	-1.608	4394	0.1078	-0.01528	0.004148
fixed	NA	count_birth_order3/3	0.001399	0.003874	0.3611	4394	0.718	-0.009476	0.01227
fixed	NA	count_birth_order1/4	-0.001895	0.003754	-0.5047	4394	0.6138	-0.01243	0.008643
fixed	NA	count_birth_order2/4	-0.00205	0.003829	-0.5353	4394	0.5925	-0.0128	0.008698
fixed	NA	count_birth_order3/4	0.001059	0.004206	0.2517	4394	0.8013	-0.01075	0.01287
fixed	NA	count_birth_order4/4	-0.00314	0.004349	-0.722	4394	0.4703	-0.01535	0.009067
fixed	NA	count_birth_order1/5	-0.004016	0.004481	-0.8961	4394	0.3702	-0.0166	0.008563
fixed	NA	count_birth_order2/5	-0.01644	0.004817	-3.413	4394	0.0006489	-0.02996	-0.002918
fixed	NA	count_birth_order3/5	0.0008529	0.004687	0.182	4394	0.8556	-0.0123	0.01401
fixed	NA	count_birth_order4/5	0.0008388	0.004914	0.1707	4394	0.8645	-0.01295	0.01463
fixed	NA	count_birth_order5/5	0.0009558	0.004891	0.1954	4394	0.8451	-0.01277	0.01468
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.05621	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-12860	-12796	6440	-12880	NA	NA	NA
11	-12859	-12789	6441	-12881	1.138	1	0.286
14	-12863	-12774	6446	-12891	10.02	3	0.01836
20	-12858	-12730	6449	-12898	6.595	6	0.3599

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9834	0.03057	32.17	4729	1.848e-205	0.8976	1.069
fixed	NA	poly(age, 3, raw = TRUE)1	0.001608	0.003572	0.4502	4729	0.6526	-0.008418	0.01163
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00005133	0.0001318	-0.3895	4729	0.6969	-0.0004213	0.0003186
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000005632	0.000001547	0.364	4729	0.7159	-0.000003781	0.000004907
fixed	NA	male	-0.002083	0.001636	-1.274	4729	0.2028	-0.006675	0.002508
fixed	NA	sibling_count3	-0.001204	0.002128	-0.5657	4729	0.5716	-0.007178	0.00477
fixed	NA	sibling_count4	-0.003955	0.002293	-1.725	4729	0.08459	-0.01039	0.002481
fixed	NA	sibling_count5	-0.003413	0.002687	-1.27	4729	0.2041	-0.01096	0.00413
ran_pars	mother_pidlink	sd__(Intercept)	0.000000007554	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.05619	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9825	0.03061	32.1	4728	1.192e-204	0.8966	1.068
fixed	NA	birth_order	0.0005388	0.0008783	0.6135	4728	0.5396	-0.001927	0.003004
fixed	NA	poly(age, 3, raw = TRUE)1	0.001642	0.003572	0.4596	4728	0.6458	-0.008386	0.01167
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00005322	0.0001318	-0.4037	4728	0.6865	-0.0004233	0.0003169
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000005956	0.000001548	0.3847	4728	0.7005	-0.000003751	0.000004942
fixed	NA	male	-0.002095	0.001636	-1.281	4728	0.2003	-0.006687	0.002496
fixed	NA	sibling_count3	-0.001451	0.002166	-0.6699	4728	0.5029	-0.007532	0.00463
fixed	NA	sibling_count4	-0.004511	0.002465	-1.83	4728	0.06737	-0.01143	0.00241
fixed	NA	sibling_count5	-0.004303	0.003054	-1.409	4728	0.1589	-0.01288	0.00427
ran_pars	mother_pidlink	sd__(Intercept)	0.000000002149	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.0562	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9856	0.03061	32.2	4725	7.279e-206	0.8996	1.071
fixed	NA	poly(age, 3, raw = TRUE)1	0.001544	0.003572	0.4323	4725	0.6656	-0.008483	0.01157
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00004998	0.0001318	-0.3791	4725	0.7046	-0.0004201	0.0003201
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000005631	0.000001548	0.3637	4725	0.7161	-0.000003783	0.000004909
fixed	NA	male	-0.002095	0.001635	-1.281	4725	0.2001	-0.006684	0.002494
fixed	NA	sibling_count3	-0.002215	0.002205	-1.004	4725	0.3152	-0.008405	0.003975
fixed	NA	sibling_count4	-0.005696	0.002506	-2.273	4725	0.02307	-0.01273	0.001338
fixed	NA	sibling_count5	-0.004886	0.003121	-1.566	4725	0.1175	-0.01365	0.003873
fixed	NA	birth_order_nonlinear2	-0.004122	0.001966	-2.097	4725	0.03609	-0.009641	0.001397
fixed	NA	birth_order_nonlinear3	0.003645	0.002506	1.455	4725	0.1458	-0.003388	0.01068
fixed	NA	birth_order_nonlinear4	0.002612	0.003452	0.7568	4725	0.4492	-0.007076	0.0123
fixed	NA	birth_order_nonlinear5	-0.003081	0.005663	-0.5441	4725	0.5864	-0.01898	0.01281
ran_pars	mother_pidlink	sd__(Intercept)	0.000000002736	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.05615	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.9865	0.03062	32.22	4719	4.308e-206	0.9006	1.072
fixed	NA	poly(age, 3, raw = TRUE)1	0.00144	0.003573	0.4028	4719	0.6871	-0.008591	0.01147
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00004624	0.0001319	-0.3506	4719	0.7259	-0.0004165	0.000324
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000005237	0.000001549	0.3381	4719	0.7353	-0.000003824	0.000004872
fixed	NA	male	-0.002104	0.001635	-1.287	4719	0.1983	-0.006695	0.002487
fixed	NA	count_birth_order2/2	-0.004447	0.003281	-1.356	4719	0.1753	-0.01366	0.004762
fixed	NA	count_birth_order1/3	-0.001683	0.002898	-0.5809	4719	0.5613	-0.009817	0.006451
fixed	NA	count_birth_order2/3	-0.006297	0.003198	-1.969	4719	0.04904	-0.01527	0.002681
fixed	NA	count_birth_order3/3	-0.0001277	0.003518	-0.03631	4719	0.971	-0.01	0.009746
fixed	NA	count_birth_order1/4	-0.009212	0.003603	-2.557	4719	0.0106	-0.01933	0.0009016
fixed	NA	count_birth_order2/4	-0.006819	0.003717	-1.835	4719	0.06662	-0.01725	0.003614
fixed	NA	count_birth_order3/4	-0.0005325	0.003895	-0.1367	4719	0.8913	-0.01147	0.0104
fixed	NA	count_birth_order4/4	-0.004344	0.004113	-1.056	4719	0.2909	-0.01589	0.007201
fixed	NA	count_birth_order1/5	-0.00103	0.0049	-0.2101	4719	0.8336	-0.01479	0.01273
fixed	NA	count_birth_order2/5	-0.01707	0.005439	-3.139	4719	0.001708	-0.03234	-0.001804
fixed	NA	count_birth_order3/5	-0.000926	0.005104	-0.1814	4719	0.856	-0.01525	0.0134
fixed	NA	count_birth_order4/5	-0.0005586	0.005017	-0.1114	4719	0.9113	-0.01464	0.01352
fixed	NA	count_birth_order5/5	-0.008091	0.005307	-1.524	4719	0.1275	-0.02299	0.006807
ran_pars	mother_pidlink	sd__(Intercept)	0.000000006019	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.05615	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-13820	-13756	6920	-13840	NA	NA	NA
11	-13819	-13748	6920	-13841	0.377	1	0.5392
14	-13823	-13733	6926	-13851	10.69	3	0.01354
20	-13818	-13689	6929	-13858	6.457	6	0.3739

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Work

Income Last Month (log) - z-standardized

birthorder <- birthorder %>% mutate(outcome = wage_last_month_z)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.49	0.4698	-5.301	2910	0.0000001237	-3.809	-1.172
fixed	NA	poly(age, 3, raw = TRUE)1	0.1928	0.04401	4.381	2904	0.00001223	0.06928	0.3164
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004761	0.001292	-3.686	2903	0.0002323	-0.008387	-0.001135
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003689	0.00001197	3.081	2909	0.002084	0.000003278	0.00007049
fixed	NA	male	0.1129	0.03649	3.095	2919	0.001988	0.0105	0.2153
fixed	NA	sibling_count3	0.102	0.0525	1.944	2122	0.05207	-0.04533	0.2494
fixed	NA	sibling_count4	0.05001	0.05263	0.9503	2019	0.3421	-0.09771	0.1977
fixed	NA	sibling_count5	0.04399	0.05502	0.7995	1914	0.4241	-0.1104	0.1984
ran_pars	mother_pidlink	sd__(Intercept)	0.423	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8809	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.491	0.4698	-5.303	2909	0.0000001228	-3.81	-1.172
fixed	NA	birth_order	0.01003	0.01754	0.5719	2449	0.5674	-0.03921	0.05927
fixed	NA	poly(age, 3, raw = TRUE)1	0.1918	0.04406	4.352	2904	0.00001393	0.06808	0.3154
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004738	0.001293	-3.666	2902	0.0002513	-0.008366	-0.00111
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003678	0.00001198	3.071	2908	0.002153	0.000003162	0.0000704
fixed	NA	male	0.113	0.03649	3.098	2917	0.00197	0.0106	0.2155
fixed	NA	sibling_count3	0.09832	0.05291	1.858	2174	0.06325	-0.05019	0.2468
fixed	NA	sibling_count4	0.04142	0.05474	0.7567	2247	0.4493	-0.1122	0.1951
fixed	NA	sibling_count5	0.03035	0.05997	0.5061	2363	0.6129	-0.138	0.1987
ran_pars	mother_pidlink	sd__(Intercept)	0.4235	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8808	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.475	0.471	-5.254	2904	0.0000001594	-3.797	-1.153
fixed	NA	poly(age, 3, raw = TRUE)1	0.1908	0.04412	4.324	2896	0.00001584	0.06693	0.3146
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004707	0.001295	-3.634	2891	0.0002841	-0.008343	-0.001071
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003648	0.00001201	3.037	2895	0.002412	0.00000276	0.00007019
fixed	NA	male	0.1122	0.03653	3.071	2916	0.002153	0.009647	0.2148
fixed	NA	sibling_count3	0.108	0.05366	2.013	2255	0.04424	-0.04261	0.2586
fixed	NA	sibling_count4	0.05079	0.05561	0.9132	2337	0.3612	-0.1053	0.2069
fixed	NA	sibling_count5	0.03047	0.06048	0.5038	2412	0.6144	-0.1393	0.2002
fixed	NA	birth_order_nonlinear2	0.02079	0.04306	0.4827	2381	0.6293	-0.1001	0.1417
fixed	NA	birth_order_nonlinear3	-0.02247	0.05386	-0.4172	2315	0.6766	-0.1737	0.1287
fixed	NA	birth_order_nonlinear4	0.03629	0.06916	0.5247	2276	0.5998	-0.1579	0.2304
fixed	NA	birth_order_nonlinear5	0.09002	0.101	0.8911	2291	0.373	-0.1935	0.3736
ran_pars	mother_pidlink	sd__(Intercept)	0.4231	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8812	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.445	0.4721	-5.178	2903	0.0000002401	-3.77	-1.119
fixed	NA	poly(age, 3, raw = TRUE)1	0.1889	0.0442	4.274	2892	0.00001982	0.06484	0.313
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004649	0.001297	-3.583	2887	0.0003452	-0.00829	-0.001007
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003591	0.00001203	2.986	2890	0.002855	0.000002147	0.00006968
fixed	NA	male	0.1122	0.03656	3.069	2907	0.002169	0.009572	0.2148
fixed	NA	count_birth_order2/2	-0.01542	0.07519	-0.205	2478	0.8376	-0.2265	0.1956
fixed	NA	count_birth_order1/3	0.09647	0.06855	1.407	2940	0.1595	-0.09596	0.2889
fixed	NA	count_birth_order2/3	0.0873	0.07801	1.119	2944	0.2632	-0.1317	0.3063
fixed	NA	count_birth_order3/3	0.1128	0.08734	1.292	2917	0.1965	-0.1323	0.358
fixed	NA	count_birth_order1/4	0.05905	0.07606	0.7764	2947	0.4376	-0.1545	0.2726
fixed	NA	count_birth_order2/4	0.08377	0.0814	1.029	2942	0.3035	-0.1447	0.3123
fixed	NA	count_birth_order3/4	-0.06199	0.08534	-0.7265	2929	0.4676	-0.3015	0.1775
fixed	NA	count_birth_order4/4	0.1005	0.09323	1.078	2909	0.281	-0.1612	0.3622
fixed	NA	count_birth_order1/5	-0.04536	0.08595	-0.5278	2941	0.5977	-0.2866	0.1959
fixed	NA	count_birth_order2/5	0.09444	0.09483	0.9959	2896	0.3194	-0.1718	0.3606
fixed	NA	count_birth_order3/5	0.05258	0.09639	0.5455	2896	0.5855	-0.218	0.3231
fixed	NA	count_birth_order4/5	0.02558	0.0982	0.2605	2864	0.7945	-0.2501	0.3012
fixed	NA	count_birth_order5/5	0.1098	0.1016	1.081	2876	0.2798	-0.1754	0.3951
ran_pars	mother_pidlink	sd__(Intercept)	0.4273	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8798	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	8262	8322	-4121	8242	NA	NA	NA
11	8264	8330	-4121	8242	0.3266	1	0.5677
14	8269	8352	-4120	8241	1.343	3	0.719
20	8276	8396	-4118	8236	4.248	6	0.6431

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.234	1.071	-2.087	1878	0.03701	-5.239	0.7706
fixed	NA	poly(age, 3, raw = TRUE)1	0.1599	0.1171	1.366	1879	0.172	-0.1686	0.4885
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003356	0.004111	-0.8162	1880	0.4145	-0.0149	0.008185
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002172	0.00004642	0.4679	1880	0.6399	-0.0001086	0.000152
fixed	NA	male	0.1531	0.04496	3.405	1894	0.0006757	0.02688	0.2793
fixed	NA	sibling_count3	0.05291	0.06084	0.8696	1517	0.3847	-0.1179	0.2237
fixed	NA	sibling_count4	-0.06268	0.06288	-0.9967	1404	0.3191	-0.2392	0.1138
fixed	NA	sibling_count5	-0.1297	0.07171	-1.809	1294	0.07062	-0.331	0.07154
ran_pars	mother_pidlink	sd__(Intercept)	0.2516	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9272	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.255	1.071	-2.106	1878	0.03534	-5.26	0.7505
fixed	NA	birth_order	0.03011	0.02277	1.322	1828	0.1862	-0.0338	0.09401
fixed	NA	poly(age, 3, raw = TRUE)1	0.1589	0.117	1.358	1879	0.1747	-0.1696	0.4874
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003371	0.004111	-0.82	1880	0.4123	-0.01491	0.008169
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002261	0.00004642	0.4871	1880	0.6262	-0.0001077	0.0001529
fixed	NA	male	0.1525	0.04495	3.394	1893	0.0007037	0.02637	0.2787
fixed	NA	sibling_count3	0.03917	0.06174	0.6345	1537	0.5259	-0.1341	0.2125
fixed	NA	sibling_count4	-0.09368	0.06713	-1.395	1508	0.1631	-0.2821	0.09476
fixed	NA	sibling_count5	-0.1829	0.08224	-2.224	1490	0.02632	-0.4137	0.04798
ran_pars	mother_pidlink	sd__(Intercept)	0.2564	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9257	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.248	1.072	-2.097	1874	0.03612	-5.258	0.7611
fixed	NA	poly(age, 3, raw = TRUE)1	0.1611	0.1172	1.374	1876	0.1696	-0.168	0.4902
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003454	0.004118	-0.8389	1877	0.4017	-0.01501	0.008104
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002356	0.00004649	0.5068	1877	0.6124	-0.0001069	0.000154
fixed	NA	male	0.1525	0.04499	3.391	1890	0.0007115	0.02626	0.2788
fixed	NA	sibling_count3	0.02772	0.06268	0.4422	1577	0.6584	-0.1482	0.2037
fixed	NA	sibling_count4	-0.1077	0.06814	-1.581	1552	0.114	-0.299	0.08351
fixed	NA	sibling_count5	-0.1635	0.08373	-1.953	1509	0.05104	-0.3985	0.07153
fixed	NA	birth_order_nonlinear2	0.05357	0.05383	0.9952	1631	0.3198	-0.09753	0.2047
fixed	NA	birth_order_nonlinear3	0.1133	0.06673	1.697	1708	0.08982	-0.07405	0.3006
fixed	NA	birth_order_nonlinear4	0.1079	0.0884	1.221	1745	0.2222	-0.1402	0.3561
fixed	NA	birth_order_nonlinear5	-0.02124	0.137	-0.155	1793	0.8769	-0.4059	0.3635
ran_pars	mother_pidlink	sd__(Intercept)	0.2587	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9253	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.207	1.074	-2.054	1869	0.04012	-5.222	0.809
fixed	NA	poly(age, 3, raw = TRUE)1	0.1576	0.1176	1.34	1871	0.1805	-0.1726	0.4877
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003291	0.004131	-0.7966	1871	0.4258	-0.01489	0.008305
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000213	0.00004664	0.4567	1872	0.6479	-0.0001096	0.0001522
fixed	NA	male	0.1514	0.04506	3.359	1883	0.0007975	0.02488	0.2779
fixed	NA	count_birth_order2/2	-0.01058	0.09597	-0.1102	1659	0.9123	-0.28	0.2588
fixed	NA	count_birth_order1/3	0.001797	0.07979	0.02252	1886	0.982	-0.2222	0.2258
fixed	NA	count_birth_order2/3	0.08769	0.0904	0.9701	1886	0.3321	-0.1661	0.3414
fixed	NA	count_birth_order3/3	0.09682	0.09987	0.9695	1883	0.3324	-0.1835	0.3772
fixed	NA	count_birth_order1/4	-0.2027	0.09365	-2.164	1887	0.03058	-0.4656	0.06021
fixed	NA	count_birth_order2/4	-0.03414	0.09687	-0.3524	1886	0.7246	-0.306	0.2378
fixed	NA	count_birth_order3/4	0.04422	0.1022	0.4326	1882	0.6653	-0.2427	0.3311
fixed	NA	count_birth_order4/4	-0.03093	0.1094	-0.2827	1880	0.7774	-0.3381	0.2762
fixed	NA	count_birth_order1/5	-0.0792	0.1269	-0.624	1887	0.5327	-0.4355	0.2771
fixed	NA	count_birth_order2/5	-0.2197	0.1478	-1.486	1878	0.1374	-0.6346	0.1952
fixed	NA	count_birth_order3/5	-0.1384	0.1324	-1.046	1884	0.2959	-0.5099	0.2331
fixed	NA	count_birth_order4/5	-0.0589	0.1257	-0.4685	1880	0.6395	-0.4118	0.294
fixed	NA	count_birth_order5/5	-0.2059	0.1296	-1.589	1881	0.1121	-0.5696	0.1578
ran_pars	mother_pidlink	sd__(Intercept)	0.2667	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9236	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	5263	5319	-2622	5243	NA	NA	NA
11	5263	5325	-2621	5241	1.747	1	0.1863
14	5267	5345	-2620	5239	2.254	3	0.5215
20	5275	5386	-2618	5235	4.102	6	0.6628

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.248	1.099	-2.045	1736	0.04101	-5.334	0.8377
fixed	NA	poly(age, 3, raw = TRUE)1	0.1627	0.1203	1.353	1738	0.1763	-0.1749	0.5002
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003424	0.004223	-0.8107	1739	0.4176	-0.01528	0.008431
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002166	0.00004767	0.4543	1740	0.6497	-0.0001122	0.0001555
fixed	NA	male	0.1355	0.04645	2.916	1746	0.003589	0.005067	0.2659
fixed	NA	sibling_count3	0.03395	0.06671	0.5089	1436	0.6109	-0.1533	0.2212
fixed	NA	sibling_count4	-0.003585	0.06781	-0.05286	1363	0.9579	-0.1939	0.1868
fixed	NA	sibling_count5	-0.1122	0.07149	-1.569	1266	0.1168	-0.3129	0.08848
ran_pars	mother_pidlink	sd__(Intercept)	0.2856	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.91	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.276	1.1	-2.07	1736	0.0386	-5.363	0.8105
fixed	NA	birth_order	0.02453	0.02258	1.086	1706	0.2775	-0.03886	0.08792
fixed	NA	poly(age, 3, raw = TRUE)1	0.1628	0.1203	1.354	1738	0.1759	-0.1747	0.5004
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003461	0.004223	-0.8196	1739	0.4126	-0.01532	0.008393
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002261	0.00004768	0.4743	1740	0.6354	-0.0001112	0.0001564
fixed	NA	male	0.1354	0.04645	2.915	1745	0.003601	0.00502	0.2658
fixed	NA	sibling_count3	0.02227	0.06758	0.3296	1448	0.7418	-0.1674	0.212
fixed	NA	sibling_count4	-0.02785	0.07142	-0.3899	1426	0.6967	-0.2283	0.1726
fixed	NA	sibling_count5	-0.1518	0.0803	-1.891	1411	0.05882	-0.3772	0.07355
ran_pars	mother_pidlink	sd__(Intercept)	0.2891	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9089	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.265	1.101	-2.056	1731	0.03989	-5.357	0.8268
fixed	NA	poly(age, 3, raw = TRUE)1	0.1629	0.1205	1.352	1734	0.1765	-0.1753	0.5012
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003483	0.004232	-0.8231	1735	0.4106	-0.01536	0.008396
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002298	0.00004777	0.4811	1735	0.6305	-0.0001111	0.0001571
fixed	NA	male	0.1348	0.0465	2.899	1742	0.003786	0.004293	0.2654
fixed	NA	sibling_count3	0.01432	0.06858	0.2088	1478	0.8346	-0.1782	0.2068
fixed	NA	sibling_count4	-0.04198	0.07236	-0.5801	1458	0.562	-0.2451	0.1612
fixed	NA	sibling_count5	-0.1367	0.08086	-1.691	1416	0.09111	-0.3637	0.09026
fixed	NA	birth_order_nonlinear2	0.08313	0.05537	1.501	1501	0.1335	-0.07229	0.2386
fixed	NA	birth_order_nonlinear3	0.08249	0.06895	1.196	1599	0.2317	-0.111	0.276
fixed	NA	birth_order_nonlinear4	0.1182	0.08989	1.315	1605	0.1886	-0.1341	0.3705
fixed	NA	birth_order_nonlinear5	-0.02157	0.1279	-0.1686	1645	0.8661	-0.3807	0.3376
ran_pars	mother_pidlink	sd__(Intercept)	0.2903	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9086	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.226	1.106	-2.012	1726	0.04437	-5.331	0.8794
fixed	NA	poly(age, 3, raw = TRUE)1	0.1608	0.1211	1.328	1728	0.1844	-0.1792	0.5008
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003377	0.004253	-0.7942	1729	0.4272	-0.01531	0.00856
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002152	0.000048	0.4483	1730	0.654	-0.0001132	0.0001563
fixed	NA	male	0.1357	0.04665	2.909	1735	0.003676	0.004742	0.2667
fixed	NA	count_birth_order2/2	-0.01203	0.1074	-0.112	1573	0.9108	-0.3135	0.2894
fixed	NA	count_birth_order1/3	-0.03039	0.08738	-0.3478	1741	0.7281	-0.2757	0.2149
fixed	NA	count_birth_order2/3	0.1045	0.0968	1.079	1742	0.2806	-0.1672	0.3762
fixed	NA	count_birth_order3/3	0.04883	0.1086	0.4495	1739	0.6531	-0.2561	0.3537
fixed	NA	count_birth_order1/4	-0.1154	0.09836	-1.173	1742	0.2409	-0.3915	0.1607
fixed	NA	count_birth_order2/4	0.06725	0.09911	0.6785	1741	0.4975	-0.2109	0.3454
fixed	NA	count_birth_order3/4	0.01112	0.1112	0.1	1737	0.9203	-0.3009	0.3232
fixed	NA	count_birth_order4/4	0.02798	0.1189	0.2353	1732	0.814	-0.3058	0.3617
fixed	NA	count_birth_order1/5	-0.1351	0.1149	-1.176	1742	0.2397	-0.4575	0.1873
fixed	NA	count_birth_order2/5	-0.1738	0.1263	-1.376	1734	0.1689	-0.5282	0.1806
fixed	NA	count_birth_order3/5	-0.05605	0.1259	-0.445	1734	0.6563	-0.4096	0.2975
fixed	NA	count_birth_order4/5	-0.02405	0.1267	-0.1898	1727	0.8495	-0.3798	0.3317
fixed	NA	count_birth_order5/5	-0.1875	0.1263	-1.484	1732	0.1379	-0.5419	0.167
ran_pars	mother_pidlink	sd__(Intercept)	0.3023	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9058	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	4837	4891	-2408	4817	NA	NA	NA
11	4838	4898	-2408	4816	1.179	1	0.2776
14	4841	4917	-2406	4813	2.727	3	0.4356
20	4850	4959	-2405	4810	2.944	6	0.8158

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.117	1.094	-1.935	1867	0.05316	-5.189	0.9544
fixed	NA	poly(age, 3, raw = TRUE)1	0.1426	0.1197	1.192	1869	0.2335	-0.1933	0.4786
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002663	0.004203	-0.6336	1869	0.5264	-0.01446	0.009135
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001294	0.00004745	0.2727	1869	0.7851	-0.0001203	0.0001461
fixed	NA	male	0.1735	0.04603	3.769	1883	0.0001692	0.04426	0.3027
fixed	NA	sibling_count3	0.04045	0.06137	0.6591	1506	0.51	-0.1318	0.2127
fixed	NA	sibling_count4	-0.08907	0.0641	-1.389	1384	0.1649	-0.269	0.09087
fixed	NA	sibling_count5	-0.1029	0.07522	-1.368	1229	0.1715	-0.3141	0.1082
ran_pars	mother_pidlink	sd__(Intercept)	0.2642	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9458	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.13	1.094	-1.946	1867	0.05175	-5.202	0.9418
fixed	NA	birth_order	0.02341	0.0237	0.9875	1802	0.3235	-0.04312	0.08994
fixed	NA	poly(age, 3, raw = TRUE)1	0.1415	0.1197	1.182	1868	0.2372	-0.1944	0.4775
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002663	0.004203	-0.6335	1869	0.5265	-0.01446	0.009136
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001349	0.00004746	0.2842	1869	0.7763	-0.0001197	0.0001467
fixed	NA	male	0.173	0.04603	3.759	1882	0.0001758	0.04382	0.3022
fixed	NA	sibling_count3	0.02954	0.06238	0.4736	1524	0.6359	-0.1456	0.2046
fixed	NA	sibling_count4	-0.1128	0.06847	-1.647	1494	0.09976	-0.305	0.07942
fixed	NA	sibling_count5	-0.1428	0.08544	-1.671	1425	0.09484	-0.3826	0.09702
ran_pars	mother_pidlink	sd__(Intercept)	0.2671	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9451	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.191	1.096	-1.999	1863	0.04575	-5.267	0.8854
fixed	NA	poly(age, 3, raw = TRUE)1	0.1507	0.1199	1.257	1864	0.209	-0.1858	0.4872
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002995	0.00421	-0.7115	1865	0.4769	-0.01481	0.008821
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001717	0.00004753	0.3613	1865	0.7179	-0.0001162	0.0001506
fixed	NA	male	0.1749	0.0461	3.794	1880	0.000153	0.04549	0.3043
fixed	NA	sibling_count3	0.009642	0.06337	0.1522	1565	0.8791	-0.1682	0.1875
fixed	NA	sibling_count4	-0.1218	0.0694	-1.755	1539	0.07946	-0.3166	0.07301
fixed	NA	sibling_count5	-0.1235	0.08717	-1.417	1453	0.1566	-0.3682	0.1211
fixed	NA	birth_order_nonlinear2	0.04081	0.05474	0.7455	1614	0.4561	-0.1128	0.1945
fixed	NA	birth_order_nonlinear3	0.1357	0.06808	1.993	1700	0.04643	-0.05542	0.3268
fixed	NA	birth_order_nonlinear4	0.017	0.09331	0.1821	1712	0.8555	-0.2449	0.2789
fixed	NA	birth_order_nonlinear5	-0.01179	0.1488	-0.07925	1776	0.9368	-0.4293	0.4058
ran_pars	mother_pidlink	sd__(Intercept)	0.2666	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9451	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.206	1.098	-2.009	1857	0.04473	-5.288	0.8769
fixed	NA	poly(age, 3, raw = TRUE)1	0.1549	0.1203	1.288	1859	0.1979	-0.1827	0.4926
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003103	0.004224	-0.7346	1859	0.4627	-0.01496	0.008755
fixed	NA	poly(age, 3, raw = TRUE)3	0.000018	0.0000477	0.3774	1860	0.7059	-0.0001159	0.0001519
fixed	NA	male	0.1754	0.04618	3.799	1873	0.0001502	0.04579	0.305
fixed	NA	count_birth_order2/2	-0.06978	0.09583	-0.7282	1627	0.4666	-0.3388	0.1992
fixed	NA	count_birth_order1/3	-0.04446	0.08074	-0.5506	1876	0.582	-0.2711	0.1822
fixed	NA	count_birth_order2/3	0.06535	0.09183	0.7116	1876	0.4768	-0.1924	0.3231
fixed	NA	count_birth_order3/3	0.0826	0.09947	0.8305	1871	0.4064	-0.1966	0.3618
fixed	NA	count_birth_order1/4	-0.2275	0.09624	-2.364	1877	0.01819	-0.4976	0.04266
fixed	NA	count_birth_order2/4	-0.08213	0.09867	-0.8324	1875	0.4053	-0.3591	0.1948
fixed	NA	count_birth_order3/4	0.04063	0.1043	0.3895	1873	0.697	-0.2522	0.3335
fixed	NA	count_birth_order4/4	-0.1586	0.1141	-1.39	1868	0.1648	-0.4789	0.1617
fixed	NA	count_birth_order1/5	-0.08721	0.1325	-0.658	1877	0.5106	-0.4593	0.2849
fixed	NA	count_birth_order2/5	-0.1772	0.1537	-1.153	1870	0.2491	-0.6085	0.2542
fixed	NA	count_birth_order3/5	-0.09323	0.1417	-0.6581	1873	0.5105	-0.4909	0.3044
fixed	NA	count_birth_order4/5	-0.1134	0.1354	-0.8372	1868	0.4026	-0.4935	0.2667
fixed	NA	count_birth_order5/5	-0.1715	0.1402	-1.223	1870	0.2215	-0.5651	0.2221
ran_pars	mother_pidlink	sd__(Intercept)	0.2728	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9438	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	5319	5374	-2649	5299	NA	NA	NA
11	5320	5381	-2649	5298	0.9746	1	0.3235
14	5322	5400	-2647	5294	3.379	3	0.3368
20	5330	5441	-2645	5290	4.503	6	0.609

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Income last year (log) - z-standardized

birthorder <- birthorder %>% mutate(outcome = wage_last_year_z)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.289	0.4717	-9.092	2886	1.758e-19	-5.613	-2.965
fixed	NA	poly(age, 3, raw = TRUE)1	0.3338	0.04424	7.546	2880	5.966e-14	0.2097	0.458
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008164	0.0013	-6.28	2879	0.0000000003898	-0.01181	-0.004515
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006366	0.00001206	5.277	2885	0.0000001412	0.0000298	0.00009753
fixed	NA	male	0.1088	0.0367	2.964	2903	0.003059	0.005768	0.2118
fixed	NA	sibling_count3	0.07339	0.05274	1.392	2141	0.1642	-0.07465	0.2214
fixed	NA	sibling_count4	0.03634	0.05287	0.6872	2038	0.492	-0.1121	0.1847
fixed	NA	sibling_count5	0.02447	0.05519	0.4433	1941	0.6576	-0.1305	0.1794
ran_pars	mother_pidlink	sd__(Intercept)	0.414	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8867	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.286	0.4716	-9.089	2884	1.809e-19	-5.61	-2.963
fixed	NA	birth_order	-0.02806	0.01766	-1.589	2472	0.1122	-0.07762	0.0215
fixed	NA	poly(age, 3, raw = TRUE)1	0.3368	0.04426	7.609	2879	3.718e-14	0.2125	0.461
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008225	0.0013	-6.327	2877	0.0000000002892	-0.01187	-0.004576
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006393	0.00001206	5.3	2883	0.0000001245	0.00003007	0.00009778
fixed	NA	male	0.1085	0.03669	2.956	2903	0.003139	0.005475	0.2115
fixed	NA	sibling_count3	0.08371	0.0531	1.576	2188	0.1151	-0.06534	0.2328
fixed	NA	sibling_count4	0.06062	0.055	1.102	2257	0.2705	-0.09376	0.215
fixed	NA	sibling_count5	0.06253	0.06012	1.04	2368	0.2984	-0.1062	0.2313
ran_pars	mother_pidlink	sd__(Intercept)	0.4114	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8875	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.29	0.4727	-9.076	2877	2.036e-19	-5.617	-2.963
fixed	NA	poly(age, 3, raw = TRUE)1	0.3347	0.04432	7.552	2869	5.717e-14	0.2103	0.4591
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008146	0.001303	-6.253	2865	0.0000000004625	-0.0118	-0.004489
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006304	0.0000121	5.212	2868	0.0000002005	0.00002909	0.00009699
fixed	NA	male	0.109	0.03673	2.968	2903	0.003023	0.005909	0.2121
fixed	NA	sibling_count3	0.09064	0.05384	1.684	2269	0.09241	-0.06048	0.2418
fixed	NA	sibling_count4	0.07197	0.05587	1.288	2344	0.1978	-0.08485	0.2288
fixed	NA	sibling_count5	0.0541	0.06059	0.8928	2415	0.372	-0.116	0.2242
fixed	NA	birth_order_nonlinear2	-0.05317	0.04338	-1.226	2404	0.2204	-0.1749	0.06859
fixed	NA	birth_order_nonlinear3	-0.09253	0.05424	-1.706	2358	0.08817	-0.2448	0.05973
fixed	NA	birth_order_nonlinear4	-0.1128	0.0697	-1.619	2332	0.1056	-0.3085	0.08282
fixed	NA	birth_order_nonlinear5	-0.01194	0.1018	-0.1173	2331	0.9066	-0.2976	0.2737
ran_pars	mother_pidlink	sd__(Intercept)	0.4074	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8893	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.291	0.4737	-9.059	2875	2.38e-19	-5.621	-2.962
fixed	NA	poly(age, 3, raw = TRUE)1	0.3342	0.04439	7.528	2864	6.879e-14	0.2096	0.4588
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008136	0.001304	-6.237	2859	0.0000000005135	-0.0118	-0.004474
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006301	0.00001211	5.203	2862	0.0000002103	0.00002901	0.000097
fixed	NA	male	0.1079	0.03676	2.936	2898	0.00335	0.004745	0.2111
fixed	NA	count_birth_order2/2	-0.02836	0.07571	-0.3746	2491	0.708	-0.2409	0.1841
fixed	NA	count_birth_order1/3	0.08944	0.06881	1.3	2917	0.1938	-0.1037	0.2826
fixed	NA	count_birth_order2/3	0.03408	0.07881	0.4324	2920	0.6655	-0.1872	0.2553
fixed	NA	count_birth_order3/3	0.04454	0.08783	0.5072	2901	0.6121	-0.202	0.2911
fixed	NA	count_birth_order1/4	0.1123	0.07681	1.462	2923	0.1439	-0.1033	0.3279
fixed	NA	count_birth_order2/4	0.01422	0.0818	0.1738	2920	0.862	-0.2154	0.2438
fixed	NA	count_birth_order3/4	-0.08973	0.08579	-1.046	2910	0.2957	-0.3305	0.1511
fixed	NA	count_birth_order4/4	0.02997	0.09353	0.3204	2896	0.7487	-0.2326	0.2925
fixed	NA	count_birth_order1/5	0.06047	0.0864	0.6999	2919	0.4841	-0.1821	0.303
fixed	NA	count_birth_order2/5	0.02106	0.09486	0.2221	2886	0.8243	-0.2452	0.2873
fixed	NA	count_birth_order3/5	0.03074	0.09699	0.317	2885	0.7513	-0.2415	0.303
fixed	NA	count_birth_order4/5	-0.1229	0.09914	-1.24	2860	0.2152	-0.4012	0.1554
fixed	NA	count_birth_order5/5	0.05153	0.1023	0.5038	2868	0.6144	-0.2356	0.3386
ran_pars	mother_pidlink	sd__(Intercept)	0.4067	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.89	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	8206	8266	-4093	8186	NA	NA	NA
11	8206	8271	-4092	8184	2.534	1	0.1114
14	8209	8293	-4091	8181	2.169	3	0.5382
20	8218	8337	-4089	8178	3.899	6	0.6904

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.041	1.155	-4.366	1866	0.00001337	-8.283	-1.8
fixed	NA	poly(age, 3, raw = TRUE)1	0.4195	0.1269	3.305	1867	0.0009669	0.06323	0.7757
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01122	0.004483	-2.504	1867	0.01238	-0.02381	0.00136
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001023	0.00005091	2.009	1866	0.04464	-0.00004061	0.0002452
fixed	NA	male	0.1532	0.04694	3.265	1882	0.001115	0.02149	0.285
fixed	NA	sibling_count3	0.03305	0.06361	0.5196	1480	0.6034	-0.1455	0.2116
fixed	NA	sibling_count4	-0.0503	0.06578	-0.7647	1362	0.4446	-0.2349	0.1343
fixed	NA	sibling_count5	-0.1586	0.0749	-2.118	1260	0.03439	-0.3689	0.05163
ran_pars	mother_pidlink	sd__(Intercept)	0.2671	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9643	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.044	1.155	-4.366	1865	0.00001335	-8.286	-1.801
fixed	NA	birth_order	0.002807	0.02376	0.1181	1812	0.906	-0.0639	0.06951
fixed	NA	poly(age, 3, raw = TRUE)1	0.4194	0.1269	3.304	1866	0.0009706	0.06311	0.7758
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01123	0.004484	-2.504	1866	0.01237	-0.02381	0.00136
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001024	0.00005093	2.011	1865	0.0445	-0.00004056	0.0002454
fixed	NA	male	0.1532	0.04695	3.263	1881	0.001124	0.02139	0.285
fixed	NA	sibling_count3	0.03178	0.06455	0.4923	1501	0.6226	-0.1494	0.213
fixed	NA	sibling_count4	-0.0532	0.07025	-0.7573	1468	0.449	-0.2504	0.144
fixed	NA	sibling_count5	-0.1636	0.08589	-1.904	1456	0.05704	-0.4047	0.07752
ran_pars	mother_pidlink	sd__(Intercept)	0.2675	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9645	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.015	1.156	-4.339	1861	0.00001505	-8.26	-1.771
fixed	NA	poly(age, 3, raw = TRUE)1	0.4156	0.127	3.271	1862	0.00109	0.05898	0.7722
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0111	0.004487	-2.475	1863	0.01342	-0.0237	0.00149
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001011	0.00005096	1.985	1861	0.0473	-0.00004189	0.0002442
fixed	NA	male	0.1517	0.04695	3.231	1878	0.001253	0.01993	0.2835
fixed	NA	sibling_count3	0.02238	0.06548	0.3418	1543	0.7326	-0.1614	0.2062
fixed	NA	sibling_count4	-0.07671	0.07122	-1.077	1515	0.2816	-0.2766	0.1232
fixed	NA	sibling_count5	-0.1312	0.08736	-1.502	1475	0.1332	-0.3765	0.114
fixed	NA	birth_order_nonlinear2	0.04756	0.05625	0.8455	1599	0.3979	-0.1103	0.2055
fixed	NA	birth_order_nonlinear3	0.05026	0.06967	0.7213	1682	0.4708	-0.1453	0.2458
fixed	NA	birth_order_nonlinear4	0.08852	0.09217	0.9604	1728	0.337	-0.1702	0.3473
fixed	NA	birth_order_nonlinear5	-0.2357	0.1428	-1.651	1775	0.09891	-0.6365	0.165
ran_pars	mother_pidlink	sd__(Intercept)	0.2674	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9638	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.943	1.158	-4.267	1854	0.00002083	-8.195	-1.691
fixed	NA	poly(age, 3, raw = TRUE)1	0.4062	0.1275	3.187	1855	0.001462	0.04841	0.764
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01073	0.004503	-2.383	1855	0.01726	-0.02337	0.001909
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000965	0.00005115	1.887	1854	0.05938	-0.00004709	0.0002401
fixed	NA	male	0.1496	0.04705	3.181	1872	0.001493	0.01758	0.2817
fixed	NA	count_birth_order2/2	0.05432	0.1003	0.5414	1632	0.5883	-0.2273	0.3359
fixed	NA	count_birth_order1/3	0.009103	0.08335	0.1092	1875	0.913	-0.2249	0.2431
fixed	NA	count_birth_order2/3	0.1111	0.09459	1.175	1874	0.2403	-0.1544	0.3766
fixed	NA	count_birth_order3/3	0.05426	0.1041	0.5212	1871	0.6023	-0.238	0.3465
fixed	NA	count_birth_order1/4	-0.09662	0.09804	-0.9855	1875	0.3245	-0.3718	0.1786
fixed	NA	count_birth_order2/4	-0.06522	0.1012	-0.6443	1874	0.5194	-0.3494	0.2189
fixed	NA	count_birth_order3/4	0.04807	0.1069	0.4499	1870	0.6528	-0.2519	0.348
fixed	NA	count_birth_order4/4	0.01509	0.1141	0.1323	1869	0.8948	-0.3051	0.3352
fixed	NA	count_birth_order1/5	-0.01062	0.1323	-0.08023	1875	0.9361	-0.3821	0.3609
fixed	NA	count_birth_order2/5	-0.1219	0.154	-0.7916	1867	0.4287	-0.5542	0.3104
fixed	NA	count_birth_order3/5	-0.1815	0.1388	-1.307	1872	0.1914	-0.5712	0.2083
fixed	NA	count_birth_order4/5	-0.04254	0.131	-0.3247	1869	0.7455	-0.4103	0.3252
fixed	NA	count_birth_order5/5	-0.366	0.135	-2.711	1870	0.006768	-0.745	0.01296
ran_pars	mother_pidlink	sd__(Intercept)	0.2669	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9647	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	5384	5440	-2682	5364	NA	NA	NA
11	5386	5447	-2682	5364	0.01322	1	0.9085
14	5386	5464	-2679	5358	5.689	3	0.1278
20	5395	5506	-2678	5355	3.141	6	0.7909

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.112	1.176	-4.348	1727	0.00001457	-8.412	-1.811
fixed	NA	poly(age, 3, raw = TRUE)1	0.4281	0.1293	3.311	1729	0.0009505	0.06511	0.7912
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0115	0.00457	-2.517	1730	0.01192	-0.02433	0.001325
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001046	0.00005193	2.015	1729	0.04409	-0.00004114	0.0002504
fixed	NA	male	0.1328	0.04798	2.767	1733	0.005719	-0.001924	0.2675
fixed	NA	sibling_count3	0.03107	0.06907	0.4499	1395	0.6529	-0.1628	0.225
fixed	NA	sibling_count4	0.01523	0.07028	0.2167	1317	0.8285	-0.182	0.2125
fixed	NA	sibling_count5	-0.1259	0.07391	-1.703	1224	0.08874	-0.3334	0.08156
ran_pars	mother_pidlink	sd__(Intercept)	0.309	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9334	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.117	1.177	-4.349	1726	0.00001448	-8.42	-1.814
fixed	NA	birth_order	0.003539	0.02331	0.1518	1689	0.8794	-0.06191	0.06898
fixed	NA	poly(age, 3, raw = TRUE)1	0.4283	0.1294	3.311	1728	0.0009504	0.06514	0.7914
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01151	0.004572	-2.518	1729	0.01188	-0.02435	0.00132
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001048	0.00005195	2.017	1728	0.04382	-0.00004103	0.0002506
fixed	NA	male	0.1328	0.048	2.766	1732	0.005737	-0.001974	0.2675
fixed	NA	sibling_count3	0.02938	0.06998	0.4199	1409	0.6746	-0.167	0.2258
fixed	NA	sibling_count4	0.01171	0.07402	0.1582	1382	0.8743	-0.1961	0.2195
fixed	NA	sibling_count5	-0.1316	0.083	-1.586	1374	0.113	-0.3646	0.1014
ran_pars	mother_pidlink	sd__(Intercept)	0.3094	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9335	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.143	1.177	-4.37	1722	0.00001315	-8.446	-1.84
fixed	NA	poly(age, 3, raw = TRUE)1	0.4305	0.1295	3.325	1724	0.0009028	0.06705	0.7939
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01159	0.004575	-2.534	1725	0.01137	-0.02443	0.001249
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001057	0.00005198	2.034	1724	0.04212	-0.00004019	0.0002516
fixed	NA	male	0.1319	0.04798	2.75	1730	0.006025	-0.002745	0.2666
fixed	NA	sibling_count3	0.01588	0.07092	0.224	1440	0.8228	-0.1832	0.2149
fixed	NA	sibling_count4	-0.02047	0.07489	-0.2733	1417	0.7847	-0.2307	0.1898
fixed	NA	sibling_count5	-0.1114	0.08345	-1.335	1379	0.1821	-0.3457	0.1228
fixed	NA	birth_order_nonlinear2	0.04053	0.05715	0.7092	1460	0.4783	-0.1199	0.201
fixed	NA	birth_order_nonlinear3	0.06525	0.07116	0.917	1567	0.3593	-0.1345	0.265
fixed	NA	birth_order_nonlinear4	0.1259	0.09257	1.36	1575	0.1739	-0.1339	0.3858
fixed	NA	birth_order_nonlinear5	-0.2428	0.1317	-1.844	1620	0.06542	-0.6124	0.1269
ran_pars	mother_pidlink	sd__(Intercept)	0.3112	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9315	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-5.113	1.182	-4.324	1715	0.00001621	-8.432	-1.794
fixed	NA	poly(age, 3, raw = TRUE)1	0.4261	0.1302	3.273	1717	0.001083	0.06072	0.7915
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0114	0.0046	-2.479	1718	0.01329	-0.02431	0.001511
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001032	0.00005227	1.975	1717	0.04847	-0.00004351	0.0002499
fixed	NA	male	0.1304	0.04817	2.707	1723	0.00685	-0.004802	0.2656
fixed	NA	count_birth_order2/2	0.03909	0.111	0.3523	1544	0.7247	-0.2724	0.3505
fixed	NA	count_birth_order1/3	-0.01466	0.09025	-0.1624	1730	0.871	-0.268	0.2387
fixed	NA	count_birth_order2/3	0.1055	0.1001	1.053	1731	0.2924	-0.1756	0.3866
fixed	NA	count_birth_order3/3	0.07192	0.1119	0.6426	1727	0.5206	-0.2422	0.3861
fixed	NA	count_birth_order1/4	-0.002117	0.1018	-0.0208	1731	0.9834	-0.2878	0.2836
fixed	NA	count_birth_order2/4	0.0178	0.1023	0.1739	1730	0.862	-0.2695	0.3051
fixed	NA	count_birth_order3/4	0.02894	0.1154	0.2509	1724	0.8019	-0.2949	0.3528
fixed	NA	count_birth_order4/4	0.08847	0.1225	0.7223	1719	0.4702	-0.2554	0.4323
fixed	NA	count_birth_order1/5	-0.07416	0.1184	-0.6263	1731	0.5312	-0.4065	0.2582
fixed	NA	count_birth_order2/5	-0.1721	0.1301	-1.323	1722	0.186	-0.5372	0.193
fixed	NA	count_birth_order3/5	-0.01529	0.1297	-0.1179	1722	0.9062	-0.3795	0.3489
fixed	NA	count_birth_order4/5	0.03177	0.1305	0.2434	1714	0.8077	-0.3347	0.3982
fixed	NA	count_birth_order5/5	-0.3552	0.1301	-2.731	1720	0.006384	-0.7204	0.009928
ran_pars	mother_pidlink	sd__(Intercept)	0.315	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9316	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	4912	4967	-2446	4892	NA	NA	NA
11	4914	4974	-2446	4892	0.02233	1	0.8812
14	4912	4989	-2442	4884	7.814	3	0.05001
20	4922	5032	-2441	4882	1.813	6	0.936

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.797	1.195	-4.015	1857	0.00006192	-8.151	-1.443
fixed	NA	poly(age, 3, raw = TRUE)1	0.3884	0.1314	2.957	1858	0.003147	0.01968	0.7571
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01	0.004639	-2.156	1859	0.03123	-0.02302	0.003022
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008709	0.00005269	1.653	1858	0.09853	-0.00006082	0.000235
fixed	NA	male	0.1802	0.04862	3.706	1868	0.000217	0.04369	0.3167
fixed	NA	sibling_count3	-0.005082	0.06501	-0.07817	1474	0.9377	-0.1876	0.1774
fixed	NA	sibling_count4	-0.1041	0.06798	-1.531	1348	0.1261	-0.2949	0.08676
fixed	NA	sibling_count5	-0.1696	0.07966	-2.129	1207	0.03345	-0.3932	0.05401
ran_pars	mother_pidlink	sd__(Intercept)	0.3022	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9897	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.799	1.195	-4.015	1856	0.00006175	-8.154	-1.444
fixed	NA	birth_order	0.003711	0.02502	0.1483	1780	0.8821	-0.06653	0.07395
fixed	NA	poly(age, 3, raw = TRUE)1	0.3883	0.1314	2.955	1857	0.003165	0.01945	0.7571
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01	0.004641	-2.156	1858	0.03124	-0.02303	0.003023
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008721	0.00005271	1.654	1857	0.09821	-0.00006076	0.0002352
fixed	NA	male	0.1801	0.04864	3.703	1867	0.0002196	0.04356	0.3166
fixed	NA	sibling_count3	-0.006814	0.06607	-0.1031	1493	0.9179	-0.1923	0.1787
fixed	NA	sibling_count4	-0.1078	0.07259	-1.485	1460	0.1377	-0.3116	0.09593
fixed	NA	sibling_count5	-0.176	0.09046	-1.945	1401	0.05195	-0.4299	0.07796
ran_pars	mother_pidlink	sd__(Intercept)	0.3026	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9898	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.85	1.197	-4.052	1853	0.00005293	-8.211	-1.49
fixed	NA	poly(age, 3, raw = TRUE)1	0.3941	0.1316	2.994	1855	0.002793	0.02457	0.7636
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01022	0.004649	-2.198	1855	0.02804	-0.02327	0.002829
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008963	0.0000528	1.698	1854	0.08975	-0.00005857	0.0002378
fixed	NA	male	0.1809	0.04871	3.714	1865	0.0002099	0.04419	0.3177
fixed	NA	sibling_count3	-0.02507	0.06715	-0.3734	1533	0.7089	-0.2136	0.1634
fixed	NA	sibling_count4	-0.1232	0.0736	-1.674	1505	0.09434	-0.3298	0.08339
fixed	NA	sibling_count5	-0.1493	0.09234	-1.617	1430	0.106	-0.4085	0.1099
fixed	NA	birth_order_nonlinear2	0.02734	0.05778	0.4731	1572	0.6362	-0.1349	0.1895
fixed	NA	birth_order_nonlinear3	0.08955	0.07184	1.247	1664	0.2127	-0.1121	0.2912
fixed	NA	birth_order_nonlinear4	0.001777	0.0986	0.01802	1679	0.9856	-0.275	0.2785
fixed	NA	birth_order_nonlinear5	-0.1624	0.1567	-1.037	1746	0.3	-0.6022	0.2774
ran_pars	mother_pidlink	sd__(Intercept)	0.3069	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9885	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-4.789	1.2	-3.992	1846	0.00006804	-8.156	-1.422
fixed	NA	poly(age, 3, raw = TRUE)1	0.3862	0.1321	2.924	1847	0.003497	0.01545	0.7569
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00988	0.004665	-2.118	1848	0.03431	-0.02298	0.003214
fixed	NA	poly(age, 3, raw = TRUE)3	0.00008515	0.00005299	1.607	1847	0.1082	-0.00006359	0.0002339
fixed	NA	male	0.1773	0.04881	3.632	1859	0.0002891	0.04025	0.3143
fixed	NA	count_birth_order2/2	0.0157	0.1012	0.1552	1595	0.8767	-0.2683	0.2997
fixed	NA	count_birth_order1/3	-0.06288	0.08534	-0.7368	1863	0.4613	-0.3024	0.1767
fixed	NA	count_birth_order2/3	0.07646	0.09722	0.7865	1862	0.4317	-0.1964	0.3494
fixed	NA	count_birth_order3/3	0.0301	0.1049	0.2869	1858	0.7742	-0.2643	0.3245
fixed	NA	count_birth_order1/4	-0.1383	0.102	-1.357	1864	0.175	-0.4245	0.1479
fixed	NA	count_birth_order2/4	-0.1647	0.1043	-1.579	1862	0.1144	-0.4576	0.1281
fixed	NA	count_birth_order3/4	0.02634	0.1104	0.2387	1859	0.8114	-0.2834	0.3361
fixed	NA	count_birth_order4/4	-0.0892	0.1208	-0.7385	1853	0.4603	-0.4283	0.2499
fixed	NA	count_birth_order1/5	-0.002734	0.1398	-0.01955	1864	0.9844	-0.3953	0.3898
fixed	NA	count_birth_order2/5	-0.1924	0.162	-1.188	1855	0.2349	-0.6471	0.2622
fixed	NA	count_birth_order3/5	-0.129	0.1505	-0.8576	1858	0.3912	-0.5514	0.2933
fixed	NA	count_birth_order4/5	-0.2067	0.1427	-1.448	1853	0.1477	-0.6074	0.1939
fixed	NA	count_birth_order5/5	-0.3173	0.1478	-2.147	1856	0.03195	-0.7321	0.09761
ran_pars	mother_pidlink	sd__(Intercept)	0.3045	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9896	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	5478	5534	-2729	5458	NA	NA	NA
11	5480	5541	-2729	5458	0.02131	1	0.8839
14	5483	5560	-2727	5455	3.279	3	0.3506
20	5490	5601	-2725	5450	4.76	6	0.575

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Self-Employment - non standardized

birthorder <- birthorder %>% mutate(outcome = Self_employed)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1206	0.1226	-0.9834	4493	0.3255	-0.4647	0.2236
fixed	NA	poly(age, 3, raw = TRUE)1	0.012	0.01094	1.097	4392	0.2727	-0.01871	0.04271
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001217	0.0003039	0.4005	4271	0.6888	-0.0007313	0.0009746
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002423	0.000002658	-0.9116	4161	0.3621	-0.000009883	0.000005038
fixed	NA	male	-0.007402	0.0124	-0.5968	4755	0.5507	-0.04222	0.02741
fixed	NA	sibling_count3	-0.02237	0.01799	-1.243	3513	0.2138	-0.07286	0.02813
fixed	NA	sibling_count4	-0.01961	0.0182	-1.078	3307	0.2812	-0.07069	0.03147
fixed	NA	sibling_count5	-0.009391	0.019	-0.4943	3086	0.6211	-0.06272	0.04394
ran_pars	mother_pidlink	sd__(Intercept)	0.1564	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3995	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1194	0.1226	-0.9736	4493	0.3303	-0.4635	0.2248
fixed	NA	birth_order	0.006512	0.006069	1.073	4244	0.2833	-0.01052	0.02355
fixed	NA	poly(age, 3, raw = TRUE)1	0.01103	0.01098	1.005	4392	0.3151	-0.01978	0.04184
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001463	0.0003047	0.4803	4262	0.6311	-0.000709	0.001002
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002589	0.000002662	-0.9726	4153	0.3308	-0.00001006	0.000004884
fixed	NA	male	-0.007341	0.0124	-0.5919	4754	0.554	-0.04215	0.02747
fixed	NA	sibling_count3	-0.02483	0.01813	-1.369	3598	0.171	-0.07573	0.02607
fixed	NA	sibling_count4	-0.02483	0.01884	-1.318	3649	0.1874	-0.07771	0.02804
fixed	NA	sibling_count5	-0.01774	0.02053	-0.8642	3771	0.3875	-0.07537	0.03989
ran_pars	mother_pidlink	sd__(Intercept)	0.1564	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3995	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1273	0.1229	-1.036	4498	0.3001	-0.4723	0.2176
fixed	NA	poly(age, 3, raw = TRUE)1	0.01147	0.01097	1.046	4389	0.2958	-0.01933	0.04228
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001204	0.0003047	0.3952	4256	0.6927	-0.0007349	0.0009757
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002249	0.000002663	-0.8444	4140	0.3985	-0.000009726	0.000005227
fixed	NA	male	-0.00794	0.0124	-0.6405	4750	0.5219	-0.04274	0.02686
fixed	NA	sibling_count3	-0.02604	0.01843	-1.413	3746	0.1577	-0.07777	0.02568
fixed	NA	sibling_count4	-0.02219	0.01914	-1.159	3802	0.2466	-0.07593	0.03155
fixed	NA	sibling_count5	-0.01043	0.02071	-0.5038	3865	0.6144	-0.06857	0.04771
fixed	NA	birth_order_nonlinear2	0.04641	0.01462	3.175	4168	0.001509	0.00538	0.08745
fixed	NA	birth_order_nonlinear3	0.02766	0.01859	1.488	4101	0.1369	-0.02453	0.07985
fixed	NA	birth_order_nonlinear4	0.01196	0.02414	0.4955	4060	0.6203	-0.0558	0.07972
fixed	NA	birth_order_nonlinear5	0.009981	0.03487	0.2862	4070	0.7747	-0.08791	0.1079
ran_pars	mother_pidlink	sd__(Intercept)	0.1568	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3991	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1265	0.123	-1.028	4502	0.3039	-0.4718	0.2189
fixed	NA	poly(age, 3, raw = TRUE)1	0.01062	0.01098	0.9672	4386	0.3335	-0.0202	0.04144
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001361	0.0003048	0.4465	4253	0.6553	-0.0007194	0.0009916
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002308	0.000002664	-0.8666	4137	0.3862	-0.000009785	0.000005168
fixed	NA	male	-0.008281	0.0124	-0.6679	4743	0.5042	-0.04309	0.02652
fixed	NA	count_birth_order2/2	0.07691	0.02482	3.098	4123	0.001961	0.007225	0.1466
fixed	NA	count_birth_order1/3	-0.02403	0.02407	-0.9984	4793	0.3182	-0.09159	0.04353
fixed	NA	count_birth_order2/3	0.03415	0.02669	1.28	4804	0.2008	-0.04077	0.1091
fixed	NA	count_birth_order3/3	0.02757	0.02937	0.9389	4806	0.3478	-0.05486	0.11
fixed	NA	count_birth_order1/4	0.01578	0.02638	0.5979	4804	0.5499	-0.05829	0.08984
fixed	NA	count_birth_order2/4	0.006164	0.0283	0.2178	4806	0.8276	-0.07327	0.0856
fixed	NA	count_birth_order3/4	-0.003886	0.03019	-0.1287	4804	0.8976	-0.08862	0.08085
fixed	NA	count_birth_order4/4	0.02151	0.03211	0.67	4803	0.5029	-0.06863	0.1117
fixed	NA	count_birth_order1/5	0.01111	0.02995	0.3709	4804	0.7107	-0.07297	0.09518
fixed	NA	count_birth_order2/5	0.0492	0.03179	1.547	4801	0.1218	-0.04004	0.1384
fixed	NA	count_birth_order3/5	0.03627	0.03346	1.084	4796	0.2785	-0.05767	0.1302
fixed	NA	count_birth_order4/5	-0.01264	0.03519	-0.359	4775	0.7196	-0.1114	0.08615
fixed	NA	count_birth_order5/5	0.01104	0.03522	0.3136	4791	0.7539	-0.08782	0.1099
ran_pars	mother_pidlink	sd__(Intercept)	0.1569	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.399	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	5504	5569	-2742	5484	NA	NA	NA
11	5505	5576	-2741	5483	1.154	1	0.2828
14	5501	5592	-2737	5473	9.456	3	0.0238
20	5506	5635	-2733	5466	7.697	6	0.2612

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.112	0.3187	3.489	2759	0.000492	0.2174	2.007
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1214	0.03531	-3.439	2760	0.0005935	-0.2205	-0.0223
fixed	NA	poly(age, 3, raw = TRUE)2	0.004639	0.001252	3.705	2760	0.0002156	0.001124	0.008154
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005136	0.00001422	-3.611	2760	0.00031	-0.00009129	-0.00001144
fixed	NA	male	-0.04191	0.0149	-2.813	2721	0.004946	-0.08373	-0.00008659
fixed	NA	sibling_count3	0.01673	0.02117	0.7903	2217	0.4294	-0.04269	0.07615
fixed	NA	sibling_count4	-0.02678	0.022	-1.217	2081	0.2236	-0.08852	0.03497
fixed	NA	sibling_count5	0.04089	0.02453	1.667	1873	0.09571	-0.02797	0.1098
ran_pars	mother_pidlink	sd__(Intercept)	0.157	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3561	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.113	0.3188	3.49	2758	0.0004908	0.2177	2.008
fixed	NA	birth_order	-0.001112	0.007469	-0.1489	2589	0.8816	-0.02208	0.01985
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1213	0.03532	-3.435	2758	0.0006009	-0.2205	-0.02218
fixed	NA	poly(age, 3, raw = TRUE)2	0.004638	0.001252	3.703	2759	0.0002169	0.001123	0.008153
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005138	0.00001423	-3.612	2759	0.0003095	-0.00009131	-0.00001145
fixed	NA	male	-0.04191	0.0149	-2.812	2720	0.004953	-0.08374	-0.00007972
fixed	NA	sibling_count3	0.01727	0.02148	0.8039	2246	0.4215	-0.04303	0.07756
fixed	NA	sibling_count4	-0.02562	0.02332	-1.099	2194	0.2719	-0.09108	0.03983
fixed	NA	sibling_count5	0.04282	0.02776	1.543	2169	0.123	-0.03509	0.1207
ran_pars	mother_pidlink	sd__(Intercept)	0.1571	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3561	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.113	0.3195	3.483	2755	0.0005044	0.2159	2.01
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1218	0.03539	-3.443	2755	0.0005845	-0.2212	-0.0225
fixed	NA	poly(age, 3, raw = TRUE)2	0.004652	0.001255	3.708	2756	0.0002134	0.00113	0.008175
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005151	0.00001425	-3.614	2756	0.0003066	-0.00009151	-0.0000115
fixed	NA	male	-0.04216	0.01491	-2.827	2718	0.004737	-0.08402	-0.0002938
fixed	NA	sibling_count3	0.01836	0.02179	0.8423	2302	0.3997	-0.04282	0.07954
fixed	NA	sibling_count4	-0.02705	0.02361	-1.146	2246	0.252	-0.09334	0.03923
fixed	NA	sibling_count5	0.0469	0.0281	1.669	2210	0.09523	-0.03198	0.1258
fixed	NA	birth_order_nonlinear2	0.01228	0.01776	0.691	2336	0.4896	-0.03759	0.06214
fixed	NA	birth_order_nonlinear3	-0.005867	0.02171	-0.2702	2396	0.787	-0.06681	0.05508
fixed	NA	birth_order_nonlinear4	0.01255	0.02887	0.4346	2459	0.6639	-0.06849	0.09359
fixed	NA	birth_order_nonlinear5	-0.02938	0.0443	-0.6631	2389	0.5073	-0.1537	0.09498
ran_pars	mother_pidlink	sd__(Intercept)	0.1575	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3561	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.101	0.3199	3.443	2749	0.0005833	0.2035	1.999
fixed	NA	poly(age, 3, raw = TRUE)1	-0.122	0.03542	-3.443	2749	0.0005832	-0.2214	-0.02254
fixed	NA	poly(age, 3, raw = TRUE)2	0.004655	0.001256	3.706	2750	0.0002145	0.001129	0.008181
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005152	0.00001427	-3.611	2750	0.0003104	-0.00009157	-0.00001147
fixed	NA	male	-0.04244	0.01494	-2.841	2712	0.00453	-0.08437	-0.0005087
fixed	NA	count_birth_order2/2	0.0532	0.03229	1.648	2406	0.09955	-0.03743	0.1438
fixed	NA	count_birth_order1/3	0.04188	0.02754	1.52	2745	0.1285	-0.03544	0.1192
fixed	NA	count_birth_order2/3	0.03959	0.03056	1.296	2750	0.1952	-0.04619	0.1254
fixed	NA	count_birth_order3/3	0.01101	0.03305	0.3331	2746	0.7391	-0.08175	0.1038
fixed	NA	count_birth_order1/4	-0.006186	0.03172	-0.195	2749	0.8454	-0.09522	0.08285
fixed	NA	count_birth_order2/4	-0.02662	0.03329	-0.7996	2747	0.424	-0.1201	0.06682
fixed	NA	count_birth_order3/4	-0.01179	0.03488	-0.338	2737	0.7354	-0.1097	0.08611
fixed	NA	count_birth_order4/4	0.01099	0.03695	0.2973	2735	0.7663	-0.09273	0.1147
fixed	NA	count_birth_order1/5	0.05724	0.04167	1.374	2747	0.1697	-0.05974	0.1742
fixed	NA	count_birth_order2/5	0.07863	0.04519	1.74	2719	0.08198	-0.04822	0.2055
fixed	NA	count_birth_order3/5	0.06885	0.0423	1.628	2724	0.1037	-0.04988	0.1876
fixed	NA	count_birth_order4/5	0.05676	0.0411	1.381	2722	0.1674	-0.0586	0.1721
fixed	NA	count_birth_order5/5	0.03067	0.04307	0.712	2715	0.4765	-0.09024	0.1516
ran_pars	mother_pidlink	sd__(Intercept)	0.1566	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3566	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	2619	2678	-1300	2599	NA	NA	NA
11	2621	2686	-1300	2599	0.02164	1	0.8831
14	2626	2709	-1299	2598	1.583	3	0.6632
20	2634	2752	-1297	2594	3.881	6	0.6928

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.049	0.3272	3.207	2531	0.001358	0.1308	1.968
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1131	0.03626	-3.118	2531	0.00184	-0.2148	-0.01128
fixed	NA	poly(age, 3, raw = TRUE)2	0.00436	0.001286	3.39	2531	0.0007086	0.0007501	0.007969
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004835	0.00001461	-3.31	2531	0.0009454	-0.00008935	-0.00000735
fixed	NA	male	-0.04432	0.01541	-2.877	2482	0.004054	-0.08756	-0.001071
fixed	NA	sibling_count3	-0.004593	0.02309	-0.1989	2047	0.8424	-0.06942	0.06023
fixed	NA	sibling_count4	-0.03224	0.02342	-1.377	1966	0.1688	-0.09797	0.0335
fixed	NA	sibling_count5	-0.005695	0.02477	-0.2299	1839	0.8182	-0.07524	0.06385
ran_pars	mother_pidlink	sd__(Intercept)	0.1675	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3479	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.05	0.3273	3.207	2530	0.001357	0.131	1.968
fixed	NA	birth_order	-0.0005907	0.007493	-0.07884	2399	0.9372	-0.02162	0.02044
fixed	NA	poly(age, 3, raw = TRUE)1	-0.113	0.03627	-3.117	2530	0.001848	-0.2148	-0.01124
fixed	NA	poly(age, 3, raw = TRUE)2	0.004359	0.001286	3.39	2530	0.0007105	0.0007493	0.00797
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004837	0.00001461	-3.31	2530	0.0009453	-0.00008938	-0.000007352
fixed	NA	male	-0.04433	0.01541	-2.877	2481	0.004051	-0.08759	-0.001076
fixed	NA	sibling_count3	-0.004297	0.0234	-0.1836	2064	0.8543	-0.06998	0.06139
fixed	NA	sibling_count4	-0.03166	0.02453	-1.291	2036	0.1969	-0.1005	0.03719
fixed	NA	sibling_count5	-0.004735	0.02761	-0.1715	2046	0.8639	-0.08223	0.07276
ran_pars	mother_pidlink	sd__(Intercept)	0.1675	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3479	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.054	0.3282	3.212	2527	0.001335	0.1329	1.975
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1141	0.03636	-3.139	2527	0.001714	-0.2162	-0.01208
fixed	NA	poly(age, 3, raw = TRUE)2	0.004394	0.001289	3.408	2527	0.0006646	0.0007749	0.008013
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004871	0.00001465	-3.326	2527	0.0008931	-0.00008982	-0.000007603
fixed	NA	male	-0.04453	0.01542	-2.888	2478	0.003913	-0.08782	-0.001246
fixed	NA	sibling_count3	-0.001584	0.02372	-0.0668	2109	0.9467	-0.06817	0.065
fixed	NA	sibling_count4	-0.02968	0.02481	-1.196	2077	0.2317	-0.09933	0.03997
fixed	NA	sibling_count5	-0.002534	0.02777	-0.09124	2064	0.9273	-0.08049	0.07542
fixed	NA	birth_order_nonlinear2	0.01805	0.01822	0.9904	2121	0.3221	-0.03311	0.06921
fixed	NA	birth_order_nonlinear3	-0.01218	0.02252	-0.5409	2207	0.5886	-0.07539	0.05103
fixed	NA	birth_order_nonlinear4	0.004847	0.02955	0.164	2254	0.8697	-0.0781	0.08779
fixed	NA	birth_order_nonlinear5	0.002927	0.04218	0.06938	2178	0.9447	-0.1155	0.1213
ran_pars	mother_pidlink	sd__(Intercept)	0.1676	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.348	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.035	0.3284	3.15	2521	0.001649	0.1128	1.957
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1142	0.03639	-3.138	2521	0.001723	-0.2163	-0.01203
fixed	NA	poly(age, 3, raw = TRUE)2	0.004394	0.00129	3.405	2521	0.0006717	0.0007717	0.008016
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000487	0.00001466	-3.323	2521	0.0009044	-0.00008985	-0.000007557
fixed	NA	male	-0.04493	0.01545	-2.908	2473	0.003673	-0.0883	-0.001556
fixed	NA	count_birth_order2/2	0.08055	0.0351	2.295	2248	0.02183	-0.01798	0.1791
fixed	NA	count_birth_order1/3	0.02443	0.03018	0.8094	2515	0.4184	-0.06028	0.1091
fixed	NA	count_birth_order2/3	0.04417	0.03276	1.348	2521	0.1777	-0.0478	0.1361
fixed	NA	count_birth_order3/3	-0.01421	0.03599	-0.3948	2516	0.693	-0.1152	0.08682
fixed	NA	count_birth_order1/4	0.01002	0.0329	0.3045	2519	0.7608	-0.08234	0.1024
fixed	NA	count_birth_order2/4	-0.0249	0.03426	-0.7267	2520	0.4675	-0.1211	0.07127
fixed	NA	count_birth_order3/4	-0.008878	0.03737	-0.2375	2505	0.8123	-0.1138	0.09603
fixed	NA	count_birth_order4/4	-0.002061	0.03984	-0.05174	2499	0.9587	-0.1139	0.1098
fixed	NA	count_birth_order1/5	0.02277	0.03946	0.5769	2520	0.5641	-0.08801	0.1335
fixed	NA	count_birth_order2/5	0.02039	0.04089	0.4985	2508	0.6182	-0.0944	0.1352
fixed	NA	count_birth_order3/5	0.01907	0.04154	0.4591	2494	0.6462	-0.09754	0.1357
fixed	NA	count_birth_order4/5	0.01981	0.04213	0.4702	2480	0.6383	-0.09846	0.1381
fixed	NA	count_birth_order5/5	0.02095	0.04244	0.4937	2480	0.6215	-0.09817	0.1401
ran_pars	mother_pidlink	sd__(Intercept)	0.1668	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3483	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	2357	2415	-1168	2337	NA	NA	NA
11	2359	2423	-1168	2337	0.006049	1	0.938
14	2363	2445	-1167	2335	1.949	3	0.5831
20	2368	2485	-1164	2328	6.778	6	0.3418

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.218	0.3247	3.753	2759	0.0001783	0.3071	2.13
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1353	0.03606	-3.752	2759	0.0001789	-0.2365	-0.03408
fixed	NA	poly(age, 3, raw = TRUE)2	0.005209	0.001282	4.064	2760	0.00004949	0.001612	0.008807
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005869	0.0000146	-4.021	2759	0.00005948	-0.00009966	-0.00001772
fixed	NA	male	-0.03916	0.01501	-2.609	2716	0.009137	-0.0813	0.002977
fixed	NA	sibling_count3	0.02419	0.02095	1.155	2215	0.2484	-0.03461	0.08299
fixed	NA	sibling_count4	-0.02397	0.02207	-1.086	2073	0.2775	-0.08592	0.03797
fixed	NA	sibling_count5	0.03404	0.02532	1.344	1808	0.179	-0.03704	0.1051
ran_pars	mother_pidlink	sd__(Intercept)	0.1622	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3573	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.22	0.3247	3.756	2758	0.0001759	0.3083	2.131
fixed	NA	birth_order	-0.003094	0.007611	-0.4066	2561	0.6844	-0.02446	0.01827
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1351	0.03607	-3.745	2758	0.0001842	-0.2363	-0.03383
fixed	NA	poly(age, 3, raw = TRUE)2	0.005206	0.001282	4.061	2758	0.00005019	0.001608	0.008804
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005873	0.0000146	-4.023	2759	0.00005891	-0.00009971	-0.00001776
fixed	NA	male	-0.03919	0.01501	-2.61	2714	0.009092	-0.08134	0.002952
fixed	NA	sibling_count3	0.02571	0.02128	1.208	2242	0.2273	-0.03404	0.08545
fixed	NA	sibling_count4	-0.02081	0.0234	-0.8891	2193	0.374	-0.08651	0.04489
fixed	NA	sibling_count5	0.03922	0.02837	1.382	2085	0.167	-0.04043	0.1189
ran_pars	mother_pidlink	sd__(Intercept)	0.1625	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3573	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.224	0.3254	3.762	2755	0.0001718	0.3109	2.138
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1362	0.03613	-3.768	2755	0.0001678	-0.2376	-0.03473
fixed	NA	poly(age, 3, raw = TRUE)2	0.005242	0.001284	4.082	2755	0.00004584	0.001638	0.008847
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005912	0.00001462	-4.043	2756	0.00005421	-0.0001002	-0.00001807
fixed	NA	male	-0.03964	0.01503	-2.638	2712	0.008387	-0.08182	0.00254
fixed	NA	sibling_count3	0.02762	0.02161	1.278	2300	0.2013	-0.03304	0.08827
fixed	NA	sibling_count4	-0.02282	0.0237	-0.9627	2246	0.3358	-0.08935	0.04371
fixed	NA	sibling_count5	0.04276	0.02883	1.483	2139	0.1382	-0.03816	0.1237
fixed	NA	birth_order_nonlinear2	0.005778	0.01769	0.3267	2306	0.744	-0.04388	0.05543
fixed	NA	birth_order_nonlinear3	-0.01319	0.0218	-0.6048	2374	0.5453	-0.07438	0.04801
fixed	NA	birth_order_nonlinear4	0.0128	0.02985	0.4288	2430	0.6681	-0.071	0.0966
fixed	NA	birth_order_nonlinear5	-0.04222	0.04702	-0.8979	2370	0.3693	-0.1742	0.08977
ran_pars	mother_pidlink	sd__(Intercept)	0.1626	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3573	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.215	0.3256	3.732	2749	0.0001938	0.3012	2.129
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1366	0.03616	-3.777	2749	0.0001618	-0.2381	-0.03509
fixed	NA	poly(age, 3, raw = TRUE)2	0.005262	0.001285	4.094	2749	0.00004364	0.001654	0.008869
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005939	0.00001464	-4.057	2750	0.000051	-0.0001005	-0.0000183
fixed	NA	male	-0.0399	0.01505	-2.652	2706	0.008054	-0.08213	0.002336
fixed	NA	count_birth_order2/2	0.04292	0.03156	1.36	2372	0.174	-0.04567	0.1315
fixed	NA	count_birth_order1/3	0.0477	0.0273	1.747	2744	0.08069	-0.02893	0.1243
fixed	NA	count_birth_order2/3	0.04547	0.03031	1.5	2749	0.1337	-0.03962	0.1306
fixed	NA	count_birth_order3/3	0.01206	0.03243	0.3719	2743	0.71	-0.07898	0.1031
fixed	NA	count_birth_order1/4	-0.005346	0.03208	-0.1667	2750	0.8677	-0.09539	0.0847
fixed	NA	count_birth_order2/4	-0.03738	0.03344	-1.118	2745	0.2638	-0.1312	0.05649
fixed	NA	count_birth_order3/4	-0.009675	0.03502	-0.2763	2734	0.7824	-0.108	0.08863
fixed	NA	count_birth_order4/4	0.02324	0.03772	0.6161	2730	0.5379	-0.08265	0.1291
fixed	NA	count_birth_order1/5	0.0641	0.04203	1.525	2748	0.1273	-0.05388	0.1821
fixed	NA	count_birth_order2/5	0.07532	0.04698	1.603	2707	0.109	-0.05657	0.2072
fixed	NA	count_birth_order3/5	0.04924	0.04493	1.096	2710	0.2732	-0.07688	0.1754
fixed	NA	count_birth_order4/5	0.03861	0.04329	0.8917	2714	0.3726	-0.08292	0.1601
fixed	NA	count_birth_order5/5	0.01255	0.04555	0.2754	2707	0.783	-0.1153	0.1404
ran_pars	mother_pidlink	sd__(Intercept)	0.1622	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3576	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	2663	2722	-1322	2643	NA	NA	NA
11	2665	2730	-1321	2643	0.1642	1	0.6853
14	2669	2752	-1321	2641	1.786	3	0.618
20	2676	2795	-1318	2636	4.918	6	0.5544

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Work Category

Category_Casual worker in agriculture

birthorder <- birthorder %>% mutate(outcome = `Category_Casual worker in agriculture`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1194	0.04345	2.748	4366	0.006022	-0.002568	0.2414
fixed	NA	poly(age, 3, raw = TRUE)1	-0.009701	0.003871	-2.506	4224	0.01224	-0.02057	0.001165
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002729	0.0001074	2.542	4068	0.01105	-0.00002842	0.0005743
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002212	0.0000009378	-2.359	3934	0.01838	-0.000004844	0.0000004203
fixed	NA	male	0.003536	0.004449	0.7948	4797	0.4268	-0.008952	0.01602
fixed	NA	sibling_count3	-0.002646	0.006308	-0.4195	3380	0.6749	-0.02035	0.01506
fixed	NA	sibling_count4	0.006909	0.006365	1.085	3103	0.2778	-0.01096	0.02478
fixed	NA	sibling_count5	-0.001435	0.006628	-0.2165	2826	0.8286	-0.02004	0.01717
ran_pars	mother_pidlink	sd__(Intercept)	0.03829	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1482	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1193	0.04346	2.745	4366	0.006072	-0.002687	0.2413
fixed	NA	birth_order	-0.0005024	0.002196	-0.2288	4298	0.819	-0.006666	0.005661
fixed	NA	poly(age, 3, raw = TRUE)1	-0.009627	0.003885	-2.478	4224	0.01324	-0.02053	0.001277
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002711	0.0001077	2.518	4059	0.01184	-0.00003112	0.0005733
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000022	0.0000009394	-2.342	3926	0.01924	-0.000004837	0.000000437
fixed	NA	male	0.003531	0.004449	0.7936	4796	0.4275	-0.008958	0.01602
fixed	NA	sibling_count3	-0.002452	0.006365	-0.3853	3476	0.7001	-0.02032	0.01542
fixed	NA	sibling_count4	0.00732	0.006614	1.107	3491	0.2685	-0.01125	0.02589
fixed	NA	sibling_count5	-0.000781	0.007218	-0.1082	3605	0.9138	-0.02104	0.01948
ran_pars	mother_pidlink	sd__(Intercept)	0.03825	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1482	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1221	0.04357	2.801	4370	0.005113	-0.0002515	0.2444
fixed	NA	poly(age, 3, raw = TRUE)1	-0.009769	0.003885	-2.514	4218	0.01196	-0.02067	0.001137
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002768	0.0001077	2.57	4048	0.0102	-0.00002551	0.0005791
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002264	0.00000094	-2.408	3908	0.01606	-0.000004903	0.0000003746
fixed	NA	male	0.003518	0.00445	0.7906	4793	0.4292	-0.008974	0.01601
fixed	NA	sibling_count3	-0.001917	0.006481	-0.2958	3643	0.7674	-0.02011	0.01627
fixed	NA	sibling_count4	0.005823	0.006736	0.8644	3666	0.3874	-0.01309	0.02473
fixed	NA	sibling_count5	-0.001364	0.007292	-0.1871	3710	0.8516	-0.02183	0.0191
fixed	NA	birth_order_nonlinear2	-0.006773	0.005299	-1.278	4172	0.2012	-0.02165	0.008101
fixed	NA	birth_order_nonlinear3	-0.004748	0.006743	-0.7041	4149	0.4814	-0.02368	0.01418
fixed	NA	birth_order_nonlinear4	0.007102	0.008757	0.8111	4144	0.4174	-0.01748	0.03168
fixed	NA	birth_order_nonlinear5	-0.00871	0.01265	-0.6886	4183	0.4911	-0.04421	0.02679
ran_pars	mother_pidlink	sd__(Intercept)	0.03817	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1482	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1229	0.04363	2.817	4376	0.004877	0.0004131	0.2454
fixed	NA	poly(age, 3, raw = TRUE)1	-0.009585	0.003887	-2.466	4215	0.01371	-0.0205	0.001326
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002733	0.0001077	2.537	4045	0.01121	-0.00002905	0.0005756
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000225	0.00000094	-2.393	3904	0.01674	-0.000004888	0.0000003887
fixed	NA	male	0.003589	0.004451	0.8063	4785	0.4201	-0.008905	0.01608
fixed	NA	count_birth_order2/2	-0.01581	0.009004	-1.756	4070	0.07909	-0.04109	0.009459
fixed	NA	count_birth_order1/3	-0.006721	0.008603	-0.7812	4801	0.4347	-0.03087	0.01743
fixed	NA	count_birth_order2/3	-0.006495	0.009548	-0.6803	4805	0.4963	-0.0333	0.02031
fixed	NA	count_birth_order3/3	-0.01486	0.01051	-1.414	4806	0.1575	-0.04436	0.01464
fixed	NA	count_birth_order1/4	-0.007151	0.009439	-0.7576	4805	0.4487	-0.03365	0.01934
fixed	NA	count_birth_order2/4	-0.002565	0.01013	-0.2533	4806	0.8001	-0.03099	0.02586
fixed	NA	count_birth_order3/4	0.01192	0.01081	1.103	4806	0.2701	-0.01842	0.04226
fixed	NA	count_birth_order4/4	0.006717	0.0115	0.5842	4806	0.5591	-0.02556	0.03899
fixed	NA	count_birth_order1/5	0.002831	0.01073	0.264	4806	0.7918	-0.02727	0.03294
fixed	NA	count_birth_order2/5	-0.01267	0.01139	-1.112	4805	0.2661	-0.04463	0.0193
fixed	NA	count_birth_order3/5	-0.02166	0.01199	-1.807	4805	0.0709	-0.05532	0.012
fixed	NA	count_birth_order4/5	0.005769	0.01262	0.4571	4800	0.6476	-0.02966	0.04119
fixed	NA	count_birth_order5/5	-0.01361	0.01262	-1.079	4804	0.2809	-0.04904	0.02182
ran_pars	mother_pidlink	sd__(Intercept)	0.03829	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1481	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-4415	-4350	2218	-4435	NA	NA	NA
11	-4413	-4342	2218	-4435	0.05262	1	0.8186
14	-4411	-4320	2219	-4439	3.738	3	0.2911
20	-4407	-4278	2224	-4447	8.343	6	0.214

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.03756	0.08345	-0.4501	2760	0.6527	-0.2718	0.1967
fixed	NA	poly(age, 3, raw = TRUE)1	0.007165	0.009243	0.7752	2760	0.4383	-0.01878	0.03311
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003047	0.0003277	-0.9298	2760	0.3525	-0.001225	0.0006152
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003864	0.000003721	1.038	2760	0.2992	-0.000006582	0.00001431
fixed	NA	male	0.004517	0.00393	1.149	2760	0.2505	-0.006516	0.01555
fixed	NA	sibling_count3	-0.005617	0.005383	-1.044	2760	0.2968	-0.02073	0.009493
fixed	NA	sibling_count4	-0.0001364	0.005558	-0.02454	2760	0.9804	-0.01574	0.01546
fixed	NA	sibling_count5	-0.006986	0.006138	-1.138	2760	0.2552	-0.02422	0.01024
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1018	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.0377	0.08347	-0.4517	2759	0.6515	-0.272	0.1966
fixed	NA	birth_order	0.0002319	0.001991	0.1165	2759	0.9073	-0.005357	0.005821
fixed	NA	poly(age, 3, raw = TRUE)1	0.007154	0.009245	0.7738	2759	0.4391	-0.0188	0.03311
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003047	0.0003278	-0.9297	2759	0.3526	-0.001225	0.0006154
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000387	0.000003722	1.04	2759	0.2986	-0.000006579	0.00001432
fixed	NA	male	0.004518	0.003931	1.149	2759	0.2505	-0.006517	0.01555
fixed	NA	sibling_count3	-0.005729	0.005469	-1.048	2759	0.2949	-0.02108	0.009622
fixed	NA	sibling_count4	-0.0003731	0.005919	-0.06304	2759	0.9497	-0.01699	0.01624
fixed	NA	sibling_count5	-0.007385	0.00703	-1.051	2759	0.2935	-0.02712	0.01235
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1018	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.03042	0.08362	-0.3638	2756	0.716	-0.2652	0.2043
fixed	NA	poly(age, 3, raw = TRUE)1	0.006443	0.00926	0.6957	2756	0.4867	-0.01955	0.03244
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002796	0.0003283	-0.8515	2756	0.3946	-0.001201	0.000642
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003596	0.000003728	0.9646	2756	0.3348	-0.000006869	0.00001406
fixed	NA	male	0.004352	0.003933	1.107	2756	0.2685	-0.006687	0.01539
fixed	NA	sibling_count3	-0.004866	0.00556	-0.8753	2756	0.3815	-0.02047	0.01074
fixed	NA	sibling_count4	-0.001313	0.006005	-0.2187	2756	0.8269	-0.01817	0.01554
fixed	NA	sibling_count5	-0.007485	0.007125	-1.051	2756	0.2936	-0.02749	0.01252
fixed	NA	birth_order_nonlinear2	-0.002069	0.004788	-0.4321	2756	0.6657	-0.01551	0.01137
fixed	NA	birth_order_nonlinear3	-0.003443	0.005834	-0.5901	2756	0.5552	-0.01982	0.01293
fixed	NA	birth_order_nonlinear4	0.008968	0.007732	1.16	2756	0.2462	-0.01274	0.03067
fixed	NA	birth_order_nonlinear5	-0.006203	0.01189	-0.5216	2756	0.602	-0.03958	0.02718
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1018	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.03194	0.08369	-0.3817	2750	0.7027	-0.2669	0.203
fixed	NA	poly(age, 3, raw = TRUE)1	0.006732	0.009267	0.7265	2750	0.4676	-0.01928	0.03275
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002877	0.0003286	-0.8755	2750	0.3814	-0.00121	0.0006347
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000366	0.000003732	0.9809	2750	0.3267	-0.000006814	0.00001413
fixed	NA	male	0.004362	0.003939	1.107	2750	0.2682	-0.006694	0.01542
fixed	NA	count_birth_order2/2	-0.006758	0.008685	-0.7781	2750	0.4366	-0.03114	0.01762
fixed	NA	count_birth_order1/3	-0.01106	0.007223	-1.531	2750	0.126	-0.03133	0.00922
fixed	NA	count_birth_order2/3	-0.008417	0.008029	-1.048	2750	0.2945	-0.03095	0.01412
fixed	NA	count_birth_order3/3	-0.001227	0.008694	-0.1411	2750	0.8878	-0.02563	0.02318
fixed	NA	count_birth_order1/4	0.001133	0.008323	0.1362	2750	0.8917	-0.02223	0.0245
fixed	NA	count_birth_order2/4	-0.0005705	0.008751	-0.06519	2750	0.948	-0.02513	0.02399
fixed	NA	count_birth_order3/4	-0.01496	0.009184	-1.628	2750	0.1035	-0.04074	0.01082
fixed	NA	count_birth_order4/4	0.004138	0.00973	0.4253	2750	0.6707	-0.02318	0.03145
fixed	NA	count_birth_order1/5	-0.00724	0.01095	-0.6611	2750	0.5086	-0.03798	0.0235
fixed	NA	count_birth_order2/5	-0.01384	0.01191	-1.162	2750	0.2454	-0.04727	0.01959
fixed	NA	count_birth_order3/5	-0.01458	0.01115	-1.308	2750	0.191	-0.04587	0.01671
fixed	NA	count_birth_order4/5	0.002521	0.01083	0.2327	2750	0.816	-0.02789	0.03293
fixed	NA	count_birth_order5/5	-0.01524	0.01136	-1.341	2750	0.18	-0.04713	0.01666
ran_pars	mother_pidlink	sd__(Intercept)	0.00000000181	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1019	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-4780	-4721	2400	-4800	NA	NA	NA
11	-4778	-4713	2400	-4800	0.01361	1	0.9071
14	-4775	-4692	2402	-4803	3.035	3	0.3862
20	-4768	-4650	2404	-4808	4.873	6	0.5601

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.03705	0.0903	-0.4103	2531	0.6816	-0.2905	0.2164
fixed	NA	poly(age, 3, raw = TRUE)1	0.007227	0.01001	0.7221	2531	0.4703	-0.02087	0.03532
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003092	0.0003548	-0.8713	2531	0.3837	-0.001305	0.0006869
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003947	0.000004029	0.9797	2531	0.3273	-0.000007363	0.00001526
fixed	NA	male	0.004916	0.004288	1.146	2531	0.2517	-0.00712	0.01695
fixed	NA	sibling_count3	-0.003734	0.00617	-0.6052	2531	0.5451	-0.02105	0.01359
fixed	NA	sibling_count4	-0.003119	0.006228	-0.5008	2531	0.6165	-0.0206	0.01436
fixed	NA	sibling_count5	-0.005237	0.006539	-0.8009	2531	0.4233	-0.02359	0.01312
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1063	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.0374	0.09035	-0.4139	2530	0.679	-0.291	0.2162
fixed	NA	birth_order	0.0002983	0.002103	0.1419	2530	0.8872	-0.005604	0.006201
fixed	NA	poly(age, 3, raw = TRUE)1	0.007227	0.01001	0.722	2530	0.4704	-0.02087	0.03533
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003096	0.0003549	-0.8722	2530	0.3832	-0.001306	0.0006867
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003958	0.000004031	0.982	2530	0.3262	-0.000007357	0.00001527
fixed	NA	male	0.004927	0.004289	1.149	2530	0.2508	-0.007114	0.01697
fixed	NA	sibling_count3	-0.003881	0.006257	-0.6202	2530	0.5352	-0.02145	0.01368
fixed	NA	sibling_count4	-0.003405	0.006546	-0.5201	2530	0.603	-0.02178	0.01497
fixed	NA	sibling_count5	-0.005717	0.007363	-0.7765	2530	0.4376	-0.02638	0.01495
ran_pars	mother_pidlink	sd__(Intercept)	0.000000001836	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1063	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.0304	0.09053	-0.3358	2527	0.737	-0.2845	0.2237
fixed	NA	poly(age, 3, raw = TRUE)1	0.006574	0.01003	0.6553	2527	0.5124	-0.02159	0.03473
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002858	0.0003557	-0.8035	2527	0.4218	-0.001284	0.0007126
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003693	0.000004039	0.9144	2527	0.3606	-0.000007645	0.00001503
fixed	NA	male	0.004788	0.004292	1.116	2527	0.2647	-0.00726	0.01684
fixed	NA	sibling_count3	-0.002776	0.006358	-0.4366	2527	0.6624	-0.02062	0.01507
fixed	NA	sibling_count4	-0.003536	0.006636	-0.5328	2527	0.5942	-0.02216	0.01509
fixed	NA	sibling_count5	-0.006162	0.007414	-0.8311	2527	0.406	-0.02697	0.01465
fixed	NA	birth_order_nonlinear2	-0.002972	0.005195	-0.5722	2527	0.5673	-0.01755	0.01161
fixed	NA	birth_order_nonlinear3	-0.004341	0.006384	-0.6799	2527	0.4967	-0.02226	0.01358
fixed	NA	birth_order_nonlinear4	0.006187	0.00835	0.741	2527	0.4588	-0.01725	0.02963
fixed	NA	birth_order_nonlinear5	0.0006858	0.01196	0.05733	2527	0.9543	-0.03289	0.03426
ran_pars	mother_pidlink	sd__(Intercept)	0.000000001149	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1064	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.03185	0.09066	-0.3513	2521	0.7254	-0.2863	0.2226
fixed	NA	poly(age, 3, raw = TRUE)1	0.006789	0.01005	0.6759	2521	0.4992	-0.02141	0.03499
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002919	0.0003562	-0.8196	2521	0.4125	-0.001292	0.0007079
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003742	0.000004045	0.9252	2521	0.3549	-0.000007611	0.0000151
fixed	NA	male	0.00488	0.004303	1.134	2521	0.2568	-0.007198	0.01696
fixed	NA	count_birth_order2/2	-0.005527	0.009966	-0.5546	2521	0.5792	-0.0335	0.02245
fixed	NA	count_birth_order1/3	-0.007423	0.008344	-0.8895	2521	0.3738	-0.03085	0.016
fixed	NA	count_birth_order2/3	-0.00799	0.009079	-0.88	2521	0.3789	-0.03347	0.0175
fixed	NA	count_birth_order3/3	0.0009479	0.009994	0.09485	2521	0.9244	-0.02711	0.029
fixed	NA	count_birth_order1/4	0.0007023	0.009102	0.07716	2521	0.9385	-0.02485	0.02625
fixed	NA	count_birth_order2/4	-0.006345	0.009498	-0.668	2521	0.5042	-0.03301	0.02032
fixed	NA	count_birth_order3/4	-0.01548	0.01039	-1.49	2521	0.1363	-0.04465	0.01368
fixed	NA	count_birth_order4/4	-0.0009842	0.01108	-0.08884	2521	0.9292	-0.03208	0.03011
fixed	NA	count_birth_order1/5	-0.009076	0.01093	-0.83	2521	0.4066	-0.03977	0.02162
fixed	NA	count_birth_order2/5	-0.006608	0.01136	-0.5819	2521	0.5607	-0.03849	0.02527
fixed	NA	count_birth_order3/5	-0.01542	0.01156	-1.334	2521	0.1823	-0.04786	0.01702
fixed	NA	count_birth_order4/5	0.0024	0.01173	0.2045	2521	0.838	-0.03054	0.03534
fixed	NA	count_birth_order5/5	-0.006338	0.01183	-0.5359	2521	0.5921	-0.03953	0.02686
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1064	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-4165	-4106	2092	-4185	NA	NA	NA
11	-4163	-4098	2092	-4185	0.02019	1	0.887
14	-4158	-4077	2093	-4186	1.75	3	0.6258
20	-4150	-4033	2095	-4190	3.425	6	0.7539

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.09021	0.08585	-1.051	2758	0.2934	-0.3312	0.1508
fixed	NA	poly(age, 3, raw = TRUE)1	0.01283	0.009534	1.346	2759	0.1784	-0.01393	0.0396
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005036	0.0003389	-1.486	2759	0.1374	-0.001455	0.0004477
fixed	NA	poly(age, 3, raw = TRUE)3	0.000006072	0.000003859	1.573	2759	0.1158	-0.000004761	0.0000169
fixed	NA	male	0.004031	0.00397	1.015	2687	0.31	-0.007112	0.01517
fixed	NA	sibling_count3	-0.003783	0.005536	-0.6832	1937	0.4945	-0.01932	0.01176
fixed	NA	sibling_count4	0.002987	0.005832	0.5122	1755	0.6086	-0.01338	0.01936
fixed	NA	sibling_count5	0.0001261	0.006691	0.01884	1443	0.985	-0.01866	0.01891
ran_pars	mother_pidlink	sd__(Intercept)	0.0426	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.0946	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.0903	0.08587	-1.052	2757	0.2931	-0.3313	0.1507
fixed	NA	birth_order	0.000237	0.002013	0.1177	2439	0.9063	-0.005414	0.005888
fixed	NA	poly(age, 3, raw = TRUE)1	0.01281	0.009537	1.344	2758	0.1792	-0.01396	0.03958
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005033	0.000339	-1.485	2758	0.1377	-0.001455	0.0004482
fixed	NA	poly(age, 3, raw = TRUE)3	0.000006075	0.00000386	1.574	2758	0.1157	-0.00000476	0.00001691
fixed	NA	male	0.004033	0.003971	1.016	2686	0.3099	-0.007113	0.01518
fixed	NA	sibling_count3	-0.003899	0.005625	-0.6931	1975	0.4883	-0.01969	0.01189
fixed	NA	sibling_count4	0.002745	0.006185	0.4438	1909	0.6572	-0.01462	0.02011
fixed	NA	sibling_count5	-0.0002713	0.007497	-0.03619	1770	0.9711	-0.02132	0.02077
ran_pars	mother_pidlink	sd__(Intercept)	0.04257	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.09464	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.08387	0.08599	-0.9754	2753	0.3295	-0.3252	0.1575
fixed	NA	poly(age, 3, raw = TRUE)1	0.01218	0.009549	1.275	2754	0.2023	-0.01463	0.03898
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0004812	0.0003394	-1.418	2754	0.1563	-0.001434	0.0004714
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000584	0.000003864	1.511	2755	0.1309	-0.000005008	0.00001669
fixed	NA	male	0.00386	0.003973	0.9714	2688	0.3314	-0.007293	0.01501
fixed	NA	sibling_count3	-0.003168	0.005703	-0.5555	2052	0.5786	-0.01918	0.01284
fixed	NA	sibling_count4	0.001371	0.006254	0.2192	1975	0.8265	-0.01618	0.01893
fixed	NA	sibling_count5	0.0000704	0.007605	0.009256	1830	0.9926	-0.02128	0.02142
fixed	NA	birth_order_nonlinear2	-0.001232	0.004682	-0.2631	2069	0.7925	-0.01437	0.01191
fixed	NA	birth_order_nonlinear3	-0.002785	0.005769	-0.4827	2167	0.6294	-0.01898	0.01341
fixed	NA	birth_order_nonlinear4	0.01128	0.0079	1.428	2250	0.1534	-0.01089	0.03346
fixed	NA	birth_order_nonlinear5	-0.01121	0.01244	-0.9008	2165	0.3678	-0.04614	0.02372
ran_pars	mother_pidlink	sd__(Intercept)	0.04195	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.09485	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.08567	0.08604	-0.9957	2747	0.3195	-0.3272	0.1558
fixed	NA	poly(age, 3, raw = TRUE)1	0.01254	0.009555	1.312	2748	0.1895	-0.01428	0.03936
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0004935	0.0003396	-1.453	2749	0.1463	-0.001447	0.0004598
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005969	0.000003868	1.543	2749	0.1229	-0.000004889	0.00001683
fixed	NA	male	0.00391	0.003977	0.9831	2680	0.3257	-0.007255	0.01507
fixed	NA	count_birth_order2/2	-0.005724	0.008349	-0.6857	2156	0.493	-0.02916	0.01771
fixed	NA	count_birth_order1/3	-0.008734	0.007213	-1.211	2741	0.226	-0.02898	0.01151
fixed	NA	count_birth_order2/3	-0.00658	0.008011	-0.8214	2748	0.4115	-0.02907	0.01591
fixed	NA	count_birth_order3/3	0.001169	0.008572	0.1364	2738	0.8915	-0.02289	0.02523
fixed	NA	count_birth_order1/4	0.005607	0.008477	0.6614	2750	0.5084	-0.01819	0.0294
fixed	NA	count_birth_order2/4	0.002235	0.008838	0.2529	2742	0.8004	-0.02257	0.02704
fixed	NA	count_birth_order3/4	-0.01064	0.009256	-1.15	2724	0.2502	-0.03663	0.01534
fixed	NA	count_birth_order4/4	0.006129	0.009971	0.6147	2717	0.5388	-0.02186	0.03412
fixed	NA	count_birth_order1/5	-0.004282	0.01111	-0.3855	2746	0.6999	-0.03546	0.0269
fixed	NA	count_birth_order2/5	-0.0007552	0.01242	-0.06081	2681	0.9515	-0.03562	0.03411
fixed	NA	count_birth_order3/5	-0.00937	0.01188	-0.7889	2685	0.4302	-0.04271	0.02397
fixed	NA	count_birth_order4/5	0.01664	0.01144	1.454	2691	0.1462	-0.01549	0.04876
fixed	NA	count_birth_order5/5	-0.01257	0.01204	-1.043	2680	0.2968	-0.04637	0.02124
ran_pars	mother_pidlink	sd__(Intercept)	0.04206	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.09482	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-4701	-4642	2361	-4721	NA	NA	NA
11	-4699	-4634	2361	-4721	0.01415	1	0.9053
14	-4697	-4614	2363	-4725	4.415	3	0.22
20	-4691	-4573	2366	-4731	5.766	6	0.4499

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Category_Casual worker not in agriculture

birthorder <- birthorder %>% mutate(outcome = `Category_Casual worker not in agriculture`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.304	0.07921	3.838	4453	0.0001256	0.08169	0.5264
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02036	0.007068	-2.88	4340	0.003998	-0.0402	-0.0005148
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004827	0.0001963	2.458	4206	0.01399	-0.00006844	0.001034
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003481	0.000001717	-2.027	4085	0.04275	-0.000008302	0.00000134
fixed	NA	male	0.06724	0.00801	8.394	4744	6.134e-17	0.04475	0.08972
fixed	NA	sibling_count3	0.002986	0.01163	0.2568	3381	0.7973	-0.02965	0.03562
fixed	NA	sibling_count4	-0.00636	0.01176	-0.5408	3166	0.5887	-0.03937	0.02665
fixed	NA	sibling_count5	-0.0005289	0.01228	-0.04307	2937	0.9656	-0.035	0.03394
ran_pars	mother_pidlink	sd__(Intercept)	0.1018	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2578	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3047	0.07921	3.847	4452	0.0001212	0.08238	0.5271
fixed	NA	birth_order	0.003714	0.003919	0.9476	4170	0.3434	-0.007288	0.01471
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02091	0.007092	-2.949	4340	0.003209	-0.04082	-0.001004
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004968	0.0001969	2.523	4197	0.01167	-0.00005588	0.001049
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003576	0.00000172	-2.079	4077	0.03769	-0.000008405	0.000001253
fixed	NA	male	0.06727	0.00801	8.398	4743	5.924e-17	0.04479	0.08976
fixed	NA	sibling_count3	0.001585	0.01172	0.1352	3471	0.8924	-0.03131	0.03448
fixed	NA	sibling_count4	-0.009337	0.01217	-0.767	3526	0.4431	-0.04351	0.02483
fixed	NA	sibling_count5	-0.005293	0.01327	-0.3989	3658	0.69	-0.04254	0.03195
ran_pars	mother_pidlink	sd__(Intercept)	0.1017	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2578	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3076	0.07944	3.873	4455	0.0001092	0.08465	0.5306
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02093	0.007094	-2.95	4332	0.003199	-0.04084	-0.001012
fixed	NA	poly(age, 3, raw = TRUE)2	0.000494	0.000197	2.508	4184	0.01219	-0.00005899	0.001047
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003523	0.000001722	-2.046	4056	0.0408	-0.000008357	0.00000131
fixed	NA	male	0.06714	0.008015	8.377	4741	7.089e-17	0.04464	0.08964
fixed	NA	sibling_count3	-0.0001352	0.01191	-0.01135	3626	0.9909	-0.03357	0.0333
fixed	NA	sibling_count4	-0.01053	0.01238	-0.8511	3687	0.3948	-0.04527	0.02421
fixed	NA	sibling_count5	-0.003783	0.01339	-0.2825	3755	0.7776	-0.04137	0.0338
fixed	NA	birth_order_nonlinear2	0.009483	0.009451	1.003	4087	0.3157	-0.01705	0.03601
fixed	NA	birth_order_nonlinear3	0.01615	0.01202	1.343	4013	0.1792	-0.01759	0.04989
fixed	NA	birth_order_nonlinear4	0.01101	0.01561	0.7055	3968	0.4806	-0.0328	0.05482
fixed	NA	birth_order_nonlinear5	0.00158	0.02255	0.07007	3979	0.9441	-0.06171	0.06487
ran_pars	mother_pidlink	sd__(Intercept)	0.1013	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.258	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3013	0.07955	3.787	4460	0.0001544	0.07797	0.5246
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02035	0.007099	-2.866	4330	0.004177	-0.04027	-0.0004183
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004822	0.0001971	2.447	4181	0.01444	-0.00007094	0.001035
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003464	0.000001722	-2.011	4053	0.04434	-0.000008299	0.00000137
fixed	NA	male	0.06747	0.008017	8.415	4733	5.126e-17	0.04496	0.08997
fixed	NA	count_birth_order2/2	0.005435	0.01605	0.3386	4038	0.7349	-0.03962	0.05049
fixed	NA	count_birth_order1/3	0.0087	0.01556	0.5591	4791	0.5762	-0.03499	0.05239
fixed	NA	count_birth_order2/3	0.008848	0.01726	0.5126	4804	0.6082	-0.0396	0.05729
fixed	NA	count_birth_order3/3	-0.006577	0.01899	-0.3464	4806	0.7291	-0.05988	0.04672
fixed	NA	count_birth_order1/4	-0.02392	0.01706	-1.402	4804	0.1609	-0.07181	0.02397
fixed	NA	count_birth_order2/4	0.008356	0.0183	0.4567	4806	0.6479	-0.043	0.05972
fixed	NA	count_birth_order3/4	0.01317	0.01952	0.6746	4804	0.5	-0.04162	0.06795
fixed	NA	count_birth_order4/4	-0.007139	0.02076	-0.3438	4802	0.731	-0.06542	0.05115
fixed	NA	count_birth_order1/5	-0.01235	0.01937	-0.6375	4804	0.5238	-0.06671	0.04202
fixed	NA	count_birth_order2/5	-0.009084	0.02056	-0.4419	4800	0.6586	-0.06678	0.04862
fixed	NA	count_birth_order3/5	0.0283	0.02164	1.308	4794	0.191	-0.03244	0.08903
fixed	NA	count_birth_order4/5	0.01301	0.02276	0.5718	4771	0.5675	-0.05086	0.07688
fixed	NA	count_birth_order5/5	-0.003641	0.02277	-0.1599	4788	0.873	-0.06756	0.06028
ran_pars	mother_pidlink	sd__(Intercept)	0.1015	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2579	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	1287	1352	-633.7	1267	NA	NA	NA
11	1288	1360	-633.2	1266	0.8999	1	0.3428
14	1293	1384	-632.5	1265	1.379	3	0.7104
20	1299	1428	-629.4	1259	6.29	6	0.3915

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6334	0.2145	2.952	2750	0.003182	0.03115	1.236
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0538	0.02377	-2.264	2749	0.02367	-0.1205	0.01291
fixed	NA	poly(age, 3, raw = TRUE)2	0.00159	0.0008428	1.887	2748	0.05927	-0.0007755	0.003956
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001566	0.000009572	-1.636	2746	0.1019	-0.00004253	0.00001121
fixed	NA	male	0.05029	0.01007	4.993	2749	0.0000006322	0.02201	0.07856
fixed	NA	sibling_count3	-0.005766	0.01403	-0.4111	2122	0.6811	-0.04514	0.03361
fixed	NA	sibling_count4	0.008109	0.01453	0.558	1931	0.5769	-0.03268	0.0489
fixed	NA	sibling_count5	-0.01658	0.01614	-1.028	1654	0.3042	-0.06187	0.02871
ran_pars	mother_pidlink	sd__(Intercept)	0.0734	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2509	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6331	0.2146	2.95	2749	0.003205	0.03068	1.235
fixed	NA	birth_order	0.0006341	0.005075	0.125	2610	0.9006	-0.01361	0.01488
fixed	NA	poly(age, 3, raw = TRUE)1	-0.05384	0.02377	-2.265	2748	0.02361	-0.1206	0.01289
fixed	NA	poly(age, 3, raw = TRUE)2	0.001591	0.000843	1.887	2747	0.05926	-0.0007756	0.003957
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001565	0.000009575	-1.634	2745	0.1023	-0.00004252	0.00001123
fixed	NA	male	0.05029	0.01007	4.992	2748	0.0000006345	0.02201	0.07856
fixed	NA	sibling_count3	-0.006071	0.01424	-0.4263	2157	0.6699	-0.04605	0.0339
fixed	NA	sibling_count4	0.007458	0.01544	0.483	2070	0.6291	-0.03588	0.0508
fixed	NA	sibling_count5	-0.01768	0.01836	-0.9627	2003	0.3358	-0.06922	0.03387
ran_pars	mother_pidlink	sd__(Intercept)	0.07335	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.251	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6346	0.2151	2.951	2745	0.003199	0.03087	1.238
fixed	NA	poly(age, 3, raw = TRUE)1	-0.05422	0.02382	-2.276	2745	0.02291	-0.1211	0.01265
fixed	NA	poly(age, 3, raw = TRUE)2	0.001602	0.0008447	1.897	2744	0.05797	-0.0007689	0.003973
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001576	0.000009592	-1.643	2742	0.1006	-0.00004268	0.00001117
fixed	NA	male	0.05021	0.01008	4.98	2745	0.0000006752	0.02191	0.07851
fixed	NA	sibling_count3	-0.004761	0.01447	-0.3291	2226	0.7421	-0.04537	0.03585
fixed	NA	sibling_count4	0.008754	0.01565	0.5593	2134	0.576	-0.03518	0.05269
fixed	NA	sibling_count5	-0.01629	0.01861	-0.8756	2049	0.3813	-0.06852	0.03594
fixed	NA	birth_order_nonlinear2	0.01022	0.01214	0.842	2330	0.3999	-0.02386	0.0443
fixed	NA	birth_order_nonlinear3	-0.003476	0.01482	-0.2345	2415	0.8146	-0.04507	0.03812
fixed	NA	birth_order_nonlinear4	0.003818	0.01967	0.1941	2499	0.8461	-0.05141	0.05904
fixed	NA	birth_order_nonlinear5	0.005898	0.03023	0.1951	2442	0.8453	-0.07896	0.09076
ran_pars	mother_pidlink	sd__(Intercept)	0.07342	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.251	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6485	0.2153	3.013	2739	0.002614	0.04426	1.253
fixed	NA	poly(age, 3, raw = TRUE)1	-0.05463	0.02384	-2.292	2739	0.022	-0.1215	0.01229
fixed	NA	poly(age, 3, raw = TRUE)2	0.001617	0.0008454	1.912	2738	0.05593	-0.0007563	0.00399
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001592	0.000009602	-1.658	2737	0.09749	-0.00004287	0.00001104
fixed	NA	male	0.05061	0.0101	5.012	2739	0.0000005732	0.02226	0.07895
fixed	NA	count_birth_order2/2	-0.02243	0.02203	-1.018	2367	0.3086	-0.08428	0.03941
fixed	NA	count_birth_order1/3	-0.0172	0.01854	-0.9279	2748	0.3535	-0.06925	0.03484
fixed	NA	count_birth_order2/3	0.002536	0.0206	0.1231	2750	0.902	-0.05528	0.06036
fixed	NA	count_birth_order3/3	-0.02527	0.02229	-1.133	2747	0.2572	-0.08785	0.03731
fixed	NA	count_birth_order1/4	-0.01996	0.02137	-0.9343	2749	0.3502	-0.07994	0.04001
fixed	NA	count_birth_order2/4	0.01785	0.02245	0.7951	2749	0.4267	-0.04517	0.08086
fixed	NA	count_birth_order3/4	0.003941	0.02355	0.1674	2744	0.8671	-0.06215	0.07004
fixed	NA	count_birth_order4/4	0.007373	0.02495	0.2955	2744	0.7676	-0.06266	0.07741
fixed	NA	count_birth_order1/5	-0.02195	0.0281	-0.7809	2750	0.4349	-0.1008	0.05694
fixed	NA	count_birth_order2/5	-0.01095	0.03054	-0.3585	2741	0.72	-0.09667	0.07477
fixed	NA	count_birth_order3/5	-0.03344	0.02858	-1.17	2741	0.2421	-0.1137	0.04678
fixed	NA	count_birth_order4/5	-0.03001	0.02777	-1.081	2738	0.2799	-0.108	0.04794
fixed	NA	count_birth_order5/5	-0.02109	0.02912	-0.7242	2734	0.469	-0.1028	0.06064
ran_pars	mother_pidlink	sd__(Intercept)	0.07333	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2511	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	434.2	493.4	-207.1	414.2	NA	NA	NA
11	436.2	501.4	-207.1	414.2	0.01566	1	0.9004
14	441.1	524.1	-206.6	413.1	1.053	3	0.7884
20	448.6	567.1	-204.3	408.6	4.535	6	0.6047

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.5885	0.2234	2.635	2526	0.008467	-0.03845	1.215
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04894	0.02476	-1.977	2526	0.0482	-0.1184	0.02056
fixed	NA	poly(age, 3, raw = TRUE)2	0.001414	0.000878	1.611	2525	0.1074	-0.00105	0.003879
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001364	0.000009972	-1.368	2524	0.1715	-0.00004163	0.00001435
fixed	NA	male	0.05694	0.01057	5.388	2517	0.00000007771	0.02728	0.08661
fixed	NA	sibling_count3	-0.01313	0.01549	-0.8472	1997	0.397	-0.05662	0.03036
fixed	NA	sibling_count4	-0.005705	0.01568	-0.3639	1886	0.7159	-0.04971	0.0383
fixed	NA	sibling_count5	0.008204	0.01653	0.4963	1711	0.6197	-0.0382	0.0546
ran_pars	mother_pidlink	sd__(Intercept)	0.07984	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2503	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.5916	0.2234	2.648	2525	0.008156	-0.03562	1.219
fixed	NA	birth_order	-0.002964	0.005159	-0.5745	2436	0.5657	-0.01745	0.01152
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04889	0.02476	-1.974	2525	0.04846	-0.1184	0.02062
fixed	NA	poly(age, 3, raw = TRUE)2	0.001416	0.0008781	1.613	2524	0.1069	-0.001049	0.003881
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001373	0.000009975	-1.376	2523	0.1689	-0.00004173	0.00001427
fixed	NA	male	0.05685	0.01057	5.378	2516	0.00000008231	0.02718	0.08652
fixed	NA	sibling_count3	-0.01166	0.0157	-0.7424	2018	0.4579	-0.05574	0.03242
fixed	NA	sibling_count4	-0.002849	0.01645	-0.1732	1970	0.8625	-0.04902	0.04332
fixed	NA	sibling_count5	0.01299	0.01851	0.7017	1954	0.4829	-0.03897	0.06495
ran_pars	mother_pidlink	sd__(Intercept)	0.07984	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2503	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.5829	0.224	2.603	2520	0.009306	-0.04578	1.212
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04867	0.02482	-1.961	2520	0.04999	-0.1183	0.021
fixed	NA	poly(age, 3, raw = TRUE)2	0.001406	0.0008802	1.597	2520	0.1104	-0.001065	0.003876
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001359	0.000009997	-1.359	2519	0.1742	-0.00004165	0.00001447
fixed	NA	male	0.05688	0.01058	5.377	2513	0.00000008265	0.02718	0.08657
fixed	NA	sibling_count3	-0.0115	0.01594	-0.7215	2069	0.4707	-0.05624	0.03324
fixed	NA	sibling_count4	-0.002333	0.01666	-0.1401	2018	0.8886	-0.04909	0.04443
fixed	NA	sibling_count5	0.01508	0.01863	0.8094	1976	0.4184	-0.03722	0.06739
fixed	NA	birth_order_nonlinear2	0.01122	0.01265	0.8872	2145	0.3751	-0.02428	0.04672
fixed	NA	birth_order_nonlinear3	-0.005925	0.01559	-0.3801	2258	0.7039	-0.04968	0.03783
fixed	NA	birth_order_nonlinear4	-0.007512	0.02043	-0.3678	2323	0.7131	-0.06485	0.04983
fixed	NA	birth_order_nonlinear5	-0.01462	0.02921	-0.5003	2253	0.6169	-0.09662	0.06739
ran_pars	mother_pidlink	sd__(Intercept)	0.08006	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2503	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.5927	0.2243	2.643	2514	0.008276	-0.03686	1.222
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04877	0.02485	-1.963	2514	0.0498	-0.1185	0.02098
fixed	NA	poly(age, 3, raw = TRUE)2	0.001409	0.0008813	1.598	2513	0.1101	-0.001065	0.003882
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000136	0.00001001	-1.359	2512	0.1743	-0.0000417	0.0000145
fixed	NA	male	0.05703	0.01061	5.377	2508	0.00000008251	0.02726	0.0868
fixed	NA	count_birth_order2/2	-0.01636	0.02431	-0.6728	2233	0.5012	-0.08459	0.05188
fixed	NA	count_birth_order1/3	-0.02062	0.0206	-1.001	2519	0.317	-0.07844	0.03721
fixed	NA	count_birth_order2/3	-0.002162	0.0224	-0.09651	2521	0.9231	-0.06504	0.06072
fixed	NA	count_birth_order3/3	-0.03625	0.02464	-1.471	2518	0.1414	-0.1054	0.03292
fixed	NA	count_birth_order1/4	-0.0266	0.02247	-1.184	2520	0.2367	-0.08968	0.03648
fixed	NA	count_birth_order2/4	0.007569	0.02343	0.323	2521	0.7467	-0.05821	0.07335
fixed	NA	count_birth_order3/4	-0.01562	0.02561	-0.6097	2515	0.5421	-0.08751	0.05628
fixed	NA	count_birth_order4/4	-0.005454	0.02731	-0.1997	2513	0.8417	-0.08211	0.0712
fixed	NA	count_birth_order1/5	0.008708	0.02699	0.3226	2521	0.747	-0.06706	0.08447
fixed	NA	count_birth_order2/5	0.01577	0.02801	0.5628	2518	0.5736	-0.06286	0.0944
fixed	NA	count_birth_order3/5	0.01232	0.02849	0.4324	2512	0.6655	-0.06765	0.09228
fixed	NA	count_birth_order4/5	-0.01694	0.02891	-0.5858	2506	0.558	-0.0981	0.06422
fixed	NA	count_birth_order5/5	-0.008884	0.02913	-0.305	2503	0.7604	-0.09065	0.07288
ran_pars	mother_pidlink	sd__(Intercept)	0.07844	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2509	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	422.4	480.8	-201.2	402.4	NA	NA	NA
11	424.1	488.3	-201	402.1	0.331	1	0.5651
14	428.5	510.3	-200.3	400.5	1.551	3	0.6706
20	436.8	553.6	-198.4	396.8	3.72	6	0.7145

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6357	0.2163	2.939	2746	0.003324	0.02847	1.243
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0548	0.02403	-2.281	2746	0.02264	-0.1223	0.01265
fixed	NA	poly(age, 3, raw = TRUE)2	0.001642	0.000854	1.922	2744	0.0547	-0.0007558	0.004039
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001622	0.000009725	-1.668	2742	0.09545	-0.00004352	0.00001108
fixed	NA	male	0.05342	0.01006	5.312	2750	0.0000001171	0.02519	0.08165
fixed	NA	sibling_count3	-0.008121	0.01371	-0.5924	2144	0.5537	-0.0466	0.03036
fixed	NA	sibling_count4	0.001207	0.01439	0.08388	1946	0.9332	-0.03919	0.0416
fixed	NA	sibling_count5	-0.02306	0.0164	-1.406	1591	0.1599	-0.0691	0.02298
ran_pars	mother_pidlink	sd__(Intercept)	0.07058	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2512	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6355	0.2164	2.936	2746	0.003347	0.02801	1.243
fixed	NA	birth_order	0.0005298	0.005132	0.1032	2602	0.9178	-0.01388	0.01494
fixed	NA	poly(age, 3, raw = TRUE)1	-0.05484	0.02403	-2.282	2744	0.02259	-0.1223	0.01263
fixed	NA	poly(age, 3, raw = TRUE)2	0.001642	0.0008542	1.922	2743	0.05471	-0.000756	0.00404
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001621	0.000009727	-1.666	2741	0.09573	-0.00004351	0.00001109
fixed	NA	male	0.05342	0.01006	5.312	2749	0.0000001174	0.02519	0.08166
fixed	NA	sibling_count3	-0.008379	0.01394	-0.6012	2176	0.5478	-0.0475	0.03074
fixed	NA	sibling_count4	0.000669	0.0153	0.04371	2089	0.9651	-0.04229	0.04363
fixed	NA	sibling_count5	-0.02394	0.0185	-1.294	1913	0.1957	-0.07586	0.02798
ran_pars	mother_pidlink	sd__(Intercept)	0.07055	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2513	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6307	0.2168	2.909	2741	0.003657	0.02208	1.239
fixed	NA	poly(age, 3, raw = TRUE)1	-0.05457	0.02408	-2.267	2741	0.0235	-0.1222	0.01301
fixed	NA	poly(age, 3, raw = TRUE)2	0.001631	0.0008558	1.906	2739	0.05676	-0.0007711	0.004033
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001609	0.000009744	-1.651	2738	0.09882	-0.00004344	0.00001126
fixed	NA	male	0.05339	0.01007	5.303	2747	0.0000001231	0.02513	0.08165
fixed	NA	sibling_count3	-0.008208	0.01417	-0.5793	2244	0.5624	-0.04798	0.03156
fixed	NA	sibling_count4	0.002095	0.01552	0.135	2152	0.8926	-0.04146	0.04565
fixed	NA	sibling_count5	-0.02175	0.01881	-1.156	1969	0.2479	-0.07456	0.03107
fixed	NA	birth_order_nonlinear2	0.01148	0.01201	0.9556	2334	0.3394	-0.02223	0.04518
fixed	NA	birth_order_nonlinear3	0.001848	0.01477	0.1251	2425	0.9005	-0.03962	0.04331
fixed	NA	birth_order_nonlinear4	-0.002733	0.0202	-0.1353	2506	0.8924	-0.05942	0.05396
fixed	NA	birth_order_nonlinear5	0.004468	0.03185	0.1403	2465	0.8884	-0.08493	0.09387
ran_pars	mother_pidlink	sd__(Intercept)	0.07032	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2514	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.6386	0.217	2.942	2736	0.003287	0.02932	1.248
fixed	NA	poly(age, 3, raw = TRUE)1	-0.05456	0.0241	-2.264	2735	0.02367	-0.1222	0.0131
fixed	NA	poly(age, 3, raw = TRUE)2	0.001629	0.0008568	1.902	2734	0.05732	-0.0007757	0.004034
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001606	0.000009757	-1.646	2732	0.09997	-0.00004344	0.00001133
fixed	NA	male	0.05378	0.01008	5.333	2741	0.0000001043	0.02547	0.08208
fixed	NA	count_birth_order2/2	-0.01225	0.0214	-0.5723	2362	0.5672	-0.07232	0.04783
fixed	NA	count_birth_order1/3	-0.01725	0.0182	-0.9474	2748	0.3435	-0.06834	0.03385
fixed	NA	count_birth_order2/3	0.0003877	0.02025	0.01914	2750	0.9847	-0.05646	0.05724
fixed	NA	count_birth_order3/3	-0.01829	0.0217	-0.8428	2746	0.3994	-0.07919	0.04262
fixed	NA	count_birth_order1/4	-0.0183	0.02141	-0.8547	2750	0.3928	-0.07841	0.04181
fixed	NA	count_birth_order2/4	0.007508	0.02236	0.3358	2748	0.7371	-0.05526	0.07027
fixed	NA	count_birth_order3/4	0.005346	0.02344	0.2281	2744	0.8196	-0.06045	0.07114
fixed	NA	count_birth_order4/4	-0.001617	0.02525	-0.06401	2745	0.949	-0.07251	0.06927
fixed	NA	count_birth_order1/5	-0.03018	0.02808	-1.074	2750	0.2827	-0.109	0.04866
fixed	NA	count_birth_order2/5	0.002559	0.03149	0.08127	2741	0.9352	-0.08582	0.09094
fixed	NA	count_birth_order3/5	-0.03558	0.03011	-1.182	2740	0.2375	-0.1201	0.04895
fixed	NA	count_birth_order4/5	-0.04183	0.02901	-1.442	2739	0.1494	-0.1233	0.0396
fixed	NA	count_birth_order5/5	-0.02515	0.03054	-0.8237	2736	0.4102	-0.1109	0.06056
ran_pars	mother_pidlink	sd__(Intercept)	0.07033	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2516	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	424.8	484.1	-202.4	404.8	NA	NA	NA
11	426.8	492	-202.4	404.8	0.01064	1	0.9178
14	431.7	514.7	-201.9	403.7	1.1	3	0.777
20	440.7	559.2	-200.3	400.7	3.055	6	0.8019

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Category_Government worker

birthorder <- birthorder %>% mutate(outcome = `Category_Government worker`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2372	0.07472	-3.174	4592	0.001513	-0.4469	-0.02742
fixed	NA	poly(age, 3, raw = TRUE)1	0.02161	0.006676	3.237	4525	0.001218	0.002868	0.04035
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000444	0.0001858	-2.39	4435	0.01689	-0.0009654	0.00007746
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002937	0.000001627	1.805	4349	0.07115	-0.00000163	0.000007504
fixed	NA	male	-0.02212	0.007447	-2.97	4679	0.002994	-0.04302	-0.001213
fixed	NA	sibling_count3	0.008962	0.01111	0.8064	3562	0.4201	-0.02223	0.04016
fixed	NA	sibling_count4	0.01113	0.01127	0.9877	3409	0.3234	-0.0205	0.04275
fixed	NA	sibling_count5	0.01694	0.01179	1.437	3231	0.1509	-0.01616	0.05004
ran_pars	mother_pidlink	sd__(Intercept)	0.1205	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2309	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2384	0.07468	-3.193	4590	0.00142	-0.448	-0.02879
fixed	NA	birth_order	-0.00761	0.003611	-2.108	4145	0.03513	-0.01774	0.002526
fixed	NA	poly(age, 3, raw = TRUE)1	0.02278	0.006695	3.402	4522	0.0006754	0.003982	0.04157
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0004742	0.0001862	-2.547	4423	0.01091	-0.0009968	0.00004849
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003143	0.000001629	1.929	4337	0.05376	-0.00000143	0.000007715
fixed	NA	male	-0.02221	0.007446	-2.983	4680	0.002869	-0.04311	-0.00131
fixed	NA	sibling_count3	0.01176	0.01118	1.052	3636	0.293	-0.01963	0.04315
fixed	NA	sibling_count4	0.0171	0.01161	1.474	3712	0.1407	-0.01548	0.04968
fixed	NA	sibling_count5	0.02655	0.01263	2.102	3843	0.03561	-0.008904	0.06201
ran_pars	mother_pidlink	sd__(Intercept)	0.12	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2311	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2421	0.07487	-3.233	4592	0.001232	-0.4522	-0.03192
fixed	NA	poly(age, 3, raw = TRUE)1	0.02267	0.006697	3.385	4516	0.0007176	0.003871	0.04147
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0004654	0.0001863	-2.498	4413	0.01252	-0.0009882	0.00005754
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003016	0.000001631	1.849	4320	0.06448	-0.000001562	0.000007593
fixed	NA	male	-0.02194	0.007448	-2.946	4677	0.003234	-0.04285	-0.001036
fixed	NA	sibling_count3	0.01291	0.01135	1.138	3767	0.2553	-0.01894	0.04477
fixed	NA	sibling_count4	0.01753	0.01178	1.488	3846	0.1368	-0.01554	0.0506
fixed	NA	sibling_count5	0.02368	0.01273	1.859	3923	0.06305	-0.01207	0.05942
fixed	NA	birth_order_nonlinear2	-0.02111	0.008698	-2.427	4102	0.01525	-0.04553	0.003301
fixed	NA	birth_order_nonlinear3	-0.02331	0.01105	-2.109	3992	0.03499	-0.05433	0.007712
fixed	NA	birth_order_nonlinear4	-0.02374	0.01434	-1.656	3919	0.09776	-0.06399	0.0165
fixed	NA	birth_order_nonlinear5	-0.01536	0.02071	-0.7416	3902	0.4583	-0.0735	0.04278
ran_pars	mother_pidlink	sd__(Intercept)	0.1199	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2311	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2452	0.07499	-3.27	4594	0.001084	-0.4557	-0.03471
fixed	NA	poly(age, 3, raw = TRUE)1	0.02301	0.006703	3.432	4513	0.0006042	0.00419	0.04182
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0004717	0.0001864	-2.53	4410	0.01143	-0.0009949	0.00005157
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003041	0.000001631	1.864	4316	0.06238	-0.000001538	0.000007621
fixed	NA	male	-0.02178	0.00745	-2.924	4667	0.003475	-0.04269	-0.0008696
fixed	NA	count_birth_order2/2	-0.02547	0.01477	-1.725	4099	0.08461	-0.06693	0.01598
fixed	NA	count_birth_order1/3	0.02047	0.01457	1.405	4781	0.1601	-0.02044	0.06138
fixed	NA	count_birth_order2/3	-0.01757	0.01614	-1.089	4803	0.2764	-0.06287	0.02773
fixed	NA	count_birth_order3/3	-0.01937	0.01773	-1.092	4804	0.2748	-0.06914	0.03041
fixed	NA	count_birth_order1/4	0.008919	0.01595	0.5591	4803	0.5761	-0.03586	0.0537
fixed	NA	count_birth_order2/4	0.01066	0.01709	0.6236	4806	0.5329	-0.03732	0.05864
fixed	NA	count_birth_order3/4	-0.01085	0.01822	-0.5957	4800	0.5514	-0.06199	0.04028
fixed	NA	count_birth_order4/4	-0.01459	0.01937	-0.7533	4793	0.4513	-0.06897	0.03978
fixed	NA	count_birth_order1/5	0.009719	0.01808	0.5376	4803	0.5909	-0.04103	0.06047
fixed	NA	count_birth_order2/5	-0.004052	0.01918	-0.2113	4796	0.8327	-0.05788	0.04978
fixed	NA	count_birth_order3/5	0.01331	0.02017	0.6599	4781	0.5094	-0.04331	0.06993
fixed	NA	count_birth_order4/5	0.006789	0.02118	0.3205	4739	0.7486	-0.05266	0.06624
fixed	NA	count_birth_order5/5	0.006999	0.02122	0.3299	4767	0.7415	-0.05255	0.06655
ran_pars	mother_pidlink	sd__(Intercept)	0.1203	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2309	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	636.2	701	-308.1	616.2	NA	NA	NA
11	633.8	705.1	-305.9	611.8	4.447	1	0.03497
14	636	726.8	-304	608	3.745	3	0.2903
20	642.9	772.5	-301.4	602.9	5.154	6	0.5242

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8446	0.2218	-3.808	2760	0.000143	-1.467	-0.222
fixed	NA	poly(age, 3, raw = TRUE)1	0.08867	0.02457	3.609	2760	0.0003123	0.01971	0.1576
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002752	0.0008712	-3.159	2760	0.001599	-0.005198	-0.0003068
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002889	0.000009896	2.92	2760	0.003529	0.000001117	0.00005667
fixed	NA	male	-0.01843	0.01034	-1.782	2712	0.07488	-0.04746	0.0106
fixed	NA	sibling_count3	0.006876	0.01486	0.4628	2315	0.6435	-0.03483	0.04858
fixed	NA	sibling_count4	0.002255	0.01546	0.1459	2211	0.884	-0.04114	0.04565
fixed	NA	sibling_count5	0.001495	0.01727	0.08656	2046	0.931	-0.047	0.04999
ran_pars	mother_pidlink	sd__(Intercept)	0.123	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.242	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8437	0.2218	-3.803	2759	0.0001458	-1.466	-0.221
fixed	NA	birth_order	-0.002808	0.005173	-0.5429	2605	0.5873	-0.01733	0.01171
fixed	NA	poly(age, 3, raw = TRUE)1	0.08891	0.02457	3.618	2759	0.0003018	0.01994	0.1579
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002756	0.0008713	-3.163	2759	0.001577	-0.005202	-0.0003104
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002886	0.000009897	2.916	2759	0.003573	0.000001079	0.00005664
fixed	NA	male	-0.01842	0.01034	-1.781	2711	0.07498	-0.04746	0.01061
fixed	NA	sibling_count3	0.008236	0.01507	0.5466	2339	0.5847	-0.03406	0.05053
fixed	NA	sibling_count4	0.005169	0.01636	0.3159	2305	0.7521	-0.04077	0.05111
fixed	NA	sibling_count5	0.006382	0.01948	0.3276	2296	0.7433	-0.04831	0.06107
ran_pars	mother_pidlink	sd__(Intercept)	0.1228	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2421	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8255	0.2223	-3.713	2756	0.0002088	-1.45	-0.2014
fixed	NA	poly(age, 3, raw = TRUE)1	0.08702	0.02462	3.535	2756	0.0004143	0.01792	0.1561
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002688	0.0008728	-3.079	2756	0.002094	-0.005138	-0.0002378
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002811	0.000009913	2.836	2756	0.004604	0.0000002856	0.00005594
fixed	NA	male	-0.01883	0.01035	-1.82	2708	0.06892	-0.04788	0.01022
fixed	NA	sibling_count3	0.01055	0.01528	0.6901	2383	0.4902	-0.03235	0.05344
fixed	NA	sibling_count4	0.004998	0.01656	0.3018	2346	0.7629	-0.0415	0.05149
fixed	NA	sibling_count5	0.002295	0.01972	0.1164	2328	0.9074	-0.05305	0.05764
fixed	NA	birth_order_nonlinear2	-0.01815	0.01226	-1.48	2386	0.139	-0.05257	0.01627
fixed	NA	birth_order_nonlinear3	-0.01674	0.015	-1.116	2432	0.2644	-0.05883	0.02535
fixed	NA	birth_order_nonlinear4	-0.0002889	0.01995	-0.01448	2482	0.9885	-0.0563	0.05572
fixed	NA	birth_order_nonlinear5	-0.000882	0.03059	-0.02883	2415	0.977	-0.08676	0.085
ran_pars	mother_pidlink	sd__(Intercept)	0.1233	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2419	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8108	0.2224	-3.646	2750	0.0002716	-1.435	-0.1865
fixed	NA	poly(age, 3, raw = TRUE)1	0.08584	0.02462	3.486	2750	0.0004981	0.01672	0.155
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002651	0.0008732	-3.036	2750	0.002421	-0.005102	-0.0001998
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002775	0.000009919	2.798	2750	0.005179	-0.00000009005	0.00005559
fixed	NA	male	-0.01918	0.01036	-1.851	2701	0.06424	-0.04826	0.009901
fixed	NA	count_birth_order2/2	-0.0267	0.02229	-1.198	2458	0.231	-0.08926	0.03586
fixed	NA	count_birth_order1/3	0.01513	0.01917	0.7894	2744	0.4299	-0.03867	0.06893
fixed	NA	count_birth_order2/3	-0.01745	0.02124	-0.8216	2750	0.4114	-0.07709	0.04218
fixed	NA	count_birth_order3/3	-0.01395	0.02296	-0.6075	2746	0.5436	-0.07838	0.05049
fixed	NA	count_birth_order1/4	-0.01733	0.02206	-0.7856	2750	0.4321	-0.07924	0.04459
fixed	NA	count_birth_order2/4	0.007161	0.02313	0.3097	2747	0.7568	-0.05776	0.07208
fixed	NA	count_birth_order3/4	0.001317	0.02421	0.05438	2736	0.9566	-0.06665	0.06928
fixed	NA	count_birth_order4/4	-0.01636	0.02565	-0.6378	2732	0.5237	-0.08835	0.05564
fixed	NA	count_birth_order1/5	0.006228	0.02895	0.2151	2746	0.8297	-0.07504	0.08749
fixed	NA	count_birth_order2/5	-0.03768	0.03135	-1.202	2713	0.2295	-0.1257	0.05032
fixed	NA	count_birth_order3/5	-0.03459	0.02935	-1.179	2720	0.2387	-0.117	0.04779
fixed	NA	count_birth_order4/5	0.02366	0.02851	0.83	2718	0.4066	-0.05637	0.1037
fixed	NA	count_birth_order5/5	-0.001001	0.02988	-0.03349	2712	0.9733	-0.08486	0.08286
ran_pars	mother_pidlink	sd__(Intercept)	0.1233	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2418	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	611.1	670.4	-295.6	591.1	NA	NA	NA
11	612.8	678	-295.4	590.8	0.2966	1	0.586
14	616.1	699.1	-294.1	588.1	2.706	3	0.4392
20	620.9	739.5	-290.5	580.9	7.19	6	0.3036

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8203	0.228	-3.598	2531	0.0003268	-1.46	-0.1803
fixed	NA	poly(age, 3, raw = TRUE)1	0.08539	0.02527	3.38	2530	0.0007366	0.01447	0.1563
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002664	0.000896	-2.973	2530	0.002975	-0.005179	-0.0001489
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002825	0.00001018	2.775	2530	0.005558	-0.0000003247	0.00005682
fixed	NA	male	-0.01378	0.01073	-1.284	2492	0.1992	-0.04388	0.01633
fixed	NA	sibling_count3	0.008393	0.01615	0.5198	2181	0.6033	-0.03693	0.05372
fixed	NA	sibling_count4	0.01724	0.01638	1.053	2121	0.2925	-0.02873	0.06322
fixed	NA	sibling_count5	0.01254	0.01734	0.7233	2024	0.4696	-0.03612	0.0612
ran_pars	mother_pidlink	sd__(Intercept)	0.1219	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2402	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.815	0.228	-3.574	2530	0.0003577	-1.455	-0.1749
fixed	NA	birth_order	-0.006519	0.005213	-1.251	2434	0.2112	-0.02115	0.008113
fixed	NA	poly(age, 3, raw = TRUE)1	0.0857	0.02527	3.392	2530	0.0007049	0.01478	0.1566
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002667	0.0008959	-2.977	2529	0.002942	-0.005182	-0.000152
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002812	0.00001018	2.763	2529	0.005767	-0.0000004469	0.00005669
fixed	NA	male	-0.01396	0.01073	-1.302	2491	0.1932	-0.04407	0.01615
fixed	NA	sibling_count3	0.01165	0.01635	0.7127	2194	0.4761	-0.03424	0.05755
fixed	NA	sibling_count4	0.0236	0.01714	1.377	2174	0.1687	-0.02452	0.07171
fixed	NA	sibling_count5	0.02314	0.01929	1.2	2184	0.2304	-0.03101	0.07729
ran_pars	mother_pidlink	sd__(Intercept)	0.1214	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2403	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7987	0.2285	-3.495	2527	0.0004817	-1.44	-0.1573
fixed	NA	poly(age, 3, raw = TRUE)1	0.08338	0.02532	3.293	2527	0.001003	0.01232	0.1544
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002584	0.0008978	-2.878	2527	0.004036	-0.005104	-0.00006367
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002721	0.0000102	2.668	2527	0.007676	-0.000001416	0.00005583
fixed	NA	male	-0.01452	0.01073	-1.353	2486	0.1761	-0.04462	0.01559
fixed	NA	sibling_count3	0.01511	0.01657	0.9116	2225	0.3621	-0.03142	0.06164
fixed	NA	sibling_count4	0.02174	0.01734	1.253	2202	0.2102	-0.02694	0.07041
fixed	NA	sibling_count5	0.02271	0.01941	1.17	2196	0.2421	-0.03177	0.0772
fixed	NA	birth_order_nonlinear2	-0.01468	0.01265	-1.16	2224	0.246	-0.05018	0.02083
fixed	NA	birth_order_nonlinear3	-0.02852	0.01563	-1.824	2287	0.06822	-0.0724	0.01536
fixed	NA	birth_order_nonlinear4	0.006131	0.02052	0.2988	2320	0.7651	-0.05147	0.06373
fixed	NA	birth_order_nonlinear5	-0.04046	0.02928	-1.382	2262	0.1672	-0.1226	0.04173
ran_pars	mother_pidlink	sd__(Intercept)	0.1227	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2397	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.7886	0.2283	-3.454	2521	0.0005614	-1.43	-0.1477
fixed	NA	poly(age, 3, raw = TRUE)1	0.08258	0.0253	3.265	2521	0.00111	0.01158	0.1536
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002554	0.000897	-2.847	2521	0.004442	-0.005072	-0.00003629
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002686	0.00001019	2.636	2521	0.008452	-0.000001748	0.00005546
fixed	NA	male	-0.01525	0.01073	-1.421	2479	0.1554	-0.04536	0.01487
fixed	NA	count_birth_order2/2	-0.02294	0.02433	-0.943	2321	0.3458	-0.09122	0.04534
fixed	NA	count_birth_order1/3	0.0179	0.02099	0.8529	2516	0.3938	-0.04102	0.07682
fixed	NA	count_birth_order2/3	-0.01219	0.02278	-0.5351	2521	0.5926	-0.07613	0.05175
fixed	NA	count_birth_order3/3	-0.01276	0.02501	-0.5102	2517	0.6099	-0.08297	0.05745
fixed	NA	count_birth_order1/4	0.006472	0.02288	0.2828	2520	0.7773	-0.05775	0.0707
fixed	NA	count_birth_order2/4	0.0439	0.02381	1.844	2520	0.06535	-0.02294	0.1107
fixed	NA	count_birth_order3/4	-0.01099	0.02596	-0.4231	2508	0.6723	-0.08387	0.0619
fixed	NA	count_birth_order4/4	-0.01307	0.02767	-0.4725	2503	0.6366	-0.09075	0.0646
fixed	NA	count_birth_order1/5	0.0234	0.02743	0.8532	2520	0.3937	-0.0536	0.1004
fixed	NA	count_birth_order2/5	-0.03431	0.02841	-1.208	2510	0.2273	-0.1141	0.04544
fixed	NA	count_birth_order3/5	-0.01171	0.02885	-0.406	2499	0.6848	-0.09271	0.06928
fixed	NA	count_birth_order4/5	0.07044	0.02926	2.408	2488	0.01613	-0.01169	0.1526
fixed	NA	count_birth_order5/5	-0.01972	0.02947	-0.6693	2488	0.5034	-0.1024	0.063
ran_pars	mother_pidlink	sd__(Intercept)	0.1229	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2391	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	523.2	581.6	-251.6	503.2	NA	NA	NA
11	523.7	587.9	-250.8	501.7	1.57	1	0.2103
14	525.3	607	-248.6	497.3	4.389	3	0.2224
20	522.3	639.1	-241.1	482.3	14.97	6	0.02049

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.9011	0.2241	-4.021	2760	0.00005945	-1.53	-0.2721
fixed	NA	poly(age, 3, raw = TRUE)1	0.09554	0.02488	3.839	2760	0.0001261	0.02569	0.1654
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003015	0.0008845	-3.408	2760	0.0006628	-0.005497	-0.0005319
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003197	0.00001007	3.174	2760	0.001522	0.000003693	0.00006024
fixed	NA	male	-0.01993	0.01034	-1.928	2710	0.05392	-0.04894	0.009082
fixed	NA	sibling_count3	0.005211	0.01457	0.3576	2325	0.7206	-0.03569	0.04611
fixed	NA	sibling_count4	0.009886	0.01537	0.6433	2216	0.5201	-0.03325	0.05302
fixed	NA	sibling_count5	0.007623	0.01767	0.4313	2004	0.6663	-0.04199	0.05723
ran_pars	mother_pidlink	sd__(Intercept)	0.1241	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2414	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.9001	0.2241	-4.016	2759	0.00006069	-1.529	-0.271
fixed	NA	birth_order	-0.002497	0.005229	-0.4776	2587	0.633	-0.01718	0.01218
fixed	NA	poly(age, 3, raw = TRUE)1	0.09575	0.02489	3.847	2759	0.0001224	0.02588	0.1656
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003018	0.0008846	-3.412	2759	0.0006545	-0.005501	-0.000535
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003194	0.00001007	3.17	2759	0.001539	0.000003661	0.00006022
fixed	NA	male	-0.01995	0.01034	-1.93	2709	0.0537	-0.04897	0.009065
fixed	NA	sibling_count3	0.006438	0.0148	0.4351	2347	0.6635	-0.0351	0.04797
fixed	NA	sibling_count4	0.01244	0.01628	0.7646	2314	0.4446	-0.03324	0.05813
fixed	NA	sibling_count5	0.01183	0.01975	0.599	2237	0.5492	-0.04361	0.06727
ran_pars	mother_pidlink	sd__(Intercept)	0.1239	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2415	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8845	0.2246	-3.939	2756	0.00008394	-1.515	-0.2541
fixed	NA	poly(age, 3, raw = TRUE)1	0.09407	0.02493	3.773	2756	0.000165	0.02408	0.1641
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002958	0.0008861	-3.338	2756	0.0008561	-0.005445	-0.0004702
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003128	0.00001009	3.1	2756	0.001953	0.000002958	0.0000596
fixed	NA	male	-0.0203	0.01035	-1.962	2706	0.04985	-0.04934	0.008742
fixed	NA	sibling_count3	0.008672	0.01501	0.5775	2392	0.5636	-0.03348	0.05082
fixed	NA	sibling_count4	0.01184	0.01648	0.7184	2355	0.4726	-0.03441	0.05809
fixed	NA	sibling_count5	0.008193	0.02006	0.4085	2281	0.683	-0.04811	0.06449
fixed	NA	birth_order_nonlinear2	-0.01399	0.01212	-1.154	2370	0.2486	-0.04801	0.02003
fixed	NA	birth_order_nonlinear3	-0.0158	0.01495	-1.057	2424	0.2905	-0.05775	0.02615
fixed	NA	birth_order_nonlinear4	0.004316	0.02048	0.2108	2465	0.8331	-0.05316	0.0618
fixed	NA	birth_order_nonlinear5	-0.00392	0.03223	-0.1216	2410	0.9032	-0.0944	0.08656
ran_pars	mother_pidlink	sd__(Intercept)	0.1243	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2414	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.8709	0.2247	-3.876	2750	0.0001085	-1.502	-0.2402
fixed	NA	poly(age, 3, raw = TRUE)1	0.09326	0.02495	3.738	2750	0.000189	0.02323	0.1633
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002939	0.0008867	-3.314	2750	0.0009308	-0.005428	-0.0004497
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003119	0.0000101	3.089	2750	0.002029	0.000002846	0.00005954
fixed	NA	male	-0.02027	0.01036	-1.958	2699	0.05039	-0.04934	0.008797
fixed	NA	count_birth_order2/2	-0.02733	0.02163	-1.264	2435	0.2065	-0.08804	0.03338
fixed	NA	count_birth_order1/3	0.01519	0.01885	0.8061	2744	0.4203	-0.03771	0.0681
fixed	NA	count_birth_order2/3	-0.01803	0.0209	-0.8624	2749	0.3885	-0.07671	0.04065
fixed	NA	count_birth_order3/3	-0.02169	0.02235	-0.9705	2743	0.3319	-0.08445	0.04106
fixed	NA	count_birth_order1/4	-0.01651	0.02213	-0.7459	2750	0.4558	-0.07864	0.04562
fixed	NA	count_birth_order2/4	0.01695	0.02305	0.7352	2745	0.4623	-0.04776	0.08166
fixed	NA	count_birth_order3/4	0.003404	0.02413	0.1411	2734	0.8878	-0.06432	0.07113
fixed	NA	count_birth_order4/4	0.003352	0.02598	0.129	2728	0.8974	-0.06958	0.07629
fixed	NA	count_birth_order1/5	-0.003096	0.02898	-0.1068	2747	0.9149	-0.08444	0.07825
fixed	NA	count_birth_order2/5	-0.01805	0.03234	-0.5583	2703	0.5767	-0.1088	0.07272
fixed	NA	count_birth_order3/5	-0.01105	0.03093	-0.3574	2707	0.7208	-0.09787	0.07576
fixed	NA	count_birth_order4/5	0.02112	0.02981	0.7087	2713	0.4786	-0.06254	0.1048
fixed	NA	count_birth_order5/5	0.0001632	0.03136	0.005205	2706	0.9958	-0.08785	0.08818
ran_pars	mother_pidlink	sd__(Intercept)	0.1246	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2412	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	609.6	668.8	-294.8	589.6	NA	NA	NA
11	611.3	676.5	-294.7	589.3	0.2297	1	0.6318
14	615.2	698.2	-293.6	587.2	2.126	3	0.5468
20	620.9	739.4	-290.5	580.9	6.288	6	0.3917

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Category_Private worker

birthorder <- birthorder %>% mutate(outcome = `Category_Private worker`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1396	0.1387	-1.006	4529	0.3144	-0.5289	0.2498
fixed	NA	poly(age, 3, raw = TRUE)1	0.06859	0.01239	5.535	4443	0.0000000329	0.03381	0.1034
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002108	0.0003447	-6.114	4331	0.000000001055	-0.003075	-0.00114
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001739	0.000003019	5.759	4227	0.000000009061	0.000008912	0.00002586
fixed	NA	male	0.02924	0.01385	2.111	4661	0.03484	-0.009644	0.06812
fixed	NA	sibling_count3	-0.0009719	0.0206	-0.04719	3351	0.9624	-0.05878	0.05684
fixed	NA	sibling_count4	-0.01074	0.02087	-0.5144	3179	0.607	-0.06933	0.04786
fixed	NA	sibling_count5	-0.03073	0.02184	-1.407	2983	0.1596	-0.09204	0.03058
ran_pars	mother_pidlink	sd__(Intercept)	0.2186	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4315	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1421	0.1387	-1.025	4531	0.3055	-0.5313	0.2471
fixed	NA	birth_order	-0.01581	0.006719	-2.353	4027	0.01868	-0.03467	0.003052
fixed	NA	poly(age, 3, raw = TRUE)1	0.071	0.01243	5.712	4446	0.00000001189	0.03611	0.1059
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00217	0.0003456	-6.279	4325	0.0000000003745	-0.00314	-0.0012
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001781	0.000003024	5.892	4221	0.000000004117	0.000009327	0.0000263
fixed	NA	male	0.02909	0.01384	2.101	4659	0.03568	-0.009772	0.06795
fixed	NA	sibling_count3	0.004861	0.02074	0.2344	3439	0.8147	-0.05336	0.06308
fixed	NA	sibling_count4	0.001696	0.02153	0.07879	3521	0.9372	-0.05873	0.06213
fixed	NA	sibling_count5	-0.01073	0.02343	-0.4579	3667	0.6471	-0.07651	0.05505
ran_pars	mother_pidlink	sd__(Intercept)	0.219	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.431	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1492	0.139	-1.073	4534	0.2833	-0.5394	0.2411
fixed	NA	poly(age, 3, raw = TRUE)1	0.07071	0.01243	5.688	4440	0.00000001369	0.03582	0.1056
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002151	0.0003458	-6.221	4314	0.0000000005401	-0.003122	-0.001181
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001755	0.000003026	5.8	4202	0.000000007104	0.000009059	0.00002605
fixed	NA	male	0.02952	0.01385	2.132	4657	0.03307	-0.009349	0.06839
fixed	NA	sibling_count3	0.007167	0.02105	0.3405	3587	0.7335	-0.05191	0.06625
fixed	NA	sibling_count4	0.00145	0.02185	0.06637	3674	0.9471	-0.05989	0.06279
fixed	NA	sibling_count5	-0.01578	0.02362	-0.6681	3759	0.5041	-0.08209	0.05053
fixed	NA	birth_order_nonlinear2	-0.04204	0.01619	-2.597	3977	0.009434	-0.08748	0.003397
fixed	NA	birth_order_nonlinear3	-0.04759	0.02057	-2.314	3855	0.02073	-0.1053	0.01014
fixed	NA	birth_order_nonlinear4	-0.04298	0.02669	-1.61	3775	0.1074	-0.1179	0.03193
fixed	NA	birth_order_nonlinear5	-0.04299	0.03855	-1.115	3759	0.2649	-0.1512	0.06523
ran_pars	mother_pidlink	sd__(Intercept)	0.2186	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4312	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1495	0.1393	-1.073	4537	0.2831	-0.5404	0.2414
fixed	NA	poly(age, 3, raw = TRUE)1	0.07115	0.01245	5.717	4436	0.00000001156	0.03622	0.1061
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00216	0.0003461	-6.241	4310	0.0000000004766	-0.003131	-0.001188
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001759	0.000003028	5.81	4197	0.000000006713	0.000009094	0.00002609
fixed	NA	male	0.02963	0.01386	2.138	4649	0.03259	-0.009276	0.06853
fixed	NA	count_birth_order2/2	-0.05761	0.0275	-2.095	3974	0.03625	-0.1348	0.01959
fixed	NA	count_birth_order1/3	-0.0008044	0.02708	-0.0297	4777	0.9763	-0.07683	0.07522
fixed	NA	count_birth_order2/3	-0.03296	0.03	-1.099	4802	0.2719	-0.1172	0.05124
fixed	NA	count_birth_order3/3	-0.0523	0.03296	-1.587	4804	0.1127	-0.1448	0.04023
fixed	NA	count_birth_order1/4	-0.006749	0.02965	-0.2276	4802	0.82	-0.08998	0.07648
fixed	NA	count_birth_order2/4	-0.04075	0.03178	-1.282	4806	0.1998	-0.1299	0.04845
fixed	NA	count_birth_order3/4	-0.04033	0.03387	-1.191	4799	0.2338	-0.1354	0.05474
fixed	NA	count_birth_order4/4	-0.06524	0.03602	-1.811	4792	0.07015	-0.1663	0.03586
fixed	NA	count_birth_order1/5	-0.02917	0.03361	-0.8679	4803	0.3855	-0.1235	0.06517
fixed	NA	count_birth_order2/5	-0.06593	0.03565	-1.849	4794	0.06448	-0.166	0.03415
fixed	NA	count_birth_order3/5	-0.07601	0.03751	-2.027	4778	0.04274	-0.1813	0.02926
fixed	NA	count_birth_order4/5	-0.04191	0.03939	-1.064	4729	0.2874	-0.1525	0.06866
fixed	NA	count_birth_order5/5	-0.06442	0.03945	-1.633	4762	0.1026	-0.1752	0.04633
ran_pars	mother_pidlink	sd__(Intercept)	0.2187	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4314	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	6616	6680	-3298	6596	NA	NA	NA
11	6612	6683	-3295	6590	5.536	1	0.01863
14	6614	6705	-3293	6586	3.852	3	0.2778
20	6624	6754	-3292	6584	1.688	6	0.946

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.628	0.4004	-6.562	2760	0.00000000006304	-3.751	-1.504
fixed	NA	poly(age, 3, raw = TRUE)1	0.3389	0.04435	7.642	2760	2.937e-14	0.2144	0.4634
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01116	0.001573	-7.098	2760	1.601e-12	-0.01558	-0.006749
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001141	0.00001787	6.386	2760	0.0000000001988	0.00006394	0.0001642
fixed	NA	male	0.02993	0.01869	1.601	2705	0.1094	-0.02253	0.08239
fixed	NA	sibling_count3	-0.03668	0.02673	-1.372	2184	0.1701	-0.1117	0.03835
fixed	NA	sibling_count4	-0.03183	0.0278	-1.145	2052	0.2523	-0.1098	0.0462
fixed	NA	sibling_count5	-0.06908	0.03104	-2.226	1851	0.02615	-0.1562	0.01804
ran_pars	mother_pidlink	sd__(Intercept)	0.2124	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.441	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.625	0.4004	-6.555	2759	0.0000000000662	-3.749	-1.501
fixed	NA	birth_order	-0.006695	0.009355	-0.7157	2563	0.4743	-0.03296	0.01957
fixed	NA	poly(age, 3, raw = TRUE)1	0.3394	0.04436	7.652	2759	2.72e-14	0.2149	0.464
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01117	0.001573	-7.102	2759	1.557e-12	-0.01559	-0.006756
fixed	NA	poly(age, 3, raw = TRUE)3	0.000114	0.00001787	6.38	2759	0.0000000002071	0.00006384	0.0001641
fixed	NA	male	0.02993	0.01869	1.601	2704	0.1095	-0.02254	0.08239
fixed	NA	sibling_count3	-0.03342	0.02711	-1.233	2216	0.2179	-0.1095	0.04269
fixed	NA	sibling_count4	-0.02488	0.02944	-0.8451	2169	0.3982	-0.1075	0.05776
fixed	NA	sibling_count5	-0.05743	0.03505	-1.639	2153	0.1014	-0.1558	0.04094
ran_pars	mother_pidlink	sd__(Intercept)	0.2122	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4411	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.648	0.4013	-6.599	2756	0.00000000004948	-3.774	-1.522
fixed	NA	poly(age, 3, raw = TRUE)1	0.3415	0.04444	7.685	2756	2.119e-14	0.2167	0.4662
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01124	0.001576	-7.133	2756	1.25e-12	-0.01566	-0.006816
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001147	0.00001789	6.409	2756	0.000000000172	0.00006445	0.0001649
fixed	NA	male	0.03068	0.0187	1.64	2702	0.1011	-0.02182	0.08317
fixed	NA	sibling_count3	-0.0364	0.02749	-1.324	2275	0.1856	-0.1136	0.04077
fixed	NA	sibling_count4	-0.02095	0.02979	-0.7031	2224	0.4821	-0.1046	0.06269
fixed	NA	sibling_count5	-0.06187	0.03546	-1.745	2196	0.08118	-0.1614	0.03767
fixed	NA	birth_order_nonlinear2	-0.01621	0.02221	-0.7302	2292	0.4654	-0.07855	0.04612
fixed	NA	birth_order_nonlinear3	-0.001198	0.02715	-0.04413	2352	0.9648	-0.07741	0.07502
fixed	NA	birth_order_nonlinear4	-0.05709	0.03612	-1.581	2415	0.1141	-0.1585	0.0443
fixed	NA	birth_order_nonlinear5	0.01887	0.0554	0.3407	2336	0.7334	-0.1366	0.1744
ran_pars	mother_pidlink	sd__(Intercept)	0.2125	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.441	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.655	0.4019	-6.607	2750	0.00000000004703	-3.783	-1.527
fixed	NA	poly(age, 3, raw = TRUE)1	0.3416	0.0445	7.678	2750	2.228e-14	0.2167	0.4665
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01125	0.001578	-7.128	2750	1.3e-12	-0.01568	-0.006818
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001148	0.00001792	6.405	2750	0.0000000001761	0.00006449	0.0001651
fixed	NA	male	0.03024	0.01874	1.614	2695	0.1067	-0.02236	0.08284
fixed	NA	count_birth_order2/2	0.002125	0.04039	0.05263	2375	0.958	-0.1112	0.1155
fixed	NA	count_birth_order1/3	-0.02675	0.03462	-0.7728	2743	0.4397	-0.1239	0.07042
fixed	NA	count_birth_order2/3	-0.04489	0.03839	-1.169	2750	0.2424	-0.1526	0.06287
fixed	NA	count_birth_order3/3	-0.04155	0.04149	-1.001	2745	0.3168	-0.158	0.07493
fixed	NA	count_birth_order1/4	-0.007495	0.03985	-0.1881	2749	0.8508	-0.1194	0.1044
fixed	NA	count_birth_order2/4	-0.031	0.0418	-0.7416	2746	0.4584	-0.1483	0.08634
fixed	NA	count_birth_order3/4	-0.02146	0.04378	-0.4902	2733	0.624	-0.1443	0.1014
fixed	NA	count_birth_order4/4	-0.07964	0.04638	-1.717	2729	0.08605	-0.2098	0.05054
fixed	NA	count_birth_order1/5	-0.06377	0.05233	-1.219	2746	0.2231	-0.2107	0.08312
fixed	NA	count_birth_order2/5	-0.1064	0.0567	-1.877	2707	0.06061	-0.2656	0.05273
fixed	NA	count_birth_order3/5	-0.03041	0.05308	-0.5729	2715	0.5667	-0.1794	0.1186
fixed	NA	count_birth_order4/5	-0.1034	0.05156	-2.006	2712	0.04498	-0.2482	0.04132
fixed	NA	count_birth_order5/5	-0.03676	0.05404	-0.6803	2704	0.4964	-0.1884	0.1149
ran_pars	mother_pidlink	sd__(Intercept)	0.2127	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4413	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	3881	3941	-1931	3861	NA	NA	NA
11	3883	3948	-1930	3861	0.5141	1	0.4734
14	3886	3969	-1929	3858	3.018	3	0.3888
20	3896	4015	-1928	3856	1.348	6	0.9689

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.616	0.4144	-6.314	2531	0.0000000003194	-3.78	-1.453
fixed	NA	poly(age, 3, raw = TRUE)1	0.3375	0.04592	7.35	2530	2.663e-13	0.2086	0.4665
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01112	0.001629	-6.83	2530	0.00000000001056	-0.0157	-0.006552
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001134	0.0000185	6.132	2530	0.000000001003	0.00006152	0.0001654
fixed	NA	male	0.02442	0.0195	1.252	2476	0.2106	-0.03032	0.07916
fixed	NA	sibling_count3	-0.01048	0.02931	-0.3575	2043	0.7207	-0.09276	0.0718
fixed	NA	sibling_count4	-0.01521	0.02973	-0.5116	1964	0.609	-0.09866	0.06824
fixed	NA	sibling_count5	-0.04316	0.03146	-1.372	1840	0.1703	-0.1315	0.04516
ran_pars	mother_pidlink	sd__(Intercept)	0.2183	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4379	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.613	0.4145	-6.303	2530	0.000000000344	-3.776	-1.449
fixed	NA	birth_order	-0.004532	0.00948	-0.478	2393	0.6327	-0.03114	0.02208
fixed	NA	poly(age, 3, raw = TRUE)1	0.3377	0.04593	7.353	2530	2.612e-13	0.2088	0.4667
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01113	0.001629	-6.83	2529	0.00000000001059	-0.0157	-0.006553
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001134	0.0000185	6.126	2529	0.000000001044	0.00006141	0.0001653
fixed	NA	male	0.02429	0.01951	1.245	2475	0.2131	-0.03046	0.07905
fixed	NA	sibling_count3	-0.008213	0.0297	-0.2765	2061	0.7822	-0.09158	0.07515
fixed	NA	sibling_count4	-0.0108	0.03113	-0.3468	2034	0.7288	-0.09819	0.0766
fixed	NA	sibling_count5	-0.03579	0.03504	-1.021	2047	0.3072	-0.1342	0.06257
ran_pars	mother_pidlink	sd__(Intercept)	0.2183	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.438	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.61	0.4154	-6.284	2527	0.0000000003879	-3.777	-1.444
fixed	NA	poly(age, 3, raw = TRUE)1	0.3377	0.04603	7.337	2527	2.928e-13	0.2085	0.4669
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01112	0.001632	-6.815	2527	0.00000000001176	-0.0157	-0.006541
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001133	0.00001854	6.111	2527	0.000000001142	0.00006125	0.0001653
fixed	NA	male	0.02479	0.01951	1.271	2471	0.2039	-0.02997	0.07954
fixed	NA	sibling_count3	-0.009925	0.0301	-0.3298	2107	0.7416	-0.09441	0.07456
fixed	NA	sibling_count4	-0.005475	0.03149	-0.1739	2076	0.862	-0.09386	0.08291
fixed	NA	sibling_count5	-0.04175	0.03524	-1.185	2067	0.2363	-0.1407	0.05718
fixed	NA	birth_order_nonlinear2	-0.0257	0.02302	-1.117	2110	0.2643	-0.09031	0.03891
fixed	NA	birth_order_nonlinear3	-0.002134	0.02845	-0.07502	2195	0.9402	-0.08198	0.07772
fixed	NA	birth_order_nonlinear4	-0.05797	0.03734	-1.553	2240	0.1206	-0.1628	0.04683
fixed	NA	birth_order_nonlinear5	0.03924	0.05328	0.7364	2162	0.4616	-0.1103	0.1888
ran_pars	mother_pidlink	sd__(Intercept)	0.2197	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4372	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.595	0.4162	-6.235	2521	0.0000000005284	-3.763	-1.427
fixed	NA	poly(age, 3, raw = TRUE)1	0.337	0.04611	7.31	2521	3.576e-13	0.2076	0.4664
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0111	0.001635	-6.789	2521	0.000000000014	-0.01569	-0.006511
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001131	0.00001857	6.089	2521	0.000000001312	0.00006095	0.0001652
fixed	NA	male	0.02467	0.01957	1.261	2466	0.2076	-0.03026	0.07959
fixed	NA	count_birth_order2/2	-0.05466	0.0444	-1.231	2242	0.2185	-0.1793	0.06999
fixed	NA	count_birth_order1/3	-0.01649	0.03825	-0.4311	2515	0.6665	-0.1238	0.09087
fixed	NA	count_birth_order2/3	-0.04109	0.04152	-0.9899	2521	0.3223	-0.1576	0.07544
fixed	NA	count_birth_order3/3	-0.03243	0.0456	-0.7113	2515	0.477	-0.1604	0.09556
fixed	NA	count_birth_order1/4	-0.03994	0.0417	-0.958	2519	0.3382	-0.157	0.0771
fixed	NA	count_birth_order2/4	-0.02837	0.0434	-0.6536	2520	0.5134	-0.1502	0.09347
fixed	NA	count_birth_order3/4	-0.007489	0.04734	-0.1582	2503	0.8743	-0.1404	0.1254
fixed	NA	count_birth_order4/4	-0.05599	0.05045	-1.11	2497	0.2673	-0.1976	0.08564
fixed	NA	count_birth_order1/5	-0.03856	0.05	-0.7712	2520	0.4407	-0.1789	0.1018
fixed	NA	count_birth_order2/5	-0.0787	0.0518	-1.519	2507	0.1288	-0.2241	0.0667
fixed	NA	count_birth_order3/5	-0.04973	0.05261	-0.9452	2491	0.3446	-0.1974	0.09796
fixed	NA	count_birth_order4/5	-0.1275	0.05336	-2.389	2476	0.01695	-0.2773	0.02229
fixed	NA	count_birth_order5/5	-0.01228	0.05374	-0.2284	2476	0.8193	-0.1631	0.1386
ran_pars	mother_pidlink	sd__(Intercept)	0.218	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4384	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	3557	3616	-1769	3537	NA	NA	NA
11	3559	3623	-1768	3537	0.2291	1	0.6322
14	3560	3642	-1766	3532	4.582	3	0.2051
20	3570	3687	-1765	3530	1.837	6	0.9341

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.586	0.4054	-6.378	2759	0.0000000002095	-3.724	-1.448
fixed	NA	poly(age, 3, raw = TRUE)1	0.3362	0.04502	7.468	2760	1.084e-13	0.2099	0.4626
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01114	0.0016	-6.959	2760	4.262e-12	-0.01563	-0.006645
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001146	0.00001822	6.291	2760	0.0000000003657	0.00006349	0.0001658
fixed	NA	male	0.02311	0.01873	1.234	2707	0.2174	-0.02947	0.07569
fixed	NA	sibling_count3	-0.0436	0.02621	-1.663	2193	0.09641	-0.1172	0.02998
fixed	NA	sibling_count4	-0.03624	0.02763	-1.312	2051	0.1898	-0.1138	0.04131
fixed	NA	sibling_count5	-0.07538	0.03172	-2.376	1788	0.0176	-0.1644	0.01367
ran_pars	mother_pidlink	sd__(Intercept)	0.2092	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4434	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.582	0.4055	-6.369	2759	0.000000000222	-3.72	-1.444
fixed	NA	birth_order	-0.007298	0.009491	-0.7689	2546	0.442	-0.03394	0.01934
fixed	NA	poly(age, 3, raw = TRUE)1	0.3368	0.04503	7.479	2759	1.002e-13	0.2104	0.4632
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01114	0.0016	-6.963	2759	4.141e-12	-0.01564	-0.006652
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001145	0.00001823	6.284	2759	0.0000000003813	0.00006338	0.0001657
fixed	NA	male	0.02304	0.01873	1.23	2706	0.2189	-0.02955	0.07562
fixed	NA	sibling_count3	-0.04001	0.02663	-1.502	2222	0.1331	-0.1148	0.03474
fixed	NA	sibling_count4	-0.02877	0.02928	-0.9824	2175	0.326	-0.111	0.05344
fixed	NA	sibling_count5	-0.06312	0.03551	-1.777	2070	0.07565	-0.1628	0.03656
ran_pars	mother_pidlink	sd__(Intercept)	0.2091	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4435	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.609	0.4061	-6.424	2755	0.0000000001555	-3.749	-1.469
fixed	NA	poly(age, 3, raw = TRUE)1	0.3393	0.0451	7.525	2756	7.108e-14	0.2127	0.4659
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01123	0.001603	-7.008	2756	3.034e-12	-0.01573	-0.006732
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001155	0.00001825	6.327	2756	0.0000000002906	0.00006424	0.0001667
fixed	NA	male	0.024	0.01874	1.28	2705	0.2006	-0.02862	0.07661
fixed	NA	sibling_count3	-0.04452	0.02702	-1.648	2282	0.09953	-0.1204	0.03132
fixed	NA	sibling_count4	-0.02571	0.02964	-0.8673	2229	0.3859	-0.1089	0.05749
fixed	NA	sibling_count5	-0.06802	0.03606	-1.886	2126	0.05937	-0.1692	0.03319
fixed	NA	birth_order_nonlinear2	-0.02078	0.02203	-0.9431	2280	0.3457	-0.08263	0.04107
fixed	NA	birth_order_nonlinear3	0.002846	0.02716	0.1048	2349	0.9165	-0.07339	0.07908
fixed	NA	birth_order_nonlinear4	-0.06343	0.0372	-1.705	2405	0.08831	-0.1678	0.04099
fixed	NA	birth_order_nonlinear5	0.01625	0.05858	0.2775	2341	0.7815	-0.1482	0.1807
ran_pars	mother_pidlink	sd__(Intercept)	0.2091	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4434	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-2.614	0.4067	-6.427	2749	0.0000000001531	-3.755	-1.472
fixed	NA	poly(age, 3, raw = TRUE)1	0.3397	0.04516	7.523	2750	7.208e-14	0.213	0.4665
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01125	0.001605	-7.007	2750	3.047e-12	-0.01575	-0.006742
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001157	0.00001828	6.329	2750	0.0000000002874	0.00006438	0.000167
fixed	NA	male	0.02395	0.01878	1.275	2698	0.2023	-0.02876	0.07666
fixed	NA	count_birth_order2/2	-0.01649	0.03934	-0.4192	2351	0.6751	-0.1269	0.09394
fixed	NA	count_birth_order1/3	-0.0441	0.0341	-1.294	2744	0.1959	-0.1398	0.0516
fixed	NA	count_birth_order2/3	-0.06242	0.03785	-1.649	2749	0.09924	-0.1687	0.04383
fixed	NA	count_birth_order3/3	-0.04046	0.04049	-0.9991	2742	0.3178	-0.1541	0.07321
fixed	NA	count_birth_order1/4	-0.0145	0.04006	-0.362	2750	0.7174	-0.127	0.09795
fixed	NA	count_birth_order2/4	-0.03479	0.04175	-0.8331	2744	0.4048	-0.152	0.08242
fixed	NA	count_birth_order3/4	-0.03409	0.04372	-0.7797	2732	0.4356	-0.1568	0.08863
fixed	NA	count_birth_order4/4	-0.1044	0.04709	-2.217	2726	0.02674	-0.2366	0.02781
fixed	NA	count_birth_order1/5	-0.07888	0.05248	-1.503	2747	0.133	-0.2262	0.06844
fixed	NA	count_birth_order2/5	-0.1248	0.05864	-2.128	2700	0.03346	-0.2894	0.03984
fixed	NA	count_birth_order3/5	-0.04011	0.05608	-0.7152	2704	0.4746	-0.1975	0.1173
fixed	NA	count_birth_order4/5	-0.1071	0.05404	-1.983	2709	0.04748	-0.2588	0.04454
fixed	NA	count_birth_order5/5	-0.05007	0.05685	-0.8807	2701	0.3786	-0.2097	0.1095
ran_pars	mother_pidlink	sd__(Intercept)	0.209	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4439	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	3892	3951	-1936	3872	NA	NA	NA
11	3894	3959	-1936	3872	0.5933	1	0.4411
14	3896	3979	-1934	3868	3.75	3	0.2897
20	3906	4025	-1933	3866	1.579	6	0.9541

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Category_Self-employed

birthorder <- birthorder %>% mutate(outcome = `Category_Self-employed`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1206	0.1226	-0.9834	4493	0.3255	-0.4647	0.2236
fixed	NA	poly(age, 3, raw = TRUE)1	0.012	0.01094	1.097	4392	0.2727	-0.01871	0.04271
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001217	0.0003039	0.4005	4271	0.6888	-0.0007313	0.0009746
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002423	0.000002658	-0.9116	4161	0.3621	-0.000009883	0.000005038
fixed	NA	male	-0.007402	0.0124	-0.5968	4755	0.5507	-0.04222	0.02741
fixed	NA	sibling_count3	-0.02237	0.01799	-1.243	3513	0.2138	-0.07286	0.02813
fixed	NA	sibling_count4	-0.01961	0.0182	-1.078	3307	0.2812	-0.07069	0.03147
fixed	NA	sibling_count5	-0.009391	0.019	-0.4943	3086	0.6211	-0.06272	0.04394
ran_pars	mother_pidlink	sd__(Intercept)	0.1564	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3995	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1194	0.1226	-0.9736	4493	0.3303	-0.4635	0.2248
fixed	NA	birth_order	0.006512	0.006069	1.073	4244	0.2833	-0.01052	0.02355
fixed	NA	poly(age, 3, raw = TRUE)1	0.01103	0.01098	1.005	4392	0.3151	-0.01978	0.04184
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001463	0.0003047	0.4803	4262	0.6311	-0.000709	0.001002
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002589	0.000002662	-0.9726	4153	0.3308	-0.00001006	0.000004884
fixed	NA	male	-0.007341	0.0124	-0.5919	4754	0.554	-0.04215	0.02747
fixed	NA	sibling_count3	-0.02483	0.01813	-1.369	3598	0.171	-0.07573	0.02607
fixed	NA	sibling_count4	-0.02483	0.01884	-1.318	3649	0.1874	-0.07771	0.02804
fixed	NA	sibling_count5	-0.01774	0.02053	-0.8642	3771	0.3875	-0.07537	0.03989
ran_pars	mother_pidlink	sd__(Intercept)	0.1564	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3995	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1273	0.1229	-1.036	4498	0.3001	-0.4723	0.2176
fixed	NA	poly(age, 3, raw = TRUE)1	0.01147	0.01097	1.046	4389	0.2958	-0.01933	0.04228
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001204	0.0003047	0.3952	4256	0.6927	-0.0007349	0.0009757
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002249	0.000002663	-0.8444	4140	0.3985	-0.000009726	0.000005227
fixed	NA	male	-0.00794	0.0124	-0.6405	4750	0.5219	-0.04274	0.02686
fixed	NA	sibling_count3	-0.02604	0.01843	-1.413	3746	0.1577	-0.07777	0.02568
fixed	NA	sibling_count4	-0.02219	0.01914	-1.159	3802	0.2466	-0.07593	0.03155
fixed	NA	sibling_count5	-0.01043	0.02071	-0.5038	3865	0.6144	-0.06857	0.04771
fixed	NA	birth_order_nonlinear2	0.04641	0.01462	3.175	4168	0.001509	0.00538	0.08745
fixed	NA	birth_order_nonlinear3	0.02766	0.01859	1.488	4101	0.1369	-0.02453	0.07985
fixed	NA	birth_order_nonlinear4	0.01196	0.02414	0.4955	4060	0.6203	-0.0558	0.07972
fixed	NA	birth_order_nonlinear5	0.009981	0.03487	0.2862	4070	0.7747	-0.08791	0.1079
ran_pars	mother_pidlink	sd__(Intercept)	0.1568	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3991	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1265	0.123	-1.028	4502	0.3039	-0.4718	0.2189
fixed	NA	poly(age, 3, raw = TRUE)1	0.01062	0.01098	0.9672	4386	0.3335	-0.0202	0.04144
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001361	0.0003048	0.4465	4253	0.6553	-0.0007194	0.0009916
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002308	0.000002664	-0.8666	4137	0.3862	-0.000009785	0.000005168
fixed	NA	male	-0.008281	0.0124	-0.6679	4743	0.5042	-0.04309	0.02652
fixed	NA	count_birth_order2/2	0.07691	0.02482	3.098	4123	0.001961	0.007225	0.1466
fixed	NA	count_birth_order1/3	-0.02403	0.02407	-0.9984	4793	0.3182	-0.09159	0.04353
fixed	NA	count_birth_order2/3	0.03415	0.02669	1.28	4804	0.2008	-0.04077	0.1091
fixed	NA	count_birth_order3/3	0.02757	0.02937	0.9389	4806	0.3478	-0.05486	0.11
fixed	NA	count_birth_order1/4	0.01578	0.02638	0.5979	4804	0.5499	-0.05829	0.08984
fixed	NA	count_birth_order2/4	0.006164	0.0283	0.2178	4806	0.8276	-0.07327	0.0856
fixed	NA	count_birth_order3/4	-0.003886	0.03019	-0.1287	4804	0.8976	-0.08862	0.08085
fixed	NA	count_birth_order4/4	0.02151	0.03211	0.67	4803	0.5029	-0.06863	0.1117
fixed	NA	count_birth_order1/5	0.01111	0.02995	0.3709	4804	0.7107	-0.07297	0.09518
fixed	NA	count_birth_order2/5	0.0492	0.03179	1.547	4801	0.1218	-0.04004	0.1384
fixed	NA	count_birth_order3/5	0.03627	0.03346	1.084	4796	0.2785	-0.05767	0.1302
fixed	NA	count_birth_order4/5	-0.01264	0.03519	-0.359	4775	0.7196	-0.1114	0.08615
fixed	NA	count_birth_order5/5	0.01104	0.03522	0.3136	4791	0.7539	-0.08782	0.1099
ran_pars	mother_pidlink	sd__(Intercept)	0.1569	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.399	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	5504	5569	-2742	5484	NA	NA	NA
11	5505	5576	-2741	5483	1.154	1	0.2828
14	5501	5592	-2737	5473	9.456	3	0.0238
20	5506	5635	-2733	5466	7.697	6	0.2612

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.112	0.3187	3.489	2759	0.000492	0.2174	2.007
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1214	0.03531	-3.439	2760	0.0005935	-0.2205	-0.0223
fixed	NA	poly(age, 3, raw = TRUE)2	0.004639	0.001252	3.705	2760	0.0002156	0.001124	0.008154
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005136	0.00001422	-3.611	2760	0.00031	-0.00009129	-0.00001144
fixed	NA	male	-0.04191	0.0149	-2.813	2721	0.004946	-0.08373	-0.00008659
fixed	NA	sibling_count3	0.01673	0.02117	0.7903	2217	0.4294	-0.04269	0.07615
fixed	NA	sibling_count4	-0.02678	0.022	-1.217	2081	0.2236	-0.08852	0.03497
fixed	NA	sibling_count5	0.04089	0.02453	1.667	1873	0.09571	-0.02797	0.1098
ran_pars	mother_pidlink	sd__(Intercept)	0.157	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3561	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.113	0.3188	3.49	2758	0.0004908	0.2177	2.008
fixed	NA	birth_order	-0.001112	0.007469	-0.1489	2589	0.8816	-0.02208	0.01985
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1213	0.03532	-3.435	2758	0.0006009	-0.2205	-0.02218
fixed	NA	poly(age, 3, raw = TRUE)2	0.004638	0.001252	3.703	2759	0.0002169	0.001123	0.008153
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005138	0.00001423	-3.612	2759	0.0003095	-0.00009131	-0.00001145
fixed	NA	male	-0.04191	0.0149	-2.812	2720	0.004953	-0.08374	-0.00007972
fixed	NA	sibling_count3	0.01727	0.02148	0.8039	2246	0.4215	-0.04303	0.07756
fixed	NA	sibling_count4	-0.02562	0.02332	-1.099	2194	0.2719	-0.09108	0.03983
fixed	NA	sibling_count5	0.04282	0.02776	1.543	2169	0.123	-0.03509	0.1207
ran_pars	mother_pidlink	sd__(Intercept)	0.1571	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3561	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.113	0.3195	3.483	2755	0.0005044	0.2159	2.01
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1218	0.03539	-3.443	2755	0.0005845	-0.2212	-0.0225
fixed	NA	poly(age, 3, raw = TRUE)2	0.004652	0.001255	3.708	2756	0.0002134	0.00113	0.008175
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005151	0.00001425	-3.614	2756	0.0003066	-0.00009151	-0.0000115
fixed	NA	male	-0.04216	0.01491	-2.827	2718	0.004737	-0.08402	-0.0002938
fixed	NA	sibling_count3	0.01836	0.02179	0.8423	2302	0.3997	-0.04282	0.07954
fixed	NA	sibling_count4	-0.02705	0.02361	-1.146	2246	0.252	-0.09334	0.03923
fixed	NA	sibling_count5	0.0469	0.0281	1.669	2210	0.09523	-0.03198	0.1258
fixed	NA	birth_order_nonlinear2	0.01228	0.01776	0.691	2336	0.4896	-0.03759	0.06214
fixed	NA	birth_order_nonlinear3	-0.005867	0.02171	-0.2702	2396	0.787	-0.06681	0.05508
fixed	NA	birth_order_nonlinear4	0.01255	0.02887	0.4346	2459	0.6639	-0.06849	0.09359
fixed	NA	birth_order_nonlinear5	-0.02938	0.0443	-0.6631	2389	0.5073	-0.1537	0.09498
ran_pars	mother_pidlink	sd__(Intercept)	0.1575	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3561	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.101	0.3199	3.443	2749	0.0005833	0.2035	1.999
fixed	NA	poly(age, 3, raw = TRUE)1	-0.122	0.03542	-3.443	2749	0.0005832	-0.2214	-0.02254
fixed	NA	poly(age, 3, raw = TRUE)2	0.004655	0.001256	3.706	2750	0.0002145	0.001129	0.008181
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005152	0.00001427	-3.611	2750	0.0003104	-0.00009157	-0.00001147
fixed	NA	male	-0.04244	0.01494	-2.841	2712	0.00453	-0.08437	-0.0005087
fixed	NA	count_birth_order2/2	0.0532	0.03229	1.648	2406	0.09955	-0.03743	0.1438
fixed	NA	count_birth_order1/3	0.04188	0.02754	1.52	2745	0.1285	-0.03544	0.1192
fixed	NA	count_birth_order2/3	0.03959	0.03056	1.296	2750	0.1952	-0.04619	0.1254
fixed	NA	count_birth_order3/3	0.01101	0.03305	0.3331	2746	0.7391	-0.08175	0.1038
fixed	NA	count_birth_order1/4	-0.006186	0.03172	-0.195	2749	0.8454	-0.09522	0.08285
fixed	NA	count_birth_order2/4	-0.02662	0.03329	-0.7996	2747	0.424	-0.1201	0.06682
fixed	NA	count_birth_order3/4	-0.01179	0.03488	-0.338	2737	0.7354	-0.1097	0.08611
fixed	NA	count_birth_order4/4	0.01099	0.03695	0.2973	2735	0.7663	-0.09273	0.1147
fixed	NA	count_birth_order1/5	0.05724	0.04167	1.374	2747	0.1697	-0.05974	0.1742
fixed	NA	count_birth_order2/5	0.07863	0.04519	1.74	2719	0.08198	-0.04822	0.2055
fixed	NA	count_birth_order3/5	0.06885	0.0423	1.628	2724	0.1037	-0.04988	0.1876
fixed	NA	count_birth_order4/5	0.05676	0.0411	1.381	2722	0.1674	-0.0586	0.1721
fixed	NA	count_birth_order5/5	0.03067	0.04307	0.712	2715	0.4765	-0.09024	0.1516
ran_pars	mother_pidlink	sd__(Intercept)	0.1566	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3566	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	2619	2678	-1300	2599	NA	NA	NA
11	2621	2686	-1300	2599	0.02164	1	0.8831
14	2626	2709	-1299	2598	1.583	3	0.6632
20	2634	2752	-1297	2594	3.881	6	0.6928

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.049	0.3272	3.207	2531	0.001358	0.1308	1.968
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1131	0.03626	-3.118	2531	0.00184	-0.2148	-0.01128
fixed	NA	poly(age, 3, raw = TRUE)2	0.00436	0.001286	3.39	2531	0.0007086	0.0007501	0.007969
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004835	0.00001461	-3.31	2531	0.0009454	-0.00008935	-0.00000735
fixed	NA	male	-0.04432	0.01541	-2.877	2482	0.004054	-0.08756	-0.001071
fixed	NA	sibling_count3	-0.004593	0.02309	-0.1989	2047	0.8424	-0.06942	0.06023
fixed	NA	sibling_count4	-0.03224	0.02342	-1.377	1966	0.1688	-0.09797	0.0335
fixed	NA	sibling_count5	-0.005695	0.02477	-0.2299	1839	0.8182	-0.07524	0.06385
ran_pars	mother_pidlink	sd__(Intercept)	0.1675	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3479	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.05	0.3273	3.207	2530	0.001357	0.131	1.968
fixed	NA	birth_order	-0.0005907	0.007493	-0.07884	2399	0.9372	-0.02162	0.02044
fixed	NA	poly(age, 3, raw = TRUE)1	-0.113	0.03627	-3.117	2530	0.001848	-0.2148	-0.01124
fixed	NA	poly(age, 3, raw = TRUE)2	0.004359	0.001286	3.39	2530	0.0007105	0.0007493	0.00797
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004837	0.00001461	-3.31	2530	0.0009453	-0.00008938	-0.000007352
fixed	NA	male	-0.04433	0.01541	-2.877	2481	0.004051	-0.08759	-0.001076
fixed	NA	sibling_count3	-0.004297	0.0234	-0.1836	2064	0.8543	-0.06998	0.06139
fixed	NA	sibling_count4	-0.03166	0.02453	-1.291	2036	0.1969	-0.1005	0.03719
fixed	NA	sibling_count5	-0.004735	0.02761	-0.1715	2046	0.8639	-0.08223	0.07276
ran_pars	mother_pidlink	sd__(Intercept)	0.1675	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3479	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.054	0.3282	3.212	2527	0.001335	0.1329	1.975
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1141	0.03636	-3.139	2527	0.001714	-0.2162	-0.01208
fixed	NA	poly(age, 3, raw = TRUE)2	0.004394	0.001289	3.408	2527	0.0006646	0.0007749	0.008013
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004871	0.00001465	-3.326	2527	0.0008931	-0.00008982	-0.000007603
fixed	NA	male	-0.04453	0.01542	-2.888	2478	0.003913	-0.08782	-0.001246
fixed	NA	sibling_count3	-0.001584	0.02372	-0.0668	2109	0.9467	-0.06817	0.065
fixed	NA	sibling_count4	-0.02968	0.02481	-1.196	2077	0.2317	-0.09933	0.03997
fixed	NA	sibling_count5	-0.002534	0.02777	-0.09124	2064	0.9273	-0.08049	0.07542
fixed	NA	birth_order_nonlinear2	0.01805	0.01822	0.9904	2121	0.3221	-0.03311	0.06921
fixed	NA	birth_order_nonlinear3	-0.01218	0.02252	-0.5409	2207	0.5886	-0.07539	0.05103
fixed	NA	birth_order_nonlinear4	0.004847	0.02955	0.164	2254	0.8697	-0.0781	0.08779
fixed	NA	birth_order_nonlinear5	0.002927	0.04218	0.06938	2178	0.9447	-0.1155	0.1213
ran_pars	mother_pidlink	sd__(Intercept)	0.1676	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.348	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.035	0.3284	3.15	2521	0.001649	0.1128	1.957
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1142	0.03639	-3.138	2521	0.001723	-0.2163	-0.01203
fixed	NA	poly(age, 3, raw = TRUE)2	0.004394	0.00129	3.405	2521	0.0006717	0.0007717	0.008016
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000487	0.00001466	-3.323	2521	0.0009044	-0.00008985	-0.000007557
fixed	NA	male	-0.04493	0.01545	-2.908	2473	0.003673	-0.0883	-0.001556
fixed	NA	count_birth_order2/2	0.08055	0.0351	2.295	2248	0.02183	-0.01798	0.1791
fixed	NA	count_birth_order1/3	0.02443	0.03018	0.8094	2515	0.4184	-0.06028	0.1091
fixed	NA	count_birth_order2/3	0.04417	0.03276	1.348	2521	0.1777	-0.0478	0.1361
fixed	NA	count_birth_order3/3	-0.01421	0.03599	-0.3948	2516	0.693	-0.1152	0.08682
fixed	NA	count_birth_order1/4	0.01002	0.0329	0.3045	2519	0.7608	-0.08234	0.1024
fixed	NA	count_birth_order2/4	-0.0249	0.03426	-0.7267	2520	0.4675	-0.1211	0.07127
fixed	NA	count_birth_order3/4	-0.008878	0.03737	-0.2375	2505	0.8123	-0.1138	0.09603
fixed	NA	count_birth_order4/4	-0.002061	0.03984	-0.05174	2499	0.9587	-0.1139	0.1098
fixed	NA	count_birth_order1/5	0.02277	0.03946	0.5769	2520	0.5641	-0.08801	0.1335
fixed	NA	count_birth_order2/5	0.02039	0.04089	0.4985	2508	0.6182	-0.0944	0.1352
fixed	NA	count_birth_order3/5	0.01907	0.04154	0.4591	2494	0.6462	-0.09754	0.1357
fixed	NA	count_birth_order4/5	0.01981	0.04213	0.4702	2480	0.6383	-0.09846	0.1381
fixed	NA	count_birth_order5/5	0.02095	0.04244	0.4937	2480	0.6215	-0.09817	0.1401
ran_pars	mother_pidlink	sd__(Intercept)	0.1668	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3483	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	2357	2415	-1168	2337	NA	NA	NA
11	2359	2423	-1168	2337	0.006049	1	0.938
14	2363	2445	-1167	2335	1.949	3	0.5831
20	2368	2485	-1164	2328	6.778	6	0.3418

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.218	0.3247	3.753	2759	0.0001783	0.3071	2.13
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1353	0.03606	-3.752	2759	0.0001789	-0.2365	-0.03408
fixed	NA	poly(age, 3, raw = TRUE)2	0.005209	0.001282	4.064	2760	0.00004949	0.001612	0.008807
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005869	0.0000146	-4.021	2759	0.00005948	-0.00009966	-0.00001772
fixed	NA	male	-0.03916	0.01501	-2.609	2716	0.009137	-0.0813	0.002977
fixed	NA	sibling_count3	0.02419	0.02095	1.155	2215	0.2484	-0.03461	0.08299
fixed	NA	sibling_count4	-0.02397	0.02207	-1.086	2073	0.2775	-0.08592	0.03797
fixed	NA	sibling_count5	0.03404	0.02532	1.344	1808	0.179	-0.03704	0.1051
ran_pars	mother_pidlink	sd__(Intercept)	0.1622	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3573	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.22	0.3247	3.756	2758	0.0001759	0.3083	2.131
fixed	NA	birth_order	-0.003094	0.007611	-0.4066	2561	0.6844	-0.02446	0.01827
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1351	0.03607	-3.745	2758	0.0001842	-0.2363	-0.03383
fixed	NA	poly(age, 3, raw = TRUE)2	0.005206	0.001282	4.061	2758	0.00005019	0.001608	0.008804
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005873	0.0000146	-4.023	2759	0.00005891	-0.00009971	-0.00001776
fixed	NA	male	-0.03919	0.01501	-2.61	2714	0.009092	-0.08134	0.002952
fixed	NA	sibling_count3	0.02571	0.02128	1.208	2242	0.2273	-0.03404	0.08545
fixed	NA	sibling_count4	-0.02081	0.0234	-0.8891	2193	0.374	-0.08651	0.04489
fixed	NA	sibling_count5	0.03922	0.02837	1.382	2085	0.167	-0.04043	0.1189
ran_pars	mother_pidlink	sd__(Intercept)	0.1625	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3573	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.224	0.3254	3.762	2755	0.0001718	0.3109	2.138
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1362	0.03613	-3.768	2755	0.0001678	-0.2376	-0.03473
fixed	NA	poly(age, 3, raw = TRUE)2	0.005242	0.001284	4.082	2755	0.00004584	0.001638	0.008847
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005912	0.00001462	-4.043	2756	0.00005421	-0.0001002	-0.00001807
fixed	NA	male	-0.03964	0.01503	-2.638	2712	0.008387	-0.08182	0.00254
fixed	NA	sibling_count3	0.02762	0.02161	1.278	2300	0.2013	-0.03304	0.08827
fixed	NA	sibling_count4	-0.02282	0.0237	-0.9627	2246	0.3358	-0.08935	0.04371
fixed	NA	sibling_count5	0.04276	0.02883	1.483	2139	0.1382	-0.03816	0.1237
fixed	NA	birth_order_nonlinear2	0.005778	0.01769	0.3267	2306	0.744	-0.04388	0.05543
fixed	NA	birth_order_nonlinear3	-0.01319	0.0218	-0.6048	2374	0.5453	-0.07438	0.04801
fixed	NA	birth_order_nonlinear4	0.0128	0.02985	0.4288	2430	0.6681	-0.071	0.0966
fixed	NA	birth_order_nonlinear5	-0.04222	0.04702	-0.8979	2370	0.3693	-0.1742	0.08977
ran_pars	mother_pidlink	sd__(Intercept)	0.1626	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3573	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.215	0.3256	3.732	2749	0.0001938	0.3012	2.129
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1366	0.03616	-3.777	2749	0.0001618	-0.2381	-0.03509
fixed	NA	poly(age, 3, raw = TRUE)2	0.005262	0.001285	4.094	2749	0.00004364	0.001654	0.008869
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00005939	0.00001464	-4.057	2750	0.000051	-0.0001005	-0.0000183
fixed	NA	male	-0.0399	0.01505	-2.652	2706	0.008054	-0.08213	0.002336
fixed	NA	count_birth_order2/2	0.04292	0.03156	1.36	2372	0.174	-0.04567	0.1315
fixed	NA	count_birth_order1/3	0.0477	0.0273	1.747	2744	0.08069	-0.02893	0.1243
fixed	NA	count_birth_order2/3	0.04547	0.03031	1.5	2749	0.1337	-0.03962	0.1306
fixed	NA	count_birth_order3/3	0.01206	0.03243	0.3719	2743	0.71	-0.07898	0.1031
fixed	NA	count_birth_order1/4	-0.005346	0.03208	-0.1667	2750	0.8677	-0.09539	0.0847
fixed	NA	count_birth_order2/4	-0.03738	0.03344	-1.118	2745	0.2638	-0.1312	0.05649
fixed	NA	count_birth_order3/4	-0.009675	0.03502	-0.2763	2734	0.7824	-0.108	0.08863
fixed	NA	count_birth_order4/4	0.02324	0.03772	0.6161	2730	0.5379	-0.08265	0.1291
fixed	NA	count_birth_order1/5	0.0641	0.04203	1.525	2748	0.1273	-0.05388	0.1821
fixed	NA	count_birth_order2/5	0.07532	0.04698	1.603	2707	0.109	-0.05657	0.2072
fixed	NA	count_birth_order3/5	0.04924	0.04493	1.096	2710	0.2732	-0.07688	0.1754
fixed	NA	count_birth_order4/5	0.03861	0.04329	0.8917	2714	0.3726	-0.08292	0.1601
fixed	NA	count_birth_order5/5	0.01255	0.04555	0.2754	2707	0.783	-0.1153	0.1404
ran_pars	mother_pidlink	sd__(Intercept)	0.1622	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3576	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	2663	2722	-1322	2643	NA	NA	NA
11	2665	2730	-1321	2643	0.1642	1	0.6853
14	2669	2752	-1321	2641	1.786	3	0.618
20	2676	2795	-1318	2636	4.918	6	0.5544

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Category_Unpaid family worker

birthorder <- birthorder %>% mutate(outcome = `Category_Unpaid family worker`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.074	0.08521	12.6	4365	8.547e-36	0.8347	1.313
fixed	NA	poly(age, 3, raw = TRUE)1	-0.07204	0.007602	-9.476	4228	4.288e-21	-0.09338	-0.0507
fixed	NA	poly(age, 3, raw = TRUE)2	0.001664	0.0002111	7.88	4069	4.185e-15	0.001071	0.002256
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001203	0.000001847	-6.516	3928	0.00000000008141	-0.00001722	-0.000006849
fixed	NA	male	-0.06956	0.008628	-8.062	4736	9.418e-16	-0.09378	-0.04534
fixed	NA	sibling_count3	0.01396	0.01249	1.117	3161	0.2639	-0.02111	0.04903
fixed	NA	sibling_count4	0.01928	0.01264	1.526	2926	0.1272	-0.01619	0.05474
fixed	NA	sibling_count5	0.02569	0.01319	1.948	2681	0.05157	-0.01134	0.06271
ran_pars	mother_pidlink	sd__(Intercept)	0.1067	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2786	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.076	0.08512	12.65	4366	5.042e-36	0.8375	1.315
fixed	NA	birth_order	0.01404	0.00422	3.327	4059	0.0008856	0.002195	0.02589
fixed	NA	poly(age, 3, raw = TRUE)1	-0.07413	0.00762	-9.728	4230	3.898e-22	-0.09552	-0.05274
fixed	NA	poly(age, 3, raw = TRUE)2	0.001717	0.0002115	8.116	4060	6.323e-16	0.001123	0.00231
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001239	0.000001848	-6.705	3920	0.00000000002296	-0.00001758	-0.000007204
fixed	NA	male	-0.06942	0.008619	-8.055	4735	9.991e-16	-0.09362	-0.04523
fixed	NA	sibling_count3	0.00864	0.01258	0.6867	3262	0.4923	-0.02668	0.04396
fixed	NA	sibling_count4	0.008	0.01307	0.6121	3318	0.5405	-0.02868	0.04468
fixed	NA	sibling_count5	0.007656	0.01425	0.5374	3461	0.591	-0.03233	0.04765
ran_pars	mother_pidlink	sd__(Intercept)	0.1065	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2783	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.09	0.08538	12.77	4371	1.082e-36	0.8506	1.33
fixed	NA	poly(age, 3, raw = TRUE)1	-0.07412	0.007624	-9.723	4223	4.11e-22	-0.09553	-0.05272
fixed	NA	poly(age, 3, raw = TRUE)2	0.001715	0.0002117	8.105	4048	6.948e-16	0.001121	0.00231
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001237	0.00000185	-6.687	3899	0.00000000002607	-0.00001756	-0.000007177
fixed	NA	male	-0.06943	0.008624	-8.051	4732	1.031e-15	-0.09364	-0.04523
fixed	NA	sibling_count3	0.007621	0.01279	0.5957	3435	0.5514	-0.02829	0.04353
fixed	NA	sibling_count4	0.007502	0.01329	0.5644	3499	0.5725	-0.02981	0.04481
fixed	NA	sibling_count5	0.007968	0.01438	0.5541	3572	0.5796	-0.0324	0.04834
fixed	NA	birth_order_nonlinear2	0.01536	0.01018	1.509	3961	0.1313	-0.01321	0.04393
fixed	NA	birth_order_nonlinear3	0.0327	0.01295	2.526	3881	0.01157	-0.003638	0.06905
fixed	NA	birth_order_nonlinear4	0.04024	0.01681	2.394	3834	0.01672	-0.006946	0.08743
fixed	NA	birth_order_nonlinear5	0.0522	0.02428	2.149	3849	0.03166	-0.01597	0.1204
ran_pars	mother_pidlink	sd__(Intercept)	0.1063	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2785	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	1.098	0.08548	12.85	4377	4.03e-37	0.8584	1.338
fixed	NA	poly(age, 3, raw = TRUE)1	-0.07481	0.007627	-9.809	4219	1.794e-22	-0.09622	-0.0534
fixed	NA	poly(age, 3, raw = TRUE)2	0.00173	0.0002117	8.172	4043	4.012e-16	0.001136	0.002324
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001245	0.00000185	-6.731	3894	0.00000000001927	-0.00001764	-0.000007259
fixed	NA	male	-0.06975	0.008626	-8.086	4726	7.789e-16	-0.09396	-0.04553
fixed	NA	count_birth_order2/2	0.0182	0.01729	1.053	3901	0.2926	-0.03033	0.06673
fixed	NA	count_birth_order1/3	0.002468	0.01674	0.1475	4790	0.8828	-0.04451	0.04945
fixed	NA	count_birth_order2/3	0.01367	0.01856	0.7364	4803	0.4615	-0.03843	0.06577
fixed	NA	count_birth_order3/3	0.06707	0.02042	3.284	4806	0.00103	0.009745	0.1244
fixed	NA	count_birth_order1/4	0.01324	0.01835	0.7216	4804	0.4706	-0.03826	0.06474
fixed	NA	count_birth_order2/4	0.01965	0.01968	0.9983	4806	0.3182	-0.03559	0.07489
fixed	NA	count_birth_order3/4	0.02922	0.02099	1.392	4804	0.164	-0.02971	0.08815
fixed	NA	count_birth_order4/4	0.0618	0.02233	2.767	4802	0.005679	-0.0008934	0.1245
fixed	NA	count_birth_order1/5	0.01713	0.02083	0.8224	4804	0.4109	-0.04134	0.0756
fixed	NA	count_birth_order2/5	0.04536	0.02211	2.051	4800	0.04028	-0.01671	0.1074
fixed	NA	count_birth_order3/5	0.02152	0.02328	0.9247	4793	0.3552	-0.04381	0.08686
fixed	NA	count_birth_order4/5	0.03329	0.02448	1.36	4768	0.174	-0.03543	0.102
fixed	NA	count_birth_order5/5	0.06105	0.0245	2.492	4787	0.01273	-0.007715	0.1298
ran_pars	mother_pidlink	sd__(Intercept)	0.1059	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2786	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	2000	2065	-990.1	1980	NA	NA	NA
11	1991	2062	-984.6	1969	11.08	1	0.0008739
14	1997	2088	-984.5	1969	0.2297	3	0.9727
20	2002	2131	-980.8	1962	7.365	6	0.2884

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.811	0.2353	11.95	2746	4.014e-32	2.151	3.472
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2645	0.02606	-10.15	2746	8.764e-24	-0.3377	-0.1914
fixed	NA	poly(age, 3, raw = TRUE)2	0.008156	0.0009243	8.824	2744	1.922e-18	0.005562	0.01075
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00008159	0.0000105	-7.772	2742	1.084e-14	-0.0001111	-0.00005212
fixed	NA	male	-0.02304	0.01104	-2.087	2732	0.03696	-0.05402	0.007945
fixed	NA	sibling_count3	0.02455	0.01542	1.592	1812	0.1116	-0.01874	0.06783
fixed	NA	sibling_count4	0.04627	0.01599	2.895	1588	0.003847	0.001401	0.09114
fixed	NA	sibling_count5	0.0495	0.01776	2.787	1293	0.005402	-0.0003603	0.09936
ran_pars	mother_pidlink	sd__(Intercept)	0.08741	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.273	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.806	0.2352	11.93	2746	4.986e-32	2.146	3.466
fixed	NA	birth_order	0.01008	0.005552	1.816	2492	0.06947	-0.005501	0.02567
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2651	0.02606	-10.18	2745	6.767e-24	-0.3383	-0.192
fixed	NA	poly(age, 3, raw = TRUE)2	0.008161	0.0009239	8.833	2744	1.788e-18	0.005567	0.01075
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00008138	0.00001049	-7.755	2742	1.24e-14	-0.0001108	-0.00005192
fixed	NA	male	-0.02304	0.01103	-2.088	2730	0.03685	-0.05401	0.007928
fixed	NA	sibling_count3	0.01969	0.01565	1.258	1855	0.2085	-0.02424	0.06363
fixed	NA	sibling_count4	0.03593	0.01697	2.117	1751	0.03443	-0.01172	0.08358
fixed	NA	sibling_count5	0.03213	0.02019	1.591	1680	0.1118	-0.02456	0.08881
ran_pars	mother_pidlink	sd__(Intercept)	0.08833	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2726	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.805	0.2357	11.9	2741	7.027e-32	2.143	3.467
fixed	NA	poly(age, 3, raw = TRUE)1	-0.264	0.0261	-10.11	2741	1.24e-23	-0.3373	-0.1907
fixed	NA	poly(age, 3, raw = TRUE)2	0.00812	0.0009256	8.773	2740	3.005e-18	0.005522	0.01072
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00008093	0.00001051	-7.699	2739	1.906e-14	-0.0001104	-0.00005142
fixed	NA	male	-0.02285	0.01104	-2.07	2729	0.03855	-0.05384	0.008138
fixed	NA	sibling_count3	0.01713	0.01589	1.078	1944	0.2812	-0.02748	0.06173
fixed	NA	sibling_count4	0.03296	0.0172	1.917	1831	0.05541	-0.01531	0.08123
fixed	NA	sibling_count5	0.03575	0.02045	1.748	1735	0.0806	-0.02165	0.09314
fixed	NA	birth_order_nonlinear2	0.01559	0.01327	1.175	2071	0.2401	-0.02166	0.05284
fixed	NA	birth_order_nonlinear3	0.03148	0.0162	1.943	2189	0.05211	-0.01399	0.07696
fixed	NA	birth_order_nonlinear4	0.03481	0.02152	1.618	2311	0.1058	-0.02559	0.0952
fixed	NA	birth_order_nonlinear5	0.00941	0.03305	0.2847	2219	0.7759	-0.08337	0.1022
ran_pars	mother_pidlink	sd__(Intercept)	0.08756	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2729	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.795	0.2357	11.86	2736	1.163e-31	2.134	3.457
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2627	0.02611	-10.06	2736	2.076e-23	-0.3359	-0.1894
fixed	NA	poly(age, 3, raw = TRUE)2	0.00808	0.0009258	8.727	2735	4.462e-18	0.005481	0.01068
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00008057	0.00001052	-7.661	2734	2.535e-14	-0.0001101	-0.00005105
fixed	NA	male	-0.02213	0.01105	-2.003	2722	0.04532	-0.05314	0.008888
fixed	NA	count_birth_order2/2	0.003644	0.02406	0.1514	2146	0.8796	-0.0639	0.07119
fixed	NA	count_birth_order1/3	-0.001973	0.0203	-0.09719	2746	0.9226	-0.05896	0.05501
fixed	NA	count_birth_order2/3	0.03066	0.02255	1.36	2750	0.174	-0.03264	0.09396
fixed	NA	count_birth_order3/3	0.07164	0.0244	2.936	2745	0.003355	0.003141	0.1401
fixed	NA	count_birth_order1/4	0.04786	0.02339	2.046	2749	0.04084	-0.0178	0.1135
fixed	NA	count_birth_order2/4	0.0325	0.02457	1.323	2748	0.186	-0.03648	0.1015
fixed	NA	count_birth_order3/4	0.0417	0.02577	1.618	2738	0.1058	-0.03064	0.114
fixed	NA	count_birth_order4/4	0.07336	0.0273	2.687	2737	0.007262	-0.003289	0.15
fixed	NA	count_birth_order1/5	0.0305	0.03076	0.9913	2749	0.3216	-0.05586	0.1168
fixed	NA	count_birth_order2/5	0.08913	0.03342	2.667	2726	0.007694	-0.004673	0.1829
fixed	NA	count_birth_order3/5	0.04419	0.03127	1.413	2728	0.1578	-0.0436	0.132
fixed	NA	count_birth_order4/5	0.05387	0.03039	1.773	2723	0.07637	-0.03143	0.1392
fixed	NA	count_birth_order5/5	0.04117	0.03186	1.292	2715	0.1964	-0.04826	0.1306
ran_pars	mother_pidlink	sd__(Intercept)	0.08807	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2727	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	943.3	1003	-461.6	923.3	NA	NA	NA
11	942	1007	-460	920	3.299	1	0.06933
14	946.1	1029	-459.1	918.1	1.856	3	0.6028
20	949.7	1068	-454.9	909.7	8.372	6	0.2121

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.879	0.2445	11.78	2518	3.354e-31	2.193	3.566
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2724	0.0271	-10.05	2517	2.452e-23	-0.3485	-0.1964
fixed	NA	poly(age, 3, raw = TRUE)2	0.008458	0.0009611	8.8	2515	2.487e-18	0.00576	0.01116
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000085	0.00001092	-7.787	2512	9.972e-15	-0.0001156	-0.00005436
fixed	NA	male	-0.0269	0.01158	-2.323	2518	0.02024	-0.05941	0.005602
fixed	NA	sibling_count3	0.02317	0.0169	1.371	1777	0.1704	-0.02426	0.0706
fixed	NA	sibling_count4	0.03722	0.01709	2.178	1632	0.02953	-0.01074	0.08519
fixed	NA	sibling_count5	0.02973	0.018	1.651	1417	0.09889	-0.0208	0.08026
ran_pars	mother_pidlink	sd__(Intercept)	0.07611	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2773	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.864	0.2443	11.72	2518	6.181e-31	2.178	3.55
fixed	NA	birth_order	0.01445	0.005651	2.558	2400	0.0106	-0.00141	0.03032
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2726	0.02707	-10.07	2517	2.07e-23	-0.3486	-0.1966
fixed	NA	poly(age, 3, raw = TRUE)2	0.008446	0.0009601	8.797	2515	2.553e-18	0.005751	0.01114
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00008455	0.00001091	-7.753	2513	1.298e-14	-0.0001152	-0.00005393
fixed	NA	male	-0.02644	0.01157	-2.286	2516	0.02236	-0.05891	0.006033
fixed	NA	sibling_count3	0.01605	0.01711	0.9378	1802	0.3485	-0.03199	0.06408
fixed	NA	sibling_count4	0.02332	0.01792	1.302	1737	0.1932	-0.02698	0.07362
fixed	NA	sibling_count5	0.006451	0.02017	0.3199	1709	0.7491	-0.05016	0.06306
ran_pars	mother_pidlink	sd__(Intercept)	0.0769	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2767	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.848	0.2447	11.64	2511	1.563e-30	2.161	3.535
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2693	0.02711	-9.932	2511	7.882e-23	-0.3454	-0.1932
fixed	NA	poly(age, 3, raw = TRUE)2	0.008331	0.0009615	8.665	2510	7.976e-18	0.005632	0.01103
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00008329	0.00001092	-7.628	2507	3.371e-14	-0.0001139	-0.00005264
fixed	NA	male	-0.02615	0.01157	-2.261	2513	0.02384	-0.05861	0.006315
fixed	NA	sibling_count3	0.01028	0.01736	0.5921	1869	0.5538	-0.03845	0.059
fixed	NA	sibling_count4	0.01685	0.01814	0.9293	1798	0.3528	-0.03405	0.06776
fixed	NA	sibling_count5	0.009426	0.02028	0.4647	1736	0.6422	-0.04751	0.06636
fixed	NA	birth_order_nonlinear2	0.01544	0.01386	1.114	1988	0.2656	-0.02348	0.05436
fixed	NA	birth_order_nonlinear3	0.05358	0.01708	3.137	2150	0.001727	0.005643	0.1015
fixed	NA	birth_order_nonlinear4	0.05188	0.02237	2.319	2247	0.02049	-0.01092	0.1147
fixed	NA	birth_order_nonlinear5	0.007977	0.03201	0.2492	2152	0.8032	-0.08187	0.09783
ran_pars	mother_pidlink	sd__(Intercept)	0.07712	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2765	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.832	0.2445	11.58	2505	2.983e-30	2.146	3.518
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2678	0.02709	-9.885	2504	1.25e-22	-0.3439	-0.1918
fixed	NA	poly(age, 3, raw = TRUE)2	0.008279	0.0009608	8.617	2502	1.202e-17	0.005582	0.01098
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00008274	0.00001091	-7.581	2500	4.794e-14	-0.0001134	-0.0000521
fixed	NA	male	-0.02514	0.01157	-2.172	2509	0.02992	-0.05763	0.007345
fixed	NA	count_birth_order2/2	0.02236	0.02659	0.8409	2100	0.4005	-0.05228	0.097
fixed	NA	count_birth_order1/3	0.001725	0.02247	0.0768	2519	0.9388	-0.06134	0.06479
fixed	NA	count_birth_order2/3	0.02104	0.02443	0.8611	2521	0.3892	-0.04755	0.08963
fixed	NA	count_birth_order3/3	0.09582	0.02688	3.564	2518	0.0003721	0.02035	0.1713
fixed	NA	count_birth_order1/4	0.04831	0.02451	1.971	2519	0.0488	-0.02048	0.1171
fixed	NA	count_birth_order2/4	0.007382	0.02556	0.2888	2521	0.7728	-0.06438	0.07914
fixed	NA	count_birth_order3/4	0.05718	0.02795	2.046	2515	0.04087	-0.02127	0.1356
fixed	NA	count_birth_order4/4	0.07931	0.0298	2.661	2513	0.007831	-0.00434	0.163
fixed	NA	count_birth_order1/5	-0.007822	0.02944	-0.2657	2521	0.7905	-0.09047	0.07482
fixed	NA	count_birth_order2/5	0.07993	0.03056	2.615	2518	0.008965	-0.005857	0.1657
fixed	NA	count_birth_order3/5	0.04252	0.03109	1.368	2512	0.1715	-0.04474	0.1298
fixed	NA	count_birth_order4/5	0.0536	0.03156	1.699	2506	0.08949	-0.03497	0.1422
fixed	NA	count_birth_order5/5	0.0195	0.03179	0.6132	2500	0.5398	-0.06975	0.1087
ran_pars	mother_pidlink	sd__(Intercept)	0.07481	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2767	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	883.9	942.3	-432	863.9	NA	NA	NA
11	879.4	943.6	-428.7	857.4	6.55	1	0.01049
14	879.4	961.1	-425.7	851.4	6.01	3	0.1111
20	878.1	994.9	-419.1	838.1	13.25	6	0.03924

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.754	0.2368	11.63	2746	1.523e-30	2.089	3.418
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2578	0.0263	-9.802	2746	2.563e-22	-0.3317	-0.184
fixed	NA	poly(age, 3, raw = TRUE)2	0.007914	0.0009349	8.464	2745	4.127e-17	0.005289	0.01054
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00007893	0.00001065	-7.414	2743	1.621e-13	-0.0001088	-0.00004905
fixed	NA	male	-0.02007	0.01099	-1.826	2728	0.06797	-0.05092	0.01078
fixed	NA	sibling_count3	0.02623	0.01509	1.739	1864	0.08224	-0.01612	0.06858
fixed	NA	sibling_count4	0.04453	0.01586	2.808	1641	0.005037	0.00002278	0.08904
fixed	NA	sibling_count5	0.05563	0.01811	3.072	1278	0.002175	0.00479	0.1065
ran_pars	mother_pidlink	sd__(Intercept)	0.09166	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2706	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.747	0.2367	11.61	2746	1.951e-30	2.083	3.411
fixed	NA	birth_order	0.01227	0.005592	2.194	2471	0.0283	-0.003426	0.02797
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2586	0.02629	-9.835	2745	1.854e-22	-0.3324	-0.1848
fixed	NA	poly(age, 3, raw = TRUE)2	0.007921	0.0009343	8.477	2744	3.708e-17	0.005298	0.01054
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000787	0.00001064	-7.397	2743	1.843e-13	-0.0001086	-0.00004884
fixed	NA	male	-0.01995	0.01098	-1.817	2726	0.06939	-0.05078	0.01088
fixed	NA	sibling_count3	0.02025	0.01533	1.321	1903	0.1865	-0.02277	0.06328
fixed	NA	sibling_count4	0.03207	0.01684	1.905	1808	0.05696	-0.01519	0.07934
fixed	NA	sibling_count5	0.03518	0.02037	1.727	1621	0.08438	-0.02201	0.09238
ran_pars	mother_pidlink	sd__(Intercept)	0.09243	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2701	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.753	0.2372	11.61	2740	1.865e-30	2.088	3.419
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2581	0.02634	-9.801	2741	2.583e-22	-0.3321	-0.1842
fixed	NA	poly(age, 3, raw = TRUE)2	0.007904	0.0009361	8.444	2740	4.912e-17	0.005276	0.01053
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00007851	0.00001066	-7.366	2739	2.311e-13	-0.0001084	-0.00004859
fixed	NA	male	-0.01989	0.011	-1.809	2726	0.07059	-0.05076	0.01098
fixed	NA	sibling_count3	0.01956	0.01557	1.256	1991	0.2093	-0.02415	0.06327
fixed	NA	sibling_count4	0.03138	0.01706	1.839	1886	0.06607	-0.01652	0.07927
fixed	NA	sibling_count5	0.03814	0.02071	1.842	1689	0.06569	-0.01999	0.09628
fixed	NA	birth_order_nonlinear2	0.01996	0.01306	1.528	2079	0.1265	-0.0167	0.05663
fixed	NA	birth_order_nonlinear3	0.02839	0.01608	1.766	2198	0.07759	-0.01674	0.07351
fixed	NA	birth_order_nonlinear4	0.03888	0.02199	1.768	2307	0.07719	-0.02285	0.1006
fixed	NA	birth_order_nonlinear5	0.03379	0.03467	0.9746	2235	0.3299	-0.06353	0.1311
ran_pars	mother_pidlink	sd__(Intercept)	0.09161	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2705	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	2.747	0.2374	11.57	2735	2.82e-30	2.081	3.413
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2576	0.02636	-9.772	2735	3.411e-22	-0.3316	-0.1836
fixed	NA	poly(age, 3, raw = TRUE)2	0.007893	0.000937	8.424	2735	5.782e-17	0.005263	0.01052
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00007851	0.00001067	-7.358	2733	2.459e-13	-0.0001085	-0.00004856
fixed	NA	male	-0.01993	0.01101	-1.81	2721	0.0704	-0.05084	0.01098
fixed	NA	count_birth_order2/2	0.01965	0.02329	0.8439	2146	0.3988	-0.04571	0.08502
fixed	NA	count_birth_order1/3	0.006341	0.0199	0.3187	2745	0.75	-0.04952	0.0622
fixed	NA	count_birth_order2/3	0.04274	0.02213	1.931	2749	0.05354	-0.01938	0.1049
fixed	NA	count_birth_order3/3	0.06814	0.0237	2.875	2741	0.004069	0.001615	0.1347
fixed	NA	count_birth_order1/4	0.04763	0.0234	2.035	2750	0.04192	-0.01806	0.1133
fixed	NA	count_birth_order2/4	0.04463	0.02443	1.827	2746	0.06782	-0.02394	0.1132
fixed	NA	count_birth_order3/4	0.04469	0.0256	1.745	2736	0.08101	-0.02718	0.1166
fixed	NA	count_birth_order4/4	0.07156	0.02758	2.594	2734	0.009532	-0.005871	0.149
fixed	NA	count_birth_order1/5	0.05139	0.03069	1.675	2749	0.09413	-0.03475	0.1375
fixed	NA	count_birth_order2/5	0.06487	0.03438	1.887	2720	0.05932	-0.03165	0.1614
fixed	NA	count_birth_order3/5	0.04752	0.03288	1.445	2719	0.1485	-0.04477	0.1398
fixed	NA	count_birth_order4/5	0.07415	0.03168	2.341	2719	0.01932	-0.01478	0.1631
fixed	NA	count_birth_order5/5	0.07159	0.03334	2.147	2712	0.03186	-0.022	0.1652
ran_pars	mother_pidlink	sd__(Intercept)	0.09081	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2709	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	921.7	980.9	-450.8	901.7	NA	NA	NA
11	918.9	984.1	-448.4	896.9	4.819	1	0.02815
14	924.2	1007	-448.1	896.2	0.6643	3	0.8816
20	932	1051	-446	892	4.182	6	0.6521

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Work Sector

Sector_Agriculture, forestry, fishing and hunting

birthorder <- birthorder %>% mutate(outcome = `Sector_Agriculture, forestry, fishing and hunting`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1096	0.1173	0.935	4355	0.3498	-0.2195	0.4388
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0003363	0.01045	-0.03218	4269	0.9743	-0.02967	0.029
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001506	0.0002899	0.5197	4162	0.6033	-0.0006631	0.0009643
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001799	0.000002532	-0.7107	4062	0.4773	-0.000008906	0.000005307
fixed	NA	male	0.02245	0.01177	1.907	4520	0.05659	-0.01059	0.05549
fixed	NA	sibling_count3	0.003521	0.01738	0.2025	3347	0.8395	-0.04528	0.05232
fixed	NA	sibling_count4	0.002892	0.01763	0.164	3164	0.8697	-0.0466	0.05238
fixed	NA	sibling_count5	0.002738	0.01839	0.1489	2976	0.8817	-0.04888	0.05436
ran_pars	mother_pidlink	sd__(Intercept)	0.1729	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3632	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1123	0.1172	0.9582	4356	0.338	-0.2168	0.4414
fixed	NA	birth_order	0.01095	0.005734	1.91	3967	0.05617	-0.005142	0.02705
fixed	NA	poly(age, 3, raw = TRUE)1	-0.002077	0.01049	-0.1981	4271	0.843	-0.03151	0.02736
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001954	0.0002907	0.672	4155	0.5016	-0.0006208	0.001012
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002106	0.000002536	-0.8305	4055	0.4063	-0.000009225	0.000005013
fixed	NA	male	0.02261	0.01177	1.921	4519	0.05476	-0.01042	0.05564
fixed	NA	sibling_count3	-0.0004637	0.0175	-0.02649	3426	0.9789	-0.0496	0.04867
fixed	NA	sibling_count4	-0.005752	0.0182	-0.3161	3484	0.7519	-0.05683	0.04533
fixed	NA	sibling_count5	-0.01102	0.01975	-0.5582	3613	0.5768	-0.06645	0.04441
ran_pars	mother_pidlink	sd__(Intercept)	0.1729	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.363	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.139	0.1175	1.183	4360	0.2371	-0.1909	0.4689
fixed	NA	poly(age, 3, raw = TRUE)1	-0.002807	0.01048	-0.2678	4265	0.7889	-0.03224	0.02662
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002178	0.0002908	0.7491	4145	0.4538	-0.0005984	0.001034
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002315	0.000002538	-0.9124	4038	0.3616	-0.000009439	0.000004808
fixed	NA	male	0.02272	0.01176	1.932	4514	0.05344	-0.01029	0.05574
fixed	NA	sibling_count3	-0.006273	0.01776	-0.3531	3558	0.724	-0.05614	0.04359
fixed	NA	sibling_count4	-0.01525	0.01848	-0.8252	3628	0.4093	-0.06713	0.03663
fixed	NA	sibling_count5	-0.01281	0.01991	-0.6433	3694	0.5201	-0.0687	0.04308
fixed	NA	birth_order_nonlinear2	-0.01236	0.0138	-0.8957	3919	0.3704	-0.0511	0.02638
fixed	NA	birth_order_nonlinear3	0.04099	0.01747	2.346	3815	0.01904	-0.00806	0.09004
fixed	NA	birth_order_nonlinear4	0.04802	0.0228	2.106	3716	0.03528	-0.01599	0.112
fixed	NA	birth_order_nonlinear5	-0.003216	0.03293	-0.09765	3745	0.9222	-0.09566	0.08923
ran_pars	mother_pidlink	sd__(Intercept)	0.1732	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3626	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1517	0.1176	1.29	4365	0.1972	-0.1785	0.482
fixed	NA	poly(age, 3, raw = TRUE)1	-0.003214	0.01049	-0.3064	4266	0.7593	-0.03266	0.02623
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002279	0.0002908	0.7837	4146	0.4333	-0.0005884	0.001044
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000239	0.000002537	-0.9417	4039	0.3464	-0.000009512	0.000004733
fixed	NA	male	0.02228	0.01176	1.895	4505	0.05818	-0.01073	0.05529
fixed	NA	count_birth_order2/2	-0.03319	0.02345	-1.415	3905	0.1571	-0.09901	0.03264
fixed	NA	count_birth_order1/3	-0.02716	0.02295	-1.184	4604	0.2366	-0.09158	0.03725
fixed	NA	count_birth_order2/3	-0.02609	0.0255	-1.023	4623	0.3063	-0.09769	0.0455
fixed	NA	count_birth_order3/3	0.05206	0.02802	1.858	4624	0.06327	-0.0266	0.1307
fixed	NA	count_birth_order1/4	-0.02378	0.02524	-0.9422	4623	0.3461	-0.09462	0.04706
fixed	NA	count_birth_order2/4	-0.03995	0.02706	-1.476	4625	0.1399	-0.1159	0.03601
fixed	NA	count_birth_order3/4	0.03713	0.02853	1.301	4622	0.1932	-0.04296	0.1172
fixed	NA	count_birth_order4/4	0.009843	0.03074	0.3202	4612	0.7488	-0.07645	0.09614
fixed	NA	count_birth_order1/5	-0.01435	0.02841	-0.505	4622	0.6136	-0.09411	0.06541
fixed	NA	count_birth_order2/5	-0.001036	0.03018	-0.03433	4616	0.9726	-0.08574	0.08367
fixed	NA	count_birth_order3/5	-0.04063	0.03172	-1.281	4601	0.2003	-0.1297	0.04841
fixed	NA	count_birth_order4/5	0.0471	0.03346	1.408	4561	0.1593	-0.04682	0.141
fixed	NA	count_birth_order5/5	-0.02448	0.03359	-0.7289	4589	0.4661	-0.1188	0.0698
ran_pars	mother_pidlink	sd__(Intercept)	0.1736	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3622	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	4670	4734	-2325	4650	NA	NA	NA
11	4668	4739	-2323	4646	3.654	1	0.05595
14	4665	4755	-2318	4637	9.263	3	0.02599
20	4666	4795	-2313	4626	11	6	0.08848

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4298	0.3118	1.378	2632	0.1682	-0.4455	1.305
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03507	0.03451	-1.016	2633	0.3096	-0.1319	0.0618
fixed	NA	poly(age, 3, raw = TRUE)2	0.001356	0.001222	1.109	2633	0.2675	-0.002076	0.004787
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001569	0.00001387	-1.131	2633	0.258	-0.00005462	0.00002324
fixed	NA	male	0.01584	0.01462	1.084	2608	0.2786	-0.02519	0.05687
fixed	NA	sibling_count3	-0.01764	0.02064	-0.8545	2071	0.393	-0.07557	0.0403
fixed	NA	sibling_count4	-0.006795	0.02141	-0.3173	1912	0.751	-0.0669	0.05331
fixed	NA	sibling_count5	0.005005	0.02395	0.209	1682	0.8345	-0.06223	0.07225
ran_pars	mother_pidlink	sd__(Intercept)	0.1401	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3446	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4294	0.3119	1.377	2631	0.1686	-0.446	1.305
fixed	NA	birth_order	0.005404	0.007337	0.7365	2443	0.4615	-0.01519	0.026
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03567	0.03452	-1.033	2631	0.3015	-0.1326	0.06123
fixed	NA	poly(age, 3, raw = TRUE)2	0.001368	0.001223	1.119	2632	0.2633	-0.002064	0.0048
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001568	0.00001387	-1.131	2632	0.2584	-0.00005461	0.00002325
fixed	NA	male	0.01584	0.01462	1.084	2607	0.2785	-0.02519	0.05688
fixed	NA	sibling_count3	-0.02019	0.02093	-0.9647	2103	0.3348	-0.07895	0.03856
fixed	NA	sibling_count4	-0.01235	0.02271	-0.544	2036	0.5865	-0.07609	0.05138
fixed	NA	sibling_count5	-0.004252	0.02705	-0.1572	1997	0.8751	-0.08019	0.07169
ran_pars	mother_pidlink	sd__(Intercept)	0.1402	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3446	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3941	0.3123	1.262	2628	0.2071	-0.4825	1.271
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03118	0.03455	-0.9025	2628	0.3669	-0.1282	0.0658
fixed	NA	poly(age, 3, raw = TRUE)2	0.001212	0.001224	0.9908	2628	0.3219	-0.002222	0.004647
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001401	0.00001388	-1.01	2628	0.3127	-0.00005297	0.00002494
fixed	NA	male	0.01663	0.01462	1.137	2606	0.2555	-0.02441	0.05767
fixed	NA	sibling_count3	-0.02898	0.02121	-1.366	2161	0.172	-0.08851	0.03055
fixed	NA	sibling_count4	-0.0191	0.02297	-0.8312	2090	0.406	-0.08358	0.04539
fixed	NA	sibling_count5	0.00167	0.02735	0.06106	2041	0.9513	-0.0751	0.07844
fixed	NA	birth_order_nonlinear2	0.006427	0.01745	0.3683	2221	0.7127	-0.04256	0.05541
fixed	NA	birth_order_nonlinear3	0.04921	0.02129	2.312	2257	0.02088	-0.01055	0.109
fixed	NA	birth_order_nonlinear4	0.007926	0.02838	0.2793	2318	0.78	-0.07173	0.08759
fixed	NA	birth_order_nonlinear5	-0.03822	0.04392	-0.8702	2233	0.3843	-0.1615	0.08506
ran_pars	mother_pidlink	sd__(Intercept)	0.1398	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3445	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3924	0.3125	1.256	2621	0.2094	-0.4848	1.27
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03153	0.03458	-0.9119	2622	0.3619	-0.1286	0.06553
fixed	NA	poly(age, 3, raw = TRUE)2	0.001212	0.001225	0.9899	2622	0.3223	-0.002225	0.00465
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001388	0.00001389	-0.999	2622	0.3179	-0.00005288	0.00002512
fixed	NA	male	0.016	0.01464	1.092	2601	0.2747	-0.02511	0.0571
fixed	NA	count_birth_order2/2	0.03144	0.03185	0.9872	2253	0.3237	-0.05796	0.1208
fixed	NA	count_birth_order1/3	-0.006786	0.0269	-0.2523	2620	0.8008	-0.08229	0.06871
fixed	NA	count_birth_order2/3	-0.03196	0.02987	-1.07	2624	0.2848	-0.1158	0.05189
fixed	NA	count_birth_order3/3	0.02356	0.03252	0.7245	2619	0.4689	-0.06772	0.1148
fixed	NA	count_birth_order1/4	-0.01457	0.03093	-0.471	2624	0.6377	-0.1014	0.07226
fixed	NA	count_birth_order2/4	0.009346	0.03271	0.2857	2621	0.7751	-0.08248	0.1012
fixed	NA	count_birth_order3/4	0.0513	0.0339	1.513	2614	0.1303	-0.04385	0.1465
fixed	NA	count_birth_order4/4	-0.0323	0.03624	-0.8914	2611	0.3728	-0.134	0.06942
fixed	NA	count_birth_order1/5	-0.001454	0.04081	-0.03564	2622	0.9716	-0.116	0.1131
fixed	NA	count_birth_order2/5	-0.001126	0.04385	-0.02567	2602	0.9795	-0.1242	0.122
fixed	NA	count_birth_order3/5	0.04489	0.04164	1.078	2601	0.2811	-0.07198	0.1618
fixed	NA	count_birth_order4/5	0.05709	0.04057	1.407	2596	0.1595	-0.0568	0.171
fixed	NA	count_birth_order5/5	-0.02803	0.04266	-0.657	2588	0.5113	-0.1478	0.09173
ran_pars	mother_pidlink	sd__(Intercept)	0.1373	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3455	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	2268	2327	-1124	2248	NA	NA	NA
11	2270	2335	-1124	2248	0.5435	1	0.461
14	2269	2351	-1120	2241	6.918	3	0.07455
20	2276	2394	-1118	2236	4.967	6	0.548

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.5068	0.3227	1.57	2418	0.1165	-0.3991	1.413
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04323	0.03574	-1.21	2419	0.2266	-0.1435	0.05709
fixed	NA	poly(age, 3, raw = TRUE)2	0.001633	0.001266	1.29	2419	0.1971	-0.00192	0.005187
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001865	0.00001436	-1.299	2418	0.1942	-0.00005898	0.00002167
fixed	NA	male	0.013	0.01525	0.8523	2395	0.3941	-0.0298	0.0558
fixed	NA	sibling_count3	-0.02287	0.02262	-1.011	1936	0.3122	-0.08636	0.04063
fixed	NA	sibling_count4	-0.004911	0.02293	-0.2142	1840	0.8304	-0.06927	0.05945
fixed	NA	sibling_count5	0.003723	0.02423	0.1537	1705	0.8779	-0.06429	0.07174
ran_pars	mother_pidlink	sd__(Intercept)	0.1411	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.344	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.5047	0.3228	1.563	2418	0.1181	-0.4014	1.411
fixed	NA	birth_order	0.00375	0.007449	0.5034	2300	0.6147	-0.01716	0.02466
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04349	0.03575	-1.217	2418	0.2238	-0.1438	0.05684
fixed	NA	poly(age, 3, raw = TRUE)2	0.001638	0.001266	1.294	2418	0.1958	-0.001916	0.005193
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001862	0.00001437	-1.296	2418	0.1951	-0.00005895	0.00002171
fixed	NA	male	0.01309	0.01525	0.8583	2394	0.3908	-0.02972	0.0559
fixed	NA	sibling_count3	-0.02466	0.0229	-1.077	1955	0.2817	-0.08895	0.03963
fixed	NA	sibling_count4	-0.008467	0.024	-0.3529	1913	0.7242	-0.07583	0.05889
fixed	NA	sibling_count5	-0.002287	0.02701	-0.08467	1924	0.9325	-0.07812	0.07354
ran_pars	mother_pidlink	sd__(Intercept)	0.1412	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.344	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4538	0.3234	1.403	2414	0.1607	-0.4541	1.362
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03751	0.0358	-1.048	2414	0.2949	-0.138	0.06299
fixed	NA	poly(age, 3, raw = TRUE)2	0.001431	0.001268	1.128	2414	0.2594	-0.002129	0.00499
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001637	0.00001439	-1.138	2414	0.2552	-0.00005676	0.00002401
fixed	NA	male	0.01364	0.01525	0.8947	2391	0.371	-0.02916	0.05645
fixed	NA	sibling_count3	-0.03351	0.02319	-1.445	2001	0.1485	-0.0986	0.03157
fixed	NA	sibling_count4	-0.0166	0.02425	-0.6845	1955	0.4937	-0.08468	0.05148
fixed	NA	sibling_count5	0.001543	0.02715	0.05683	1946	0.9547	-0.07466	0.07775
fixed	NA	birth_order_nonlinear2	0.005632	0.01808	0.3114	2047	0.7555	-0.04513	0.05639
fixed	NA	birth_order_nonlinear3	0.04672	0.02231	2.094	2124	0.03638	-0.01591	0.1093
fixed	NA	birth_order_nonlinear4	0.01262	0.02948	0.4281	2183	0.6687	-0.07013	0.09537
fixed	NA	birth_order_nonlinear5	-0.04778	0.04225	-1.131	2088	0.2583	-0.1664	0.07083
ran_pars	mother_pidlink	sd__(Intercept)	0.141	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3438	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4586	0.3237	1.417	2408	0.1567	-0.4502	1.367
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03856	0.03584	-1.076	2408	0.2821	-0.1392	0.06205
fixed	NA	poly(age, 3, raw = TRUE)2	0.001456	0.00127	1.147	2408	0.2515	-0.002108	0.00502
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001655	0.0000144	-1.149	2408	0.2506	-0.00005698	0.00002388
fixed	NA	male	0.01382	0.01528	0.904	2387	0.3661	-0.02909	0.05672
fixed	NA	count_birth_order2/2	0.02845	0.03493	0.8146	2128	0.4154	-0.06959	0.1265
fixed	NA	count_birth_order1/3	-0.01219	0.02974	-0.4098	2406	0.682	-0.09567	0.0713
fixed	NA	count_birth_order2/3	-0.02868	0.03234	-0.887	2409	0.3751	-0.1195	0.06209
fixed	NA	count_birth_order3/3	0.00595	0.03581	0.1661	2404	0.8681	-0.09458	0.1065
fixed	NA	count_birth_order1/4	-0.02077	0.03237	-0.6417	2408	0.5211	-0.1116	0.07008
fixed	NA	count_birth_order2/4	-0.01071	0.03402	-0.3148	2408	0.753	-0.1062	0.0848
fixed	NA	count_birth_order3/4	0.08524	0.03678	2.317	2400	0.02056	-0.01801	0.1885
fixed	NA	count_birth_order4/4	-0.0201	0.03989	-0.5039	2393	0.6144	-0.1321	0.09186
fixed	NA	count_birth_order1/5	0.0172	0.03916	0.4393	2408	0.6605	-0.09273	0.1271
fixed	NA	count_birth_order2/5	0.02253	0.04005	0.5626	2403	0.5738	-0.0899	0.135
fixed	NA	count_birth_order3/5	0.01266	0.04114	0.3079	2391	0.7582	-0.1028	0.1281
fixed	NA	count_birth_order4/5	0.04984	0.04178	1.193	2383	0.233	-0.06743	0.1671
fixed	NA	count_birth_order5/5	-0.03877	0.0424	-0.9143	2376	0.3607	-0.1578	0.08026
ran_pars	mother_pidlink	sd__(Intercept)	0.1379	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3449	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	2082	2140	-1031	2062	NA	NA	NA
11	2084	2148	-1031	2062	0.2536	1	0.6146
14	2083	2164	-1028	2055	6.959	3	0.07323
20	2088	2204	-1024	2048	6.971	6	0.3235

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3212	0.3165	1.015	2636	0.3103	-0.5673	1.21
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02337	0.03513	-0.6652	2636	0.506	-0.122	0.07524
fixed	NA	poly(age, 3, raw = TRUE)2	0.0009649	0.001247	0.7736	2636	0.4392	-0.002536	0.004466
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001167	0.00001419	-0.8222	2636	0.411	-0.00005149	0.00002816
fixed	NA	male	0.0154	0.01468	1.049	2609	0.2943	-0.0258	0.05659
fixed	NA	sibling_count3	-0.00634	0.02034	-0.3117	2075	0.7553	-0.06343	0.05075
fixed	NA	sibling_count4	-0.008444	0.0214	-0.3946	1922	0.6932	-0.0685	0.05162
fixed	NA	sibling_count5	0.007433	0.02465	0.3015	1622	0.7631	-0.06177	0.07664
ran_pars	mother_pidlink	sd__(Intercept)	0.1445	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.345	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3206	0.3165	1.013	2635	0.3112	-0.5679	1.209
fixed	NA	birth_order	0.006712	0.007454	0.9006	2422	0.3679	-0.01421	0.02763
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02413	0.03514	-0.6866	2635	0.4924	-0.1228	0.07451
fixed	NA	poly(age, 3, raw = TRUE)2	0.000981	0.001247	0.7864	2635	0.4317	-0.002521	0.004483
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001167	0.00001419	-0.8227	2635	0.4108	-0.0000515	0.00002815
fixed	NA	male	0.01548	0.01468	1.055	2608	0.2915	-0.02571	0.05668
fixed	NA	sibling_count3	-0.009568	0.02065	-0.4633	2108	0.6432	-0.06755	0.04841
fixed	NA	sibling_count4	-0.01528	0.02271	-0.6731	2054	0.5009	-0.07902	0.04845
fixed	NA	sibling_count5	-0.00364	0.02755	-0.1321	1910	0.8949	-0.08098	0.0737
ran_pars	mother_pidlink	sd__(Intercept)	0.1445	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.345	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.2863	0.3169	0.9035	2631	0.3663	-0.6033	1.176
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01983	0.03517	-0.5639	2632	0.5729	-0.1185	0.07888
fixed	NA	poly(age, 3, raw = TRUE)2	0.0008281	0.001248	0.6633	2632	0.5072	-0.002676	0.004332
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001001	0.0000142	-0.7047	2632	0.481	-0.00004986	0.00002985
fixed	NA	male	0.01645	0.01468	1.12	2607	0.2626	-0.02476	0.05765
fixed	NA	sibling_count3	-0.0174	0.02094	-0.831	2168	0.4061	-0.07619	0.04138
fixed	NA	sibling_count4	-0.02097	0.02297	-0.913	2108	0.3614	-0.08545	0.04351
fixed	NA	sibling_count5	0.006	0.02795	0.2147	1966	0.83	-0.07245	0.08445
fixed	NA	birth_order_nonlinear2	0.01739	0.01733	1.004	2204	0.3157	-0.03125	0.06602
fixed	NA	birth_order_nonlinear3	0.04795	0.02131	2.25	2249	0.02453	-0.01186	0.1078
fixed	NA	birth_order_nonlinear4	0.01351	0.02923	0.4624	2296	0.6439	-0.06853	0.09556
fixed	NA	birth_order_nonlinear5	-0.04285	0.04669	-0.9177	2229	0.3589	-0.1739	0.0882
ran_pars	mother_pidlink	sd__(Intercept)	0.1436	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3451	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.2873	0.3172	0.9057	2624	0.3652	-0.603	1.178
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02013	0.0352	-0.5718	2625	0.5675	-0.1189	0.07868
fixed	NA	poly(age, 3, raw = TRUE)2	0.000828	0.00125	0.6626	2625	0.5077	-0.00268	0.004336
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000009881	0.00001421	-0.6951	2625	0.4871	-0.00004978	0.00003002
fixed	NA	male	0.01642	0.0147	1.117	2602	0.264	-0.02484	0.05768
fixed	NA	count_birth_order2/2	0.02988	0.03109	0.9611	2243	0.3366	-0.05739	0.1172
fixed	NA	count_birth_order1/3	-0.001197	0.02656	-0.04507	2624	0.9641	-0.07576	0.07337
fixed	NA	count_birth_order2/3	-0.007073	0.0295	-0.2398	2628	0.8105	-0.08989	0.07574
fixed	NA	count_birth_order3/3	0.02579	0.03175	0.8122	2622	0.4167	-0.06334	0.1149
fixed	NA	count_birth_order1/4	-0.02618	0.03123	-0.8382	2628	0.402	-0.1138	0.06149
fixed	NA	count_birth_order2/4	0.01164	0.03273	0.3557	2623	0.7221	-0.08022	0.1035
fixed	NA	count_birth_order3/4	0.05322	0.03394	1.568	2616	0.117	-0.04205	0.1485
fixed	NA	count_birth_order4/4	-0.03173	0.03683	-0.8616	2611	0.389	-0.1351	0.07165
fixed	NA	count_birth_order1/5	0.001533	0.04093	0.03745	2627	0.9701	-0.1134	0.1164
fixed	NA	count_birth_order2/5	0.01608	0.0455	0.3534	2596	0.7238	-0.1116	0.1438
fixed	NA	count_birth_order3/5	0.03446	0.04429	0.7781	2593	0.4366	-0.08986	0.1588
fixed	NA	count_birth_order4/5	0.06496	0.0426	1.525	2594	0.1274	-0.05461	0.1845
fixed	NA	count_birth_order5/5	-0.03273	0.04522	-0.7239	2586	0.4692	-0.1597	0.09419
ran_pars	mother_pidlink	sd__(Intercept)	0.1408	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3462	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	2298	2357	-1139	2278	NA	NA	NA
11	2299	2364	-1139	2277	0.813	1	0.3672
14	2299	2381	-1136	2271	6.307	3	0.09758
20	2307	2424	-1133	2267	4.482	6	0.6118

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Sector_Construction

birthorder <- birthorder %>% mutate(outcome = `Sector_Construction`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)

## boundary (singular) fit: see ?isSingular

compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.001036	0.01029	0.1007	4635	0.9198	-0.02785	0.02992
fixed	NA	poly(age, 3, raw = TRUE)1	-0.00001562	0.0009133	-0.0171	4635	0.9864	-0.002579	0.002548
fixed	NA	poly(age, 3, raw = TRUE)2	0.0000002511	0.00002523	0.009951	4635	0.9921	-0.00007057	0.00007107
fixed	NA	poly(age, 3, raw = TRUE)3	0.000000002046	0.0000002196	0.009316	4635	0.9926	-0.0000006143	0.0000006184
fixed	NA	male	0.0014	0.001066	1.313	4635	0.1893	-0.001593	0.004393
fixed	NA	sibling_count3	-0.001717	0.001486	-1.155	4635	0.248	-0.005888	0.002454
fixed	NA	sibling_count4	0.0007807	0.001496	0.5218	4635	0.6018	-0.003419	0.004981
fixed	NA	sibling_count5	-0.0007588	0.00155	-0.4896	4635	0.6244	-0.005109	0.003592
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03594	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.0008323	0.01029	0.08088	4634	0.9355	-0.02805	0.02972
fixed	NA	birth_order	-0.0007178	0.000531	-1.352	4634	0.1765	-0.002208	0.0007727
fixed	NA	poly(age, 3, raw = TRUE)1	0.00009303	0.0009168	0.1015	4634	0.9192	-0.00248	0.002666
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000002422	0.0000253	-0.09571	4634	0.9238	-0.00007345	0.00006861
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000002	0.00000022	0.09094	4634	0.9275	-0.0000005974	0.0000006375
fixed	NA	male	0.001391	0.001066	1.304	4634	0.1922	-0.001602	0.004384
fixed	NA	sibling_count3	-0.001439	0.0015	-0.9591	4634	0.3375	-0.005649	0.002772
fixed	NA	sibling_count4	0.001377	0.00156	0.8827	4634	0.3774	-0.003001	0.005755
fixed	NA	sibling_count5	0.0001781	0.001698	0.1049	4634	0.9165	-0.004587	0.004943
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03593	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.0005132	0.01033	-0.0497	4631	0.9604	-0.0295	0.02847
fixed	NA	poly(age, 3, raw = TRUE)1	0.0001149	0.0009171	0.1252	4631	0.9003	-0.00246	0.002689
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000003243	0.00002532	-0.1281	4631	0.8981	-0.00007431	0.00006783
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000002885	0.0000002202	0.131	4631	0.8958	-0.0000005892	0.0000006468
fixed	NA	male	0.001379	0.001067	1.293	4631	0.1962	-0.001615	0.004373
fixed	NA	sibling_count3	-0.001281	0.001529	-0.8377	4631	0.4022	-0.005574	0.003012
fixed	NA	sibling_count4	0.001694	0.001592	1.064	4631	0.2874	-0.002775	0.006164
fixed	NA	sibling_count5	0.000358	0.001717	0.2084	4631	0.8349	-0.004463	0.005179
fixed	NA	birth_order_nonlinear2	0.0005383	0.001283	0.4196	4631	0.6748	-0.003062	0.004139
fixed	NA	birth_order_nonlinear3	-0.001747	0.001626	-1.074	4631	0.2827	-0.006313	0.002818
fixed	NA	birth_order_nonlinear4	-0.002672	0.002125	-1.257	4631	0.2087	-0.008637	0.003293
fixed	NA	birth_order_nonlinear5	-0.00185	0.003064	-0.6037	4631	0.5461	-0.01045	0.006751
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03594	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.0001367	0.01035	-0.01321	4625	0.9895	-0.02918	0.02891
fixed	NA	poly(age, 3, raw = TRUE)1	0.00007536	0.0009182	0.08207	4625	0.9346	-0.002502	0.002653
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00000237	0.00002534	-0.09355	4625	0.9255	-0.0000735	0.00006876
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000002363	0.0000002203	0.1073	4625	0.9146	-0.0000005947	0.0000006419
fixed	NA	male	0.001365	0.001067	1.279	4625	0.2011	-0.001631	0.004361
fixed	NA	count_birth_order2/2	0.0008685	0.002187	0.3972	4625	0.6912	-0.005269	0.007006
fixed	NA	count_birth_order1/3	-0.001391	0.002061	-0.6751	4625	0.4996	-0.007176	0.004393
fixed	NA	count_birth_order2/3	-0.001409	0.002295	-0.614	4625	0.5392	-0.00785	0.005032
fixed	NA	count_birth_order3/3	-0.001426	0.002525	-0.5648	4625	0.5722	-0.008513	0.005661
fixed	NA	count_birth_order1/4	0.00372	0.002271	1.638	4625	0.1016	-0.002656	0.01009
fixed	NA	count_birth_order2/4	0.001717	0.002437	0.7045	4625	0.4811	-0.005123	0.008556
fixed	NA	count_birth_order3/4	-0.001372	0.002572	-0.5335	4625	0.5937	-0.008591	0.005847
fixed	NA	count_birth_order4/4	-0.001397	0.002773	-0.5038	4625	0.6144	-0.00918	0.006386
fixed	NA	count_birth_order1/5	-0.001436	0.002563	-0.5605	4625	0.5752	-0.008631	0.005758
fixed	NA	count_birth_order2/5	0.002839	0.002724	1.042	4625	0.2973	-0.004807	0.01048
fixed	NA	count_birth_order3/5	-0.001355	0.002866	-0.4728	4625	0.6363	-0.0094	0.00669
fixed	NA	count_birth_order4/5	-0.00145	0.003029	-0.4787	4625	0.6322	-0.009952	0.007052
fixed	NA	count_birth_order5/5	-0.001345	0.003035	-0.4431	4625	0.6577	-0.009864	0.007174
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03595	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-17697	-17632	8858	-17717	NA	NA	NA
11	-17697	-17626	8859	-17719	1.831	1	0.1761
14	-17692	-17602	8860	-17720	1.564	3	0.6675
20	-17684	-17555	8862	-17724	3.873	6	0.6938

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01011	0.03261	-0.31	2634	0.7565	-0.1017	0.08143
fixed	NA	poly(age, 3, raw = TRUE)1	0.001089	0.003609	0.3018	2634	0.7628	-0.009041	0.01122
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002568	0.0001278	-0.2009	2634	0.8408	-0.0003845	0.0003331
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001472	0.00000145	0.1016	2634	0.9191	-0.000003922	0.000004217
fixed	NA	male	0.001146	0.001537	0.7457	2634	0.4559	-0.003169	0.005461
fixed	NA	sibling_count3	-0.002189	0.002107	-1.039	2634	0.2989	-0.008104	0.003725
fixed	NA	sibling_count4	-0.003388	0.002173	-1.559	2634	0.1191	-0.009488	0.002712
fixed	NA	sibling_count5	-0.001382	0.00241	-0.5736	2634	0.5663	-0.008146	0.005382
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03891	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.009762	0.0326	-0.2995	2633	0.7646	-0.1013	0.08174
fixed	NA	birth_order	-0.001465	0.0007791	-1.881	2633	0.06009	-0.003652	0.0007215
fixed	NA	poly(age, 3, raw = TRUE)1	0.001218	0.003608	0.3375	2633	0.7358	-0.00891	0.01134
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0000277	0.0001278	-0.2168	2633	0.8284	-0.0003863	0.0003309
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001336	0.000001449	0.0922	2633	0.9265	-0.000003934	0.000004201
fixed	NA	male	0.001142	0.001536	0.743	2633	0.4576	-0.003171	0.005455
fixed	NA	sibling_count3	-0.001498	0.002138	-0.7008	2633	0.4835	-0.007499	0.004503
fixed	NA	sibling_count4	-0.001896	0.002312	-0.8198	2633	0.4124	-0.008386	0.004595
fixed	NA	sibling_count5	0.001111	0.002749	0.4042	2633	0.6861	-0.006606	0.008828
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03889	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.009893	0.03267	-0.3028	2630	0.762	-0.1016	0.0818
fixed	NA	poly(age, 3, raw = TRUE)1	0.001136	0.003614	0.3143	2630	0.7533	-0.009009	0.01128
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002449	0.000128	-0.1914	2630	0.8482	-0.0003837	0.0003347
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000009634	0.000001451	0.06638	2630	0.9471	-0.000003978	0.00000417
fixed	NA	male	0.001101	0.001538	0.7162	2630	0.474	-0.003216	0.005418
fixed	NA	sibling_count3	-0.001443	0.002173	-0.6642	2630	0.5066	-0.007542	0.004656
fixed	NA	sibling_count4	-0.002054	0.002346	-0.8755	2630	0.3814	-0.008641	0.004532
fixed	NA	sibling_count5	0.0006755	0.002786	0.2424	2630	0.8085	-0.007146	0.008497
fixed	NA	birth_order_nonlinear2	-0.003604	0.00187	-1.927	2630	0.05408	-0.008854	0.001646
fixed	NA	birth_order_nonlinear3	-0.003351	0.002277	-1.471	2630	0.1413	-0.009743	0.003042
fixed	NA	birth_order_nonlinear4	-0.003911	0.003028	-1.292	2630	0.1966	-0.01241	0.004588
fixed	NA	birth_order_nonlinear5	-0.005469	0.004696	-1.165	2630	0.2443	-0.01865	0.007714
ran_pars	mother_pidlink	sd__(Intercept)	0.0000000007183	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.0389	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.008155	0.0327	-0.2494	2624	0.8031	-0.09995	0.08364
fixed	NA	poly(age, 3, raw = TRUE)1	0.0009659	0.003618	0.267	2624	0.7895	-0.00919	0.01112
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00001708	0.0001281	-0.1333	2624	0.8939	-0.0003768	0.0003426
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000000002605	0.000001453	-0.001792	2624	0.9986	-0.000004082	0.000004077
fixed	NA	male	0.001071	0.001541	0.6952	2624	0.487	-0.003253	0.005395
fixed	NA	count_birth_order2/2	-0.00524	0.003411	-1.536	2624	0.1246	-0.01481	0.004335
fixed	NA	count_birth_order1/3	-0.002433	0.002821	-0.8625	2624	0.3885	-0.01035	0.005486
fixed	NA	count_birth_order2/3	-0.005071	0.003136	-1.617	2624	0.106	-0.01387	0.003733
fixed	NA	count_birth_order3/3	-0.005146	0.003419	-1.505	2624	0.1324	-0.01474	0.004451
fixed	NA	count_birth_order1/4	-0.004864	0.003245	-1.499	2624	0.1341	-0.01397	0.004246
fixed	NA	count_birth_order2/4	-0.005094	0.003437	-1.482	2624	0.1384	-0.01474	0.004554
fixed	NA	count_birth_order3/4	-0.005095	0.003566	-1.429	2624	0.1532	-0.0151	0.004914
fixed	NA	count_birth_order4/4	-0.005329	0.003812	-1.398	2624	0.1623	-0.01603	0.005372
fixed	NA	count_birth_order1/5	0.004688	0.004286	1.094	2624	0.2742	-0.007342	0.01672
fixed	NA	count_birth_order2/5	-0.004959	0.004614	-1.075	2624	0.2825	-0.01791	0.007992
fixed	NA	count_birth_order3/5	-0.005094	0.004383	-1.162	2624	0.2452	-0.0174	0.007208
fixed	NA	count_birth_order4/5	-0.005384	0.004272	-1.26	2624	0.2077	-0.01738	0.006608
fixed	NA	count_birth_order5/5	-0.005355	0.004495	-1.191	2624	0.2336	-0.01797	0.007263
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03892	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-9645	-9586	4832	-9665	NA	NA	NA
11	-9647	-9582	4834	-9669	3.548	1	0.05963
14	-9642	-9560	4835	-9670	1.618	3	0.6553
20	-9634	-9516	4837	-9674	3.518	6	0.7416

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01089	0.03525	-0.3091	2419	0.7573	-0.1098	0.08805
fixed	NA	poly(age, 3, raw = TRUE)1	0.001186	0.003903	0.3038	2419	0.7613	-0.00977	0.01214
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002695	0.0001382	-0.1949	2419	0.8455	-0.000415	0.0003611
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001427	0.000001568	0.09099	2419	0.9275	-0.000004259	0.000004545
fixed	NA	male	0.001312	0.001674	0.7836	2419	0.4333	-0.003387	0.00601
fixed	NA	sibling_count3	-0.00277	0.002413	-1.148	2419	0.2511	-0.009544	0.004004
fixed	NA	sibling_count4	-0.004254	0.002437	-1.746	2419	0.08093	-0.01109	0.002585
fixed	NA	sibling_count5	-0.002457	0.00256	-0.9595	2419	0.3374	-0.009644	0.00473
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.04059	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.009765	0.03524	-0.2771	2418	0.7817	-0.1087	0.08915
fixed	NA	birth_order	-0.001436	0.0008233	-1.745	2418	0.08116	-0.003747	0.0008745
fixed	NA	poly(age, 3, raw = TRUE)1	0.001244	0.003902	0.3189	2418	0.7498	-0.009708	0.0122
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002709	0.0001382	-0.196	2418	0.8446	-0.000415	0.0003608
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001131	0.000001568	0.07217	2418	0.9425	-0.000004287	0.000004513
fixed	NA	male	0.001269	0.001673	0.7584	2418	0.4483	-0.003428	0.005966
fixed	NA	sibling_count3	-0.002089	0.002444	-0.8549	2418	0.3927	-0.008948	0.00477
fixed	NA	sibling_count4	-0.002906	0.002555	-1.137	2418	0.2556	-0.01008	0.004267
fixed	NA	sibling_count5	-0.0001687	0.002876	-0.05865	2418	0.9532	-0.008241	0.007903
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.04057	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.009526	0.03532	-0.2697	2415	0.7874	-0.1087	0.08963
fixed	NA	poly(age, 3, raw = TRUE)1	0.001139	0.003911	0.2912	2415	0.7709	-0.009839	0.01212
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002289	0.0001385	-0.1653	2415	0.8687	-0.0004117	0.0003659
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000006329	0.000001571	0.04029	2415	0.9679	-0.000004346	0.000004473
fixed	NA	male	0.001228	0.001675	0.7331	2415	0.4636	-0.003474	0.005929
fixed	NA	sibling_count3	-0.001974	0.002481	-0.7957	2415	0.4263	-0.008937	0.004989
fixed	NA	sibling_count4	-0.002999	0.002589	-1.158	2415	0.2469	-0.01027	0.00427
fixed	NA	sibling_count5	-0.0005531	0.002896	-0.191	2415	0.8485	-0.008681	0.007575
fixed	NA	birth_order_nonlinear2	-0.003996	0.002023	-1.976	2415	0.04829	-0.009674	0.001681
fixed	NA	birth_order_nonlinear3	-0.003559	0.002486	-1.432	2415	0.1524	-0.01054	0.00342
fixed	NA	birth_order_nonlinear4	-0.003896	0.003276	-1.19	2415	0.2344	-0.01309	0.005299
fixed	NA	birth_order_nonlinear5	-0.005202	0.004711	-1.104	2415	0.2696	-0.01842	0.008021
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.04058	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.006905	0.0354	-0.1951	2409	0.8453	-0.1063	0.09245
fixed	NA	poly(age, 3, raw = TRUE)1	0.0009308	0.003919	0.2375	2409	0.8123	-0.01007	0.01193
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00001523	0.0001388	-0.1098	2409	0.9126	-0.0004048	0.0003743
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000002515	0.000001574	-0.01597	2409	0.9873	-0.000004444	0.000004394
fixed	NA	male	0.001195	0.00168	0.7114	2409	0.4769	-0.00352	0.00591
fixed	NA	count_birth_order2/2	-0.00646	0.003899	-1.657	2409	0.09768	-0.01741	0.004485
fixed	NA	count_birth_order1/3	-0.003133	0.003258	-0.9616	2409	0.3364	-0.01228	0.006012
fixed	NA	count_birth_order2/3	-0.006349	0.003546	-1.79	2409	0.07351	-0.0163	0.003605
fixed	NA	count_birth_order3/3	-0.006378	0.003934	-1.621	2409	0.1051	-0.01742	0.004664
fixed	NA	count_birth_order1/4	-0.006219	0.003546	-1.754	2409	0.0796	-0.01617	0.003735
fixed	NA	count_birth_order2/4	-0.006401	0.003733	-1.715	2409	0.08649	-0.01688	0.004076
fixed	NA	count_birth_order3/4	-0.006432	0.004041	-1.592	2409	0.1115	-0.01777	0.00491
fixed	NA	count_birth_order4/4	-0.00667	0.004384	-1.521	2409	0.1283	-0.01898	0.005636
fixed	NA	count_birth_order1/5	0.001545	0.004294	0.3598	2409	0.719	-0.01051	0.0136
fixed	NA	count_birth_order2/5	-0.006309	0.004397	-1.435	2409	0.1514	-0.01865	0.006033
fixed	NA	count_birth_order3/5	-0.006286	0.004522	-1.39	2409	0.1646	-0.01898	0.006408
fixed	NA	count_birth_order4/5	-0.006491	0.004595	-1.413	2409	0.1579	-0.01939	0.006407
fixed	NA	count_birth_order5/5	-0.006595	0.004667	-1.413	2409	0.1578	-0.01969	0.006505
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.04061	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-8654	-8596	4337	-8674	NA	NA	NA
11	-8655	-8591	4338	-8677	3.054	1	0.08056
14	-8651	-8570	4339	-8679	1.967	3	0.5794
20	-8641	-8525	4341	-8681	2.604	6	0.8567

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01083	0.0329	-0.3293	2638	0.7419	-0.1032	0.08151
fixed	NA	poly(age, 3, raw = TRUE)1	0.001152	0.003651	0.3154	2638	0.7524	-0.009096	0.0114
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002768	0.0001296	-0.2136	2638	0.8309	-0.0003915	0.0003361
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001659	0.000001474	0.1126	2638	0.9104	-0.000003971	0.000004303
fixed	NA	male	0.001165	0.001535	0.7592	2638	0.4478	-0.003143	0.005474
fixed	NA	sibling_count3	-0.002126	0.002061	-1.031	2638	0.3025	-0.007912	0.00366
fixed	NA	sibling_count4	-0.003264	0.002155	-1.515	2638	0.1299	-0.009314	0.002785
fixed	NA	sibling_count5	-0.001038	0.002452	-0.4232	2638	0.6722	-0.007922	0.005846
ran_pars	mother_pidlink	sd__(Intercept)	0.0000000009743	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03888	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01045	0.03288	-0.3178	2637	0.7507	-0.1028	0.08185
fixed	NA	birth_order	-0.001479	0.0007882	-1.877	2637	0.06064	-0.003692	0.0007332
fixed	NA	poly(age, 3, raw = TRUE)1	0.001284	0.00365	0.3517	2637	0.7251	-0.008961	0.01153
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002994	0.0001295	-0.2311	2637	0.8172	-0.0003936	0.0003337
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001561	0.000001473	0.1059	2637	0.9156	-0.000003979	0.000004291
fixed	NA	male	0.001144	0.001534	0.7458	2637	0.4559	-0.003163	0.005451
fixed	NA	sibling_count3	-0.00142	0.002094	-0.678	2637	0.4979	-0.007299	0.004459
fixed	NA	sibling_count4	-0.001771	0.002296	-0.7715	2637	0.4405	-0.008217	0.004674
fixed	NA	sibling_count5	0.001379	0.002769	0.498	2637	0.6186	-0.006393	0.009151
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03886	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01096	0.03294	-0.3326	2634	0.7394	-0.1034	0.08151
fixed	NA	poly(age, 3, raw = TRUE)1	0.001241	0.003655	0.3394	2634	0.7343	-0.00902	0.0115
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002818	0.0001297	-0.2172	2634	0.8281	-0.0003924	0.000336
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001361	0.000001475	0.09224	2634	0.9265	-0.000004005	0.000004277
fixed	NA	male	0.001132	0.001536	0.737	2634	0.4612	-0.003179	0.005442
fixed	NA	sibling_count3	-0.00141	0.002131	-0.6616	2634	0.5083	-0.00739	0.004571
fixed	NA	sibling_count4	-0.001969	0.00233	-0.8451	2634	0.3981	-0.00851	0.004572
fixed	NA	sibling_count5	0.0009169	0.002818	0.3254	2634	0.7449	-0.006992	0.008826
fixed	NA	birth_order_nonlinear2	-0.003533	0.001849	-1.911	2634	0.05615	-0.008723	0.001657
fixed	NA	birth_order_nonlinear3	-0.003265	0.002269	-1.439	2634	0.1503	-0.009635	0.003105
fixed	NA	birth_order_nonlinear4	-0.003861	0.003105	-1.244	2634	0.2138	-0.01258	0.004854
fixed	NA	birth_order_nonlinear5	-0.005587	0.004968	-1.125	2634	0.2608	-0.01953	0.008357
ran_pars	mother_pidlink	sd__(Intercept)	0.0000000008166	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03887	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.009204	0.03298	-0.2791	2628	0.7802	-0.1018	0.08337
fixed	NA	poly(age, 3, raw = TRUE)1	0.00107	0.00366	0.2923	2628	0.77	-0.009203	0.01134
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002089	0.0001299	-0.1608	2628	0.8723	-0.0003856	0.0003438
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000004016	0.000001478	0.02718	2628	0.9783	-0.000004107	0.000004188
fixed	NA	male	0.001082	0.001538	0.7034	2628	0.4819	-0.003235	0.005398
fixed	NA	count_birth_order2/2	-0.005017	0.003314	-1.514	2628	0.1302	-0.01432	0.004287
fixed	NA	count_birth_order1/3	-0.002348	0.002769	-0.8478	2628	0.3966	-0.01012	0.005426
fixed	NA	count_birth_order2/3	-0.004927	0.00308	-1.6	2628	0.1098	-0.01357	0.003719
fixed	NA	count_birth_order3/3	-0.005008	0.003321	-1.508	2628	0.1316	-0.01433	0.004313
fixed	NA	count_birth_order1/4	-0.004708	0.003258	-1.445	2628	0.1486	-0.01385	0.004438
fixed	NA	count_birth_order2/4	-0.00494	0.00342	-1.444	2628	0.1488	-0.01454	0.004661
fixed	NA	count_birth_order3/4	-0.004936	0.003551	-1.39	2628	0.1646	-0.0149	0.005031
fixed	NA	count_birth_order4/4	-0.005147	0.003853	-1.336	2628	0.1817	-0.01596	0.005668
fixed	NA	count_birth_order1/5	0.004821	0.004272	1.129	2628	0.2592	-0.00717	0.01681
fixed	NA	count_birth_order2/5	-0.00476	0.004762	-0.9995	2628	0.3176	-0.01813	0.008607
fixed	NA	count_birth_order3/5	-0.004904	0.004637	-1.058	2628	0.2904	-0.01792	0.008113
fixed	NA	count_birth_order4/5	-0.005181	0.004461	-1.161	2628	0.2456	-0.0177	0.007342
fixed	NA	count_birth_order5/5	-0.005186	0.004738	-1.095	2628	0.2738	-0.01849	0.008114
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03889	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-9664	-9605	4842	-9684	NA	NA	NA
11	-9665	-9600	4844	-9687	3.532	1	0.06018
14	-9661	-9578	4844	-9689	1.543	3	0.6723
20	-9652	-9534	4846	-9692	3.354	6	0.7633

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Sector_Electricity, gas, water

birthorder <- birthorder %>% mutate(outcome = `Sector_Electricity, gas, water`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.007924	0.03945	0.2009	4200	0.8408	-0.1028	0.1187
fixed	NA	poly(age, 3, raw = TRUE)1	0.0003106	0.003504	0.08864	4058	0.9294	-0.009525	0.01015
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001944	0.00009688	0.2007	3909	0.8409	-0.0002525	0.0002914
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000003744	0.0000008437	-0.4437	3783	0.6573	-0.000002743	0.000001994
fixed	NA	male	-0.000236	0.004065	-0.05806	4627	0.9537	-0.01165	0.01117
fixed	NA	sibling_count3	-0.006399	0.005721	-1.119	3375	0.2634	-0.02246	0.009659
fixed	NA	sibling_count4	0.0007961	0.00577	0.138	3069	0.8903	-0.0154	0.01699
fixed	NA	sibling_count5	-0.01126	0.005987	-1.881	2792	0.06007	-0.02807	0.005543
ran_pars	mother_pidlink	sd__(Intercept)	0.0251	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1348	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.008121	0.03945	0.2058	4200	0.8369	-0.1026	0.1189
fixed	NA	birth_order	0.0007092	0.002016	0.3517	4232	0.7251	-0.004951	0.006369
fixed	NA	poly(age, 3, raw = TRUE)1	0.0002023	0.003518	0.05751	4059	0.9541	-0.009672	0.01008
fixed	NA	poly(age, 3, raw = TRUE)2	0.00002213	0.00009719	0.2277	3902	0.8199	-0.0002507	0.0002949
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000003925	0.0000008454	-0.4643	3776	0.6425	-0.000002766	0.000001981
fixed	NA	male	-0.0002264	0.004066	-0.0557	4626	0.9556	-0.01164	0.01119
fixed	NA	sibling_count3	-0.006671	0.005773	-1.156	3462	0.248	-0.02288	0.009534
fixed	NA	sibling_count4	0.0002128	0.006004	0.03544	3439	0.9717	-0.01664	0.01707
fixed	NA	sibling_count5	-0.01218	0.006532	-1.865	3533	0.06232	-0.03052	0.006156
ran_pars	mother_pidlink	sd__(Intercept)	0.02511	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1348	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.007238	0.03958	0.1829	4206	0.8549	-0.1039	0.1183
fixed	NA	poly(age, 3, raw = TRUE)1	0.0001906	0.003519	0.05416	4055	0.9568	-0.009686	0.01007
fixed	NA	poly(age, 3, raw = TRUE)2	0.00002024	0.00009723	0.2082	3894	0.8351	-0.0002527	0.0002932
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000003576	0.0000008461	-0.4226	3762	0.6726	-0.000002733	0.000002017
fixed	NA	male	-0.0004508	0.004066	-0.1109	4623	0.9117	-0.01186	0.01096
fixed	NA	sibling_count3	-0.006238	0.005881	-1.061	3618	0.2889	-0.02275	0.01027
fixed	NA	sibling_count4	-0.0003201	0.006124	-0.05228	3611	0.9583	-0.01751	0.01687
fixed	NA	sibling_count5	-0.01017	0.006604	-1.54	3632	0.1237	-0.02871	0.00837
fixed	NA	birth_order_nonlinear2	0.007765	0.004864	1.596	4103	0.1105	-0.00589	0.02142
fixed	NA	birth_order_nonlinear3	0.001531	0.006168	0.2482	4095	0.804	-0.01578	0.01884
fixed	NA	birth_order_nonlinear4	0.009456	0.008059	1.173	4086	0.2407	-0.01317	0.03208
fixed	NA	birth_order_nonlinear5	-0.009664	0.01162	-0.8314	4161	0.4058	-0.0423	0.02297
ran_pars	mother_pidlink	sd__(Intercept)	0.02548	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1347	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.004712	0.03964	0.1189	4211	0.9054	-0.1066	0.116
fixed	NA	poly(age, 3, raw = TRUE)1	0.0003728	0.003521	0.1059	4053	0.9157	-0.009511	0.01026
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001582	0.00009726	0.1627	3891	0.8708	-0.0002572	0.0002888
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000003263	0.0000008461	-0.3856	3759	0.6998	-0.000002701	0.000002049
fixed	NA	male	-0.0005614	0.004067	-0.1381	4616	0.8902	-0.01198	0.01085
fixed	NA	count_birth_order2/2	0.008889	0.008283	1.073	3992	0.2832	-0.01436	0.03214
fixed	NA	count_birth_order1/3	-0.002423	0.007857	-0.3085	4623	0.7578	-0.02448	0.01963
fixed	NA	count_birth_order2/3	-0.003753	0.008748	-0.429	4624	0.6679	-0.02831	0.0208
fixed	NA	count_birth_order3/3	-0.003139	0.009626	-0.3261	4624	0.7444	-0.03016	0.02388
fixed	NA	count_birth_order1/4	-0.006796	0.008658	-0.7849	4625	0.4325	-0.0311	0.01751
fixed	NA	count_birth_order2/4	0.02095	0.00929	2.255	4624	0.02419	-0.005129	0.04702
fixed	NA	count_birth_order3/4	0.001924	0.009805	0.1962	4624	0.8444	-0.0256	0.02945
fixed	NA	count_birth_order4/4	0.002518	0.01057	0.2381	4624	0.8118	-0.02716	0.0322
fixed	NA	count_birth_order1/5	-0.005337	0.009769	-0.5463	4625	0.5849	-0.03276	0.02209
fixed	NA	count_birth_order2/5	-0.01199	0.01038	-1.155	4625	0.248	-0.04114	0.01715
fixed	NA	count_birth_order3/5	-0.01041	0.01092	-0.9534	4625	0.3405	-0.04108	0.02025
fixed	NA	count_birth_order4/5	0.008429	0.01155	0.7301	4624	0.4653	-0.02398	0.04084
fixed	NA	count_birth_order5/5	-0.01946	0.01157	-1.682	4625	0.0926	-0.05194	0.01302
ran_pars	mother_pidlink	sd__(Intercept)	0.02536	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1347	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-5266	-5201	2643	-5286	NA	NA	NA
11	-5264	-5193	2643	-5286	0.1235	1	0.7252
14	-5263	-5173	2645	-5291	4.849	3	0.1832
20	-5259	-5130	2649	-5299	7.929	6	0.2433

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.06505	0.1025	-0.6344	2624	0.5259	-0.3529	0.2228
fixed	NA	poly(age, 3, raw = TRUE)1	0.008055	0.01135	0.7098	2623	0.4779	-0.0238	0.03991
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002381	0.000402	-0.5924	2622	0.5537	-0.001366	0.0008902
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002178	0.00000456	0.4776	2620	0.633	-0.00001062	0.00001498
fixed	NA	male	-0.002941	0.004826	-0.6092	2633	0.5424	-0.01649	0.01061
fixed	NA	sibling_count3	-0.00462	0.006672	-0.6924	2231	0.4887	-0.02335	0.01411
fixed	NA	sibling_count4	0.0006138	0.006895	0.08902	2065	0.9291	-0.01874	0.01997
fixed	NA	sibling_count5	-0.003055	0.00767	-0.3983	1816	0.6904	-0.02458	0.01847
ran_pars	mother_pidlink	sd__(Intercept)	0.02553	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1195	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.06472	0.1026	-0.6311	2623	0.528	-0.3526	0.2232
fixed	NA	birth_order	-0.001559	0.002439	-0.6389	2548	0.5229	-0.008406	0.005289
fixed	NA	poly(age, 3, raw = TRUE)1	0.008198	0.01135	0.7222	2622	0.4703	-0.02367	0.04006
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002405	0.000402	-0.5982	2621	0.5498	-0.001369	0.000888
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002165	0.00000456	0.4748	2619	0.635	-0.00001064	0.00001497
fixed	NA	male	-0.002944	0.004827	-0.6099	2632	0.542	-0.01649	0.01061
fixed	NA	sibling_count3	-0.003886	0.006772	-0.5738	2256	0.5662	-0.02289	0.01512
fixed	NA	sibling_count4	0.002203	0.007333	0.3004	2173	0.7639	-0.01838	0.02279
fixed	NA	sibling_count5	-0.0004021	0.008726	-0.04608	2108	0.9633	-0.0249	0.02409
ran_pars	mother_pidlink	sd__(Intercept)	0.02568	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1195	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.06863	0.1028	-0.6679	2619	0.5042	-0.3571	0.2198
fixed	NA	poly(age, 3, raw = TRUE)1	0.008229	0.01137	0.7239	2619	0.4692	-0.02368	0.04014
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002427	0.0004026	-0.6028	2618	0.5467	-0.001373	0.0008875
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002196	0.000004566	0.4809	2617	0.6306	-0.00001062	0.00001501
fixed	NA	male	-0.002772	0.00483	-0.5738	2629	0.5661	-0.01633	0.01079
fixed	NA	sibling_count3	-0.003353	0.006877	-0.4876	2302	0.6259	-0.02266	0.01595
fixed	NA	sibling_count4	0.004133	0.007436	0.5557	2219	0.5784	-0.01674	0.02501
fixed	NA	sibling_count5	0.00002649	0.00884	0.002997	2144	0.9976	-0.02479	0.02484
fixed	NA	birth_order_nonlinear2	0.005631	0.005837	0.9647	2392	0.3348	-0.01075	0.02202
fixed	NA	birth_order_nonlinear3	-0.004838	0.007113	-0.6802	2435	0.4965	-0.0248	0.01513
fixed	NA	birth_order_nonlinear4	-0.01005	0.009466	-1.062	2487	0.2885	-0.03662	0.01652
fixed	NA	birth_order_nonlinear5	0.005323	0.01467	0.3627	2450	0.7168	-0.03587	0.04651
ran_pars	mother_pidlink	sd__(Intercept)	0.02606	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1194	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.06998	0.1029	-0.6802	2614	0.4965	-0.3588	0.2188
fixed	NA	poly(age, 3, raw = TRUE)1	0.00842	0.01138	0.7397	2613	0.4596	-0.02353	0.04037
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002508	0.0004032	-0.622	2612	0.534	-0.001383	0.0008809
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002296	0.000004573	0.502	2611	0.6157	-0.00001054	0.00001513
fixed	NA	male	-0.002537	0.004839	-0.5243	2623	0.6001	-0.01612	0.01105
fixed	NA	count_birth_order2/2	0.005499	0.01065	0.5166	2380	0.6055	-0.02438	0.03538
fixed	NA	count_birth_order1/3	-0.004257	0.008863	-0.4804	2624	0.631	-0.02914	0.02062
fixed	NA	count_birth_order2/3	0.00115	0.009852	0.1168	2624	0.907	-0.0265	0.0288
fixed	NA	count_birth_order3/3	-0.005093	0.01074	-0.4744	2623	0.6352	-0.03523	0.02504
fixed	NA	count_birth_order1/4	0.007385	0.0102	0.7242	2624	0.469	-0.02124	0.03601
fixed	NA	count_birth_order2/4	0.005426	0.0108	0.5026	2624	0.6153	-0.02488	0.03573
fixed	NA	count_birth_order3/4	0.001932	0.0112	0.1726	2622	0.863	-0.0295	0.03336
fixed	NA	count_birth_order4/4	-0.008564	0.01197	-0.7153	2623	0.4745	-0.04217	0.02504
fixed	NA	count_birth_order1/5	-0.004143	0.01347	-0.3077	2624	0.7583	-0.04194	0.03365
fixed	NA	count_birth_order2/5	0.01853	0.01449	1.279	2623	0.201	-0.02214	0.05921
fixed	NA	count_birth_order3/5	-0.0153	0.01376	-1.112	2622	0.2664	-0.05393	0.02333
fixed	NA	count_birth_order4/5	-0.006532	0.01341	-0.4869	2620	0.6263	-0.04419	0.03112
fixed	NA	count_birth_order5/5	0.005351	0.01411	0.3792	2619	0.7046	-0.03426	0.04496
ran_pars	mother_pidlink	sd__(Intercept)	0.02613	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1195	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-3599	-3540	1809	-3619	NA	NA	NA
11	-3597	-3533	1810	-3619	0.4076	1	0.5232
14	-3595	-3512	1811	-3623	3.435	3	0.3292
20	-3585	-3468	1813	-3625	2.7	6	0.8454

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.0684	0.1066	-0.6415	2413	0.5212	-0.3677	0.2309
fixed	NA	poly(age, 3, raw = TRUE)1	0.008918	0.01181	0.7553	2413	0.4501	-0.02422	0.04206
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002817	0.0004182	-0.6735	2412	0.5007	-0.001456	0.0008923
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002804	0.000004745	0.5909	2410	0.5546	-0.00001052	0.00001612
fixed	NA	male	-0.001801	0.005055	-0.3564	2417	0.7216	-0.01599	0.01239
fixed	NA	sibling_count3	-0.005572	0.007359	-0.7571	2062	0.4491	-0.02623	0.01509
fixed	NA	sibling_count4	-0.005431	0.007442	-0.7298	1963	0.4656	-0.02632	0.01546
fixed	NA	sibling_count5	-0.001223	0.007839	-0.156	1818	0.8761	-0.02323	0.02078
ran_pars	mother_pidlink	sd__(Intercept)	0.0282	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1194	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.06819	0.1067	-0.6394	2412	0.5226	-0.3676	0.2312
fixed	NA	birth_order	-0.0002783	0.002481	-0.1122	2369	0.9107	-0.007241	0.006685
fixed	NA	poly(age, 3, raw = TRUE)1	0.008931	0.01181	0.7563	2411	0.4496	-0.02422	0.04208
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002818	0.0004183	-0.6736	2411	0.5006	-0.001456	0.0008924
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002799	0.000004746	0.5897	2409	0.5554	-0.00001052	0.00001612
fixed	NA	male	-0.001809	0.005056	-0.3578	2416	0.7205	-0.016	0.01238
fixed	NA	sibling_count3	-0.00544	0.007455	-0.7297	2076	0.4657	-0.02637	0.01549
fixed	NA	sibling_count4	-0.005169	0.007802	-0.6626	2028	0.5077	-0.02707	0.01673
fixed	NA	sibling_count5	-0.0007793	0.008783	-0.08872	2017	0.9293	-0.02543	0.02387
ran_pars	mother_pidlink	sd__(Intercept)	0.02823	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1194	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.07223	0.1068	-0.6763	2408	0.4989	-0.372	0.2276
fixed	NA	poly(age, 3, raw = TRUE)1	0.008882	0.01182	0.7511	2408	0.4527	-0.02431	0.04207
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002831	0.0004188	-0.676	2407	0.4991	-0.001459	0.0008925
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002837	0.000004751	0.5972	2406	0.5504	-0.0000105	0.00001617
fixed	NA	male	-0.001594	0.005054	-0.3155	2413	0.7524	-0.01578	0.01259
fixed	NA	sibling_count3	-0.004946	0.007559	-0.6542	2111	0.513	-0.02617	0.01627
fixed	NA	sibling_count4	-0.003435	0.007899	-0.4349	2062	0.6637	-0.02561	0.01874
fixed	NA	sibling_count5	0.0009294	0.008838	0.1052	2035	0.9163	-0.02388	0.02574
fixed	NA	birth_order_nonlinear2	0.01469	0.006057	2.425	2185	0.01539	-0.002313	0.03169
fixed	NA	birth_order_nonlinear3	-0.001744	0.007458	-0.2338	2257	0.8152	-0.02268	0.01919
fixed	NA	birth_order_nonlinear4	-0.004062	0.009839	-0.4129	2307	0.6798	-0.03168	0.02356
fixed	NA	birth_order_nonlinear5	0.004612	0.01413	0.3264	2253	0.7442	-0.03506	0.04428
ran_pars	mother_pidlink	sd__(Intercept)	0.02951	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.119	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.06056	0.1069	-0.5663	2402	0.5713	-0.3608	0.2396
fixed	NA	poly(age, 3, raw = TRUE)1	0.007735	0.01184	0.6532	2402	0.5137	-0.0255	0.04097
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002404	0.0004194	-0.5731	2401	0.5666	-0.001418	0.0009369
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002332	0.000004758	0.4902	2400	0.624	-0.00001102	0.00001569
fixed	NA	male	-0.001669	0.005065	-0.3296	2407	0.7417	-0.01589	0.01255
fixed	NA	count_birth_order2/2	0.009072	0.01167	0.7773	2210	0.437	-0.02369	0.04183
fixed	NA	count_birth_order1/3	-0.0123	0.009829	-1.252	2408	0.2108	-0.03989	0.01529
fixed	NA	count_birth_order2/3	0.01163	0.0107	1.087	2409	0.277	-0.0184	0.04165
fixed	NA	count_birth_order3/3	-0.003251	0.01186	-0.2742	2407	0.784	-0.03654	0.03004
fixed	NA	count_birth_order1/4	-0.01014	0.0107	-0.9474	2409	0.3435	-0.04017	0.0199
fixed	NA	count_birth_order2/4	0.0107	0.01126	0.9503	2409	0.342	-0.0209	0.0423
fixed	NA	count_birth_order3/4	-0.002765	0.01218	-0.227	2407	0.8204	-0.03696	0.03143
fixed	NA	count_birth_order4/4	-0.007614	0.01322	-0.5761	2406	0.5646	-0.04471	0.02948
fixed	NA	count_birth_order1/5	0.01608	0.01296	1.241	2409	0.2146	-0.02029	0.05245
fixed	NA	count_birth_order2/5	0.009684	0.01326	0.7302	2408	0.4653	-0.02754	0.04691
fixed	NA	count_birth_order3/5	-0.01653	0.01363	-1.212	2405	0.2255	-0.05479	0.02174
fixed	NA	count_birth_order4/5	-0.00712	0.01385	-0.5141	2404	0.6073	-0.046	0.03176
fixed	NA	count_birth_order5/5	0.003503	0.01406	0.2491	2401	0.8033	-0.03597	0.04298
ran_pars	mother_pidlink	sd__(Intercept)	0.03001	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1188	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-3288	-3230	1654	-3308	NA	NA	NA
11	-3286	-3222	1654	-3308	0.01217	1	0.9121
14	-3288	-3207	1658	-3316	8.215	3	0.04177
20	-3282	-3166	1661	-3322	6.093	6	0.4128

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01603	0.1034	-0.155	2626	0.8768	-0.3063	0.2743
fixed	NA	poly(age, 3, raw = TRUE)1	0.002543	0.01148	0.2216	2625	0.8246	-0.02968	0.03476
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00004377	0.0004075	-0.1074	2624	0.9145	-0.001188	0.0011
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000001926	0.000004635	0.004155	2622	0.9967	-0.00001299	0.00001303
fixed	NA	male	-0.004404	0.004819	-0.9138	2637	0.3609	-0.01793	0.009124
fixed	NA	sibling_count3	-0.005568	0.006519	-0.8542	2266	0.3931	-0.02387	0.01273
fixed	NA	sibling_count4	0.002938	0.006828	0.4302	2110	0.6671	-0.01623	0.0221
fixed	NA	sibling_count5	-0.001104	0.007798	-0.1415	1787	0.8875	-0.02299	0.02079
ran_pars	mother_pidlink	sd__(Intercept)	0.02368	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1198	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01566	0.1034	-0.1514	2625	0.8797	-0.306	0.2747
fixed	NA	birth_order	-0.001587	0.002468	-0.6431	2554	0.5202	-0.008516	0.005342
fixed	NA	poly(age, 3, raw = TRUE)1	0.002691	0.01148	0.2344	2624	0.8147	-0.02954	0.03492
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0000464	0.0004076	-0.1139	2622	0.9094	-0.00119	0.001098
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000001012	0.000004635	0.002184	2621	0.9983	-0.000013	0.00001302
fixed	NA	male	-0.004425	0.00482	-0.9182	2636	0.3586	-0.01795	0.009104
fixed	NA	sibling_count3	-0.00481	0.006626	-0.7259	2289	0.468	-0.02341	0.01379
fixed	NA	sibling_count4	0.004543	0.007271	0.6248	2219	0.5322	-0.01587	0.02495
fixed	NA	sibling_count5	0.001493	0.008785	0.17	2055	0.865	-0.02317	0.02615
ran_pars	mother_pidlink	sd__(Intercept)	0.02381	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1198	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01826	0.1036	-0.1763	2621	0.8601	-0.3091	0.2725
fixed	NA	poly(age, 3, raw = TRUE)1	0.002578	0.0115	0.2243	2621	0.8226	-0.02969	0.03485
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00004309	0.0004081	-0.1056	2619	0.9159	-0.001189	0.001102
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000002531	0.00000464	-0.005454	2618	0.9956	-0.00001305	0.000013
fixed	NA	male	-0.004399	0.004822	-0.9122	2634	0.3617	-0.01793	0.009137
fixed	NA	sibling_count3	-0.004139	0.006735	-0.6145	2334	0.539	-0.02304	0.01477
fixed	NA	sibling_count4	0.006655	0.007373	0.9026	2261	0.3669	-0.01404	0.02735
fixed	NA	sibling_count5	0.001748	0.008933	0.1956	2099	0.8449	-0.02333	0.02682
fixed	NA	birth_order_nonlinear2	0.005275	0.005774	0.9135	2414	0.3611	-0.01093	0.02148
fixed	NA	birth_order_nonlinear3	-0.005142	0.007092	-0.725	2458	0.4685	-0.02505	0.01476
fixed	NA	birth_order_nonlinear4	-0.0109	0.009711	-1.123	2503	0.2616	-0.03816	0.01636
fixed	NA	birth_order_nonlinear5	0.007513	0.01553	0.4837	2483	0.6287	-0.03609	0.05111
ran_pars	mother_pidlink	sd__(Intercept)	0.02398	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1197	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01895	0.1037	-0.1827	2615	0.855	-0.3101	0.2722
fixed	NA	poly(age, 3, raw = TRUE)1	0.002754	0.01151	0.2393	2615	0.8109	-0.02955	0.03506
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00005161	0.0004086	-0.1263	2613	0.8995	-0.001199	0.001095
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000008738	0.000004648	0.0188	2612	0.985	-0.00001296	0.00001313
fixed	NA	male	-0.004255	0.004829	-0.8812	2628	0.3783	-0.01781	0.0093
fixed	NA	count_birth_order2/2	0.004488	0.01035	0.4336	2403	0.6646	-0.02457	0.03354
fixed	NA	count_birth_order1/3	-0.004156	0.008698	-0.4778	2628	0.6328	-0.02857	0.02026
fixed	NA	count_birth_order2/3	-0.002799	0.009673	-0.2894	2628	0.7723	-0.02995	0.02435
fixed	NA	count_birth_order3/3	-0.00523	0.01042	-0.5017	2626	0.6159	-0.03449	0.02403
fixed	NA	count_birth_order1/4	0.008228	0.01023	0.8039	2628	0.4215	-0.0205	0.03695
fixed	NA	count_birth_order2/4	0.0111	0.01074	1.034	2628	0.3013	-0.01904	0.04125
fixed	NA	count_birth_order3/4	0.002136	0.01115	0.1916	2627	0.848	-0.02915	0.03343
fixed	NA	count_birth_order4/4	-0.007515	0.0121	-0.6212	2627	0.5345	-0.04147	0.02644
fixed	NA	count_birth_order1/5	-0.003897	0.01342	-0.2904	2628	0.7715	-0.04157	0.03377
fixed	NA	count_birth_order2/5	0.02158	0.01495	1.443	2627	0.1491	-0.02039	0.06355
fixed	NA	count_birth_order3/5	-0.01539	0.01456	-1.057	2626	0.2907	-0.05626	0.02548
fixed	NA	count_birth_order4/5	-0.004958	0.014	-0.354	2625	0.7234	-0.04427	0.03435
fixed	NA	count_birth_order5/5	0.00907	0.01487	0.6098	2624	0.542	-0.03268	0.05082
ran_pars	mother_pidlink	sd__(Intercept)	0.02393	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1198	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-3609	-3550	1815	-3629	NA	NA	NA
11	-3607	-3543	1815	-3629	0.4132	1	0.5204
14	-3605	-3523	1817	-3633	3.637	3	0.3035
20	-3596	-3479	1818	-3636	3.027	6	0.8055

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Sector_Finance, insurance, real estate and business services

birthorder <- birthorder %>% mutate(outcome = `Sector_Finance, insurance, real estate and business services`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.0952	0.1248	-0.7629	4271	0.4456	-0.4455	0.2551
fixed	NA	poly(age, 3, raw = TRUE)1	0.02768	0.01111	2.492	4156	0.01275	-0.003503	0.05886
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007003	0.0003078	-2.275	4024	0.02294	-0.001564	0.0001637
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005302	0.000002685	1.975	3905	0.04838	-0.000002235	0.00001284
fixed	NA	male	0.05929	0.01266	4.683	4573	0.000002906	0.02375	0.09483
fixed	NA	sibling_count3	-0.009161	0.01833	-0.4998	3296	0.6173	-0.06062	0.04229
fixed	NA	sibling_count4	-0.02675	0.01856	-1.442	3068	0.1495	-0.07884	0.02534
fixed	NA	sibling_count5	-0.0301	0.01932	-1.558	2846	0.1193	-0.08434	0.02413
ran_pars	mother_pidlink	sd__(Intercept)	0.1521	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4017	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.09684	0.1248	-0.776	4271	0.4378	-0.4471	0.2535
fixed	NA	birth_order	-0.006404	0.006212	-1.031	4040	0.3027	-0.02384	0.01103
fixed	NA	poly(age, 3, raw = TRUE)1	0.02868	0.01115	2.572	4157	0.01015	-0.002621	0.05997
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007255	0.0003087	-2.35	4015	0.01882	-0.001592	0.0001411
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005474	0.00000269	2.035	3896	0.04194	-0.000002077	0.00001303
fixed	NA	male	0.0592	0.01266	4.676	4572	0.000003013	0.02366	0.09474
fixed	NA	sibling_count3	-0.006781	0.01847	-0.3671	3381	0.7136	-0.05863	0.04507
fixed	NA	sibling_count4	-0.02162	0.01921	-1.125	3415	0.2605	-0.07555	0.03231
fixed	NA	sibling_count5	-0.02195	0.02087	-1.052	3538	0.293	-0.08053	0.03663
ran_pars	mother_pidlink	sd__(Intercept)	0.1518	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4018	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.105	0.1252	-0.8384	4275	0.4018	-0.4563	0.2464
fixed	NA	poly(age, 3, raw = TRUE)1	0.02888	0.01115	2.589	4151	0.009654	-0.00243	0.06018
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007299	0.0003089	-2.363	4004	0.01818	-0.001597	0.0001372
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005501	0.000002693	2.043	3879	0.04111	-0.000002057	0.00001306
fixed	NA	male	0.05957	0.01267	4.703	4570	0.000002641	0.02401	0.09513
fixed	NA	sibling_count3	-0.008454	0.01878	-0.4502	3530	0.6526	-0.06116	0.04426
fixed	NA	sibling_count4	-0.01924	0.01955	-0.9846	3577	0.3249	-0.07411	0.03562
fixed	NA	sibling_count5	-0.02423	0.02107	-1.15	3631	0.2501	-0.08338	0.03491
fixed	NA	birth_order_nonlinear2	-0.009479	0.01497	-0.6331	3965	0.5267	-0.05151	0.03255
fixed	NA	birth_order_nonlinear3	-0.006589	0.01897	-0.3473	3895	0.7284	-0.05985	0.04667
fixed	NA	birth_order_nonlinear4	-0.04194	0.02478	-1.692	3827	0.09064	-0.1115	0.02762
fixed	NA	birth_order_nonlinear5	0.0004922	0.03578	0.01376	3878	0.989	-0.09993	0.1009
ran_pars	mother_pidlink	sd__(Intercept)	0.1513	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.402	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1004	0.1254	-0.8004	4280	0.4235	-0.4523	0.2516
fixed	NA	poly(age, 3, raw = TRUE)1	0.02951	0.01116	2.644	4149	0.008233	-0.001824	0.06085
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007396	0.0003091	-2.393	4003	0.01675	-0.001607	0.0001279
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005515	0.000002694	2.047	3877	0.04069	-0.000002046	0.00001308
fixed	NA	male	0.06008	0.01267	4.742	4562	0.000002184	0.02451	0.09565
fixed	NA	count_birth_order2/2	-0.0483	0.02547	-1.896	3910	0.058	-0.1198	0.0232
fixed	NA	count_birth_order1/3	-0.01707	0.02459	-0.6942	4613	0.4876	-0.0861	0.05196
fixed	NA	count_birth_order2/3	-0.0285	0.02736	-1.042	4623	0.2977	-0.1053	0.04831
fixed	NA	count_birth_order3/3	-0.04638	0.03009	-1.541	4625	0.1233	-0.1308	0.03809
fixed	NA	count_birth_order1/4	-0.0567	0.02708	-2.094	4624	0.03629	-0.1327	0.0193
fixed	NA	count_birth_order2/4	-0.0309	0.02905	-1.064	4625	0.2874	-0.1124	0.05063
fixed	NA	count_birth_order3/4	-0.03242	0.03065	-1.058	4624	0.2902	-0.1184	0.0536
fixed	NA	count_birth_order4/4	-0.06348	0.03304	-1.922	4621	0.05472	-0.1562	0.02925
fixed	NA	count_birth_order1/5	-0.05637	0.03052	-1.847	4623	0.06482	-0.142	0.0293
fixed	NA	count_birth_order2/5	-0.02747	0.03243	-0.8471	4620	0.397	-0.1185	0.06355
fixed	NA	count_birth_order3/5	-0.03353	0.03411	-0.9832	4613	0.3255	-0.1293	0.0622
fixed	NA	count_birth_order4/5	-0.09669	0.03602	-2.685	4593	0.007288	-0.1978	0.00441
fixed	NA	count_birth_order5/5	-0.03857	0.03612	-1.068	4609	0.2857	-0.14	0.06283
ran_pars	mother_pidlink	sd__(Intercept)	0.1515	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.402	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	5313	5378	-2647	5293	NA	NA	NA
11	5314	5385	-2646	5292	1.066	1	0.3019
14	5318	5408	-2645	5290	2.037	3	0.5648
20	5324	5453	-2642	5284	6.17	6	0.4045

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.5641	0.3703	-1.523	2623	0.1278	-1.604	0.4753
fixed	NA	poly(age, 3, raw = TRUE)1	0.08228	0.04098	2.008	2623	0.04478	-0.03276	0.1973
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002539	0.001452	-1.749	2622	0.08041	-0.006614	0.001536
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002533	0.00001647	1.538	2620	0.1242	-0.0000209	0.00007155
fixed	NA	male	0.04971	0.01742	2.855	2630	0.004344	0.0008273	0.0986
fixed	NA	sibling_count3	-0.03371	0.02417	-1.394	2085	0.1633	-0.1016	0.03415
fixed	NA	sibling_count4	-0.04468	0.02501	-1.787	1891	0.07414	-0.1149	0.02551
fixed	NA	sibling_count5	-0.09709	0.02785	-3.486	1617	0.000503	-0.1753	-0.01892
ran_pars	mother_pidlink	sd__(Intercept)	0.1114	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.427	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.5634	0.3703	-1.521	2622	0.1283	-1.603	0.4762
fixed	NA	birth_order	-0.004376	0.00879	-0.4979	2499	0.6186	-0.02905	0.0203
fixed	NA	poly(age, 3, raw = TRUE)1	0.0827	0.041	2.017	2621	0.04377	-0.03238	0.1978
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002546	0.001452	-1.754	2620	0.07957	-0.006622	0.001529
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000253	0.00001647	1.536	2619	0.1246	-0.00002093	0.00007153
fixed	NA	male	0.0497	0.01742	2.854	2629	0.004357	0.0008102	0.0986
fixed	NA	sibling_count3	-0.03164	0.02453	-1.29	2119	0.1972	-0.1005	0.03721
fixed	NA	sibling_count4	-0.04021	0.02657	-1.513	2023	0.1304	-0.1148	0.03438
fixed	NA	sibling_count5	-0.08963	0.03163	-2.833	1953	0.004653	-0.1784	-0.000833
ran_pars	mother_pidlink	sd__(Intercept)	0.1113	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.427	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.541	0.371	-1.458	2618	0.1449	-1.582	0.5003
fixed	NA	poly(age, 3, raw = TRUE)1	0.0795	0.04105	1.937	2618	0.05287	-0.03572	0.1947
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002436	0.001454	-1.676	2617	0.09389	-0.006516	0.001644
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002412	0.00001649	1.463	2616	0.1436	-0.00002216	0.0000704
fixed	NA	male	0.04944	0.01743	2.837	2626	0.004588	0.0005227	0.09835
fixed	NA	sibling_count3	-0.0241	0.0249	-0.968	2179	0.3332	-0.09399	0.04579
fixed	NA	sibling_count4	-0.03172	0.02693	-1.178	2080	0.239	-0.1073	0.04388
fixed	NA	sibling_count5	-0.09454	0.03203	-2.952	1997	0.003196	-0.1844	-0.004636
fixed	NA	birth_order_nonlinear2	0.002414	0.02101	0.1149	2287	0.9085	-0.05655	0.06138
fixed	NA	birth_order_nonlinear3	-0.0408	0.0256	-1.594	2339	0.1112	-0.1127	0.03107
fixed	NA	birth_order_nonlinear4	-0.01793	0.03409	-0.5259	2409	0.599	-0.1136	0.07775
fixed	NA	birth_order_nonlinear5	0.05211	0.05282	0.9865	2350	0.324	-0.09617	0.2004
ran_pars	mother_pidlink	sd__(Intercept)	0.1121	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4267	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.5359	0.3714	-1.443	2612	0.1491	-1.578	0.5066
fixed	NA	poly(age, 3, raw = TRUE)1	0.08014	0.04109	1.95	2612	0.05123	-0.0352	0.1955
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002451	0.001455	-1.684	2611	0.09226	-0.006537	0.001634
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002421	0.00001651	1.466	2610	0.1426	-0.00002213	0.00007055
fixed	NA	male	0.05036	0.01745	2.885	2620	0.003947	0.00136	0.09935
fixed	NA	count_birth_order2/2	-0.03881	0.03831	-1.013	2282	0.3111	-0.1464	0.06873
fixed	NA	count_birth_order1/3	-0.04922	0.03198	-1.539	2623	0.1239	-0.139	0.04055
fixed	NA	count_birth_order2/3	-0.01473	0.03554	-0.4144	2624	0.6786	-0.1145	0.08504
fixed	NA	count_birth_order3/3	-0.0825	0.03873	-2.13	2622	0.03326	-0.1912	0.02622
fixed	NA	count_birth_order1/4	-0.05063	0.03679	-1.376	2624	0.1689	-0.1539	0.05265
fixed	NA	count_birth_order2/4	-0.05041	0.03895	-1.294	2623	0.1957	-0.1597	0.05892
fixed	NA	count_birth_order3/4	-0.09033	0.04039	-2.236	2621	0.02541	-0.2037	0.02305
fixed	NA	count_birth_order4/4	-0.03833	0.04319	-0.8876	2620	0.3748	-0.1596	0.08289
fixed	NA	count_birth_order1/5	-0.1059	0.04858	-2.18	2624	0.02936	-0.2423	0.03047
fixed	NA	count_birth_order2/5	-0.08639	0.05227	-1.653	2620	0.09851	-0.2331	0.06034
fixed	NA	count_birth_order3/5	-0.133	0.04964	-2.679	2618	0.007422	-0.2724	0.006338
fixed	NA	count_birth_order4/5	-0.1591	0.04838	-3.289	2616	0.001017	-0.295	-0.02334
fixed	NA	count_birth_order5/5	-0.05616	0.0509	-1.103	2612	0.2699	-0.199	0.08671
ran_pars	mother_pidlink	sd__(Intercept)	0.1109	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4272	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	3183	3242	-1582	3163	NA	NA	NA
11	3185	3250	-1581	3163	0.2487	1	0.618
14	3186	3269	-1579	3158	4.646	3	0.1997
20	3195	3312	-1577	3155	3.491	6	0.7452

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.6825	0.384	-1.778	2414	0.0756	-1.76	0.3953
fixed	NA	poly(age, 3, raw = TRUE)1	0.09304	0.04252	2.188	2414	0.02876	-0.02632	0.2124
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002874	0.001506	-1.908	2413	0.05649	-0.007102	0.001354
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002847	0.00001709	1.666	2412	0.09582	-0.0000195	0.00007644
fixed	NA	male	0.05795	0.01819	3.186	2413	0.001461	0.006892	0.109
fixed	NA	sibling_count3	-0.01966	0.02661	-0.7388	1954	0.4601	-0.09436	0.05504
fixed	NA	sibling_count4	-0.03128	0.02693	-1.162	1842	0.2455	-0.1069	0.04431
fixed	NA	sibling_count5	-0.07082	0.02839	-2.494	1683	0.01272	-0.1505	0.008883
ran_pars	mother_pidlink	sd__(Intercept)	0.1233	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4242	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.6803	0.3841	-1.771	2413	0.07666	-1.758	0.3979
fixed	NA	birth_order	-0.00328	0.008915	-0.3679	2339	0.713	-0.0283	0.02174
fixed	NA	poly(age, 3, raw = TRUE)1	0.09322	0.04253	2.192	2412	0.02849	-0.02617	0.2126
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002876	0.001507	-1.909	2412	0.05635	-0.007105	0.001353
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002842	0.00001709	1.663	2411	0.09646	-0.00001956	0.0000764
fixed	NA	male	0.05785	0.01819	3.18	2412	0.001491	0.006786	0.1089
fixed	NA	sibling_count3	-0.0181	0.02695	-0.6715	1973	0.502	-0.09375	0.05756
fixed	NA	sibling_count4	-0.02819	0.02822	-0.9991	1919	0.3179	-0.1074	0.05101
fixed	NA	sibling_count5	-0.06558	0.03177	-2.065	1913	0.03909	-0.1548	0.02358
ran_pars	mother_pidlink	sd__(Intercept)	0.1232	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4243	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.6344	0.3848	-1.649	2408	0.09935	-1.715	0.4458
fixed	NA	poly(age, 3, raw = TRUE)1	0.08752	0.0426	2.054	2409	0.04006	-0.03207	0.2071
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00268	0.001509	-1.776	2408	0.07586	-0.006916	0.001556
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000263	0.00001712	1.536	2407	0.1246	-0.00002175	0.00007435
fixed	NA	male	0.05767	0.01819	3.17	2408	0.001544	0.0066	0.1087
fixed	NA	sibling_count3	-0.008869	0.02733	-0.3245	2017	0.7456	-0.0856	0.06786
fixed	NA	sibling_count4	-0.01803	0.02857	-0.6311	1960	0.5281	-0.09823	0.06217
fixed	NA	sibling_count5	-0.06864	0.03197	-2.147	1936	0.03194	-0.1584	0.02111
fixed	NA	birth_order_nonlinear2	0.005051	0.02173	0.2324	2096	0.8162	-0.05596	0.06606
fixed	NA	birth_order_nonlinear3	-0.04662	0.02678	-1.741	2184	0.08184	-0.1218	0.02855
fixed	NA	birth_order_nonlinear4	-0.0179	0.03534	-0.5064	2247	0.6127	-0.1171	0.08131
fixed	NA	birth_order_nonlinear5	0.06078	0.05073	1.198	2170	0.2311	-0.08164	0.2032
ran_pars	mother_pidlink	sd__(Intercept)	0.1272	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4229	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.6039	0.3852	-1.568	2402	0.117	-1.685	0.4772
fixed	NA	poly(age, 3, raw = TRUE)1	0.08648	0.04264	2.028	2402	0.04267	-0.03322	0.2062
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002637	0.001511	-1.746	2402	0.08098	-0.006877	0.001603
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002579	0.00001714	1.505	2401	0.1324	-0.00002231	0.00007389
fixed	NA	male	0.05756	0.01823	3.158	2403	0.00161	0.006393	0.1087
fixed	NA	count_birth_order2/2	-0.06508	0.04191	-1.553	2145	0.1206	-0.1827	0.05257
fixed	NA	count_birth_order1/3	-0.03693	0.03539	-1.043	2408	0.2968	-0.1363	0.06241
fixed	NA	count_birth_order2/3	-0.01343	0.03851	-0.3487	2409	0.7274	-0.1215	0.09466
fixed	NA	count_birth_order3/3	-0.08976	0.04268	-2.103	2406	0.03557	-0.2096	0.03005
fixed	NA	count_birth_order1/4	-0.08182	0.03852	-2.124	2408	0.03378	-0.19	0.02632
fixed	NA	count_birth_order2/4	0.001392	0.04053	0.03436	2409	0.9726	-0.1124	0.1152
fixed	NA	count_birth_order3/4	-0.08294	0.04384	-1.892	2405	0.05865	-0.206	0.04013
fixed	NA	count_birth_order4/4	-0.04982	0.04756	-1.047	2403	0.295	-0.1833	0.08369
fixed	NA	count_birth_order1/5	-0.06937	0.04664	-1.487	2409	0.1371	-0.2003	0.06155
fixed	NA	count_birth_order2/5	-0.1115	0.04773	-2.335	2407	0.0196	-0.2455	0.02251
fixed	NA	count_birth_order3/5	-0.1305	0.04906	-2.66	2402	0.007866	-0.2682	0.007213
fixed	NA	count_birth_order4/5	-0.1209	0.04984	-2.426	2398	0.01535	-0.2608	0.01901
fixed	NA	count_birth_order5/5	-0.0318	0.0506	-0.6285	2394	0.5298	-0.1738	0.1102
ran_pars	mother_pidlink	sd__(Intercept)	0.1237	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4237	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	2929	2987	-1455	2909	NA	NA	NA
11	2931	2995	-1455	2909	0.1361	1	0.7122
14	2931	3012	-1451	2903	6.233	3	0.1008
20	2935	3051	-1448	2895	7.511	6	0.2761

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.5427	0.3734	-1.453	2623	0.1462	-1.591	0.5055
fixed	NA	poly(age, 3, raw = TRUE)1	0.07979	0.04144	1.925	2623	0.05432	-0.03655	0.1961
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002416	0.001471	-1.642	2621	0.1007	-0.006546	0.001715
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002346	0.00001674	1.402	2619	0.1611	-0.00002352	0.00007044
fixed	NA	male	0.05437	0.01739	3.127	2635	0.001783	0.005569	0.1032
fixed	NA	sibling_count3	-0.05622	0.02361	-2.381	2094	0.01737	-0.1225	0.01007
fixed	NA	sibling_count4	-0.04845	0.02475	-1.957	1901	0.05045	-0.1179	0.02103
fixed	NA	sibling_count5	-0.1087	0.02832	-3.838	1533	0.0001292	-0.1882	-0.02919
ran_pars	mother_pidlink	sd__(Intercept)	0.1054	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4279	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.5412	0.3735	-1.449	2623	0.1474	-1.589	0.5071
fixed	NA	birth_order	-0.007669	0.008892	-0.8625	2495	0.3885	-0.03263	0.01729
fixed	NA	poly(age, 3, raw = TRUE)1	0.08053	0.04146	1.943	2621	0.05217	-0.03583	0.1969
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00243	0.001472	-1.651	2620	0.09883	-0.00656	0.001701
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002343	0.00001674	1.4	2618	0.1617	-0.00002355	0.00007041
fixed	NA	male	0.05427	0.01739	3.121	2634	0.001823	0.005457	0.1031
fixed	NA	sibling_count3	-0.05255	0.02399	-2.19	2128	0.02863	-0.1199	0.0148
fixed	NA	sibling_count4	-0.04069	0.02634	-1.545	2041	0.1225	-0.1146	0.03324
fixed	NA	sibling_count5	-0.09613	0.03185	-3.018	1845	0.002577	-0.1855	-0.006726
ran_pars	mother_pidlink	sd__(Intercept)	0.1052	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.428	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.5204	0.374	-1.391	2618	0.1642	-1.57	0.5294
fixed	NA	poly(age, 3, raw = TRUE)1	0.07746	0.0415	1.866	2618	0.06209	-0.03904	0.194
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00232	0.001473	-1.575	2616	0.1154	-0.006455	0.001815
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002223	0.00001675	1.327	2615	0.1847	-0.0000248	0.00006925
fixed	NA	male	0.05369	0.0174	3.087	2632	0.002046	0.004863	0.1025
fixed	NA	sibling_count3	-0.04592	0.02438	-1.884	2189	0.05975	-0.1143	0.02251
fixed	NA	sibling_count4	-0.03335	0.0267	-1.249	2098	0.2117	-0.1083	0.04159
fixed	NA	sibling_count5	-0.105	0.03237	-3.244	1901	0.001198	-0.1959	-0.01415
fixed	NA	birth_order_nonlinear2	-0.01285	0.02078	-0.6185	2290	0.5363	-0.07118	0.04547
fixed	NA	birth_order_nonlinear3	-0.04392	0.02553	-1.72	2350	0.08548	-0.1156	0.02774
fixed	NA	birth_order_nonlinear4	-0.03008	0.03497	-0.8602	2413	0.3898	-0.1282	0.06807
fixed	NA	birth_order_nonlinear5	0.05012	0.05592	0.8964	2377	0.3701	-0.1068	0.2071
ran_pars	mother_pidlink	sd__(Intercept)	0.1052	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4279	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.5216	0.3745	-1.393	2612	0.1638	-1.573	0.5297
fixed	NA	poly(age, 3, raw = TRUE)1	0.07852	0.04156	1.889	2612	0.05898	-0.03815	0.1952
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002356	0.001476	-1.596	2610	0.1105	-0.006498	0.001786
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000226	0.00001678	1.347	2609	0.1782	-0.00002451	0.00006971
fixed	NA	male	0.0543	0.01742	3.116	2625	0.001851	0.005388	0.1032
fixed	NA	count_birth_order2/2	-0.0402	0.03725	-1.079	2286	0.2806	-0.1448	0.06437
fixed	NA	count_birth_order1/3	-0.06318	0.03139	-2.012	2627	0.04427	-0.1513	0.02494
fixed	NA	count_birth_order2/3	-0.05513	0.03491	-1.579	2628	0.1144	-0.1531	0.04286
fixed	NA	count_birth_order3/3	-0.09972	0.03761	-2.651	2625	0.008067	-0.2053	0.005858
fixed	NA	count_birth_order1/4	-0.04047	0.03694	-1.096	2628	0.2733	-0.1442	0.06321
fixed	NA	count_birth_order2/4	-0.06359	0.03875	-1.641	2627	0.1009	-0.1724	0.04519
fixed	NA	count_birth_order3/4	-0.09215	0.04022	-2.291	2625	0.02203	-0.205	0.02074
fixed	NA	count_birth_order4/4	-0.05644	0.04365	-1.293	2625	0.1961	-0.179	0.06608
fixed	NA	count_birth_order1/5	-0.124	0.04843	-2.56	2628	0.01053	-0.2599	0.01198
fixed	NA	count_birth_order2/5	-0.1018	0.05395	-1.887	2624	0.0593	-0.2532	0.04965
fixed	NA	count_birth_order3/5	-0.1439	0.05253	-2.74	2622	0.006181	-0.2914	0.003508
fixed	NA	count_birth_order4/5	-0.1673	0.05052	-3.312	2620	0.0009396	-0.3092	-0.0255
fixed	NA	count_birth_order5/5	-0.06397	0.05365	-1.192	2618	0.2333	-0.2146	0.08664
ran_pars	mother_pidlink	sd__(Intercept)	0.1051	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4283	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	3182	3241	-1581	3162	NA	NA	NA
11	3184	3248	-1581	3162	0.7466	1	0.3875
14	3185	3268	-1579	3157	4.143	3	0.2465
20	3196	3313	-1578	3156	1.874	6	0.9309

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Sector_Manufacturing

birthorder <- birthorder %>% mutate(outcome = Sector_Manufacturing)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4453	0.1239	3.595	4256	0.000328	0.0976	0.793
fixed	NA	poly(age, 3, raw = TRUE)1	-0.009442	0.01103	-0.8562	4137	0.3919	-0.04039	0.02151
fixed	NA	poly(age, 3, raw = TRUE)2	0.00007207	0.0003056	0.2359	4000	0.8135	-0.0007857	0.0009298
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000006005	0.000002666	0.2252	3877	0.8218	-0.000006884	0.000008085
fixed	NA	male	-0.02272	0.01255	-1.81	4563	0.07036	-0.05795	0.01251
fixed	NA	sibling_count3	-0.005581	0.01821	-0.3064	3230	0.7593	-0.0567	0.04554
fixed	NA	sibling_count4	-0.005379	0.01844	-0.2917	3002	0.7705	-0.05714	0.04638
fixed	NA	sibling_count5	0.0145	0.0192	0.7549	2780	0.4504	-0.03941	0.0684
ran_pars	mother_pidlink	sd__(Intercept)	0.1548	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3971	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4441	0.1239	3.585	4256	0.0003409	0.09637	0.7918
fixed	NA	birth_order	-0.004553	0.006154	-0.7399	3992	0.4594	-0.02183	0.01272
fixed	NA	poly(age, 3, raw = TRUE)1	-0.008725	0.01107	-0.7882	4138	0.4306	-0.0398	0.02235
fixed	NA	poly(age, 3, raw = TRUE)2	0.00005388	0.0003065	0.1758	3991	0.8605	-0.0008066	0.0009144
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000007249	0.000002671	0.2713	3868	0.7861	-0.000006774	0.000008224
fixed	NA	male	-0.02279	0.01255	-1.815	4562	0.06954	-0.05802	0.01245
fixed	NA	sibling_count3	-0.003895	0.01835	-0.2122	3317	0.832	-0.05542	0.04763
fixed	NA	sibling_count4	-0.001735	0.01909	-0.09088	3356	0.9276	-0.05531	0.05184
fixed	NA	sibling_count5	0.02028	0.02073	0.978	3485	0.3282	-0.03792	0.07847
ran_pars	mother_pidlink	sd__(Intercept)	0.1547	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3971	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4327	0.1243	3.482	4262	0.0005028	0.08386	0.7815
fixed	NA	poly(age, 3, raw = TRUE)1	-0.008547	0.01107	-0.7719	4134	0.4402	-0.03963	0.02253
fixed	NA	poly(age, 3, raw = TRUE)2	0.00004687	0.0003067	0.1528	3982	0.8786	-0.0008141	0.0009079
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000008012	0.000002674	0.2996	3852	0.7645	-0.000006706	0.000008308
fixed	NA	male	-0.0232	0.01256	-1.848	4558	0.06469	-0.05845	0.01204
fixed	NA	sibling_count3	0.001244	0.01866	0.0667	3469	0.9468	-0.05113	0.05362
fixed	NA	sibling_count4	0.001444	0.01942	0.07434	3522	0.9407	-0.05307	0.05595
fixed	NA	sibling_count5	0.02355	0.02093	1.125	3580	0.2606	-0.0352	0.08231
fixed	NA	birth_order_nonlinear2	0.01144	0.01483	0.7719	3915	0.4402	-0.03017	0.05306
fixed	NA	birth_order_nonlinear3	-0.02673	0.01879	-1.423	3836	0.1548	-0.07947	0.026
fixed	NA	birth_order_nonlinear4	0.0003358	0.02453	0.01369	3759	0.9891	-0.06853	0.0692
fixed	NA	birth_order_nonlinear5	-0.01665	0.03542	-0.4701	3810	0.6383	-0.1161	0.08278
ran_pars	mother_pidlink	sd__(Intercept)	0.155	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.397	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4257	0.1245	3.42	4266	0.000631	0.07635	0.775
fixed	NA	poly(age, 3, raw = TRUE)1	-0.008696	0.01108	-0.7846	4130	0.4328	-0.03981	0.02242
fixed	NA	poly(age, 3, raw = TRUE)2	0.00004825	0.0003069	0.1572	3978	0.8751	-0.0008132	0.0009097
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000008123	0.000002675	0.3037	3847	0.7614	-0.000006696	0.000008321
fixed	NA	male	-0.0231	0.01256	-1.839	4551	0.06604	-0.05836	0.01217
fixed	NA	count_birth_order2/2	0.03699	0.02523	1.466	3863	0.1427	-0.03382	0.1078
fixed	NA	count_birth_order1/3	0.02035	0.02439	0.8342	4611	0.4042	-0.04812	0.08882
fixed	NA	count_birth_order2/3	0.01117	0.02714	0.4117	4623	0.6806	-0.06501	0.08735
fixed	NA	count_birth_order3/3	-0.01932	0.02984	-0.6473	4625	0.5175	-0.1031	0.06445
fixed	NA	count_birth_order1/4	0.00998	0.02685	0.3716	4624	0.7102	-0.0654	0.08536
fixed	NA	count_birth_order2/4	0.02797	0.02881	0.9711	4625	0.3316	-0.05289	0.1088
fixed	NA	count_birth_order3/4	-0.03503	0.03039	-1.153	4624	0.2492	-0.1203	0.05028
fixed	NA	count_birth_order4/4	0.02918	0.03276	0.8906	4620	0.3732	-0.06279	0.1211
fixed	NA	count_birth_order1/5	0.04134	0.03027	1.366	4623	0.1721	-0.04362	0.1263
fixed	NA	count_birth_order2/5	0.02482	0.03216	0.772	4619	0.4402	-0.06544	0.1151
fixed	NA	count_birth_order3/5	0.03738	0.03382	1.105	4611	0.269	-0.05755	0.1323
fixed	NA	count_birth_order4/5	0.01092	0.03571	0.3059	4587	0.7597	-0.08932	0.1112
fixed	NA	count_birth_order5/5	0.01666	0.03582	0.4651	4606	0.6419	-0.08389	0.1172
ran_pars	mother_pidlink	sd__(Intercept)	0.1545	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3972	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	5236	5301	-2608	5216	NA	NA	NA
11	5238	5309	-2608	5216	0.5488	1	0.4588
14	5240	5330	-2606	5212	3.545	3	0.315
20	5247	5376	-2604	5207	4.996	6	0.5444

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4024	0.3641	1.105	2632	0.2692	-0.6197	1.424
fixed	NA	poly(age, 3, raw = TRUE)1	-0.004128	0.0403	-0.1025	2632	0.9184	-0.1172	0.109
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001751	0.001427	-0.1226	2632	0.9024	-0.004182	0.003832
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003959	0.00001619	0.2445	2632	0.8069	-0.0000415	0.00004942
fixed	NA	male	-0.01904	0.01708	-1.115	2612	0.265	-0.06697	0.02889
fixed	NA	sibling_count3	0.00216	0.02406	0.08977	2082	0.9285	-0.06538	0.0697
fixed	NA	sibling_count4	0.02206	0.02496	0.8839	1922	0.3769	-0.04799	0.09211
fixed	NA	sibling_count5	0.03022	0.0279	1.083	1690	0.2789	-0.0481	0.1085
ran_pars	mother_pidlink	sd__(Intercept)	0.1583	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4044	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4019	0.3642	1.104	2631	0.2698	-0.6203	1.424
fixed	NA	birth_order	0.004375	0.008576	0.5101	2453	0.61	-0.0197	0.02845
fixed	NA	poly(age, 3, raw = TRUE)1	-0.004594	0.04031	-0.114	2631	0.9093	-0.1178	0.1086
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001661	0.001428	-0.1163	2631	0.9074	-0.004174	0.003842
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003975	0.0000162	0.2454	2631	0.8061	-0.00004149	0.00004944
fixed	NA	male	-0.01903	0.01708	-1.114	2611	0.2652	-0.06697	0.02891
fixed	NA	sibling_count3	0.00009149	0.02441	0.003749	2114	0.997	-0.06842	0.0686
fixed	NA	sibling_count4	0.01755	0.02647	0.6629	2045	0.5075	-0.05676	0.09186
fixed	NA	sibling_count5	0.02273	0.03154	0.7207	2003	0.4711	-0.0658	0.1113
ran_pars	mother_pidlink	sd__(Intercept)	0.1587	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4043	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4162	0.3649	1.141	2627	0.2542	-0.6081	1.441
fixed	NA	poly(age, 3, raw = TRUE)1	-0.006038	0.04037	-0.1496	2628	0.8811	-0.1194	0.1073
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001192	0.00143	-0.08336	2628	0.9336	-0.004133	0.003895
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003505	0.00001622	0.2161	2628	0.8289	-0.00004202	0.00004903
fixed	NA	male	-0.01979	0.01709	-1.158	2609	0.247	-0.06776	0.02818
fixed	NA	sibling_count3	0.003015	0.02475	0.1218	2170	0.9031	-0.06647	0.0725
fixed	NA	sibling_count4	0.01462	0.02681	0.5451	2097	0.5858	-0.06065	0.08988
fixed	NA	sibling_count5	0.02757	0.03192	0.8637	2046	0.3878	-0.06203	0.1172
fixed	NA	birth_order_nonlinear2	0.01772	0.02042	0.8681	2234	0.3854	-0.03959	0.07504
fixed	NA	birth_order_nonlinear3	-0.003046	0.02491	-0.1223	2270	0.9027	-0.07296	0.06687
fixed	NA	birth_order_nonlinear4	0.0467	0.0332	1.407	2332	0.1596	-0.04649	0.1399
fixed	NA	birth_order_nonlinear5	-0.02429	0.05138	-0.4727	2250	0.6365	-0.1685	0.1199
ran_pars	mother_pidlink	sd__(Intercept)	0.1593	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4041	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4303	0.3652	1.178	2621	0.2388	-0.5947	1.455
fixed	NA	poly(age, 3, raw = TRUE)1	-0.006869	0.0404	-0.17	2622	0.865	-0.1203	0.1065
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001017	0.001431	-0.07106	2622	0.9434	-0.004119	0.003915
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003435	0.00001623	0.2116	2622	0.8324	-0.00004213	0.000049
fixed	NA	male	-0.01933	0.01711	-1.13	2601	0.2586	-0.06736	0.02869
fixed	NA	count_birth_order2/2	0.005388	0.03721	0.1448	2256	0.8849	-0.09907	0.1098
fixed	NA	count_birth_order1/3	0.0145	0.03143	0.4612	2620	0.6447	-0.07372	0.1027
fixed	NA	count_birth_order2/3	0.009415	0.0349	0.2698	2624	0.7874	-0.08855	0.1074
fixed	NA	count_birth_order3/3	-0.02462	0.03799	-0.6481	2619	0.517	-0.1313	0.08202
fixed	NA	count_birth_order1/4	-0.01828	0.03614	-0.5058	2624	0.613	-0.1197	0.08317
fixed	NA	count_birth_order2/4	0.02588	0.03822	0.6772	2621	0.4984	-0.0814	0.1332
fixed	NA	count_birth_order3/4	0.05347	0.03961	1.35	2614	0.1771	-0.05771	0.1646
fixed	NA	count_birth_order4/4	0.05344	0.04234	1.262	2611	0.207	-0.06541	0.1723
fixed	NA	count_birth_order1/5	0.01748	0.04768	0.3665	2622	0.714	-0.1164	0.1513
fixed	NA	count_birth_order2/5	0.08537	0.05123	1.666	2602	0.09577	-0.05844	0.2292
fixed	NA	count_birth_order3/5	-0.01865	0.04865	-0.3834	2601	0.7015	-0.1552	0.1179
fixed	NA	count_birth_order4/5	0.07684	0.0474	1.621	2596	0.1051	-0.05622	0.2099
fixed	NA	count_birth_order5/5	-0.0006437	0.04985	-0.01291	2588	0.9897	-0.1406	0.1393
ran_pars	mother_pidlink	sd__(Intercept)	0.1606	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4036	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	3088	3147	-1534	3068	NA	NA	NA
11	3090	3154	-1534	3068	0.2587	1	0.611
14	3093	3175	-1532	3065	3.273	3	0.3515
20	3098	3216	-1529	3058	6.141	6	0.4076

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4734	0.3758	1.26	2418	0.2079	-0.5816	1.528
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01121	0.04162	-0.2694	2419	0.7876	-0.128	0.1056
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001013	0.001474	0.006874	2419	0.9945	-0.004129	0.004149
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002715	0.00001673	0.1623	2418	0.8711	-0.00004425	0.00004968
fixed	NA	male	-0.02601	0.01776	-1.465	2397	0.1432	-0.07587	0.02384
fixed	NA	sibling_count3	0.02154	0.02633	0.8181	1943	0.4134	-0.05237	0.09545
fixed	NA	sibling_count4	0.01969	0.02669	0.7376	1847	0.4608	-0.05523	0.0946
fixed	NA	sibling_count5	0.03169	0.0282	1.124	1713	0.2613	-0.04747	0.1108
ran_pars	mother_pidlink	sd__(Intercept)	0.1625	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4013	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4726	0.376	1.257	2417	0.2089	-0.5827	1.528
fixed	NA	birth_order	0.00139	0.008678	0.1602	2304	0.8727	-0.02297	0.02575
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01131	0.04163	-0.2716	2418	0.7859	-0.1282	0.1056
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001177	0.001475	0.007984	2418	0.9936	-0.004128	0.004151
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002729	0.00001673	0.1631	2417	0.8705	-0.00004424	0.0000497
fixed	NA	male	-0.02598	0.01777	-1.462	2396	0.1438	-0.07584	0.02389
fixed	NA	sibling_count3	0.02088	0.02666	0.783	1961	0.4337	-0.05396	0.09572
fixed	NA	sibling_count4	0.01837	0.02793	0.6576	1919	0.5109	-0.06004	0.09677
fixed	NA	sibling_count5	0.02946	0.03145	0.9368	1929	0.349	-0.05881	0.1177
ran_pars	mother_pidlink	sd__(Intercept)	0.1626	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4014	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4823	0.3769	1.28	2414	0.2008	-0.5756	1.54
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01246	0.04172	-0.2987	2414	0.7652	-0.1296	0.1047
fixed	NA	poly(age, 3, raw = TRUE)2	0.00005189	0.001478	0.03511	2414	0.972	-0.004097	0.0042
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002313	0.00001677	0.138	2414	0.8903	-0.00004475	0.00004938
fixed	NA	male	-0.027	0.01777	-1.519	2392	0.1289	-0.07688	0.02289
fixed	NA	sibling_count3	0.0236	0.02702	0.8736	2004	0.3824	-0.05224	0.09945
fixed	NA	sibling_count4	0.01345	0.02826	0.476	1959	0.6341	-0.06589	0.09279
fixed	NA	sibling_count5	0.03285	0.03164	1.038	1950	0.2993	-0.05596	0.1217
fixed	NA	birth_order_nonlinear2	0.008117	0.02107	0.3852	2050	0.7001	-0.05104	0.06727
fixed	NA	birth_order_nonlinear3	-0.009046	0.026	-0.3479	2126	0.7279	-0.08203	0.06394
fixed	NA	birth_order_nonlinear4	0.04929	0.03435	1.435	2185	0.1515	-0.04715	0.1457
fixed	NA	birth_order_nonlinear5	-0.04467	0.04924	-0.9073	2091	0.3644	-0.1829	0.09355
ran_pars	mother_pidlink	sd__(Intercept)	0.1642	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4006	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4692	0.3776	1.243	2408	0.2141	-0.5907	1.529
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01088	0.0418	-0.2602	2408	0.7948	-0.1282	0.1065
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00001648	0.001481	-0.01113	2408	0.9911	-0.004173	0.00414
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003221	0.0000168	0.1917	2408	0.848	-0.00004394	0.00005038
fixed	NA	male	-0.02625	0.01782	-1.473	2384	0.1408	-0.07627	0.02377
fixed	NA	count_birth_order2/2	0.01227	0.04069	0.3015	2125	0.7631	-0.1019	0.1265
fixed	NA	count_birth_order1/3	0.04134	0.03469	1.192	2405	0.2335	-0.05603	0.1387
fixed	NA	count_birth_order2/3	0.03165	0.03771	0.8393	2409	0.4014	-0.07421	0.1375
fixed	NA	count_birth_order3/3	-0.0141	0.04176	-0.3375	2403	0.7358	-0.1313	0.1031
fixed	NA	count_birth_order1/4	0.008425	0.03775	0.2232	2408	0.8234	-0.09754	0.1144
fixed	NA	count_birth_order2/4	0.00617	0.03968	0.1555	2408	0.8764	-0.1052	0.1175
fixed	NA	count_birth_order3/4	0.03581	0.04289	0.835	2399	0.4038	-0.08457	0.1562
fixed	NA	count_birth_order4/4	0.06662	0.04651	1.432	2392	0.1522	-0.06393	0.1972
fixed	NA	count_birth_order1/5	0.009166	0.04567	0.2007	2408	0.841	-0.119	0.1374
fixed	NA	count_birth_order2/5	0.06819	0.0467	1.46	2402	0.1444	-0.06292	0.1993
fixed	NA	count_birth_order3/5	0.02842	0.04796	0.5925	2389	0.5536	-0.1062	0.1631
fixed	NA	count_birth_order4/5	0.08194	0.04871	1.682	2380	0.09263	-0.05478	0.2187
fixed	NA	count_birth_order5/5	-0.01018	0.04943	-0.2059	2373	0.8369	-0.1489	0.1286
ran_pars	mother_pidlink	sd__(Intercept)	0.1654	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4005	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	2822	2880	-1401	2802	NA	NA	NA
11	2824	2888	-1401	2802	0.0254	1	0.8734
14	2826	2907	-1399	2798	4.247	3	0.236
20	2835	2950	-1397	2795	3.294	6	0.7711

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4815	0.3681	1.308	2634	0.191	-0.5518	1.515
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01328	0.04085	-0.3251	2635	0.7451	-0.128	0.1014
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001476	0.00145	0.1018	2635	0.919	-0.003924	0.004219
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000005726	0.0000165	0.03471	2634	0.9723	-0.00004574	0.00004689
fixed	NA	male	-0.02288	0.01708	-1.339	2617	0.1805	-0.07083	0.02507
fixed	NA	sibling_count3	0.007384	0.02357	0.3133	2091	0.7541	-0.05878	0.07355
fixed	NA	sibling_count4	0.01739	0.02478	0.7018	1932	0.4829	-0.05217	0.08694
fixed	NA	sibling_count5	0.03453	0.02851	1.211	1622	0.226	-0.0455	0.1146
ran_pars	mother_pidlink	sd__(Intercept)	0.1567	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4054	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4807	0.3681	1.306	2633	0.1917	-0.5526	1.514
fixed	NA	birth_order	0.006053	0.008688	0.6967	2442	0.4861	-0.01833	0.03044
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01394	0.04087	-0.341	2633	0.7331	-0.1287	0.1008
fixed	NA	poly(age, 3, raw = TRUE)2	0.000161	0.001451	0.1109	2633	0.9117	-0.003911	0.004233
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000005789	0.0000165	0.03509	2633	0.972	-0.00004574	0.0000469
fixed	NA	male	-0.0228	0.01708	-1.334	2616	0.1822	-0.07075	0.02516
fixed	NA	sibling_count3	0.004481	0.02394	0.1871	2122	0.8516	-0.06273	0.07169
fixed	NA	sibling_count4	0.01121	0.02632	0.4261	2064	0.67	-0.06265	0.08508
fixed	NA	sibling_count5	0.02457	0.03191	0.7698	1912	0.4415	-0.06501	0.1141
ran_pars	mother_pidlink	sd__(Intercept)	0.1572	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4053	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4948	0.3689	1.341	2629	0.18	-0.5407	1.53
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01525	0.04093	-0.3727	2630	0.7094	-0.1302	0.09965
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002064	0.001453	0.142	2630	0.8871	-0.003873	0.004285
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000008827	0.00001653	0.005341	2630	0.9957	-0.0000463	0.00004648
fixed	NA	male	-0.0234	0.0171	-1.368	2614	0.1713	-0.0714	0.0246
fixed	NA	sibling_count3	0.007534	0.02431	0.3099	2180	0.7566	-0.0607	0.07577
fixed	NA	sibling_count4	0.01047	0.02666	0.3928	2116	0.6945	-0.06436	0.0853
fixed	NA	sibling_count5	0.02813	0.03242	0.8678	1967	0.3856	-0.06286	0.1191
fixed	NA	birth_order_nonlinear2	0.01926	0.02023	0.952	2229	0.3412	-0.03753	0.07604
fixed	NA	birth_order_nonlinear3	0.0006313	0.02488	0.02538	2277	0.9798	-0.0692	0.07046
fixed	NA	birth_order_nonlinear4	0.04094	0.03411	1.2	2325	0.2302	-0.05482	0.1367
fixed	NA	birth_order_nonlinear5	0.0005619	0.0545	0.01031	2265	0.9918	-0.1524	0.1535
ran_pars	mother_pidlink	sd__(Intercept)	0.157	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4055	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.5024	0.3693	1.36	2623	0.1739	-0.5344	1.539
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01596	0.04099	-0.3894	2624	0.697	-0.131	0.09909
fixed	NA	poly(age, 3, raw = TRUE)2	0.000227	0.001455	0.156	2624	0.876	-0.003858	0.004312
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000009427	0.00001655	-0.005695	2624	0.9955	-0.00004656	0.00004637
fixed	NA	male	-0.02334	0.01713	-1.363	2607	0.1731	-0.07141	0.02473
fixed	NA	count_birth_order2/2	0.01831	0.03626	0.505	2253	0.6136	-0.08348	0.1201
fixed	NA	count_birth_order1/3	0.01864	0.03093	0.6026	2624	0.5468	-0.06819	0.1055
fixed	NA	count_birth_order2/3	0.02321	0.03436	0.6754	2628	0.4995	-0.07325	0.1197
fixed	NA	count_birth_order3/3	-0.009623	0.03699	-0.2602	2622	0.7947	-0.1134	0.0942
fixed	NA	count_birth_order1/4	-0.01195	0.03637	-0.3286	2628	0.7425	-0.1141	0.09015
fixed	NA	count_birth_order2/4	0.02546	0.03812	0.6679	2624	0.5043	-0.08155	0.1325
fixed	NA	count_birth_order3/4	0.04243	0.03954	1.073	2617	0.2833	-0.06856	0.1534
fixed	NA	count_birth_order4/4	0.05387	0.04291	1.255	2613	0.2094	-0.06657	0.1743
fixed	NA	count_birth_order1/5	0.0315	0.04767	0.6608	2627	0.5088	-0.1023	0.1653
fixed	NA	count_birth_order2/5	0.06755	0.05301	1.274	2601	0.2027	-0.08125	0.2164
fixed	NA	count_birth_order3/5	0.007274	0.0516	0.141	2597	0.8879	-0.1376	0.1521
fixed	NA	count_birth_order4/5	0.0658	0.04963	1.326	2598	0.185	-0.07351	0.2051
fixed	NA	count_birth_order5/5	0.02832	0.05268	0.5375	2591	0.591	-0.1196	0.1762
ran_pars	mother_pidlink	sd__(Intercept)	0.1581	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4054	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	3098	3157	-1539	3078	NA	NA	NA
11	3100	3164	-1539	3078	0.484	1	0.4866
14	3104	3186	-1538	3076	1.797	3	0.6155
20	3113	3231	-1537	3073	2.644	6	0.8521

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Sector_Mining and quarrying

birthorder <- birthorder %>% mutate(outcome = `Sector_Mining and quarrying`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.04114	0.05247	-0.7841	4234	0.433	-0.1884	0.1061
fixed	NA	poly(age, 3, raw = TRUE)1	0.003259	0.004667	0.6983	4106	0.485	-0.009841	0.01636
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00005486	0.0001292	-0.4246	3964	0.6712	-0.0004176	0.0003078
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000002653	0.000001127	0.2355	3839	0.8138	-0.000002897	0.000003428
fixed	NA	male	0.03387	0.005354	6.326	4598	0.0000000002757	0.01884	0.04889
fixed	NA	sibling_count3	-0.0006718	0.00767	-0.08759	3300	0.9302	-0.0222	0.02086
fixed	NA	sibling_count4	0.005238	0.007756	0.6754	3045	0.4995	-0.01653	0.02701
fixed	NA	sibling_count5	0.006951	0.008066	0.8618	2804	0.3889	-0.01569	0.02959
ran_pars	mother_pidlink	sd__(Intercept)	0.05504	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1726	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.04073	0.05247	-0.7763	4234	0.4376	-0.188	0.1066
fixed	NA	birth_order	0.001501	0.002637	0.5691	4100	0.5693	-0.005901	0.008902
fixed	NA	poly(age, 3, raw = TRUE)1	0.003026	0.004685	0.6459	4108	0.5184	-0.01013	0.01618
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000049	0.0001296	-0.378	3956	0.7054	-0.0004129	0.0003149
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000002255	0.000001129	0.1998	3832	0.8417	-0.000002943	0.000003394
fixed	NA	male	0.03389	0.005354	6.329	4597	0.0000000002699	0.01886	0.04892
fixed	NA	sibling_count3	-0.001236	0.007734	-0.1598	3387	0.873	-0.02294	0.02047
fixed	NA	sibling_count4	0.004022	0.008044	0.5	3404	0.6171	-0.01856	0.0266
fixed	NA	sibling_count5	0.005029	0.008743	0.5752	3519	0.5652	-0.01951	0.02957
ran_pars	mother_pidlink	sd__(Intercept)	0.05495	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1726	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.04036	0.05264	-0.7667	4240	0.4433	-0.1881	0.1074
fixed	NA	poly(age, 3, raw = TRUE)1	0.003043	0.004687	0.6493	4103	0.5162	-0.01011	0.0162
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00004848	0.0001297	-0.3738	3947	0.7086	-0.0004126	0.0003156
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000002116	0.00000113	0.1873	3816	0.8514	-0.00000296	0.000003383
fixed	NA	male	0.03378	0.005355	6.308	4593	0.0000000003098	0.01875	0.04881
fixed	NA	sibling_count3	0.00156	0.007869	0.1982	3539	0.8429	-0.02053	0.02365
fixed	NA	sibling_count4	0.005291	0.008192	0.6459	3570	0.5184	-0.0177	0.02829
fixed	NA	sibling_count5	0.005474	0.008832	0.6198	3614	0.5355	-0.01932	0.03027
fixed	NA	birth_order_nonlinear2	0.003364	0.006355	0.5294	4002	0.5966	-0.01447	0.0212
fixed	NA	birth_order_nonlinear3	-0.00828	0.008056	-1.028	3952	0.3041	-0.03089	0.01433
fixed	NA	birth_order_nonlinear4	0.01241	0.01052	1.179	3904	0.2384	-0.01713	0.04195
fixed	NA	birth_order_nonlinear5	0.01004	0.01519	0.6613	3965	0.5085	-0.03259	0.05268
ran_pars	mother_pidlink	sd__(Intercept)	0.05526	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1725	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.04424	0.05271	-0.8394	4245	0.4013	-0.1922	0.1037
fixed	NA	poly(age, 3, raw = TRUE)1	0.003113	0.004689	0.6638	4101	0.5069	-0.01005	0.01628
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00005035	0.0001297	-0.3881	3945	0.6979	-0.0004145	0.0003138
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000002263	0.00000113	0.2003	3814	0.8413	-0.000002945	0.000003398
fixed	NA	male	0.03403	0.005356	6.353	4586	0.0000000002315	0.01899	0.04906
fixed	NA	count_birth_order2/2	0.01135	0.01081	1.05	3927	0.2939	-0.019	0.0417
fixed	NA	count_birth_order1/3	0.005884	0.01037	0.5672	4617	0.5706	-0.02323	0.035
fixed	NA	count_birth_order2/3	0.01735	0.01155	1.503	4624	0.1329	-0.01505	0.04976
fixed	NA	count_birth_order3/3	-0.01868	0.0127	-1.47	4625	0.1415	-0.05433	0.01698
fixed	NA	count_birth_order1/4	0.01405	0.01143	1.229	4624	0.219	-0.01803	0.04612
fixed	NA	count_birth_order2/4	-0.005288	0.01226	-0.4314	4625	0.6662	-0.0397	0.02912
fixed	NA	count_birth_order3/4	0.009742	0.01294	0.753	4625	0.4515	-0.02657	0.04605
fixed	NA	count_birth_order4/4	0.02266	0.01395	1.625	4624	0.1043	-0.01649	0.06181
fixed	NA	count_birth_order1/5	0.005603	0.01288	0.4348	4624	0.6637	-0.03056	0.04177
fixed	NA	count_birth_order2/5	0.009956	0.01369	0.7272	4622	0.4671	-0.02848	0.04839
fixed	NA	count_birth_order3/5	0.008266	0.0144	0.5739	4619	0.566	-0.03216	0.0487
fixed	NA	count_birth_order4/5	0.01827	0.01522	1.201	4608	0.2298	-0.02444	0.06099
fixed	NA	count_birth_order5/5	0.01856	0.01526	1.216	4618	0.224	-0.02427	0.06138
ran_pars	mother_pidlink	sd__(Intercept)	0.05503	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1725	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-2693	-2629	1357	-2713	NA	NA	NA
11	-2692	-2621	1357	-2714	0.3253	1	0.5685
14	-2690	-2599	1359	-2718	3.947	3	0.2672
20	-2686	-2557	1363	-2726	8.434	6	0.208

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.05793	0.1314	-0.4408	2617	0.6594	-0.4268	0.311
fixed	NA	poly(age, 3, raw = TRUE)1	0.006296	0.01454	0.4329	2616	0.6651	-0.03453	0.04712
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002183	0.0005152	-0.4237	2613	0.6718	-0.001664	0.001228
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002348	0.000005844	0.4018	2610	0.6878	-0.00001406	0.00001875
fixed	NA	male	0.02987	0.006185	4.83	2632	0.000001447	0.01251	0.04723
fixed	NA	sibling_count3	0.01389	0.008552	1.624	1997	0.1046	-0.01012	0.03789
fixed	NA	sibling_count4	0.01745	0.008839	1.974	1772	0.0485	-0.00736	0.04226
fixed	NA	sibling_count5	0.005046	0.009832	0.5132	1469	0.6079	-0.02255	0.03264
ran_pars	mother_pidlink	sd__(Intercept)	0.03304	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1531	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.05741	0.1314	-0.4369	2616	0.6622	-0.4263	0.3115
fixed	NA	birth_order	-0.003042	0.003126	-0.9732	2485	0.3306	-0.01182	0.005732
fixed	NA	poly(age, 3, raw = TRUE)1	0.006589	0.01455	0.4529	2614	0.6506	-0.03425	0.04742
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002234	0.0005152	-0.4336	2612	0.6646	-0.00167	0.001223
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002329	0.000005844	0.3985	2610	0.6903	-0.00001408	0.00001873
fixed	NA	male	0.02987	0.006185	4.829	2631	0.000001448	0.01251	0.04723
fixed	NA	sibling_count3	0.01533	0.00868	1.766	2032	0.07761	-0.009039	0.03969
fixed	NA	sibling_count4	0.02056	0.009399	2.187	1917	0.02884	-0.005824	0.04694
fixed	NA	sibling_count5	0.01022	0.01119	0.9141	1830	0.3608	-0.02117	0.04162
ran_pars	mother_pidlink	sd__(Intercept)	0.03344	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.153	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.05802	0.1317	-0.4404	2611	0.6597	-0.4278	0.3118
fixed	NA	poly(age, 3, raw = TRUE)1	0.006437	0.01458	0.4416	2610	0.6588	-0.03448	0.04735
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002174	0.0005162	-0.4212	2608	0.6736	-0.001666	0.001232
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002259	0.000005854	0.3859	2606	0.6996	-0.00001417	0.00001869
fixed	NA	male	0.02985	0.006193	4.819	2629	0.000001522	0.01246	0.04723
fixed	NA	sibling_count3	0.01552	0.008817	1.76	2104	0.07848	-0.009228	0.04027
fixed	NA	sibling_count4	0.02093	0.009533	2.196	1984	0.02823	-0.005828	0.04769
fixed	NA	sibling_count5	0.008965	0.01133	0.7912	1880	0.4289	-0.02284	0.04077
fixed	NA	birth_order_nonlinear2	-0.006992	0.007484	-0.9343	2240	0.3503	-0.028	0.01402
fixed	NA	birth_order_nonlinear3	-0.007257	0.00912	-0.7957	2306	0.4263	-0.03286	0.01834
fixed	NA	birth_order_nonlinear4	-0.0112	0.01214	-0.9224	2391	0.3564	-0.04527	0.02287
fixed	NA	birth_order_nonlinear5	-0.005136	0.01882	-0.273	2330	0.7849	-0.05795	0.04768
ran_pars	mother_pidlink	sd__(Intercept)	0.03315	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1532	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.05972	0.1319	-0.4528	2606	0.6507	-0.4299	0.3105
fixed	NA	poly(age, 3, raw = TRUE)1	0.006849	0.01459	0.4694	2605	0.6388	-0.03411	0.04781
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002286	0.0005168	-0.4422	2603	0.6583	-0.001679	0.001222
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002352	0.000005863	0.4012	2601	0.6883	-0.00001411	0.00001881
fixed	NA	male	0.03006	0.006203	4.845	2622	0.000001339	0.01264	0.04747
fixed	NA	count_birth_order2/2	-0.01628	0.01365	-1.193	2223	0.233	-0.05459	0.02203
fixed	NA	count_birth_order1/3	0.007834	0.01136	0.6895	2623	0.4906	-0.02406	0.03973
fixed	NA	count_birth_order2/3	0.01593	0.01263	1.261	2624	0.2072	-0.01952	0.05138
fixed	NA	count_birth_order3/3	0.0004743	0.01376	0.03446	2622	0.9725	-0.03816	0.03911
fixed	NA	count_birth_order1/4	0.01964	0.01307	1.502	2624	0.1332	-0.01706	0.05633
fixed	NA	count_birth_order2/4	0.005646	0.01384	0.4079	2624	0.6834	-0.0332	0.04449
fixed	NA	count_birth_order3/4	0.009496	0.01435	0.6616	2621	0.5083	-0.0308	0.04979
fixed	NA	count_birth_order4/4	0.01226	0.01535	0.7987	2622	0.4246	-0.03082	0.05534
fixed	NA	count_birth_order1/5	0.006802	0.01726	0.3941	2624	0.6936	-0.04165	0.05526
fixed	NA	count_birth_order2/5	-0.005763	0.01858	-0.3102	2622	0.7564	-0.05791	0.04638
fixed	NA	count_birth_order3/5	0.009764	0.01764	0.5534	2620	0.58	-0.03976	0.05929
fixed	NA	count_birth_order4/5	-0.01283	0.0172	-0.7459	2618	0.4558	-0.0611	0.03544
fixed	NA	count_birth_order5/5	0.0007238	0.01809	0.04001	2615	0.9681	-0.05006	0.05151
ran_pars	mother_pidlink	sd__(Intercept)	0.03326	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1532	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-2288	-2229	1154	-2308	NA	NA	NA
11	-2287	-2222	1154	-2309	0.9458	1	0.3308
14	-2281	-2199	1155	-2309	0.5254	3	0.9133
20	-2273	-2155	1156	-2313	3.4	6	0.7572

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.07806	0.1354	-0.5767	2408	0.5642	-0.458	0.3019
fixed	NA	poly(age, 3, raw = TRUE)1	0.008781	0.01499	0.5858	2408	0.5581	-0.0333	0.05086
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003152	0.000531	-0.5936	2406	0.5528	-0.001806	0.001175
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003566	0.000006024	0.592	2404	0.5539	-0.00001334	0.00002047
fixed	NA	male	0.03138	0.00642	4.888	2418	0.000001086	0.01336	0.0494
fixed	NA	sibling_count3	0.00778	0.009328	0.8341	1938	0.4043	-0.0184	0.03396
fixed	NA	sibling_count4	0.02212	0.00943	2.346	1812	0.0191	-0.004351	0.04859
fixed	NA	sibling_count5	-0.0002185	0.009928	-0.02201	1632	0.9824	-0.02809	0.02765
ran_pars	mother_pidlink	sd__(Intercept)	0.03196	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1524	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.07547	0.1354	-0.5575	2408	0.5773	-0.4555	0.3045
fixed	NA	birth_order	-0.003698	0.003151	-1.174	2353	0.2406	-0.01254	0.005147
fixed	NA	poly(age, 3, raw = TRUE)1	0.008972	0.01499	0.5985	2407	0.5496	-0.03311	0.05105
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003171	0.0005309	-0.5972	2405	0.5505	-0.001807	0.001173
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003505	0.000006024	0.5819	2403	0.5607	-0.0000134	0.00002041
fixed	NA	male	0.03128	0.00642	4.873	2417	0.000001173	0.01326	0.0493
fixed	NA	sibling_count3	0.009543	0.009448	1.01	1957	0.3126	-0.01698	0.03606
fixed	NA	sibling_count4	0.0256	0.009887	2.59	1894	0.009676	-0.002148	0.05336
fixed	NA	sibling_count5	0.005673	0.01113	0.5097	1877	0.6103	-0.02557	0.03691
ran_pars	mother_pidlink	sd__(Intercept)	0.03238	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1523	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.07254	0.1357	-0.5344	2402	0.5931	-0.4536	0.3085
fixed	NA	poly(age, 3, raw = TRUE)1	0.008351	0.01503	0.5556	2402	0.5785	-0.03384	0.05054
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002951	0.0005323	-0.5543	2400	0.5794	-0.001789	0.001199
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003262	0.000006038	0.5403	2399	0.589	-0.00001369	0.00002021
fixed	NA	male	0.03128	0.006427	4.867	2414	0.000001208	0.01324	0.04932
fixed	NA	sibling_count3	0.01042	0.009587	1.086	2008	0.2774	-0.0165	0.03733
fixed	NA	sibling_count4	0.02687	0.01002	2.683	1941	0.007359	-0.001242	0.05498
fixed	NA	sibling_count5	0.004529	0.0112	0.4042	1903	0.6861	-0.02692	0.03598
fixed	NA	birth_order_nonlinear2	-0.007134	0.007718	-0.9244	2111	0.3554	-0.0288	0.01453
fixed	NA	birth_order_nonlinear3	-0.01143	0.009499	-1.203	2210	0.229	-0.0381	0.01523
fixed	NA	birth_order_nonlinear4	-0.01486	0.01253	-1.186	2279	0.2357	-0.05002	0.02031
fixed	NA	birth_order_nonlinear5	-0.002616	0.018	-0.1453	2210	0.8845	-0.05314	0.04791
ran_pars	mother_pidlink	sd__(Intercept)	0.03216	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1524	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.07761	0.136	-0.5708	2397	0.5682	-0.4592	0.304
fixed	NA	poly(age, 3, raw = TRUE)1	0.009171	0.01505	0.6093	2396	0.5424	-0.03308	0.05142
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003208	0.0005332	-0.6018	2394	0.5474	-0.001817	0.001176
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003526	0.000006048	0.583	2392	0.5599	-0.00001345	0.0000205
fixed	NA	male	0.03181	0.006443	4.937	2408	0.0000008484	0.01372	0.04989
fixed	NA	count_birth_order2/2	-0.01758	0.01487	-1.182	2140	0.2373	-0.05934	0.02417
fixed	NA	count_birth_order1/3	-0.001176	0.0125	-0.09409	2408	0.925	-0.03626	0.03391
fixed	NA	count_birth_order2/3	0.01443	0.0136	1.061	2409	0.2889	-0.02375	0.05262
fixed	NA	count_birth_order3/3	-0.009638	0.01508	-0.6389	2407	0.5229	-0.05198	0.03271
fixed	NA	count_birth_order1/4	0.02995	0.01361	2.201	2408	0.0278	-0.008241	0.06815
fixed	NA	count_birth_order2/4	0.008284	0.01432	0.5786	2409	0.5629	-0.03191	0.04848
fixed	NA	count_birth_order3/4	0.01229	0.0155	0.793	2407	0.4279	-0.03121	0.05578
fixed	NA	count_birth_order4/4	0.007536	0.01681	0.4483	2407	0.654	-0.03965	0.05473
fixed	NA	count_birth_order1/5	-0.0008688	0.01648	-0.05273	2409	0.958	-0.04712	0.04538
fixed	NA	count_birth_order2/5	-0.01143	0.01687	-0.6776	2409	0.4981	-0.05878	0.03592
fixed	NA	count_birth_order3/5	-0.003623	0.01734	-0.2089	2406	0.8345	-0.0523	0.04506
fixed	NA	count_birth_order4/5	-0.01296	0.01762	-0.7354	2405	0.4621	-0.06242	0.0365
fixed	NA	count_birth_order5/5	-0.001646	0.01789	-0.09197	2401	0.9267	-0.05187	0.04858
ran_pars	mother_pidlink	sd__(Intercept)	0.03227	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1525	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-2128	-2070	1074	-2148	NA	NA	NA
11	-2127	-2064	1075	-2149	1.378	1	0.2405
14	-2122	-2041	1075	-2150	1.057	3	0.7874
20	-2115	-1999	1078	-2155	4.807	6	0.5688

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.05874	0.1336	-0.4396	2615	0.6603	-0.4338	0.3163
fixed	NA	poly(age, 3, raw = TRUE)1	0.006903	0.01483	0.4655	2614	0.6416	-0.03472	0.04853
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002496	0.0005265	-0.4741	2611	0.6355	-0.001727	0.001228
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000279	0.000005988	0.4659	2608	0.6413	-0.00001402	0.0000196
fixed	NA	male	0.02883	0.006223	4.633	2635	0.000003787	0.01136	0.0463
fixed	NA	sibling_count3	0.01377	0.00844	1.632	1928	0.1029	-0.009918	0.03747
fixed	NA	sibling_count4	0.01583	0.008845	1.79	1698	0.07363	-0.008996	0.04066
fixed	NA	sibling_count5	0.003767	0.01011	0.3725	1294	0.7096	-0.02462	0.03216
ran_pars	mother_pidlink	sd__(Intercept)	0.03542	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1537	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.05824	0.1336	-0.4358	2615	0.663	-0.4334	0.3169
fixed	NA	birth_order	-0.002799	0.003184	-0.879	2444	0.3795	-0.01174	0.006138
fixed	NA	poly(age, 3, raw = TRUE)1	0.007181	0.01483	0.4841	2613	0.6284	-0.03446	0.04882
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002549	0.0005266	-0.4841	2610	0.6284	-0.001733	0.001223
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002781	0.000005989	0.4643	2607	0.6425	-0.00001403	0.00001959
fixed	NA	male	0.0288	0.006223	4.627	2634	0.000003883	0.01133	0.04627
fixed	NA	sibling_count3	0.01512	0.008579	1.762	1965	0.07819	-0.008964	0.0392
fixed	NA	sibling_count4	0.01867	0.009417	1.982	1859	0.04757	-0.007765	0.0451
fixed	NA	sibling_count5	0.008339	0.01138	0.7325	1629	0.464	-0.02362	0.0403
ran_pars	mother_pidlink	sd__(Intercept)	0.03594	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1536	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.06563	0.1339	-0.4902	2609	0.6241	-0.4415	0.3102
fixed	NA	poly(age, 3, raw = TRUE)1	0.00784	0.01486	0.5277	2608	0.5978	-0.03387	0.04955
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002779	0.0005274	-0.5269	2606	0.5983	-0.001758	0.001203
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003031	0.000005998	0.5054	2604	0.6133	-0.0000138	0.00001987
fixed	NA	male	0.02898	0.006229	4.652	2632	0.000003448	0.01149	0.04647
fixed	NA	sibling_count3	0.01359	0.008719	1.558	2042	0.1193	-0.01089	0.03806
fixed	NA	sibling_count4	0.0178	0.009548	1.865	1927	0.06239	-0.008998	0.0446
fixed	NA	sibling_count5	0.008181	0.01157	0.7069	1690	0.4797	-0.02431	0.04067
fixed	NA	birth_order_nonlinear2	-0.006987	0.007448	-0.9381	2175	0.3483	-0.02789	0.01392
fixed	NA	birth_order_nonlinear3	0.0003167	0.009148	0.03462	2255	0.9724	-0.02536	0.026
fixed	NA	birth_order_nonlinear4	-0.01251	0.01253	-0.9988	2340	0.318	-0.04769	0.02266
fixed	NA	birth_order_nonlinear5	-0.01491	0.02004	-0.7439	2295	0.457	-0.07116	0.04134
ran_pars	mother_pidlink	sd__(Intercept)	0.03539	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1537	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.06923	0.1341	-0.5164	2604	0.6056	-0.4455	0.3071
fixed	NA	poly(age, 3, raw = TRUE)1	0.008296	0.01488	0.5576	2603	0.5771	-0.03347	0.05006
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002913	0.0005282	-0.5515	2601	0.5813	-0.001774	0.001191
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003154	0.000006008	0.525	2599	0.5997	-0.00001371	0.00002002
fixed	NA	male	0.02916	0.006238	4.674	2625	0.000003099	0.01165	0.04667
fixed	NA	count_birth_order2/2	-0.01085	0.01335	-0.8131	2164	0.4163	-0.04831	0.02661
fixed	NA	count_birth_order1/3	0.007549	0.01124	0.6717	2627	0.5018	-0.024	0.0391
fixed	NA	count_birth_order2/3	0.01493	0.0125	1.195	2628	0.2324	-0.02015	0.05001
fixed	NA	count_birth_order3/3	0.009299	0.01347	0.6905	2624	0.4899	-0.0285	0.0471
fixed	NA	count_birth_order1/4	0.02208	0.01322	1.67	2628	0.09513	-0.01504	0.0592
fixed	NA	count_birth_order2/4	0.001129	0.01387	0.08139	2627	0.9351	-0.03782	0.04007
fixed	NA	count_birth_order3/4	0.01645	0.0144	1.143	2624	0.2533	-0.02397	0.05687
fixed	NA	count_birth_order4/4	0.007081	0.01563	0.4531	2624	0.6505	-0.03678	0.05095
fixed	NA	count_birth_order1/5	0.007274	0.01734	0.4196	2628	0.6748	-0.0414	0.05594
fixed	NA	count_birth_order2/5	-0.004573	0.01932	-0.2367	2623	0.8129	-0.0588	0.04965
fixed	NA	count_birth_order3/5	0.01592	0.01881	0.8464	2620	0.3974	-0.03688	0.06871
fixed	NA	count_birth_order4/5	-0.01022	0.01809	-0.5652	2618	0.572	-0.061	0.04055
fixed	NA	count_birth_order5/5	-0.008063	0.01921	-0.4197	2615	0.6747	-0.06199	0.04586
ran_pars	mother_pidlink	sd__(Intercept)	0.03601	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1537	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-2255	-2197	1138	-2275	NA	NA	NA
11	-2254	-2189	1138	-2276	0.769	1	0.3805
14	-2249	-2167	1139	-2277	1.322	3	0.724
20	-2240	-2123	1140	-2280	2.826	6	0.8303

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Sector_Social services

birthorder <- birthorder %>% mutate(outcome = `Sector_Social services`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.0106	0.06663	-0.1591	4184	0.8736	-0.1976	0.1764
fixed	NA	poly(age, 3, raw = TRUE)1	0.006198	0.005921	1.047	4039	0.2952	-0.01042	0.02282
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001645	0.0001637	-1.005	3885	0.3152	-0.0006241	0.0002952
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001291	0.000001426	0.9048	3755	0.3656	-0.000002714	0.000005295
fixed	NA	male	0.007712	0.006854	1.125	4623	0.2605	-0.01153	0.02695
fixed	NA	sibling_count3	-0.001109	0.009679	-0.1146	3309	0.9088	-0.02828	0.02606
fixed	NA	sibling_count4	-0.006758	0.009768	-0.6918	3009	0.4891	-0.03418	0.02066
fixed	NA	sibling_count5	-0.0159	0.01014	-1.568	2736	0.1171	-0.04436	0.01257
ran_pars	mother_pidlink	sd__(Intercept)	0.04924	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2259	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01059	0.06665	-0.159	4185	0.8737	-0.1977	0.1765
fixed	NA	birth_order	0.000004172	0.003395	0.001229	4186	0.999	-0.009524	0.009533
fixed	NA	poly(age, 3, raw = TRUE)1	0.006197	0.005944	1.043	4041	0.2972	-0.01049	0.02288
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001645	0.0001643	-1.001	3878	0.3168	-0.0006256	0.0002967
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000129	0.000001429	0.9028	3748	0.3667	-0.000002722	0.000005302
fixed	NA	male	0.007713	0.006854	1.125	4622	0.2606	-0.01153	0.02695
fixed	NA	sibling_count3	-0.001111	0.009766	-0.1137	3399	0.9095	-0.02852	0.0263
fixed	NA	sibling_count4	-0.006761	0.01016	-0.6656	3384	0.5057	-0.03527	0.02175
fixed	NA	sibling_count5	-0.0159	0.01105	-1.439	3486	0.1502	-0.04692	0.01511
ran_pars	mother_pidlink	sd__(Intercept)	0.0492	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.226	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01191	0.06687	-0.1781	4191	0.8586	-0.1996	0.1758
fixed	NA	poly(age, 3, raw = TRUE)1	0.006289	0.005947	1.057	4036	0.2904	-0.0104	0.02298
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000166	0.0001644	-1.01	3869	0.3127	-0.0006274	0.0002954
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001294	0.000001431	0.9045	3733	0.3658	-0.000002722	0.00000531
fixed	NA	male	0.007815	0.006858	1.139	4619	0.2546	-0.01144	0.02707
fixed	NA	sibling_count3	-0.0002059	0.009947	-0.0207	3561	0.9835	-0.02813	0.02772
fixed	NA	sibling_count4	-0.004984	0.01036	-0.4813	3562	0.6304	-0.03406	0.02409
fixed	NA	sibling_count5	-0.01664	0.01117	-1.49	3589	0.1364	-0.04799	0.01471
fixed	NA	birth_order_nonlinear2	-0.0002603	0.008193	-0.03178	4061	0.9747	-0.02326	0.02274
fixed	NA	birth_order_nonlinear3	-0.003861	0.01039	-0.3717	4044	0.7101	-0.03302	0.0253
fixed	NA	birth_order_nonlinear4	-0.005168	0.01357	-0.3808	4028	0.7034	-0.04327	0.03293
fixed	NA	birth_order_nonlinear5	0.01357	0.01958	0.6931	4104	0.4883	-0.04139	0.06853
ran_pars	mother_pidlink	sd__(Intercept)	0.04904	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2261	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.01779	0.06699	-0.2656	4197	0.7906	-0.2058	0.1703
fixed	NA	poly(age, 3, raw = TRUE)1	0.006093	0.005953	1.023	4035	0.3062	-0.01062	0.0228
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001639	0.0001645	-0.9966	3868	0.319	-0.0006257	0.0002978
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001307	0.000001431	0.9128	3731	0.3614	-0.000002711	0.000005324
fixed	NA	male	0.00761	0.006859	1.109	4611	0.2673	-0.01164	0.02686
fixed	NA	count_birth_order2/2	0.02447	0.01394	1.755	3949	0.07939	-0.01467	0.06361
fixed	NA	count_birth_order1/3	0.01066	0.01326	0.8039	4622	0.4215	-0.02656	0.04787
fixed	NA	count_birth_order2/3	0.002391	0.01476	0.162	4624	0.8713	-0.03904	0.04383
fixed	NA	count_birth_order3/3	0.01103	0.01624	0.6791	4625	0.4971	-0.03456	0.05662
fixed	NA	count_birth_order1/4	0.01603	0.01461	1.097	4625	0.2727	-0.02498	0.05703
fixed	NA	count_birth_order2/4	0.00377	0.01567	0.2405	4624	0.8099	-0.04023	0.04777
fixed	NA	count_birth_order3/4	-0.01053	0.01654	-0.6363	4625	0.5246	-0.05697	0.03591
fixed	NA	count_birth_order4/4	-0.006882	0.01784	-0.3858	4625	0.6997	-0.05696	0.04319
fixed	NA	count_birth_order1/5	-0.002279	0.01648	-0.1383	4625	0.89	-0.04854	0.04399
fixed	NA	count_birth_order2/5	-0.02511	0.01752	-1.433	4624	0.1518	-0.07428	0.02406
fixed	NA	count_birth_order3/5	-0.004062	0.01843	-0.2204	4624	0.8256	-0.0558	0.04767
fixed	NA	count_birth_order4/5	-0.004579	0.01948	-0.2351	4622	0.8141	-0.05925	0.05009
fixed	NA	count_birth_order5/5	0.006435	0.01952	0.3296	4625	0.7417	-0.04836	0.06123
ran_pars	mother_pidlink	sd__(Intercept)	0.04993	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2258	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-413.3	-348.9	216.6	-433.3	NA	NA	NA
11	-411.3	-340.4	216.6	-433.3	0.000003217	1	0.9986
14	-406.2	-316	217.1	-434.2	0.9419	3	0.8153
20	-401.6	-272.8	220.8	-441.6	7.4	6	0.2854

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2246	0.1959	-1.147	2616	0.2515	-0.7745	0.3252
fixed	NA	poly(age, 3, raw = TRUE)1	0.02944	0.02168	1.358	2615	0.1745	-0.03141	0.09029
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009834	0.0007678	-1.281	2612	0.2003	-0.003139	0.001172
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001074	0.000008708	1.233	2609	0.2176	-0.00001371	0.00003518
fixed	NA	male	0.009916	0.009229	1.074	2634	0.2827	-0.01599	0.03582
fixed	NA	sibling_count3	-0.006129	0.01268	-0.4833	2173	0.6289	-0.04172	0.02947
fixed	NA	sibling_count4	-0.01875	0.01309	-1.433	1973	0.152	-0.05549	0.01798
fixed	NA	sibling_count5	-0.002224	0.01452	-0.1531	1683	0.8783	-0.043	0.03855
ran_pars	mother_pidlink	sd__(Intercept)	0.02621	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2321	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2243	0.1959	-1.145	2616	0.2524	-0.7742	0.3256
fixed	NA	birth_order	-0.001622	0.004676	-0.3468	2550	0.7287	-0.01475	0.0115
fixed	NA	poly(age, 3, raw = TRUE)1	0.02959	0.02168	1.364	2613	0.1725	-0.03128	0.09046
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009858	0.0007679	-1.284	2611	0.1994	-0.003141	0.00117
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001073	0.00000871	1.231	2608	0.2183	-0.00001372	0.00003517
fixed	NA	male	0.009911	0.009231	1.074	2633	0.2831	-0.016	0.03582
fixed	NA	sibling_count3	-0.005364	0.01287	-0.4167	2202	0.677	-0.0415	0.03077
fixed	NA	sibling_count4	-0.0171	0.01393	-1.228	2098	0.2197	-0.0562	0.022
fixed	NA	sibling_count5	0.0005365	0.01657	0.03239	2010	0.9742	-0.04596	0.04704
ran_pars	mother_pidlink	sd__(Intercept)	0.02621	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2322	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2206	0.1963	-1.124	2612	0.2611	-0.7716	0.3303
fixed	NA	poly(age, 3, raw = TRUE)1	0.02947	0.02172	1.357	2610	0.1748	-0.03148	0.09043
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009792	0.000769	-1.273	2608	0.203	-0.003138	0.001179
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001063	0.000008721	1.219	2606	0.2228	-0.00001385	0.00003512
fixed	NA	male	0.009571	0.009236	1.036	2630	0.3002	-0.01636	0.0355
fixed	NA	sibling_count3	-0.006408	0.01308	-0.4899	2255	0.6243	-0.04313	0.03031
fixed	NA	sibling_count4	-0.02085	0.01413	-1.476	2150	0.1402	-0.06052	0.01882
fixed	NA	sibling_count5	-0.0005539	0.01679	-0.03299	2050	0.9737	-0.04768	0.04657
fixed	NA	birth_order_nonlinear2	-0.01649	0.01121	-1.471	2373	0.1414	-0.04795	0.01497
fixed	NA	birth_order_nonlinear3	-0.00008333	0.01365	-0.006104	2427	0.9951	-0.03841	0.03824
fixed	NA	birth_order_nonlinear4	0.005212	0.01816	0.2871	2491	0.7741	-0.04576	0.05618
fixed	NA	birth_order_nonlinear5	-0.02791	0.02816	-0.9913	2456	0.3216	-0.107	0.05113
ran_pars	mother_pidlink	sd__(Intercept)	0.0282	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2319	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2203	0.1965	-1.121	2606	0.2623	-0.7718	0.3312
fixed	NA	poly(age, 3, raw = TRUE)1	0.02899	0.02174	1.334	2604	0.1825	-0.03203	0.09
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009596	0.0007699	-1.246	2602	0.2127	-0.003121	0.001201
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001037	0.000008732	1.188	2599	0.235	-0.00001414	0.00003489
fixed	NA	male	0.009276	0.009252	1.003	2624	0.3161	-0.01669	0.03525
fixed	NA	count_birth_order2/2	-0.004822	0.02045	-0.2358	2349	0.8136	-0.06221	0.05257
fixed	NA	count_birth_order1/3	-0.004718	0.01694	-0.2785	2624	0.7806	-0.05227	0.04284
fixed	NA	count_birth_order2/3	-0.03044	0.01883	-1.616	2624	0.1062	-0.0833	0.02243
fixed	NA	count_birth_order3/3	0.01643	0.02053	0.8003	2623	0.4236	-0.0412	0.07406
fixed	NA	count_birth_order1/4	-0.01174	0.01949	-0.6022	2624	0.5471	-0.06645	0.04297
fixed	NA	count_birth_order2/4	-0.02657	0.02064	-1.288	2624	0.198	-0.08451	0.03136
fixed	NA	count_birth_order3/4	-0.03235	0.02141	-1.511	2624	0.1309	-0.09245	0.02775
fixed	NA	count_birth_order4/4	-0.01096	0.02289	-0.4786	2624	0.6322	-0.07522	0.0533
fixed	NA	count_birth_order1/5	0.01401	0.02574	0.5445	2623	0.5862	-0.05823	0.08626
fixed	NA	count_birth_order2/5	-0.01272	0.02771	-0.459	2624	0.6463	-0.09049	0.06506
fixed	NA	count_birth_order3/5	-0.007082	0.02632	-0.2691	2624	0.7879	-0.08095	0.06679
fixed	NA	count_birth_order4/5	0.007286	0.02565	0.284	2623	0.7764	-0.06472	0.0793
fixed	NA	count_birth_order5/5	-0.02465	0.02699	-0.9132	2622	0.3612	-0.1004	0.05112
ran_pars	mother_pidlink	sd__(Intercept)	0.02655	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2322	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-174	-115.2	97	-194	NA	NA	NA
11	-172.1	-107.4	97.06	-194.1	0.1205	1	0.7285
14	-169.8	-87.46	98.89	-197.8	3.655	3	0.3012
20	-161.5	-43.91	100.7	-201.5	3.72	6	0.7145

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2967	0.2013	-1.474	2409	0.1406	-0.8616	0.2683
fixed	NA	poly(age, 3, raw = TRUE)1	0.0381	0.02229	1.709	2408	0.08752	-0.02447	0.1007
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001307	0.0007895	-1.656	2406	0.09794	-0.003523	0.000909
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001457	0.000008956	1.627	2404	0.1039	-0.00001057	0.00003971
fixed	NA	male	0.01207	0.009549	1.264	2419	0.2062	-0.01473	0.03888
fixed	NA	sibling_count3	-0.009292	0.01384	-0.6713	2014	0.5021	-0.04815	0.02956
fixed	NA	sibling_count4	-0.01757	0.01399	-1.256	1899	0.2094	-0.05683	0.0217
fixed	NA	sibling_count5	-0.01353	0.01472	-0.919	1729	0.3582	-0.05485	0.02779
ran_pars	mother_pidlink	sd__(Intercept)	0.04002	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2281	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.295	0.2013	-1.465	2408	0.143	-0.8601	0.2701
fixed	NA	birth_order	-0.002264	0.004692	-0.4826	2370	0.6294	-0.01543	0.01091
fixed	NA	poly(age, 3, raw = TRUE)1	0.0382	0.02229	1.714	2407	0.08672	-0.02437	0.1008
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001308	0.0007896	-1.656	2405	0.09781	-0.003524	0.0009087
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001453	0.000008958	1.622	2403	0.105	-0.00001062	0.00003967
fixed	NA	male	0.01201	0.009552	1.257	2418	0.2088	-0.0148	0.03882
fixed	NA	sibling_count3	-0.008216	0.01402	-0.5859	2031	0.558	-0.04758	0.03115
fixed	NA	sibling_count4	-0.01544	0.01467	-1.052	1973	0.2928	-0.05662	0.02574
fixed	NA	sibling_count5	-0.009919	0.01651	-0.6006	1953	0.5482	-0.05627	0.03644
ran_pars	mother_pidlink	sd__(Intercept)	0.03999	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2282	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3003	0.2018	-1.488	2403	0.1369	-0.8669	0.2662
fixed	NA	poly(age, 3, raw = TRUE)1	0.03889	0.02235	1.741	2402	0.08189	-0.02383	0.1016
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001329	0.0007915	-1.679	2401	0.09323	-0.003551	0.0008926
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001474	0.000008978	1.641	2399	0.1008	-0.00001046	0.00003994
fixed	NA	male	0.01188	0.00956	1.243	2415	0.2141	-0.01496	0.03871
fixed	NA	sibling_count3	-0.009676	0.01423	-0.6798	2073	0.4967	-0.04963	0.03028
fixed	NA	sibling_count4	-0.0179	0.01487	-1.204	2013	0.2288	-0.05962	0.02383
fixed	NA	sibling_count5	-0.01075	0.01663	-0.6465	1975	0.518	-0.05743	0.03593
fixed	NA	birth_order_nonlinear2	-0.01379	0.0115	-1.199	2167	0.2305	-0.04606	0.01848
fixed	NA	birth_order_nonlinear3	0.001024	0.01415	0.07239	2253	0.9423	-0.03869	0.04074
fixed	NA	birth_order_nonlinear4	-0.003478	0.01865	-0.1865	2311	0.8521	-0.05583	0.04888
fixed	NA	birth_order_nonlinear5	-0.02216	0.0268	-0.8266	2257	0.4086	-0.0974	0.05309
ran_pars	mother_pidlink	sd__(Intercept)	0.04086	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2281	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2995	0.2022	-1.481	2397	0.1387	-0.8671	0.2681
fixed	NA	poly(age, 3, raw = TRUE)1	0.03831	0.02239	1.711	2396	0.08712	-0.02453	0.1012
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001308	0.0007929	-1.65	2395	0.09917	-0.003534	0.0009178
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001448	0.000008994	1.609	2392	0.1076	-0.00001077	0.00003972
fixed	NA	male	0.01165	0.009586	1.215	2409	0.2245	-0.01526	0.03856
fixed	NA	count_birth_order2/2	-0.00005427	0.02217	-0.002448	2189	0.998	-0.06229	0.06218
fixed	NA	count_birth_order1/3	-0.009228	0.0186	-0.4963	2409	0.6198	-0.06143	0.04297
fixed	NA	count_birth_order2/3	-0.02607	0.02024	-1.288	2409	0.1979	-0.08288	0.03074
fixed	NA	count_birth_order3/3	0.01425	0.02245	0.635	2408	0.5255	-0.04875	0.07726
fixed	NA	count_birth_order1/4	-0.003288	0.02024	-0.1624	2409	0.871	-0.06011	0.05353
fixed	NA	count_birth_order2/4	-0.03242	0.0213	-1.522	2409	0.1281	-0.09222	0.02737
fixed	NA	count_birth_order3/4	-0.02672	0.02306	-1.159	2408	0.2467	-0.09144	0.038
fixed	NA	count_birth_order4/4	-0.008554	0.02502	-0.342	2408	0.7324	-0.07877	0.06166
fixed	NA	count_birth_order1/5	-0.001764	0.02451	-0.07195	2409	0.9426	-0.07057	0.06704
fixed	NA	count_birth_order2/5	-0.009901	0.0251	-0.3945	2409	0.6932	-0.08034	0.06054
fixed	NA	count_birth_order3/5	-0.01172	0.0258	-0.4541	2408	0.6498	-0.08415	0.06072
fixed	NA	count_birth_order4/5	-0.01896	0.02622	-0.7231	2407	0.4697	-0.09255	0.05464
fixed	NA	count_birth_order5/5	-0.02826	0.02662	-1.061	2405	0.2886	-0.103	0.04648
ran_pars	mother_pidlink	sd__(Intercept)	0.03943	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2284	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-201.1	-143.2	110.6	-221.1	NA	NA	NA
11	-199.4	-135.6	110.7	-221.4	0.2337	1	0.6288
14	-195.4	-114.2	111.7	-223.4	2.013	3	0.5697
20	-186.9	-71.01	113.4	-226.9	3.526	6	0.7405

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2046	0.1926	-1.062	2638	0.2882	-0.7453	0.336
fixed	NA	poly(age, 3, raw = TRUE)1	0.02761	0.02137	1.292	2638	0.1965	-0.03238	0.08761
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009597	0.0007588	-1.265	2638	0.2061	-0.00309	0.00117
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001091	0.000008629	1.265	2638	0.206	-0.00001331	0.00003514
fixed	NA	male	0.01092	0.008987	1.215	2638	0.2243	-0.0143	0.03615
fixed	NA	sibling_count3	-0.004119	0.01207	-0.3413	2638	0.7329	-0.038	0.02976
fixed	NA	sibling_count4	-0.0145	0.01262	-1.149	2638	0.2505	-0.04992	0.02092
fixed	NA	sibling_count5	0.003273	0.01436	0.228	2638	0.8197	-0.03703	0.04358
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2276	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2049	0.1926	-1.064	2637	0.2875	-0.7457	0.3358
fixed	NA	birth_order	0.001188	0.004618	0.2573	2637	0.7969	-0.01177	0.01415
fixed	NA	poly(age, 3, raw = TRUE)1	0.02751	0.02138	1.287	2637	0.1984	-0.03251	0.08753
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009579	0.0007589	-1.262	2637	0.207	-0.003088	0.001172
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001092	0.000008631	1.266	2637	0.2058	-0.0000133	0.00003515
fixed	NA	male	0.01094	0.008989	1.217	2637	0.2237	-0.01429	0.03617
fixed	NA	sibling_count3	-0.004686	0.01227	-0.3819	2637	0.7025	-0.03913	0.02976
fixed	NA	sibling_count4	-0.0157	0.01345	-1.167	2637	0.2433	-0.05346	0.02206
fixed	NA	sibling_count5	0.001332	0.01622	0.08212	2637	0.9346	-0.0442	0.04687
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2277	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2013	0.1929	-1.044	2634	0.2968	-0.7429	0.3402
fixed	NA	poly(age, 3, raw = TRUE)1	0.02774	0.02141	1.296	2634	0.1951	-0.03235	0.08784
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009645	0.0007598	-1.269	2634	0.2044	-0.003097	0.001168
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001099	0.00000864	1.272	2634	0.2034	-0.00001326	0.00003524
fixed	NA	male	0.01093	0.008993	1.215	2634	0.2244	-0.01431	0.03617
fixed	NA	sibling_count3	-0.006049	0.01248	-0.4848	2634	0.6278	-0.04107	0.02897
fixed	NA	sibling_count4	-0.01936	0.01365	-1.419	2634	0.1562	-0.05766	0.01895
fixed	NA	sibling_count5	-0.0001196	0.0165	-0.007248	2634	0.9942	-0.04644	0.0462
fixed	NA	birth_order_nonlinear2	-0.01424	0.01083	-1.315	2634	0.1887	-0.04463	0.01616
fixed	NA	birth_order_nonlinear3	0.006096	0.01329	0.4587	2634	0.6465	-0.03121	0.0434
fixed	NA	birth_order_nonlinear4	0.01221	0.01818	0.6715	2634	0.502	-0.03883	0.06325
fixed	NA	birth_order_nonlinear5	-0.01491	0.02909	-0.5124	2634	0.6084	-0.09657	0.06676
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2276	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2	0.1932	-1.035	2628	0.3006	-0.7422	0.3422
fixed	NA	poly(age, 3, raw = TRUE)1	0.02738	0.02144	1.277	2628	0.2016	-0.03279	0.08755
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009506	0.0007609	-1.249	2628	0.2117	-0.003087	0.001185
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001081	0.000008654	1.25	2628	0.2116	-0.00001348	0.00003511
fixed	NA	male	0.01061	0.009007	1.178	2628	0.2391	-0.01468	0.03589
fixed	NA	count_birth_order2/2	-0.008312	0.01941	-0.4281	2628	0.6686	-0.0628	0.04618
fixed	NA	count_birth_order1/3	-0.005054	0.01622	-0.3116	2628	0.7554	-0.05058	0.04047
fixed	NA	count_birth_order2/3	-0.02742	0.01804	-1.52	2628	0.1287	-0.07806	0.02323
fixed	NA	count_birth_order3/3	0.01547	0.01945	0.7955	2628	0.4264	-0.03912	0.07007
fixed	NA	count_birth_order1/4	-0.01451	0.01908	-0.7606	2628	0.447	-0.06809	0.03906
fixed	NA	count_birth_order2/4	-0.02173	0.02003	-1.085	2628	0.2782	-0.07796	0.0345
fixed	NA	count_birth_order3/4	-0.0271	0.0208	-1.303	2628	0.1926	-0.08548	0.03127
fixed	NA	count_birth_order4/4	-0.003558	0.02257	-0.1577	2628	0.8747	-0.0669	0.05979
fixed	NA	count_birth_order1/5	0.007468	0.02502	0.2984	2628	0.7654	-0.06277	0.0777
fixed	NA	count_birth_order2/5	-0.01613	0.02789	-0.5784	2628	0.563	-0.09442	0.06216
fixed	NA	count_birth_order3/5	0.007383	0.02716	0.2718	2628	0.7858	-0.06886	0.08363
fixed	NA	count_birth_order4/5	0.01181	0.02613	0.4519	2628	0.6514	-0.06154	0.08515
fixed	NA	count_birth_order5/5	-0.01303	0.02775	-0.4695	2628	0.6388	-0.09093	0.06487
ran_pars	mother_pidlink	sd__(Intercept)	0.000000003253	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2278	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-311.1	-252.3	165.6	-331.1	NA	NA	NA
11	-309.2	-244.5	165.6	-331.2	0.06645	1	0.7966
14	-307	-224.6	167.5	-335	3.759	3	0.2887
20	-297.5	-179.9	168.8	-337.5	2.584	6	0.859

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Sector_Transportation, storage and communications

birthorder <- birthorder %>% mutate(outcome = `Sector_Transportation, storage and communications`)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1106	0.05168	2.14	4215	0.0324	-0.03447	0.2557
fixed	NA	poly(age, 3, raw = TRUE)1	-0.007407	0.004589	-1.614	4077	0.1066	-0.02029	0.005474
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001961	0.0001268	1.546	3932	0.1221	-0.0001599	0.0005521
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001494	0.000001104	-1.353	3812	0.176	-0.000004594	0.000001605
fixed	NA	male	-0.01298	0.005339	-2.431	4632	0.0151	-0.02797	0.002009
fixed	NA	sibling_count3	0.009016	0.007479	1.205	3447	0.2281	-0.01198	0.03001
fixed	NA	sibling_count4	0.01098	0.007539	1.457	3133	0.1453	-0.01018	0.03214
fixed	NA	sibling_count5	0.0234	0.007815	2.995	2849	0.002771	0.001466	0.04534
ran_pars	mother_pidlink	sd__(Intercept)	0.02411	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1784	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1111	0.05168	2.149	4214	0.03168	-0.034	0.2561
fixed	NA	birth_order	0.00181	0.002653	0.6821	4285	0.4952	-0.005638	0.009258
fixed	NA	poly(age, 3, raw = TRUE)1	-0.00768	0.004606	-1.667	4076	0.09555	-0.02061	0.00525
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002029	0.0001272	1.595	3924	0.1109	-0.0001542	0.0005599
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000154	0.000001106	-1.392	3804	0.1639	-0.000004645	0.000001565
fixed	NA	male	-0.01296	0.00534	-2.427	4631	0.01527	-0.02795	0.00203
fixed	NA	sibling_count3	0.008324	0.007548	1.103	3532	0.2702	-0.01286	0.02951
fixed	NA	sibling_count4	0.009485	0.00785	1.208	3496	0.227	-0.01255	0.03152
fixed	NA	sibling_count5	0.02105	0.008542	2.464	3581	0.01379	-0.00293	0.04502
ran_pars	mother_pidlink	sd__(Intercept)	0.02369	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1784	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1115	0.05184	2.151	4219	0.03153	-0.03401	0.257
fixed	NA	poly(age, 3, raw = TRUE)1	-0.00755	0.004606	-1.639	4072	0.1013	-0.02048	0.005381
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001993	0.0001272	1.567	3916	0.1173	-0.0001578	0.0005565
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000151	0.000001107	-1.364	3789	0.1725	-0.000004617	0.000001597
fixed	NA	male	-0.01274	0.005341	-2.386	4628	0.01705	-0.02774	0.002246
fixed	NA	sibling_count3	0.006757	0.007691	0.8786	3684	0.3797	-0.01483	0.02834
fixed	NA	sibling_count4	0.01084	0.008007	1.354	3666	0.1758	-0.01163	0.03332
fixed	NA	sibling_count5	0.01992	0.008636	2.307	3678	0.02112	-0.004319	0.04416
fixed	NA	birth_order_nonlinear2	0.001177	0.006405	0.1838	4156	0.8542	-0.0168	0.01916
fixed	NA	birth_order_nonlinear3	0.009914	0.008122	1.221	4158	0.2223	-0.01288	0.03271
fixed	NA	birth_order_nonlinear4	-0.00988	0.01061	-0.931	4160	0.3519	-0.03967	0.01991
fixed	NA	birth_order_nonlinear5	0.02139	0.0153	1.398	4235	0.1623	-0.02157	0.06435
ran_pars	mother_pidlink	sd__(Intercept)	0.02371	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1784	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1132	0.05194	2.179	4223	0.0294	-0.03263	0.259
fixed	NA	poly(age, 3, raw = TRUE)1	-0.00751	0.004612	-1.628	4068	0.1035	-0.02046	0.005436
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001992	0.0001273	1.564	3912	0.1178	-0.0001582	0.0005566
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001516	0.000001107	-1.369	3785	0.1711	-0.000004624	0.000001592
fixed	NA	male	-0.01268	0.005344	-2.374	4621	0.01766	-0.02769	0.002317
fixed	NA	count_birth_order2/2	-0.005555	0.01092	-0.5089	4038	0.6109	-0.0362	0.02509
fixed	NA	count_birth_order1/3	0.003489	0.01032	0.338	4624	0.7354	-0.02548	0.03246
fixed	NA	count_birth_order2/3	0.00642	0.01149	0.5586	4624	0.5764	-0.02584	0.03868
fixed	NA	count_birth_order3/3	0.01413	0.01264	1.118	4624	0.2638	-0.02136	0.04963
fixed	NA	count_birth_order1/4	0.01342	0.01137	1.18	4625	0.2382	-0.01851	0.04535
fixed	NA	count_birth_order2/4	0.007184	0.0122	0.5887	4624	0.5561	-0.02707	0.04144
fixed	NA	count_birth_order3/4	0.01613	0.01288	1.252	4624	0.2106	-0.02003	0.05228
fixed	NA	count_birth_order4/4	-0.004703	0.01389	-0.3386	4623	0.7349	-0.04369	0.03428
fixed	NA	count_birth_order1/5	0.004813	0.01283	0.375	4625	0.7077	-0.03121	0.04084
fixed	NA	count_birth_order2/5	0.02775	0.01364	2.034	4625	0.04198	-0.01054	0.06604
fixed	NA	count_birth_order3/5	0.03003	0.01435	2.092	4625	0.03649	-0.01026	0.07031
fixed	NA	count_birth_order4/5	0.01143	0.01517	0.7536	4625	0.4511	-0.03115	0.05401
fixed	NA	count_birth_order5/5	0.0388	0.0152	2.553	4624	0.01072	-0.003867	0.08147
ran_pars	mother_pidlink	sd__(Intercept)	0.02323	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1785	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-2736	-2672	1378	-2756	NA	NA	NA
11	-2735	-2664	1378	-2757	0.4679	1	0.494
14	-2734	-2643	1381	-2762	4.864	3	0.182
20	-2725	-2596	1382	-2765	2.98	6	0.8114

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.185	0.1511	1.225	2634	0.2208	-0.239	0.609
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01421	0.01672	-0.8503	2634	0.3952	-0.06114	0.03271
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004341	0.000592	0.7333	2634	0.4635	-0.001228	0.002096
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004419	0.000006715	-0.6581	2634	0.5105	-0.00002327	0.00001443
fixed	NA	male	-0.01574	0.00712	-2.21	2634	0.02718	-0.03572	0.00425
fixed	NA	sibling_count3	0.004938	0.00976	0.5059	2634	0.613	-0.02246	0.03233
fixed	NA	sibling_count4	0.006176	0.01007	0.6136	2634	0.5396	-0.02208	0.03443
fixed	NA	sibling_count5	0.02625	0.01116	2.352	2634	0.01874	-0.005077	0.05758
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1802	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1862	0.151	1.233	2633	0.2177	-0.2377	0.6102
fixed	NA	birth_order	-0.005075	0.00361	-1.406	2633	0.1598	-0.01521	0.005058
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01377	0.01672	-0.8237	2633	0.4102	-0.06069	0.03315
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004271	0.000592	0.7216	2633	0.4706	-0.001235	0.002089
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004466	0.000006714	-0.6653	2633	0.5059	-0.00002331	0.00001438
fixed	NA	male	-0.01575	0.007119	-2.213	2633	0.027	-0.03574	0.004231
fixed	NA	sibling_count3	0.007332	0.009905	0.7402	2633	0.4593	-0.02047	0.03514
fixed	NA	sibling_count4	0.01134	0.01071	1.059	2633	0.2898	-0.01873	0.04142
fixed	NA	sibling_count5	0.03489	0.01274	2.739	2633	0.006205	-0.0008673	0.07064
ran_pars	mother_pidlink	sd__(Intercept)	0.000000002183	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1802	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1769	0.1514	1.168	2630	0.2427	-0.248	0.6018
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01325	0.01675	-0.7913	2630	0.4288	-0.06027	0.03376
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004094	0.0005931	0.6903	2630	0.4901	-0.001255	0.002074
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004277	0.000006726	-0.636	2630	0.5249	-0.00002316	0.0000146
fixed	NA	male	-0.0157	0.007127	-2.203	2630	0.0277	-0.03571	0.004307
fixed	NA	sibling_count3	0.006067	0.01007	0.6025	2630	0.5469	-0.0222	0.03433
fixed	NA	sibling_count4	0.01006	0.01087	0.9256	2630	0.3547	-0.02046	0.04059
fixed	NA	sibling_count5	0.03557	0.01291	2.755	2630	0.005917	-0.0006773	0.07182
fixed	NA	birth_order_nonlinear2	-0.006373	0.008667	-0.7354	2630	0.4622	-0.0307	0.01795
fixed	NA	birth_order_nonlinear3	-0.004844	0.01055	-0.459	2630	0.6462	-0.03447	0.02478
fixed	NA	birth_order_nonlinear4	-0.0152	0.01403	-1.084	2630	0.2787	-0.05459	0.02418
fixed	NA	birth_order_nonlinear5	-0.03036	0.02176	-1.395	2630	0.1631	-0.09145	0.03073
ran_pars	mother_pidlink	sd__(Intercept)	0.000000001973	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1803	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1735	0.1516	1.144	2624	0.2526	-0.252	0.599
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01337	0.01677	-0.7972	2624	0.4254	-0.06044	0.03371
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004147	0.0005939	0.6983	2624	0.485	-0.001252	0.002082
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004356	0.000006737	-0.6466	2624	0.5179	-0.00002327	0.00001455
fixed	NA	male	-0.01603	0.007141	-2.245	2624	0.02487	-0.03607	0.004015
fixed	NA	count_birth_order2/2	0.007068	0.01581	0.4471	2624	0.6549	-0.03731	0.05145
fixed	NA	count_birth_order1/3	0.00987	0.01308	0.7548	2624	0.4504	-0.02684	0.04658
fixed	NA	count_birth_order2/3	-0.0002422	0.01454	-0.01666	2624	0.9867	-0.04105	0.04056
fixed	NA	count_birth_order3/3	0.01252	0.01585	0.7898	2624	0.4297	-0.03197	0.057
fixed	NA	count_birth_order1/4	0.02086	0.01504	1.387	2624	0.1656	-0.02136	0.06309
fixed	NA	count_birth_order2/4	0.009328	0.01593	0.5855	2624	0.5582	-0.03539	0.05405
fixed	NA	count_birth_order3/4	0.0003236	0.01653	0.01958	2624	0.9844	-0.04607	0.04672
fixed	NA	count_birth_order4/4	-0.001404	0.01767	-0.07945	2624	0.9367	-0.05101	0.0482
fixed	NA	count_birth_order1/5	0.0448	0.01987	2.255	2624	0.0242	-0.01096	0.1006
fixed	NA	count_birth_order2/5	0.02365	0.02139	1.106	2624	0.2689	-0.03638	0.08368
fixed	NA	count_birth_order3/5	0.03798	0.02031	1.87	2624	0.06163	-0.01904	0.095
fixed	NA	count_birth_order4/5	0.02571	0.0198	1.298	2624	0.1944	-0.02988	0.08129
fixed	NA	count_birth_order5/5	0.009607	0.02084	0.4611	2624	0.6448	-0.04888	0.0681
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1804	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-1545	-1486	782.3	-1565	NA	NA	NA
11	-1545	-1480	783.3	-1567	1.983	1	0.1591
14	-1539	-1457	783.7	-1567	0.6754	3	0.879
20	-1530	-1412	784.8	-1570	2.307	6	0.8894

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1902	0.1546	1.23	2419	0.2188	-0.2438	0.6242
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01507	0.01712	-0.8803	2419	0.3788	-0.06313	0.03299
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004658	0.0006064	0.7681	2419	0.4425	-0.001236	0.002168
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004832	0.000006879	-0.7025	2419	0.4825	-0.00002414	0.00001448
fixed	NA	male	-0.01975	0.007343	-2.69	2419	0.007186	-0.04036	0.0008565
fixed	NA	sibling_count3	0.01015	0.01059	0.9585	2419	0.3379	-0.01957	0.03986
fixed	NA	sibling_count4	0.00702	0.01069	0.6568	2419	0.5113	-0.02298	0.03702
fixed	NA	sibling_count5	0.03426	0.01123	3.05	2419	0.002313	0.002728	0.06578
ran_pars	mother_pidlink	sd__(Intercept)	0.000000002039	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1781	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1911	0.1547	1.235	2418	0.2168	-0.2431	0.6252
fixed	NA	birth_order	-0.00116	0.003613	-0.3211	2418	0.7482	-0.0113	0.008983
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01502	0.01713	-0.8773	2418	0.3804	-0.0631	0.03305
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004657	0.0006065	0.7677	2418	0.4427	-0.001237	0.002168
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004856	0.000006881	-0.7058	2418	0.4804	-0.00002417	0.00001446
fixed	NA	male	-0.01979	0.007345	-2.694	2418	0.007103	-0.04041	0.000828
fixed	NA	sibling_count3	0.0107	0.01073	0.9973	2418	0.3187	-0.01941	0.0408
fixed	NA	sibling_count4	0.00811	0.01122	0.7231	2418	0.4697	-0.02337	0.03959
fixed	NA	sibling_count5	0.0361	0.01262	2.86	2418	0.004269	0.0006722	0.07153
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1781	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1911	0.1551	1.232	2415	0.218	-0.2443	0.6265
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01505	0.01717	-0.8763	2415	0.381	-0.06325	0.03315
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004673	0.0006081	0.7684	2415	0.4423	-0.00124	0.002174
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000488	0.000006898	-0.7075	2415	0.4793	-0.00002424	0.00001448
fixed	NA	male	-0.01987	0.007354	-2.702	2415	0.006933	-0.04052	0.0007697
fixed	NA	sibling_count3	0.01065	0.01089	0.9777	2415	0.3283	-0.01993	0.04122
fixed	NA	sibling_count4	0.007511	0.01137	0.6606	2415	0.509	-0.02441	0.03943
fixed	NA	sibling_count5	0.03579	0.01271	2.815	2415	0.004921	0.00009795	0.07147
fixed	NA	birth_order_nonlinear2	-0.004707	0.008881	-0.53	2415	0.5961	-0.02964	0.02022
fixed	NA	birth_order_nonlinear3	-0.00238	0.01092	-0.218	2415	0.8275	-0.03303	0.02827
fixed	NA	birth_order_nonlinear4	-0.001274	0.01438	-0.08861	2415	0.9294	-0.04165	0.0391
fixed	NA	birth_order_nonlinear5	-0.007768	0.02068	-0.3755	2415	0.7073	-0.06583	0.05029
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1782	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1648	0.1549	1.064	2409	0.2875	-0.27	0.5997
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01283	0.01715	-0.7481	2409	0.4545	-0.06098	0.03531
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003896	0.0006074	0.6414	2409	0.5213	-0.001315	0.002095
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004026	0.00000689	-0.5843	2409	0.5591	-0.00002337	0.00001532
fixed	NA	male	-0.01961	0.007352	-2.668	2409	0.007684	-0.04025	0.001023
fixed	NA	count_birth_order2/2	0.01414	0.01707	0.8283	2409	0.4076	-0.03377	0.06204
fixed	NA	count_birth_order1/3	0.015	0.01426	1.052	2409	0.2929	-0.02503	0.05503
fixed	NA	count_birth_order2/3	0.005775	0.01552	0.372	2409	0.7099	-0.0378	0.04935
fixed	NA	count_birth_order3/3	0.02757	0.01722	1.601	2409	0.1094	-0.02076	0.0759
fixed	NA	count_birth_order1/4	0.04263	0.01552	2.746	2409	0.006069	-0.0009404	0.0862
fixed	NA	count_birth_order2/4	0.002113	0.01634	0.1293	2409	0.8971	-0.04375	0.04797
fixed	NA	count_birth_order3/4	-0.01526	0.01769	-0.8631	2409	0.3882	-0.06491	0.03438
fixed	NA	count_birth_order4/4	0.002613	0.01919	0.1362	2409	0.8917	-0.05125	0.05647
fixed	NA	count_birth_order1/5	0.0119	0.01879	0.6331	2409	0.5267	-0.04086	0.06466
fixed	NA	count_birth_order2/5	0.04407	0.01925	2.29	2409	0.0221	-0.009949	0.0981
fixed	NA	count_birth_order3/5	0.05792	0.01979	2.926	2409	0.003464	0.002357	0.1135
fixed	NA	count_birth_order4/5	0.05222	0.02011	2.597	2409	0.009472	-0.004232	0.1087
fixed	NA	count_birth_order5/5	0.03439	0.02043	1.684	2409	0.09235	-0.02294	0.09173
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1778	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-1477	-1419	748.3	-1497	NA	NA	NA
11	-1475	-1411	748.4	-1497	0.1035	1	0.7477
14	-1469	-1388	748.5	-1497	0.2679	3	0.9659
20	-1475	-1359	757.5	-1515	18.02	6	0.006178

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))

## boundary (singular) fit: see ?isSingular

compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1656	0.1532	1.081	2638	0.2797	-0.2643	0.5955
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01208	0.017	-0.7107	2638	0.4774	-0.05979	0.03563
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003581	0.0006033	0.5936	2638	0.5529	-0.001335	0.002052
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003593	0.000006861	-0.5237	2638	0.6005	-0.00002285	0.00001567
fixed	NA	male	-0.01661	0.007146	-2.324	2638	0.02018	-0.03667	0.003449
fixed	NA	sibling_count3	0.006755	0.009596	0.7039	2638	0.4816	-0.02018	0.03369
fixed	NA	sibling_count4	0.01013	0.01003	1.009	2638	0.3128	-0.01803	0.03829
fixed	NA	sibling_count5	0.03126	0.01142	2.738	2638	0.006224	-0.000789	0.06331
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.181	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1671	0.1531	1.091	2637	0.2753	-0.2627	0.5969
fixed	NA	birth_order	-0.005689	0.00367	-1.55	2637	0.1213	-0.01599	0.004614
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01157	0.01699	-0.6808	2637	0.496	-0.05927	0.03613
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003494	0.0006032	0.5793	2637	0.5625	-0.001344	0.002043
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003631	0.000006859	-0.5294	2637	0.5966	-0.00002289	0.00001562
fixed	NA	male	-0.01669	0.007144	-2.336	2637	0.01955	-0.03675	0.003363
fixed	NA	sibling_count3	0.009469	0.009752	0.971	2637	0.3316	-0.0179	0.03684
fixed	NA	sibling_count4	0.01587	0.01069	1.484	2637	0.1379	-0.01414	0.04588
fixed	NA	sibling_count5	0.04055	0.01289	3.145	2637	0.001678	0.00436	0.07674
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.181	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)

## boundary (singular) fit: see ?isSingular

tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1558	0.1534	1.015	2634	0.3101	-0.2749	0.5864
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01093	0.01702	-0.642	2634	0.5209	-0.05872	0.03686
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003265	0.0006043	0.5404	2634	0.589	-0.00137	0.002023
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000338	0.000006871	-0.492	2634	0.6228	-0.00002267	0.00001591
fixed	NA	male	-0.01653	0.007152	-2.311	2634	0.02091	-0.0366	0.003547
fixed	NA	sibling_count3	0.008106	0.009922	0.817	2634	0.414	-0.01975	0.03596
fixed	NA	sibling_count4	0.0152	0.01085	1.401	2634	0.1613	-0.01526	0.04567
fixed	NA	sibling_count5	0.04143	0.01312	3.157	2634	0.001612	0.004593	0.07826
fixed	NA	birth_order_nonlinear2	-0.005676	0.008611	-0.6591	2634	0.5099	-0.02985	0.0185
fixed	NA	birth_order_nonlinear3	-0.005663	0.01057	-0.5358	2634	0.5921	-0.03533	0.024
fixed	NA	birth_order_nonlinear4	-0.02034	0.01446	-1.407	2634	0.1596	-0.06094	0.02025
fixed	NA	birth_order_nonlinear5	-0.02933	0.02314	-1.268	2634	0.205	-0.09427	0.03561
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.181	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)

## boundary (singular) fit: see ?isSingular

tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.1514	0.1536	0.9857	2628	0.3244	-0.2798	0.5826
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0109	0.01705	-0.6394	2628	0.5226	-0.05875	0.03695
fixed	NA	poly(age, 3, raw = TRUE)2	0.000327	0.0006051	0.5403	2628	0.589	-0.001372	0.002026
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003406	0.000006882	-0.4949	2628	0.6207	-0.00002272	0.00001591
fixed	NA	male	-0.01672	0.007163	-2.335	2628	0.01962	-0.03683	0.003381
fixed	NA	count_birth_order2/2	0.006029	0.01544	0.3905	2628	0.6962	-0.03731	0.04936
fixed	NA	count_birth_order1/3	0.01013	0.0129	0.785	2628	0.4325	-0.02608	0.04633
fixed	NA	count_birth_order2/3	0.004701	0.01435	0.3277	2628	0.7432	-0.03557	0.04498
fixed	NA	count_birth_order3/3	0.01197	0.01547	0.7742	2628	0.4389	-0.03144	0.05539
fixed	NA	count_birth_order1/4	0.02871	0.01518	1.892	2628	0.05862	-0.01389	0.07131
fixed	NA	count_birth_order2/4	0.01124	0.01593	0.7059	2628	0.4803	-0.03347	0.05596
fixed	NA	count_birth_order3/4	0.001901	0.01654	0.115	2628	0.9085	-0.04452	0.04832
fixed	NA	count_birth_order4/4	0.0007442	0.01795	0.04147	2628	0.9669	-0.04963	0.05112
fixed	NA	count_birth_order1/5	0.04729	0.0199	2.377	2628	0.01755	-0.008565	0.1031
fixed	NA	count_birth_order2/5	0.0305	0.02218	1.375	2628	0.1693	-0.03176	0.09276
fixed	NA	count_birth_order3/5	0.0493	0.0216	2.282	2628	0.02254	-0.01133	0.1099
fixed	NA	count_birth_order4/5	0.02215	0.02078	1.066	2628	0.2866	-0.03618	0.08047
fixed	NA	count_birth_order5/5	0.016	0.02207	0.7251	2628	0.4685	-0.04595	0.07795
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1812	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	-1524	-1466	772.2	-1544	NA	NA	NA
11	-1525	-1460	773.4	-1547	2.409	1	0.1206
14	-1519	-1437	773.6	-1547	0.5734	3	0.9025
20	-1510	-1392	775	-1550	2.717	6	0.8435

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Smoking Behaviour

ever_smoked

birthorder <- birthorder %>% mutate(outcome = ever_smoked)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.01	0.06453	-15.65	7307	2.377e-54	-1.191	-0.829
fixed	NA	poly(age, 3, raw = TRUE)1	0.0818	0.006139	13.32	7210	4.944e-40	0.06457	0.09903
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001932	0.0001772	-10.9	7080	1.913e-27	-0.002429	-0.001434
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001445	0.000001586	9.112	6974	1.041e-19	0.000009999	0.0000189
fixed	NA	male	0.6104	0.007689	79.39	7358	0	0.5889	0.632
fixed	NA	sibling_count3	-0.008623	0.01125	-0.7666	5083	0.4433	-0.0402	0.02295
fixed	NA	sibling_count4	0.0002562	0.01161	0.02207	4545	0.9824	-0.03233	0.03284
fixed	NA	sibling_count5	0.01052	0.01217	0.8645	4043	0.3874	-0.02364	0.04469
ran_pars	mother_pidlink	sd__(Intercept)	0.1273	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.312	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.011	0.06455	-15.66	7295	2.183e-54	-1.192	-0.8297
fixed	NA	birth_order	0.001735	0.003814	0.4549	6287	0.6492	-0.008971	0.01244
fixed	NA	poly(age, 3, raw = TRUE)1	0.08163	0.00615	13.27	7232	9.717e-40	0.06437	0.0989
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001927	0.0001775	-10.86	7093	3.005e-27	-0.002426	-0.001429
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001442	0.000001587	9.085	6981	1.324e-19	0.000009966	0.00001888
fixed	NA	male	0.6104	0.00769	79.37	7357	0	0.5888	0.632
fixed	NA	sibling_count3	-0.009235	0.01133	-0.8152	5221	0.415	-0.04103	0.02256
fixed	NA	sibling_count4	-0.001164	0.01202	-0.09679	5097	0.9229	-0.03491	0.03258
fixed	NA	sibling_count5	0.008236	0.01317	0.6254	5123	0.5317	-0.02873	0.0452
ran_pars	mother_pidlink	sd__(Intercept)	0.1273	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.312	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.011	0.0647	-15.63	7315	3.422e-54	-1.193	-0.8296
fixed	NA	poly(age, 3, raw = TRUE)1	0.08161	0.006152	13.26	7220	1.076e-39	0.06434	0.09888
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00193	0.0001776	-10.86	7072	2.793e-27	-0.002428	-0.001431
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001447	0.000001589	9.105	6948	1.105e-19	0.00001001	0.00001893
fixed	NA	male	0.6105	0.007689	79.39	7354	0	0.5889	0.6321
fixed	NA	sibling_count3	-0.007945	0.01149	-0.6914	5453	0.4893	-0.0402	0.02431
fixed	NA	sibling_count4	-0.003305	0.0122	-0.2708	5348	0.7865	-0.03755	0.03094
fixed	NA	sibling_count5	0.01166	0.01328	0.8774	5301	0.3803	-0.02563	0.04894
fixed	NA	birth_order_nonlinear2	0.01073	0.009057	1.185	6131	0.236	-0.01469	0.03616
fixed	NA	birth_order_nonlinear3	-0.00006619	0.01159	-0.005712	6040	0.9954	-0.03259	0.03246
fixed	NA	birth_order_nonlinear4	0.02572	0.01516	1.696	6043	0.08992	-0.01685	0.06828
fixed	NA	birth_order_nonlinear5	-0.02264	0.02226	-1.017	5904	0.3092	-0.08513	0.03985
ran_pars	mother_pidlink	sd__(Intercept)	0.1271	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.312	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.015	0.06481	-15.66	7318	2.079e-54	-1.197	-0.8331
fixed	NA	poly(age, 3, raw = TRUE)1	0.08158	0.006151	13.26	7217	1.108e-39	0.06432	0.09885
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001933	0.0001776	-10.88	7066	2.289e-27	-0.002431	-0.001434
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001452	0.000001589	9.142	6939	7.947e-20	0.00001006	0.00001898
fixed	NA	male	0.6102	0.007689	79.35	7348	0	0.5886	0.6318
fixed	NA	count_birth_order2/2	0.02546	0.01546	1.647	6092	0.09959	-0.01793	0.06884
fixed	NA	count_birth_order1/3	-0.01326	0.01477	-0.8972	7475	0.3696	-0.05473	0.02821
fixed	NA	count_birth_order2/3	0.01553	0.01651	0.9403	7511	0.3471	-0.03082	0.06187
fixed	NA	count_birth_order3/3	0.009555	0.01841	0.5191	7523	0.6037	-0.04212	0.06123
fixed	NA	count_birth_order1/4	0.01465	0.01672	0.8759	7512	0.3811	-0.03229	0.06159
fixed	NA	count_birth_order2/4	0.007809	0.01778	0.4392	7521	0.6605	-0.0421	0.05772
fixed	NA	count_birth_order3/4	0.0003214	0.01929	0.01666	7520	0.9867	-0.05382	0.05447
fixed	NA	count_birth_order4/4	0.01523	0.02023	0.7526	7514	0.4517	-0.04157	0.07202
fixed	NA	count_birth_order1/5	0.0381	0.01915	1.99	7523	0.04663	-0.01564	0.09184
fixed	NA	count_birth_order2/5	0.004619	0.02023	0.2284	7515	0.8194	-0.05215	0.06139
fixed	NA	count_birth_order3/5	0.003229	0.02065	0.1564	7509	0.8757	-0.05473	0.06119
fixed	NA	count_birth_order4/5	0.05861	0.02212	2.65	7483	0.008066	-0.003473	0.1207
fixed	NA	count_birth_order5/5	-0.005772	0.02254	-0.2561	7478	0.7979	-0.06904	0.05749
ran_pars	mother_pidlink	sd__(Intercept)	0.1268	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3121	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	4935	5005	-2458	4915	NA	NA	NA
11	4937	5013	-2458	4915	0.2072	1	0.649
14	4937	5034	-2455	4909	5.918	3	0.1157
20	4940	5078	-2450	4900	9.404	6	0.1521

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.65	0.1851	-8.914	4718	6.901e-19	-2.169	-1.13
fixed	NA	poly(age, 3, raw = TRUE)1	0.1578	0.02162	7.3	4724	3.364e-13	0.09712	0.2185
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00466	0.0007975	-5.843	4728	0.000000005481	-0.006898	-0.002421
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004461	0.000009355	4.768	4731	0.000001917	0.00001835	0.00007087
fixed	NA	male	0.5543	0.009918	55.88	4617	0	0.5264	0.5821
fixed	NA	sibling_count3	0.008032	0.01375	0.584	3405	0.5593	-0.03058	0.04664
fixed	NA	sibling_count4	0.005352	0.01489	0.3596	2997	0.7192	-0.03643	0.04714
fixed	NA	sibling_count5	0.03346	0.01715	1.95	2679	0.05122	-0.01469	0.08161
ran_pars	mother_pidlink	sd__(Intercept)	0.1376	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3162	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.654	0.1853	-8.927	4718	6.177e-19	-2.175	-1.134
fixed	NA	birth_order	0.002531	0.005204	0.4864	4335	0.6267	-0.01208	0.01714
fixed	NA	poly(age, 3, raw = TRUE)1	0.158	0.02162	7.306	4723	3.205e-13	0.09729	0.2187
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004669	0.0007978	-5.852	4727	0.000000005187	-0.006908	-0.002429
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004476	0.000009362	4.782	4730	0.000001793	0.00001848	0.00007104
fixed	NA	male	0.5542	0.009921	55.86	4616	0	0.5264	0.582
fixed	NA	sibling_count3	0.006841	0.01397	0.4896	3471	0.6244	-0.03238	0.04606
fixed	NA	sibling_count4	0.002657	0.01588	0.1673	3228	0.8672	-0.04193	0.04724
fixed	NA	sibling_count5	0.02899	0.01946	1.49	3208	0.1363	-0.02562	0.08361
ran_pars	mother_pidlink	sd__(Intercept)	0.1376	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3162	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.672	0.1856	-9.009	4721	2.95e-19	-2.194	-1.151
fixed	NA	poly(age, 3, raw = TRUE)1	0.1598	0.02166	7.38	4724	1.855e-13	0.09905	0.2206
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004735	0.000799	-5.926	4727	0.000000003326	-0.006978	-0.002492
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004548	0.000009374	4.851	4728	0.000001265	0.00001916	0.00007179
fixed	NA	male	0.5544	0.009924	55.87	4614	0	0.5266	0.5823
fixed	NA	sibling_count3	0.004789	0.01418	0.3379	3597	0.7355	-0.035	0.04458
fixed	NA	sibling_count4	0.00303	0.0161	0.1882	3335	0.8507	-0.04216	0.04822
fixed	NA	sibling_count5	0.03381	0.01977	1.71	3313	0.08734	-0.02168	0.0893
fixed	NA	birth_order_nonlinear2	0.01646	0.0117	1.407	3702	0.1596	-0.01639	0.0493
fixed	NA	birth_order_nonlinear3	0.0149	0.01496	0.996	3950	0.3193	-0.02709	0.05689
fixed	NA	birth_order_nonlinear4	0.0003706	0.02023	0.01832	4147	0.9854	-0.05641	0.05715
fixed	NA	birth_order_nonlinear5	-0.003738	0.03166	-0.1181	3948	0.906	-0.09262	0.08514
ran_pars	mother_pidlink	sd__(Intercept)	0.137	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3165	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.675	0.1857	-9.016	4715	2.781e-19	-2.196	-1.153
fixed	NA	poly(age, 3, raw = TRUE)1	0.1594	0.02167	7.357	4717	2.206e-13	0.09859	0.2202
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004725	0.0007995	-5.91	4720	0.00000000367	-0.006969	-0.002481
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004542	0.000009382	4.842	4722	0.000001329	0.00001909	0.00007176
fixed	NA	male	0.5543	0.009931	55.82	4608	0	0.5265	0.5822
fixed	NA	count_birth_order2/2	0.0373	0.02004	1.861	3898	0.06277	-0.01895	0.09354
fixed	NA	count_birth_order1/3	0.02359	0.01802	1.309	4703	0.1906	-0.02699	0.07416
fixed	NA	count_birth_order2/3	0.01814	0.01957	0.9267	4721	0.3541	-0.0368	0.07308
fixed	NA	count_birth_order3/3	0.01768	0.02184	0.8094	4717	0.4183	-0.04363	0.07898
fixed	NA	count_birth_order1/4	0.005862	0.022	0.2664	4717	0.79	-0.05591	0.06763
fixed	NA	count_birth_order2/4	0.02353	0.02269	1.037	4721	0.2999	-0.04018	0.08723
fixed	NA	count_birth_order3/4	0.03487	0.024	1.453	4701	0.1463	-0.0325	0.1022
fixed	NA	count_birth_order4/4	0.009375	0.02492	0.3762	4697	0.7068	-0.06058	0.07933
fixed	NA	count_birth_order1/5	0.03575	0.02996	1.193	4716	0.2328	-0.04835	0.1199
fixed	NA	count_birth_order2/5	0.05873	0.0321	1.829	4671	0.06739	-0.03138	0.1488
fixed	NA	count_birth_order3/5	0.05768	0.02984	1.933	4677	0.05331	-0.02609	0.1415
fixed	NA	count_birth_order4/5	0.04303	0.02924	1.472	4685	0.1412	-0.03905	0.1251
fixed	NA	count_birth_order5/5	0.03718	0.03031	1.227	4663	0.2199	-0.04789	0.1223
ran_pars	mother_pidlink	sd__(Intercept)	0.1368	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3167	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	3323	3388	-1652	3303	NA	NA	NA
11	3325	3396	-1651	3303	0.2371	1	0.6263
14	3328	3419	-1650	3300	2.435	3	0.4871
20	3337	3467	-1649	3297	3.029	6	0.8052

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.604	0.191	-8.399	4378	6.019e-17	-2.14	-1.068
fixed	NA	poly(age, 3, raw = TRUE)1	0.1527	0.02233	6.836	4383	9.256e-12	0.08997	0.2153
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004458	0.0008243	-5.408	4388	0.00000006696	-0.006772	-0.002144
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004212	0.000009672	4.355	4391	0.0000136	0.00001497	0.00006927
fixed	NA	male	0.5479	0.01032	53.08	4279	0	0.5189	0.5769
fixed	NA	sibling_count3	0.009907	0.01493	0.6634	3256	0.5071	-0.03201	0.05183
fixed	NA	sibling_count4	-0.00009172	0.0158	-0.005807	2955	0.9954	-0.04443	0.04425
fixed	NA	sibling_count5	0.02209	0.01703	1.297	2677	0.1948	-0.02572	0.0699
ran_pars	mother_pidlink	sd__(Intercept)	0.1393	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3162	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.605	0.1912	-8.391	4377	6.441e-17	-2.141	-1.068
fixed	NA	birth_order	0.0002651	0.00522	0.05079	4112	0.9595	-0.01439	0.01492
fixed	NA	poly(age, 3, raw = TRUE)1	0.1527	0.02234	6.835	4382	9.302e-12	0.08997	0.2154
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004459	0.0008245	-5.408	4387	0.00000006719	-0.006773	-0.002144
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004214	0.000009677	4.354	4390	0.00001365	0.00001497	0.0000693
fixed	NA	male	0.5479	0.01032	53.07	4278	0	0.5189	0.5769
fixed	NA	sibling_count3	0.009783	0.01513	0.6465	3300	0.518	-0.0327	0.05226
fixed	NA	sibling_count4	-0.0003638	0.01668	-0.02181	3121	0.9826	-0.04718	0.04646
fixed	NA	sibling_count5	0.02166	0.01905	1.137	3065	0.2556	-0.0318	0.07512
ran_pars	mother_pidlink	sd__(Intercept)	0.1393	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3163	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.62	0.1915	-8.459	4381	3.624e-17	-2.158	-1.083
fixed	NA	poly(age, 3, raw = TRUE)1	0.1539	0.02237	6.88	4384	6.839e-12	0.09111	0.2167
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004503	0.0008257	-5.453	4386	0.00000005217	-0.006821	-0.002185
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004262	0.000009689	4.398	4388	0.00001118	0.00001542	0.00006981
fixed	NA	male	0.5482	0.01033	53.09	4275	0	0.5192	0.5772
fixed	NA	sibling_count3	0.009929	0.01535	0.6471	3407	0.5176	-0.03314	0.053
fixed	NA	sibling_count4	0.001297	0.0169	0.07672	3216	0.9389	-0.04614	0.04874
fixed	NA	sibling_count5	0.02456	0.01924	1.277	3118	0.2018	-0.02944	0.07857
fixed	NA	birth_order_nonlinear2	0.01625	0.01221	1.331	3483	0.1834	-0.01803	0.05053
fixed	NA	birth_order_nonlinear3	0.0009867	0.01547	0.06379	3729	0.9491	-0.04243	0.0444
fixed	NA	birth_order_nonlinear4	-0.00312	0.02062	-0.1513	3894	0.8797	-0.06101	0.05477
fixed	NA	birth_order_nonlinear5	0.002301	0.03024	0.07609	3774	0.9394	-0.08258	0.08718
ran_pars	mother_pidlink	sd__(Intercept)	0.1391	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3164	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.627	0.1917	-8.489	4375	2.819e-17	-2.166	-1.089
fixed	NA	poly(age, 3, raw = TRUE)1	0.1537	0.02238	6.865	4377	7.565e-12	0.09083	0.2165
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004488	0.0008263	-5.432	4380	0.00000005868	-0.006808	-0.002169
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004236	0.000009697	4.369	4382	0.00001279	0.00001514	0.00006958
fixed	NA	male	0.5476	0.01033	52.99	4269	0	0.5186	0.5766
fixed	NA	count_birth_order2/2	0.04198	0.02202	1.907	3681	0.05666	-0.01983	0.1038
fixed	NA	count_birth_order1/3	0.01979	0.01956	1.012	4365	0.3116	-0.03511	0.0747
fixed	NA	count_birth_order2/3	0.02229	0.02121	1.051	4381	0.2932	-0.03724	0.08183
fixed	NA	count_birth_order3/3	0.0354	0.02368	1.495	4377	0.1351	-0.03108	0.1019
fixed	NA	count_birth_order1/4	0.01327	0.02306	0.5757	4378	0.5649	-0.05145	0.078
fixed	NA	count_birth_order2/4	0.03501	0.02348	1.491	4382	0.136	-0.0309	0.1009
fixed	NA	count_birth_order3/4	0.0003181	0.02568	0.01238	4359	0.9901	-0.07178	0.07241
fixed	NA	count_birth_order4/4	0.001083	0.02654	0.04082	4357	0.9674	-0.07341	0.07558
fixed	NA	count_birth_order1/5	0.05315	0.02751	1.932	4382	0.05344	-0.02408	0.1304
fixed	NA	count_birth_order2/5	0.03151	0.02943	1.071	4355	0.2843	-0.05109	0.1141
fixed	NA	count_birth_order3/5	0.02205	0.02873	0.7676	4349	0.4427	-0.05858	0.1027
fixed	NA	count_birth_order4/5	0.03722	0.02994	1.243	4325	0.214	-0.04684	0.1213
fixed	NA	count_birth_order5/5	0.03533	0.02979	1.186	4326	0.2358	-0.0483	0.119
ran_pars	mother_pidlink	sd__(Intercept)	0.139	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3165	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	3104	3168	-1542	3084	NA	NA	NA
11	3106	3176	-1542	3084	0.002569	1	0.9596
14	3110	3199	-1541	3082	2.191	3	0.5338
20	3117	3245	-1538	3077	4.856	6	0.5625

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.707	0.1866	-9.144	4703	8.738e-20	-2.231	-1.183
fixed	NA	poly(age, 3, raw = TRUE)1	0.1645	0.02183	7.536	4709	5.78e-14	0.1032	0.2258
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004886	0.0008064	-6.059	4714	0.000000001476	-0.00715	-0.002622
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004705	0.000009477	4.965	4716	0.0000007105	0.00002045	0.00007365
fixed	NA	male	0.5556	0.009933	55.94	4606	0	0.5278	0.5835
fixed	NA	sibling_count3	0.003996	0.01357	0.2945	3399	0.7684	-0.03409	0.04209
fixed	NA	sibling_count4	-0.0005728	0.01478	-0.03875	2998	0.9691	-0.04207	0.04092
fixed	NA	sibling_count5	0.01582	0.01756	0.9008	2595	0.3678	-0.03347	0.0651
ran_pars	mother_pidlink	sd__(Intercept)	0.1371	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3162	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.714	0.1869	-9.17	4703	6.911e-20	-2.238	-1.189
fixed	NA	birth_order	0.003948	0.005265	0.7498	4293	0.4534	-0.01083	0.01873
fixed	NA	poly(age, 3, raw = TRUE)1	0.1647	0.02183	7.546	4708	5.344e-14	0.1035	0.226
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004899	0.0008066	-6.074	4713	0.000000001349	-0.007163	-0.002635
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004728	0.000009482	4.987	4715	0.0000006362	0.00002067	0.0000739
fixed	NA	male	0.5556	0.009934	55.93	4605	0	0.5277	0.5834
fixed	NA	sibling_count3	0.002145	0.01379	0.1556	3458	0.8764	-0.03657	0.04086
fixed	NA	sibling_count4	-0.004748	0.0158	-0.3006	3240	0.7638	-0.04909	0.03959
fixed	NA	sibling_count5	0.009144	0.01968	0.4646	3076	0.6422	-0.0461	0.06439
ran_pars	mother_pidlink	sd__(Intercept)	0.137	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3162	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.729	0.1872	-9.238	4706	3.707e-20	-2.254	-1.204
fixed	NA	poly(age, 3, raw = TRUE)1	0.1663	0.02186	7.607	4709	3.359e-14	0.105	0.2277
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004954	0.0008077	-6.134	4712	0.0000000009295	-0.007222	-0.002687
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004786	0.000009493	5.042	4713	0.0000004782	0.00002122	0.00007451
fixed	NA	male	0.5558	0.009936	55.94	4601	0	0.5279	0.5837
fixed	NA	sibling_count3	0.001336	0.014	0.09543	3588	0.924	-0.03797	0.04065
fixed	NA	sibling_count4	-0.002221	0.01602	-0.1386	3350	0.8897	-0.04719	0.04275
fixed	NA	sibling_count5	0.01349	0.02007	0.6723	3197	0.5015	-0.04284	0.06982
fixed	NA	birth_order_nonlinear2	0.01982	0.01163	1.705	3691	0.08829	-0.01281	0.05246
fixed	NA	birth_order_nonlinear3	0.01355	0.0149	0.9094	3917	0.3632	-0.02828	0.05539
fixed	NA	birth_order_nonlinear4	-0.0005506	0.02064	-0.02667	4109	0.9787	-0.05849	0.05739
fixed	NA	birth_order_nonlinear5	0.01623	0.03375	0.4809	3974	0.6306	-0.07851	0.111
ran_pars	mother_pidlink	sd__(Intercept)	0.1367	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3163	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-1.729	0.1873	-9.234	4700	3.86e-20	-2.255	-1.204
fixed	NA	poly(age, 3, raw = TRUE)1	0.1656	0.02188	7.572	4703	4.412e-14	0.1042	0.2271
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00493	0.0008083	-6.099	4705	0.000000001149	-0.007199	-0.002661
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004759	0.0000095	5.01	4707	0.0000005656	0.00002092	0.00007426
fixed	NA	male	0.5556	0.009943	55.89	4595	0	0.5277	0.5836
fixed	NA	count_birth_order2/2	0.03848	0.01947	1.977	3849	0.04815	-0.01616	0.09312
fixed	NA	count_birth_order1/3	0.01826	0.01779	1.026	4687	0.3048	-0.03167	0.06819
fixed	NA	count_birth_order2/3	0.01654	0.01956	0.8459	4707	0.3977	-0.03836	0.07145
fixed	NA	count_birth_order3/3	0.01559	0.02146	0.7263	4700	0.4677	-0.04465	0.07582
fixed	NA	count_birth_order1/4	-0.006886	0.02208	-0.3119	4705	0.7551	-0.06887	0.05509
fixed	NA	count_birth_order2/4	0.0283	0.02271	1.246	4704	0.2128	-0.03545	0.09204
fixed	NA	count_birth_order3/4	0.02324	0.02377	0.9776	4683	0.3283	-0.04349	0.08996
fixed	NA	count_birth_order4/4	0.007944	0.02508	0.3167	4673	0.7515	-0.06247	0.07836
fixed	NA	count_birth_order1/5	0.03237	0.02995	1.081	4705	0.2799	-0.05171	0.1164
fixed	NA	count_birth_order2/5	0.02752	0.03313	0.8307	4652	0.4062	-0.06547	0.1205
fixed	NA	count_birth_order3/5	0.03652	0.03116	1.172	4657	0.2413	-0.05096	0.124
fixed	NA	count_birth_order4/5	0.01262	0.03054	0.4133	4665	0.6794	-0.07311	0.09836
fixed	NA	count_birth_order5/5	0.03596	0.03227	1.114	4641	0.2653	-0.05464	0.1266
ran_pars	mother_pidlink	sd__(Intercept)	0.1365	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3165	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	3306	3371	-1643	3286	NA	NA	NA
11	3308	3379	-1643	3286	0.5636	1	0.4528
14	3311	3401	-1641	3283	2.883	3	0.41
20	3319	3449	-1640	3279	3.289	6	0.7718

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

still_smoking

birthorder <- birthorder %>% mutate(outcome = still_smoking)
model = lmer(outcome ~ birth_order + poly(age, 3, raw = TRUE) + male + sibling_count + (1 | mother_pidlink),
                   data = birthorder)
compare_birthorder_specs(model)

Naive birth order

outcome_naive_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_naive_factor,
                            birth_order_nonlinear = birthorder_naive_factor,
                            birth_order = birthorder_naive,
                            count_birth_order = count_birthorder_naive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_naive_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3968	0.1066	3.722	2209	0.0002026	0.09753	0.696
fixed	NA	poly(age, 3, raw = TRUE)1	0.023	0.008962	2.567	2051	0.01033	-0.002151	0.04816
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006366	0.0002435	-2.614	1898	0.009019	-0.00132	0.00004701
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005083	0.000002062	2.465	1720	0.0138	-0.0000007052	0.00001087
fixed	NA	male	0.2759	0.03476	7.936	2330	3.219e-15	0.1783	0.3734
fixed	NA	sibling_count3	0.01577	0.01672	0.9432	1903	0.3457	-0.03116	0.0627
fixed	NA	sibling_count4	0.003126	0.01683	0.1857	1777	0.8527	-0.04413	0.05038
fixed	NA	sibling_count5	0.009951	0.01747	0.5695	1659	0.5691	-0.03909	0.059
ran_pars	mother_pidlink	sd__(Intercept)	0.07966	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2708	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3953	0.1066	3.708	2208	0.0002144	0.09602	0.6946
fixed	NA	birth_order	0.004797	0.005766	0.832	2140	0.4055	-0.01139	0.02098
fixed	NA	poly(age, 3, raw = TRUE)1	0.0225	0.008983	2.505	2052	0.01234	-0.002717	0.04771
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006234	0.0002441	-2.554	1897	0.01072	-0.001309	0.00006168
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004993	0.000002065	2.418	1719	0.01573	-0.0000008042	0.00001079
fixed	NA	male	0.2756	0.03477	7.926	2329	3.464e-15	0.178	0.3732
fixed	NA	sibling_count3	0.0138	0.01689	0.8172	1940	0.4139	-0.0336	0.0612
fixed	NA	sibling_count4	-0.0007215	0.01746	-0.04133	1913	0.967	-0.04973	0.04829
fixed	NA	sibling_count5	0.003878	0.01894	0.2048	1943	0.8378	-0.04928	0.05704
ran_pars	mother_pidlink	sd__(Intercept)	0.07975	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2708	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.4011	0.1066	3.761	2209	0.0001734	0.1018	0.7003
fixed	NA	poly(age, 3, raw = TRUE)1	0.02251	0.008979	2.508	2051	0.01223	-0.002689	0.04772
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006194	0.0002439	-2.539	1895	0.01119	-0.001304	0.0000653
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004923	0.000002064	2.386	1716	0.01716	-0.0000008698	0.00001072
fixed	NA	male	0.2756	0.03474	7.935	2326	3.248e-15	0.1781	0.3732
fixed	NA	sibling_count3	0.02249	0.01724	1.304	2010	0.1924	-0.02592	0.07089
fixed	NA	sibling_count4	0.003533	0.01779	0.1986	1966	0.8426	-0.04641	0.05348
fixed	NA	sibling_count5	0.0008832	0.01921	0.04598	1989	0.9633	-0.05304	0.05481
fixed	NA	birth_order_nonlinear2	-0.002417	0.01404	-0.1722	2117	0.8633	-0.04181	0.03698
fixed	NA	birth_order_nonlinear3	-0.02579	0.01777	-1.451	2110	0.1468	-0.07566	0.02409
fixed	NA	birth_order_nonlinear4	0.02512	0.0223	1.127	2119	0.26	-0.03747	0.08772
fixed	NA	birth_order_nonlinear5	0.05765	0.03472	1.661	2122	0.09695	-0.03981	0.1551
ran_pars	mother_pidlink	sd__(Intercept)	0.07991	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2705	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	0.3958	0.1069	3.704	2206	0.0002177	0.09582	0.6958
fixed	NA	poly(age, 3, raw = TRUE)1	0.02236	0.008988	2.488	2046	0.01293	-0.00287	0.04759
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006152	0.0002441	-2.521	1889	0.01179	-0.0013	0.00006988
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004896	0.000002064	2.372	1708	0.01781	-0.0000008984	0.00001069
fixed	NA	male	0.275	0.03475	7.914	2320	3.828e-15	0.1775	0.3726
fixed	NA	count_birth_order2/2	0.01497	0.02387	0.6268	2085	0.5308	-0.05205	0.08198
fixed	NA	count_birth_order1/3	0.02417	0.02377	1.017	2321	0.3093	-0.04256	0.0909
fixed	NA	count_birth_order2/3	0.03211	0.02528	1.27	2321	0.2042	-0.03887	0.1031
fixed	NA	count_birth_order3/3	0.006457	0.02736	0.236	2321	0.8134	-0.07033	0.08325
fixed	NA	count_birth_order1/4	0.001714	0.0253	0.06774	2321	0.946	-0.06931	0.07274
fixed	NA	count_birth_order2/4	0.007243	0.02719	0.2664	2319	0.79	-0.06908	0.08357
fixed	NA	count_birth_order3/4	-0.001215	0.02931	-0.04144	2320	0.9669	-0.0835	0.08107
fixed	NA	count_birth_order4/4	0.03801	0.0301	1.263	2321	0.2068	-0.04649	0.1225
fixed	NA	count_birth_order1/5	0.04659	0.02818	1.653	2319	0.09839	-0.03251	0.1257
fixed	NA	count_birth_order2/5	-0.02261	0.03104	-0.7285	2314	0.4664	-0.1097	0.06452
fixed	NA	count_birth_order3/5	-0.03955	0.03235	-1.223	2317	0.2215	-0.1303	0.05124
fixed	NA	count_birth_order4/5	0.03088	0.0317	0.9744	2316	0.33	-0.05809	0.1199
fixed	NA	count_birth_order5/5	0.06597	0.03501	1.884	2313	0.05968	-0.03232	0.1643
ran_pars	mother_pidlink	sd__(Intercept)	0.07912	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2708	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	729.8	787.4	-354.9	709.8	NA	NA	NA
11	731.1	794.5	-354.6	709.1	0.6939	1	0.4049
14	730.1	810.7	-351	702.1	7.08	3	0.06939
20	736.3	851.4	-348.1	696.3	5.769	6	0.4495

Maternal birth order

outcome_uterus_m1 <- update(m2_birthorder_linear, data = birthorder %>%
                     mutate(sibling_count = sibling_count_uterus_alive_factor,
                            birth_order_nonlinear = birthorder_uterus_alive_factor,
                            birth_order = birthorder_uterus_alive,
                            count_birth_order = count_birthorder_uterus_alive) %>% 
                     filter(sibling_count != "1"))
compare_models_markdown(outcome_uterus_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3133	0.3052	-1.026	1324	0.3049	-1.17	0.5436
fixed	NA	poly(age, 3, raw = TRUE)1	0.09584	0.03384	2.832	1322	0.004694	0.00085	0.1908
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003267	0.001213	-2.694	1320	0.007153	-0.006672	0.0001373
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003403	0.0000139	2.447	1319	0.01453	-0.000005003	0.00007306
fixed	NA	male	0.3579	0.05252	6.816	1328	0.00000000001417	0.2105	0.5054
fixed	NA	sibling_count3	0.01207	0.02094	0.5765	1141	0.5644	-0.04671	0.07085
fixed	NA	sibling_count4	0.03844	0.02207	1.741	1083	0.08189	-0.02352	0.1004
fixed	NA	sibling_count5	0.03008	0.02412	1.247	979.3	0.2127	-0.03763	0.09779
ran_pars	mother_pidlink	sd__(Intercept)	0.04403	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2749	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3059	0.3056	-1.001	1323	0.317	-1.164	0.5519
fixed	NA	birth_order	-0.005042	0.007896	-0.6385	1316	0.5232	-0.02721	0.01712
fixed	NA	poly(age, 3, raw = TRUE)1	0.09569	0.03385	2.827	1321	0.00477	0.0006745	0.1907
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003258	0.001213	-2.685	1319	0.00735	-0.006663	0.0001484
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003383	0.00001391	2.431	1318	0.01517	-0.000005225	0.00007288
fixed	NA	male	0.3584	0.05253	6.822	1327	0.00000000001363	0.2109	0.5058
fixed	NA	sibling_count3	0.01421	0.02122	0.6698	1152	0.5031	-0.04535	0.07377
fixed	NA	sibling_count4	0.04369	0.02356	1.854	1112	0.06397	-0.02245	0.1098
fixed	NA	sibling_count5	0.03869	0.0276	1.402	1093	0.1612	-0.03878	0.1162
ran_pars	mother_pidlink	sd__(Intercept)	0.04661	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2745	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3127	0.3056	-1.023	1320	0.3065	-1.171	0.5452
fixed	NA	poly(age, 3, raw = TRUE)1	0.09628	0.03389	2.841	1318	0.004565	0.001156	0.1914
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00328	0.001215	-2.7	1316	0.007021	-0.00669	0.0001299
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003412	0.00001393	2.449	1315	0.01444	-0.000004983	0.00007322
fixed	NA	male	0.3588	0.05258	6.823	1325	0.00000000001352	0.2112	0.5064
fixed	NA	sibling_count3	0.01497	0.02161	0.6924	1180	0.4888	-0.0457	0.07563
fixed	NA	sibling_count4	0.04146	0.02399	1.728	1130	0.08427	-0.02589	0.1088
fixed	NA	sibling_count5	0.03627	0.02815	1.289	1101	0.1978	-0.04274	0.1153
fixed	NA	birth_order_nonlinear2	-0.01501	0.01863	-0.8057	1213	0.4206	-0.0673	0.03728
fixed	NA	birth_order_nonlinear3	-0.01689	0.02281	-0.7401	1232	0.4594	-0.08092	0.04715
fixed	NA	birth_order_nonlinear4	-0.002029	0.03051	-0.06651	1303	0.947	-0.08766	0.0836
fixed	NA	birth_order_nonlinear5	-0.02822	0.04732	-0.5964	1290	0.551	-0.161	0.1046
ran_pars	mother_pidlink	sd__(Intercept)	0.04722	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2747	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3222	0.3068	-1.05	1315	0.2939	-1.183	0.5391
fixed	NA	poly(age, 3, raw = TRUE)1	0.09484	0.03405	2.785	1313	0.005427	-0.0007443	0.1904
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00322	0.001221	-2.637	1311	0.008453	-0.006647	0.0002071
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003333	0.00001401	2.38	1310	0.01748	-0.000005988	0.00007265
fixed	NA	male	0.3613	0.05264	6.863	1318	0.00000000001035	0.2135	0.5091
fixed	NA	count_birth_order2/2	0.03187	0.03258	0.9782	1222	0.3282	-0.05958	0.1233
fixed	NA	count_birth_order1/3	0.02401	0.02858	0.8399	1321	0.4011	-0.05623	0.1042
fixed	NA	count_birth_order2/3	0.01613	0.03187	0.506	1321	0.6129	-0.07334	0.1056
fixed	NA	count_birth_order3/3	0.03606	0.03414	1.056	1320	0.2911	-0.05978	0.1319
fixed	NA	count_birth_order1/4	0.1005	0.03488	2.881	1321	0.004025	0.00259	0.1984
fixed	NA	count_birth_order2/4	0.01663	0.03511	0.4737	1321	0.6358	-0.08193	0.1152
fixed	NA	count_birth_order3/4	0.03511	0.0363	0.9674	1320	0.3335	-0.06678	0.137
fixed	NA	count_birth_order4/4	0.04822	0.03882	1.242	1321	0.2144	-0.06075	0.1572
fixed	NA	count_birth_order1/5	0.07725	0.04435	1.742	1321	0.0818	-0.04725	0.2017
fixed	NA	count_birth_order2/5	0.02911	0.04781	0.6088	1321	0.5428	-0.1051	0.1633
fixed	NA	count_birth_order3/5	0.01078	0.04388	0.2456	1320	0.806	-0.1124	0.1339
fixed	NA	count_birth_order4/5	0.06346	0.04195	1.513	1320	0.1306	-0.0543	0.1812
fixed	NA	count_birth_order5/5	0.02605	0.04547	0.573	1320	0.5668	-0.1016	0.1537
ran_pars	mother_pidlink	sd__(Intercept)	0.04716	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2745	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_alive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	387.2	439.2	-183.6	367.2	NA	NA	NA
11	388.8	446	-183.4	366.8	0.4035	1	0.5253
14	394	466.8	-183	366	0.7669	3	0.8574
20	398.9	502.9	-179.4	358.9	7.133	6	0.3087

Maternal pregnancy order

outcome_preg_m1 <- update(m2_birthorder_linear, data = birthorder %>% 
  mutate(sibling_count = sibling_count_uterus_preg_factor,
         birth_order_nonlinear = birthorder_uterus_preg_factor,
         birth_order = birthorder_uterus_preg,
         count_birth_order = count_birthorder_uterus_preg
         ) %>% 
    filter(sibling_count != "1"))
compare_models_markdown(outcome_preg_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3422	0.3223	-1.062	1211	0.2885	-1.247	0.5624
fixed	NA	poly(age, 3, raw = TRUE)1	0.09807	0.03593	2.729	1209	0.006442	-0.002799	0.1989
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003374	0.00129	-2.615	1207	0.009027	-0.006996	0.0002474
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003564	0.00001481	2.406	1207	0.01628	-0.000005942	0.00007722
fixed	NA	male	0.3741	0.05472	6.836	1214	0.00000000001283	0.2205	0.5277
fixed	NA	sibling_count3	0.02237	0.02347	0.9533	1072	0.3407	-0.04351	0.08825
fixed	NA	sibling_count4	0.01799	0.02422	0.7425	1008	0.4579	-0.05001	0.08598
fixed	NA	sibling_count5	0.004768	0.02562	0.1861	974.3	0.8524	-0.06715	0.07668
ran_pars	mother_pidlink	sd__(Intercept)	0.04332	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2816	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3446	0.3227	-1.068	1210	0.2858	-1.251	0.5613
fixed	NA	birth_order	0.001409	0.008034	0.1754	1215	0.8608	-0.02114	0.02396
fixed	NA	poly(age, 3, raw = TRUE)1	0.09816	0.03595	2.73	1208	0.006419	-0.002758	0.1991
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003379	0.001291	-2.617	1206	0.008983	-0.007002	0.0002454
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000357	0.00001482	2.409	1206	0.01617	-0.000005907	0.00007732
fixed	NA	male	0.3738	0.05476	6.825	1213	0.00000000001384	0.22	0.5275
fixed	NA	sibling_count3	0.02175	0.02375	0.9161	1080	0.3598	-0.0449	0.08841
fixed	NA	sibling_count4	0.01668	0.02536	0.6576	1027	0.511	-0.05451	0.08786
fixed	NA	sibling_count5	0.002659	0.02827	0.09404	1035	0.9251	-0.0767	0.08201
ran_pars	mother_pidlink	sd__(Intercept)	0.04231	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2818	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3527	0.3228	-1.092	1208	0.2749	-1.259	0.5536
fixed	NA	poly(age, 3, raw = TRUE)1	0.09996	0.03601	2.776	1206	0.005591	-0.001123	0.201
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003439	0.001293	-2.66	1204	0.007928	-0.007068	0.0001907
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003638	0.00001485	2.45	1204	0.01442	-0.000005298	0.00007805
fixed	NA	male	0.3735	0.0548	6.815	1210	0.00000000001484	0.2196	0.5273
fixed	NA	sibling_count3	0.02105	0.02421	0.8696	1103	0.3847	-0.04691	0.08902
fixed	NA	sibling_count4	0.01203	0.02577	0.4669	1040	0.6406	-0.0603	0.08436
fixed	NA	sibling_count5	-0.001058	0.02876	-0.03679	1034	0.9707	-0.08178	0.07967
fixed	NA	birth_order_nonlinear2	-0.01748	0.01981	-0.8823	1114	0.3778	-0.07308	0.03813
fixed	NA	birth_order_nonlinear3	-0.001777	0.02426	-0.07324	1141	0.9416	-0.06988	0.06633
fixed	NA	birth_order_nonlinear4	0.02172	0.032	0.6787	1201	0.4975	-0.06811	0.1115
fixed	NA	birth_order_nonlinear5	-0.01202	0.04728	-0.2541	1203	0.7994	-0.1447	0.1207
ran_pars	mother_pidlink	sd__(Intercept)	0.03958	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2824	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.3511	0.3243	-1.083	1204	0.2791	-1.261	0.5591
fixed	NA	poly(age, 3, raw = TRUE)1	0.09842	0.03616	2.722	1202	0.006583	-0.003075	0.1999
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003363	0.001298	-2.59	1200	0.009701	-0.007007	0.0002811
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000353	0.00001491	2.368	1200	0.01805	-0.000006546	0.00007714
fixed	NA	male	0.3774	0.055	6.861	1203	0.0000000000109	0.223	0.5318
fixed	NA	count_birth_order2/2	-0.009392	0.03705	-0.2535	1151	0.7999	-0.1134	0.0946
fixed	NA	count_birth_order1/3	0.01043	0.03251	0.3207	1211	0.7485	-0.08084	0.1017
fixed	NA	count_birth_order2/3	0.02732	0.03557	0.7679	1211	0.4427	-0.07254	0.1272
fixed	NA	count_birth_order3/3	0.02145	0.03751	0.5718	1211	0.5676	-0.08385	0.1267
fixed	NA	count_birth_order1/4	0.01322	0.03691	0.3582	1211	0.7203	-0.09038	0.1168
fixed	NA	count_birth_order2/4	-0.007754	0.03737	-0.2075	1211	0.8357	-0.1127	0.09715
fixed	NA	count_birth_order3/4	0.02008	0.04177	0.4807	1211	0.6308	-0.09717	0.1373
fixed	NA	count_birth_order4/4	0.04027	0.04254	0.9467	1211	0.344	-0.07913	0.1597
fixed	NA	count_birth_order1/5	0.04257	0.04153	1.025	1211	0.3055	-0.07401	0.1592
fixed	NA	count_birth_order2/5	-0.06287	0.04753	-1.323	1210	0.1862	-0.1963	0.07055
fixed	NA	count_birth_order3/5	-0.007506	0.04641	-0.1617	1210	0.8715	-0.1378	0.1228
fixed	NA	count_birth_order4/5	0.01863	0.04687	0.3974	1211	0.6911	-0.1129	0.1502
fixed	NA	count_birth_order5/5	-0.01039	0.04757	-0.2184	1210	0.8271	-0.1439	0.1231
ran_pars	mother_pidlink	sd__(Intercept)	0.03879	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2827	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_uterus_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	413.3	464.4	-196.6	393.3	NA	NA	NA
11	415.2	471.5	-196.6	393.2	0.03241	1	0.8571
14	419.4	491	-195.7	391.4	1.779	3	0.6195
20	427.4	529.7	-193.7	387.4	4.005	6	0.676

Parental full sibling order

outcome_parental_m1 <- update(m2_birthorder_linear, data = birthorder %>%
  mutate(sibling_count = sibling_count_genes_factor,
         birth_order_nonlinear = birthorder_genes_factor,
         birth_order = birthorder_genes,
         count_birth_order = count_birthorder_genes
         ) %>% 
      filter(sibling_count != "1"))
compare_models_markdown(outcome_parental_m1)

Basic Model

Model Summary

m1_covariates_only <- update(m2_birthorder_linear, formula = . ~ . - birth_order)
tidy(m1_covariates_only, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1924	0.3072	-0.6264	1320	0.5312	-1.055	0.6699
fixed	NA	poly(age, 3, raw = TRUE)1	0.09213	0.03404	2.706	1319	0.006894	-0.003434	0.1877
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003132	0.00122	-2.567	1317	0.01037	-0.006556	0.0002928
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003253	0.00001398	2.326	1317	0.02017	-0.000006728	0.00007178
fixed	NA	male	0.2769	0.05175	5.351	1286	0.0000001036	0.1316	0.4222
fixed	NA	sibling_count3	0.004604	0.02055	0.224	1120	0.8228	-0.05309	0.06229
fixed	NA	sibling_count4	0.02018	0.02195	0.9191	1080	0.3582	-0.04145	0.08181
fixed	NA	sibling_count5	0.01941	0.02495	0.7782	946.8	0.4366	-0.05061	0.08944
ran_pars	mother_pidlink	sd__(Intercept)	0.04391	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2752	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot(allEffects(m1_covariates_only, confidence.level = 0.995))

Add Birth Order Linear

Model Summary

tidy(m2_birthorder_linear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1862	0.3075	-0.6056	1320	0.5449	-1.049	0.677
fixed	NA	birth_order	-0.004468	0.00797	-0.5606	1309	0.5752	-0.02684	0.0179
fixed	NA	poly(age, 3, raw = TRUE)1	0.09211	0.03405	2.705	1318	0.006921	-0.003479	0.1877
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003127	0.00122	-2.563	1316	0.0105	-0.006553	0.0002984
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000324	0.00001399	2.316	1316	0.02071	-0.000006871	0.00007167
fixed	NA	male	0.2767	0.05178	5.343	1287	0.0000001078	0.1313	0.422
fixed	NA	sibling_count3	0.006499	0.02084	0.3119	1131	0.7552	-0.052	0.06499
fixed	NA	sibling_count4	0.02481	0.02346	1.058	1113	0.2905	-0.04105	0.09067
fixed	NA	sibling_count5	0.02672	0.02811	0.9505	1047	0.3421	-0.05219	0.1056
ran_pars	mother_pidlink	sd__(Intercept)	0.04572	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.275	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder2(m2_birthorder_linear, separate = FALSE)

Add Birth Order Factor

Model Summary

m3_birthorder_nonlinear = update(m1_covariates_only, formula = . ~ . + birth_order_nonlinear)
tidy(m3_birthorder_nonlinear, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.1924	0.3076	-0.6253	1317	0.5319	-1.056	0.6712
fixed	NA	poly(age, 3, raw = TRUE)1	0.0927	0.03411	2.718	1315	0.006659	-0.003046	0.1884
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003149	0.001222	-2.576	1314	0.01009	-0.00658	0.0002819
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003268	0.00001401	2.332	1314	0.01986	-0.00000666	0.00007201
fixed	NA	male	0.2771	0.05184	5.346	1284	0.0000001064	0.1316	0.4226
fixed	NA	sibling_count3	0.005655	0.02126	0.2661	1162	0.7902	-0.05401	0.06532
fixed	NA	sibling_count4	0.02156	0.02392	0.9013	1133	0.3676	-0.04558	0.0887
fixed	NA	sibling_count5	0.02512	0.02883	0.8714	1055	0.3837	-0.0558	0.106
fixed	NA	birth_order_nonlinear2	-0.01438	0.01845	-0.7793	1198	0.436	-0.06617	0.03741
fixed	NA	birth_order_nonlinear3	-0.009366	0.02295	-0.4081	1226	0.6833	-0.07379	0.05506
fixed	NA	birth_order_nonlinear4	-0.002693	0.03149	-0.08552	1295	0.9319	-0.09108	0.0857
fixed	NA	birth_order_nonlinear5	-0.03263	0.04933	-0.6616	1294	0.5084	-0.1711	0.1058
ran_pars	mother_pidlink	sd__(Intercept)	0.04506	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2753	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m3_birthorder_nonlinear, separate = FALSE)

Add Interaction

Model Summary

m4_interaction = update(m3_birthorder_nonlinear, formula = . ~ . - birth_order_nonlinear - sibling_count + count_birth_order)
tidy(m4_interaction, conf.int = T, conf.level = 0.995)

effect	group	term	estimate	std.error	statistic	df	p.value	conf.low	conf.high
fixed	NA	(Intercept)	-0.2037	0.3092	-0.6587	1311	0.5102	-1.072	0.6642
fixed	NA	poly(age, 3, raw = TRUE)1	0.09236	0.03433	2.69	1310	0.007226	-0.004002	0.1887
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003131	0.00123	-2.545	1309	0.01105	-0.006585	0.0003229
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003238	0.00001411	2.295	1308	0.0219	-0.000007227	0.00007198
fixed	NA	male	0.2773	0.05191	5.341	1280	0.0000001092	0.1316	0.423
fixed	NA	count_birth_order2/2	0.01851	0.03189	0.5805	1208	0.5617	-0.07101	0.108
fixed	NA	count_birth_order1/3	0.009038	0.02813	0.3213	1318	0.7481	-0.06994	0.08801
fixed	NA	count_birth_order2/3	0.003769	0.03138	0.1201	1318	0.9044	-0.08431	0.09185
fixed	NA	count_birth_order3/3	0.02768	0.03344	0.8276	1317	0.408	-0.0662	0.1216
fixed	NA	count_birth_order1/4	0.07038	0.0353	1.994	1318	0.04637	-0.0287	0.1695
fixed	NA	count_birth_order2/4	-0.007811	0.0348	-0.2244	1318	0.8225	-0.1055	0.08988
fixed	NA	count_birth_order3/4	0.01806	0.03662	0.4931	1316	0.622	-0.08474	0.1209
fixed	NA	count_birth_order4/4	0.03149	0.03871	0.8135	1317	0.4161	-0.07717	0.1402
fixed	NA	count_birth_order1/5	0.05928	0.04426	1.339	1318	0.1807	-0.06495	0.1835
fixed	NA	count_birth_order2/5	0.03278	0.04989	0.657	1318	0.5113	-0.1073	0.1728
fixed	NA	count_birth_order3/5	-0.005393	0.04783	-0.1127	1317	0.9102	-0.1397	0.1289
fixed	NA	count_birth_order4/5	0.03581	0.04598	0.7788	1317	0.4362	-0.09325	0.1649
fixed	NA	count_birth_order5/5	0.005418	0.04712	0.115	1317	0.9085	-0.1269	0.1377
ran_pars	mother_pidlink	sd__(Intercept)	0.04845	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2748	NA	NA	NA	NA	NA	NA

Coefficient Plot

plot_birthorder(m4_interaction)

Model Comparison

###### Model 1 - Model 2
anova(m1_covariates_only, m2_birthorder_linear, m3_birthorder_nonlinear, m4_interaction)

## refitting model(s) with ML (instead of REML)

Data: birthorder %>% mutate(sibling_count = sibling_count_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
10	389.2	441.2	-184.6	369.2	NA	NA	NA
11	390.9	448.1	-184.5	368.9	0.3117	1	0.5767
14	396.3	469	-184.1	368.3	0.664	3	0.8816
20	402.8	506.8	-181.4	362.8	5.434	6	0.4894

Compare birth order specifications

library(coefplot)
multiplot(outcome_naive_m1, outcome_preg_m1, outcome_uterus_m1, outcome_parental_m1, dodgeHeight = 0.6,
          intercept = FALSE)

Multiplot Linear Birth Order Effect

Models

Intelligence = lmer(g_factor_2015_old ~ birthorder_genes + poly(age, 3, raw = TRUE) + male +
                        sibling_count_genes_factor +
               (1 | mother_pidlink),
                   data = birthorder)

`Educational Attainment` = lmer(years_of_education_z ~ birthorder_genes + poly(age, 3, raw = TRUE) + male +
                                  sibling_count_genes_factor + (1 | mother_pidlink),
                   data = birthorder)

Extraversion = lmer(big5_ext ~ birthorder_genes + poly(age, 3, raw = TRUE) + male +
                                  sibling_count_genes_factor + (1 | mother_pidlink),
                   data = birthorder)

Neuroticism = lmer(big5_neu ~ birthorder_genes + poly(age, 3, raw = TRUE) + male +
                                  sibling_count_genes_factor + (1 | mother_pidlink),
                   data = birthorder)

Conscientiousness = lmer(big5_con ~ birthorder_genes + poly(age, 3, raw = TRUE) + male +
                                  sibling_count_genes_factor + (1 | mother_pidlink),
                   data = birthorder)

Agreeableness = lmer(big5_agree ~ birthorder_genes + poly(age, 3, raw = TRUE) + male +
                                  sibling_count_genes_factor + (1 | mother_pidlink),
                   data = birthorder)

Openness = lmer(big5_open ~ birthorder_genes + poly(age, 3, raw = TRUE) + male +
                                  sibling_count_genes_factor + (1 | mother_pidlink),
                   data = birthorder)

RiskA = lmer(riskA ~ birthorder_genes + poly(age, 3, raw = TRUE) + male +
                                  sibling_count_genes_factor + (1 | mother_pidlink),
                   data = birthorder)

RiskB = lmer(riskB ~ birthorder_genes + poly(age, 3, raw = TRUE) + male +
                                  sibling_count_genes_factor + (1 | mother_pidlink),
                   data = birthorder)

Plot

x = multiplot(Intelligence, `Educational Attainment`, Agreeableness, Conscientiousness,
              Extraversion, Neuroticism, Openness, RiskA, RiskB,
              intercept = FALSE,
              coefficients = c("birthorder_genes"),
              outerCI = 2.807,
              plot = F)
        

x = data.frame(x) %>%
  mutate(Model = ifelse(Model == "`Educational Attainment`", "Educational Attainment", Model),
         Model = ifelse(Model == "RiskA", "Risk Aversion A", Model),
         Model = ifelse(Model == "RiskB", "Risk Aversion B", Model),
         Model = as.factor(Model))


levels(x$Coefficient)

birthorder_genes

x$Coefficient = ifelse(x$Coefficient == "birthorder_genes", "Birth order")

ggplot(x, aes(Model, Value)) +
  scale_colour_brewer(palette = "Set2") +
  geom_hline(yintercept = 0, size = 1.5)  +
  geom_rect(aes(xmin=0, xmax=Inf, ymin=-0.20, ymax=-0.07), fill = "lightgrey") +
  geom_hline(yintercept = -.135, linetype = "dotted", size = 1.5) + 
  scale_x_discrete(limits=c("Risk Aversion B", "Risk Aversion A", "Openness", "Neuroticism",
                            "Extraversion", "Conscientiousness", "Agreeableness",
                            "Educational Attainment", "Intelligence")) +
  geom_pointrange(data = x, mapping = aes(x=Model, y=Value, ymin=HighOuter, ymax=LowOuter, 
                                    color = Coefficient),
                  position = position_dodge(width=0.3), size = 1) +
  coord_flip() +
  labs(y = "Linear effect size", x = "Outcome") +
  apatheme  +
  theme(text = element_text(size=25), axis.text.x = element_text(size = 20),
        axis.text.y = element_text(size = 20), legend.position = "none")