4_analyses

Birth Order Effects

Helper

source("0_helpers.R")

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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, >5
    birthorder_naive_factor = as.character(birthorder_naive),
    birthorder_naive_factor = ifelse(birthorder_naive > 5, ">5",
                                            birthorder_naive_factor),
    birthorder_naive_factor = factor(birthorder_naive_factor, 
                                            levels = c("1","2","3","4","5",">5")),
    sibling_count_naive_factor = as.character(sibling_count_naive),
    sibling_count_naive_factor = ifelse(sibling_count_naive > 5, ">5",
                                               sibling_count_naive_factor),
    sibling_count_naive_factor = factor(sibling_count_naive_factor, 
                                               levels = c("2","3","4","5",">5")),

    birthorder_uterus_alive_factor = as.character(birthorder_uterus_alive),
    birthorder_uterus_alive_factor = ifelse(birthorder_uterus_alive > 5, ">5",
                                            birthorder_uterus_alive_factor),
    birthorder_uterus_alive_factor = factor(birthorder_uterus_alive_factor, 
                                            levels = c("1","2","3","4","5",">5")),
    sibling_count_uterus_alive_factor = as.character(sibling_count_uterus_alive),
    sibling_count_uterus_alive_factor = ifelse(sibling_count_uterus_alive > 5, ">5",
                                               sibling_count_uterus_alive_factor),
    sibling_count_uterus_alive_factor = factor(sibling_count_uterus_alive_factor, 
                                               levels = c("2","3","4","5",">5")),
    birthorder_uterus_preg_factor = as.character(birthorder_uterus_preg),
    birthorder_uterus_preg_factor = ifelse(birthorder_uterus_preg > 5, ">5",
                                           birthorder_uterus_preg_factor),
    birthorder_uterus_preg_factor = factor(birthorder_uterus_preg_factor,
                                           levels = c("1","2","3","4","5",">5")),
    sibling_count_uterus_preg_factor = as.character(sibling_count_uterus_preg),
    sibling_count_uterus_preg_factor = ifelse(sibling_count_uterus_preg > 5, ">5",
                                              sibling_count_uterus_preg_factor),
    sibling_count_uterus_preg_factor = factor(sibling_count_uterus_preg_factor, 
                                              levels = c("2","3","4","5",">5")),
    birthorder_genes_factor = as.character(birthorder_genes),
    birthorder_genes_factor = ifelse(birthorder_genes >5 , ">5", birthorder_genes_factor),
    birthorder_genes_factor = factor(birthorder_genes_factor, 
                                     levels = c("1","2","3","4","5",">5")),
    sibling_count_genes_factor = as.character(sibling_count_genes),
    sibling_count_genes_factor = ifelse(sibling_count_genes >5 , ">5",
                                        sibling_count_genes_factor),
    sibling_count_genes_factor = factor(sibling_count_genes_factor, 
                                        levels = c("2","3","4","5",">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",
                                                        "1/>5", "2/>5", "3/>5", "4/>5",
                                                        "5/>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",
                                                        "1/>5", "2/>5", "3/>5", "4/>5",
                                                        "5/>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",
                                                        "1/>5", "2/>5", "3/>5", "4/>5",
                                                        "5/>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",
                                                        "1/>5", "2/>5", "3/>5", "4/>5",
                                                        "5/>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)	0.1911	0.2	0.9555	12937	0.3394	-0.3702	0.7523
fixed	NA	poly(age, 3, raw = TRUE)1	0.0243	0.02056	1.182	12872	0.2371	-0.0334	0.082
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001017	0.0006584	-1.544	12882	0.1226	-0.002865	0.0008315
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003728	0.000006632	0.5621	12904	0.5741	-0.00001489	0.00002234
fixed	NA	male	0.06205	0.01493	4.156	11916	0.00003257	0.02014	0.104
fixed	NA	sibling_count3	0.03391	0.03437	0.9865	8796	0.3239	-0.06257	0.1304
fixed	NA	sibling_count4	-0.0006889	0.03585	-0.01922	8292	0.9847	-0.1013	0.09993
fixed	NA	sibling_count5	-0.001687	0.03755	-0.04492	7786	0.9642	-0.1071	0.1037
fixed	NA	sibling_count>5	-0.1915	0.02919	-6.56	8383	0.00000000005705	-0.2734	-0.1096
ran_pars	mother_pidlink	sd__(Intercept)	0.5824	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7438	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)	0.1824	0.2002	0.9114	12932	0.3621	-0.3795	0.7444
fixed	NA	birth_order	-0.003077	0.00332	-0.9269	13491	0.354	-0.01239	0.006241
fixed	NA	poly(age, 3, raw = TRUE)1	0.02632	0.02067	1.273	12936	0.203	-0.03171	0.08435
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001092	0.0006635	-1.646	13003	0.09983	-0.002955	0.0007705
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000448	0.000006683	0.6704	13031	0.5026	-0.00001428	0.00002324
fixed	NA	male	0.06218	0.01493	4.164	11914	0.00003142	0.02027	0.1041
fixed	NA	sibling_count3	0.03436	0.03437	0.9997	8799	0.3175	-0.06211	0.1308
fixed	NA	sibling_count4	0.001231	0.0359	0.0343	8343	0.9726	-0.09954	0.102
fixed	NA	sibling_count5	0.001859	0.03773	0.04927	7893	0.9607	-0.1041	0.1078
fixed	NA	sibling_count>5	-0.18	0.0317	-5.679	9540	0.00000001392	-0.269	-0.09105
ran_pars	mother_pidlink	sd__(Intercept)	0.582	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.744	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)	0.1974	0.2017	0.9789	13030	0.3276	-0.3687	0.7636
fixed	NA	poly(age, 3, raw = TRUE)1	0.02456	0.02074	1.184	12998	0.2363	-0.03365	0.08276
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001027	0.0006661	-1.542	13061	0.1232	-0.002896	0.0008429
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003763	0.000006717	0.5601	13102	0.5754	-0.00001509	0.00002262
fixed	NA	male	0.06205	0.01493	4.155	11911	0.00003274	0.02013	0.104
fixed	NA	sibling_count3	0.03503	0.0347	1.01	9051	0.3128	-0.06237	0.1324
fixed	NA	sibling_count4	0.005935	0.03659	0.1622	8837	0.8711	-0.09677	0.1086
fixed	NA	sibling_count5	0.001283	0.03871	0.03314	8517	0.9736	-0.1074	0.1099
fixed	NA	sibling_count>5	-0.1803	0.03284	-5.489	10296	0.00000004129	-0.2724	-0.08808
fixed	NA	birth_order_nonlinear2	-0.01433	0.02147	-0.6675	11566	0.5045	-0.07459	0.04593
fixed	NA	birth_order_nonlinear3	-0.0118	0.02501	-0.4716	10932	0.6372	-0.08201	0.05842
fixed	NA	birth_order_nonlinear4	-0.03464	0.0284	-1.22	10886	0.2226	-0.1144	0.04507
fixed	NA	birth_order_nonlinear5	0.01513	0.03228	0.4688	10781	0.6392	-0.07549	0.1058
fixed	NA	birth_order_nonlinear>5	-0.02847	0.02793	-1.019	12922	0.308	-0.1069	0.04992
ran_pars	mother_pidlink	sd__(Intercept)	0.5822	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.744	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)	0.1955	0.203	0.9634	13102	0.3354	-0.3742	0.7652
fixed	NA	poly(age, 3, raw = TRUE)1	0.02567	0.02079	1.235	13049	0.2169	-0.03268	0.08403
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00106	0.0006683	-1.586	13115	0.1128	-0.002936	0.000816
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004077	0.000006744	0.6046	13160	0.5454	-0.00001485	0.00002301
fixed	NA	male	0.06191	0.01493	4.145	11899	0.00003418	0.01999	0.1038
fixed	NA	count_birth_order2/2	-0.04118	0.04236	-0.9722	12345	0.331	-0.1601	0.07772
fixed	NA	count_birth_order1/3	0.02571	0.04281	0.6006	12456	0.5481	-0.09446	0.1459
fixed	NA	count_birth_order2/3	0.01942	0.04732	0.4103	12963	0.6816	-0.1134	0.1523
fixed	NA	count_birth_order3/3	0.0007667	0.05251	0.0146	13323	0.9883	-0.1466	0.1482
fixed	NA	count_birth_order1/4	-0.01819	0.04862	-0.374	12948	0.7084	-0.1547	0.1183
fixed	NA	count_birth_order2/4	0.01964	0.05083	0.3863	13147	0.6993	-0.1231	0.1623
fixed	NA	count_birth_order3/4	-0.02461	0.05444	-0.4519	13381	0.6513	-0.1774	0.1282
fixed	NA	count_birth_order4/4	-0.059	0.05719	-1.032	13447	0.3022	-0.2195	0.1015
fixed	NA	count_birth_order1/5	-0.09978	0.05416	-1.842	13259	0.06544	-0.2518	0.05225
fixed	NA	count_birth_order2/5	-0.00005492	0.05667	-0.0009691	13379	0.9992	-0.1591	0.159
fixed	NA	count_birth_order3/5	0.003105	0.05811	0.05344	13443	0.9574	-0.16	0.1662
fixed	NA	count_birth_order4/5	-0.01033	0.06116	-0.1689	13479	0.8659	-0.182	0.1614
fixed	NA	count_birth_order5/5	0.0591	0.06229	0.9489	13479	0.3427	-0.1157	0.2339
fixed	NA	count_birth_order1/>5	-0.1474	0.04374	-3.371	13431	0.000752	-0.2702	-0.02466
fixed	NA	count_birth_order2/>5	-0.2332	0.04485	-5.198	13471	0.0000002042	-0.3591	-0.1073
fixed	NA	count_birth_order3/>5	-0.1994	0.04399	-4.531	13469	0.000005911	-0.3228	-0.07586
fixed	NA	count_birth_order4/>5	-0.2272	0.04306	-5.276	13449	0.0000001338	-0.3481	-0.1063
fixed	NA	count_birth_order5/>5	-0.1914	0.04332	-4.419	13465	0.000009987	-0.313	-0.06984
fixed	NA	count_birth_order>5/>5	-0.2187	0.03572	-6.122	11512	0.0000000009539	-0.319	-0.1184
ran_pars	mother_pidlink	sd__(Intercept)	0.5821	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7439	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)
11	35518	35600	-17748	35496	NA	NA	NA
12	35519	35609	-17747	35495	0.8602	1	0.3537
16	35524	35644	-17746	35492	2.576	4	0.631
26	35532	35728	-17740	35480	11.82	10	0.2971

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)	-0.8339	0.3708	-2.249	5418	0.02455	-1.875	0.2069
fixed	NA	poly(age, 3, raw = TRUE)1	0.1467	0.04203	3.489	5384	0.0004886	0.02867	0.2646
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004903	0.001499	-3.271	5361	0.001079	-0.00911	-0.0006951
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004724	0.00001697	2.784	5351	0.005384	-0.0000003866	0.00009487
fixed	NA	male	-0.02065	0.02158	-0.9572	5211	0.3385	-0.08122	0.03991
fixed	NA	sibling_count3	0.0003067	0.03701	0.008289	4039	0.9934	-0.1036	0.1042
fixed	NA	sibling_count4	-0.0771	0.04036	-1.91	3743	0.05616	-0.1904	0.03619
fixed	NA	sibling_count5	-0.1511	0.04636	-3.26	3538	0.001126	-0.2812	-0.02098
fixed	NA	sibling_count>5	-0.2821	0.04094	-6.891	3492	6.533e-12	-0.3971	-0.1672
ran_pars	mother_pidlink	sd__(Intercept)	0.5177	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6977	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)	-0.8412	0.3708	-2.269	5416	0.02332	-1.882	0.1996
fixed	NA	birth_order	0.009041	0.007302	1.238	5681	0.2157	-0.01146	0.02954
fixed	NA	poly(age, 3, raw = TRUE)1	0.146	0.04203	3.473	5385	0.0005188	0.02799	0.264
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004888	0.001499	-3.261	5362	0.001117	-0.009095	-0.0006806
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004746	0.00001697	2.797	5347	0.005177	-0.000000171	0.00009508
fixed	NA	male	-0.02114	0.02158	-0.9795	5210	0.3274	-0.0817	0.03943
fixed	NA	sibling_count3	-0.004319	0.0372	-0.1161	4053	0.9076	-0.1087	0.1001
fixed	NA	sibling_count4	-0.08824	0.04135	-2.134	3778	0.03293	-0.2043	0.02784
fixed	NA	sibling_count5	-0.169	0.04857	-3.48	3665	0.0005071	-0.3054	-0.03269
fixed	NA	sibling_count>5	-0.3178	0.05005	-6.349	4053	0.0000000002406	-0.4583	-0.1773
ran_pars	mother_pidlink	sd__(Intercept)	0.518	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6974	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)	-0.8705	0.3718	-2.341	5449	0.01925	-1.914	0.1731
fixed	NA	poly(age, 3, raw = TRUE)1	0.1492	0.04209	3.546	5405	0.0003944	0.0311	0.2674
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005006	0.001501	-3.336	5376	0.000857	-0.009218	-0.0007932
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004879	0.00001699	2.872	5356	0.004092	0.000001108	0.00009648
fixed	NA	male	-0.02051	0.02158	-0.9504	5204	0.342	-0.08109	0.04007
fixed	NA	sibling_count3	-0.006197	0.0378	-0.164	4209	0.8698	-0.1123	0.0999
fixed	NA	sibling_count4	-0.08533	0.04264	-2.001	4040	0.04544	-0.205	0.03436
fixed	NA	sibling_count5	-0.175	0.05049	-3.466	4004	0.0005347	-0.3167	-0.03325
fixed	NA	sibling_count>5	-0.3206	0.05119	-6.263	4234	0.0000000004144	-0.4643	-0.1769
fixed	NA	birth_order_nonlinear2	0.03959	0.02714	1.459	4385	0.1448	-0.0366	0.1158
fixed	NA	birth_order_nonlinear3	0.02682	0.03361	0.7981	4542	0.4249	-0.06751	0.1212
fixed	NA	birth_order_nonlinear4	0.0122	0.04178	0.292	4691	0.7703	-0.1051	0.1295
fixed	NA	birth_order_nonlinear5	0.09656	0.05185	1.862	4475	0.06265	-0.049	0.2421
fixed	NA	birth_order_nonlinear>5	0.06261	0.05372	1.166	5388	0.2438	-0.08818	0.2134
ran_pars	mother_pidlink	sd__(Intercept)	0.5179	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6975	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)	-0.8752	0.3728	-2.348	5450	0.01892	-1.922	0.1712
fixed	NA	poly(age, 3, raw = TRUE)1	0.1489	0.04219	3.53	5397	0.0004186	0.03051	0.2674
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004981	0.001505	-3.311	5370	0.0009373	-0.009204	-0.0007576
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004837	0.00001704	2.839	5353	0.00454	0.0000005476	0.00009619
fixed	NA	male	-0.02137	0.0216	-0.9894	5190	0.3225	-0.082	0.03926
fixed	NA	count_birth_order2/2	0.05487	0.04968	1.105	4871	0.2694	-0.08458	0.1943
fixed	NA	count_birth_order1/3	-0.006477	0.04639	-0.1396	5611	0.889	-0.1367	0.1237
fixed	NA	count_birth_order2/3	0.04298	0.05006	0.8586	5747	0.3906	-0.09754	0.1835
fixed	NA	count_birth_order3/3	0.02919	0.0557	0.5241	5788	0.6003	-0.1272	0.1856
fixed	NA	count_birth_order1/4	-0.1094	0.05641	-1.939	5741	0.05254	-0.2677	0.04896
fixed	NA	count_birth_order2/4	-0.02503	0.05803	-0.4314	5787	0.6662	-0.1879	0.1379
fixed	NA	count_birth_order3/4	-0.06345	0.06065	-1.046	5776	0.2955	-0.2337	0.1068
fixed	NA	count_birth_order4/4	-0.03422	0.06329	-0.5408	5767	0.5887	-0.2119	0.1434
fixed	NA	count_birth_order1/5	-0.1232	0.07517	-1.639	5781	0.1012	-0.3342	0.08776
fixed	NA	count_birth_order2/5	-0.0938	0.08081	-1.161	5673	0.2458	-0.3206	0.133
fixed	NA	count_birth_order3/5	-0.1584	0.07568	-2.093	5702	0.03641	-0.3708	0.05405
fixed	NA	count_birth_order4/5	-0.1877	0.07323	-2.563	5750	0.0104	-0.3932	0.01787
fixed	NA	count_birth_order5/5	-0.1089	0.07511	-1.45	5726	0.1471	-0.3197	0.1019
fixed	NA	count_birth_order1/>5	-0.2572	0.07465	-3.446	5691	0.0005734	-0.4668	-0.04768
fixed	NA	count_birth_order2/>5	-0.373	0.07449	-5.008	5643	0.0000005675	-0.5821	-0.1639
fixed	NA	count_birth_order3/>5	-0.2644	0.07378	-3.583	5591	0.0003422	-0.4715	-0.05727
fixed	NA	count_birth_order4/>5	-0.3211	0.06919	-4.641	5619	0.000003543	-0.5153	-0.1269
fixed	NA	count_birth_order5/>5	-0.1957	0.06586	-2.972	5637	0.002974	-0.3806	-0.01084
fixed	NA	count_birth_order>5/>5	-0.2531	0.05163	-4.903	5494	0.0000009697	-0.3981	-0.1082
ran_pars	mother_pidlink	sd__(Intercept)	0.5182	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6977	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)
11	14535	14608	-7257	14513	NA	NA	NA
12	14536	14616	-7256	14512	1.533	1	0.2156
16	14540	14647	-7254	14508	3.603	4	0.4623
26	14553	14727	-7251	14501	6.45	10	0.7761

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)	-0.8021	0.3701	-2.168	5459	0.03024	-1.841	0.2367
fixed	NA	poly(age, 3, raw = TRUE)1	0.1431	0.04197	3.41	5421	0.0006539	0.02531	0.2609
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004819	0.001497	-3.219	5397	0.001293	-0.009021	-0.0006169
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004624	0.00001695	2.728	5386	0.006384	-0.000001332	0.00009382
fixed	NA	male	-0.02123	0.02151	-0.9869	5249	0.3237	-0.08162	0.03916
fixed	NA	sibling_count3	0.006856	0.03997	0.1715	4166	0.8638	-0.1053	0.1191
fixed	NA	sibling_count4	-0.0426	0.0426	-1	3920	0.3174	-0.1622	0.07698
fixed	NA	sibling_count5	-0.07804	0.04578	-1.705	3698	0.08831	-0.2065	0.05046
fixed	NA	sibling_count>5	-0.1916	0.04007	-4.783	3860	0.000001794	-0.3041	-0.07917
ran_pars	mother_pidlink	sd__(Intercept)	0.5208	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6974	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)	-0.7996	0.3702	-2.16	5458	0.03081	-1.839	0.2395
fixed	NA	birth_order	-0.002276	0.006431	-0.354	5827	0.7234	-0.02033	0.01578
fixed	NA	poly(age, 3, raw = TRUE)1	0.1432	0.04197	3.412	5421	0.0006499	0.02539	0.261
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00482	0.001497	-3.219	5397	0.001293	-0.009022	-0.0006171
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004615	0.00001695	2.722	5382	0.0065	-0.000001433	0.00009374
fixed	NA	male	-0.02113	0.02152	-0.9817	5249	0.3263	-0.08153	0.03928
fixed	NA	sibling_count3	0.008026	0.04011	0.2001	4170	0.8414	-0.1046	0.1206
fixed	NA	sibling_count4	-0.03991	0.04327	-0.9224	3928	0.3564	-0.1614	0.08155
fixed	NA	sibling_count5	-0.07387	0.04727	-1.563	3750	0.1182	-0.2066	0.05882
fixed	NA	sibling_count>5	-0.183	0.04692	-3.9	4229	0.00009751	-0.3147	-0.0513
ran_pars	mother_pidlink	sd__(Intercept)	0.5206	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6975	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)	-0.8363	0.371	-2.254	5489	0.02424	-1.878	0.2052
fixed	NA	poly(age, 3, raw = TRUE)1	0.1458	0.04202	3.469	5440	0.0005261	0.02782	0.2637
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004913	0.001499	-3.278	5411	0.001053	-0.00912	-0.0007057
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004722	0.00001697	2.782	5393	0.005418	-0.0000004217	0.00009485
fixed	NA	male	-0.02023	0.02152	-0.9401	5244	0.3472	-0.08065	0.04018
fixed	NA	sibling_count3	0.008151	0.04069	0.2003	4306	0.8412	-0.1061	0.1224
fixed	NA	sibling_count4	-0.03462	0.04449	-0.7782	4167	0.4365	-0.1595	0.09026
fixed	NA	sibling_count5	-0.0762	0.04905	-1.554	4063	0.1204	-0.2139	0.06148
fixed	NA	sibling_count>5	-0.1822	0.04805	-3.792	4413	0.0001514	-0.3171	-0.04733
fixed	NA	birth_order_nonlinear2	0.0345	0.02777	1.242	4518	0.2142	-0.04345	0.1125
fixed	NA	birth_order_nonlinear3	-0.005354	0.03358	-0.1595	4642	0.8733	-0.09961	0.0889
fixed	NA	birth_order_nonlinear4	-0.02399	0.0407	-0.5894	4817	0.5556	-0.1382	0.09026
fixed	NA	birth_order_nonlinear5	0.04948	0.0496	0.9975	4667	0.3186	-0.08975	0.1887
fixed	NA	birth_order_nonlinear>5	-0.009693	0.04843	-0.2002	5619	0.8414	-0.1456	0.1262
ran_pars	mother_pidlink	sd__(Intercept)	0.5206	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6975	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)	-0.8476	0.3718	-2.28	5494	0.02267	-1.891	0.1961
fixed	NA	poly(age, 3, raw = TRUE)1	0.1447	0.04207	3.438	5435	0.00059	0.02656	0.2628
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004861	0.001501	-3.238	5408	0.00121	-0.009074	-0.0006473
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004649	0.000017	2.734	5391	0.006271	-0.000001236	0.00009421
fixed	NA	male	-0.02115	0.02153	-0.9822	5231	0.326	-0.08157	0.03928
fixed	NA	count_birth_order2/2	0.09269	0.05458	1.698	5017	0.0895	-0.06051	0.2459
fixed	NA	count_birth_order1/3	0.03991	0.05027	0.7939	5665	0.4273	-0.1012	0.181
fixed	NA	count_birth_order2/3	0.02977	0.05389	0.5524	5789	0.5807	-0.1215	0.181
fixed	NA	count_birth_order3/3	0.04257	0.06031	0.7058	5839	0.4803	-0.1267	0.2119
fixed	NA	count_birth_order1/4	-0.07608	0.05917	-1.286	5785	0.1986	-0.2422	0.09002
fixed	NA	count_birth_order2/4	0.08764	0.06018	1.456	5832	0.1454	-0.0813	0.2566
fixed	NA	count_birth_order3/4	-0.0303	0.065	-0.4661	5822	0.6411	-0.2128	0.1522
fixed	NA	count_birth_order4/4	-0.03003	0.06725	-0.4466	5821	0.6552	-0.2188	0.1587
fixed	NA	count_birth_order1/5	-0.0001437	0.06919	-0.002077	5837	0.9983	-0.1944	0.1941
fixed	NA	count_birth_order2/5	-0.01429	0.07426	-0.1925	5782	0.8474	-0.2227	0.1942
fixed	NA	count_birth_order3/5	-0.1014	0.07188	-1.411	5792	0.1584	-0.3032	0.1004
fixed	NA	count_birth_order4/5	-0.1037	0.07452	-1.391	5759	0.1641	-0.3129	0.1055
fixed	NA	count_birth_order5/5	-0.02898	0.07439	-0.3896	5767	0.6969	-0.2378	0.1798
fixed	NA	count_birth_order1/>5	-0.1089	0.06599	-1.65	5835	0.09905	-0.2941	0.07637
fixed	NA	count_birth_order2/>5	-0.2303	0.06883	-3.346	5750	0.0008244	-0.4235	-0.03712
fixed	NA	count_birth_order3/>5	-0.1537	0.06699	-2.294	5736	0.02182	-0.3417	0.03436
fixed	NA	count_birth_order4/>5	-0.1817	0.06466	-2.81	5752	0.00497	-0.3632	-0.0001943
fixed	NA	count_birth_order5/>5	-0.1002	0.06589	-1.52	5664	0.1284	-0.2851	0.08477
fixed	NA	count_birth_order>5/>5	-0.1736	0.05057	-3.433	5562	0.0006013	-0.3156	-0.03166
ran_pars	mother_pidlink	sd__(Intercept)	0.5209	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6971	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)
11	14682	14755	-7330	14660	NA	NA	NA
12	14684	14764	-7330	14660	0.1261	1	0.7225
16	14687	14794	-7328	14655	4.215	4	0.3777
26	14694	14868	-7321	14642	13.01	10	0.2232

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)	-0.9226	0.3751	-2.46	5314	0.01394	-1.976	0.1303
fixed	NA	poly(age, 3, raw = TRUE)1	0.1559	0.04254	3.665	5280	0.0002495	0.03651	0.2753
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005258	0.001517	-3.465	5254	0.0005345	-0.009517	-0.0009983
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000515	0.00001718	2.997	5240	0.002742	0.000003259	0.00009974
fixed	NA	male	-0.02117	0.0218	-0.9713	5119	0.3314	-0.08236	0.04001
fixed	NA	sibling_count3	0.01472	0.03647	0.4035	4008	0.6866	-0.08767	0.1171
fixed	NA	sibling_count4	-0.06404	0.04	-1.601	3736	0.1095	-0.1763	0.04826
fixed	NA	sibling_count5	-0.1279	0.04754	-2.691	3450	0.007154	-0.2614	0.005507
fixed	NA	sibling_count>5	-0.271	0.04142	-6.541	3409	0.00000000007002	-0.3872	-0.1547
ran_pars	mother_pidlink	sd__(Intercept)	0.5155	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6986	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)	-0.9298	0.3751	-2.479	5313	0.01321	-1.983	0.1231
fixed	NA	birth_order	0.01005	0.007512	1.338	5537	0.181	-0.01104	0.03114
fixed	NA	poly(age, 3, raw = TRUE)1	0.1551	0.04254	3.646	5281	0.000269	0.03569	0.2745
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005241	0.001517	-3.454	5255	0.0005566	-0.009499	-0.0009817
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005174	0.00001718	3.011	5237	0.002619	0.0000035	0.00009997
fixed	NA	male	-0.0215	0.0218	-0.9866	5118	0.3239	-0.08269	0.03968
fixed	NA	sibling_count3	0.009523	0.03668	0.2596	4021	0.7952	-0.09344	0.1125
fixed	NA	sibling_count4	-0.07619	0.04102	-1.857	3784	0.06335	-0.1913	0.03896
fixed	NA	sibling_count5	-0.147	0.04963	-2.962	3564	0.003076	-0.2863	-0.007695
fixed	NA	sibling_count>5	-0.3101	0.0507	-6.116	4032	0.000000001052	-0.4524	-0.1678
ran_pars	mother_pidlink	sd__(Intercept)	0.5157	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6984	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)	-0.9568	0.3761	-2.544	5347	0.01098	-2.013	0.0989
fixed	NA	poly(age, 3, raw = TRUE)1	0.1581	0.0426	3.711	5301	0.0002086	0.0385	0.2776
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005346	0.001519	-3.519	5270	0.0004364	-0.00961	-0.001082
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000529	0.0000172	3.075	5247	0.002118	0.000004605	0.0001012
fixed	NA	male	-0.0212	0.0218	-0.9723	5112	0.3309	-0.0824	0.04
fixed	NA	sibling_count3	0.00883	0.03729	0.2368	4177	0.8129	-0.09586	0.1135
fixed	NA	sibling_count4	-0.07612	0.04236	-1.797	4044	0.07238	-0.195	0.04278
fixed	NA	sibling_count5	-0.1499	0.05142	-2.914	3864	0.003586	-0.2942	-0.005511
fixed	NA	sibling_count>5	-0.3102	0.05189	-5.978	4227	0.000000002442	-0.4559	-0.1646
fixed	NA	birth_order_nonlinear2	0.04352	0.02709	1.606	4296	0.1083	-0.03253	0.1196
fixed	NA	birth_order_nonlinear3	0.02617	0.03362	0.7785	4446	0.4363	-0.0682	0.1205
fixed	NA	birth_order_nonlinear4	0.0344	0.04292	0.8015	4559	0.4229	-0.08607	0.1549
fixed	NA	birth_order_nonlinear5	0.07337	0.05415	1.355	4375	0.1755	-0.07862	0.2254
fixed	NA	birth_order_nonlinear>5	0.06926	0.0553	1.252	5207	0.2105	-0.08596	0.2245
ran_pars	mother_pidlink	sd__(Intercept)	0.5155	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6987	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	0.3773	-2.554	5349	0.01067	-2.023	0.09537
fixed	NA	poly(age, 3, raw = TRUE)1	0.1579	0.04271	3.697	5297	0.0002206	0.038	0.2778
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005325	0.001524	-3.495	5268	0.0004781	-0.009602	-0.001048
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000525	0.00001726	3.042	5248	0.002365	0.00000405	0.000101
fixed	NA	male	-0.02235	0.02182	-1.024	5097	0.3058	-0.08361	0.03891
fixed	NA	count_birth_order2/2	0.06086	0.04827	1.261	4697	0.2074	-0.07464	0.1964
fixed	NA	count_birth_order1/3	0.007247	0.04578	0.1583	5515	0.8742	-0.1212	0.1357
fixed	NA	count_birth_order2/3	0.0644	0.04994	1.29	5653	0.1973	-0.07578	0.2046
fixed	NA	count_birth_order3/3	0.04643	0.05471	0.8486	5674	0.3962	-0.1071	0.2
fixed	NA	count_birth_order1/4	-0.09561	0.05654	-1.691	5649	0.09087	-0.2543	0.06309
fixed	NA	count_birth_order2/4	-0.0208	0.05792	-0.3592	5674	0.7195	-0.1834	0.1418
fixed	NA	count_birth_order3/4	-0.04594	0.06005	-0.765	5657	0.4443	-0.2145	0.1226
fixed	NA	count_birth_order4/4	-0.004906	0.06335	-0.07745	5632	0.9383	-0.1827	0.1729
fixed	NA	count_birth_order1/5	-0.1047	0.07511	-1.394	5672	0.1633	-0.3156	0.1061
fixed	NA	count_birth_order2/5	-0.07203	0.08321	-0.8656	5534	0.3867	-0.3056	0.1616
fixed	NA	count_birth_order3/5	-0.1374	0.0791	-1.738	5567	0.08235	-0.3595	0.0846
fixed	NA	count_birth_order4/5	-0.1243	0.0766	-1.623	5620	0.1046	-0.3394	0.09067
fixed	NA	count_birth_order5/5	-0.112	0.08027	-1.395	5586	0.163	-0.3373	0.1133
fixed	NA	count_birth_order1/>5	-0.2309	0.07637	-3.024	5564	0.002509	-0.4453	-0.01654
fixed	NA	count_birth_order2/>5	-0.3469	0.07643	-4.539	5509	0.000005763	-0.5615	-0.1324
fixed	NA	count_birth_order3/>5	-0.2686	0.07462	-3.599	5471	0.0003218	-0.4781	-0.05913
fixed	NA	count_birth_order4/>5	-0.3014	0.07262	-4.15	5417	0.0000337	-0.5052	-0.09755
fixed	NA	count_birth_order5/>5	-0.2063	0.06741	-3.061	5498	0.002217	-0.3956	-0.01712
fixed	NA	count_birth_order>5/>5	-0.2356	0.05257	-4.482	5397	0.000007558	-0.3832	-0.08803
ran_pars	mother_pidlink	sd__(Intercept)	0.5157	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.699	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)
11	14247	14320	-7112	14225	NA	NA	NA
12	14247	14327	-7111	14223	1.792	1	0.1807
16	14253	14359	-7110	14221	2.106	4	0.7163
26	14267	14440	-7108	14215	5.623	10	0.8458

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)	-0.2589	0.1483	-1.745	13929	0.08095	-0.6753	0.1575
fixed	NA	poly(age, 3, raw = TRUE)1	0.05817	0.01424	4.085	13917	0.00004427	0.0182	0.09814
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001978	0.0004199	-4.709	13856	0.000002507	-0.003156	-0.0007989
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001287	0.000003875	3.32	13750	0.0009022	0.000001988	0.00002374
fixed	NA	male	0.1522	0.01535	9.916	13196	4.293e-23	0.1091	0.1953
fixed	NA	sibling_count3	0.03526	0.0328	1.075	9632	0.2824	-0.05682	0.1273
fixed	NA	sibling_count4	-0.001169	0.03399	-0.03439	8938	0.9726	-0.09657	0.09424
fixed	NA	sibling_count5	0.03681	0.03559	1.034	8256	0.301	-0.06309	0.1367
fixed	NA	sibling_count>5	-0.1097	0.02774	-3.955	9049	0.000077	-0.1876	-0.03185
ran_pars	mother_pidlink	sd__(Intercept)	0.4621	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8175	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)	-0.2593	0.1483	-1.748	13928	0.08044	-0.6757	0.1571
fixed	NA	birth_order	-0.006107	0.003326	-1.836	13743	0.06633	-0.01544	0.003228
fixed	NA	poly(age, 3, raw = TRUE)1	0.06006	0.01428	4.207	13911	0.00002601	0.01999	0.1001
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002051	0.0004218	-4.862	13823	0.000001175	-0.003235	-0.0008667
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001355	0.000003893	3.482	13690	0.0004996	0.000002627	0.00002448
fixed	NA	male	0.1523	0.01535	9.924	13197	3.93e-23	0.1092	0.1954
fixed	NA	sibling_count3	0.03641	0.0328	1.11	9645	0.267	-0.05566	0.1285
fixed	NA	sibling_count4	0.00274	0.03404	0.0805	9001	0.9358	-0.09282	0.0983
fixed	NA	sibling_count5	0.04392	0.03578	1.227	8376	0.2198	-0.05653	0.1444
fixed	NA	sibling_count>5	-0.08692	0.03038	-2.861	10247	0.004227	-0.1722	-0.001649
ran_pars	mother_pidlink	sd__(Intercept)	0.4614	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8177	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)	-0.2533	0.1487	-1.703	13924	0.08852	-0.6707	0.1641
fixed	NA	poly(age, 3, raw = TRUE)1	0.05911	0.01428	4.14	13910	0.0000349	0.01903	0.09918
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002023	0.0004217	-4.798	13823	0.000001623	-0.003207	-0.0008395
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001335	0.000003894	3.429	13683	0.0006066	0.000002424	0.00002428
fixed	NA	male	0.1521	0.01535	9.913	13190	4.402e-23	0.109	0.1952
fixed	NA	sibling_count3	0.02663	0.03319	0.8024	9945	0.4223	-0.06653	0.1198
fixed	NA	sibling_count4	-0.00795	0.03484	-0.2282	9597	0.8195	-0.1058	0.08986
fixed	NA	sibling_count5	0.02496	0.03693	0.6759	9146	0.4991	-0.0787	0.1286
fixed	NA	sibling_count>5	-0.1004	0.0317	-3.166	11147	0.00155	-0.1894	-0.01138
fixed	NA	birth_order_nonlinear2	-0.01635	0.02205	-0.7413	12346	0.4585	-0.07825	0.04555
fixed	NA	birth_order_nonlinear3	0.03193	0.02594	1.231	11954	0.2184	-0.04089	0.1048
fixed	NA	birth_order_nonlinear4	-0.01247	0.02955	-0.4222	11946	0.6729	-0.09542	0.07047
fixed	NA	birth_order_nonlinear5	0.02924	0.03368	0.8682	11900	0.3853	-0.0653	0.1238
fixed	NA	birth_order_nonlinear>5	-0.04653	0.02843	-1.636	13682	0.1018	-0.1263	0.03328
ran_pars	mother_pidlink	sd__(Intercept)	0.4618	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8174	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)	-0.23	0.1493	-1.54	13913	0.1235	-0.6492	0.1892
fixed	NA	poly(age, 3, raw = TRUE)1	0.05915	0.01428	4.142	13898	0.00003458	0.01907	0.09923
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002015	0.0004219	-4.777	13806	0.000001799	-0.003199	-0.000831
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000132	0.000003896	3.389	13657	0.0007026	0.000002269	0.00002414
fixed	NA	male	0.1523	0.01535	9.921	13184	4.082e-23	0.1092	0.1954
fixed	NA	count_birth_order2/2	-0.08968	0.04298	-2.087	12674	0.03694	-0.2103	0.03096
fixed	NA	count_birth_order1/3	0.001331	0.04216	0.03157	13409	0.9748	-0.117	0.1197
fixed	NA	count_birth_order2/3	-0.01655	0.04682	-0.3534	13662	0.7238	-0.148	0.1149
fixed	NA	count_birth_order3/3	0.02862	0.05232	0.547	13843	0.5844	-0.1182	0.1755
fixed	NA	count_birth_order1/4	-0.05712	0.04776	-1.196	13656	0.2318	-0.1912	0.07695
fixed	NA	count_birth_order2/4	-0.00643	0.0504	-0.1276	13758	0.8985	-0.1479	0.135
fixed	NA	count_birth_order3/4	-0.003269	0.0545	-0.05998	13880	0.9522	-0.1563	0.1497
fixed	NA	count_birth_order4/4	-0.07443	0.05735	-1.298	13912	0.1943	-0.2354	0.08654
fixed	NA	count_birth_order1/5	-0.06156	0.05424	-1.135	13827	0.2564	-0.2138	0.09069
fixed	NA	count_birth_order2/5	0.001736	0.05671	0.03062	13883	0.9756	-0.1574	0.1609
fixed	NA	count_birth_order3/5	0.04451	0.05839	0.7622	13912	0.4459	-0.1194	0.2084
fixed	NA	count_birth_order4/5	-0.03346	0.06165	-0.5427	13925	0.5874	-0.2065	0.1396
fixed	NA	count_birth_order5/5	0.09651	0.06314	1.529	13921	0.1264	-0.08072	0.2737
fixed	NA	count_birth_order1/>5	-0.1224	0.04362	-2.805	13915	0.005039	-0.2448	0.00009071
fixed	NA	count_birth_order2/>5	-0.1417	0.04493	-3.153	13925	0.001617	-0.2678	-0.01556
fixed	NA	count_birth_order3/>5	-0.1007	0.04394	-2.291	13925	0.02199	-0.224	0.02268
fixed	NA	count_birth_order4/>5	-0.1217	0.04315	-2.82	13922	0.004806	-0.2428	-0.0005698
fixed	NA	count_birth_order5/>5	-0.1216	0.04345	-2.798	13925	0.005143	-0.2436	0.0003755
fixed	NA	count_birth_order>5/>5	-0.174	0.0348	-5	12310	0.0000005819	-0.2717	-0.07631
ran_pars	mother_pidlink	sd__(Intercept)	0.4612	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8177	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)
11	37283	37366	-18631	37261	NA	NA	NA
12	37282	37372	-18629	37258	3.375	1	0.06621
16	37283	37404	-18625	37251	6.817	4	0.1459
26	37293	37489	-18621	37241	9.765	10	0.4614

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)	-0.5241	0.3667	-1.429	5788	0.153	-1.553	0.5053
fixed	NA	poly(age, 3, raw = TRUE)1	0.09035	0.04162	2.171	5785	0.02997	-0.02647	0.2072
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002746	0.001486	-1.849	5785	0.06455	-0.006916	0.001424
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002114	0.00001683	1.256	5789	0.2092	-0.00002611	0.00006838
fixed	NA	male	0.09392	0.02139	4.392	5674	0.00001146	0.03389	0.154
fixed	NA	sibling_count3	0.0296	0.03472	0.8526	4233	0.394	-0.06786	0.1271
fixed	NA	sibling_count4	-0.0397	0.03752	-1.058	3809	0.2901	-0.145	0.06562
fixed	NA	sibling_count5	-0.08843	0.04313	-2.05	3485	0.04042	-0.2095	0.03265
fixed	NA	sibling_count>5	-0.1438	0.03792	-3.792	3348	0.0001518	-0.2503	-0.03737
ran_pars	mother_pidlink	sd__(Intercept)	0.3938	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7424	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)	-0.5258	0.3668	-1.434	5786	0.1517	-1.555	0.5037
fixed	NA	birth_order	0.002299	0.007146	0.3216	5923	0.7477	-0.01776	0.02236
fixed	NA	poly(age, 3, raw = TRUE)1	0.09021	0.04162	2.167	5784	0.03025	-0.02662	0.207
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002745	0.001486	-1.848	5784	0.06472	-0.006915	0.001425
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002121	0.00001683	1.26	5786	0.2077	-0.00002604	0.00006846
fixed	NA	male	0.09381	0.02139	4.386	5673	0.00001177	0.03377	0.1538
fixed	NA	sibling_count3	0.02845	0.03491	0.815	4241	0.4151	-0.06954	0.1264
fixed	NA	sibling_count4	-0.0424	0.03845	-1.103	3831	0.2702	-0.1503	0.06554
fixed	NA	sibling_count5	-0.09284	0.04527	-2.051	3592	0.04035	-0.2199	0.03423
fixed	NA	sibling_count>5	-0.1526	0.04681	-3.261	3900	0.001121	-0.2841	-0.02123
ran_pars	mother_pidlink	sd__(Intercept)	0.394	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7423	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)	-0.5665	0.3675	-1.541	5802	0.1233	-1.598	0.4652
fixed	NA	poly(age, 3, raw = TRUE)1	0.09346	0.04166	2.243	5792	0.02491	-0.02348	0.2104
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00286	0.001487	-1.923	5790	0.05454	-0.007034	0.001315
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002249	0.00001685	1.335	5790	0.182	-0.00002481	0.00006979
fixed	NA	male	0.09389	0.02139	4.389	5669	0.00001161	0.03384	0.1539
fixed	NA	sibling_count3	0.01664	0.03555	0.468	4419	0.6398	-0.08316	0.1164
fixed	NA	sibling_count4	-0.05847	0.03981	-1.469	4138	0.142	-0.1702	0.05329
fixed	NA	sibling_count5	-0.1133	0.04732	-2.394	3993	0.0167	-0.2462	0.01953
fixed	NA	sibling_count>5	-0.1617	0.04806	-3.365	4136	0.0007719	-0.2966	-0.02683
fixed	NA	birth_order_nonlinear2	0.04528	0.02729	1.659	4735	0.09717	-0.03133	0.1219
fixed	NA	birth_order_nonlinear3	0.0584	0.03378	1.729	4941	0.08393	-0.03643	0.1532
fixed	NA	birth_order_nonlinear4	0.03984	0.04188	0.9514	5104	0.3415	-0.07771	0.1574
fixed	NA	birth_order_nonlinear5	0.05613	0.05225	1.074	4916	0.2827	-0.09053	0.2028
fixed	NA	birth_order_nonlinear>5	0.01605	0.05306	0.3025	5783	0.7623	-0.1329	0.165
ran_pars	mother_pidlink	sd__(Intercept)	0.3928	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7428	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)	-0.5931	0.3685	-1.61	5797	0.1076	-1.627	0.4412
fixed	NA	poly(age, 3, raw = TRUE)1	0.09665	0.04176	2.314	5784	0.02068	-0.02057	0.2139
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002961	0.001491	-1.986	5783	0.04709	-0.007146	0.001224
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002349	0.0000169	1.39	5784	0.1646	-0.00002395	0.00007092
fixed	NA	male	0.09428	0.02141	4.403	5659	0.00001087	0.03418	0.1544
fixed	NA	count_birth_order2/2	0.03312	0.04956	0.6683	5102	0.5039	-0.106	0.1722
fixed	NA	count_birth_order1/3	-0.01387	0.04484	-0.3094	5827	0.757	-0.1398	0.112
fixed	NA	count_birth_order2/3	0.08776	0.04873	1.801	5891	0.07174	-0.04902	0.2245
fixed	NA	count_birth_order3/3	0.08144	0.0544	1.497	5909	0.1345	-0.07127	0.2341
fixed	NA	count_birth_order1/4	-0.06891	0.05445	-1.265	5884	0.2057	-0.2217	0.08394
fixed	NA	count_birth_order2/4	-0.02435	0.05634	-0.4322	5909	0.6656	-0.1825	0.1338
fixed	NA	count_birth_order3/4	0.006464	0.05937	0.1089	5899	0.9133	-0.1602	0.1731
fixed	NA	count_birth_order4/4	-0.0157	0.06178	-0.2541	5897	0.7994	-0.1891	0.1577
fixed	NA	count_birth_order1/5	-0.05962	0.07384	-0.8075	5906	0.4194	-0.2669	0.1476
fixed	NA	count_birth_order2/5	-0.04247	0.07901	-0.5376	5853	0.5909	-0.2642	0.1793
fixed	NA	count_birth_order3/5	-0.05223	0.07429	-0.703	5863	0.4821	-0.2608	0.1563
fixed	NA	count_birth_order4/5	-0.1066	0.07177	-1.486	5884	0.1374	-0.3081	0.09481
fixed	NA	count_birth_order5/5	-0.1237	0.07425	-1.666	5866	0.09572	-0.3321	0.0847
fixed	NA	count_birth_order1/>5	-0.1206	0.07347	-1.642	5868	0.1007	-0.3269	0.0856
fixed	NA	count_birth_order2/>5	-0.1956	0.07265	-2.693	5846	0.007103	-0.3996	0.00829
fixed	NA	count_birth_order3/>5	-0.1502	0.07269	-2.066	5800	0.0389	-0.3542	0.05389
fixed	NA	count_birth_order4/>5	-0.1115	0.06833	-1.631	5806	0.1029	-0.3033	0.08034
fixed	NA	count_birth_order5/>5	-0.06799	0.06468	-1.051	5817	0.2932	-0.2495	0.1136
fixed	NA	count_birth_order>5/>5	-0.1493	0.0495	-3.016	5523	0.002577	-0.2882	-0.01032
ran_pars	mother_pidlink	sd__(Intercept)	0.3924	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7433	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)
11	14652	14726	-7315	14630	NA	NA	NA
12	14654	14734	-7315	14630	0.1023	1	0.7491
16	14657	14764	-7313	14625	4.598	4	0.3311
26	14671	14844	-7309	14619	6.858	10	0.7388

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)	-0.4997	0.3654	-1.367	5839	0.1716	-1.525	0.5261
fixed	NA	poly(age, 3, raw = TRUE)1	0.08706	0.04149	2.098	5834	0.03592	-0.02941	0.2035
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002669	0.001481	-1.801	5833	0.0717	-0.006827	0.00149
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000203	0.00001679	1.209	5838	0.2266	-0.00002682	0.00006742
fixed	NA	male	0.09351	0.02129	4.392	5722	0.00001146	0.03374	0.1533
fixed	NA	sibling_count3	0.03147	0.0375	0.8392	4389	0.4014	-0.0738	0.1367
fixed	NA	sibling_count4	-0.009716	0.03964	-0.2451	4039	0.8064	-0.121	0.1016
fixed	NA	sibling_count5	-0.01839	0.04258	-0.4318	3719	0.6659	-0.1379	0.1011
fixed	NA	sibling_count>5	-0.0805	0.03731	-2.157	3862	0.03103	-0.1852	0.02424
ran_pars	mother_pidlink	sd__(Intercept)	0.3954	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7416	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)	-0.4938	0.3655	-1.351	5839	0.1768	-1.52	0.5323
fixed	NA	birth_order	-0.005347	0.006257	-0.8546	5930	0.3928	-0.02291	0.01222
fixed	NA	poly(age, 3, raw = TRUE)1	0.08718	0.0415	2.101	5834	0.03568	-0.0293	0.2037
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002665	0.001482	-1.799	5833	0.07212	-0.006824	0.001494
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002004	0.00001679	1.193	5836	0.2329	-0.0000271	0.00006717
fixed	NA	male	0.09375	0.0213	4.402	5723	0.00001092	0.03397	0.1535
fixed	NA	sibling_count3	0.03414	0.03762	0.9075	4389	0.3642	-0.07147	0.1398
fixed	NA	sibling_count4	-0.003681	0.04025	-0.09145	4036	0.9271	-0.1167	0.1093
fixed	NA	sibling_count5	-0.008885	0.044	-0.2019	3753	0.84	-0.1324	0.1146
fixed	NA	sibling_count>5	-0.06066	0.04394	-1.381	4203	0.1675	-0.184	0.06268
ran_pars	mother_pidlink	sd__(Intercept)	0.3946	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7419	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)	-0.5303	0.3662	-1.448	5853	0.1477	-1.558	0.4977
fixed	NA	poly(age, 3, raw = TRUE)1	0.08914	0.04153	2.146	5842	0.03189	-0.02744	0.2057
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002734	0.001483	-1.844	5840	0.06528	-0.006897	0.001429
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002084	0.00001681	1.24	5841	0.2152	-0.00002635	0.00006802
fixed	NA	male	0.09355	0.0213	4.391	5720	0.00001148	0.03375	0.1533
fixed	NA	sibling_count3	0.02214	0.03824	0.579	4541	0.5626	-0.0852	0.1295
fixed	NA	sibling_count4	-0.02317	0.04153	-0.558	4308	0.5769	-0.1398	0.09341
fixed	NA	sibling_count5	-0.03049	0.04591	-0.6641	4121	0.5066	-0.1594	0.09838
fixed	NA	sibling_count>5	-0.07221	0.04516	-1.599	4447	0.1099	-0.199	0.05456
fixed	NA	birth_order_nonlinear2	0.036	0.02783	1.294	4879	0.1959	-0.04213	0.1141
fixed	NA	birth_order_nonlinear3	0.04407	0.03368	1.309	5071	0.1907	-0.05046	0.1386
fixed	NA	birth_order_nonlinear4	0.03472	0.04065	0.8542	5249	0.393	-0.07937	0.1488
fixed	NA	birth_order_nonlinear5	0.01614	0.04974	0.3245	5143	0.7456	-0.1235	0.1558
fixed	NA	birth_order_nonlinear>5	-0.03226	0.04754	-0.6786	5933	0.4974	-0.1657	0.1012
ran_pars	mother_pidlink	sd__(Intercept)	0.3933	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7425	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)	-0.527	0.3668	-1.437	5847	0.1509	-1.557	0.5027
fixed	NA	poly(age, 3, raw = TRUE)1	0.08859	0.04158	2.131	5831	0.03316	-0.02812	0.2053
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002699	0.001485	-1.817	5829	0.06921	-0.006867	0.00147
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002026	0.00001683	1.203	5832	0.2288	-0.00002699	0.00006751
fixed	NA	male	0.09351	0.0213	4.389	5705	0.00001157	0.03371	0.1533
fixed	NA	count_birth_order2/2	0.03047	0.05428	0.5614	5243	0.5745	-0.1219	0.1828
fixed	NA	count_birth_order1/3	-0.005049	0.0485	-0.1041	5879	0.9171	-0.1412	0.1311
fixed	NA	count_birth_order2/3	0.07102	0.05237	1.356	5939	0.1751	-0.07598	0.218
fixed	NA	count_birth_order3/3	0.09355	0.05888	1.589	5962	0.1121	-0.07173	0.2588
fixed	NA	count_birth_order1/4	-0.07743	0.05693	-1.36	5934	0.1738	-0.2372	0.08236
fixed	NA	count_birth_order2/4	0.04346	0.05822	0.7466	5959	0.4554	-0.12	0.2069
fixed	NA	count_birth_order3/4	0.04852	0.0635	0.7642	5951	0.4448	-0.1297	0.2268
fixed	NA	count_birth_order4/4	0.01437	0.06557	0.2191	5953	0.8266	-0.1697	0.1984
fixed	NA	count_birth_order1/5	0.02045	0.06753	0.3029	5961	0.762	-0.1691	0.21
fixed	NA	count_birth_order2/5	0.05005	0.07271	0.6884	5933	0.4912	-0.154	0.2542
fixed	NA	count_birth_order3/5	-0.02403	0.07055	-0.3406	5935	0.7334	-0.2221	0.174
fixed	NA	count_birth_order4/5	-0.03049	0.07305	-0.4174	5915	0.6764	-0.2356	0.1746
fixed	NA	count_birth_order5/5	-0.06213	0.07291	-0.8522	5922	0.3941	-0.2668	0.1425
fixed	NA	count_birth_order1/>5	0.008191	0.06447	0.127	5961	0.8989	-0.1728	0.1892
fixed	NA	count_birth_order2/>5	-0.146	0.06705	-2.177	5922	0.02949	-0.3342	0.04221
fixed	NA	count_birth_order3/>5	-0.06925	0.06562	-1.055	5907	0.2913	-0.2534	0.1149
fixed	NA	count_birth_order4/>5	-0.02285	0.06336	-0.3607	5909	0.7184	-0.2007	0.155
fixed	NA	count_birth_order5/>5	-0.02685	0.06489	-0.4137	5852	0.6791	-0.209	0.1553
fixed	NA	count_birth_order>5/>5	-0.1068	0.04849	-2.204	5614	0.02759	-0.2429	0.02925
ran_pars	mother_pidlink	sd__(Intercept)	0.3949	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7416	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)
11	14783	14856	-7380	14761	NA	NA	NA
12	14784	14864	-7380	14760	0.7334	1	0.3918
16	14788	14895	-7378	14756	3.844	4	0.4275
26	14795	14969	-7371	14743	13.4	10	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)	-0.5761	0.3711	-1.552	5678	0.1206	-1.618	0.4656
fixed	NA	poly(age, 3, raw = TRUE)1	0.09716	0.04213	2.306	5675	0.02115	-0.02111	0.2154
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003018	0.001504	-2.006	5673	0.04491	-0.007241	0.001205
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002451	0.00001705	1.437	5676	0.1507	-0.00002336	0.00007238
fixed	NA	male	0.09125	0.02161	4.222	5570	0.00002462	0.03058	0.1519
fixed	NA	sibling_count3	0.01999	0.03422	0.5842	4169	0.5591	-0.07607	0.1161
fixed	NA	sibling_count4	-0.03413	0.03724	-0.9165	3759	0.3595	-0.1387	0.07041
fixed	NA	sibling_count5	-0.08933	0.0442	-2.021	3351	0.04336	-0.2134	0.03474
fixed	NA	sibling_count>5	-0.1448	0.03831	-3.779	3215	0.00016	-0.2523	-0.03725
ran_pars	mother_pidlink	sd__(Intercept)	0.3902	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)	-0.5775	0.3712	-1.556	5677	0.1198	-1.619	0.4643
fixed	NA	birth_order	0.002238	0.007356	0.3042	5802	0.761	-0.01841	0.02289
fixed	NA	poly(age, 3, raw = TRUE)1	0.097	0.04214	2.302	5674	0.02138	-0.02129	0.2153
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003016	0.001505	-2.004	5672	0.04508	-0.007239	0.001208
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002458	0.00001706	1.441	5674	0.1496	-0.0000233	0.00007246
fixed	NA	male	0.09118	0.02162	4.218	5568	0.00002501	0.03051	0.1519
fixed	NA	sibling_count3	0.01887	0.03442	0.5481	4174	0.5837	-0.07776	0.1155
fixed	NA	sibling_count4	-0.03673	0.03821	-0.9612	3791	0.3365	-0.144	0.07053
fixed	NA	sibling_count5	-0.09345	0.04623	-2.022	3448	0.0433	-0.2232	0.03631
fixed	NA	sibling_count>5	-0.1533	0.04742	-3.233	3844	0.001236	-0.2864	-0.02019
ran_pars	mother_pidlink	sd__(Intercept)	0.3905	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7437	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)	-0.6256	0.3718	-1.683	5691	0.09253	-1.669	0.4181
fixed	NA	poly(age, 3, raw = TRUE)1	0.1004	0.04217	2.382	5682	0.01725	-0.01792	0.2188
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003136	0.001506	-2.083	5678	0.03731	-0.007362	0.00109
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002589	0.00001707	1.517	5677	0.1293	-0.00002202	0.00007381
fixed	NA	male	0.0914	0.02162	4.228	5564	0.00002394	0.03072	0.1521
fixed	NA	sibling_count3	0.008164	0.03508	0.2327	4353	0.816	-0.09031	0.1066
fixed	NA	sibling_count4	-0.05403	0.03961	-1.364	4097	0.1727	-0.1652	0.05717
fixed	NA	sibling_count5	-0.1078	0.04814	-2.239	3804	0.02522	-0.2429	0.02735
fixed	NA	sibling_count>5	-0.1591	0.04873	-3.265	4097	0.001103	-0.2959	-0.02233
fixed	NA	birth_order_nonlinear2	0.06079	0.02726	2.23	4637	0.02578	-0.01572	0.1373
fixed	NA	birth_order_nonlinear3	0.05707	0.03379	1.689	4822	0.09131	-0.03778	0.1519
fixed	NA	birth_order_nonlinear4	0.05315	0.04308	1.234	4972	0.2174	-0.06778	0.1741
fixed	NA	birth_order_nonlinear5	0.02966	0.05454	0.5438	4817	0.5866	-0.1234	0.1828
fixed	NA	birth_order_nonlinear>5	0.02338	0.05469	0.4275	5627	0.669	-0.1301	0.1769
ran_pars	mother_pidlink	sd__(Intercept)	0.3892	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)	-0.6437	0.3729	-1.726	5687	0.08436	-1.69	0.403
fixed	NA	poly(age, 3, raw = TRUE)1	0.1026	0.04228	2.427	5675	0.01527	-0.01609	0.2213
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003204	0.00151	-2.122	5672	0.03389	-0.007443	0.001034
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002657	0.00001712	1.552	5673	0.1208	-0.0000215	0.00007463
fixed	NA	male	0.09147	0.02164	4.227	5553	0.0000241	0.03072	0.1522
fixed	NA	count_birth_order2/2	0.05327	0.04822	1.105	4942	0.2693	-0.08207	0.1886
fixed	NA	count_birth_order1/3	-0.01454	0.04425	-0.3286	5715	0.7425	-0.1388	0.1097
fixed	NA	count_birth_order2/3	0.09972	0.04866	2.049	5781	0.04046	-0.03686	0.2363
fixed	NA	count_birth_order3/3	0.05742	0.05341	1.075	5790	0.2824	-0.0925	0.2073
fixed	NA	count_birth_order1/4	-0.0668	0.05467	-1.222	5776	0.2219	-0.2203	0.08668
fixed	NA	count_birth_order2/4	-0.003471	0.05641	-0.06154	5790	0.9509	-0.1618	0.1549
fixed	NA	count_birth_order3/4	0.0155	0.05882	0.2634	5778	0.7922	-0.1496	0.1806
fixed	NA	count_birth_order4/4	0.004197	0.06202	0.06768	5767	0.946	-0.1699	0.1783
fixed	NA	count_birth_order1/5	-0.05474	0.07389	-0.7408	5789	0.4588	-0.2621	0.1527
fixed	NA	count_birth_order2/5	-0.04276	0.08163	-0.5239	5725	0.6004	-0.2719	0.1864
fixed	NA	count_birth_order3/5	-0.04845	0.07764	-0.624	5735	0.5326	-0.2664	0.1695
fixed	NA	count_birth_order4/5	-0.07973	0.07529	-1.059	5758	0.2897	-0.2911	0.1316
fixed	NA	count_birth_order5/5	-0.1367	0.07946	-1.72	5737	0.08545	-0.3597	0.08636
fixed	NA	count_birth_order1/>5	-0.1208	0.0752	-1.607	5743	0.1081	-0.3319	0.09024
fixed	NA	count_birth_order2/>5	-0.1781	0.07448	-2.391	5721	0.01683	-0.3872	0.03098
fixed	NA	count_birth_order3/>5	-0.1208	0.07353	-1.643	5680	0.1004	-0.3272	0.0856
fixed	NA	count_birth_order4/>5	-0.1009	0.07186	-1.404	5640	0.1603	-0.3026	0.1008
fixed	NA	count_birth_order5/>5	-0.09842	0.06622	-1.486	5687	0.1372	-0.2843	0.08745
fixed	NA	count_birth_order>5/>5	-0.1381	0.0504	-2.74	5392	0.006161	-0.2796	0.003369
ran_pars	mother_pidlink	sd__(Intercept)	0.3886	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7447	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)
11	14356	14429	-7167	14334	NA	NA	NA
12	14358	14438	-7167	14334	0.09157	1	0.7622
16	14360	14467	-7164	14328	6.1	4	0.1918
26	14375	14548	-7161	14323	5.282	10	0.8716

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)	0.3193	0.2143	1.49	13784	0.1362	-0.2822	0.9207
fixed	NA	poly(age, 3, raw = TRUE)1	0.007294	0.02199	0.3316	13792	0.7402	-0.05444	0.06903
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005758	0.0007025	-0.8196	13807	0.4124	-0.002548	0.001396
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004245	0.000007055	0.6017	13815	0.5474	-0.00001556	0.00002405
fixed	NA	male	-0.07804	0.01633	-4.778	13293	0.000001792	-0.1239	-0.03219
fixed	NA	sibling_count3	0.03562	0.03434	1.037	9605	0.2997	-0.06078	0.132
fixed	NA	sibling_count4	-0.04503	0.03547	-1.27	8825	0.2042	-0.1446	0.05452
fixed	NA	sibling_count5	-0.01284	0.03704	-0.3466	8040	0.7289	-0.1168	0.09114
fixed	NA	sibling_count>5	-0.1715	0.02895	-5.922	8946	0.000000003304	-0.2527	-0.09018
ran_pars	mother_pidlink	sd__(Intercept)	0.4447	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.881	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)	0.3021	0.2145	1.409	13785	0.1589	-0.2999	0.9042
fixed	NA	birth_order	-0.006092	0.003514	-1.734	13386	0.08303	-0.01596	0.003773
fixed	NA	poly(age, 3, raw = TRUE)1	0.01092	0.02209	0.4941	13820	0.6212	-0.0511	0.07293
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007057	0.0007065	-0.9988	13848	0.3179	-0.002689	0.001278
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005524	0.000007093	0.7787	13856	0.4362	-0.00001439	0.00002544
fixed	NA	male	-0.07783	0.01633	-4.765	13294	0.000001906	-0.1237	-0.03198
fixed	NA	sibling_count3	0.03689	0.03434	1.074	9620	0.2827	-0.05951	0.1333
fixed	NA	sibling_count4	-0.04087	0.03554	-1.15	8893	0.2502	-0.1406	0.05889
fixed	NA	sibling_count5	-0.005543	0.03727	-0.1487	8162	0.8818	-0.1102	0.09907
fixed	NA	sibling_count>5	-0.1485	0.03184	-4.664	10121	0.000003137	-0.2378	-0.05912
ran_pars	mother_pidlink	sd__(Intercept)	0.4442	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8811	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)	0.3361	0.2158	1.558	13816	0.1193	-0.2696	0.9419
fixed	NA	poly(age, 3, raw = TRUE)1	0.006561	0.02214	0.2963	13834	0.767	-0.05559	0.06871
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005546	0.0007086	-0.7827	13859	0.4338	-0.002544	0.001435
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004035	0.000007122	0.5665	13869	0.571	-0.00001596	0.00002403
fixed	NA	male	-0.0781	0.01634	-4.781	13289	0.000001761	-0.124	-0.03225
fixed	NA	sibling_count3	0.03465	0.03477	0.9965	9939	0.319	-0.06296	0.1323
fixed	NA	sibling_count4	-0.05003	0.03642	-1.374	9533	0.1696	-0.1523	0.05221
fixed	NA	sibling_count5	-0.02144	0.03854	-0.5564	8989	0.578	-0.1296	0.08673
fixed	NA	sibling_count>5	-0.1731	0.03329	-5.201	11107	0.0000002017	-0.2666	-0.07969
fixed	NA	birth_order_nonlinear2	-0.02299	0.02364	-0.9727	12407	0.3307	-0.08935	0.04336
fixed	NA	birth_order_nonlinear3	-0.002078	0.02775	-0.07488	11992	0.9403	-0.07998	0.07583
fixed	NA	birth_order_nonlinear4	0.01697	0.03155	0.5378	11980	0.5907	-0.0716	0.1055
fixed	NA	birth_order_nonlinear5	0.01641	0.03594	0.4564	11936	0.6481	-0.08449	0.1173
fixed	NA	birth_order_nonlinear>5	-0.01964	0.03019	-0.6505	13718	0.5154	-0.1044	0.0651
ran_pars	mother_pidlink	sd__(Intercept)	0.4443	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)	0.3273	0.217	1.509	13830	0.1314	-0.2817	0.9363
fixed	NA	poly(age, 3, raw = TRUE)1	0.006943	0.02219	0.3129	13840	0.7543	-0.05533	0.06922
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005669	0.0007105	-0.7979	13862	0.425	-0.002561	0.001428
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004164	0.000007146	0.5828	13870	0.5601	-0.00001589	0.00002422
fixed	NA	male	-0.07788	0.01634	-4.766	13281	0.0000019	-0.1238	-0.03201
fixed	NA	count_birth_order2/2	-0.00982	0.04618	-0.2127	12703	0.8316	-0.1394	0.1198
fixed	NA	count_birth_order1/3	0.05031	0.04467	1.126	13464	0.2601	-0.07508	0.1757
fixed	NA	count_birth_order2/3	0.01198	0.04969	0.2411	13653	0.8095	-0.1275	0.1515
fixed	NA	count_birth_order3/3	0.0213	0.05561	0.3831	13805	0.7016	-0.1348	0.1774
fixed	NA	count_birth_order1/4	-0.05016	0.05062	-0.9909	13664	0.3218	-0.1923	0.09194
fixed	NA	count_birth_order2/4	-0.06037	0.05338	-1.131	13741	0.2581	-0.2102	0.08946
fixed	NA	count_birth_order3/4	-0.03141	0.05772	-0.5442	13835	0.5863	-0.1934	0.1306
fixed	NA	count_birth_order4/4	-0.04884	0.06074	-0.8041	13865	0.4213	-0.2193	0.1217
fixed	NA	count_birth_order1/5	-0.05318	0.05742	-0.9263	13802	0.3543	-0.2144	0.108
fixed	NA	count_birth_order2/5	-0.08221	0.06012	-1.367	13844	0.1715	-0.251	0.08654
fixed	NA	count_birth_order3/5	0.01386	0.06183	0.2241	13866	0.8227	-0.1597	0.1874
fixed	NA	count_birth_order4/5	0.01906	0.06531	0.2918	13877	0.7704	-0.1643	0.2024
fixed	NA	count_birth_order5/5	0.05706	0.06688	0.8531	13873	0.3936	-0.1307	0.2448
fixed	NA	count_birth_order1/>5	-0.1509	0.04641	-3.251	13867	0.001153	-0.2811	-0.0206
fixed	NA	count_birth_order2/>5	-0.1789	0.04772	-3.75	13877	0.0001776	-0.3129	-0.045
fixed	NA	count_birth_order3/>5	-0.183	0.04667	-3.921	13877	0.00008855	-0.314	-0.05199
fixed	NA	count_birth_order4/>5	-0.1483	0.04581	-3.238	13876	0.001208	-0.2769	-0.01973
fixed	NA	count_birth_order5/>5	-0.1708	0.04611	-3.705	13877	0.0002124	-0.3002	-0.04139
fixed	NA	count_birth_order>5/>5	-0.1879	0.03668	-5.123	12289	0.0000003045	-0.2909	-0.08497
ran_pars	mother_pidlink	sd__(Intercept)	0.444	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8815	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)
11	38695	38778	-19337	38673	NA	NA	NA
12	38694	38785	-19335	38670	3.008	1	0.08286
16	38702	38823	-19335	38670	0.06628	4	0.9995
26	38718	38914	-19333	38666	4.383	10	0.9284

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)	-0.4124	0.4482	-0.92	5845	0.3576	-1.671	0.8458
fixed	NA	poly(age, 3, raw = TRUE)1	0.09996	0.05087	1.965	5846	0.04947	-0.04284	0.2428
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003619	0.001816	-1.993	5850	0.04632	-0.008716	0.001478
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003836	0.00002057	1.865	5855	0.06226	-0.00001938	0.00009611
fixed	NA	male	-0.1536	0.02616	-5.869	5765	0.000000004617	-0.227	-0.08012
fixed	NA	sibling_count3	0.01062	0.04193	0.2533	4427	0.8001	-0.1071	0.1283
fixed	NA	sibling_count4	-0.08796	0.04522	-1.945	3988	0.05182	-0.2149	0.03898
fixed	NA	sibling_count5	-0.1347	0.05191	-2.594	3643	0.009518	-0.2804	0.01105
fixed	NA	sibling_count>5	-0.2428	0.04561	-5.325	3482	0.0000001076	-0.3708	-0.1148
ran_pars	mother_pidlink	sd__(Intercept)	0.4377	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.923	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)	-0.4249	0.4482	-0.9481	5844	0.3431	-1.683	0.8332
fixed	NA	birth_order	0.01582	0.008711	1.817	5914	0.06933	-0.008628	0.04028
fixed	NA	poly(age, 3, raw = TRUE)1	0.09906	0.05086	1.948	5846	0.0515	-0.04371	0.2418
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003611	0.001816	-1.989	5849	0.04676	-0.008707	0.001485
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003891	0.00002057	1.892	5853	0.0586	-0.00001883	0.00009665
fixed	NA	male	-0.1543	0.02616	-5.898	5765	0.000000003898	-0.2277	-0.08085
fixed	NA	sibling_count3	0.002788	0.04214	0.06616	4435	0.9473	-0.1155	0.1211
fixed	NA	sibling_count4	-0.1064	0.04634	-2.296	4008	0.02172	-0.2365	0.02368
fixed	NA	sibling_count5	-0.1648	0.05449	-3.024	3744	0.002508	-0.3178	-0.01185
fixed	NA	sibling_count>5	-0.3032	0.05643	-5.374	4014	0.00000008157	-0.4616	-0.1448
ran_pars	mother_pidlink	sd__(Intercept)	0.4378	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9227	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)	-0.4289	0.4491	-0.955	5852	0.3396	-1.69	0.8317
fixed	NA	poly(age, 3, raw = TRUE)1	0.1012	0.05091	1.987	5850	0.04695	-0.04174	0.2441
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003688	0.001817	-2.029	5851	0.04247	-0.008789	0.001413
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003982	0.00002059	1.934	5854	0.0532	-0.00001798	0.00009762
fixed	NA	male	-0.1543	0.02617	-5.895	5760	0.000000003967	-0.2277	-0.0808
fixed	NA	sibling_count3	-0.006667	0.04296	-0.1552	4608	0.8767	-0.1273	0.1139
fixed	NA	sibling_count4	-0.1178	0.04805	-2.451	4313	0.01427	-0.2527	0.0171
fixed	NA	sibling_count5	-0.1912	0.05708	-3.35	4147	0.0008158	-0.3514	-0.03098
fixed	NA	sibling_count>5	-0.317	0.058	-5.465	4255	0.00000004897	-0.4798	-0.1542
fixed	NA	birth_order_nonlinear2	0.02081	0.03354	0.6204	4919	0.535	-0.07334	0.115
fixed	NA	birth_order_nonlinear3	0.07339	0.04148	1.769	5119	0.07687	-0.04303	0.1898
fixed	NA	birth_order_nonlinear4	0.05819	0.05138	1.132	5267	0.2575	-0.08604	0.2024
fixed	NA	birth_order_nonlinear5	0.1455	0.06415	2.269	5115	0.02334	-0.03455	0.3256
fixed	NA	birth_order_nonlinear>5	0.09315	0.06484	1.437	5851	0.1509	-0.08886	0.2752
ran_pars	mother_pidlink	sd__(Intercept)	0.4367	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9232	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)	-0.4642	0.4503	-1.031	5845	0.3026	-1.728	0.7998
fixed	NA	poly(age, 3, raw = TRUE)1	0.1045	0.05104	2.048	5840	0.04057	-0.03872	0.2478
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003813	0.001822	-2.093	5842	0.03643	-0.008928	0.001302
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004129	0.00002065	1.999	5846	0.04563	-0.00001668	0.00009925
fixed	NA	male	-0.1531	0.0262	-5.845	5749	0.000000005357	-0.2266	-0.07957
fixed	NA	count_birth_order2/2	0.03911	0.06081	0.6432	5211	0.5201	-0.1316	0.2098
fixed	NA	count_birth_order1/3	0.004539	0.0546	0.08314	5856	0.9337	-0.1487	0.1578
fixed	NA	count_birth_order2/3	0.02779	0.05938	0.4679	5897	0.6399	-0.1389	0.1945
fixed	NA	count_birth_order3/3	0.05161	0.06635	0.7778	5909	0.4367	-0.1346	0.2379
fixed	NA	count_birth_order1/4	-0.1031	0.06635	-1.553	5892	0.1204	-0.2893	0.08318
fixed	NA	count_birth_order2/4	-0.131	0.06871	-1.907	5909	0.05654	-0.3239	0.06182
fixed	NA	count_birth_order3/4	-0.03292	0.07245	-0.4543	5902	0.6496	-0.2363	0.1704
fixed	NA	count_birth_order4/4	-0.02071	0.0754	-0.2747	5900	0.7836	-0.2324	0.191
fixed	NA	count_birth_order1/5	-0.1396	0.09008	-1.55	5907	0.1212	-0.3925	0.1133
fixed	NA	count_birth_order2/5	-0.1104	0.0965	-1.144	5873	0.2527	-0.3813	0.1605
fixed	NA	count_birth_order3/5	-0.06116	0.09072	-0.6741	5878	0.5003	-0.3158	0.1935
fixed	NA	count_birth_order4/5	-0.2161	0.08761	-2.466	5891	0.01368	-0.462	0.02986
fixed	NA	count_birth_order5/5	-0.08756	0.09067	-0.9657	5878	0.3342	-0.3421	0.1669
fixed	NA	count_birth_order1/>5	-0.3657	0.08971	-4.076	5887	0.00004633	-0.6175	-0.1139
fixed	NA	count_birth_order2/>5	-0.3071	0.08873	-3.461	5871	0.0005426	-0.5562	-0.05801
fixed	NA	count_birth_order3/>5	-0.2507	0.08883	-2.822	5838	0.004793	-0.5	-0.001302
fixed	NA	count_birth_order4/>5	-0.2177	0.0835	-2.607	5839	0.009165	-0.4521	0.01673
fixed	NA	count_birth_order5/>5	-0.1333	0.07903	-1.687	5845	0.09166	-0.3552	0.08852
fixed	NA	count_birth_order>5/>5	-0.2173	0.06012	-3.614	5535	0.0003043	-0.386	-0.04851
ran_pars	mother_pidlink	sd__(Intercept)	0.4363	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9239	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)
11	17008	17082	-8493	16986	NA	NA	NA
12	17007	17087	-8492	16983	3.304	1	0.06913
16	17012	17119	-8490	16980	3.482	4	0.4806
26	17027	17200	-8487	16975	4.996	10	0.8914

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)	-0.3743	0.4477	-0.8361	5896	0.4031	-1.631	0.8824
fixed	NA	poly(age, 3, raw = TRUE)1	0.09573	0.05083	1.883	5896	0.05971	-0.04696	0.2384
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003491	0.001815	-1.924	5899	0.05445	-0.008586	0.001603
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003683	0.00002057	1.791	5904	0.0734	-0.0000209	0.00009456
fixed	NA	male	-0.1544	0.02611	-5.913	5811	0.000000003555	-0.2277	-0.08109
fixed	NA	sibling_count3	0.02706	0.04542	0.5958	4569	0.5513	-0.1004	0.1546
fixed	NA	sibling_count4	-0.07306	0.04794	-1.524	4212	0.1276	-0.2076	0.0615
fixed	NA	sibling_count5	-0.08228	0.05143	-1.6	3875	0.1097	-0.2266	0.06207
fixed	NA	sibling_count>5	-0.1821	0.04509	-4.039	4006	0.00005475	-0.3087	-0.05553
ran_pars	mother_pidlink	sd__(Intercept)	0.4413	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.924	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)	-0.3791	0.4478	-0.8465	5894	0.3973	-1.636	0.8779
fixed	NA	birth_order	0.004275	0.007636	0.5599	5883	0.5756	-0.01716	0.02571
fixed	NA	poly(age, 3, raw = TRUE)1	0.09565	0.05084	1.882	5895	0.05994	-0.04705	0.2384
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003495	0.001815	-1.926	5897	0.05421	-0.00859	0.0016
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003704	0.00002057	1.801	5902	0.07182	-0.0000207	0.00009478
fixed	NA	male	-0.1546	0.02611	-5.919	5811	0.000000003432	-0.2279	-0.08125
fixed	NA	sibling_count3	0.02495	0.04558	0.5475	4569	0.5841	-0.103	0.1529
fixed	NA	sibling_count4	-0.07783	0.04869	-1.598	4210	0.11	-0.2145	0.05885
fixed	NA	sibling_count5	-0.08982	0.05317	-1.689	3906	0.0912	-0.2391	0.05941
fixed	NA	sibling_count>5	-0.1979	0.05319	-3.721	4325	0.0002013	-0.3472	-0.04859
ran_pars	mother_pidlink	sd__(Intercept)	0.4415	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.924	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)	-0.3883	0.4486	-0.8654	5902	0.3868	-1.648	0.8711
fixed	NA	poly(age, 3, raw = TRUE)1	0.09661	0.05088	1.899	5897	0.05764	-0.04621	0.2394
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003535	0.001817	-1.946	5899	0.05174	-0.008635	0.001565
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003765	0.00002059	1.828	5903	0.06754	-0.00002015	0.00009545
fixed	NA	male	-0.1548	0.02612	-5.928	5806	0.000000003245	-0.2282	-0.08152
fixed	NA	sibling_count3	0.01383	0.04637	0.2983	4713	0.7655	-0.1163	0.144
fixed	NA	sibling_count4	-0.09552	0.05032	-1.898	4474	0.05772	-0.2368	0.04573
fixed	NA	sibling_count5	-0.1103	0.05558	-1.984	4271	0.04728	-0.2663	0.04573
fixed	NA	sibling_count>5	-0.2216	0.05474	-4.048	4571	0.00005241	-0.3753	-0.06796
fixed	NA	birth_order_nonlinear2	0.02009	0.03426	0.5864	5042	0.5576	-0.07609	0.1163
fixed	NA	birth_order_nonlinear3	0.05782	0.04142	1.396	5231	0.1628	-0.05846	0.1741
fixed	NA	birth_order_nonlinear4	0.05083	0.04996	1.018	5390	0.3089	-0.0894	0.1911
fixed	NA	birth_order_nonlinear5	0.0438	0.06117	0.716	5309	0.474	-0.1279	0.2155
fixed	NA	birth_order_nonlinear>5	0.05985	0.05819	1.029	5960	0.3037	-0.1035	0.2232
ran_pars	mother_pidlink	sd__(Intercept)	0.4413	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9242	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)	-0.4364	0.4495	-0.9708	5896	0.3317	-1.698	0.8255
fixed	NA	poly(age, 3, raw = TRUE)1	0.1003	0.05096	1.969	5888	0.04902	-0.04271	0.2434
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003676	0.00182	-2.02	5890	0.04343	-0.008785	0.001432
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003931	0.00002063	1.906	5895	0.05675	-0.0000186	0.00009723
fixed	NA	male	-0.1557	0.02614	-5.956	5795	0.00000000273	-0.229	-0.08231
fixed	NA	count_birth_order2/2	0.07481	0.06677	1.12	5335	0.2626	-0.1126	0.2622
fixed	NA	count_birth_order1/3	0.06574	0.05921	1.11	5908	0.267	-0.1005	0.232
fixed	NA	count_birth_order2/3	0.007638	0.06399	0.1194	5947	0.905	-0.172	0.1873
fixed	NA	count_birth_order3/3	0.08768	0.07201	1.218	5962	0.2234	-0.1145	0.2898
fixed	NA	count_birth_order1/4	-0.1036	0.06955	-1.49	5943	0.1363	-0.2989	0.0916
fixed	NA	count_birth_order2/4	-0.03628	0.07118	-0.5097	5960	0.6103	-0.2361	0.1635
fixed	NA	count_birth_order3/4	-0.02561	0.07771	-0.3295	5954	0.7418	-0.2437	0.1925
fixed	NA	count_birth_order4/4	-0.006286	0.08024	-0.07833	5955	0.9376	-0.2315	0.219
fixed	NA	count_birth_order1/5	-0.007333	0.08258	-0.0888	5961	0.9292	-0.2391	0.2245
fixed	NA	count_birth_order2/5	-0.07043	0.08902	-0.7912	5943	0.4288	-0.3203	0.1794
fixed	NA	count_birth_order3/5	0.01048	0.08637	0.1213	5944	0.9034	-0.232	0.2529
fixed	NA	count_birth_order4/5	-0.1567	0.08947	-1.752	5929	0.07989	-0.4078	0.09442
fixed	NA	count_birth_order5/5	-0.09262	0.08928	-1.037	5933	0.2996	-0.3432	0.158
fixed	NA	count_birth_order1/>5	-0.2681	0.07886	-3.399	5962	0.00068	-0.4894	-0.0467
fixed	NA	count_birth_order2/>5	-0.1808	0.0821	-2.202	5938	0.02769	-0.4113	0.04966
fixed	NA	count_birth_order3/>5	-0.1727	0.08036	-2.149	5926	0.03167	-0.3983	0.05287
fixed	NA	count_birth_order4/>5	-0.09252	0.0776	-1.192	5925	0.2332	-0.3103	0.1253
fixed	NA	count_birth_order5/>5	-0.128	0.07952	-1.61	5885	0.1075	-0.3512	0.09521
fixed	NA	count_birth_order>5/>5	-0.1425	0.05907	-2.413	5628	0.01584	-0.3083	0.02325
ran_pars	mother_pidlink	sd__(Intercept)	0.4412	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9243	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)
11	17187	17261	-8583	17165	NA	NA	NA
12	17189	17269	-8582	17165	0.3133	1	0.5757
16	17195	17302	-8581	17163	2.203	4	0.6986
26	17205	17379	-8577	17153	9.439	10	0.491

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)	-0.5356	0.4544	-1.179	5726	0.2386	-1.811	0.7399
fixed	NA	poly(age, 3, raw = TRUE)1	0.1138	0.05159	2.206	5726	0.0274	-0.03099	0.2587
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004171	0.001842	-2.264	5728	0.02359	-0.009342	0.0009998
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004509	0.00002088	2.16	5733	0.03084	-0.00001352	0.0001037
fixed	NA	male	-0.1506	0.02649	-5.685	5646	0.0000000137	-0.2249	-0.07623
fixed	NA	sibling_count3	0.01379	0.04149	0.3323	4340	0.7397	-0.1027	0.1303
fixed	NA	sibling_count4	-0.06312	0.04509	-1.4	3922	0.1616	-0.1897	0.06344
fixed	NA	sibling_count5	-0.1219	0.05343	-2.282	3498	0.02258	-0.2719	0.02808
fixed	NA	sibling_count>5	-0.2157	0.04628	-4.662	3343	0.00000326	-0.3457	-0.08583
ran_pars	mother_pidlink	sd__(Intercept)	0.4422	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9234	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)	-0.5462	0.4544	-1.202	5725	0.2294	-1.822	0.7292
fixed	NA	birth_order	0.01591	0.008989	1.77	5803	0.07671	-0.009318	0.04115
fixed	NA	poly(age, 3, raw = TRUE)1	0.1127	0.05159	2.185	5726	0.0289	-0.03207	0.2575
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004158	0.001842	-2.258	5727	0.02401	-0.009328	0.001012
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000456	0.00002088	2.184	5731	0.02902	-0.00001301	0.0001042
fixed	NA	male	-0.151	0.02648	-5.703	5645	0.00000001235	-0.2254	-0.0767
fixed	NA	sibling_count3	0.005873	0.04173	0.1408	4346	0.8881	-0.1113	0.123
fixed	NA	sibling_count4	-0.08142	0.04625	-1.76	3953	0.0784	-0.2112	0.0484
fixed	NA	sibling_count5	-0.1509	0.05588	-2.701	3591	0.006953	-0.3078	0.005945
fixed	NA	sibling_count>5	-0.2759	0.0574	-4.806	3956	0.000001597	-0.437	-0.1147
ran_pars	mother_pidlink	sd__(Intercept)	0.4423	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9231	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)	-0.5386	0.4552	-1.183	5733	0.2368	-1.816	0.7392
fixed	NA	poly(age, 3, raw = TRUE)1	0.1138	0.05163	2.205	5729	0.02753	-0.03111	0.2587
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004199	0.001843	-2.278	5729	0.02276	-0.009374	0.000975
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004613	0.0000209	2.207	5731	0.02733	-0.00001253	0.0001048
fixed	NA	male	-0.1512	0.02649	-5.709	5640	0.00000001192	-0.2256	-0.07688
fixed	NA	sibling_count3	-0.002021	0.04257	-0.04749	4520	0.9621	-0.1215	0.1175
fixed	NA	sibling_count4	-0.09644	0.04802	-2.008	4255	0.0447	-0.2312	0.03837
fixed	NA	sibling_count5	-0.1759	0.0583	-3.017	3950	0.002569	-0.3395	-0.01224
fixed	NA	sibling_count>5	-0.2909	0.05907	-4.924	4212	0.0000008797	-0.4567	-0.1251
fixed	NA	birth_order_nonlinear2	0.01337	0.03353	0.3987	4805	0.6901	-0.08075	0.1075
fixed	NA	birth_order_nonlinear3	0.06506	0.04154	1.566	4981	0.1174	-0.05154	0.1817
fixed	NA	birth_order_nonlinear4	0.08177	0.05293	1.545	5123	0.1225	-0.06681	0.2303
fixed	NA	birth_order_nonlinear5	0.1201	0.06705	1.791	4995	0.07334	-0.06812	0.3083
fixed	NA	birth_order_nonlinear>5	0.09651	0.06699	1.441	5696	0.1497	-0.09153	0.2845
ran_pars	mother_pidlink	sd__(Intercept)	0.4415	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9236	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)	-0.5806	0.4565	-1.272	5727	0.2035	-1.862	0.7009
fixed	NA	poly(age, 3, raw = TRUE)1	0.1187	0.05177	2.292	5721	0.02193	-0.02665	0.264
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004378	0.001849	-2.368	5722	0.0179	-0.009568	0.0008111
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004819	0.00002096	2.299	5725	0.02154	-0.00001065	0.000107
fixed	NA	male	-0.15	0.02652	-5.658	5629	0.00000001609	-0.2245	-0.0756
fixed	NA	count_birth_order2/2	0.01536	0.05925	0.2592	5053	0.7955	-0.1509	0.1817
fixed	NA	count_birth_order1/3	0.003387	0.05402	0.0627	5738	0.95	-0.1482	0.155
fixed	NA	count_birth_order2/3	0.008751	0.05945	0.1472	5784	0.883	-0.1581	0.1756
fixed	NA	count_birth_order3/3	0.05884	0.06529	0.9012	5790	0.3675	-0.1244	0.2421
fixed	NA	count_birth_order1/4	-0.09925	0.06679	-1.486	5780	0.1373	-0.2867	0.08823
fixed	NA	count_birth_order2/4	-0.123	0.06896	-1.783	5790	0.07458	-0.3165	0.07059
fixed	NA	count_birth_order3/4	0.001164	0.07194	0.01618	5781	0.9871	-0.2008	0.2031
fixed	NA	count_birth_order4/4	0.008341	0.07586	0.11	5773	0.9125	-0.2046	0.2213
fixed	NA	count_birth_order1/5	-0.123	0.09033	-1.361	5790	0.1735	-0.3765	0.1306
fixed	NA	count_birth_order2/5	-0.0875	0.0999	-0.8758	5745	0.3812	-0.3679	0.1929
fixed	NA	count_birth_order3/5	-0.0931	0.09501	-0.9799	5751	0.3272	-0.3598	0.1736
fixed	NA	count_birth_order4/5	-0.1781	0.09211	-1.934	5767	0.05316	-0.4367	0.08042
fixed	NA	count_birth_order5/5	-0.11	0.09724	-1.131	5751	0.2581	-0.383	0.163
fixed	NA	count_birth_order1/>5	-0.3524	0.09201	-3.83	5761	0.0001293	-0.6107	-0.09416
fixed	NA	count_birth_order2/>5	-0.2463	0.09116	-2.702	5745	0.006907	-0.5022	0.009553
fixed	NA	count_birth_order3/>5	-0.2817	0.09003	-3.129	5714	0.001761	-0.5345	-0.02901
fixed	NA	count_birth_order4/>5	-0.1651	0.08801	-1.876	5683	0.06067	-0.4122	0.08192
fixed	NA	count_birth_order5/>5	-0.1366	0.08107	-1.685	5715	0.09204	-0.3642	0.09096
fixed	NA	count_birth_order>5/>5	-0.1927	0.06138	-3.139	5405	0.001704	-0.365	-0.02038
ran_pars	mother_pidlink	sd__(Intercept)	0.4406	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9244	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)
11	16690	16763	-8334	16668	NA	NA	NA
12	16689	16769	-8332	16665	3.138	1	0.07648
16	16695	16801	-8331	16663	2.443	4	0.6549
26	16709	16882	-8329	16657	5.429	10	0.8607

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)	-2.913	0.1161	-25.09	11555	2.58e-135	-3.239	-2.587
fixed	NA	poly(age, 3, raw = TRUE)1	0.4204	0.02155	19.5	11680	2.191e-83	0.3599	0.4809
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01677	0.00125	-13.41	11811	1.002e-40	-0.02028	-0.01326
fixed	NA	poly(age, 3, raw = TRUE)3	0.000206	0.00002297	8.97	11829	3.408e-19	0.0001416	0.0002705
fixed	NA	male	0.04925	0.01654	2.977	11006	0.002914	0.002818	0.09569
fixed	NA	sibling_count3	-0.03514	0.02866	-1.226	7714	0.2202	-0.1156	0.0453
fixed	NA	sibling_count4	-0.08887	0.03214	-2.765	7047	0.005701	-0.1791	0.001339
fixed	NA	sibling_count5	-0.07689	0.03636	-2.115	6427	0.03447	-0.1789	0.02516
fixed	NA	sibling_count>5	-0.244	0.02882	-8.467	7187	3.014e-17	-0.3249	-0.1631
ran_pars	mother_pidlink	sd__(Intercept)	0.5099	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.786	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)	-2.899	0.1165	-24.88	11582	3.297e-133	-3.226	-2.572
fixed	NA	birth_order	-0.006508	0.004435	-1.467	9943	0.1423	-0.01896	0.00594
fixed	NA	poly(age, 3, raw = TRUE)1	0.4199	0.02156	19.48	11679	3.334e-83	0.3594	0.4804
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01677	0.00125	-13.41	11810	1.04e-40	-0.02028	-0.01326
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002058	0.00002297	8.96	11828	3.716e-19	0.0001413	0.0002703
fixed	NA	male	0.04936	0.01654	2.984	11007	0.002855	0.002922	0.09579
fixed	NA	sibling_count3	-0.03129	0.02878	-1.087	7689	0.2769	-0.1121	0.04949
fixed	NA	sibling_count4	-0.07961	0.03275	-2.431	6933	0.01508	-0.1715	0.01231
fixed	NA	sibling_count5	-0.06196	0.03775	-1.641	6268	0.1007	-0.1679	0.044
fixed	NA	sibling_count>5	-0.2073	0.03816	-5.432	6679	0.0000000577	-0.3144	-0.1002
ran_pars	mother_pidlink	sd__(Intercept)	0.5097	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7861	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)	-2.907	0.1177	-24.7	11650	2.209e-131	-3.237	-2.577
fixed	NA	poly(age, 3, raw = TRUE)1	0.4201	0.02164	19.42	11706	1.131e-82	0.3593	0.4808
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01679	0.001252	-13.41	11810	1.118e-40	-0.0203	-0.01327
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002063	0.00002299	8.976	11824	3.216e-19	0.0001418	0.0002709
fixed	NA	male	0.04912	0.01655	2.969	11003	0.002995	0.002679	0.09557
fixed	NA	sibling_count3	-0.03626	0.02964	-1.223	8172	0.2213	-0.1195	0.04694
fixed	NA	sibling_count4	-0.08243	0.03527	-2.337	7997	0.01945	-0.1814	0.01657
fixed	NA	sibling_count5	-0.05136	0.04155	-1.236	7548	0.2164	-0.168	0.06526
fixed	NA	sibling_count>5	-0.1992	0.04201	-4.74	8504	0.000002171	-0.3171	-0.08122
fixed	NA	birth_order_nonlinear2	-0.0004814	0.02252	-0.02137	9154	0.983	-0.06371	0.06275
fixed	NA	birth_order_nonlinear3	0.007394	0.02843	0.2601	9816	0.7948	-0.0724	0.08719
fixed	NA	birth_order_nonlinear4	-0.02942	0.03523	-0.835	10040	0.4037	-0.1283	0.06948
fixed	NA	birth_order_nonlinear5	-0.06717	0.04142	-1.622	10362	0.1049	-0.1834	0.0491
fixed	NA	birth_order_nonlinear>5	-0.05048	0.03943	-1.28	11825	0.2005	-0.1612	0.06021
ran_pars	mother_pidlink	sd__(Intercept)	0.51	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)	-2.913	0.1186	-24.56	11674	7.1e-130	-3.246	-2.58
fixed	NA	poly(age, 3, raw = TRUE)1	0.4217	0.02167	19.46	11712	5.229e-83	0.3609	0.4826
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01689	0.001254	-13.47	11803	4.996e-41	-0.0204	-0.01337
fixed	NA	poly(age, 3, raw = TRUE)3	0.000208	0.00002301	9.043	11813	1.755e-19	0.0001435	0.0002726
fixed	NA	male	0.04874	0.01655	2.945	10994	0.003232	0.002289	0.09519
fixed	NA	count_birth_order2/2	-0.004616	0.0367	-0.1258	9686	0.8999	-0.1076	0.09841
fixed	NA	count_birth_order1/3	-0.06756	0.03753	-1.8	11550	0.07182	-0.1729	0.03777
fixed	NA	count_birth_order2/3	-0.03873	0.03826	-1.012	11657	0.3115	-0.1461	0.06869
fixed	NA	count_birth_order3/3	0.02046	0.04332	0.4722	11790	0.6368	-0.1012	0.1421
fixed	NA	count_birth_order1/4	-0.06759	0.05129	-1.318	11816	0.1876	-0.2116	0.07639
fixed	NA	count_birth_order2/4	-0.04354	0.04874	-0.8935	11815	0.3716	-0.1803	0.09326
fixed	NA	count_birth_order3/4	-0.1544	0.04591	-3.362	11784	0.0007749	-0.2833	-0.0255
fixed	NA	count_birth_order4/4	-0.07384	0.05012	-1.473	11817	0.1406	-0.2145	0.06683
fixed	NA	count_birth_order1/5	0.0104	0.0696	0.1495	11533	0.8812	-0.185	0.2058
fixed	NA	count_birth_order2/5	-0.08665	0.06625	-1.308	11634	0.1909	-0.2726	0.09932
fixed	NA	count_birth_order3/5	-0.01868	0.06002	-0.3112	11768	0.7557	-0.1872	0.1498
fixed	NA	count_birth_order4/5	-0.1326	0.05643	-2.35	11815	0.01879	-0.291	0.02579
fixed	NA	count_birth_order5/5	-0.1062	0.05597	-1.897	11816	0.05781	-0.2633	0.05091
fixed	NA	count_birth_order1/>5	-0.1548	0.0697	-2.221	11101	0.0264	-0.3504	0.04088
fixed	NA	count_birth_order2/>5	-0.2376	0.06527	-3.64	11201	0.000274	-0.4208	-0.05436
fixed	NA	count_birth_order3/>5	-0.1763	0.0581	-3.035	11506	0.002412	-0.3394	-0.01323
fixed	NA	count_birth_order4/>5	-0.2312	0.05287	-4.372	11629	0.0000124	-0.3796	-0.08276
fixed	NA	count_birth_order5/>5	-0.2756	0.0475	-5.802	11774	0.00000000672	-0.4089	-0.1423
fixed	NA	count_birth_order>5/>5	-0.2508	0.03316	-7.564	10427	4.239e-14	-0.3439	-0.1577
ran_pars	mother_pidlink	sd__(Intercept)	0.5098	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)
11	31548	31629	-15763	31526	NA	NA	NA
12	31548	31636	-15762	31524	2.156	1	0.142
16	31554	31672	-15761	31522	2.168	4	0.705
26	31560	31752	-15754	31508	14.05	10	0.1707

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)	-3.135	0.1776	-17.65	6969	3.073e-68	-3.634	-2.637
fixed	NA	poly(age, 3, raw = TRUE)1	0.4673	0.03646	12.82	6899	3.477e-37	0.365	0.5696
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01963	0.00231	-8.494	6902	2.413e-17	-0.02611	-0.01314
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002649	0.0000455	5.821	6905	0.000000006115	0.0001371	0.0003926
fixed	NA	male	0.03061	0.01923	1.592	7906	0.1115	-0.02338	0.0846
fixed	NA	sibling_count3	-0.05946	0.02726	-2.182	5246	0.02919	-0.136	0.01705
fixed	NA	sibling_count4	-0.1194	0.03344	-3.571	4564	0.0003592	-0.2133	-0.02555
fixed	NA	sibling_count5	-0.2169	0.04292	-5.054	4129	0.0000004515	-0.3374	-0.09643
fixed	NA	sibling_count>5	-0.2597	0.03991	-6.508	4298	0.00000000008506	-0.3718	-0.1477
ran_pars	mother_pidlink	sd__(Intercept)	0.4912	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7717	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)	-3.103	0.1799	-17.25	7201	2.301e-65	-3.608	-2.598
fixed	NA	birth_order	-0.009805	0.008629	-1.136	8264	0.2559	-0.03403	0.01442
fixed	NA	poly(age, 3, raw = TRUE)1	0.4643	0.03656	12.7	6958	1.483e-36	0.3617	0.5669
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01948	0.002314	-8.417	6927	4.631e-17	-0.02597	-0.01298
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002623	0.00004557	5.756	6926	0.000000008997	0.0001344	0.0003902
fixed	NA	male	0.0307	0.01923	1.596	7907	0.1105	-0.02329	0.0847
fixed	NA	sibling_count3	-0.05286	0.02786	-1.897	5212	0.05782	-0.1311	0.02534
fixed	NA	sibling_count4	-0.1048	0.03583	-2.924	4584	0.003471	-0.2054	-0.004197
fixed	NA	sibling_count5	-0.1926	0.04793	-4.018	4318	0.0000596	-0.3271	-0.05806
fixed	NA	sibling_count>5	-0.2124	0.05769	-3.682	5150	0.0002337	-0.3744	-0.05049
ran_pars	mother_pidlink	sd__(Intercept)	0.4907	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7719	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)	-3.137	0.1795	-17.48	7152	5.132e-67	-3.64	-2.633
fixed	NA	poly(age, 3, raw = TRUE)1	0.4676	0.03657	12.79	6956	5.175e-37	0.3649	0.5703
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01965	0.002314	-8.493	6918	2.445e-17	-0.02615	-0.01316
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002655	0.00004556	5.826	6921	0.000000005938	0.0001375	0.0003934
fixed	NA	male	0.02997	0.01924	1.558	7903	0.1193	-0.02403	0.08397
fixed	NA	sibling_count3	-0.0652	0.02908	-2.242	5705	0.02498	-0.1468	0.01642
fixed	NA	sibling_count4	-0.1234	0.03863	-3.194	5346	0.001412	-0.2318	-0.01495
fixed	NA	sibling_count5	-0.1819	0.05257	-3.459	5238	0.0005461	-0.3294	-0.03428
fixed	NA	sibling_count>5	-0.2346	0.06227	-3.768	5989	0.0001662	-0.4094	-0.05983
fixed	NA	birth_order_nonlinear2	0.0033	0.02304	0.1432	6116	0.8861	-0.06137	0.06797
fixed	NA	birth_order_nonlinear3	0.0203	0.03226	0.6294	7022	0.5291	-0.07024	0.1108
fixed	NA	birth_order_nonlinear4	-0.002993	0.04418	-0.06775	7409	0.946	-0.127	0.121
fixed	NA	birth_order_nonlinear5	-0.1088	0.05943	-1.831	7381	0.06711	-0.2756	0.05799
fixed	NA	birth_order_nonlinear>5	-0.01069	0.06881	-0.1554	8447	0.8765	-0.2038	0.1825
ran_pars	mother_pidlink	sd__(Intercept)	0.4915	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7716	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)	-3.146	0.1802	-17.46	7170	7.311e-67	-3.652	-2.64
fixed	NA	poly(age, 3, raw = TRUE)1	0.4697	0.03664	12.82	6956	3.382e-37	0.3669	0.5726
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01981	0.002319	-8.545	6912	1.564e-17	-0.02632	-0.01331
fixed	NA	poly(age, 3, raw = TRUE)3	0.000269	0.00004566	5.891	6911	0.00000000402	0.0001408	0.0003972
fixed	NA	male	0.03042	0.01924	1.581	7884	0.1139	-0.02359	0.08443
fixed	NA	count_birth_order2/2	0.006774	0.03232	0.2096	6664	0.834	-0.08394	0.09749
fixed	NA	count_birth_order1/3	-0.08009	0.038	-2.108	8391	0.0351	-0.1868	0.02658
fixed	NA	count_birth_order2/3	-0.07185	0.03655	-1.966	8401	0.04936	-0.1745	0.03075
fixed	NA	count_birth_order3/3	-0.01001	0.04001	-0.2501	8438	0.8025	-0.1223	0.1023
fixed	NA	count_birth_order1/4	-0.04987	0.05992	-0.8323	8326	0.4052	-0.2181	0.1183
fixed	NA	count_birth_order2/4	-0.09864	0.05259	-1.876	8435	0.06075	-0.2463	0.04899
fixed	NA	count_birth_order3/4	-0.1871	0.05021	-3.726	8436	0.0001958	-0.328	-0.04614
fixed	NA	count_birth_order4/4	-0.1056	0.04973	-2.124	8446	0.03372	-0.2452	0.03398
fixed	NA	count_birth_order1/5	-0.2007	0.1043	-1.924	7369	0.05443	-0.4936	0.09218
fixed	NA	count_birth_order2/5	-0.146	0.09299	-1.57	7769	0.1164	-0.407	0.115
fixed	NA	count_birth_order3/5	-0.08258	0.07873	-1.049	8171	0.2943	-0.3036	0.1384
fixed	NA	count_birth_order4/5	-0.2497	0.06518	-3.83	8440	0.0001288	-0.4326	-0.0667
fixed	NA	count_birth_order5/5	-0.2776	0.06325	-4.388	8446	0.00001155	-0.4551	-0.1
fixed	NA	count_birth_order1/>5	-0.268	0.1333	-2.01	6843	0.04445	-0.6422	0.1062
fixed	NA	count_birth_order2/>5	-0.262	0.122	-2.148	6913	0.03172	-0.6044	0.08034
fixed	NA	count_birth_order3/>5	-0.2095	0.1009	-2.077	7561	0.03784	-0.4927	0.07364
fixed	NA	count_birth_order4/>5	-0.179	0.09054	-1.977	7764	0.04811	-0.4331	0.07518
fixed	NA	count_birth_order5/>5	-0.359	0.07278	-4.933	8225	0.0000008267	-0.5633	-0.1547
fixed	NA	count_birth_order>5/>5	-0.244	0.04847	-5.033	7297	0.0000004942	-0.38	-0.1079
ran_pars	mother_pidlink	sd__(Intercept)	0.4921	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7711	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)
11	22246	22323	-11112	22224	NA	NA	NA
12	22246	22331	-11111	22222	1.293	1	0.2554
16	22250	22363	-11109	22218	4.165	4	0.3842
26	22259	22442	-11103	22207	11.6	10	0.3129

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)	-3.141	0.177	-17.75	7058	5.705e-69	-3.638	-2.644
fixed	NA	poly(age, 3, raw = TRUE)1	0.4677	0.03633	12.87	6968	1.719e-37	0.3657	0.5697
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01973	0.002303	-8.564	6967	1.324e-17	-0.02619	-0.01326
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002666	0.00004538	5.876	6968	0.000000004403	0.0001393	0.000394
fixed	NA	male	0.02784	0.01915	1.454	7992	0.1461	-0.02592	0.0816
fixed	NA	sibling_count3	-0.04184	0.0286	-1.463	5531	0.1435	-0.1221	0.03843
fixed	NA	sibling_count4	-0.07294	0.03364	-2.168	4993	0.03018	-0.1674	0.02149
fixed	NA	sibling_count5	-0.08591	0.03944	-2.178	4612	0.02944	-0.1966	0.0248
fixed	NA	sibling_count>5	-0.1944	0.03514	-5.532	4639	0.00000003339	-0.2931	-0.09576
ran_pars	mother_pidlink	sd__(Intercept)	0.4946	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7717	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)	-3.082	0.1787	-17.25	7233	2.258e-65	-3.583	-2.58
fixed	NA	birth_order	-0.0174	0.007239	-2.404	8279	0.01625	-0.03772	0.002919
fixed	NA	poly(age, 3, raw = TRUE)1	0.4622	0.0364	12.7	7010	1.553e-36	0.36	0.5644
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01947	0.002306	-8.443	6984	3.712e-17	-0.02594	-0.013
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002621	0.00004541	5.772	6983	0.000000008185	0.0001346	0.0003896
fixed	NA	male	0.02841	0.01915	1.484	7995	0.1379	-0.02534	0.08217
fixed	NA	sibling_count3	-0.03073	0.02895	-1.062	5517	0.2884	-0.112	0.05053
fixed	NA	sibling_count4	-0.04801	0.03518	-1.364	4998	0.1725	-0.1468	0.05075
fixed	NA	sibling_count5	-0.04672	0.04264	-1.096	4706	0.2733	-0.1664	0.07298
fixed	NA	sibling_count>5	-0.1149	0.04825	-2.381	5317	0.01728	-0.2503	0.02053
ran_pars	mother_pidlink	sd__(Intercept)	0.4935	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.772	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)	-3.112	0.1786	-17.42	7207	1.296e-66	-3.613	-2.61
fixed	NA	poly(age, 3, raw = TRUE)1	0.4643	0.03643	12.75	7008	8.484e-37	0.362	0.5665
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01959	0.002306	-8.495	6975	2.4e-17	-0.02607	-0.01312
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002645	0.00004542	5.823	6976	0.000000006049	0.000137	0.000392
fixed	NA	male	0.0276	0.01915	1.441	7990	0.1496	-0.02617	0.08137
fixed	NA	sibling_count3	-0.03796	0.0301	-1.261	5961	0.2073	-0.1225	0.04653
fixed	NA	sibling_count4	-0.05896	0.03796	-1.553	5744	0.1204	-0.1655	0.04758
fixed	NA	sibling_count5	-0.03642	0.0465	-0.7831	5574	0.4336	-0.1669	0.09412
fixed	NA	sibling_count>5	-0.1248	0.05121	-2.436	6161	0.01487	-0.2685	0.01899
fixed	NA	birth_order_nonlinear2	-0.01198	0.02373	-0.5048	6214	0.6137	-0.07858	0.05462
fixed	NA	birth_order_nonlinear3	-0.00978	0.03163	-0.3092	7225	0.7572	-0.09856	0.079
fixed	NA	birth_order_nonlinear4	-0.03695	0.04151	-0.8903	7595	0.3734	-0.1535	0.07956
fixed	NA	birth_order_nonlinear5	-0.132	0.05216	-2.532	7529	0.01138	-0.2784	0.01437
fixed	NA	birth_order_nonlinear>5	-0.08421	0.05662	-1.487	8540	0.137	-0.2431	0.07472
ran_pars	mother_pidlink	sd__(Intercept)	0.4944	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7717	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)	-3.121	0.1796	-17.38	7231	2.423e-66	-3.625	-2.617
fixed	NA	poly(age, 3, raw = TRUE)1	0.467	0.03649	12.8	7014	4.397e-37	0.3646	0.5694
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0198	0.00231	-8.57	6970	1.262e-17	-0.02628	-0.01331
fixed	NA	poly(age, 3, raw = TRUE)3	0.000269	0.00004549	5.914	6965	0.000000003502	0.0001413	0.0003967
fixed	NA	male	0.02854	0.01916	1.489	7974	0.1364	-0.02525	0.08233
fixed	NA	count_birth_order2/2	-0.01543	0.03533	-0.4366	6716	0.6624	-0.1146	0.08375
fixed	NA	count_birth_order1/3	-0.06278	0.03938	-1.594	8494	0.1109	-0.1733	0.04776
fixed	NA	count_birth_order2/3	-0.05192	0.03852	-1.348	8511	0.1777	-0.16	0.0562
fixed	NA	count_birth_order3/3	-0.0183	0.04222	-0.4335	8538	0.6647	-0.1368	0.1002
fixed	NA	count_birth_order1/4	-0.05623	0.05864	-0.9588	8481	0.3377	-0.2208	0.1084
fixed	NA	count_birth_order2/4	-0.0529	0.05265	-1.005	8530	0.3151	-0.2007	0.0949
fixed	NA	count_birth_order3/4	-0.1333	0.0504	-2.644	8539	0.008209	-0.2747	0.008219
fixed	NA	count_birth_order4/4	-0.05557	0.05097	-1.09	8548	0.2756	-0.1987	0.08751
fixed	NA	count_birth_order1/5	0.07905	0.08526	0.9271	7943	0.3539	-0.1603	0.3184
fixed	NA	count_birth_order2/5	-0.03706	0.07632	-0.4856	8242	0.6273	-0.2513	0.1772
fixed	NA	count_birth_order3/5	-0.03526	0.06854	-0.5144	8385	0.607	-0.2277	0.1571
fixed	NA	count_birth_order4/5	-0.1447	0.06314	-2.291	8484	0.02196	-0.3219	0.03255
fixed	NA	count_birth_order5/5	-0.1711	0.06082	-2.813	8548	0.004927	-0.3418	-0.0003337
fixed	NA	count_birth_order1/>5	-0.1041	0.09126	-1.14	7671	0.2542	-0.3603	0.1521
fixed	NA	count_birth_order2/>5	-0.2198	0.1014	-2.167	7149	0.03023	-0.5043	0.06484
fixed	NA	count_birth_order3/>5	-0.1055	0.07852	-1.344	7935	0.1789	-0.3259	0.1149
fixed	NA	count_birth_order4/>5	-0.1646	0.07207	-2.283	8091	0.02243	-0.3669	0.03774
fixed	NA	count_birth_order5/>5	-0.2587	0.06275	-4.123	8328	0.00003776	-0.4349	-0.08258
fixed	NA	count_birth_order>5/>5	-0.2101	0.04393	-4.782	7699	0.000001765	-0.3334	-0.08677
ran_pars	mother_pidlink	sd__(Intercept)	0.4947	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7716	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)
11	22545	22623	-11262	22523	NA	NA	NA
12	22542	22626	-11259	22518	5.783	1	0.01618
16	22548	22661	-11258	22516	1.276	4	0.8654
26	22558	22742	-11253	22506	9.852	10	0.4535

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)	-3.112	0.1791	-17.38	6789	3.385e-66	-3.615	-2.609
fixed	NA	poly(age, 3, raw = TRUE)1	0.4625	0.03675	12.58	6728	6.582e-36	0.3593	0.5656
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0194	0.002327	-8.337	6734	9.142e-17	-0.02594	-0.01287
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002614	0.00004581	5.706	6739	0.00000001203	0.0001328	0.00039
fixed	NA	male	0.03031	0.01944	1.559	7696	0.1189	-0.02425	0.08487
fixed	NA	sibling_count3	-0.04685	0.02732	-1.715	5100	0.08647	-0.1235	0.02984
fixed	NA	sibling_count4	-0.09949	0.0338	-2.944	4416	0.003262	-0.1944	-0.004613
fixed	NA	sibling_count5	-0.2019	0.04473	-4.514	4008	0.000006538	-0.3275	-0.07636
fixed	NA	sibling_count>5	-0.2519	0.04129	-6.1	4167	0.000000001156	-0.3678	-0.136
ran_pars	mother_pidlink	sd__(Intercept)	0.4914	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7689	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)	-3.086	0.1816	-17	7021	1.622e-63	-3.596	-2.577
fixed	NA	birth_order	-0.00767	0.008849	-0.8668	8133	0.3861	-0.03251	0.01717
fixed	NA	poly(age, 3, raw = TRUE)1	0.46	0.03687	12.48	6788	2.442e-35	0.3565	0.5634
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01928	0.002332	-8.267	6760	1.636e-16	-0.02583	-0.01273
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002592	0.00004589	5.648	6760	0.00000001688	0.0001304	0.000388
fixed	NA	male	0.03038	0.01944	1.563	7697	0.1181	-0.02418	0.08494
fixed	NA	sibling_count3	-0.04173	0.02795	-1.493	5076	0.1354	-0.1202	0.03671
fixed	NA	sibling_count4	-0.08812	0.03625	-2.431	4466	0.01511	-0.1899	0.01365
fixed	NA	sibling_count5	-0.1833	0.04961	-3.695	4215	0.0002223	-0.3226	-0.04407
fixed	NA	sibling_count>5	-0.2153	0.05902	-3.649	5066	0.0002662	-0.381	-0.04967
ran_pars	mother_pidlink	sd__(Intercept)	0.4911	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7691	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)	-3.115	0.181	-17.21	6973	5.081e-65	-3.623	-2.607
fixed	NA	poly(age, 3, raw = TRUE)1	0.4631	0.03688	12.56	6789	9.093e-36	0.3596	0.5667
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01947	0.002332	-8.347	6757	8.441e-17	-0.02601	-0.01292
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002629	0.00004589	5.729	6764	0.00000001057	0.0001341	0.0003917
fixed	NA	male	0.03004	0.01944	1.545	7692	0.1223	-0.02452	0.08461
fixed	NA	sibling_count3	-0.04791	0.02914	-1.644	5555	0.1002	-0.1297	0.0339
fixed	NA	sibling_count4	-0.102	0.03901	-2.615	5218	0.008942	-0.2115	0.007483
fixed	NA	sibling_count5	-0.1672	0.05419	-3.085	5048	0.002047	-0.3193	-0.01506
fixed	NA	sibling_count>5	-0.2479	0.06378	-3.887	5853	0.0001026	-0.427	-0.06888
fixed	NA	birth_order_nonlinear2	0.003997	0.02302	0.1737	5944	0.8621	-0.06062	0.06861
fixed	NA	birth_order_nonlinear3	0.003994	0.03243	0.1232	6780	0.902	-0.08704	0.09503
fixed	NA	birth_order_nonlinear4	0.006891	0.04507	0.1529	7110	0.8785	-0.1196	0.1334
fixed	NA	birth_order_nonlinear5	-0.1106	0.06204	-1.782	7190	0.07473	-0.2847	0.06357
fixed	NA	birth_order_nonlinear>5	0.02731	0.07101	0.3846	8210	0.7005	-0.172	0.2266
ran_pars	mother_pidlink	sd__(Intercept)	0.4917	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7688	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)	-3.121	0.1818	-17.17	6983	8.982e-65	-3.632	-2.611
fixed	NA	poly(age, 3, raw = TRUE)1	0.4648	0.03695	12.58	6782	6.807e-36	0.3611	0.5685
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01959	0.002337	-8.384	6743	6.16e-17	-0.02615	-0.01303
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002656	0.00004598	5.776	6745	0.000000007998	0.0001365	0.0003946
fixed	NA	male	0.03075	0.01944	1.582	7672	0.1137	-0.02382	0.08532
fixed	NA	count_birth_order2/2	0.001768	0.03197	0.0553	6418	0.9559	-0.08796	0.0915
fixed	NA	count_birth_order1/3	-0.06413	0.03815	-1.681	8172	0.09279	-0.1712	0.04296
fixed	NA	count_birth_order2/3	-0.05242	0.03664	-1.431	8180	0.1526	-0.1553	0.05044
fixed	NA	count_birth_order3/3	-0.0167	0.04017	-0.4156	8217	0.6777	-0.1295	0.09606
fixed	NA	count_birth_order1/4	-0.0457	0.06025	-0.7585	8115	0.4481	-0.2148	0.1234
fixed	NA	count_birth_order2/4	-0.07186	0.05325	-1.349	8208	0.1772	-0.2213	0.07762
fixed	NA	count_birth_order3/4	-0.1843	0.05056	-3.645	8213	0.0002691	-0.3262	-0.04236
fixed	NA	count_birth_order4/4	-0.07292	0.05041	-1.447	8224	0.148	-0.2144	0.06857
fixed	NA	count_birth_order1/5	-0.1909	0.1042	-1.832	7330	0.06699	-0.4835	0.1016
fixed	NA	count_birth_order2/5	-0.1379	0.09972	-1.383	7456	0.1667	-0.4178	0.142
fixed	NA	count_birth_order3/5	-0.07514	0.0808	-0.9299	8008	0.3524	-0.302	0.1517
fixed	NA	count_birth_order4/5	-0.2494	0.06853	-3.639	8214	0.0002757	-0.4417	-0.05699
fixed	NA	count_birth_order5/5	-0.2528	0.06699	-3.774	8224	0.0001619	-0.4409	-0.06477
fixed	NA	count_birth_order1/>5	-0.2926	0.1343	-2.179	6611	0.02934	-0.6695	0.08428
fixed	NA	count_birth_order2/>5	-0.2989	0.1239	-2.412	6839	0.01588	-0.6467	0.04891
fixed	NA	count_birth_order3/>5	-0.2104	0.1014	-2.076	7472	0.03795	-0.495	0.07413
fixed	NA	count_birth_order4/>5	-0.1581	0.09617	-1.644	7459	0.1001	-0.4281	0.1118
fixed	NA	count_birth_order5/>5	-0.3945	0.07643	-5.161	7979	0.0000002513	-0.609	-0.1799
fixed	NA	count_birth_order>5/>5	-0.2215	0.05033	-4.401	7128	0.00001093	-0.3628	-0.08024
ran_pars	mother_pidlink	sd__(Intercept)	0.4926	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7681	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)
11	21616	21693	-10797	21594	NA	NA	NA
12	21617	21701	-10796	21593	0.753	1	0.3855
16	21620	21732	-10794	21588	4.805	4	0.3079
26	21627	21810	-10788	21575	12.77	10	0.2369

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)	-2.466	0.1215	-20.3	11620	4.621e-90	-2.807	-2.125
fixed	NA	poly(age, 3, raw = TRUE)1	0.4048	0.02252	17.97	11708	2.803e-71	0.3416	0.468
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01815	0.001303	-13.93	11808	8.797e-44	-0.02181	-0.0145
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002515	0.00002388	10.53	11832	8.169e-26	0.0001845	0.0003185
fixed	NA	male	-0.1617	0.01737	-9.306	11421	1.566e-20	-0.2104	-0.1129
fixed	NA	sibling_count3	-0.003588	0.02894	-0.124	7959	0.9013	-0.08483	0.07765
fixed	NA	sibling_count4	-0.08819	0.03232	-2.729	7151	0.00637	-0.1789	0.002524
fixed	NA	sibling_count5	-0.04881	0.0364	-1.341	6386	0.18	-0.151	0.05337
fixed	NA	sibling_count>5	-0.2076	0.02899	-7.16	7116	8.847e-13	-0.2889	-0.1262
ran_pars	mother_pidlink	sd__(Intercept)	0.4412	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.857	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)	-2.454	0.1219	-20.14	11640	1.067e-88	-2.796	-2.112
fixed	NA	birth_order	-0.00565	0.004521	-1.25	9229	0.2115	-0.01834	0.007042
fixed	NA	poly(age, 3, raw = TRUE)1	0.4044	0.02252	17.95	11706	4.06e-71	0.3411	0.4676
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01814	0.001303	-13.93	11806	9.745e-44	-0.0218	-0.01449
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002512	0.00002388	10.52	11831	9.269e-26	0.0001842	0.0003183
fixed	NA	male	-0.1616	0.01737	-9.302	11421	1.629e-20	-0.2104	-0.1128
fixed	NA	sibling_count3	-0.000338	0.02905	-0.01163	7928	0.9907	-0.08189	0.08122
fixed	NA	sibling_count4	-0.08042	0.0329	-2.444	7013	0.01454	-0.1728	0.01194
fixed	NA	sibling_count5	-0.03629	0.03775	-0.9613	6187	0.3365	-0.1423	0.06968
fixed	NA	sibling_count>5	-0.1764	0.03825	-4.612	6410	0.00000406	-0.2838	-0.06904
ran_pars	mother_pidlink	sd__(Intercept)	0.4408	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8571	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)	-2.481	0.1229	-20.18	11694	5.025e-89	-2.826	-2.135
fixed	NA	poly(age, 3, raw = TRUE)1	0.4066	0.02259	18	11728	1.712e-71	0.3432	0.47
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01824	0.001304	-13.98	11807	4.62e-44	-0.0219	-0.01457
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002523	0.00002389	10.56	11827	5.96e-26	0.0001853	0.0003194
fixed	NA	male	-0.1618	0.01737	-9.315	11416	1.447e-20	-0.2106	-0.113
fixed	NA	sibling_count3	-0.01878	0.03001	-0.6259	8433	0.5314	-0.103	0.06545
fixed	NA	sibling_count4	-0.09841	0.03565	-2.76	8109	0.005791	-0.1985	0.001673
fixed	NA	sibling_count5	-0.04989	0.04188	-1.191	7489	0.2335	-0.1674	0.06766
fixed	NA	sibling_count>5	-0.1826	0.04255	-4.29	8265	0.00001806	-0.302	-0.06311
fixed	NA	birth_order_nonlinear2	0.01111	0.02393	0.4642	9512	0.6425	-0.05606	0.07827
fixed	NA	birth_order_nonlinear3	0.06162	0.03008	2.048	10195	0.04056	-0.02283	0.1461
fixed	NA	birth_order_nonlinear4	-0.02853	0.03724	-0.7662	10438	0.4436	-0.1331	0.07599
fixed	NA	birth_order_nonlinear5	-0.008226	0.04369	-0.1883	10754	0.8507	-0.1309	0.1144
fixed	NA	birth_order_nonlinear>5	-0.03737	0.04097	-0.912	11786	0.3618	-0.1524	0.07764
ran_pars	mother_pidlink	sd__(Intercept)	0.4416	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8566	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)	-2.495	0.1239	-20.13	11707	1.24e-88	-2.843	-2.147
fixed	NA	poly(age, 3, raw = TRUE)1	0.4073	0.02263	18	11731	1.786e-71	0.3438	0.4709
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01828	0.001306	-13.99	11800	3.917e-44	-0.02194	-0.01461
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002531	0.00002392	10.58	11817	4.758e-26	0.000186	0.0003202
fixed	NA	male	-0.1617	0.01738	-9.306	11410	1.575e-20	-0.2105	-0.1129
fixed	NA	count_birth_order2/2	0.0442	0.0389	1.136	9894	0.256	-0.06501	0.1534
fixed	NA	count_birth_order1/3	0.003874	0.03882	0.09977	11677	0.9205	-0.1051	0.1129
fixed	NA	count_birth_order2/3	0.01011	0.03964	0.2552	11737	0.7986	-0.1012	0.1214
fixed	NA	count_birth_order3/3	0.02486	0.04499	0.5525	11805	0.5806	-0.1014	0.1512
fixed	NA	count_birth_order1/4	-0.09987	0.05334	-1.872	11816	0.06118	-0.2496	0.04986
fixed	NA	count_birth_order2/4	-0.08891	0.05068	-1.754	11817	0.07938	-0.2312	0.05334
fixed	NA	count_birth_order3/4	-0.031	0.04767	-0.6502	11803	0.5156	-0.1648	0.1028
fixed	NA	count_birth_order4/4	-0.0841	0.05214	-1.613	11816	0.1067	-0.2305	0.06225
fixed	NA	count_birth_order1/5	-0.03411	0.07281	-0.4685	11659	0.6394	-0.2385	0.1703
fixed	NA	count_birth_order2/5	-0.04574	0.06923	-0.6606	11708	0.5089	-0.2401	0.1486
fixed	NA	count_birth_order3/5	0.04814	0.06259	0.7691	11784	0.4418	-0.1276	0.2238
fixed	NA	count_birth_order4/5	-0.1116	0.05873	-1.9	11814	0.05743	-0.2765	0.05326
fixed	NA	count_birth_order5/5	-0.01722	0.05821	-0.2958	11817	0.7674	-0.1806	0.1462
fixed	NA	count_birth_order1/>5	-0.1167	0.07317	-1.595	11436	0.1107	-0.3221	0.08866
fixed	NA	count_birth_order2/>5	-0.2274	0.06847	-3.322	11490	0.0008975	-0.4196	-0.03524
fixed	NA	count_birth_order3/>5	-0.06418	0.06079	-1.056	11658	0.2911	-0.2348	0.1065
fixed	NA	count_birth_order4/>5	-0.1983	0.05525	-3.589	11720	0.0003331	-0.3534	-0.04321
fixed	NA	count_birth_order5/>5	-0.1984	0.04952	-4.007	11794	0.00006199	-0.3374	-0.0594
fixed	NA	count_birth_order>5/>5	-0.209	0.03399	-6.149	10554	0.0000000008089	-0.3044	-0.1136
ran_pars	mother_pidlink	sd__(Intercept)	0.4408	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8571	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)
11	32480	32561	-16229	32458	NA	NA	NA
12	32480	32569	-16228	32456	1.564	1	0.2111
16	32480	32598	-16224	32448	7.826	4	0.09815
26	32494	32686	-16221	32442	6.537	10	0.7683

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)	-3.104	0.1915	-16.21	7417	4.273e-58	-3.642	-2.567
fixed	NA	poly(age, 3, raw = TRUE)1	0.5371	0.03932	13.66	7380	5.565e-42	0.4268	0.6475
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02639	0.002491	-10.59	7396	4.852e-26	-0.03339	-0.0194
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004132	0.00004907	8.422	7408	4.397e-17	0.0002755	0.000551
fixed	NA	male	-0.1782	0.0206	-8.647	8178	6.295e-18	-0.236	-0.1203
fixed	NA	sibling_count3	-0.004614	0.02826	-0.1633	5422	0.8703	-0.08395	0.07472
fixed	NA	sibling_count4	-0.0559	0.03451	-1.62	4621	0.1054	-0.1528	0.04097
fixed	NA	sibling_count5	-0.1578	0.04412	-3.575	4100	0.0003541	-0.2816	-0.03389
fixed	NA	sibling_count>5	-0.2106	0.04109	-5.126	4237	0.0000003098	-0.3259	-0.09526
ran_pars	mother_pidlink	sd__(Intercept)	0.4467	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8555	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)	-3.11	0.1937	-16.06	7596	4.176e-57	-3.654	-2.567
fixed	NA	birth_order	0.001986	0.009122	0.2177	8089	0.8276	-0.02362	0.02759
fixed	NA	poly(age, 3, raw = TRUE)1	0.5377	0.03941	13.64	7423	6.926e-42	0.4271	0.6483
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02642	0.002495	-10.59	7414	5.039e-26	-0.03343	-0.01942
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004138	0.00004912	8.423	7423	4.379e-17	0.0002759	0.0005517
fixed	NA	male	-0.1782	0.0206	-8.647	8177	6.298e-18	-0.236	-0.1203
fixed	NA	sibling_count3	-0.005917	0.02889	-0.2048	5377	0.8377	-0.08702	0.07518
fixed	NA	sibling_count4	-0.05879	0.03699	-1.589	4607	0.112	-0.1626	0.04504
fixed	NA	sibling_count5	-0.1626	0.04936	-3.293	4248	0.0009976	-0.3011	-0.02401
fixed	NA	sibling_count>5	-0.22	0.05974	-3.683	4985	0.000233	-0.3877	-0.05233
ran_pars	mother_pidlink	sd__(Intercept)	0.4468	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)	-3.126	0.1933	-16.18	7553	6.955e-58	-3.669	-2.584
fixed	NA	poly(age, 3, raw = TRUE)1	0.5394	0.03943	13.68	7421	4.39e-42	0.4287	0.65
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02653	0.002495	-10.63	7407	3.295e-26	-0.03353	-0.01952
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004159	0.00004913	8.465	7420	3.048e-17	0.000278	0.0005538
fixed	NA	male	-0.1786	0.02061	-8.664	8175	5.425e-18	-0.2364	-0.1207
fixed	NA	sibling_count3	-0.00646	0.03024	-0.2136	5876	0.8309	-0.09135	0.07843
fixed	NA	sibling_count4	-0.05353	0.04007	-1.336	5368	0.1816	-0.166	0.05895
fixed	NA	sibling_count5	-0.1354	0.05447	-2.485	5132	0.01299	-0.2882	0.01755
fixed	NA	sibling_count>5	-0.2334	0.06479	-3.603	5696	0.0003171	-0.4153	-0.05158
fixed	NA	birth_order_nonlinear2	0.02891	0.02498	1.157	6415	0.2472	-0.04121	0.09903
fixed	NA	birth_order_nonlinear3	0.004704	0.03478	0.1352	7295	0.8924	-0.09294	0.1023
fixed	NA	birth_order_nonlinear4	-0.002522	0.04752	-0.05308	7690	0.9577	-0.1359	0.1309
fixed	NA	birth_order_nonlinear5	-0.04888	0.06391	-0.7648	7734	0.4444	-0.2283	0.1305
fixed	NA	birth_order_nonlinear>5	0.07078	0.07314	0.9677	8425	0.3332	-0.1345	0.2761
ran_pars	mother_pidlink	sd__(Intercept)	0.447	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8554	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)	-3.134	0.1942	-16.14	7569	1.232e-57	-3.679	-2.589
fixed	NA	poly(age, 3, raw = TRUE)1	0.5388	0.03953	13.63	7426	8.181e-42	0.4279	0.6498
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0265	0.002502	-10.59	7408	5.046e-26	-0.03352	-0.01947
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004153	0.00004926	8.43	7417	4.116e-17	0.000277	0.0005536
fixed	NA	male	-0.1777	0.02062	-8.619	8162	8.038e-18	-0.2356	-0.1199
fixed	NA	count_birth_order2/2	0.05606	0.03495	1.604	6889	0.1088	-0.04205	0.1542
fixed	NA	count_birth_order1/3	0.03115	0.04032	0.7725	8415	0.4398	-0.08204	0.1443
fixed	NA	count_birth_order2/3	0.02824	0.0388	0.7279	8425	0.4667	-0.08067	0.1372
fixed	NA	count_birth_order3/3	-0.01949	0.04253	-0.4582	8444	0.6468	-0.1389	0.09989
fixed	NA	count_birth_order1/4	-0.082	0.06396	-1.282	8381	0.1999	-0.2615	0.09755
fixed	NA	count_birth_order2/4	-0.06803	0.05601	-1.215	8439	0.2245	-0.2252	0.08919
fixed	NA	count_birth_order3/4	-0.009767	0.05347	-0.1827	8438	0.8551	-0.1599	0.1403
fixed	NA	count_birth_order4/4	-0.007113	0.05289	-0.1345	8447	0.893	-0.1556	0.1414
fixed	NA	count_birth_order1/5	-0.079	0.1123	-0.7037	7786	0.4816	-0.3941	0.2361
fixed	NA	count_birth_order2/5	-0.0711	0.09979	-0.7125	8036	0.4762	-0.3512	0.209
fixed	NA	count_birth_order3/5	-0.07822	0.08421	-0.9289	8281	0.353	-0.3146	0.1582
fixed	NA	count_birth_order4/5	-0.1583	0.0694	-2.281	8440	0.02256	-0.3531	0.03648
fixed	NA	count_birth_order5/5	-0.192	0.06727	-2.855	8447	0.00432	-0.3808	-0.003196
fixed	NA	count_birth_order1/>5	-0.1892	0.1439	-1.315	7433	0.1886	-0.593	0.2147
fixed	NA	count_birth_order2/>5	-0.1647	0.1316	-1.252	7474	0.2105	-0.5341	0.2046
fixed	NA	count_birth_order3/>5	-0.2041	0.1084	-1.883	7920	0.05978	-0.5083	0.1002
fixed	NA	count_birth_order4/>5	-0.3053	0.09716	-3.142	8039	0.001684	-0.578	-0.03255
fixed	NA	count_birth_order5/>5	-0.2496	0.07779	-3.208	8316	0.001341	-0.4679	-0.03121
fixed	NA	count_birth_order>5/>5	-0.1526	0.05088	-2.999	7313	0.00272	-0.2954	-0.009756
ran_pars	mother_pidlink	sd__(Intercept)	0.446	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8561	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)
11	23286	23364	-11632	23264	NA	NA	NA
12	23288	23373	-11632	23264	0.04718	1	0.828
16	23292	23405	-11630	23260	4.367	4	0.3586
26	23305	23489	-11627	23253	6.595	10	0.7631

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)	-3.094	0.1905	-16.24	7523	2.541e-58	-3.628	-2.559
fixed	NA	poly(age, 3, raw = TRUE)1	0.5341	0.03912	13.65	7470	6.124e-42	0.4243	0.6439
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02625	0.00248	-10.58	7484	5.384e-26	-0.03321	-0.01929
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004103	0.00004886	8.398	7495	5.374e-17	0.0002732	0.0005474
fixed	NA	male	-0.1813	0.02048	-8.849	8275	1.062e-18	-0.2388	-0.1238
fixed	NA	sibling_count3	0.01962	0.02964	0.6619	5744	0.5081	-0.06358	0.1028
fixed	NA	sibling_count4	-0.04539	0.03474	-1.307	5116	0.1914	-0.1429	0.05212
fixed	NA	sibling_count5	-0.05441	0.0406	-1.34	4649	0.1803	-0.1684	0.05956
fixed	NA	sibling_count>5	-0.1553	0.03618	-4.292	4658	0.00001809	-0.2569	-0.05372
ran_pars	mother_pidlink	sd__(Intercept)	0.4484	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8547	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)	-3.063	0.1921	-15.94	7656	2.648e-56	-3.602	-2.523
fixed	NA	birth_order	-0.009473	0.007631	-1.241	8058	0.2145	-0.03089	0.01195
fixed	NA	poly(age, 3, raw = TRUE)1	0.5313	0.03919	13.56	7501	2.249e-41	0.4213	0.6413
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02611	0.002483	-10.52	7496	1.084e-25	-0.03308	-0.01914
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004079	0.0000489	8.342	7505	8.62e-17	0.0002706	0.0005452
fixed	NA	male	-0.181	0.02048	-8.835	8275	1.203e-18	-0.2385	-0.1235
fixed	NA	sibling_count3	0.02553	0.03001	0.8508	5719	0.3949	-0.05871	0.1098
fixed	NA	sibling_count4	-0.0321	0.03634	-0.8832	5090	0.3772	-0.1341	0.06992
fixed	NA	sibling_count5	-0.03351	0.04394	-0.7625	4701	0.4458	-0.1569	0.08985
fixed	NA	sibling_count>5	-0.1126	0.04991	-2.256	5220	0.02408	-0.2527	0.02748
ran_pars	mother_pidlink	sd__(Intercept)	0.4477	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.855	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)	-3.096	0.192	-16.12	7629	1.584e-57	-3.635	-2.557
fixed	NA	poly(age, 3, raw = TRUE)1	0.5334	0.03921	13.61	7495	1.165e-41	0.4234	0.6435
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02621	0.002483	-10.56	7485	7.226e-26	-0.03318	-0.01924
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004093	0.00004889	8.372	7495	6.712e-17	0.0002721	0.0005466
fixed	NA	male	-0.1816	0.02048	-8.865	8270	9.264e-19	-0.2391	-0.1241
fixed	NA	sibling_count3	0.008918	0.03129	0.2851	6162	0.7756	-0.0789	0.09674
fixed	NA	sibling_count4	-0.04393	0.03939	-1.115	5828	0.2647	-0.1545	0.06662
fixed	NA	sibling_count5	-0.02658	0.04819	-0.5516	5560	0.5812	-0.1619	0.1087
fixed	NA	sibling_count>5	-0.1216	0.05324	-2.285	6031	0.02237	-0.2711	0.02781
fixed	NA	birth_order_nonlinear2	0.01922	0.02567	0.7485	6552	0.4542	-0.05285	0.09128
fixed	NA	birth_order_nonlinear3	0.03887	0.03402	1.143	7520	0.2532	-0.05662	0.1344
fixed	NA	birth_order_nonlinear4	-0.03314	0.04453	-0.7443	7873	0.4567	-0.1581	0.09186
fixed	NA	birth_order_nonlinear5	-0.07932	0.05598	-1.417	7851	0.1565	-0.2365	0.07781
fixed	NA	birth_order_nonlinear>5	-0.02667	0.06012	-0.4437	8550	0.6573	-0.1954	0.1421
ran_pars	mother_pidlink	sd__(Intercept)	0.449	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8544	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)	-3.101	0.193	-16.06	7645	3.947e-57	-3.642	-2.559
fixed	NA	poly(age, 3, raw = TRUE)1	0.5322	0.03927	13.55	7501	2.367e-41	0.422	0.6424
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02612	0.002487	-10.51	7484	1.232e-25	-0.0331	-0.01914
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004076	0.00004897	8.324	7489	1.005e-16	0.0002701	0.0005451
fixed	NA	male	-0.1814	0.02049	-8.852	8258	1.036e-18	-0.2389	-0.1239
fixed	NA	count_birth_order2/2	0.04505	0.03813	1.182	6967	0.2373	-0.06196	0.1521
fixed	NA	count_birth_order1/3	0.05846	0.0417	1.402	8520	0.161	-0.0586	0.1755
fixed	NA	count_birth_order2/3	0.03561	0.0408	0.8727	8530	0.3828	-0.07892	0.1501
fixed	NA	count_birth_order3/3	0.009352	0.04477	0.2089	8544	0.8345	-0.1163	0.135
fixed	NA	count_birth_order1/4	-0.1275	0.0624	-2.043	8513	0.04111	-0.3026	0.04769
fixed	NA	count_birth_order2/4	-0.05352	0.05596	-0.9563	8537	0.3389	-0.2106	0.1036
fixed	NA	count_birth_order3/4	0.04619	0.05355	0.8626	8542	0.3884	-0.1041	0.1965
fixed	NA	count_birth_order4/4	-0.01379	0.05409	-0.2549	8549	0.7988	-0.1656	0.138
fixed	NA	count_birth_order1/5	0.04611	0.09122	0.5055	8195	0.6132	-0.21	0.3022
fixed	NA	count_birth_order2/5	-0.02527	0.08146	-0.3102	8369	0.7564	-0.2539	0.2034
fixed	NA	count_birth_order3/5	0.07466	0.07305	1.022	8450	0.3068	-0.1304	0.2797
fixed	NA	count_birth_order4/5	-0.09296	0.06719	-1.384	8507	0.1665	-0.2816	0.09564
fixed	NA	count_birth_order5/5	-0.108	0.06459	-1.672	8547	0.09456	-0.2893	0.07331
fixed	NA	count_birth_order1/>5	-0.1115	0.09781	-1.14	8043	0.2542	-0.3861	0.163
fixed	NA	count_birth_order2/>5	-0.04052	0.109	-0.3718	7682	0.7101	-0.3465	0.2655
fixed	NA	count_birth_order3/>5	-0.05131	0.08401	-0.6108	8194	0.5413	-0.2871	0.1845
fixed	NA	count_birth_order4/>5	-0.2026	0.07702	-2.63	8284	0.008547	-0.4188	0.01361
fixed	NA	count_birth_order5/>5	-0.1804	0.06692	-2.697	8418	0.007021	-0.3683	0.007396
fixed	NA	count_birth_order>5/>5	-0.139	0.04611	-3.015	7713	0.002581	-0.2685	-0.009577
ran_pars	mother_pidlink	sd__(Intercept)	0.4485	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8545	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)
11	23568	23646	-11773	23546	NA	NA	NA
12	23568	23653	-11772	23544	1.543	1	0.2141
16	23572	23685	-11770	23540	4.59	4	0.332
26	23580	23763	-11764	23528	12.22	10	0.2709

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)	-3.076	0.1931	-15.93	7213	3.423e-56	-3.619	-2.534
fixed	NA	poly(age, 3, raw = TRUE)1	0.5318	0.03963	13.42	7180	1.442e-40	0.4206	0.6431
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02602	0.00251	-10.37	7198	5.199e-25	-0.03307	-0.01898
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004051	0.0000494	8.201	7210	2.792e-16	0.0002665	0.0005438
fixed	NA	male	-0.1757	0.02083	-8.438	7953	3.797e-17	-0.2342	-0.1173
fixed	NA	sibling_count3	-0.01308	0.02837	-0.461	5265	0.6448	-0.09271	0.06655
fixed	NA	sibling_count4	-0.05899	0.03492	-1.689	4471	0.09122	-0.157	0.03903
fixed	NA	sibling_count5	-0.1589	0.04606	-3.449	3979	0.0005685	-0.2882	-0.02957
fixed	NA	sibling_count>5	-0.2128	0.04257	-4.998	4119	0.0000006033	-0.3322	-0.09326
ran_pars	mother_pidlink	sd__(Intercept)	0.4509	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8514	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)	-3.092	0.1955	-15.81	7393	2.017e-55	-3.64	-2.543
fixed	NA	birth_order	0.00463	0.009373	0.494	8010	0.6213	-0.02168	0.03094
fixed	NA	poly(age, 3, raw = TRUE)1	0.5333	0.03974	13.42	7227	1.437e-40	0.4217	0.6448
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02609	0.002514	-10.38	7218	4.644e-25	-0.03315	-0.01904
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004064	0.00004947	8.216	7226	2.476e-16	0.0002676	0.0005453
fixed	NA	male	-0.1758	0.02083	-8.439	7952	3.774e-17	-0.2342	-0.1173
fixed	NA	sibling_count3	-0.01609	0.02902	-0.5545	5232	0.5793	-0.09754	0.06536
fixed	NA	sibling_count4	-0.0657	0.03747	-1.753	4494	0.07961	-0.1709	0.03949
fixed	NA	sibling_count5	-0.1699	0.05117	-3.32	4154	0.0009083	-0.3135	-0.02624
fixed	NA	sibling_count>5	-0.2345	0.06122	-3.83	4925	0.0001297	-0.4063	-0.06263
ran_pars	mother_pidlink	sd__(Intercept)	0.451	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8514	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)	-3.104	0.195	-15.92	7354	4.046e-56	-3.652	-2.557
fixed	NA	poly(age, 3, raw = TRUE)1	0.535	0.03977	13.45	7229	9.088e-41	0.4234	0.6467
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0262	0.002515	-10.42	7218	3.192e-25	-0.03326	-0.01914
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004084	0.00004949	8.251	7233	1.85e-16	0.0002694	0.0005473
fixed	NA	male	-0.1762	0.02083	-8.455	7950	3.277e-17	-0.2346	-0.1177
fixed	NA	sibling_count3	-0.01488	0.03034	-0.4904	5716	0.6239	-0.1001	0.07029
fixed	NA	sibling_count4	-0.06779	0.04052	-1.673	5244	0.09435	-0.1815	0.04594
fixed	NA	sibling_count5	-0.1548	0.05619	-2.754	4945	0.005902	-0.3125	0.002959
fixed	NA	sibling_count>5	-0.2456	0.06644	-3.696	5579	0.0002211	-0.4321	-0.05907
fixed	NA	birth_order_nonlinear2	0.02627	0.02496	1.052	6231	0.2926	-0.0438	0.09634
fixed	NA	birth_order_nonlinear3	0.003957	0.03499	0.1131	7046	0.91	-0.09427	0.1022
fixed	NA	birth_order_nonlinear4	0.03323	0.04852	0.6848	7395	0.4935	-0.103	0.1694
fixed	NA	birth_order_nonlinear5	-0.02669	0.06674	-0.3999	7529	0.6892	-0.214	0.1607
fixed	NA	birth_order_nonlinear>5	0.07335	0.07557	0.9707	8221	0.3317	-0.1388	0.2855
ran_pars	mother_pidlink	sd__(Intercept)	0.4505	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8517	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)	-3.108	0.1959	-15.87	7368	8.98e-56	-3.658	-2.558
fixed	NA	poly(age, 3, raw = TRUE)1	0.5337	0.03987	13.39	7233	2.135e-40	0.4218	0.6456
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02612	0.002521	-10.36	7218	5.6e-25	-0.0332	-0.01905
fixed	NA	poly(age, 3, raw = TRUE)3	0.0004071	0.00004962	8.205	7228	2.71e-16	0.0002678	0.0005464
fixed	NA	male	-0.1755	0.02085	-8.42	7940	4.413e-17	-0.234	-0.117
fixed	NA	count_birth_order2/2	0.05598	0.0346	1.618	6647	0.1057	-0.04113	0.1531
fixed	NA	count_birth_order1/3	0.0261	0.04051	0.6443	8194	0.5194	-0.08761	0.1398
fixed	NA	count_birth_order2/3	0.01806	0.03892	0.464	8202	0.6427	-0.09119	0.1273
fixed	NA	count_birth_order3/3	-0.02986	0.04272	-0.6989	8222	0.4846	-0.1498	0.09006
fixed	NA	count_birth_order1/4	-0.09554	0.06434	-1.485	8164	0.1376	-0.2761	0.08506
fixed	NA	count_birth_order2/4	-0.0866	0.05675	-1.526	8214	0.1271	-0.2459	0.0727
fixed	NA	count_birth_order3/4	-0.0142	0.05387	-0.2637	8215	0.792	-0.1654	0.137
fixed	NA	count_birth_order4/4	0.009754	0.05365	0.1818	8224	0.8557	-0.1408	0.1604
fixed	NA	count_birth_order1/5	-0.05029	0.1121	-0.4487	7670	0.6537	-0.3649	0.2643
fixed	NA	count_birth_order2/5	-0.1172	0.1071	-1.094	7742	0.2739	-0.418	0.1835
fixed	NA	count_birth_order3/5	-0.1053	0.08641	-1.218	8091	0.2231	-0.3479	0.1373
fixed	NA	count_birth_order4/5	-0.123	0.07302	-1.685	8215	0.0921	-0.328	0.08196
fixed	NA	count_birth_order5/5	-0.2081	0.0713	-2.919	8224	0.003519	-0.4083	-0.007998
fixed	NA	count_birth_order1/>5	-0.2608	0.145	-1.799	7182	0.07205	-0.6678	0.1461
fixed	NA	count_birth_order2/>5	-0.1588	0.1336	-1.188	7341	0.2347	-0.5339	0.2163
fixed	NA	count_birth_order3/>5	-0.2241	0.1089	-2.058	7773	0.03964	-0.5298	0.08158
fixed	NA	count_birth_order4/>5	-0.3077	0.1033	-2.979	7755	0.002905	-0.5977	-0.01772
fixed	NA	count_birth_order5/>5	-0.2128	0.08176	-2.602	8076	0.00928	-0.4423	0.01675
fixed	NA	count_birth_order>5/>5	-0.1609	0.05288	-3.043	7148	0.002353	-0.3094	-0.01246
ran_pars	mother_pidlink	sd__(Intercept)	0.4492	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8523	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)
11	22637	22714	-11307	22615	NA	NA	NA
12	22638	22723	-11307	22614	0.2439	1	0.6214
16	22643	22756	-11306	22611	3.053	4	0.549
26	22655	22837	-11302	22603	8.409	10	0.5889

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)	-0.5158	0.1653	-3.12	13453	0.001811	-0.9798	-0.05176
fixed	NA	poly(age, 3, raw = TRUE)1	0.06972	0.01599	4.359	13347	0.00001318	0.02482	0.1146
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002356	0.0004765	-4.944	13137	0.0000007756	-0.003693	-0.001018
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002179	0.000004446	4.9	12884	0.0000009705	0.000009305	0.00003427
fixed	NA	male	0.04321	0.01663	2.599	13172	0.009371	-0.003466	0.08989
fixed	NA	sibling_count3	0.002307	0.03444	0.06697	9806	0.9466	-0.09438	0.09899
fixed	NA	sibling_count4	0.03135	0.03566	0.8792	9020	0.3793	-0.06874	0.1314
fixed	NA	sibling_count5	0.0143	0.03708	0.3855	8214	0.6999	-0.0898	0.1184
fixed	NA	sibling_count>5	-0.1004	0.0291	-3.449	9139	0.0005653	-0.1821	-0.01868
ran_pars	mother_pidlink	sd__(Intercept)	0.4186	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8969	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)	-0.521	0.1653	-3.152	13453	0.001623	-0.985	-0.05707
fixed	NA	birth_order	-0.007541	0.003559	-2.119	13003	0.0341	-0.01753	0.002448
fixed	NA	poly(age, 3, raw = TRUE)1	0.07236	0.01604	4.511	13322	0.000006498	0.02734	0.1174
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002453	0.0004786	-5.125	13056	0.0000003019	-0.003796	-0.001109
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000227	0.000004466	5.083	12770	0.0000003776	0.00001016	0.00003523
fixed	NA	male	0.04349	0.01663	2.615	13175	0.00893	-0.003192	0.09016
fixed	NA	sibling_count3	0.00394	0.03443	0.1144	9820	0.9089	-0.09272	0.1006
fixed	NA	sibling_count4	0.03655	0.03572	1.023	9082	0.3062	-0.06372	0.1368
fixed	NA	sibling_count5	0.0234	0.03731	0.6272	8326	0.5305	-0.08132	0.1281
fixed	NA	sibling_count>5	-0.07194	0.03204	-2.246	10244	0.02475	-0.1619	0.01799
ran_pars	mother_pidlink	sd__(Intercept)	0.4172	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8973	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)	-0.5287	0.1657	-3.19	13447	0.001427	-0.994	-0.06345
fixed	NA	poly(age, 3, raw = TRUE)1	0.07327	0.01604	4.567	13329	0.000004985	0.02824	0.1183
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002467	0.0004786	-5.154	13064	0.0000002584	-0.003811	-0.001123
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002265	0.000004468	5.069	12764	0.0000004065	0.0000101	0.00003519
fixed	NA	male	0.04386	0.01662	2.638	13164	0.008342	-0.002805	0.09052
fixed	NA	sibling_count3	0.0181	0.03489	0.5187	10123	0.604	-0.07984	0.116
fixed	NA	sibling_count4	0.05936	0.03668	1.618	9717	0.1056	-0.0436	0.1623
fixed	NA	sibling_count5	0.05141	0.03865	1.33	9147	0.1835	-0.05708	0.1599
fixed	NA	sibling_count>5	-0.04218	0.03354	-1.258	11185	0.2086	-0.1363	0.05197
fixed	NA	birth_order_nonlinear2	-0.03426	0.02401	-1.427	12248	0.1537	-0.1017	0.03314
fixed	NA	birth_order_nonlinear3	-0.08943	0.02829	-3.162	11909	0.001573	-0.1688	-0.01003
fixed	NA	birth_order_nonlinear4	-0.08064	0.03218	-2.506	11938	0.01223	-0.171	0.009694
fixed	NA	birth_order_nonlinear5	-0.08633	0.03661	-2.358	11926	0.01837	-0.1891	0.01642
fixed	NA	birth_order_nonlinear>5	-0.09508	0.03072	-3.095	13503	0.001974	-0.1813	-0.008838
ran_pars	mother_pidlink	sd__(Intercept)	0.4188	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8965	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)	-0.5266	0.1665	-3.163	13433	0.001562	-0.9939	-0.05933
fixed	NA	poly(age, 3, raw = TRUE)1	0.07317	0.01605	4.56	13313	0.000005162	0.02813	0.1182
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002458	0.0004789	-5.132	13037	0.00000029	-0.003802	-0.001114
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002251	0.000004471	5.034	12723	0.0000004873	0.000009957	0.00003506
fixed	NA	male	0.04425	0.01663	2.661	13153	0.007799	-0.002427	0.09092
fixed	NA	count_birth_order2/2	-0.04338	0.04687	-0.9254	12433	0.3548	-0.175	0.0882
fixed	NA	count_birth_order1/3	0.03772	0.04498	0.8386	13309	0.4017	-0.08854	0.164
fixed	NA	count_birth_order2/3	-0.0197	0.05012	-0.393	13454	0.6943	-0.1604	0.121
fixed	NA	count_birth_order3/3	-0.1232	0.05612	-2.195	13559	0.02821	-0.2807	0.03437
fixed	NA	count_birth_order1/4	0.0815	0.05147	1.583	13460	0.1134	-0.06298	0.226
fixed	NA	count_birth_order2/4	0.005026	0.05402	0.09305	13510	0.9259	-0.1466	0.1567
fixed	NA	count_birth_order3/4	-0.06449	0.05836	-1.105	13578	0.2692	-0.2283	0.09933
fixed	NA	count_birth_order4/4	-0.009001	0.06157	-0.1462	13598	0.8838	-0.1818	0.1638
fixed	NA	count_birth_order1/5	-0.0384	0.05782	-0.6642	13554	0.5066	-0.2007	0.1239
fixed	NA	count_birth_order2/5	0.06285	0.06083	1.033	13587	0.3015	-0.1079	0.2336
fixed	NA	count_birth_order3/5	0.03161	0.06263	0.5048	13600	0.6137	-0.1442	0.2074
fixed	NA	count_birth_order4/5	-0.05632	0.06619	-0.851	13605	0.3948	-0.2421	0.1295
fixed	NA	count_birth_order5/5	-0.03531	0.06734	-0.5243	13602	0.6001	-0.2243	0.1537
fixed	NA	count_birth_order1/>5	-0.05063	0.04693	-1.079	13601	0.2807	-0.1824	0.08112
fixed	NA	count_birth_order2/>5	-0.08895	0.04831	-1.841	13605	0.06562	-0.2246	0.04666
fixed	NA	count_birth_order3/>5	-0.1235	0.04744	-2.604	13604	0.00923	-0.2567	0.009641
fixed	NA	count_birth_order4/>5	-0.1254	0.04636	-2.705	13605	0.006841	-0.2556	0.004736
fixed	NA	count_birth_order5/>5	-0.1327	0.0467	-2.842	13604	0.004491	-0.2638	-0.001628
fixed	NA	count_birth_order>5/>5	-0.1408	0.03701	-3.804	12216	0.0001434	-0.2447	-0.03688
ran_pars	mother_pidlink	sd__(Intercept)	0.4189	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8965	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)
11	38110	38193	-19044	38088	NA	NA	NA
12	38108	38198	-19042	38084	4.489	1	0.03411
16	38105	38225	-19037	38073	10.57	4	0.03183
26	38116	38311	-19032	38064	9.266	10	0.507

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)	-1.742	0.4065	-4.284	5752	0.00001864	-2.883	-0.6005
fixed	NA	poly(age, 3, raw = TRUE)1	0.2094	0.04611	4.543	5754	0.000005671	0.08002	0.3389
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006882	0.001645	-4.185	5757	0.00002899	-0.0115	-0.002266
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007036	0.00001862	3.779	5763	0.000159	0.0000181	0.0001226
fixed	NA	male	-0.002035	0.02375	-0.08571	5664	0.9317	-0.06869	0.06462
fixed	NA	sibling_count3	-0.00724	0.0379	-0.191	4223	0.8485	-0.1136	0.09914
fixed	NA	sibling_count4	-0.0264	0.04103	-0.6435	3750	0.52	-0.1416	0.08876
fixed	NA	sibling_count5	-0.07347	0.04681	-1.569	3408	0.1166	-0.2049	0.05794
fixed	NA	sibling_count>5	-0.1963	0.04127	-4.756	3243	0.00000206	-0.3121	-0.08044
ran_pars	mother_pidlink	sd__(Intercept)	0.3845	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8347	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)	-1.734	0.4066	-4.266	5752	0.00002025	-2.876	-0.593
fixed	NA	birth_order	-0.008164	0.00792	-1.031	5827	0.3027	-0.0304	0.01407
fixed	NA	poly(age, 3, raw = TRUE)1	0.2098	0.04611	4.55	5754	0.000005469	0.08038	0.3392
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006883	0.001645	-4.185	5757	0.00002896	-0.0115	-0.002266
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007005	0.00001862	3.762	5761	0.0001706	0.00001777	0.0001223
fixed	NA	male	-0.001657	0.02375	-0.06975	5664	0.9444	-0.06833	0.06501
fixed	NA	sibling_count3	-0.003215	0.03809	-0.08441	4230	0.9327	-0.1101	0.1037
fixed	NA	sibling_count4	-0.01684	0.04205	-0.4004	3768	0.6889	-0.1349	0.1012
fixed	NA	sibling_count5	-0.05794	0.04916	-1.179	3509	0.2387	-0.1959	0.08006
fixed	NA	sibling_count>5	-0.1653	0.05105	-3.238	3789	0.001215	-0.3086	-0.02199
ran_pars	mother_pidlink	sd__(Intercept)	0.3836	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.835	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)	-1.751	0.4073	-4.3	5759	0.00001736	-2.894	-0.608
fixed	NA	poly(age, 3, raw = TRUE)1	0.2103	0.04614	4.558	5755	0.000005264	0.08081	0.3399
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006901	0.001646	-4.193	5756	0.00002796	-0.01152	-0.002281
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007025	0.00001864	3.769	5760	0.0001655	0.00001793	0.0001226
fixed	NA	male	-0.001182	0.02375	-0.04974	5657	0.9603	-0.06786	0.0655
fixed	NA	sibling_count3	0.007384	0.03885	0.1901	4413	0.8493	-0.1017	0.1164
fixed	NA	sibling_count4	-0.003047	0.04364	-0.06983	4087	0.9443	-0.1256	0.1195
fixed	NA	sibling_count5	-0.04944	0.05155	-0.9591	3926	0.3376	-0.1941	0.09526
fixed	NA	sibling_count>5	-0.1575	0.05246	-3.002	4038	0.002694	-0.3048	-0.01025
fixed	NA	birth_order_nonlinear2	0.003951	0.03053	0.1294	4749	0.897	-0.08174	0.08965
fixed	NA	birth_order_nonlinear3	-0.06261	0.03762	-1.664	4959	0.09608	-0.1682	0.04298
fixed	NA	birth_order_nonlinear4	-0.03636	0.0466	-0.7802	5103	0.4353	-0.1672	0.09444
fixed	NA	birth_order_nonlinear5	-0.007188	0.05817	-0.1236	4949	0.9017	-0.1705	0.1561
fixed	NA	birth_order_nonlinear>5	-0.05932	0.05891	-1.007	5758	0.3141	-0.2247	0.1061
ran_pars	mother_pidlink	sd__(Intercept)	0.3846	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8348	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)	-1.724	0.408	-4.227	5751	0.00002407	-2.87	-0.5792
fixed	NA	poly(age, 3, raw = TRUE)1	0.205	0.04622	4.435	5744	0.000009364	0.07526	0.3347
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0067	0.001649	-4.063	5746	0.00004908	-0.01133	-0.002071
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006785	0.00001868	3.633	5750	0.0002826	0.00001543	0.0001203
fixed	NA	male	-0.003637	0.02376	-0.1531	5644	0.8783	-0.07034	0.06306
fixed	NA	count_birth_order2/2	0.06035	0.0554	1.089	5061	0.276	-0.09516	0.2159
fixed	NA	count_birth_order1/3	0.04137	0.04935	0.8382	5765	0.4019	-0.09717	0.1799
fixed	NA	count_birth_order2/3	0.006316	0.05378	0.1175	5808	0.9065	-0.1446	0.1573
fixed	NA	count_birth_order3/3	-0.03376	0.05998	-0.5628	5820	0.5736	-0.2021	0.1346
fixed	NA	count_birth_order1/4	-0.03262	0.06047	-0.5395	5802	0.5896	-0.2024	0.1371
fixed	NA	count_birth_order2/4	0.0837	0.06257	1.338	5820	0.181	-0.09192	0.2593
fixed	NA	count_birth_order3/4	-0.07312	0.06565	-1.114	5813	0.2654	-0.2574	0.1112
fixed	NA	count_birth_order4/4	-0.002899	0.06845	-0.04236	5808	0.9662	-0.195	0.1892
fixed	NA	count_birth_order1/5	0.01161	0.08139	0.1427	5818	0.8866	-0.2168	0.2401
fixed	NA	count_birth_order2/5	-0.07328	0.08756	-0.837	5783	0.4027	-0.3191	0.1725
fixed	NA	count_birth_order3/5	-0.1484	0.0822	-1.806	5785	0.071	-0.3792	0.0823
fixed	NA	count_birth_order4/5	-0.03242	0.07917	-0.4095	5801	0.6822	-0.2547	0.1898
fixed	NA	count_birth_order5/5	-0.02795	0.08174	-0.342	5788	0.7324	-0.2574	0.2015
fixed	NA	count_birth_order1/>5	-0.05036	0.0809	-0.6225	5798	0.5336	-0.2774	0.1767
fixed	NA	count_birth_order2/>5	-0.2429	0.0813	-2.987	5776	0.002828	-0.4711	-0.01464
fixed	NA	count_birth_order3/>5	-0.1141	0.08049	-1.418	5749	0.1563	-0.3401	0.1118
fixed	NA	count_birth_order4/>5	-0.227	0.07547	-3.008	5749	0.00264	-0.4389	-0.01518
fixed	NA	count_birth_order5/>5	-0.1526	0.07184	-2.124	5749	0.03375	-0.3542	0.04909
fixed	NA	count_birth_order>5/>5	-0.1988	0.05463	-3.639	5402	0.0002762	-0.3521	-0.04545
ran_pars	mother_pidlink	sd__(Intercept)	0.385	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8344	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)
11	15526	15600	-7752	15504	NA	NA	NA
12	15527	15607	-7752	15503	1.066	1	0.3018
16	15532	15639	-7750	15500	3.189	4	0.5268
26	15540	15713	-7744	15488	12.37	10	0.2613

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)	-1.735	0.4053	-4.282	5803	0.00001886	-2.873	-0.5976
fixed	NA	poly(age, 3, raw = TRUE)1	0.2105	0.04599	4.578	5803	0.0000048	0.08143	0.3396
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006937	0.001641	-4.228	5806	0.00002394	-0.01154	-0.002331
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007079	0.00001858	3.81	5813	0.0001403	0.00001864	0.0001229
fixed	NA	male	-0.001301	0.02365	-0.05501	5711	0.9561	-0.0677	0.06509
fixed	NA	sibling_count3	-0.03781	0.04097	-0.923	4375	0.356	-0.1528	0.07718
fixed	NA	sibling_count4	-0.007388	0.04336	-0.1704	4006	0.8647	-0.1291	0.1143
fixed	NA	sibling_count5	-0.06853	0.04634	-1.479	3649	0.1393	-0.1986	0.06155
fixed	NA	sibling_count>5	-0.1464	0.04069	-3.598	3779	0.0003249	-0.2606	-0.03218
ran_pars	mother_pidlink	sd__(Intercept)	0.3853	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8346	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)	-1.721	0.4053	-4.247	5803	0.00002201	-2.859	-0.5836
fixed	NA	birth_order	-0.01171	0.006915	-1.694	5782	0.09032	-0.03113	0.007697
fixed	NA	poly(age, 3, raw = TRUE)1	0.2106	0.04598	4.58	5804	0.000004737	0.08154	0.3397
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006923	0.001641	-4.22	5806	0.00002485	-0.01153	-0.002317
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007016	0.00001858	3.776	5812	0.000161	0.000018	0.0001223
fixed	NA	male	-0.0008451	0.02365	-0.03573	5713	0.9715	-0.06724	0.06555
fixed	NA	sibling_count3	-0.03205	0.04109	-0.7799	4376	0.4355	-0.1474	0.0833
fixed	NA	sibling_count4	0.005742	0.04403	0.1304	4001	0.8962	-0.1178	0.1293
fixed	NA	sibling_count5	-0.04796	0.04788	-1.002	3677	0.3165	-0.1823	0.08643
fixed	NA	sibling_count>5	-0.1033	0.04796	-2.154	4106	0.03134	-0.2379	0.03134
ran_pars	mother_pidlink	sd__(Intercept)	0.384	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8349	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)	-1.737	0.4058	-4.28	5809	0.00001901	-2.876	-0.5976
fixed	NA	poly(age, 3, raw = TRUE)1	0.2108	0.046	4.584	5804	0.000004666	0.08172	0.3399
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006929	0.001641	-4.222	5806	0.00002462	-0.01154	-0.002322
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007018	0.00001859	3.775	5810	0.0001615	0.000018	0.0001224
fixed	NA	male	0.0001426	0.02365	0.006028	5706	0.9952	-0.06625	0.06653
fixed	NA	sibling_count3	-0.02208	0.04182	-0.5281	4533	0.5975	-0.1395	0.0953
fixed	NA	sibling_count4	0.0252	0.04553	0.5535	4287	0.58	-0.1026	0.153
fixed	NA	sibling_count5	-0.04036	0.05006	-0.8061	4062	0.4202	-0.1809	0.1002
fixed	NA	sibling_count>5	-0.08923	0.04936	-1.808	4370	0.07069	-0.2278	0.04931
fixed	NA	birth_order_nonlinear2	-0.007419	0.03111	-0.2385	4896	0.8115	-0.09474	0.0799
fixed	NA	birth_order_nonlinear3	-0.06747	0.03749	-1.8	5088	0.07198	-0.1727	0.03777
fixed	NA	birth_order_nonlinear4	-0.08405	0.04525	-1.857	5239	0.06331	-0.2111	0.04297
fixed	NA	birth_order_nonlinear5	0.01327	0.05537	0.2397	5169	0.8105	-0.1421	0.1687
fixed	NA	birth_order_nonlinear>5	-0.1017	0.05263	-1.933	5872	0.05324	-0.2495	0.04598
ran_pars	mother_pidlink	sd__(Intercept)	0.3854	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8342	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)	-1.753	0.4063	-4.315	5800	0.00001622	-2.894	-0.6127
fixed	NA	poly(age, 3, raw = TRUE)1	0.2086	0.04603	4.531	5791	0.000005994	0.07934	0.3378
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006848	0.001643	-4.168	5793	0.00003112	-0.01146	-0.002236
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006923	0.00001861	3.72	5798	0.0002011	0.00001699	0.0001215
fixed	NA	male	-0.0008112	0.02365	-0.03431	5689	0.9726	-0.06718	0.06556
fixed	NA	count_birth_order2/2	0.1046	0.0606	1.727	5189	0.08424	-0.06545	0.2747
fixed	NA	count_birth_order1/3	0.04638	0.05345	0.8677	5815	0.3856	-0.1037	0.1964
fixed	NA	count_birth_order2/3	-0.03838	0.05776	-0.6645	5856	0.5064	-0.2005	0.1238
fixed	NA	count_birth_order3/3	-0.04669	0.06486	-0.7199	5871	0.4716	-0.2288	0.1354
fixed	NA	count_birth_order1/4	0.08308	0.06328	1.313	5851	0.1893	-0.09456	0.2607
fixed	NA	count_birth_order2/4	0.1233	0.06453	1.91	5869	0.05612	-0.05786	0.3044
fixed	NA	count_birth_order3/4	-0.09541	0.07025	-1.358	5864	0.1745	-0.2926	0.1018
fixed	NA	count_birth_order4/4	-0.0516	0.07268	-0.71	5862	0.4778	-0.2556	0.1524
fixed	NA	count_birth_order1/5	-0.01385	0.07452	-0.1859	5870	0.8526	-0.223	0.1953
fixed	NA	count_birth_order2/5	-0.068	0.08025	-0.8473	5853	0.3968	-0.2933	0.1573
fixed	NA	count_birth_order3/5	-0.08213	0.078	-1.053	5851	0.2924	-0.3011	0.1368
fixed	NA	count_birth_order4/5	-0.01231	0.08102	-0.1519	5834	0.8792	-0.2397	0.2151
fixed	NA	count_birth_order5/5	0.02339	0.08067	0.29	5838	0.7718	-0.203	0.2498
fixed	NA	count_birth_order1/>5	-0.04074	0.07093	-0.5743	5871	0.5658	-0.2398	0.1584
fixed	NA	count_birth_order2/>5	-0.1348	0.0748	-1.802	5843	0.07154	-0.3448	0.07515
fixed	NA	count_birth_order3/>5	-0.02254	0.07276	-0.3097	5831	0.7568	-0.2268	0.1817
fixed	NA	count_birth_order4/>5	-0.1605	0.07	-2.292	5832	0.02192	-0.357	0.03603
fixed	NA	count_birth_order5/>5	-0.04646	0.07191	-0.6462	5790	0.5182	-0.2483	0.1554
fixed	NA	count_birth_order>5/>5	-0.1536	0.05342	-2.876	5498	0.004038	-0.3036	-0.003707
ran_pars	mother_pidlink	sd__(Intercept)	0.3886	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)
11	15665	15738	-7821	15643	NA	NA	NA
12	15664	15744	-7820	15640	2.876	1	0.08993
16	15665	15772	-7817	15633	6.217	4	0.1835
26	15669	15843	-7809	15617	16.19	10	0.09423

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)	-1.758	0.4107	-4.281	5640	0.00001893	-2.911	-0.6052
fixed	NA	poly(age, 3, raw = TRUE)1	0.2094	0.0466	4.494	5641	0.00000714	0.07859	0.3402
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006886	0.001663	-4.142	5644	0.000035	-0.01155	-0.002219
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007041	0.00001883	3.738	5649	0.0001871	0.00001754	0.0001233
fixed	NA	male	-0.001767	0.02395	-0.07378	5556	0.9412	-0.06901	0.06547
fixed	NA	sibling_count3	0.02318	0.03734	0.6207	4163	0.5348	-0.08164	0.128
fixed	NA	sibling_count4	-0.01709	0.04066	-0.4203	3726	0.6743	-0.1312	0.09704
fixed	NA	sibling_count5	-0.03092	0.04791	-0.6453	3290	0.5188	-0.1654	0.1036
fixed	NA	sibling_count>5	-0.1816	0.04168	-4.358	3134	0.00001356	-0.2986	-0.06464
ran_pars	mother_pidlink	sd__(Intercept)	0.3835	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8335	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)	-1.751	0.4107	-4.263	5639	0.00002046	-2.904	-0.5982
fixed	NA	birth_order	-0.009102	0.00815	-1.117	5717	0.2641	-0.03198	0.01378
fixed	NA	poly(age, 3, raw = TRUE)1	0.2099	0.0466	4.505	5642	0.000006786	0.0791	0.3407
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006889	0.001663	-4.144	5643	0.0000347	-0.01156	-0.002222
fixed	NA	poly(age, 3, raw = TRUE)3	0.00007008	0.00001884	3.72	5648	0.0002008	0.00001721	0.000123
fixed	NA	male	-0.001512	0.02396	-0.06313	5556	0.9497	-0.06876	0.06573
fixed	NA	sibling_count3	0.02767	0.03755	0.737	4170	0.4612	-0.07773	0.1331
fixed	NA	sibling_count4	-0.006581	0.04173	-0.1577	3757	0.8747	-0.1237	0.1105
fixed	NA	sibling_count5	-0.01437	0.05014	-0.2867	3385	0.7744	-0.1551	0.1264
fixed	NA	sibling_count>5	-0.1474	0.05172	-2.85	3768	0.0044	-0.2926	-0.002208
ran_pars	mother_pidlink	sd__(Intercept)	0.3829	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8337	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)	-1.75	0.4113	-4.255	5646	0.00002129	-2.905	-0.5954
fixed	NA	poly(age, 3, raw = TRUE)1	0.2089	0.04663	4.48	5642	0.000007605	0.07801	0.3398
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006853	0.001664	-4.119	5642	0.00003861	-0.01152	-0.002183
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006965	0.00001885	3.695	5645	0.0002217	0.00001674	0.0001226
fixed	NA	male	-0.001605	0.02396	-0.06699	5549	0.9466	-0.06886	0.06565
fixed	NA	sibling_count3	0.03932	0.03833	1.026	4350	0.3051	-0.06828	0.1469
fixed	NA	sibling_count4	0.006506	0.04337	0.15	4071	0.8808	-0.1152	0.1283
fixed	NA	sibling_count5	-0.001042	0.05236	-0.01989	3752	0.9841	-0.148	0.1459
fixed	NA	sibling_count>5	-0.1381	0.05322	-2.595	4031	0.009494	-0.2875	0.01128
fixed	NA	birth_order_nonlinear2	-0.01308	0.03042	-0.4302	4660	0.6671	-0.09846	0.07229
fixed	NA	birth_order_nonlinear3	-0.06863	0.03759	-1.826	4850	0.06794	-0.1741	0.03688
fixed	NA	birth_order_nonlinear4	-0.03461	0.04784	-0.7235	4985	0.4694	-0.1689	0.09968
fixed	NA	birth_order_nonlinear5	-0.0511	0.06064	-0.8426	4862	0.3995	-0.2213	0.1191
fixed	NA	birth_order_nonlinear>5	-0.06211	0.06069	-1.023	5609	0.3062	-0.2325	0.1082
ran_pars	mother_pidlink	sd__(Intercept)	0.384	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8334	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)	-1.72	0.4121	-4.173	5638	0.00003048	-2.877	-0.563
fixed	NA	poly(age, 3, raw = TRUE)1	0.2027	0.04671	4.339	5632	0.00001455	0.07157	0.3338
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006614	0.001667	-3.968	5633	0.00007349	-0.01129	-0.001935
fixed	NA	poly(age, 3, raw = TRUE)3	0.00006677	0.00001889	3.535	5637	0.0004113	0.00001375	0.0001198
fixed	NA	male	-0.004393	0.02396	-0.1833	5534	0.8545	-0.07166	0.06287
fixed	NA	count_birth_order2/2	0.05125	0.0538	0.9527	4914	0.3408	-0.09976	0.2023
fixed	NA	count_birth_order1/3	0.06193	0.04865	1.273	5651	0.203	-0.07463	0.1985
fixed	NA	count_birth_order2/3	0.0383	0.05364	0.7141	5697	0.4752	-0.1123	0.1889
fixed	NA	count_birth_order3/3	0.00373	0.05886	0.06337	5704	0.9495	-0.1615	0.169
fixed	NA	count_birth_order1/4	0.008194	0.06064	0.1351	5694	0.8925	-0.162	0.1784
fixed	NA	count_birth_order2/4	0.05461	0.06234	0.8759	5704	0.3811	-0.1204	0.2296
fixed	NA	count_birth_order3/4	-0.07707	0.06483	-1.189	5694	0.2346	-0.2591	0.1049
fixed	NA	count_birth_order4/4	0.01361	0.06861	0.1983	5684	0.8428	-0.179	0.2062
fixed	NA	count_birth_order1/5	0.06726	0.08109	0.8294	5704	0.4069	-0.1604	0.2949
fixed	NA	count_birth_order2/5	-0.03652	0.09006	-0.4055	5659	0.6851	-0.2893	0.2163
fixed	NA	count_birth_order3/5	-0.1304	0.0861	-1.515	5660	0.1299	-0.3721	0.1113
fixed	NA	count_birth_order4/5	0.03388	0.0827	0.4096	5680	0.6821	-0.1983	0.266
fixed	NA	count_birth_order5/5	-0.01935	0.08732	-0.2216	5665	0.8246	-0.2645	0.2258
fixed	NA	count_birth_order1/>5	-0.01061	0.08265	-0.1284	5675	0.8979	-0.2426	0.2214
fixed	NA	count_birth_order2/>5	-0.2631	0.08334	-3.158	5653	0.001599	-0.4971	-0.02921
fixed	NA	count_birth_order3/>5	-0.07723	0.0815	-0.9476	5629	0.3434	-0.306	0.1515
fixed	NA	count_birth_order4/>5	-0.2221	0.07927	-2.802	5599	0.005092	-0.4446	0.0003803
fixed	NA	count_birth_order5/>5	-0.174	0.07346	-2.368	5623	0.0179	-0.3802	0.03223
fixed	NA	count_birth_order>5/>5	-0.1797	0.05555	-3.235	5279	0.001225	-0.3356	-0.02376
ran_pars	mother_pidlink	sd__(Intercept)	0.3852	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8326	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)
11	15200	15273	-7589	15178	NA	NA	NA
12	15200	15280	-7588	15176	1.251	1	0.2634
16	15206	15312	-7587	15174	2.534	4	0.6385
26	15211	15384	-7580	15159	14.26	10	0.1615

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)	0.3533	0.1522	2.322	13861	0.02026	-0.07384	0.7804
fixed	NA	poly(age, 3, raw = TRUE)1	0.006171	0.01459	0.4228	13811	0.6724	-0.0348	0.04714
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0004583	0.0004298	-1.066	13691	0.2864	-0.001665	0.0007483
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000006377	0.000003962	0.161	13541	0.8721	-0.00001048	0.00001176
fixed	NA	male	-0.1026	0.01588	-6.461	13510	0.0000000001074	-0.1472	-0.05803
fixed	NA	sibling_count3	0.02844	0.03284	0.8661	9962	0.3865	-0.06374	0.1206
fixed	NA	sibling_count4	0.0288	0.03393	0.8488	9172	0.396	-0.06644	0.124
fixed	NA	sibling_count5	-0.005082	0.03538	-0.1436	8311	0.8858	-0.1044	0.09423
fixed	NA	sibling_count>5	-0.1109	0.02768	-4.006	9265	0.00006234	-0.1886	-0.03318
ran_pars	mother_pidlink	sd__(Intercept)	0.3956	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8692	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)	0.3527	0.1522	2.318	13861	0.02046	-0.07442	0.7799
fixed	NA	birth_order	-0.002253	0.003393	-0.6641	13247	0.5066	-0.01178	0.00727
fixed	NA	poly(age, 3, raw = TRUE)1	0.006857	0.01463	0.4687	13801	0.6393	-0.03421	0.04793
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0004838	0.0004315	-1.121	13642	0.2622	-0.001695	0.0007275
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000008756	0.000003978	0.2201	13467	0.8258	-0.00001029	0.00001204
fixed	NA	male	-0.1025	0.01588	-6.457	13510	0.0000000001105	-0.1471	-0.05796
fixed	NA	sibling_count3	0.02891	0.03285	0.8802	9978	0.3788	-0.06329	0.1211
fixed	NA	sibling_count4	0.03031	0.034	0.8913	9240	0.3728	-0.06514	0.1257
fixed	NA	sibling_count5	-0.002406	0.03561	-0.06757	8434	0.9461	-0.1024	0.09755
fixed	NA	sibling_count>5	-0.1024	0.03047	-3.361	10417	0.0007793	-0.188	-0.01688
ran_pars	mother_pidlink	sd__(Intercept)	0.3954	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8693	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)	0.3551	0.1526	2.327	13859	0.01998	-0.07323	0.7834
fixed	NA	poly(age, 3, raw = TRUE)1	0.007002	0.01463	0.4784	13804	0.6324	-0.03408	0.04808
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0004887	0.0004316	-1.132	13647	0.2575	-0.0017	0.0007229
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000009008	0.00000398	0.2264	13462	0.8209	-0.00001027	0.00001207
fixed	NA	male	-0.1025	0.01588	-6.451	13505	0.0000000001149	-0.147	-0.05788
fixed	NA	sibling_count3	0.02886	0.03328	0.8672	10301	0.3859	-0.06455	0.1223
fixed	NA	sibling_count4	0.02953	0.0349	0.8461	9895	0.3975	-0.06843	0.1275
fixed	NA	sibling_count5	-0.00005737	0.03689	-0.001555	9291	0.9988	-0.1036	0.1035
fixed	NA	sibling_count>5	-0.09666	0.03193	-3.027	11404	0.002472	-0.1863	-0.007037
fixed	NA	birth_order_nonlinear2	-0.01544	0.02294	-0.6729	12530	0.501	-0.07983	0.04896
fixed	NA	birth_order_nonlinear3	-0.008737	0.02705	-0.323	12226	0.7467	-0.08467	0.06719
fixed	NA	birth_order_nonlinear4	-0.005941	0.03082	-0.1928	12252	0.8471	-0.09245	0.08057
fixed	NA	birth_order_nonlinear5	-0.03387	0.03506	-0.9661	12247	0.334	-0.1323	0.06455
fixed	NA	birth_order_nonlinear>5	-0.03147	0.02934	-1.073	13837	0.2834	-0.1138	0.05088
ran_pars	mother_pidlink	sd__(Intercept)	0.3954	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8694	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)	0.3423	0.1532	2.234	13851	0.02551	-0.08784	0.7725
fixed	NA	poly(age, 3, raw = TRUE)1	0.007367	0.01464	0.5033	13793	0.6148	-0.03372	0.04846
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005014	0.0004317	-1.161	13630	0.2455	-0.001713	0.0007105
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001029	0.000003981	0.2583	13437	0.7962	-0.00001015	0.0000122
fixed	NA	male	-0.1027	0.01589	-6.463	13496	0.000000000106	-0.1473	-0.05809
fixed	NA	count_birth_order2/2	0.01152	0.04462	0.2582	12658	0.7963	-0.1137	0.1368
fixed	NA	count_birth_order1/3	0.03433	0.04294	0.7994	13632	0.4241	-0.08621	0.1549
fixed	NA	count_birth_order2/3	0.03836	0.04795	0.8002	13776	0.4236	-0.09622	0.173
fixed	NA	count_birth_order3/3	0.01806	0.05364	0.3367	13878	0.7364	-0.1325	0.1686
fixed	NA	count_birth_order1/4	0.009683	0.04898	0.1977	13779	0.8433	-0.1278	0.1472
fixed	NA	count_birth_order2/4	0.06327	0.05141	1.231	13827	0.2185	-0.08104	0.2076
fixed	NA	count_birth_order3/4	0.0178	0.0558	0.3189	13896	0.7498	-0.1388	0.1744
fixed	NA	count_birth_order4/4	0.04206	0.05908	0.7118	13918	0.4766	-0.1238	0.2079
fixed	NA	count_birth_order1/5	0.06302	0.05549	1.136	13874	0.2561	-0.09274	0.2188
fixed	NA	count_birth_order2/5	-0.05377	0.05819	-0.9241	13906	0.3554	-0.2171	0.1096
fixed	NA	count_birth_order3/5	-0.02803	0.05982	-0.4686	13919	0.6394	-0.196	0.1399
fixed	NA	count_birth_order4/5	-0.007194	0.06332	-0.1136	13926	0.9095	-0.1849	0.1705
fixed	NA	count_birth_order5/5	0.007012	0.06469	0.1084	13924	0.9137	-0.1746	0.1886
fixed	NA	count_birth_order1/>5	-0.07213	0.0447	-1.614	13923	0.1066	-0.1976	0.05333
fixed	NA	count_birth_order2/>5	-0.135	0.04606	-2.931	13926	0.003388	-0.2643	-0.005695
fixed	NA	count_birth_order3/>5	-0.06838	0.04515	-1.514	13925	0.13	-0.1951	0.05837
fixed	NA	count_birth_order4/>5	-0.09254	0.04425	-2.091	13926	0.03652	-0.2168	0.03167
fixed	NA	count_birth_order5/>5	-0.1312	0.04458	-2.943	13925	0.003258	-0.2563	-0.006053
fixed	NA	count_birth_order>5/>5	-0.1183	0.03526	-3.355	12476	0.0007951	-0.2173	-0.01934
ran_pars	mother_pidlink	sd__(Intercept)	0.3952	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8695	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)
11	38025	38108	-19002	38003	NA	NA	NA
12	38027	38117	-19001	38003	0.4421	1	0.5061
16	38034	38154	-19001	38002	1.325	4	0.8572
26	38046	38242	-18997	37994	7.138	10	0.7124

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)	0.2703	0.4011	0.6739	5871	0.5004	-0.8556	1.396
fixed	NA	poly(age, 3, raw = TRUE)1	0.0125	0.04552	0.2745	5875	0.7837	-0.1153	0.1403
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003482	0.001625	-0.2144	5880	0.8303	-0.004909	0.004212
fixed	NA	poly(age, 3, raw = TRUE)3	0.000000429	0.0000184	0.02331	5886	0.9814	-0.00005122	0.00005208
fixed	NA	male	-0.1315	0.02342	-5.616	5806	0.00000002042	-0.1973	-0.06579
fixed	NA	sibling_count3	0.03636	0.03708	0.9806	4374	0.3269	-0.06773	0.1405
fixed	NA	sibling_count4	-0.08697	0.03999	-2.175	3878	0.02971	-0.1992	0.02528
fixed	NA	sibling_count5	-0.1077	0.04571	-2.357	3490	0.01849	-0.236	0.02058
fixed	NA	sibling_count>5	-0.1732	0.04014	-4.315	3295	0.00001642	-0.2859	-0.06054
ran_pars	mother_pidlink	sd__(Intercept)	0.3506	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)	0.2706	0.4012	0.6746	5870	0.4999	-0.8555	1.397
fixed	NA	birth_order	-0.0004093	0.007764	-0.05271	5876	0.958	-0.0222	0.02139
fixed	NA	poly(age, 3, raw = TRUE)1	0.01252	0.04552	0.2749	5874	0.7834	-0.1153	0.1403
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003483	0.001625	-0.2144	5879	0.8303	-0.004909	0.004212
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000004136	0.0000184	0.02247	5884	0.9821	-0.00005125	0.00005208
fixed	NA	male	-0.1315	0.02342	-5.614	5805	0.00000002065	-0.1973	-0.06576
fixed	NA	sibling_count3	0.03656	0.03728	0.9808	4381	0.3268	-0.06808	0.1412
fixed	NA	sibling_count4	-0.08649	0.04099	-2.11	3892	0.0349	-0.2015	0.02856
fixed	NA	sibling_count5	-0.107	0.04802	-2.227	3582	0.02599	-0.2417	0.02784
fixed	NA	sibling_count>5	-0.1717	0.04976	-3.45	3832	0.0005666	-0.3114	-0.032
ran_pars	mother_pidlink	sd__(Intercept)	0.3506	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8393	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)	0.3012	0.4018	0.7496	5874	0.4535	-0.8266	1.429
fixed	NA	poly(age, 3, raw = TRUE)1	0.01015	0.04555	0.2228	5874	0.8237	-0.1177	0.138
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002567	0.001626	-0.1579	5877	0.8745	-0.00482	0.004307
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000007896	0.00001842	-0.04287	5882	0.9658	-0.00005249	0.00005091
fixed	NA	male	-0.1317	0.02342	-5.625	5799	0.0000000194	-0.1975	-0.066
fixed	NA	sibling_count3	0.03149	0.03803	0.8279	4565	0.4077	-0.07527	0.1382
fixed	NA	sibling_count4	-0.08309	0.04257	-1.952	4220	0.05101	-0.2026	0.0364
fixed	NA	sibling_count5	-0.08576	0.05042	-1.701	4018	0.08907	-0.2273	0.05578
fixed	NA	sibling_count>5	-0.1567	0.05121	-3.06	4096	0.00223	-0.3005	-0.01294
fixed	NA	birth_order_nonlinear2	-0.03205	0.03018	-1.062	4910	0.2882	-0.1168	0.05265
fixed	NA	birth_order_nonlinear3	0.02066	0.03726	0.5544	5133	0.5793	-0.08393	0.1252
fixed	NA	birth_order_nonlinear4	-0.04889	0.04612	-1.06	5285	0.2891	-0.1783	0.08056
fixed	NA	birth_order_nonlinear5	-0.09808	0.05756	-1.704	5140	0.08844	-0.2597	0.06349
fixed	NA	birth_order_nonlinear>5	-0.00781	0.05794	-0.1348	5888	0.8928	-0.1704	0.1548
ran_pars	mother_pidlink	sd__(Intercept)	0.3513	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8389	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)	0.326	0.4027	0.8094	5866	0.4183	-0.8044	1.456
fixed	NA	poly(age, 3, raw = TRUE)1	0.007183	0.04565	0.1573	5864	0.875	-0.121	0.1353
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001525	0.00163	-0.09357	5868	0.9255	-0.004727	0.004422
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000193	0.00001846	-0.1045	5873	0.9167	-0.00005376	0.0000499
fixed	NA	male	-0.1314	0.02344	-5.606	5788	0.00000002162	-0.1972	-0.06562
fixed	NA	count_birth_order2/2	-0.02869	0.05464	-0.5251	5190	0.5995	-0.1821	0.1247
fixed	NA	count_birth_order1/3	0.03888	0.04861	0.7998	5867	0.4239	-0.09758	0.1753
fixed	NA	count_birth_order2/3	0.0252	0.05306	0.475	5899	0.6348	-0.1238	0.1742
fixed	NA	count_birth_order3/3	0.006071	0.05925	0.1025	5908	0.9184	-0.1603	0.1724
fixed	NA	count_birth_order1/4	-0.09194	0.05943	-1.547	5893	0.1219	-0.2588	0.07489
fixed	NA	count_birth_order2/4	-0.1157	0.0614	-1.883	5908	0.05968	-0.288	0.05671
fixed	NA	count_birth_order3/4	-0.0483	0.06482	-0.7451	5902	0.4562	-0.2303	0.1337
fixed	NA	count_birth_order4/4	-0.1287	0.06748	-1.907	5900	0.05655	-0.3181	0.06072
fixed	NA	count_birth_order1/5	-0.1045	0.08064	-1.296	5907	0.1951	-0.3308	0.1219
fixed	NA	count_birth_order2/5	-0.07683	0.08625	-0.8907	5883	0.3731	-0.3189	0.1653
fixed	NA	count_birth_order3/5	-0.06136	0.08085	-0.7589	5884	0.4479	-0.2883	0.1656
fixed	NA	count_birth_order4/5	-0.1804	0.0779	-2.316	5895	0.02059	-0.3991	0.03825
fixed	NA	count_birth_order5/5	-0.1471	0.08104	-1.816	5882	0.06946	-0.3746	0.08034
fixed	NA	count_birth_order1/>5	-0.1353	0.07997	-1.692	5896	0.09067	-0.3598	0.08916
fixed	NA	count_birth_order2/>5	-0.2916	0.07915	-3.684	5884	0.0002313	-0.5138	-0.06944
fixed	NA	count_birth_order3/>5	-0.06251	0.07924	-0.7889	5857	0.4302	-0.2849	0.1599
fixed	NA	count_birth_order4/>5	-0.1658	0.07465	-2.221	5854	0.02637	-0.3754	0.04373
fixed	NA	count_birth_order5/>5	-0.2781	0.07055	-3.942	5858	0.00008161	-0.4762	-0.0801
fixed	NA	count_birth_order>5/>5	-0.1635	0.05347	-3.058	5448	0.002235	-0.3136	-0.01344
ran_pars	mother_pidlink	sd__(Intercept)	0.3506	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8395	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)
11	15660	15733	-7819	15638	NA	NA	NA
12	15662	15742	-7819	15638	0.002809	1	0.9577
16	15664	15771	-7816	15632	6.129	4	0.1897
26	15677	15851	-7813	15625	6.632	10	0.7597

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)	0.3023	0.4002	0.7553	5922	0.4501	-0.8211	1.426
fixed	NA	poly(age, 3, raw = TRUE)1	0.00985	0.04544	0.2168	5925	0.8284	-0.1177	0.1374
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002896	0.001622	-0.1786	5930	0.8583	-0.004843	0.004264
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000002249	0.00001838	-0.01224	5936	0.9902	-0.00005181	0.00005136
fixed	NA	male	-0.1318	0.02335	-5.645	5854	0.00000001732	-0.1973	-0.06625
fixed	NA	sibling_count3	0.03106	0.04014	0.7739	4530	0.439	-0.08161	0.1437
fixed	NA	sibling_count4	-0.06748	0.04232	-1.595	4143	0.1109	-0.1863	0.05131
fixed	NA	sibling_count5	-0.05013	0.04535	-1.105	3744	0.269	-0.1774	0.07717
fixed	NA	sibling_count>5	-0.1294	0.03973	-3.257	3867	0.001135	-0.2409	-0.01788
ran_pars	mother_pidlink	sd__(Intercept)	0.3519	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8397	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)	0.3119	0.4003	0.7792	5921	0.4359	-0.8116	1.435
fixed	NA	birth_order	-0.008494	0.00679	-1.251	5774	0.211	-0.02755	0.01057
fixed	NA	poly(age, 3, raw = TRUE)1	0.009959	0.04544	0.2192	5924	0.8265	-0.1176	0.1375
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002798	0.001622	-0.1725	5928	0.8631	-0.004833	0.004273
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000006759	0.00001838	-0.03678	5935	0.9707	-0.00005226	0.00005091
fixed	NA	male	-0.1315	0.02335	-5.631	5853	0.00000001873	-0.197	-0.06594
fixed	NA	sibling_count3	0.03519	0.04027	0.8737	4530	0.3823	-0.07786	0.1482
fixed	NA	sibling_count4	-0.05807	0.04298	-1.351	4137	0.1767	-0.1787	0.06257
fixed	NA	sibling_count5	-0.03529	0.04687	-0.7529	3767	0.4515	-0.1669	0.09628
fixed	NA	sibling_count>5	-0.09817	0.04692	-2.092	4181	0.03648	-0.2299	0.03354
ran_pars	mother_pidlink	sd__(Intercept)	0.3517	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8398	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)	0.3142	0.4008	0.7839	5924	0.4331	-0.8108	1.439
fixed	NA	poly(age, 3, raw = TRUE)1	0.009226	0.04545	0.203	5923	0.8392	-0.1184	0.1368
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002426	0.001623	-0.1495	5927	0.8812	-0.004798	0.004313
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001365	0.00001839	-0.07425	5932	0.9408	-0.00005298	0.00005025
fixed	NA	male	-0.1316	0.02335	-5.636	5847	0.00000001818	-0.1971	-0.06606
fixed	NA	sibling_count3	0.03017	0.04099	0.7361	4682	0.4617	-0.0849	0.1452
fixed	NA	sibling_count4	-0.05283	0.04447	-1.188	4420	0.235	-0.1777	0.07201
fixed	NA	sibling_count5	-0.02045	0.04908	-0.4166	4158	0.677	-0.1582	0.1173
fixed	NA	sibling_count>5	-0.07574	0.04836	-1.566	4456	0.1174	-0.2115	0.06
fixed	NA	birth_order_nonlinear2	-0.02291	0.03076	-0.7446	5045	0.4566	-0.1093	0.06345
fixed	NA	birth_order_nonlinear3	0.00622	0.03718	0.1673	5257	0.8671	-0.09814	0.1106
fixed	NA	birth_order_nonlinear4	-0.07617	0.04479	-1.701	5413	0.08908	-0.2019	0.04956
fixed	NA	birth_order_nonlinear5	-0.09325	0.05494	-1.697	5348	0.08968	-0.2475	0.06096
fixed	NA	birth_order_nonlinear>5	-0.09131	0.05184	-1.761	5969	0.07821	-0.2368	0.0542
ran_pars	mother_pidlink	sd__(Intercept)	0.353	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8392	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)	0.3186	0.4016	0.7935	5918	0.4275	-0.8086	1.446
fixed	NA	poly(age, 3, raw = TRUE)1	0.00678	0.04552	0.1489	5915	0.8816	-0.121	0.1346
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001478	0.001626	-0.09093	5920	0.9275	-0.004711	0.004415
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002497	0.00001842	-0.1355	5925	0.8922	-0.00005421	0.00004922
fixed	NA	male	-0.1314	0.02337	-5.623	5839	0.00000001967	-0.197	-0.06579
fixed	NA	count_birth_order2/2	0.02163	0.05991	0.361	5313	0.7181	-0.1465	0.1898
fixed	NA	count_birth_order1/3	0.05145	0.05267	0.9768	5919	0.3287	-0.09639	0.1993
fixed	NA	count_birth_order2/3	0.03833	0.05711	0.6712	5948	0.5021	-0.122	0.1986
fixed	NA	count_birth_order3/3	0.01506	0.06423	0.2345	5959	0.8146	-0.1652	0.1953
fixed	NA	count_birth_order1/4	-0.06686	0.06228	-1.073	5944	0.2831	-0.2417	0.108
fixed	NA	count_birth_order2/4	-0.05847	0.06323	-0.9247	5957	0.3552	-0.236	0.119
fixed	NA	count_birth_order3/4	-0.03496	0.06945	-0.5034	5954	0.6147	-0.2299	0.16
fixed	NA	count_birth_order4/4	-0.06921	0.07172	-0.965	5953	0.3346	-0.2705	0.1321
fixed	NA	count_birth_order1/5	0.02871	0.07388	0.3886	5958	0.6976	-0.1787	0.2361
fixed	NA	count_birth_order2/5	0.0003236	0.07927	0.004082	5948	0.9967	-0.2222	0.2228
fixed	NA	count_birth_order3/5	-0.009014	0.07708	-0.1169	5946	0.9069	-0.2254	0.2074
fixed	NA	count_birth_order4/5	-0.09693	0.07987	-1.214	5934	0.225	-0.3211	0.1273
fixed	NA	count_birth_order5/5	-0.1483	0.08009	-1.851	5934	0.06419	-0.3731	0.07655
fixed	NA	count_birth_order1/>5	-0.02559	0.07021	-0.3644	5959	0.7156	-0.2227	0.1715
fixed	NA	count_birth_order2/>5	-0.1887	0.07328	-2.575	5944	0.01004	-0.3944	0.01698
fixed	NA	count_birth_order3/>5	0.00315	0.07175	0.04391	5932	0.965	-0.1983	0.2046
fixed	NA	count_birth_order4/>5	-0.1667	0.06916	-2.41	5931	0.01597	-0.3609	0.02744
fixed	NA	count_birth_order5/>5	-0.1191	0.07104	-1.676	5900	0.09374	-0.3185	0.08032
fixed	NA	count_birth_order>5/>5	-0.1524	0.0524	-2.909	5556	0.003643	-0.2995	-0.00533
ran_pars	mother_pidlink	sd__(Intercept)	0.3507	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8402	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)
11	15806	15880	-7892	15784	NA	NA	NA
12	15807	15887	-7891	15783	1.568	1	0.2105
16	15810	15917	-7889	15778	5.324	4	0.2556
26	15821	15996	-7885	15769	8.136	10	0.6156

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)	0.2817	0.4058	0.6942	5753	0.4876	-0.8573	1.421
fixed	NA	poly(age, 3, raw = TRUE)1	0.0102	0.04607	0.2214	5757	0.8248	-0.1191	0.1395
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002244	0.001645	-0.1364	5761	0.8915	-0.004841	0.004392
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001458	0.00001864	-0.0782	5767	0.9377	-0.00005378	0.00005086
fixed	NA	male	-0.127	0.02366	-5.368	5688	0.00000008287	-0.1934	-0.06058
fixed	NA	sibling_count3	0.01622	0.03661	0.443	4282	0.6578	-0.08655	0.119
fixed	NA	sibling_count4	-0.08336	0.03974	-2.098	3812	0.03597	-0.1949	0.02818
fixed	NA	sibling_count5	-0.1066	0.04688	-2.274	3333	0.02303	-0.2382	0.02499
fixed	NA	sibling_count>5	-0.1814	0.04062	-4.467	3144	0.000008212	-0.2955	-0.06742
ran_pars	mother_pidlink	sd__(Intercept)	0.3519	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8386	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)	0.2826	0.4058	0.6965	5752	0.4862	-0.8566	1.422
fixed	NA	birth_order	-0.001434	0.007998	-0.1793	5778	0.8577	-0.02388	0.02102
fixed	NA	poly(age, 3, raw = TRUE)1	0.01029	0.04608	0.2234	5756	0.8232	-0.119	0.1396
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002252	0.001645	-0.1369	5760	0.8911	-0.004842	0.004392
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001507	0.00001864	-0.08082	5765	0.9356	-0.00005384	0.00005082
fixed	NA	male	-0.127	0.02366	-5.365	5687	0.00000008392	-0.1934	-0.06054
fixed	NA	sibling_count3	0.01692	0.03683	0.4595	4287	0.6459	-0.08645	0.1203
fixed	NA	sibling_count4	-0.08173	0.04077	-2.005	3838	0.04508	-0.1962	0.03272
fixed	NA	sibling_count5	-0.104	0.04907	-2.12	3420	0.03411	-0.2417	0.03373
fixed	NA	sibling_count>5	-0.1761	0.05051	-3.486	3773	0.0004965	-0.3178	-0.03428
ran_pars	mother_pidlink	sd__(Intercept)	0.3519	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8387	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)	0.3087	0.4063	0.7598	5755	0.4474	-0.8318	1.449
fixed	NA	poly(age, 3, raw = TRUE)1	0.008334	0.04608	0.1809	5754	0.8565	-0.121	0.1377
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001465	0.001645	-0.08904	5757	0.9291	-0.004765	0.004472
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002585	0.00001865	-0.1386	5761	0.8898	-0.00005493	0.00004976
fixed	NA	male	-0.1268	0.02365	-5.361	5678	0.00000008592	-0.1932	-0.06042
fixed	NA	sibling_count3	0.007929	0.03761	0.2108	4468	0.833	-0.09764	0.1135
fixed	NA	sibling_count4	-0.08449	0.04241	-1.992	4162	0.04639	-0.2035	0.03455
fixed	NA	sibling_count5	-0.08849	0.05131	-1.724	3804	0.08471	-0.2325	0.05555
fixed	NA	sibling_count>5	-0.1624	0.05206	-3.12	4052	0.001822	-0.3085	-0.01628
fixed	NA	birth_order_nonlinear2	-0.03418	0.03009	-1.136	4792	0.2561	-0.1186	0.05029
fixed	NA	birth_order_nonlinear3	0.03246	0.03725	0.8714	4995	0.3836	-0.0721	0.137
fixed	NA	birth_order_nonlinear4	-0.04026	0.04743	-0.8487	5143	0.3961	-0.1734	0.09289
fixed	NA	birth_order_nonlinear5	-0.1089	0.06002	-1.814	5024	0.06979	-0.2774	0.05963
fixed	NA	birth_order_nonlinear>5	-0.01919	0.05976	-0.3212	5744	0.7481	-0.1869	0.1485
ran_pars	mother_pidlink	sd__(Intercept)	0.3542	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8375	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)	0.3267	0.4074	0.8019	5748	0.4226	-0.8169	1.47
fixed	NA	poly(age, 3, raw = TRUE)1	0.006268	0.04621	0.1357	5746	0.8921	-0.1234	0.136
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00007614	0.00165	-0.04615	5749	0.9632	-0.004707	0.004555
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003334	0.0000187	-0.1783	5754	0.8585	-0.00005584	0.00004917
fixed	NA	male	-0.1272	0.02368	-5.373	5667	0.00000008065	-0.1937	-0.06076
fixed	NA	count_birth_order2/2	-0.03157	0.05319	-0.5935	5032	0.5529	-0.1809	0.1177
fixed	NA	count_birth_order1/3	0.00815	0.04803	0.1697	5748	0.8653	-0.1267	0.143
fixed	NA	count_birth_order2/3	-0.003243	0.05303	-0.06115	5784	0.9512	-0.1521	0.1456
fixed	NA	count_birth_order3/3	0.01332	0.0582	0.2289	5789	0.8189	-0.15	0.1767
fixed	NA	count_birth_order1/4	-0.07328	0.05972	-1.227	5780	0.2198	-0.2409	0.09435
fixed	NA	count_birth_order2/4	-0.1149	0.0613	-1.874	5789	0.06101	-0.287	0.05721
fixed	NA	count_birth_order3/4	-0.05864	0.06415	-0.9141	5781	0.3607	-0.2387	0.1214
fixed	NA	count_birth_order4/4	-0.1343	0.06788	-1.978	5774	0.04795	-0.3248	0.05626
fixed	NA	count_birth_order1/5	-0.112	0.08048	-1.391	5789	0.1642	-0.3379	0.1139
fixed	NA	count_birth_order2/5	-0.09691	0.08883	-1.091	5757	0.2753	-0.3463	0.1524
fixed	NA	count_birth_order3/5	-0.05437	0.08475	-0.6416	5757	0.5212	-0.2923	0.1835
fixed	NA	count_birth_order4/5	-0.1419	0.08168	-1.738	5771	0.08234	-0.3712	0.08735
fixed	NA	count_birth_order5/5	-0.174	0.08675	-2.006	5757	0.04491	-0.4175	0.06949
fixed	NA	count_birth_order1/>5	-0.1511	0.08185	-1.846	5771	0.065	-0.3808	0.07869
fixed	NA	count_birth_order2/>5	-0.2914	0.08114	-3.591	5759	0.0003317	-0.5192	-0.06364
fixed	NA	count_birth_order3/>5	-0.05562	0.08034	-0.6923	5731	0.4888	-0.2812	0.1699
fixed	NA	count_birth_order4/>5	-0.1748	0.07855	-2.226	5705	0.02606	-0.3953	0.04565
fixed	NA	count_birth_order5/>5	-0.2837	0.07222	-3.929	5730	0.00008646	-0.4864	-0.08099
fixed	NA	count_birth_order>5/>5	-0.1808	0.05448	-3.319	5307	0.0009102	-0.3337	-0.02788
ran_pars	mother_pidlink	sd__(Intercept)	0.3538	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8382	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)
11	15343	15417	-7661	15321	NA	NA	NA
12	15345	15425	-7661	15321	0.03222	1	0.8575
16	15346	15453	-7657	15314	7.259	4	0.1228
26	15362	15535	-7655	15310	4.273	10	0.9342

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)	0.309	0.1522	2.03	13839	0.04237	-0.1183	0.7362
fixed	NA	poly(age, 3, raw = TRUE)1	0.01178	0.0146	0.8074	13779	0.4194	-0.02919	0.05275
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006651	0.0004297	-1.548	13646	0.1217	-0.001871	0.0005411
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001695	0.00000396	0.4279	13487	0.6687	-0.00000942	0.00001281
fixed	NA	male	-0.07984	0.01592	-5.015	13572	0.0000005358	-0.1245	-0.03515
fixed	NA	sibling_count3	0.05182	0.03269	1.585	10021	0.113	-0.03996	0.1436
fixed	NA	sibling_count4	0.03874	0.03375	1.148	9202	0.2511	-0.056	0.1335
fixed	NA	sibling_count5	0.007162	0.03517	0.2037	8305	0.8386	-0.09155	0.1059
fixed	NA	sibling_count>5	-0.06697	0.02754	-2.432	9296	0.01505	-0.1443	0.01034
ran_pars	mother_pidlink	sd__(Intercept)	0.3767	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8767	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)	0.3084	0.1522	2.026	13839	0.04274	-0.1188	0.7357
fixed	NA	birth_order	-0.001883	0.003389	-0.5557	13060	0.5784	-0.0114	0.007629
fixed	NA	poly(age, 3, raw = TRUE)1	0.01235	0.01463	0.8444	13767	0.3985	-0.02872	0.05343
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006861	0.0004314	-1.591	13594	0.1117	-0.001897	0.0005248
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000189	0.000003975	0.4754	13410	0.6345	-0.000009269	0.00001305
fixed	NA	male	-0.07979	0.01592	-5.012	13571	0.0000005458	-0.1245	-0.0351
fixed	NA	sibling_count3	0.05222	0.0327	1.597	10038	0.1103	-0.03958	0.144
fixed	NA	sibling_count4	0.04001	0.03383	1.183	9270	0.2369	-0.05495	0.135
fixed	NA	sibling_count5	0.00941	0.0354	0.2658	8426	0.7904	-0.08995	0.1088
fixed	NA	sibling_count>5	-0.05988	0.03035	-1.973	10433	0.04853	-0.1451	0.02532
ran_pars	mother_pidlink	sd__(Intercept)	0.3766	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8767	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)	0.3002	0.1526	1.967	13838	0.04921	-0.1282	0.7285
fixed	NA	poly(age, 3, raw = TRUE)1	0.01267	0.01463	0.8656	13771	0.3867	-0.02841	0.05375
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007038	0.0004314	-1.631	13599	0.1029	-0.001915	0.0005073
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002105	0.000003976	0.5294	13405	0.5966	-0.000009057	0.00001327
fixed	NA	male	-0.07975	0.01592	-5.009	13568	0.0000005541	-0.1244	-0.03506
fixed	NA	sibling_count3	0.054	0.03314	1.63	10368	0.1032	-0.03901	0.147
fixed	NA	sibling_count4	0.03784	0.03474	1.089	9942	0.276	-0.05967	0.1353
fixed	NA	sibling_count5	0.00649	0.03669	0.1769	9307	0.8596	-0.09651	0.1095
fixed	NA	sibling_count>5	-0.05398	0.03183	-1.696	11448	0.08992	-0.1433	0.03536
fixed	NA	birth_order_nonlinear2	0.01565	0.02303	0.6794	12559	0.4969	-0.04899	0.08029
fixed	NA	birth_order_nonlinear3	-0.008068	0.02716	-0.2971	12278	0.7664	-0.08431	0.06817
fixed	NA	birth_order_nonlinear4	0.01986	0.03094	0.6418	12316	0.521	-0.067	0.1067
fixed	NA	birth_order_nonlinear5	0.005391	0.0352	0.1531	12321	0.8783	-0.09343	0.1042
fixed	NA	birth_order_nonlinear>5	-0.02652	0.02938	-0.9024	13865	0.3668	-0.109	0.05596
ran_pars	mother_pidlink	sd__(Intercept)	0.3763	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8769	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)	0.2999	0.1533	1.957	13832	0.0504	-0.1303	0.7302
fixed	NA	poly(age, 3, raw = TRUE)1	0.0129	0.01464	0.8813	13762	0.3782	-0.02819	0.05399
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007085	0.0004316	-1.642	13584	0.1007	-0.00192	0.0005029
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002131	0.000003979	0.5357	13382	0.5922	-0.000009037	0.0000133
fixed	NA	male	-0.07974	0.01593	-5.007	13556	0.0000005593	-0.1244	-0.03504
fixed	NA	count_birth_order2/2	0.008045	0.04478	0.1796	12640	0.8574	-0.1177	0.1338
fixed	NA	count_birth_order1/3	0.06475	0.04293	1.508	13673	0.1315	-0.05575	0.1853
fixed	NA	count_birth_order2/3	0.05148	0.04795	1.074	13795	0.283	-0.08311	0.1861
fixed	NA	count_birth_order3/3	0.03626	0.05366	0.6757	13884	0.4992	-0.1144	0.1869
fixed	NA	count_birth_order1/4	0.006214	0.04899	0.1268	13799	0.8991	-0.1313	0.1437
fixed	NA	count_birth_order2/4	0.1041	0.05142	2.024	13840	0.04303	-0.04029	0.2484
fixed	NA	count_birth_order3/4	0.02208	0.05583	0.3954	13899	0.6925	-0.1346	0.1788
fixed	NA	count_birth_order4/4	0.03046	0.05912	0.5152	13919	0.6064	-0.1355	0.1964
fixed	NA	count_birth_order1/5	-0.04227	0.05551	-0.7614	13882	0.4464	-0.1981	0.1136
fixed	NA	count_birth_order2/5	0.02579	0.05822	0.4429	13909	0.6578	-0.1376	0.1892
fixed	NA	count_birth_order3/5	-0.005886	0.05987	-0.09831	13920	0.9217	-0.1739	0.1622
fixed	NA	count_birth_order4/5	0.03416	0.06337	0.539	13926	0.5899	-0.1437	0.212
fixed	NA	count_birth_order5/5	0.06224	0.06476	0.9611	13924	0.3365	-0.1195	0.244
fixed	NA	count_birth_order1/>5	-0.03199	0.04473	-0.7153	13923	0.4745	-0.1576	0.09356
fixed	NA	count_birth_order2/>5	-0.06433	0.0461	-1.395	13926	0.1629	-0.1937	0.06508
fixed	NA	count_birth_order3/>5	-0.058	0.0452	-1.283	13925	0.1995	-0.1849	0.06888
fixed	NA	count_birth_order4/>5	-0.03051	0.04429	-0.6888	13926	0.491	-0.1548	0.09382
fixed	NA	count_birth_order5/>5	-0.06936	0.04462	-1.554	13925	0.1201	-0.1946	0.05589
fixed	NA	count_birth_order>5/>5	-0.08347	0.0352	-2.372	12499	0.01773	-0.1823	0.01533
ran_pars	mother_pidlink	sd__(Intercept)	0.3767	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8769	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)
11	38051	38134	-19015	38029	NA	NA	NA
12	38053	38143	-19014	38029	0.3095	1	0.578
16	38058	38179	-19013	38026	2.904	4	0.574
26	38072	38268	-19010	38020	6.247	10	0.7941

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)	0.5229	0.4116	1.27	5873	0.204	-0.6325	1.678
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01788	0.04671	-0.3827	5877	0.7019	-0.149	0.1132
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007731	0.001667	0.4637	5882	0.6429	-0.003907	0.005453
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001439	0.00001888	-0.762	5888	0.4461	-0.00006739	0.00003862
fixed	NA	male	-0.115	0.02403	-4.784	5811	0.000001765	-0.1824	-0.04751
fixed	NA	sibling_count3	0.0267	0.03804	0.7019	4409	0.4828	-0.08008	0.1335
fixed	NA	sibling_count4	-0.04166	0.04102	-1.016	3917	0.3098	-0.1568	0.07348
fixed	NA	sibling_count5	-0.06095	0.04688	-1.3	3531	0.1937	-0.1926	0.07066
fixed	NA	sibling_count>5	-0.09835	0.04118	-2.388	3335	0.01698	-0.2139	0.01724
ran_pars	mother_pidlink	sd__(Intercept)	0.3583	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8618	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)	0.5171	0.4117	1.256	5872	0.2091	-0.6385	1.673
fixed	NA	birth_order	0.007062	0.007967	0.8865	5876	0.3754	-0.0153	0.02943
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01823	0.04672	-0.3902	5877	0.6964	-0.1494	0.1129
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007744	0.001667	0.4645	5881	0.6423	-0.003906	0.005455
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001412	0.00001889	-0.7477	5886	0.4547	-0.00006714	0.00003889
fixed	NA	male	-0.1153	0.02404	-4.796	5810	0.000001657	-0.1828	-0.04782
fixed	NA	sibling_count3	0.02326	0.03824	0.6082	4415	0.5431	-0.08409	0.1306
fixed	NA	sibling_count4	-0.04983	0.04204	-1.185	3930	0.236	-0.1678	0.06819
fixed	NA	sibling_count5	-0.07432	0.04925	-1.509	3621	0.1314	-0.2126	0.06393
fixed	NA	sibling_count>5	-0.1251	0.05104	-2.451	3868	0.0143	-0.2684	0.01819
ran_pars	mother_pidlink	sd__(Intercept)	0.3584	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8618	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)	0.519	0.4125	1.258	5877	0.2084	-0.639	1.677
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01781	0.04676	-0.3809	5877	0.7033	-0.1491	0.1135
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007623	0.001669	0.4567	5881	0.6479	-0.003923	0.005448
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001408	0.00001891	-0.7446	5885	0.4565	-0.00006716	0.000039
fixed	NA	male	-0.115	0.02405	-4.78	5806	0.000001797	-0.1825	-0.04745
fixed	NA	sibling_count3	0.02667	0.03902	0.6834	4598	0.4944	-0.08286	0.1362
fixed	NA	sibling_count4	-0.04087	0.04367	-0.9359	4255	0.3494	-0.1635	0.08171
fixed	NA	sibling_count5	-0.05821	0.05172	-1.125	4052	0.2605	-0.2034	0.08698
fixed	NA	sibling_count>5	-0.1119	0.05254	-2.13	4127	0.03319	-0.2594	0.03554
fixed	NA	birth_order_nonlinear2	0.01206	0.031	0.3889	4938	0.6973	-0.07495	0.09907
fixed	NA	birth_order_nonlinear3	0.0001107	0.03827	0.002894	5157	0.9977	-0.1073	0.1075
fixed	NA	birth_order_nonlinear4	-0.003256	0.04736	-0.06875	5306	0.9452	-0.1362	0.1297
fixed	NA	birth_order_nonlinear5	-0.004436	0.05912	-0.07503	5167	0.9402	-0.1704	0.1615
fixed	NA	birth_order_nonlinear>5	0.04355	0.05949	0.7321	5892	0.4641	-0.1234	0.2105
ran_pars	mother_pidlink	sd__(Intercept)	0.3573	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8625	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)	0.5809	0.4133	1.406	5869	0.1599	-0.5792	1.741
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02288	0.04685	-0.4885	5868	0.6252	-0.1544	0.1086
fixed	NA	poly(age, 3, raw = TRUE)2	0.0009401	0.001672	0.5622	5872	0.574	-0.003754	0.005634
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001602	0.00001895	-0.8455	5877	0.3978	-0.00006921	0.00003717
fixed	NA	male	-0.115	0.02406	-4.778	5796	0.000001813	-0.1825	-0.04743
fixed	NA	count_birth_order2/2	-0.03987	0.0561	-0.7107	5209	0.4773	-0.1973	0.1176
fixed	NA	count_birth_order1/3	0.01812	0.04988	0.3633	5870	0.7164	-0.1219	0.1581
fixed	NA	count_birth_order2/3	0.03543	0.05445	0.6507	5900	0.5153	-0.1174	0.1883
fixed	NA	count_birth_order3/3	-0.0276	0.06081	-0.4539	5908	0.6499	-0.1983	0.1431
fixed	NA	count_birth_order1/4	-0.09582	0.06099	-1.571	5894	0.1162	-0.267	0.07537
fixed	NA	count_birth_order2/4	0.009069	0.06301	0.1439	5908	0.8856	-0.1678	0.1859
fixed	NA	count_birth_order3/4	-0.06621	0.06652	-0.9952	5903	0.3197	-0.2529	0.1205
fixed	NA	count_birth_order4/4	-0.06907	0.06925	-0.9974	5900	0.3186	-0.2635	0.1253
fixed	NA	count_birth_order1/5	-0.1395	0.08275	-1.686	5907	0.09183	-0.3718	0.09276
fixed	NA	count_birth_order2/5	-0.03975	0.08852	-0.4491	5884	0.6534	-0.2882	0.2087
fixed	NA	count_birth_order3/5	-0.08459	0.08298	-1.019	5885	0.308	-0.3175	0.1483
fixed	NA	count_birth_order4/5	-0.1223	0.07995	-1.53	5895	0.1261	-0.3467	0.1021
fixed	NA	count_birth_order5/5	0.02383	0.08317	0.2865	5884	0.7745	-0.2096	0.2573
fixed	NA	count_birth_order1/>5	-0.1065	0.08207	-1.298	5897	0.1944	-0.3369	0.1239
fixed	NA	count_birth_order2/>5	-0.199	0.08123	-2.45	5886	0.0143	-0.427	0.02897
fixed	NA	count_birth_order3/>5	-0.03194	0.08132	-0.3928	5860	0.6945	-0.2602	0.1963
fixed	NA	count_birth_order4/>5	-0.08364	0.07662	-1.092	5857	0.275	-0.2987	0.1314
fixed	NA	count_birth_order5/>5	-0.2049	0.0724	-2.831	5861	0.004662	-0.4082	-0.001705
fixed	NA	count_birth_order>5/>5	-0.08616	0.05485	-1.571	5455	0.1163	-0.2401	0.06781
ran_pars	mother_pidlink	sd__(Intercept)	0.3559	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8628	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)
11	15967	16040	-7972	15945	NA	NA	NA
12	15968	16048	-7972	15944	0.7869	1	0.375
16	15976	16083	-7972	15944	0.1261	4	0.9981
26	15984	16158	-7966	15932	11.94	10	0.2889

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)	0.5618	0.4105	1.368	5925	0.1712	-0.5906	1.714
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02052	0.04661	-0.4403	5928	0.6597	-0.1514	0.1103
fixed	NA	poly(age, 3, raw = TRUE)2	0.0008411	0.001664	0.5055	5933	0.6132	-0.003829	0.005512
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000151	0.00001885	-0.801	5939	0.4231	-0.00006801	0.00003781
fixed	NA	male	-0.117	0.02395	-4.887	5859	0.000001049	-0.1843	-0.04982
fixed	NA	sibling_count3	0.01493	0.04115	0.3629	4565	0.7167	-0.1006	0.1305
fixed	NA	sibling_count4	-0.04601	0.04339	-1.061	4182	0.289	-0.1678	0.07577
fixed	NA	sibling_count5	-0.007199	0.04649	-0.1548	3785	0.877	-0.1377	0.1233
fixed	NA	sibling_count>5	-0.08743	0.04073	-2.147	3907	0.03189	-0.2018	0.0269
ran_pars	mother_pidlink	sd__(Intercept)	0.3588	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8621	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)	0.5616	0.4106	1.368	5924	0.1715	-0.5911	1.714
fixed	NA	birth_order	0.000166	0.006964	0.02383	5775	0.981	-0.01938	0.01972
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02052	0.04661	-0.4403	5927	0.6598	-0.1514	0.1103
fixed	NA	poly(age, 3, raw = TRUE)2	0.0008408	0.001664	0.5053	5931	0.6134	-0.00383	0.005512
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001509	0.00001885	-0.8003	5937	0.4236	-0.00006801	0.00003783
fixed	NA	male	-0.1171	0.02395	-4.887	5859	0.000001052	-0.1843	-0.04982
fixed	NA	sibling_count3	0.01485	0.0413	0.3596	4565	0.7191	-0.1011	0.1308
fixed	NA	sibling_count4	-0.0462	0.04407	-1.048	4175	0.2946	-0.1699	0.07751
fixed	NA	sibling_count5	-0.007488	0.04806	-0.1558	3807	0.8762	-0.1424	0.1274
fixed	NA	sibling_count>5	-0.08804	0.04811	-1.83	4216	0.06735	-0.2231	0.04702
ran_pars	mother_pidlink	sd__(Intercept)	0.3589	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8622	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)	0.5356	0.4112	1.302	5927	0.1928	-0.6188	1.69
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01871	0.04664	-0.4011	5927	0.6883	-0.1496	0.1122
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007845	0.001665	0.4711	5930	0.6376	-0.00389	0.005459
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001472	0.00001887	-0.7799	5936	0.4355	-0.00006769	0.00003825
fixed	NA	male	-0.1163	0.02396	-4.853	5854	0.000001246	-0.1835	-0.04903
fixed	NA	sibling_count3	0.01644	0.04204	0.3912	4716	0.6957	-0.1016	0.1344
fixed	NA	sibling_count4	-0.03607	0.0456	-0.7909	4457	0.4291	-0.1641	0.09194
fixed	NA	sibling_count5	0.00655	0.05033	0.1302	4196	0.8965	-0.1347	0.1478
fixed	NA	sibling_count>5	-0.05999	0.04958	-1.21	4489	0.2264	-0.1992	0.07919
fixed	NA	birth_order_nonlinear2	0.03067	0.03158	0.9712	5073	0.3315	-0.05798	0.1193
fixed	NA	birth_order_nonlinear3	-0.00388	0.03816	-0.1017	5281	0.919	-0.111	0.1032
fixed	NA	birth_order_nonlinear4	-0.03289	0.04598	-0.7153	5434	0.4745	-0.1619	0.09617
fixed	NA	birth_order_nonlinear5	-0.004899	0.05639	-0.08687	5371	0.9308	-0.1632	0.1534
fixed	NA	birth_order_nonlinear>5	-0.03593	0.05319	-0.6756	5969	0.4993	-0.1852	0.1134
ran_pars	mother_pidlink	sd__(Intercept)	0.359	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8622	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)	0.5631	0.4121	1.366	5921	0.1719	-0.5938	1.72
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02195	0.04672	-0.4699	5918	0.6384	-0.1531	0.1092
fixed	NA	poly(age, 3, raw = TRUE)2	0.0009012	0.001668	0.5401	5922	0.5891	-0.003782	0.005584
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001601	0.00001891	-0.8466	5928	0.3972	-0.00006909	0.00003707
fixed	NA	male	-0.1161	0.02398	-4.841	5845	0.000001323	-0.1834	-0.04879
fixed	NA	count_birth_order2/2	0.031	0.06149	0.5042	5331	0.6142	-0.1416	0.2036
fixed	NA	count_birth_order1/3	0.03858	0.05405	0.7138	5921	0.4754	-0.1131	0.1903
fixed	NA	count_birth_order2/3	0.04624	0.05861	0.789	5949	0.4302	-0.1183	0.2108
fixed	NA	count_birth_order3/3	-0.03029	0.06591	-0.4596	5959	0.6458	-0.2153	0.1547
fixed	NA	count_birth_order1/4	-0.09284	0.06392	-1.452	5945	0.1464	-0.2723	0.08658
fixed	NA	count_birth_order2/4	0.04085	0.06489	0.6295	5957	0.529	-0.1413	0.223
fixed	NA	count_birth_order3/4	-0.03359	0.07128	-0.4712	5954	0.6375	-0.2337	0.1665
fixed	NA	count_birth_order4/4	-0.05443	0.0736	-0.7396	5954	0.4596	-0.261	0.1522
fixed	NA	count_birth_order1/5	0.01304	0.07582	0.172	5958	0.8635	-0.1998	0.2259
fixed	NA	count_birth_order2/5	0.04794	0.08135	0.5893	5948	0.5557	-0.1804	0.2763
fixed	NA	count_birth_order3/5	-0.003747	0.07911	-0.04736	5946	0.9622	-0.2258	0.2183
fixed	NA	count_birth_order4/5	-0.05214	0.08197	-0.6361	5935	0.5248	-0.2822	0.178
fixed	NA	count_birth_order5/5	0.01449	0.0822	0.1763	5935	0.86	-0.2162	0.2452
fixed	NA	count_birth_order1/>5	-0.04045	0.07206	-0.5613	5959	0.5746	-0.2427	0.1618
fixed	NA	count_birth_order2/>5	-0.1055	0.07521	-1.403	5945	0.1607	-0.3166	0.1056
fixed	NA	count_birth_order3/>5	-0.01007	0.07364	-0.1367	5933	0.8913	-0.2168	0.1966
fixed	NA	count_birth_order4/>5	-0.08782	0.07098	-1.237	5932	0.2161	-0.2871	0.1114
fixed	NA	count_birth_order5/>5	-0.07425	0.07291	-1.018	5902	0.3085	-0.2789	0.1304
fixed	NA	count_birth_order>5/>5	-0.09624	0.05377	-1.79	5566	0.07355	-0.2472	0.0547
ran_pars	mother_pidlink	sd__(Intercept)	0.3582	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8629	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)
11	16110	16184	-8044	16088	NA	NA	NA
12	16112	16192	-8044	16088	0.0005688	1	0.981
16	16117	16225	-8043	16085	2.665	4	0.6153
26	16132	16306	-8040	16080	5.799	10	0.8318

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)	0.4531	0.4156	1.09	5754	0.2757	-0.7136	1.62
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01023	0.04719	-0.2168	5757	0.8284	-0.1427	0.1222
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004686	0.001685	0.2781	5761	0.7809	-0.004261	0.005198
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001034	0.00001909	-0.5417	5767	0.588	-0.00006394	0.00004325
fixed	NA	male	-0.1113	0.02423	-4.593	5690	0.000004467	-0.1793	-0.04328
fixed	NA	sibling_count3	0.0278	0.03751	0.7411	4312	0.4587	-0.0775	0.1331
fixed	NA	sibling_count4	-0.03086	0.04071	-0.7581	3848	0.4484	-0.1451	0.08342
fixed	NA	sibling_count5	-0.05099	0.04803	-1.062	3372	0.2885	-0.1858	0.08383
fixed	NA	sibling_count>5	-0.1063	0.04162	-2.554	3184	0.01071	-0.2231	0.01055
ran_pars	mother_pidlink	sd__(Intercept)	0.3613	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8587	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)	0.4481	0.4157	1.078	5753	0.2811	-0.7188	1.615
fixed	NA	birth_order	0.007437	0.008192	0.9078	5780	0.364	-0.01556	0.03043
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01071	0.04719	-0.2268	5757	0.8206	-0.1432	0.1218
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004727	0.001685	0.2806	5760	0.779	-0.004257	0.005202
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001009	0.0000191	-0.5283	5765	0.5973	-0.00006369	0.00004351
fixed	NA	male	-0.1115	0.02424	-4.601	5689	0.000004298	-0.1795	-0.04347
fixed	NA	sibling_count3	0.02415	0.03773	0.6402	4316	0.5221	-0.08175	0.1301
fixed	NA	sibling_count4	-0.03934	0.04177	-0.9419	3873	0.3463	-0.1566	0.07791
fixed	NA	sibling_count5	-0.06446	0.05027	-1.282	3458	0.1999	-0.2056	0.07666
fixed	NA	sibling_count>5	-0.1342	0.05175	-2.593	3809	0.009545	-0.2794	0.01106
ran_pars	mother_pidlink	sd__(Intercept)	0.3613	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8587	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)	0.4518	0.4165	1.085	5758	0.278	-0.7172	1.621
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01037	0.04723	-0.2196	5758	0.8262	-0.143	0.1222
fixed	NA	poly(age, 3, raw = TRUE)2	0.0004663	0.001686	0.2765	5760	0.7821	-0.004267	0.0052
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001016	0.00001911	-0.5316	5764	0.595	-0.00006382	0.00004349
fixed	NA	male	-0.1112	0.02425	-4.585	5685	0.000004632	-0.1792	-0.04311
fixed	NA	sibling_count3	0.02459	0.03852	0.6384	4500	0.5232	-0.08354	0.1327
fixed	NA	sibling_count4	-0.03243	0.04344	-0.7466	4196	0.4553	-0.1544	0.08949
fixed	NA	sibling_count5	-0.04803	0.05255	-0.9139	3839	0.3608	-0.1955	0.09949
fixed	NA	sibling_count>5	-0.119	0.05332	-2.231	4083	0.02571	-0.2686	0.03069
fixed	NA	birth_order_nonlinear2	0.009103	0.03086	0.295	4820	0.768	-0.07751	0.09571
fixed	NA	birth_order_nonlinear3	0.01424	0.03819	0.3728	5019	0.7093	-0.09296	0.1214
fixed	NA	birth_order_nonlinear4	-0.008	0.04863	-0.1645	5165	0.8693	-0.1445	0.1285
fixed	NA	birth_order_nonlinear5	-0.01714	0.06154	-0.2786	5050	0.7806	-0.1899	0.1556
fixed	NA	birth_order_nonlinear>5	0.04256	0.06125	0.6948	5748	0.4872	-0.1294	0.2145
ran_pars	mother_pidlink	sd__(Intercept)	0.3603	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8594	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)	0.4984	0.4175	1.194	5751	0.2326	-0.6735	1.67
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01432	0.04735	-0.3024	5749	0.7623	-0.1472	0.1186
fixed	NA	poly(age, 3, raw = TRUE)2	0.0006025	0.001691	0.3564	5752	0.7216	-0.004143	0.005348
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001163	0.00001917	-0.6066	5757	0.5441	-0.00006543	0.00004218
fixed	NA	male	-0.1119	0.02427	-4.613	5674	0.000004065	-0.1801	-0.04382
fixed	NA	count_birth_order2/2	-0.02321	0.05452	-0.4258	5052	0.6703	-0.1763	0.1298
fixed	NA	count_birth_order1/3	0.0164	0.0492	0.3334	5750	0.7389	-0.1217	0.1545
fixed	NA	count_birth_order2/3	0.0359	0.05434	0.6607	5785	0.5089	-0.1166	0.1884
fixed	NA	count_birth_order3/3	0.005022	0.05963	0.08422	5789	0.9329	-0.1624	0.1724
fixed	NA	count_birth_order1/4	-0.05444	0.06119	-0.8898	5781	0.3736	-0.2262	0.1173
fixed	NA	count_birth_order2/4	0.01122	0.06281	0.1786	5789	0.8583	-0.1651	0.1875
fixed	NA	count_birth_order3/4	-0.05586	0.06573	-0.8499	5781	0.3954	-0.2404	0.1286
fixed	NA	count_birth_order4/4	-0.06476	0.06956	-0.9311	5775	0.3519	-0.26	0.1305
fixed	NA	count_birth_order1/5	-0.1147	0.08246	-1.39	5789	0.1645	-0.3461	0.1168
fixed	NA	count_birth_order2/5	-0.0301	0.09102	-0.3307	5759	0.7409	-0.2856	0.2254
fixed	NA	count_birth_order3/5	-0.04437	0.08684	-0.511	5759	0.6094	-0.2881	0.1994
fixed	NA	count_birth_order4/5	-0.08581	0.0837	-1.025	5772	0.3053	-0.3208	0.1491
fixed	NA	count_birth_order5/5	-0.004708	0.08889	-0.05296	5759	0.9578	-0.2542	0.2448
fixed	NA	count_birth_order1/>5	-0.1188	0.08387	-1.416	5772	0.1568	-0.3542	0.1167
fixed	NA	count_birth_order2/>5	-0.2097	0.08314	-2.522	5761	0.01169	-0.4431	0.02369
fixed	NA	count_birth_order3/>5	-0.02078	0.08233	-0.2523	5735	0.8008	-0.2519	0.2103
fixed	NA	count_birth_order4/>5	-0.1022	0.0805	-1.27	5709	0.2043	-0.3281	0.1238
fixed	NA	count_birth_order5/>5	-0.1908	0.07401	-2.578	5733	0.009954	-0.3985	0.01693
fixed	NA	count_birth_order>5/>5	-0.08773	0.0558	-1.572	5314	0.116	-0.2444	0.06892
ran_pars	mother_pidlink	sd__(Intercept)	0.3595	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8599	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)
11	15623	15696	-7801	15601	NA	NA	NA
12	15624	15704	-7800	15600	0.8254	1	0.3636
16	15632	15739	-7800	15600	0.2888	4	0.9905
26	15645	15818	-7796	15593	7.352	10	0.6918

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)	0.3787	0.1518	2.495	13899	0.01262	-0.04741	0.8049
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0186	0.01457	-1.276	13882	0.2019	-0.05949	0.0223
fixed	NA	poly(age, 3, raw = TRUE)2	0.00058	0.0004296	1.35	13811	0.177	-0.0006259	0.001786
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001002	0.000003964	-2.527	13702	0.01151	-0.00002115	0.00000111
fixed	NA	male	0.09485	0.01571	6.038	13201	0.000000001602	0.05075	0.1389
fixed	NA	sibling_count3	0.032	0.03342	0.9577	9639	0.3382	-0.0618	0.1258
fixed	NA	sibling_count4	-0.01255	0.03463	-0.3623	8940	0.7171	-0.1098	0.08466
fixed	NA	sibling_count5	0.0188	0.03622	0.519	8209	0.6037	-0.08287	0.1205
fixed	NA	sibling_count>5	-0.1474	0.02824	-5.219	9034	0.0000001843	-0.2266	-0.06809
ran_pars	mother_pidlink	sd__(Intercept)	0.4629	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8391	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)	0.3788	0.1518	2.495	13899	0.0126	-0.04736	0.805
fixed	NA	birth_order	0.0008488	0.003398	0.2498	13686	0.8028	-0.008691	0.01039
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01886	0.01461	-1.291	13876	0.1968	-0.05986	0.02215
fixed	NA	poly(age, 3, raw = TRUE)2	0.00059	0.0004315	1.367	13776	0.1715	-0.0006213	0.001801
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001011	0.000003983	-2.539	13641	0.01113	-0.00002129	0.000001068
fixed	NA	male	0.09483	0.01571	6.036	13198	0.000000001619	0.05073	0.1389
fixed	NA	sibling_count3	0.03184	0.03343	0.9526	9643	0.3408	-0.06199	0.1257
fixed	NA	sibling_count4	-0.01309	0.0347	-0.3773	8996	0.7059	-0.1105	0.08431
fixed	NA	sibling_count5	0.0178	0.03644	0.4886	8323	0.6252	-0.08448	0.1201
fixed	NA	sibling_count>5	-0.1505	0.03095	-4.863	10228	0.000001174	-0.2374	-0.06363
ran_pars	mother_pidlink	sd__(Intercept)	0.4631	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.839	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)	0.3755	0.1522	2.467	13895	0.01363	-0.05173	0.8028
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01884	0.01461	-1.289	13875	0.1974	-0.05985	0.02218
fixed	NA	poly(age, 3, raw = TRUE)2	0.000594	0.0004315	1.376	13777	0.1687	-0.0006173	0.001805
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001017	0.000003984	-2.554	13635	0.01067	-0.00002136	0.000001009
fixed	NA	male	0.0947	0.01571	6.028	13194	0.000000001706	0.0506	0.1388
fixed	NA	sibling_count3	0.03351	0.03383	0.9908	9953	0.3218	-0.06144	0.1285
fixed	NA	sibling_count4	-0.006042	0.03553	-0.1701	9610	0.865	-0.1058	0.09369
fixed	NA	sibling_count5	0.01888	0.03763	0.5017	9115	0.6159	-0.08674	0.1245
fixed	NA	sibling_count>5	-0.1519	0.03232	-4.701	11144	0.000002616	-0.2427	-0.06122
fixed	NA	birth_order_nonlinear2	0.006312	0.02259	0.2794	12336	0.7799	-0.0571	0.06972
fixed	NA	birth_order_nonlinear3	-0.004016	0.02658	-0.1511	11948	0.8799	-0.07863	0.0706
fixed	NA	birth_order_nonlinear4	-0.02674	0.03029	-0.8829	11934	0.3773	-0.1118	0.05828
fixed	NA	birth_order_nonlinear5	0.04054	0.03445	1.177	11911	0.2394	-0.05617	0.1372
fixed	NA	birth_order_nonlinear>5	0.0124	0.02911	0.4258	13684	0.6702	-0.06933	0.09412
ran_pars	mother_pidlink	sd__(Intercept)	0.4633	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.839	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)	0.3813	0.1528	2.495	13885	0.01261	-0.04771	0.8103
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01851	0.01461	-1.267	13865	0.2053	-0.05952	0.0225
fixed	NA	poly(age, 3, raw = TRUE)2	0.0005781	0.0004316	1.339	13762	0.1804	-0.0006334	0.00179
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000009971	0.000003985	-2.502	13612	0.01237	-0.00002116	0.000001216
fixed	NA	male	0.09384	0.01571	5.974	13182	0.000000002376	0.04975	0.1379
fixed	NA	count_birth_order2/2	-0.01282	0.04393	-0.2919	12643	0.7704	-0.1361	0.1105
fixed	NA	count_birth_order1/3	-0.01112	0.04301	-0.2585	13409	0.796	-0.1318	0.1096
fixed	NA	count_birth_order2/3	0.06464	0.04793	1.349	13659	0.1775	-0.0699	0.1992
fixed	NA	count_birth_order3/3	0.0586	0.05349	1.095	13826	0.2733	-0.09156	0.2088
fixed	NA	count_birth_order1/4	-0.04414	0.04894	-0.9019	13651	0.3671	-0.1815	0.09324
fixed	NA	count_birth_order2/4	-0.00802	0.05143	-0.156	13743	0.8761	-0.1524	0.1363
fixed	NA	count_birth_order3/4	0.01828	0.05567	0.3283	13860	0.7427	-0.138	0.1746
fixed	NA	count_birth_order4/4	-0.02113	0.05884	-0.3592	13893	0.7195	-0.1863	0.144
fixed	NA	count_birth_order1/5	-0.0386	0.05535	-0.6975	13811	0.4855	-0.194	0.1168
fixed	NA	count_birth_order2/5	0.0696	0.05811	1.198	13868	0.231	-0.09351	0.2327
fixed	NA	count_birth_order3/5	-0.01428	0.05957	-0.2397	13892	0.8106	-0.1815	0.1529
fixed	NA	count_birth_order4/5	0.002029	0.06299	0.03221	13904	0.9743	-0.1748	0.1788
fixed	NA	count_birth_order5/5	0.07302	0.06434	1.135	13901	0.2564	-0.1076	0.2536
fixed	NA	count_birth_order1/>5	-0.0773	0.04455	-1.735	13896	0.08278	-0.2024	0.04777
fixed	NA	count_birth_order2/>5	-0.1907	0.04587	-4.157	13904	0.00003243	-0.3195	-0.06193
fixed	NA	count_birth_order3/>5	-0.1895	0.04493	-4.217	13904	0.0000249	-0.3156	-0.06336
fixed	NA	count_birth_order4/>5	-0.1979	0.04407	-4.49	13902	0.000007175	-0.3216	-0.07418
fixed	NA	count_birth_order5/>5	-0.1246	0.04435	-2.81	13904	0.004968	-0.2491	-0.0001122
fixed	NA	count_birth_order>5/>5	-0.1466	0.03553	-4.125	12295	0.00003725	-0.2463	-0.04684
ran_pars	mother_pidlink	sd__(Intercept)	0.4635	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_naive_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
11	37830	37913	-18904	37808	NA	NA	NA
12	37832	37922	-18904	37808	0.0613	1	0.8045
16	37836	37957	-18902	37804	3.594	4	0.4637
26	37840	38036	-18894	37788	15.97	10	0.1004

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)	-0.5739	0.3823	-1.501	5774	0.1333	-1.647	0.4992
fixed	NA	poly(age, 3, raw = TRUE)1	0.102	0.04338	2.351	5769	0.01874	-0.01977	0.2238
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003674	0.001548	-2.373	5767	0.01768	-0.00802	0.0006721
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004194	0.00001754	2.391	5770	0.01681	-0.000007288	0.00009117
fixed	NA	male	0.03722	0.02229	1.67	5660	0.09505	-0.02535	0.09979
fixed	NA	sibling_count3	-0.02318	0.03623	-0.6397	4238	0.5224	-0.1249	0.07853
fixed	NA	sibling_count4	-0.07966	0.03922	-2.031	3813	0.04233	-0.1898	0.03044
fixed	NA	sibling_count5	-0.09175	0.04495	-2.041	3496	0.04132	-0.2179	0.03444
fixed	NA	sibling_count>5	-0.2292	0.03956	-5.795	3364	0.000000007481	-0.3403	-0.1182
ran_pars	mother_pidlink	sd__(Intercept)	0.4128	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7721	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)	-0.581	0.3823	-1.52	5773	0.1286	-1.654	0.4921
fixed	NA	birth_order	0.009145	0.007438	1.229	5911	0.2189	-0.01173	0.03002
fixed	NA	poly(age, 3, raw = TRUE)1	0.1014	0.04338	2.338	5769	0.01942	-0.02035	0.2232
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003667	0.001548	-2.368	5766	0.0179	-0.008013	0.0006791
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004223	0.00001754	2.408	5767	0.01607	-0.000006998	0.00009147
fixed	NA	male	0.03681	0.02229	1.651	5659	0.09872	-0.02576	0.09938
fixed	NA	sibling_count3	-0.02771	0.03642	-0.7608	4249	0.4468	-0.1299	0.07452
fixed	NA	sibling_count4	-0.09046	0.0402	-2.251	3839	0.02447	-0.2033	0.02237
fixed	NA	sibling_count5	-0.1094	0.04718	-2.318	3609	0.02052	-0.2418	0.02309
fixed	NA	sibling_count>5	-0.2643	0.04877	-5.419	3923	0.00000006361	-0.4012	-0.1274
ran_pars	mother_pidlink	sd__(Intercept)	0.4131	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7719	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)	-0.5991	0.3831	-1.564	5786	0.1179	-1.674	0.4763
fixed	NA	poly(age, 3, raw = TRUE)1	0.104	0.04342	2.395	5775	0.01665	-0.01788	0.2259
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003757	0.00155	-2.425	5770	0.01536	-0.008108	0.0005927
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004323	0.00001756	2.462	5769	0.01384	-0.000006057	0.00009251
fixed	NA	male	0.03724	0.0223	1.67	5654	0.09492	-0.02534	0.09982
fixed	NA	sibling_count3	-0.03169	0.0371	-0.8543	4426	0.393	-0.1358	0.07245
fixed	NA	sibling_count4	-0.09277	0.04163	-2.228	4143	0.02591	-0.2096	0.02409
fixed	NA	sibling_count5	-0.1259	0.04936	-2.55	4008	0.01081	-0.2644	0.01268
fixed	NA	sibling_count>5	-0.2684	0.05009	-5.359	4152	0.00000008805	-0.409	-0.1278
fixed	NA	birth_order_nonlinear2	0.02271	0.02845	0.7982	4741	0.4248	-0.05715	0.1026
fixed	NA	birth_order_nonlinear3	0.0366	0.03519	1.04	4938	0.2984	-0.06219	0.1354
fixed	NA	birth_order_nonlinear4	0.02322	0.04359	0.5326	5098	0.5943	-0.09914	0.1456
fixed	NA	birth_order_nonlinear5	0.1172	0.05437	2.156	4908	0.03115	-0.0354	0.2698
fixed	NA	birth_order_nonlinear>5	0.04245	0.05526	0.7682	5770	0.4424	-0.1127	0.1976
ran_pars	mother_pidlink	sd__(Intercept)	0.413	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.772	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)	-0.5894	0.384	-1.535	5781	0.1248	-1.667	0.4884
fixed	NA	poly(age, 3, raw = TRUE)1	0.1022	0.04351	2.348	5765	0.01891	-0.01997	0.2243
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003663	0.001553	-2.358	5762	0.0184	-0.008023	0.0006972
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004183	0.0000176	2.376	5762	0.01751	-0.000007578	0.00009124
fixed	NA	male	0.03646	0.02231	1.634	5641	0.1023	-0.02617	0.09909
fixed	NA	count_birth_order2/2	0.02404	0.05166	0.4654	5112	0.6417	-0.121	0.1691
fixed	NA	count_birth_order1/3	-0.05451	0.04671	-1.167	5813	0.2433	-0.1856	0.07661
fixed	NA	count_birth_order2/3	0.01584	0.05088	0.3112	5880	0.7557	-0.127	0.1587
fixed	NA	count_birth_order3/3	0.01729	0.05675	0.3047	5898	0.7606	-0.142	0.1766
fixed	NA	count_birth_order1/4	-0.1283	0.05698	-2.251	5872	0.0244	-0.2882	0.03166
fixed	NA	count_birth_order2/4	-0.06935	0.05883	-1.179	5897	0.2386	-0.2345	0.0958
fixed	NA	count_birth_order3/4	-0.03725	0.06203	-0.6005	5888	0.5482	-0.2114	0.1369
fixed	NA	count_birth_order4/4	-0.03674	0.06447	-0.5699	5886	0.5688	-0.2177	0.1442
fixed	NA	count_birth_order1/5	-0.03692	0.07709	-0.4789	5894	0.632	-0.2533	0.1795
fixed	NA	count_birth_order2/5	-0.1199	0.0823	-1.457	5843	0.1452	-0.3509	0.1111
fixed	NA	count_birth_order3/5	-0.154	0.07716	-1.996	5852	0.04598	-0.3706	0.06257
fixed	NA	count_birth_order4/5	-0.1267	0.0744	-1.704	5876	0.08851	-0.3356	0.08209
fixed	NA	count_birth_order5/5	0.002534	0.07733	0.03277	5856	0.9739	-0.2145	0.2196
fixed	NA	count_birth_order1/>5	-0.1809	0.07635	-2.37	5857	0.01783	-0.3952	0.03338
fixed	NA	count_birth_order2/>5	-0.3047	0.07551	-4.035	5833	0.00005528	-0.5166	-0.09273
fixed	NA	count_birth_order3/>5	-0.2237	0.07552	-2.963	5789	0.003061	-0.4357	-0.01177
fixed	NA	count_birth_order4/>5	-0.2646	0.07115	-3.718	5793	0.0002025	-0.4643	-0.06484
fixed	NA	count_birth_order5/>5	-0.1598	0.06737	-2.372	5806	0.01771	-0.3489	0.02929
fixed	NA	count_birth_order>5/>5	-0.2265	0.05166	-4.384	5516	0.00001186	-0.3715	-0.08147
ran_pars	mother_pidlink	sd__(Intercept)	0.413	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7722	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)
11	15107	15181	-7543	15085	NA	NA	NA
12	15108	15188	-7542	15084	1.512	1	0.2188
16	15112	15219	-7540	15080	3.495	4	0.4787
26	15124	15298	-7536	15072	7.814	10	0.647

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)	-0.547	0.381	-1.436	5823	0.1511	-1.617	0.5225
fixed	NA	poly(age, 3, raw = TRUE)1	0.09819	0.04326	2.27	5816	0.02324	-0.02323	0.2196
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003581	0.001544	-2.319	5813	0.02043	-0.007916	0.0007537
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000409	0.0000175	2.338	5816	0.01943	-0.000008209	0.00009001
fixed	NA	male	0.03865	0.0222	1.741	5706	0.08169	-0.02365	0.101
fixed	NA	sibling_count3	-0.001308	0.03913	-0.03344	4392	0.9733	-0.1111	0.1085
fixed	NA	sibling_count4	-0.05356	0.04142	-1.293	4053	0.1961	-0.1698	0.06272
fixed	NA	sibling_count5	-0.04134	0.04448	-0.9294	3723	0.3527	-0.1662	0.08352
fixed	NA	sibling_count>5	-0.1437	0.03893	-3.692	3869	0.0002256	-0.253	-0.03445
ran_pars	mother_pidlink	sd__(Intercept)	0.4147	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7712	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)	-0.548	0.3811	-1.438	5822	0.1505	-1.618	0.5218
fixed	NA	birth_order	0.0009386	0.006519	0.144	5926	0.8855	-0.01736	0.01924
fixed	NA	poly(age, 3, raw = TRUE)1	0.09817	0.04326	2.269	5815	0.02329	-0.02326	0.2196
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003582	0.001544	-2.319	5812	0.02042	-0.007916	0.0007535
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004095	0.0000175	2.34	5814	0.01933	-0.000008176	0.00009007
fixed	NA	male	0.03861	0.0222	1.739	5705	0.082	-0.0237	0.1009
fixed	NA	sibling_count3	-0.001773	0.03926	-0.04515	4393	0.964	-0.112	0.1084
fixed	NA	sibling_count4	-0.05462	0.04208	-1.298	4053	0.1943	-0.1727	0.06349
fixed	NA	sibling_count5	-0.04301	0.04597	-0.9356	3759	0.3495	-0.1721	0.08603
fixed	NA	sibling_count>5	-0.1472	0.04585	-3.211	4213	0.001332	-0.2759	-0.01853
ran_pars	mother_pidlink	sd__(Intercept)	0.4149	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7712	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)	-0.5634	0.3817	-1.476	5834	0.1399	-1.635	0.5079
fixed	NA	poly(age, 3, raw = TRUE)1	0.09955	0.04328	2.3	5821	0.02147	-0.02193	0.221
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003632	0.001545	-2.35	5817	0.01878	-0.007969	0.0007054
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004154	0.00001751	2.373	5816	0.0177	-0.000007607	0.00009069
fixed	NA	male	0.03953	0.0222	1.781	5701	0.07498	-0.02278	0.1018
fixed	NA	sibling_count3	0.0002314	0.03989	0.005801	4546	0.9954	-0.1118	0.1122
fixed	NA	sibling_count4	-0.04784	0.04341	-1.102	4325	0.2705	-0.1697	0.07402
fixed	NA	sibling_count5	-0.05674	0.04795	-1.183	4125	0.2367	-0.1913	0.07785
fixed	NA	sibling_count>5	-0.1505	0.04712	-3.194	4452	0.001413	-0.2828	-0.01824
fixed	NA	birth_order_nonlinear2	0.01206	0.02899	0.416	4884	0.6774	-0.06931	0.09343
fixed	NA	birth_order_nonlinear3	-0.007123	0.03509	-0.203	5065	0.8391	-0.1056	0.09137
fixed	NA	birth_order_nonlinear4	-0.02017	0.04232	-0.4766	5235	0.6337	-0.139	0.09862
fixed	NA	birth_order_nonlinear5	0.119	0.05185	2.294	5125	0.0218	-0.02658	0.2645
fixed	NA	birth_order_nonlinear>5	-0.007059	0.04951	-0.1426	5918	0.8866	-0.146	0.1319
ran_pars	mother_pidlink	sd__(Intercept)	0.4146	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.771	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)	-0.5329	0.3822	-1.394	5831	0.1633	-1.606	0.54
fixed	NA	poly(age, 3, raw = TRUE)1	0.09492	0.04332	2.191	5813	0.02846	-0.02667	0.2165
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00344	0.001547	-2.224	5809	0.02617	-0.007782	0.0009015
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003911	0.00001753	2.231	5810	0.02573	-0.0000101	0.00008832
fixed	NA	male	0.03859	0.0222	1.739	5690	0.08215	-0.02371	0.1009
fixed	NA	count_birth_order2/2	0.02549	0.05653	0.4508	5251	0.6521	-0.1332	0.1842
fixed	NA	count_birth_order1/3	-0.01494	0.05051	-0.2957	5865	0.7675	-0.1567	0.1268
fixed	NA	count_birth_order2/3	0.0181	0.05465	0.3312	5927	0.7405	-0.1353	0.1715
fixed	NA	count_birth_order3/3	0.03519	0.06135	0.5737	5949	0.5662	-0.137	0.2074
fixed	NA	count_birth_order1/4	-0.1124	0.05962	-1.886	5920	0.05939	-0.2798	0.05493
fixed	NA	count_birth_order2/4	0.02033	0.06071	0.3348	5945	0.7378	-0.1501	0.1907
fixed	NA	count_birth_order3/4	-0.01424	0.06636	-0.2146	5938	0.8301	-0.2005	0.172
fixed	NA	count_birth_order4/4	-0.06868	0.06842	-1.004	5940	0.3155	-0.2607	0.1234
fixed	NA	count_birth_order1/5	0.01101	0.07059	0.1559	5948	0.8761	-0.1871	0.2092
fixed	NA	count_birth_order2/5	-0.05006	0.07557	-0.6624	5923	0.5077	-0.2622	0.1621
fixed	NA	count_birth_order3/5	-0.1674	0.07348	-2.278	5922	0.02277	-0.3736	0.03889
fixed	NA	count_birth_order4/5	-0.07244	0.07609	-0.952	5904	0.3411	-0.286	0.1411
fixed	NA	count_birth_order5/5	0.1097	0.0763	1.438	5906	0.1504	-0.1044	0.3239
fixed	NA	count_birth_order1/>5	-0.0476	0.06705	-0.7099	5948	0.4778	-0.2358	0.1406
fixed	NA	count_birth_order2/>5	-0.2193	0.06985	-3.139	5909	0.001703	-0.4153	-0.02319
fixed	NA	count_birth_order3/>5	-0.1526	0.06844	-2.229	5891	0.02584	-0.3447	0.03955
fixed	NA	count_birth_order4/>5	-0.1628	0.06588	-2.471	5896	0.01352	-0.3477	0.02217
fixed	NA	count_birth_order5/>5	-0.06021	0.06758	-0.891	5842	0.373	-0.2499	0.1295
fixed	NA	count_birth_order>5/>5	-0.1548	0.05053	-3.063	5608	0.002199	-0.2966	-0.01295
ran_pars	mother_pidlink	sd__(Intercept)	0.4146	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7706	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)
11	15237	15311	-7608	15215	NA	NA	NA
12	15239	15319	-7608	15215	0.02042	1	0.8864
16	15239	15346	-7604	15207	7.892	4	0.09562
26	15244	15418	-7596	15192	15.53	10	0.1138

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)	-0.6109	0.3868	-1.579	5647	0.1143	-1.697	0.4749
fixed	NA	poly(age, 3, raw = TRUE)1	0.1055	0.04391	2.404	5640	0.01627	-0.01772	0.2288
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003789	0.001568	-2.417	5636	0.0157	-0.008189	0.0006121
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004303	0.00001777	2.422	5637	0.01548	-0.000006848	0.0000929
fixed	NA	male	0.03418	0.02252	1.518	5529	0.1291	-0.02903	0.09739
fixed	NA	sibling_count3	-0.01054	0.03585	-0.294	4150	0.7688	-0.1112	0.0901
fixed	NA	sibling_count4	-0.08272	0.03907	-2.117	3755	0.03428	-0.1924	0.02694
fixed	NA	sibling_count5	-0.07539	0.04627	-1.629	3360	0.1033	-0.2053	0.05449
fixed	NA	sibling_count>5	-0.2279	0.04017	-5.672	3233	0.00000001533	-0.3406	-0.1151
ran_pars	mother_pidlink	sd__(Intercept)	0.4197	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7695	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)	-0.6191	0.3868	-1.601	5646	0.1095	-1.705	0.4665
fixed	NA	birth_order	0.0126	0.007659	1.645	5784	0.09994	-0.008897	0.0341
fixed	NA	poly(age, 3, raw = TRUE)1	0.1046	0.04391	2.383	5640	0.01723	-0.01864	0.2279
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003775	0.001567	-2.408	5635	0.01606	-0.008175	0.0006249
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000434	0.00001777	2.443	5634	0.0146	-0.00000647	0.00009327
fixed	NA	male	0.03386	0.02252	1.504	5528	0.1327	-0.02935	0.09706
fixed	NA	sibling_count3	-0.01685	0.03605	-0.4673	4161	0.6403	-0.1181	0.08436
fixed	NA	sibling_count4	-0.0974	0.04007	-2.431	3795	0.01511	-0.2099	0.01507
fixed	NA	sibling_count5	-0.09864	0.04838	-2.039	3465	0.04152	-0.2344	0.03715
fixed	NA	sibling_count>5	-0.2758	0.04961	-5.559	3874	0.00000002902	-0.4151	-0.1365
ran_pars	mother_pidlink	sd__(Intercept)	0.42	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7693	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)	-0.638	0.3876	-1.646	5661	0.09976	-1.726	0.4499
fixed	NA	poly(age, 3, raw = TRUE)1	0.1074	0.04395	2.444	5648	0.01454	-0.01594	0.2308
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003874	0.001569	-2.469	5641	0.01356	-0.008278	0.0005296
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004448	0.00001778	2.501	5638	0.0124	-0.000005438	0.0000944
fixed	NA	male	0.03404	0.02252	1.511	5524	0.1308	-0.02918	0.09725
fixed	NA	sibling_count3	-0.0171	0.03674	-0.4653	4339	0.6417	-0.1202	0.08604
fixed	NA	sibling_count4	-0.09868	0.04153	-2.376	4097	0.01754	-0.2153	0.01789
fixed	NA	sibling_count5	-0.1131	0.05037	-2.245	3816	0.02482	-0.2545	0.02831
fixed	NA	sibling_count>5	-0.2769	0.05098	-5.432	4118	0.00000005882	-0.42	-0.1338
fixed	NA	birth_order_nonlinear2	0.03343	0.02836	1.179	4610	0.2385	-0.04617	0.113
fixed	NA	birth_order_nonlinear3	0.02907	0.03517	0.8265	4793	0.4085	-0.06965	0.1278
fixed	NA	birth_order_nonlinear4	0.04795	0.04482	1.07	4936	0.2847	-0.07785	0.1738
fixed	NA	birth_order_nonlinear5	0.1317	0.05668	2.324	4775	0.02016	-0.02737	0.2909
fixed	NA	birth_order_nonlinear>5	0.06088	0.05697	1.069	5592	0.2853	-0.09903	0.2208
ran_pars	mother_pidlink	sd__(Intercept)	0.4191	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7697	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)	-0.6225	0.3884	-1.602	5657	0.1091	-1.713	0.4679
fixed	NA	poly(age, 3, raw = TRUE)1	0.1047	0.04404	2.378	5640	0.01743	-0.01889	0.2284
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003746	0.001573	-2.382	5635	0.01726	-0.00816	0.0006687
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004268	0.00001783	2.394	5634	0.01671	-0.00000737	0.00009272
fixed	NA	male	0.03277	0.02253	1.454	5510	0.146	-0.03049	0.09602
fixed	NA	count_birth_order2/2	0.0373	0.05023	0.7426	4934	0.4578	-0.1037	0.1783
fixed	NA	count_birth_order1/3	-0.0397	0.04617	-0.86	5695	0.3898	-0.1693	0.08989
fixed	NA	count_birth_order2/3	0.04364	0.05085	0.8583	5769	0.3908	-0.09909	0.1864
fixed	NA	count_birth_order3/3	0.02499	0.05573	0.4484	5779	0.6539	-0.1315	0.1814
fixed	NA	count_birth_order1/4	-0.1454	0.05724	-2.54	5764	0.01112	-0.306	0.0153
fixed	NA	count_birth_order2/4	-0.06066	0.05873	-1.033	5779	0.3017	-0.2255	0.1042
fixed	NA	count_birth_order3/4	-0.04567	0.06138	-0.744	5765	0.4569	-0.218	0.1266
fixed	NA	count_birth_order4/4	-0.009882	0.06483	-0.1524	5754	0.8788	-0.1919	0.1721
fixed	NA	count_birth_order1/5	-0.03364	0.07699	-0.4369	5778	0.6622	-0.2497	0.1825
fixed	NA	count_birth_order2/5	-0.1226	0.08473	-1.447	5710	0.1479	-0.3604	0.1152
fixed	NA	count_birth_order3/5	-0.1298	0.08084	-1.606	5717	0.1083	-0.3568	0.09709
fixed	NA	count_birth_order4/5	-0.08387	0.07798	-1.075	5747	0.2822	-0.3028	0.135
fixed	NA	count_birth_order5/5	0.0319	0.08276	0.3854	5722	0.6999	-0.2004	0.2642
fixed	NA	count_birth_order1/>5	-0.1417	0.07812	-1.814	5726	0.06966	-0.361	0.07754
fixed	NA	count_birth_order2/>5	-0.3013	0.07739	-3.893	5700	0.0001002	-0.5185	-0.08403
fixed	NA	count_birth_order3/>5	-0.2695	0.07655	-3.521	5658	0.0004334	-0.4844	-0.05465
fixed	NA	count_birth_order4/>5	-0.2658	0.07478	-3.554	5615	0.0003827	-0.4757	-0.05585
fixed	NA	count_birth_order5/>5	-0.1536	0.06895	-2.227	5669	0.02596	-0.3471	0.03996
fixed	NA	count_birth_order>5/>5	-0.2161	0.05268	-4.102	5393	0.0000416	-0.364	-0.06821
ran_pars	mother_pidlink	sd__(Intercept)	0.4191	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.7697	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)
11	14808	14882	-7393	14786	NA	NA	NA
12	14808	14888	-7392	14784	2.71	1	0.09974
16	14813	14919	-7390	14781	3.147	4	0.5336
26	14822	14995	-7385	14770	10.48	10	0.3993

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)	0.5858	0.1594	3.676	13656	0.0002379	0.1385	1.033
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0431	0.01526	-2.824	13524	0.004743	-0.08593	-0.0002659
fixed	NA	poly(age, 3, raw = TRUE)2	0.001286	0.0004482	2.868	13337	0.004134	0.00002742	0.002544
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001265	0.000004122	-3.068	13167	0.002158	-0.00002422	-0.000001077
fixed	NA	male	-0.2258	0.01689	-13.37	13875	1.703e-40	-0.2732	-0.1784
fixed	NA	sibling_count3	0.009322	0.03332	0.2798	10744	0.7796	-0.0842	0.1028
fixed	NA	sibling_count4	-0.02026	0.03419	-0.5925	9730	0.5535	-0.1162	0.07572
fixed	NA	sibling_count5	-0.02693	0.03538	-0.7611	8569	0.4466	-0.1262	0.07238
fixed	NA	sibling_count>5	-0.01081	0.02791	-0.3874	9811	0.6985	-0.08917	0.06754
ran_pars	mother_pidlink	sd__(Intercept)	0.2287	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9711	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)	0.5841	0.1594	3.665	13657	0.0002481	0.1368	1.032
fixed	NA	birth_order	-0.003173	0.003493	-0.9085	10861	0.3636	-0.01298	0.006632
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04216	0.01529	-2.757	13506	0.005845	-0.08509	0.0007685
fixed	NA	poly(age, 3, raw = TRUE)2	0.001253	0.0004497	2.786	13275	0.00534	-0.000009359	0.002515
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001235	0.000004135	-2.987	13084	0.002821	-0.00002396	-0.0000007446
fixed	NA	male	-0.2257	0.01689	-13.36	13875	1.846e-40	-0.2731	-0.1783
fixed	NA	sibling_count3	0.01013	0.03333	0.304	10759	0.7611	-0.08342	0.1037
fixed	NA	sibling_count4	-0.01798	0.03428	-0.5243	9787	0.6001	-0.1142	0.07826
fixed	NA	sibling_count5	-0.02301	0.03564	-0.6457	8664	0.5185	-0.123	0.07702
fixed	NA	sibling_count>5	0.001366	0.03097	0.0441	10715	0.9648	-0.08556	0.08829
ran_pars	mother_pidlink	sd__(Intercept)	0.2281	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9712	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)	0.5626	0.1598	3.521	13662	0.000432	0.114	1.011
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04263	0.0153	-2.787	13519	0.005334	-0.08558	0.0003127
fixed	NA	poly(age, 3, raw = TRUE)2	0.001264	0.0004498	2.809	13289	0.004972	0.000001024	0.002526
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001237	0.000004136	-2.991	13086	0.00279	-0.00002398	-0.0000007589
fixed	NA	male	-0.2257	0.01689	-13.36	13869	1.765e-40	-0.2731	-0.1783
fixed	NA	sibling_count3	0.01351	0.03385	0.3991	11096	0.6898	-0.08151	0.1085
fixed	NA	sibling_count4	-0.01763	0.03537	-0.4984	10527	0.6182	-0.1169	0.08165
fixed	NA	sibling_count5	-0.02496	0.03719	-0.6712	9678	0.5021	-0.1294	0.07943
fixed	NA	sibling_count>5	-0.005669	0.03271	-0.1733	11890	0.8624	-0.09749	0.08616
fixed	NA	birth_order_nonlinear2	0.05536	0.02472	2.239	12810	0.02515	-0.01404	0.1248
fixed	NA	birth_order_nonlinear3	-0.003555	0.02919	-0.1218	12714	0.903	-0.08548	0.07837
fixed	NA	birth_order_nonlinear4	0.02086	0.03323	0.6278	12831	0.5301	-0.07242	0.1141
fixed	NA	birth_order_nonlinear5	0.02606	0.03779	0.6897	12919	0.4904	-0.08001	0.1321
fixed	NA	birth_order_nonlinear>5	0.01193	0.031	0.3846	13899	0.7005	-0.07511	0.09896
ran_pars	mother_pidlink	sd__(Intercept)	0.229	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)	0.5658	0.1605	3.525	13666	0.0004256	0.1152	1.016
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04235	0.0153	-2.767	13511	0.005661	-0.0853	0.0006092
fixed	NA	poly(age, 3, raw = TRUE)2	0.001259	0.0004499	2.799	13275	0.00514	-0.000003788	0.002522
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001236	0.000004137	-2.987	13066	0.002821	-0.00002397	-0.0000007454
fixed	NA	male	-0.2255	0.0169	-13.35	13859	2.147e-40	-0.273	-0.1781
fixed	NA	count_birth_order2/2	0.03555	0.04808	0.7393	12561	0.4597	-0.09941	0.1705
fixed	NA	count_birth_order1/3	0.006548	0.04502	0.1454	13872	0.8844	-0.1198	0.1329
fixed	NA	count_birth_order2/3	0.0579	0.05035	1.15	13888	0.2502	-0.08343	0.1992
fixed	NA	count_birth_order3/3	0.006575	0.05641	0.1166	13902	0.9072	-0.1518	0.1649
fixed	NA	count_birth_order1/4	-0.03226	0.05142	-0.6274	13891	0.5304	-0.1766	0.1121
fixed	NA	count_birth_order2/4	0.09717	0.05408	1.797	13895	0.07239	-0.05463	0.249
fixed	NA	count_birth_order3/4	-0.06283	0.05877	-1.069	13902	0.285	-0.2278	0.1021
fixed	NA	count_birth_order4/4	-0.0513	0.06223	-0.8244	13907	0.4097	-0.226	0.1234
fixed	NA	count_birth_order1/5	-0.04349	0.05836	-0.7453	13903	0.4561	-0.2073	0.1203
fixed	NA	count_birth_order2/5	-0.01869	0.06139	-0.3045	13907	0.7608	-0.191	0.1536
fixed	NA	count_birth_order3/5	-0.0007656	0.06302	-0.01215	13908	0.9903	-0.1777	0.1761
fixed	NA	count_birth_order4/5	0.04999	0.06676	0.7488	13910	0.454	-0.1374	0.2374
fixed	NA	count_birth_order5/5	-0.04369	0.06825	-0.6402	13910	0.5221	-0.2353	0.1479
fixed	NA	count_birth_order1/>5	-0.01372	0.04714	-0.2911	13908	0.771	-0.146	0.1186
fixed	NA	count_birth_order2/>5	0.03022	0.04863	0.6215	13910	0.5343	-0.1063	0.1667
fixed	NA	count_birth_order3/>5	-0.01704	0.04765	-0.3577	13910	0.7205	-0.1508	0.1167
fixed	NA	count_birth_order4/>5	0.005439	0.04669	0.1165	13910	0.9073	-0.1256	0.1365
fixed	NA	count_birth_order5/>5	0.02545	0.04704	0.5409	13910	0.5886	-0.1066	0.1575
fixed	NA	count_birth_order>5/>5	-0.001348	0.03641	-0.03702	12691	0.9705	-0.1036	0.1009
ran_pars	mother_pidlink	sd__(Intercept)	0.2285	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9712	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)
11	39460	39543	-19719	39438	NA	NA	NA
12	39461	39552	-19719	39437	0.8272	1	0.3631
16	39464	39585	-19716	39432	5.522	4	0.2378
26	39477	39673	-19713	39425	6.545	10	0.7676

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)	1.152	0.4495	2.564	5915	0.01038	-0.1093	2.414
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1016	0.05098	-1.992	5912	0.04638	-0.2447	0.04154
fixed	NA	poly(age, 3, raw = TRUE)2	0.003476	0.001819	1.912	5905	0.05597	-0.001628	0.008581
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003723	0.00002058	-1.809	5894	0.07052	-0.00009501	0.00002054
fixed	NA	male	-0.2631	0.02631	-10	5907	2.341e-23	-0.337	-0.1892
fixed	NA	sibling_count3	-0.03372	0.04026	-0.8374	4587	0.4024	-0.1467	0.0793
fixed	NA	sibling_count4	-0.08771	0.04309	-2.036	3960	0.04186	-0.2087	0.03324
fixed	NA	sibling_count5	-0.08529	0.04889	-1.744	3420	0.08116	-0.2225	0.05195
fixed	NA	sibling_count>5	-0.09583	0.04277	-2.241	3060	0.02513	-0.2159	0.02423
ran_pars	mother_pidlink	sd__(Intercept)	0.1894	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9934	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)	1.141	0.4495	2.539	5914	0.01115	-0.1206	2.403
fixed	NA	birth_order	0.01356	0.008594	1.578	5399	0.1147	-0.01057	0.03768
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1021	0.05098	-2.003	5911	0.04524	-0.2452	0.041
fixed	NA	poly(age, 3, raw = TRUE)2	0.003471	0.001818	1.909	5905	0.05636	-0.001634	0.008575
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003665	0.00002058	-1.78	5894	0.07507	-0.00009443	0.00002113
fixed	NA	male	-0.2636	0.02631	-10.02	5906	1.892e-23	-0.3375	-0.1898
fixed	NA	sibling_count3	-0.04022	0.04048	-0.9935	4582	0.3205	-0.1539	0.07341
fixed	NA	sibling_count4	-0.103	0.04417	-2.331	3945	0.01981	-0.227	0.02103
fixed	NA	sibling_count5	-0.1104	0.05143	-2.146	3462	0.03195	-0.2548	0.034
fixed	NA	sibling_count>5	-0.1462	0.05344	-2.736	3559	0.006244	-0.2963	0.003781
ran_pars	mother_pidlink	sd__(Intercept)	0.1924	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9927	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)	1.11	0.4497	2.467	5909	0.01365	-0.1529	2.372
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09789	0.05096	-1.921	5906	0.05481	-0.2409	0.04517
fixed	NA	poly(age, 3, raw = TRUE)2	0.003318	0.001818	1.825	5899	0.068	-0.001785	0.008421
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003493	0.00002058	-1.697	5887	0.08976	-0.00009271	0.00002285
fixed	NA	male	-0.2635	0.02629	-10.02	5902	1.924e-23	-0.3373	-0.1896
fixed	NA	sibling_count3	-0.04151	0.04136	-1.004	4779	0.3156	-0.1576	0.07458
fixed	NA	sibling_count4	-0.1168	0.04604	-2.538	4319	0.01119	-0.2461	0.0124
fixed	NA	sibling_count5	-0.1589	0.0543	-2.927	3964	0.003447	-0.3113	-0.006488
fixed	NA	sibling_count>5	-0.1572	0.05516	-2.85	3888	0.004398	-0.312	-0.002359
fixed	NA	birth_order_nonlinear2	0.03992	0.03448	1.158	5118	0.247	-0.05687	0.1367
fixed	NA	birth_order_nonlinear3	0.03437	0.04242	0.8102	5378	0.4178	-0.0847	0.1534
fixed	NA	birth_order_nonlinear4	0.1099	0.05233	2.101	5536	0.03571	-0.03696	0.2568
fixed	NA	birth_order_nonlinear5	0.2364	0.06542	3.614	5478	0.0003043	0.05279	0.4201
fixed	NA	birth_order_nonlinear>5	0.03262	0.06472	0.504	5852	0.6143	-0.149	0.2143
ran_pars	mother_pidlink	sd__(Intercept)	0.1872	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9929	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)	1.085	0.4508	2.407	5899	0.01613	-0.1805	2.35
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09453	0.05108	-1.851	5896	0.06429	-0.2379	0.04886
fixed	NA	poly(age, 3, raw = TRUE)2	0.003205	0.001822	1.758	5889	0.07873	-0.001911	0.00832
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003372	0.00002064	-1.634	5878	0.1024	-0.00009164	0.00002421
fixed	NA	male	-0.2623	0.02632	-9.964	5892	3.326e-23	-0.3361	-0.1884
fixed	NA	count_birth_order2/2	0.02096	0.06225	0.3367	5228	0.7364	-0.1538	0.1957
fixed	NA	count_birth_order1/3	-0.08328	0.05417	-1.537	5897	0.1243	-0.2354	0.06878
fixed	NA	count_birth_order2/3	0.03793	0.05923	0.6403	5899	0.522	-0.1283	0.2042
fixed	NA	count_birth_order3/3	-0.01001	0.06626	-0.151	5900	0.88	-0.196	0.176
fixed	NA	count_birth_order1/4	-0.06131	0.06625	-0.9255	5896	0.3548	-0.2473	0.1247
fixed	NA	count_birth_order2/4	-0.1186	0.06863	-1.728	5900	0.08396	-0.3113	0.07402
fixed	NA	count_birth_order3/4	-0.1046	0.07259	-1.442	5899	0.1495	-0.3084	0.09912
fixed	NA	count_birth_order4/4	-0.04082	0.07548	-0.5408	5898	0.5886	-0.2527	0.171
fixed	NA	count_birth_order1/5	-0.1233	0.09008	-1.368	5900	0.1712	-0.3761	0.1296
fixed	NA	count_birth_order2/5	-0.163	0.09652	-1.689	5899	0.09127	-0.434	0.1079
fixed	NA	count_birth_order3/5	-0.1296	0.0905	-1.432	5898	0.1521	-0.3836	0.1244
fixed	NA	count_birth_order4/5	-0.05215	0.08716	-0.5983	5898	0.5497	-0.2968	0.1925
fixed	NA	count_birth_order5/5	0.05478	0.09073	0.6037	5895	0.5461	-0.1999	0.3095
fixed	NA	count_birth_order1/>5	-0.2236	0.08934	-2.503	5891	0.01235	-0.4744	0.02719
fixed	NA	count_birth_order2/>5	-0.1293	0.0885	-1.461	5896	0.144	-0.3777	0.1191
fixed	NA	count_birth_order3/>5	-0.1131	0.08873	-1.275	5900	0.2025	-0.3622	0.136
fixed	NA	count_birth_order4/>5	-0.0233	0.08363	-0.2786	5899	0.7806	-0.258	0.2114
fixed	NA	count_birth_order5/>5	0.08399	0.07903	1.063	5898	0.2879	-0.1379	0.3058
fixed	NA	count_birth_order>5/>5	-0.1312	0.05874	-2.234	5149	0.02554	-0.2961	0.03367
ran_pars	mother_pidlink	sd__(Intercept)	0.1883	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9931	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)
11	16954	17028	-8466	16932	NA	NA	NA
12	16954	17034	-8465	16930	2.483	1	0.1151
16	16948	17055	-8458	16916	13.26	4	0.01007
26	16963	17137	-8456	16911	5.148	10	0.8811

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)	1.163	0.4489	2.591	5966	0.009594	-0.09699	2.423
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1022	0.05094	-2.007	5963	0.04481	-0.2452	0.04076
fixed	NA	poly(age, 3, raw = TRUE)2	0.003524	0.001817	1.939	5956	0.05255	-0.001577	0.008625
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003799	0.00002057	-1.847	5944	0.06485	-0.00009574	0.00001976
fixed	NA	male	-0.2654	0.02625	-10.11	5957	7.751e-24	-0.3391	-0.1917
fixed	NA	sibling_count3	-0.03632	0.04368	-0.8315	4742	0.4057	-0.1589	0.08629
fixed	NA	sibling_count4	-0.07942	0.04582	-1.733	4276	0.08311	-0.208	0.0492
fixed	NA	sibling_count5	-0.1033	0.04875	-2.119	3745	0.03416	-0.2401	0.03354
fixed	NA	sibling_count>5	-0.1059	0.04277	-2.477	3778	0.01329	-0.226	0.01411
ran_pars	mother_pidlink	sd__(Intercept)	0.1912	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9951	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)	1.15	0.4489	2.561	5965	0.01046	-0.1104	2.41
fixed	NA	birth_order	0.01209	0.007482	1.616	5017	0.1061	-0.008911	0.03309
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1023	0.05093	-2.009	5962	0.04463	-0.2453	0.04067
fixed	NA	poly(age, 3, raw = TRUE)2	0.003505	0.001817	1.929	5956	0.05384	-0.001596	0.008605
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003732	0.00002058	-1.813	5945	0.06981	-0.00009508	0.00002044
fixed	NA	male	-0.2658	0.02625	-10.13	5956	6.65e-24	-0.3395	-0.1921
fixed	NA	sibling_count3	-0.04207	0.04384	-0.9598	4733	0.3372	-0.1651	0.08098
fixed	NA	sibling_count4	-0.0925	0.04655	-1.987	4245	0.04695	-0.2232	0.03815
fixed	NA	sibling_count5	-0.1239	0.05041	-2.458	3726	0.01402	-0.2654	0.0176
fixed	NA	sibling_count>5	-0.1499	0.05073	-2.954	4023	0.003152	-0.2922	-0.007471
ran_pars	mother_pidlink	sd__(Intercept)	0.1956	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9941	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)	1.141	0.4493	2.539	5960	0.01115	-0.1206	2.402
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1002	0.05094	-1.968	5957	0.04915	-0.2432	0.04276
fixed	NA	poly(age, 3, raw = TRUE)2	0.003429	0.001818	1.887	5950	0.05926	-0.001673	0.008532
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003645	0.00002059	-1.771	5938	0.07669	-0.00009423	0.00002134
fixed	NA	male	-0.2649	0.02625	-10.09	5952	9.261e-24	-0.3386	-0.1913
fixed	NA	sibling_count3	-0.04594	0.0447	-1.028	4891	0.3041	-0.1714	0.07953
fixed	NA	sibling_count4	-0.09413	0.04833	-1.948	4558	0.05151	-0.2298	0.04153
fixed	NA	sibling_count5	-0.1497	0.05306	-2.821	4177	0.004811	-0.2986	-0.0007377
fixed	NA	sibling_count>5	-0.1589	0.05247	-3.027	4390	0.002481	-0.3061	-0.01156
fixed	NA	birth_order_nonlinear2	0.02093	0.03515	0.5955	5239	0.5515	-0.07773	0.1196
fixed	NA	birth_order_nonlinear3	0.04145	0.04233	0.9792	5491	0.3275	-0.07736	0.1603
fixed	NA	birth_order_nonlinear4	0.02811	0.05083	0.5529	5639	0.5803	-0.1146	0.1708
fixed	NA	birth_order_nonlinear5	0.1845	0.06237	2.959	5642	0.003104	0.009447	0.3596
fixed	NA	birth_order_nonlinear>5	0.06251	0.0578	1.081	5821	0.2796	-0.09974	0.2248
ran_pars	mother_pidlink	sd__(Intercept)	0.1939	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9942	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)	1.137	0.4502	2.525	5950	0.01159	-0.1269	2.4
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09952	0.05102	-1.95	5947	0.05116	-0.2427	0.0437
fixed	NA	poly(age, 3, raw = TRUE)2	0.003409	0.001821	1.872	5940	0.06123	-0.001702	0.008521
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003628	0.00002062	-1.759	5927	0.07862	-0.00009417	0.00002161
fixed	NA	male	-0.265	0.02627	-10.08	5942	1.002e-23	-0.3387	-0.1912
fixed	NA	count_birth_order2/2	0.01043	0.06822	0.153	5332	0.8784	-0.1811	0.2019
fixed	NA	count_birth_order1/3	-0.08321	0.05879	-1.415	5948	0.157	-0.2483	0.08182
fixed	NA	count_birth_order2/3	0.01868	0.06381	0.2928	5950	0.7697	-0.1604	0.1978
fixed	NA	count_birth_order3/3	-0.0109	0.07186	-0.1517	5951	0.8794	-0.2126	0.1908
fixed	NA	count_birth_order1/4	-0.05074	0.06955	-0.7296	5948	0.4657	-0.246	0.1445
fixed	NA	count_birth_order2/4	-0.06652	0.07091	-0.938	5951	0.3483	-0.2656	0.1325
fixed	NA	count_birth_order3/4	-0.06716	0.07791	-0.862	5950	0.3887	-0.2858	0.1515
fixed	NA	count_birth_order4/4	-0.1452	0.08033	-1.808	5950	0.07073	-0.3707	0.08029
fixed	NA	count_birth_order1/5	-0.1287	0.08259	-1.559	5950	0.1191	-0.3606	0.1031
fixed	NA	count_birth_order2/5	-0.1947	0.08878	-2.193	5951	0.02835	-0.4439	0.05452
fixed	NA	count_birth_order3/5	-0.1136	0.08636	-1.316	5950	0.1883	-0.3561	0.1288
fixed	NA	count_birth_order4/5	-0.123	0.08956	-1.373	5947	0.1698	-0.3744	0.1284
fixed	NA	count_birth_order5/5	0.06422	0.08981	0.7151	5946	0.4746	-0.1879	0.3163
fixed	NA	count_birth_order1/>5	-0.1769	0.07848	-2.255	5943	0.02418	-0.3972	0.04334
fixed	NA	count_birth_order2/>5	-0.1904	0.08206	-2.32	5949	0.02038	-0.4207	0.03998
fixed	NA	count_birth_order3/>5	-0.1052	0.08055	-1.306	5951	0.1916	-0.3313	0.1209
fixed	NA	count_birth_order4/>5	-0.07007	0.07755	-0.9036	5950	0.3663	-0.2878	0.1476
fixed	NA	count_birth_order5/>5	-0.001767	0.07974	-0.02216	5947	0.9823	-0.2256	0.2221
fixed	NA	count_birth_order>5/>5	-0.1002	0.05776	-1.736	5338	0.08268	-0.2624	0.06188
ran_pars	mother_pidlink	sd__(Intercept)	0.1906	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9952	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)
11	17123	17197	-8551	17101	NA	NA	NA
12	17123	17203	-8549	17099	2.6	1	0.1069
16	17124	17231	-8546	17092	6.411	4	0.1705
26	17138	17312	-8543	17086	6.211	10	0.7972

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)	1.072	0.4545	2.359	5795	0.01835	-0.2035	2.348
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0908	0.05157	-1.761	5792	0.07833	-0.2356	0.05395
fixed	NA	poly(age, 3, raw = TRUE)2	0.003071	0.00184	1.669	5785	0.09512	-0.002094	0.008236
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003239	0.00002084	-1.555	5772	0.1201	-0.00009089	0.0000261
fixed	NA	male	-0.2616	0.02657	-9.846	5789	1.075e-22	-0.3362	-0.187
fixed	NA	sibling_count3	-0.04465	0.03971	-1.124	4468	0.2609	-0.1561	0.06682
fixed	NA	sibling_count4	-0.08125	0.04277	-1.899	3871	0.05759	-0.2013	0.03882
fixed	NA	sibling_count5	-0.115	0.05	-2.3	3209	0.02154	-0.2553	0.02538
fixed	NA	sibling_count>5	-0.1278	0.04315	-2.963	2877	0.003073	-0.249	-0.006722
ran_pars	mother_pidlink	sd__(Intercept)	0.1898	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9926	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)	1.06	0.4544	2.334	5795	0.01964	-0.2151	2.336
fixed	NA	birth_order	0.01785	0.008858	2.016	5372	0.0439	-0.007011	0.04272
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09181	0.05156	-1.781	5791	0.07501	-0.2365	0.05291
fixed	NA	poly(age, 3, raw = TRUE)2	0.003073	0.00184	1.671	5784	0.09484	-0.00209	0.008237
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003172	0.00002084	-1.522	5773	0.128	-0.00009021	0.00002677
fixed	NA	male	-0.262	0.02656	-9.864	5787	9.017e-23	-0.3366	-0.1874
fixed	NA	sibling_count3	-0.05323	0.03994	-1.333	4462	0.1827	-0.1653	0.05888
fixed	NA	sibling_count4	-0.1011	0.0439	-2.303	3868	0.02135	-0.2243	0.02214
fixed	NA	sibling_count5	-0.1465	0.0524	-2.795	3260	0.005213	-0.2936	0.0006075
fixed	NA	sibling_count>5	-0.1938	0.05419	-3.576	3483	0.0003539	-0.3459	-0.04166
ran_pars	mother_pidlink	sd__(Intercept)	0.1929	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9917	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)	1.044	0.4546	2.297	5790	0.02165	-0.2319	2.32
fixed	NA	poly(age, 3, raw = TRUE)1	-0.08873	0.05154	-1.722	5786	0.0852	-0.2334	0.05595
fixed	NA	poly(age, 3, raw = TRUE)2	0.002964	0.001839	1.612	5778	0.1071	-0.002199	0.008127
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00003055	0.00002083	-1.466	5766	0.1426	-0.00008903	0.00002793
fixed	NA	male	-0.2626	0.02655	-9.892	5783	6.841e-23	-0.3371	-0.1881
fixed	NA	sibling_count3	-0.05612	0.04085	-1.374	4661	0.1695	-0.1708	0.05854
fixed	NA	sibling_count4	-0.124	0.04582	-2.706	4240	0.006837	-0.2526	0.004629
fixed	NA	sibling_count5	-0.1948	0.05506	-3.537	3704	0.0004094	-0.3493	-0.0402
fixed	NA	sibling_count>5	-0.2001	0.05603	-3.572	3826	0.0003583	-0.3574	-0.04287
fixed	NA	birth_order_nonlinear2	0.04114	0.03439	1.196	5008	0.2317	-0.0554	0.1377
fixed	NA	birth_order_nonlinear3	0.05162	0.04243	1.217	5240	0.2238	-0.06748	0.1707
fixed	NA	birth_order_nonlinear4	0.1592	0.05384	2.957	5413	0.003124	0.00805	0.3103
fixed	NA	birth_order_nonlinear5	0.2166	0.06823	3.175	5373	0.001507	0.0251	0.4081
fixed	NA	birth_order_nonlinear>5	0.04953	0.06681	0.7413	5756	0.4585	-0.138	0.2371
ran_pars	mother_pidlink	sd__(Intercept)	0.1887	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9919	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	0.4558	2.227	5779	0.026	-0.2645	2.294
fixed	NA	poly(age, 3, raw = TRUE)1	-0.08443	0.05168	-1.634	5776	0.1024	-0.2295	0.06063
fixed	NA	poly(age, 3, raw = TRUE)2	0.002813	0.001844	1.525	5768	0.1273	-0.002364	0.00799
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002887	0.0000209	-1.382	5755	0.1672	-0.00008752	0.00002978
fixed	NA	male	-0.2616	0.02658	-9.842	5773	1.114e-22	-0.3362	-0.187
fixed	NA	count_birth_order2/2	0.01484	0.06064	0.2447	5095	0.8067	-0.1554	0.1851
fixed	NA	count_birth_order1/3	-0.09202	0.05348	-1.721	5777	0.08537	-0.2422	0.0581
fixed	NA	count_birth_order2/3	0.009075	0.05919	0.1533	5781	0.8781	-0.1571	0.1752
fixed	NA	count_birth_order3/3	-0.006927	0.06507	-0.1065	5780	0.9152	-0.1896	0.1757
fixed	NA	count_birth_order1/4	-0.1042	0.06656	-1.565	5778	0.1176	-0.291	0.08268
fixed	NA	count_birth_order2/4	-0.1136	0.06851	-1.658	5781	0.09733	-0.3059	0.0787
fixed	NA	count_birth_order3/4	-0.08828	0.07183	-1.229	5779	0.2191	-0.2899	0.1133
fixed	NA	count_birth_order4/4	0.02013	0.07593	0.2651	5778	0.7909	-0.193	0.2333
fixed	NA	count_birth_order1/5	-0.1585	0.08983	-1.765	5780	0.07762	-0.4107	0.09361
fixed	NA	count_birth_order2/5	-0.151	0.09939	-1.519	5780	0.1287	-0.43	0.128
fixed	NA	count_birth_order3/5	-0.1459	0.09485	-1.538	5779	0.124	-0.4121	0.1203
fixed	NA	count_birth_order4/5	-0.05101	0.09137	-0.5583	5779	0.5767	-0.3075	0.2055
fixed	NA	count_birth_order5/5	-0.05376	0.09711	-0.5536	5776	0.5799	-0.3263	0.2188
fixed	NA	count_birth_order1/>5	-0.2499	0.09145	-2.732	5775	0.006309	-0.5066	0.006836
fixed	NA	count_birth_order2/>5	-0.1872	0.09072	-2.063	5778	0.03912	-0.4418	0.06746
fixed	NA	count_birth_order3/>5	-0.1664	0.08997	-1.85	5781	0.06437	-0.419	0.0861
fixed	NA	count_birth_order4/>5	-0.03704	0.08803	-0.4208	5779	0.6739	-0.2842	0.2101
fixed	NA	count_birth_order5/>5	0.04899	0.0809	0.6055	5778	0.5449	-0.1781	0.2761
fixed	NA	count_birth_order>5/>5	-0.1598	0.05974	-2.675	4968	0.007497	-0.3275	0.007886
ran_pars	mother_pidlink	sd__(Intercept)	0.1888	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9924	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)
11	16605	16679	-8292	16583	NA	NA	NA
12	16603	16683	-8290	16579	4.058	1	0.04397
16	16600	16706	-8284	16568	11.43	4	0.0221
26	16617	16790	-8282	16565	3.206	10	0.9761

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)	0.5805	0.1576	3.684	13711	0.0002301	0.1382	1.023
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01912	0.01509	-1.267	13603	0.2052	-0.06149	0.02325
fixed	NA	poly(age, 3, raw = TRUE)2	0.00009704	0.0004437	0.2187	13429	0.8269	-0.001148	0.001342
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001933	0.000004082	0.04736	13256	0.9622	-0.00001127	0.00001165
fixed	NA	male	-0.2605	0.01664	-15.66	13806	9.038e-55	-0.3072	-0.2138
fixed	NA	sibling_count3	-0.009417	0.03319	-0.2838	10517	0.7766	-0.1026	0.08374
fixed	NA	sibling_count4	-0.002559	0.03413	-0.07498	9566	0.9402	-0.09835	0.09323
fixed	NA	sibling_count5	-0.03946	0.03539	-1.115	8500	0.2649	-0.1388	0.05989
fixed	NA	sibling_count>5	0.02614	0.02785	0.9384	9661	0.3481	-0.05205	0.1043
ran_pars	mother_pidlink	sd__(Intercept)	0.2846	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)	0.58	0.1576	3.681	13713	0.0002335	0.1377	1.022
fixed	NA	birth_order	-0.001117	0.003475	-0.3215	11756	0.7479	-0.01087	0.008638
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01879	0.01513	-1.242	13587	0.2143	-0.06126	0.02368
fixed	NA	poly(age, 3, raw = TRUE)2	0.00008512	0.0004452	0.1912	13370	0.8484	-0.001165	0.001335
fixed	NA	poly(age, 3, raw = TRUE)3	0.000000302	0.000004096	0.07372	13174	0.9412	-0.0000112	0.0000118
fixed	NA	male	-0.2604	0.01664	-15.65	13804	9.417e-55	-0.3071	-0.2137
fixed	NA	sibling_count3	-0.009148	0.0332	-0.2755	10529	0.7829	-0.1023	0.08405
fixed	NA	sibling_count4	-0.001769	0.03422	-0.05169	9624	0.9588	-0.09782	0.09428
fixed	NA	sibling_count5	-0.03809	0.03565	-1.069	8603	0.2853	-0.1382	0.06197
fixed	NA	sibling_count>5	0.0304	0.03085	0.9854	10648	0.3245	-0.05619	0.117
ran_pars	mother_pidlink	sd__(Intercept)	0.2849	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9435	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)	0.5764	0.158	3.648	13716	0.0002652	0.1329	1.02
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01814	0.01514	-1.199	13597	0.2307	-0.06063	0.02434
fixed	NA	poly(age, 3, raw = TRUE)2	0.00005994	0.0004453	0.1346	13381	0.8929	-0.00119	0.00131
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000005424	0.000004098	0.1324	13174	0.8947	-0.00001096	0.00001205
fixed	NA	male	-0.2604	0.01664	-15.65	13799	1.021e-54	-0.3071	-0.2137
fixed	NA	sibling_count3	-0.007709	0.0337	-0.2287	10868	0.8191	-0.1023	0.08689
fixed	NA	sibling_count4	-0.001011	0.03525	-0.02867	10345	0.9771	-0.09996	0.09794
fixed	NA	sibling_count5	-0.03826	0.03713	-1.031	9574	0.3027	-0.1425	0.06595
fixed	NA	sibling_count>5	0.04189	0.03251	1.288	11764	0.1976	-0.04937	0.1332
fixed	NA	birth_order_nonlinear2	-0.002359	0.02426	-0.09724	12739	0.9225	-0.07045	0.06573
fixed	NA	birth_order_nonlinear3	-0.01075	0.02863	-0.3755	12588	0.7073	-0.09111	0.06961
fixed	NA	birth_order_nonlinear4	-0.0006682	0.03261	-0.02049	12677	0.9836	-0.09219	0.09086
fixed	NA	birth_order_nonlinear5	0.0002819	0.03708	0.007603	12741	0.9939	-0.1038	0.1044
fixed	NA	birth_order_nonlinear>5	-0.03676	0.0306	-1.202	13920	0.2295	-0.1226	0.04912
ran_pars	mother_pidlink	sd__(Intercept)	0.2852	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)	0.5674	0.1587	3.575	13715	0.0003515	0.1219	1.013
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01774	0.01514	-1.172	13588	0.2414	-0.06024	0.02476
fixed	NA	poly(age, 3, raw = TRUE)2	0.00004913	0.0004455	0.1103	13366	0.9122	-0.001201	0.0013
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000006254	0.000004099	0.1525	13152	0.8788	-0.00001088	0.00001213
fixed	NA	male	-0.2604	0.01664	-15.64	13789	1.073e-54	-0.3071	-0.2137
fixed	NA	count_birth_order2/2	0.01066	0.04715	0.2261	12596	0.8211	-0.1217	0.143
fixed	NA	count_birth_order1/3	0.0004386	0.04446	0.009865	13825	0.9921	-0.1244	0.1252
fixed	NA	count_birth_order2/3	-0.00866	0.04971	-0.1742	13864	0.8617	-0.1482	0.1309
fixed	NA	count_birth_order3/3	-0.01581	0.05567	-0.2839	13894	0.7765	-0.1721	0.1405
fixed	NA	count_birth_order1/4	-0.02016	0.05076	-0.3971	13867	0.6913	-0.1627	0.1223
fixed	NA	count_birth_order2/4	0.02738	0.05339	0.5129	13879	0.608	-0.1225	0.1772
fixed	NA	count_birth_order3/4	0.01082	0.058	0.1866	13897	0.852	-0.152	0.1736
fixed	NA	count_birth_order4/4	-0.01496	0.0614	-0.2437	13906	0.8075	-0.1873	0.1574
fixed	NA	count_birth_order1/5	0.01294	0.0576	0.2247	13895	0.8222	-0.1487	0.1746
fixed	NA	count_birth_order2/5	-0.0134	0.06058	-0.2212	13905	0.8249	-0.1835	0.1567
fixed	NA	count_birth_order3/5	-0.03575	0.06218	-0.5749	13907	0.5654	-0.2103	0.1388
fixed	NA	count_birth_order4/5	-0.0666	0.06586	-1.011	13910	0.312	-0.2515	0.1183
fixed	NA	count_birth_order5/5	-0.1109	0.06733	-1.648	13910	0.09939	-0.2999	0.07804
fixed	NA	count_birth_order1/>5	0.04369	0.04651	0.9394	13909	0.3476	-0.08686	0.1742
fixed	NA	count_birth_order2/>5	0.009542	0.04797	0.1989	13910	0.8423	-0.1251	0.1442
fixed	NA	count_birth_order3/>5	0.02378	0.047	0.5059	13910	0.613	-0.1081	0.1557
fixed	NA	count_birth_order4/>5	0.06431	0.04606	1.396	13910	0.1626	-0.06497	0.1936
fixed	NA	count_birth_order5/>5	0.07289	0.0464	1.571	13909	0.1162	-0.05735	0.2031
fixed	NA	count_birth_order>5/>5	0.009809	0.03612	0.2716	12651	0.786	-0.09159	0.1112
ran_pars	mother_pidlink	sd__(Intercept)	0.2849	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9437	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)
11	39076	39159	-19527	39054	NA	NA	NA
12	39078	39168	-19527	39054	0.1024	1	0.749
16	39084	39205	-19526	39052	1.999	4	0.736
26	39098	39294	-19523	39046	6.132	10	0.804

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)	-0.3543	0.4352	-0.814	5906	0.4157	-1.576	0.8675
fixed	NA	poly(age, 3, raw = TRUE)1	0.09127	0.04938	1.848	5910	0.06462	-0.04735	0.2299
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004075	0.001762	-2.313	5913	0.02077	-0.009022	0.000871
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004695	0.00001995	2.353	5915	0.01865	-0.000009057	0.000103
fixed	NA	male	-0.2664	0.02545	-10.47	5874	2.056e-25	-0.3378	-0.1949
fixed	NA	sibling_count3	0.01865	0.03952	0.4719	4540	0.6371	-0.09229	0.1296
fixed	NA	sibling_count4	0.02037	0.04245	0.4798	3988	0.6314	-0.09879	0.1395
fixed	NA	sibling_count5	0.07006	0.04833	1.449	3532	0.1473	-0.06561	0.2057
fixed	NA	sibling_count>5	0.1134	0.04237	2.676	3266	0.007478	-0.005534	0.2324
ran_pars	mother_pidlink	sd__(Intercept)	0.2875	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9381	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)	-0.3506	0.4353	-0.8054	5905	0.4206	-1.573	0.8713
fixed	NA	birth_order	-0.004386	0.008375	-0.5237	5712	0.6005	-0.0279	0.01912
fixed	NA	poly(age, 3, raw = TRUE)1	0.09146	0.04939	1.852	5909	0.06409	-0.04717	0.2301
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004074	0.001762	-2.312	5912	0.02081	-0.009021	0.0008722
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004677	0.00001996	2.343	5914	0.01914	-0.000009251	0.0001028
fixed	NA	male	-0.2662	0.02546	-10.46	5874	2.257e-25	-0.3377	-0.1947
fixed	NA	sibling_count3	0.02077	0.03973	0.5227	4543	0.6012	-0.09076	0.1323
fixed	NA	sibling_count4	0.02537	0.04351	0.583	3990	0.5599	-0.09677	0.1475
fixed	NA	sibling_count5	0.07826	0.05081	1.54	3602	0.1236	-0.06437	0.2209
fixed	NA	sibling_count>5	0.1299	0.05275	2.462	3776	0.01386	-0.0182	0.2779
ran_pars	mother_pidlink	sd__(Intercept)	0.2875	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9382	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)	-0.3461	0.4357	-0.7943	5904	0.4271	-1.569	0.8769
fixed	NA	poly(age, 3, raw = TRUE)1	0.09076	0.04938	1.838	5906	0.06614	-0.04786	0.2294
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00404	0.001762	-2.293	5909	0.0219	-0.008987	0.0009064
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004615	0.00001996	2.312	5910	0.02079	-0.000009872	0.0001022
fixed	NA	male	-0.2659	0.02544	-10.45	5870	2.41e-25	-0.3373	-0.1945
fixed	NA	sibling_count3	0.002937	0.04055	0.07242	4732	0.9423	-0.1109	0.1168
fixed	NA	sibling_count4	0.02674	0.04526	0.5908	4336	0.5547	-0.1003	0.1538
fixed	NA	sibling_count5	0.09421	0.05348	1.762	4065	0.07822	-0.05591	0.2443
fixed	NA	sibling_count>5	0.1447	0.05434	2.662	4069	0.007796	-0.007876	0.2972
fixed	NA	birth_order_nonlinear2	-0.01411	0.0331	-0.4264	5070	0.6698	-0.107	0.07879
fixed	NA	birth_order_nonlinear3	0.06996	0.04079	1.715	5302	0.08636	-0.04453	0.1844
fixed	NA	birth_order_nonlinear4	-0.1062	0.05038	-2.109	5452	0.03501	-0.2477	0.03518
fixed	NA	birth_order_nonlinear5	-0.0758	0.06294	-1.204	5358	0.2285	-0.2525	0.1009
fixed	NA	birth_order_nonlinear>5	-0.0365	0.06279	-0.5813	5909	0.5611	-0.2128	0.1398
ran_pars	mother_pidlink	sd__(Intercept)	0.2848	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9382	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)	-0.4027	0.4364	-0.9229	5894	0.3561	-1.628	0.8221
fixed	NA	poly(age, 3, raw = TRUE)1	0.09799	0.04946	1.981	5896	0.04762	-0.04085	0.2368
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004291	0.001765	-2.431	5898	0.0151	-0.009245	0.0006642
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000489	0.00002	2.445	5900	0.0145	-0.00000723	0.000105
fixed	NA	male	-0.2654	0.02545	-10.43	5858	2.97e-25	-0.3369	-0.194
fixed	NA	count_birth_order2/2	-0.039	0.05976	-0.6525	5248	0.5141	-0.2068	0.1288
fixed	NA	count_birth_order1/3	-0.04149	0.0525	-0.7903	5886	0.4294	-0.1889	0.1059
fixed	NA	count_birth_order2/3	0.01587	0.05738	0.2765	5897	0.7822	-0.1452	0.1769
fixed	NA	count_birth_order3/3	0.08473	0.06415	1.321	5900	0.1866	-0.09534	0.2648
fixed	NA	count_birth_order1/4	0.04092	0.0642	0.6374	5892	0.5239	-0.1393	0.2211
fixed	NA	count_birth_order2/4	0.04203	0.06646	0.6324	5900	0.5271	-0.1445	0.2286
fixed	NA	count_birth_order3/4	0.0375	0.07026	0.5337	5897	0.5936	-0.1597	0.2347
fixed	NA	count_birth_order4/4	-0.1151	0.07304	-1.576	5896	0.1151	-0.3201	0.08992
fixed	NA	count_birth_order1/5	0.2044	0.08723	2.344	5900	0.01914	-0.04043	0.4493
fixed	NA	count_birth_order2/5	-0.11	0.09341	-1.177	5893	0.2391	-0.3722	0.1522
fixed	NA	count_birth_order3/5	0.2414	0.08757	2.757	5891	0.005853	-0.004389	0.4872
fixed	NA	count_birth_order4/5	-0.0007861	0.08435	-0.00932	5894	0.9926	-0.2375	0.236
fixed	NA	count_birth_order5/5	-0.06552	0.08778	-0.7464	5888	0.4555	-0.3119	0.1809
fixed	NA	count_birth_order1/>5	0.07957	0.08655	0.9194	5900	0.3579	-0.1634	0.3225
fixed	NA	count_birth_order2/>5	0.1312	0.0857	1.531	5898	0.1259	-0.1094	0.3717
fixed	NA	count_birth_order3/>5	0.1658	0.08586	1.93	5887	0.0536	-0.07527	0.4068
fixed	NA	count_birth_order4/>5	0.04447	0.08091	0.5497	5884	0.5826	-0.1826	0.2716
fixed	NA	count_birth_order5/>5	0.1124	0.07646	1.47	5883	0.1417	-0.1023	0.327
fixed	NA	count_birth_order>5/>5	0.09957	0.05735	1.736	5353	0.08261	-0.06142	0.2606
ran_pars	mother_pidlink	sd__(Intercept)	0.2864	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9374	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)
11	16578	16652	-8278	16556	NA	NA	NA
12	16580	16660	-8278	16556	0.2748	1	0.6001
16	16576	16683	-8272	16544	12.34	4	0.01502
26	16582	16755	-8265	16530	14.13	10	0.1673

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)	-0.3839	0.4336	-0.8853	5958	0.376	-1.601	0.8332
fixed	NA	poly(age, 3, raw = TRUE)1	0.09637	0.04922	1.958	5961	0.05029	-0.04179	0.2345
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004224	0.001757	-2.405	5964	0.01621	-0.009155	0.0007065
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004839	0.00001989	2.432	5966	0.01503	-0.000007456	0.0001042
fixed	NA	male	-0.2706	0.02533	-10.68	5925	2.202e-26	-0.3417	-0.1994
fixed	NA	sibling_count3	-0.001241	0.04271	-0.02905	4700	0.9768	-0.1211	0.1187
fixed	NA	sibling_count4	-0.001944	0.04493	-0.04327	4282	0.9655	-0.1281	0.1242
fixed	NA	sibling_count5	-0.03667	0.04794	-0.765	3824	0.4443	-0.1712	0.09789
fixed	NA	sibling_count>5	0.0932	0.04204	2.217	3909	0.0267	-0.02482	0.2112
ran_pars	mother_pidlink	sd__(Intercept)	0.2852	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9382	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)	-0.3782	0.4337	-0.8721	5957	0.3832	-1.596	0.8392
fixed	NA	birth_order	-0.004982	0.00729	-0.6834	5481	0.4944	-0.02544	0.01548
fixed	NA	poly(age, 3, raw = TRUE)1	0.0964	0.04922	1.958	5960	0.05022	-0.04177	0.2346
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004217	0.001757	-2.4	5963	0.01641	-0.009148	0.0007144
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004811	0.0000199	2.418	5965	0.01565	-0.000007749	0.000104
fixed	NA	male	-0.2704	0.02534	-10.67	5925	2.389e-26	-0.3415	-0.1993
fixed	NA	sibling_count3	0.00115	0.04286	0.02684	4698	0.9786	-0.1192	0.1215
fixed	NA	sibling_count4	0.003495	0.04563	0.0766	4266	0.9389	-0.1246	0.1316
fixed	NA	sibling_count5	-0.02809	0.04956	-0.5667	3829	0.571	-0.1672	0.111
fixed	NA	sibling_count>5	0.1114	0.04977	2.238	4182	0.02526	-0.02831	0.2511
ran_pars	mother_pidlink	sd__(Intercept)	0.2853	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9382	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)	-0.3631	0.434	-0.8366	5955	0.4028	-1.582	0.8552
fixed	NA	poly(age, 3, raw = TRUE)1	0.09484	0.04922	1.927	5958	0.05405	-0.04333	0.233
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004152	0.001757	-2.363	5960	0.01815	-0.009084	0.0007798
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004717	0.0000199	2.37	5961	0.01782	-0.000008698	0.000103
fixed	NA	male	-0.2712	0.02533	-10.71	5921	1.678e-26	-0.3423	-0.2001
fixed	NA	sibling_count3	-0.01381	0.04365	-0.3164	4850	0.7517	-0.1363	0.1087
fixed	NA	sibling_count4	-0.007871	0.04728	-0.1665	4558	0.8678	-0.1406	0.1248
fixed	NA	sibling_count5	-0.02175	0.05201	-0.4181	4241	0.6759	-0.1677	0.1243
fixed	NA	sibling_count>5	0.1204	0.05136	2.344	4492	0.0191	-0.02376	0.2646
fixed	NA	birth_order_nonlinear2	-0.02501	0.03368	-0.7427	5200	0.4577	-0.1196	0.06953
fixed	NA	birth_order_nonlinear3	0.05665	0.04062	1.395	5424	0.1632	-0.05738	0.1707
fixed	NA	birth_order_nonlinear4	-0.0316	0.04884	-0.6469	5570	0.5177	-0.1687	0.1055
fixed	NA	birth_order_nonlinear5	-0.1226	0.05993	-2.045	5545	0.04086	-0.2908	0.04564
fixed	NA	birth_order_nonlinear>5	-0.04813	0.05599	-0.8595	5926	0.3901	-0.2053	0.109
ran_pars	mother_pidlink	sd__(Intercept)	0.2834	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9383	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)	-0.3939	0.4347	-0.906	5946	0.365	-1.614	0.8264
fixed	NA	poly(age, 3, raw = TRUE)1	0.09802	0.04928	1.989	5948	0.04674	-0.04031	0.2364
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004261	0.001759	-2.422	5950	0.01547	-0.009199	0.0006777
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004832	0.00001993	2.424	5951	0.01539	-0.000007638	0.0001043
fixed	NA	male	-0.2715	0.02534	-10.71	5911	1.53e-26	-0.3426	-0.2004
fixed	NA	count_birth_order2/2	-0.01787	0.06539	-0.2732	5358	0.7847	-0.2014	0.1657
fixed	NA	count_birth_order1/3	-0.02834	0.05683	-0.4987	5938	0.618	-0.1879	0.1312
fixed	NA	count_birth_order2/3	-0.04075	0.06165	-0.6609	5948	0.5087	-0.2138	0.1323
fixed	NA	count_birth_order3/3	0.08512	0.0694	1.227	5951	0.22	-0.1097	0.2799
fixed	NA	count_birth_order1/4	-0.05575	0.06722	-0.8294	5944	0.4069	-0.2444	0.1329
fixed	NA	count_birth_order2/4	-0.006205	0.06851	-0.09057	5950	0.9278	-0.1985	0.1861
fixed	NA	count_birth_order3/4	0.09585	0.07522	1.274	5949	0.2026	-0.1153	0.307
fixed	NA	count_birth_order4/4	-0.0416	0.07755	-0.5364	5948	0.5917	-0.2593	0.1761
fixed	NA	count_birth_order1/5	0.116	0.07979	1.454	5950	0.1459	-0.1079	0.34
fixed	NA	count_birth_order2/5	-0.04191	0.08573	-0.4888	5948	0.625	-0.2825	0.1987
fixed	NA	count_birth_order3/5	0.005031	0.08338	0.06034	5947	0.9519	-0.229	0.2391
fixed	NA	count_birth_order4/5	-0.08346	0.08643	-0.9656	5940	0.3343	-0.3261	0.1592
fixed	NA	count_birth_order5/5	-0.249	0.08667	-2.873	5939	0.004081	-0.4923	-0.005715
fixed	NA	count_birth_order1/>5	0.1245	0.07584	1.642	5949	0.1006	-0.08835	0.3374
fixed	NA	count_birth_order2/>5	0.06323	0.07926	0.7977	5950	0.4251	-0.1593	0.2857
fixed	NA	count_birth_order3/>5	0.1071	0.07777	1.377	5944	0.1687	-0.1112	0.3254
fixed	NA	count_birth_order4/>5	0.1166	0.07485	1.558	5942	0.1193	-0.09349	0.3268
fixed	NA	count_birth_order5/>5	0.07651	0.07694	0.9944	5930	0.3201	-0.1395	0.2925
fixed	NA	count_birth_order>5/>5	0.075	0.05618	1.335	5485	0.182	-0.08271	0.2327
ran_pars	mother_pidlink	sd__(Intercept)	0.2831	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9382	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)
11	16714	16788	-8346	16692	NA	NA	NA
12	16716	16796	-8346	16692	0.4677	1	0.4941
16	16714	16821	-8341	16682	9.387	4	0.05213
26	16723	16897	-8335	16671	11.66	10	0.3085

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)	-0.3119	0.4401	-0.7089	5790	0.4784	-1.547	0.9233
fixed	NA	poly(age, 3, raw = TRUE)1	0.08493	0.04995	1.7	5793	0.08912	-0.05528	0.2251
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003823	0.001783	-2.144	5795	0.03206	-0.008827	0.001182
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004382	0.0000202	2.17	5796	0.03008	-0.00001287	0.0001005
fixed	NA	male	-0.2671	0.0257	-10.39	5761	4.477e-25	-0.3392	-0.195
fixed	NA	sibling_count3	0.02263	0.03892	0.5814	4439	0.561	-0.08662	0.1319
fixed	NA	sibling_count4	0.02637	0.04206	0.6269	3907	0.5308	-0.0917	0.1444
fixed	NA	sibling_count5	0.06156	0.04935	1.247	3337	0.2123	-0.07697	0.2001
fixed	NA	sibling_count>5	0.1362	0.04268	3.191	3077	0.001431	0.0164	0.256
ran_pars	mother_pidlink	sd__(Intercept)	0.2779	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9399	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)	-0.31	0.4401	-0.7044	5789	0.4812	-1.546	0.9254
fixed	NA	birth_order	-0.002816	0.008623	-0.3265	5619	0.744	-0.02702	0.02139
fixed	NA	poly(age, 3, raw = TRUE)1	0.0851	0.04996	1.703	5792	0.08855	-0.05513	0.2253
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003823	0.001783	-2.144	5794	0.03204	-0.008828	0.001181
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004372	0.0000202	2.164	5795	0.0305	-0.00001299	0.0001004
fixed	NA	male	-0.267	0.0257	-10.39	5760	4.66e-25	-0.3392	-0.1949
fixed	NA	sibling_count3	0.02399	0.03915	0.6129	4440	0.54	-0.08589	0.1339
fixed	NA	sibling_count4	0.02953	0.04316	0.6841	3920	0.494	-0.09164	0.1507
fixed	NA	sibling_count5	0.06659	0.0517	1.288	3405	0.1978	-0.07853	0.2117
fixed	NA	sibling_count>5	0.1467	0.05338	2.748	3686	0.006033	-0.003175	0.2965
ran_pars	mother_pidlink	sd__(Intercept)	0.2779	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.94	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)	-0.3089	0.4404	-0.7015	5787	0.483	-1.545	0.9274
fixed	NA	poly(age, 3, raw = TRUE)1	0.08496	0.04995	1.701	5789	0.08902	-0.05525	0.2252
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003814	0.001783	-2.139	5791	0.03244	-0.008818	0.00119
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004349	0.0000202	2.153	5791	0.03138	-0.00001322	0.0001002
fixed	NA	male	-0.2661	0.02569	-10.36	5757	6.318e-25	-0.3383	-0.194
fixed	NA	sibling_count3	0.00615	0.04	0.1538	4631	0.8778	-0.1061	0.1184
fixed	NA	sibling_count4	0.03058	0.04497	0.68	4267	0.4966	-0.09566	0.1568
fixed	NA	sibling_count5	0.08032	0.05419	1.482	3821	0.1384	-0.07179	0.2324
fixed	NA	sibling_count>5	0.1524	0.05509	2.766	3999	0.005705	-0.002274	0.307
fixed	NA	birth_order_nonlinear2	-0.01162	0.03304	-0.3517	4967	0.7251	-0.1044	0.08113
fixed	NA	birth_order_nonlinear3	0.0701	0.04082	1.717	5177	0.086	-0.04449	0.1847
fixed	NA	birth_order_nonlinear4	-0.1025	0.05187	-1.975	5336	0.04827	-0.248	0.04313
fixed	NA	birth_order_nonlinear5	-0.06008	0.06569	-0.9146	5266	0.3604	-0.2445	0.1243
fixed	NA	birth_order_nonlinear>5	-0.008558	0.06479	-0.1321	5791	0.8949	-0.1904	0.1733
ran_pars	mother_pidlink	sd__(Intercept)	0.2758	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9399	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)	-0.3435	0.4413	-0.7782	5778	0.4365	-1.582	0.8954
fixed	NA	poly(age, 3, raw = TRUE)1	0.08974	0.05005	1.793	5779	0.07301	-0.05075	0.2302
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003982	0.001787	-2.229	5781	0.02587	-0.008997	0.001033
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004536	0.00002025	2.24	5781	0.02512	-0.00001148	0.0001022
fixed	NA	male	-0.2651	0.02571	-10.31	5745	1.02e-24	-0.3373	-0.1929
fixed	NA	count_birth_order2/2	-0.03673	0.05826	-0.6303	5107	0.5285	-0.2003	0.1268
fixed	NA	count_birth_order1/3	-0.03504	0.05183	-0.6761	5768	0.499	-0.1805	0.1104
fixed	NA	count_birth_order2/3	0.02112	0.05733	0.3685	5780	0.7125	-0.1398	0.182
fixed	NA	count_birth_order3/3	0.08289	0.063	1.316	5780	0.1883	-0.09395	0.2597
fixed	NA	count_birth_order1/4	0.03566	0.06449	0.5529	5777	0.5804	-0.1454	0.2167
fixed	NA	count_birth_order2/4	0.05259	0.06634	0.7926	5781	0.428	-0.1336	0.2388
fixed	NA	count_birth_order3/4	0.06513	0.06952	0.9368	5777	0.3489	-0.13	0.2603
fixed	NA	count_birth_order4/4	-0.1268	0.07348	-1.725	5775	0.0846	-0.333	0.07952
fixed	NA	count_birth_order1/5	0.1824	0.087	2.097	5781	0.03602	-0.06176	0.4267
fixed	NA	count_birth_order2/5	-0.1091	0.09619	-1.135	5774	0.2566	-0.3792	0.1609
fixed	NA	count_birth_order3/5	0.1727	0.09178	1.882	5771	0.05994	-0.08494	0.4303
fixed	NA	count_birth_order4/5	0.01715	0.08843	0.1939	5774	0.8462	-0.2311	0.2654
fixed	NA	count_birth_order5/5	-0.05352	0.09396	-0.5696	5769	0.569	-0.3173	0.2102
fixed	NA	count_birth_order1/>5	0.09742	0.08857	1.1	5781	0.2714	-0.1512	0.3461
fixed	NA	count_birth_order2/>5	0.1182	0.08785	1.346	5779	0.1785	-0.1284	0.3648
fixed	NA	count_birth_order3/>5	0.1982	0.08707	2.276	5768	0.02285	-0.04619	0.4426
fixed	NA	count_birth_order4/>5	0.06053	0.08517	0.7107	5759	0.4773	-0.1785	0.2996
fixed	NA	count_birth_order5/>5	0.1239	0.07828	1.582	5764	0.1136	-0.09587	0.3436
fixed	NA	count_birth_order>5/>5	0.1351	0.05831	2.316	5172	0.02058	-0.02862	0.2987
ran_pars	mother_pidlink	sd__(Intercept)	0.2761	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9398	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)
11	16235	16308	-8106	16213	NA	NA	NA
12	16237	16317	-8106	16213	0.1071	1	0.7435
16	16234	16340	-8101	16202	11.14	4	0.02506
26	16243	16416	-8096	16191	10.72	10	0.3799

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)	-1.384	0.1564	-8.846	13621	1.016e-18	-1.823	-0.9446
fixed	NA	poly(age, 3, raw = TRUE)1	0.07934	0.01497	5.299	13475	0.0000001185	0.03731	0.1214
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001195	0.0004398	-2.718	13274	0.006579	-0.00243	0.00003921
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005148	0.000004043	1.273	13095	0.203	-0.000006202	0.0000165
fixed	NA	male	0.0443	0.01659	2.669	13887	0.00761	-0.002285	0.09088
fixed	NA	sibling_count3	-0.01129	0.03263	-0.346	10656	0.7293	-0.1029	0.08031
fixed	NA	sibling_count4	-0.01053	0.03347	-0.3145	9594	0.7531	-0.1045	0.08343
fixed	NA	sibling_count5	-0.0000886	0.03461	-0.00256	8380	0.998	-0.09724	0.09706
fixed	NA	sibling_count>5	0.02139	0.02733	0.7829	9670	0.4337	-0.05532	0.0981
ran_pars	mother_pidlink	sd__(Intercept)	0.2052	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9578	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)	-1.384	0.1564	-8.85	13624	9.775e-19	-1.824	-0.9454
fixed	NA	birth_order	-0.001557	0.003422	-0.4549	10419	0.6492	-0.01116	0.008049
fixed	NA	poly(age, 3, raw = TRUE)1	0.0798	0.01501	5.317	13457	0.0000001072	0.03767	0.1219
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001211	0.0004412	-2.745	13209	0.006056	-0.00245	0.00002729
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005292	0.000004056	1.305	13010	0.192	-0.000006094	0.00001668
fixed	NA	male	0.04434	0.0166	2.672	13886	0.007552	-0.002243	0.09092
fixed	NA	sibling_count3	-0.01089	0.03265	-0.3337	10671	0.7386	-0.1025	0.08075
fixed	NA	sibling_count4	-0.009402	0.03357	-0.2801	9650	0.7794	-0.1036	0.08482
fixed	NA	sibling_count5	0.00183	0.03487	0.05247	8475	0.9582	-0.09605	0.09971
fixed	NA	sibling_count>5	0.02738	0.03034	0.9025	10573	0.3668	-0.05777	0.1125
ran_pars	mother_pidlink	sd__(Intercept)	0.2055	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9578	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)	-1.373	0.1568	-8.753	13630	2.309e-18	-1.813	-0.9327
fixed	NA	poly(age, 3, raw = TRUE)1	0.07988	0.01501	5.32	13469	0.0000001051	0.03773	0.122
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001203	0.0004413	-2.726	13222	0.006414	-0.002442	0.00003564
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005103	0.000004057	1.258	13011	0.2085	-0.000006285	0.00001649
fixed	NA	male	0.04452	0.0166	2.682	13882	0.007316	-0.002067	0.0911
fixed	NA	sibling_count3	-0.004833	0.03316	-0.1457	11026	0.8841	-0.09792	0.08825
fixed	NA	sibling_count4	-0.003616	0.03464	-0.1044	10422	0.9169	-0.1008	0.09362
fixed	NA	sibling_count5	0.01333	0.0364	0.3662	9524	0.7142	-0.08885	0.1155
fixed	NA	sibling_count>5	0.0351	0.03206	1.095	11818	0.2736	-0.0549	0.1251
fixed	NA	birth_order_nonlinear2	-0.04456	0.02432	-1.832	12767	0.06694	-0.1128	0.02371
fixed	NA	birth_order_nonlinear3	-0.04247	0.02871	-1.479	12682	0.1391	-0.1231	0.03813
fixed	NA	birth_order_nonlinear4	-0.01607	0.03269	-0.4915	12813	0.6231	-0.1078	0.07569
fixed	NA	birth_order_nonlinear5	-0.06266	0.03717	-1.686	12914	0.09183	-0.167	0.04167
fixed	NA	birth_order_nonlinear>5	-0.03018	0.03045	-0.9914	13881	0.3215	-0.1156	0.05528
ran_pars	mother_pidlink	sd__(Intercept)	0.2051	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9578	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)	-1.345	0.1575	-8.541	13635	1.476e-17	-1.787	-0.9032
fixed	NA	poly(age, 3, raw = TRUE)1	0.08008	0.01501	5.333	13463	0.00000009791	0.03793	0.1222
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001199	0.0004413	-2.717	13210	0.006586	-0.002438	0.00003951
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004988	0.000004057	1.229	12991	0.219	-0.000006402	0.00001638
fixed	NA	male	0.0447	0.0166	2.693	13872	0.007085	-0.001889	0.09129
fixed	NA	count_birth_order2/2	-0.1323	0.04729	-2.798	12473	0.005147	-0.2651	0.0004197
fixed	NA	count_birth_order1/3	-0.05977	0.0442	-1.352	13880	0.1763	-0.1838	0.06429
fixed	NA	count_birth_order2/3	-0.05331	0.04943	-1.078	13893	0.2808	-0.1921	0.08545
fixed	NA	count_birth_order3/3	-0.07588	0.05538	-1.37	13904	0.1707	-0.2313	0.07959
fixed	NA	count_birth_order1/4	-0.03678	0.05048	-0.7286	13895	0.4663	-0.1785	0.1049
fixed	NA	count_birth_order2/4	-0.08135	0.0531	-1.532	13897	0.1255	-0.2304	0.06769
fixed	NA	count_birth_order3/4	-0.0356	0.0577	-0.6169	13903	0.5373	-0.1976	0.1264
fixed	NA	count_birth_order4/4	-0.1034	0.0611	-1.692	13907	0.09073	-0.2749	0.06815
fixed	NA	count_birth_order1/5	0.02975	0.0573	0.5192	13904	0.6037	-0.1311	0.1906
fixed	NA	count_birth_order2/5	-0.03593	0.06028	-0.596	13908	0.5512	-0.2052	0.1333
fixed	NA	count_birth_order3/5	-0.08495	0.06188	-1.373	13908	0.1698	-0.2586	0.08875
fixed	NA	count_birth_order4/5	-0.04652	0.06556	-0.7095	13909	0.478	-0.2305	0.1375
fixed	NA	count_birth_order5/5	-0.1564	0.06702	-2.333	13910	0.01966	-0.3445	0.03176
fixed	NA	count_birth_order1/>5	-0.04653	0.04629	-1.005	13908	0.3148	-0.1765	0.0834
fixed	NA	count_birth_order2/>5	-0.02981	0.04775	-0.6243	13910	0.5324	-0.1639	0.1042
fixed	NA	count_birth_order3/>5	-0.05692	0.04679	-1.217	13910	0.2238	-0.1883	0.07441
fixed	NA	count_birth_order4/>5	0.01003	0.04585	0.2187	13910	0.8269	-0.1187	0.1387
fixed	NA	count_birth_order5/>5	-0.03622	0.04619	-0.7841	13910	0.433	-0.1659	0.09345
fixed	NA	count_birth_order>5/>5	-0.02832	0.0357	-0.7933	12628	0.4276	-0.1285	0.0719
ran_pars	mother_pidlink	sd__(Intercept)	0.2051	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9577	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)
11	38959	39042	-19468	38937	NA	NA	NA
12	38960	39051	-19468	38936	0.2064	1	0.6496
16	38963	39084	-19466	38931	5.284	4	0.2594
26	38971	39167	-19459	38919	12.56	10	0.2493

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)	-0.8647	0.4405	-1.963	5915	0.04968	-2.101	0.3717
fixed	NA	poly(age, 3, raw = TRUE)1	0.01416	0.04997	0.2834	5914	0.7769	-0.1261	0.1544
fixed	NA	poly(age, 3, raw = TRUE)2	0.001255	0.001782	0.7039	5911	0.4815	-0.003749	0.006258
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002195	0.00002018	-1.088	5904	0.2767	-0.00007859	0.00003469
fixed	NA	male	0.05224	0.02578	2.026	5900	0.04277	-0.02012	0.1246
fixed	NA	sibling_count3	-0.02611	0.03958	-0.6597	4507	0.5095	-0.1372	0.085
fixed	NA	sibling_count4	-0.04355	0.0424	-1.027	3883	0.3044	-0.1626	0.07547
fixed	NA	sibling_count5	-0.01096	0.04815	-0.2276	3356	0.8199	-0.1461	0.1242
fixed	NA	sibling_count>5	0.03937	0.04215	0.9341	3021	0.3503	-0.07894	0.1577
ran_pars	mother_pidlink	sd__(Intercept)	0.2157	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9676	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)	-0.85	0.4404	-1.93	5914	0.05364	-2.086	0.3862
fixed	NA	birth_order	-0.01736	0.008434	-2.058	5468	0.03961	-0.04104	0.006316
fixed	NA	poly(age, 3, raw = TRUE)1	0.01482	0.04995	0.2967	5913	0.7667	-0.1254	0.155
fixed	NA	poly(age, 3, raw = TRUE)2	0.001262	0.001782	0.7084	5910	0.4787	-0.00374	0.006264
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000227	0.00002018	-1.125	5903	0.2605	-0.00007934	0.00003393
fixed	NA	male	0.05295	0.02577	2.054	5899	0.03999	-0.0194	0.1253
fixed	NA	sibling_count3	-0.01776	0.03978	-0.4464	4506	0.6553	-0.1294	0.09391
fixed	NA	sibling_count4	-0.02394	0.04345	-0.551	3873	0.5817	-0.1459	0.09802
fixed	NA	sibling_count5	0.02124	0.05063	0.4196	3407	0.6748	-0.1209	0.1634
fixed	NA	sibling_count>5	0.1041	0.0526	1.98	3526	0.04777	-0.04349	0.2518
ran_pars	mother_pidlink	sd__(Intercept)	0.2163	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9672	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)	-0.8407	0.4411	-1.906	5910	0.05671	-2.079	0.3975
fixed	NA	poly(age, 3, raw = TRUE)1	0.01289	0.04999	0.2579	5909	0.7965	-0.1274	0.1532
fixed	NA	poly(age, 3, raw = TRUE)2	0.001337	0.001783	0.7497	5905	0.4535	-0.003669	0.006343
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002361	0.00002019	-1.169	5898	0.2424	-0.0000803	0.00003308
fixed	NA	male	0.05276	0.02578	2.046	5895	0.04077	-0.01961	0.1251
fixed	NA	sibling_count3	-0.01599	0.04069	-0.393	4706	0.6943	-0.1302	0.09822
fixed	NA	sibling_count4	-0.01708	0.04533	-0.3768	4249	0.7064	-0.1443	0.1102
fixed	NA	sibling_count5	0.02747	0.05349	0.5135	3911	0.6076	-0.1227	0.1776
fixed	NA	sibling_count>5	0.1085	0.05435	1.997	3858	0.0459	-0.04402	0.2611
fixed	NA	birth_order_nonlinear2	-0.05026	0.03374	-1.49	5060	0.1363	-0.145	0.04444
fixed	NA	birth_order_nonlinear3	-0.04458	0.04152	-1.074	5325	0.283	-0.1611	0.07198
fixed	NA	birth_order_nonlinear4	-0.08636	0.05124	-1.685	5489	0.09199	-0.2302	0.05748
fixed	NA	birth_order_nonlinear5	-0.08063	0.06405	-1.259	5418	0.2081	-0.2604	0.09917
fixed	NA	birth_order_nonlinear>5	-0.127	0.06351	-2	5876	0.04551	-0.3053	0.05123
ran_pars	mother_pidlink	sd__(Intercept)	0.2164	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9674	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)	-0.8614	0.4418	-1.95	5900	0.05126	-2.102	0.3788
fixed	NA	poly(age, 3, raw = TRUE)1	0.01798	0.05007	0.3591	5899	0.7195	-0.1226	0.1585
fixed	NA	poly(age, 3, raw = TRUE)2	0.001121	0.001787	0.6275	5896	0.5303	-0.003894	0.006136
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002076	0.00002023	-1.026	5889	0.3049	-0.00007756	0.00003603
fixed	NA	male	0.05421	0.02579	2.102	5884	0.03562	-0.01819	0.1266
fixed	NA	count_birth_order2/2	-0.1018	0.06088	-1.672	5195	0.09458	-0.2727	0.0691
fixed	NA	count_birth_order1/3	-0.004458	0.05311	-0.08395	5894	0.9331	-0.1535	0.1446
fixed	NA	count_birth_order2/3	-0.1003	0.05806	-1.727	5899	0.08428	-0.2632	0.06273
fixed	NA	count_birth_order3/3	-0.1107	0.06495	-1.705	5900	0.08831	-0.293	0.07159
fixed	NA	count_birth_order1/4	-0.05653	0.06495	-0.8703	5895	0.3842	-0.2388	0.1258
fixed	NA	count_birth_order2/4	-0.05995	0.06727	-0.8911	5900	0.3729	-0.2488	0.1289
fixed	NA	count_birth_order3/4	-0.02575	0.07114	-0.362	5898	0.7174	-0.2255	0.174
fixed	NA	count_birth_order4/4	-0.1802	0.07397	-2.437	5897	0.01485	-0.3879	0.02739
fixed	NA	count_birth_order1/5	-0.09011	0.0883	-1.021	5900	0.3075	-0.338	0.1577
fixed	NA	count_birth_order2/5	0.09637	0.0946	1.019	5898	0.3084	-0.1692	0.3619
fixed	NA	count_birth_order3/5	0.02785	0.08869	0.314	5896	0.7535	-0.2211	0.2768
fixed	NA	count_birth_order4/5	-0.06482	0.08542	-0.7588	5896	0.448	-0.3046	0.175
fixed	NA	count_birth_order5/5	-0.1599	0.08892	-1.798	5893	0.07225	-0.4095	0.08973
fixed	NA	count_birth_order1/>5	0.03187	0.08759	0.3638	5895	0.716	-0.214	0.2777
fixed	NA	count_birth_order2/>5	0.01605	0.08675	0.1851	5899	0.8532	-0.2275	0.2596
fixed	NA	count_birth_order3/>5	-0.03007	0.08697	-0.3458	5898	0.7295	-0.2742	0.214
fixed	NA	count_birth_order4/>5	0.06919	0.08196	0.8442	5896	0.3986	-0.1609	0.2992
fixed	NA	count_birth_order5/>5	0.07304	0.07745	0.943	5895	0.3457	-0.1444	0.2905
fixed	NA	count_birth_order>5/>5	-0.03498	0.05771	-0.6062	5174	0.5444	-0.197	0.127
ran_pars	mother_pidlink	sd__(Intercept)	0.2171	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.967	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)
11	16715	16788	-8346	16693	NA	NA	NA
12	16713	16793	-8344	16689	4.241	1	0.03947
16	16719	16826	-8344	16687	1.514	4	0.8241
26	16726	16900	-8337	16674	13.11	10	0.2177

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)	-0.8294	0.439	-1.889	5966	0.0589	-2.062	0.4029
fixed	NA	poly(age, 3, raw = TRUE)1	0.01291	0.04982	0.259	5965	0.7956	-0.1269	0.1528
fixed	NA	poly(age, 3, raw = TRUE)2	0.001314	0.001778	0.7389	5962	0.46	-0.003677	0.006304
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002253	0.00002013	-1.12	5954	0.263	-0.00007903	0.00003397
fixed	NA	male	0.05108	0.02567	1.99	5950	0.04666	-0.02098	0.1231
fixed	NA	sibling_count3	-0.06959	0.04285	-1.624	4674	0.1044	-0.1899	0.05069
fixed	NA	sibling_count4	-0.06697	0.04498	-1.489	4208	0.1366	-0.1932	0.0593
fixed	NA	sibling_count5	-0.0582	0.04789	-1.215	3688	0.2243	-0.1926	0.07623
fixed	NA	sibling_count>5	-0.01844	0.04201	-0.4389	3738	0.6607	-0.1364	0.09949
ran_pars	mother_pidlink	sd__(Intercept)	0.2172	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9672	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)	-0.8205	0.4391	-1.869	5965	0.06171	-2.053	0.412
fixed	NA	birth_order	-0.007815	0.007334	-1.066	5112	0.2867	-0.0284	0.01277
fixed	NA	poly(age, 3, raw = TRUE)1	0.01293	0.04982	0.2596	5964	0.7952	-0.1269	0.1528
fixed	NA	poly(age, 3, raw = TRUE)2	0.001327	0.001778	0.7463	5961	0.4555	-0.003664	0.006317
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002298	0.00002013	-1.141	5954	0.2537	-0.00007949	0.00003353
fixed	NA	male	0.05132	0.02567	1.999	5949	0.04563	-0.02074	0.1234
fixed	NA	sibling_count3	-0.06585	0.04299	-1.532	4668	0.1257	-0.1865	0.05483
fixed	NA	sibling_count4	-0.0585	0.04568	-1.281	4181	0.2004	-0.1867	0.06973
fixed	NA	sibling_count5	-0.04485	0.04951	-0.9058	3674	0.3651	-0.1838	0.09413
fixed	NA	sibling_count>5	0.01003	0.0498	0.2014	3993	0.8404	-0.1297	0.1498
ran_pars	mother_pidlink	sd__(Intercept)	0.2179	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.967	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)	-0.7972	0.4396	-1.813	5961	0.06981	-2.031	0.4368
fixed	NA	poly(age, 3, raw = TRUE)1	0.01086	0.04984	0.2178	5960	0.8276	-0.1291	0.1508
fixed	NA	poly(age, 3, raw = TRUE)2	0.001404	0.001779	0.7896	5956	0.4298	-0.003588	0.006397
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002385	0.00002015	-1.184	5948	0.2365	-0.0000804	0.0000327
fixed	NA	male	0.05093	0.02568	1.983	5945	0.04736	-0.02115	0.123
fixed	NA	sibling_count3	-0.05132	0.04384	-1.171	4834	0.2418	-0.1744	0.07174
fixed	NA	sibling_count4	-0.04716	0.04742	-0.9943	4502	0.3201	-0.1803	0.08596
fixed	NA	sibling_count5	-0.03619	0.0521	-0.6946	4129	0.4874	-0.1824	0.1101
fixed	NA	sibling_count>5	0.01453	0.0515	0.2822	4358	0.7778	-0.13	0.1591
fixed	NA	birth_order_nonlinear2	-0.0495	0.03432	-1.442	5196	0.1493	-0.1458	0.04683
fixed	NA	birth_order_nonlinear3	-0.08248	0.04134	-1.995	5451	0.04609	-0.1985	0.03357
fixed	NA	birth_order_nonlinear4	-0.02223	0.04967	-0.4476	5606	0.6545	-0.1616	0.1172
fixed	NA	birth_order_nonlinear5	-0.04183	0.06094	-0.6863	5601	0.4925	-0.2129	0.1292
fixed	NA	birth_order_nonlinear>5	-0.0672	0.05659	-1.187	5850	0.2351	-0.2261	0.09166
ran_pars	mother_pidlink	sd__(Intercept)	0.2171	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9672	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)	-0.8331	0.4403	-1.892	5951	0.05855	-2.069	0.403
fixed	NA	poly(age, 3, raw = TRUE)1	0.01647	0.04991	0.3301	5950	0.7414	-0.1236	0.1566
fixed	NA	poly(age, 3, raw = TRUE)2	0.001182	0.001781	0.6636	5946	0.507	-0.003818	0.006183
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002112	0.00002018	-1.047	5938	0.2952	-0.00007777	0.00003552
fixed	NA	male	0.0522	0.02569	2.032	5935	0.04221	-0.01992	0.1243
fixed	NA	count_birth_order2/2	-0.07531	0.06659	-1.131	5310	0.2581	-0.2622	0.1116
fixed	NA	count_birth_order1/3	-0.04684	0.05752	-0.8144	5946	0.4154	-0.2083	0.1146
fixed	NA	count_birth_order2/3	-0.1051	0.06241	-1.683	5950	0.09236	-0.2803	0.07013
fixed	NA	count_birth_order3/3	-0.1749	0.07028	-2.489	5951	0.01284	-0.3722	0.02236
fixed	NA	count_birth_order1/4	-0.04383	0.06804	-0.6442	5947	0.5194	-0.2348	0.1472
fixed	NA	count_birth_order2/4	-0.09198	0.06936	-1.326	5950	0.1849	-0.2867	0.1027
fixed	NA	count_birth_order3/4	-0.08984	0.07619	-1.179	5950	0.2384	-0.3037	0.124
fixed	NA	count_birth_order4/4	-0.1675	0.07856	-2.132	5949	0.03303	-0.388	0.05301
fixed	NA	count_birth_order1/5	-0.03052	0.08079	-0.3778	5950	0.7056	-0.2573	0.1962
fixed	NA	count_birth_order2/5	-0.122	0.08684	-1.404	5951	0.1602	-0.3657	0.1218
fixed	NA	count_birth_order3/5	-0.09178	0.08447	-1.087	5949	0.2773	-0.3289	0.1453
fixed	NA	count_birth_order4/5	0.002615	0.08758	0.02985	5945	0.9762	-0.2432	0.2485
fixed	NA	count_birth_order5/5	-0.1843	0.08783	-2.098	5944	0.03592	-0.4308	0.06225
fixed	NA	count_birth_order1/>5	-0.07646	0.07677	-0.9959	5945	0.3193	-0.292	0.139
fixed	NA	count_birth_order2/>5	-0.0221	0.08027	-0.2753	5951	0.7831	-0.2474	0.2032
fixed	NA	count_birth_order3/>5	-0.1136	0.07879	-1.442	5950	0.1494	-0.3348	0.1075
fixed	NA	count_birth_order4/>5	0.01616	0.07584	0.2131	5948	0.8313	-0.1967	0.2291
fixed	NA	count_birth_order5/>5	0.03516	0.07798	0.4509	5942	0.6521	-0.1837	0.2541
fixed	NA	count_birth_order>5/>5	-0.06057	0.05661	-1.07	5357	0.2847	-0.2195	0.09833
ran_pars	mother_pidlink	sd__(Intercept)	0.2173	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9672	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)
11	16858	16931	-8418	16836	NA	NA	NA
12	16859	16939	-8417	16835	1.136	1	0.2865
16	16863	16970	-8415	16831	3.922	4	0.4166
26	16873	17047	-8411	16821	9.357	10	0.4986

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)	-0.7476	0.4452	-1.679	5796	0.09314	-1.997	0.502
fixed	NA	poly(age, 3, raw = TRUE)1	0.003025	0.05052	0.05987	5795	0.9523	-0.1388	0.1448
fixed	NA	poly(age, 3, raw = TRUE)2	0.001617	0.001803	0.8969	5791	0.3698	-0.003444	0.006678
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002573	0.00002042	-1.26	5782	0.2077	-0.00008305	0.00003159
fixed	NA	male	0.05245	0.02602	2.016	5782	0.04386	-0.02059	0.1255
fixed	NA	sibling_count3	-0.06345	0.03902	-1.626	4365	0.104	-0.173	0.04609
fixed	NA	sibling_count4	-0.05627	0.04207	-1.338	3764	0.1811	-0.1744	0.06182
fixed	NA	sibling_count5	0.01114	0.04923	0.2263	3116	0.821	-0.127	0.1493
fixed	NA	sibling_count>5	0.04261	0.04251	1.002	2805	0.3162	-0.07671	0.1619
ran_pars	mother_pidlink	sd__(Intercept)	0.215	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9666	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)	-0.7362	0.4451	-1.654	5795	0.09818	-1.986	0.5132
fixed	NA	birth_order	-0.0169	0.008689	-1.945	5418	0.05178	-0.04129	0.007487
fixed	NA	poly(age, 3, raw = TRUE)1	0.003965	0.05051	0.07849	5794	0.9374	-0.1378	0.1458
fixed	NA	poly(age, 3, raw = TRUE)2	0.001616	0.001802	0.8963	5790	0.3701	-0.003444	0.006675
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002637	0.00002042	-1.292	5782	0.1965	-0.00008369	0.00003094
fixed	NA	male	0.05286	0.02601	2.032	5781	0.0422	-0.02016	0.1259
fixed	NA	sibling_count3	-0.0553	0.03924	-1.409	4361	0.1588	-0.1654	0.05484
fixed	NA	sibling_count4	-0.03742	0.04316	-0.8669	3763	0.386	-0.1586	0.08374
fixed	NA	sibling_count5	0.04108	0.05157	0.7966	3169	0.4257	-0.1037	0.1858
fixed	NA	sibling_count>5	0.1052	0.05331	1.974	3411	0.04849	-0.04442	0.2549
ran_pars	mother_pidlink	sd__(Intercept)	0.2149	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9664	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)	-0.7235	0.4458	-1.623	5791	0.1047	-1.975	0.5279
fixed	NA	poly(age, 3, raw = TRUE)1	0.001757	0.05055	0.03477	5789	0.9723	-0.1401	0.1436
fixed	NA	poly(age, 3, raw = TRUE)2	0.001695	0.001804	0.9395	5785	0.3475	-0.003369	0.006758
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002722	0.00002044	-1.332	5777	0.1829	-0.00008459	0.00003014
fixed	NA	male	0.05268	0.02603	2.024	5776	0.04299	-0.02037	0.1257
fixed	NA	sibling_count3	-0.05402	0.04017	-1.345	4568	0.1787	-0.1668	0.05873
fixed	NA	sibling_count4	-0.03311	0.04509	-0.7342	4144	0.4629	-0.1597	0.09347
fixed	NA	sibling_count5	0.04809	0.05423	0.8869	3618	0.3752	-0.1041	0.2003
fixed	NA	sibling_count>5	0.1025	0.05516	1.858	3761	0.06325	-0.05235	0.2573
fixed	NA	birth_order_nonlinear2	-0.04874	0.03365	-1.449	4934	0.1475	-0.1432	0.04571
fixed	NA	birth_order_nonlinear3	-0.0439	0.04152	-1.057	5175	0.2905	-0.1605	0.07266
fixed	NA	birth_order_nonlinear4	-0.07397	0.05271	-1.403	5357	0.1606	-0.2219	0.074
fixed	NA	birth_order_nonlinear5	-0.09912	0.06679	-1.484	5305	0.1379	-0.2866	0.08836
fixed	NA	birth_order_nonlinear>5	-0.1016	0.06554	-1.55	5773	0.1211	-0.2856	0.08236
ran_pars	mother_pidlink	sd__(Intercept)	0.2148	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9667	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)	-0.7227	0.4465	-1.619	5781	0.1056	-1.976	0.5305
fixed	NA	poly(age, 3, raw = TRUE)1	0.004249	0.05062	0.08394	5780	0.9331	-0.1378	0.1463
fixed	NA	poly(age, 3, raw = TRUE)2	0.001573	0.001807	0.8707	5775	0.384	-0.003498	0.006645
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002548	0.00002047	-1.244	5766	0.2134	-0.00008294	0.00003199
fixed	NA	male	0.0537	0.02603	2.063	5765	0.03913	-0.01936	0.1268
fixed	NA	count_birth_order2/2	-0.09551	0.05926	-1.612	5042	0.1071	-0.2618	0.07083
fixed	NA	count_birth_order1/3	-0.0317	0.05239	-0.6052	5774	0.5451	-0.1788	0.1154
fixed	NA	count_birth_order2/3	-0.1419	0.05797	-2.447	5780	0.01442	-0.3046	0.02086
fixed	NA	count_birth_order3/3	-0.1565	0.06373	-2.456	5780	0.01408	-0.3354	0.02237
fixed	NA	count_birth_order1/4	-0.1047	0.0652	-1.606	5777	0.1083	-0.2877	0.0783
fixed	NA	count_birth_order2/4	-0.03028	0.0671	-0.4513	5781	0.6518	-0.2186	0.1581
fixed	NA	count_birth_order3/4	-0.01813	0.07034	-0.2577	5778	0.7966	-0.2156	0.1793
fixed	NA	count_birth_order4/4	-0.2182	0.07436	-2.935	5777	0.003354	-0.4269	-0.00948
fixed	NA	count_birth_order1/5	-0.08435	0.08798	-0.9588	5780	0.3377	-0.3313	0.1626
fixed	NA	count_birth_order2/5	0.0693	0.09733	0.712	5779	0.4765	-0.2039	0.3425
fixed	NA	count_birth_order3/5	0.05283	0.09288	0.5688	5777	0.5695	-0.2079	0.3135
fixed	NA	count_birth_order4/5	-0.0298	0.08948	-0.333	5777	0.7391	-0.281	0.2214
fixed	NA	count_birth_order5/5	-0.08705	0.09509	-0.9154	5774	0.36	-0.354	0.1799
fixed	NA	count_birth_order1/>5	0.07337	0.08958	0.8191	5779	0.4128	-0.1781	0.3248
fixed	NA	count_birth_order2/>5	-0.01039	0.08886	-0.1169	5780	0.9069	-0.2598	0.239
fixed	NA	count_birth_order3/>5	-0.04537	0.08811	-0.515	5778	0.6066	-0.2927	0.2019
fixed	NA	count_birth_order4/>5	0.1355	0.08621	1.571	5775	0.1161	-0.1065	0.3775
fixed	NA	count_birth_order5/>5	0.0005431	0.07922	0.006856	5775	0.9945	-0.2218	0.2229
fixed	NA	count_birth_order>5/>5	-0.01412	0.05865	-0.2408	4974	0.8097	-0.1788	0.1505
ran_pars	mother_pidlink	sd__(Intercept)	0.2155	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9659	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)
11	16366	16440	-8172	16344	NA	NA	NA
12	16364	16444	-8170	16340	3.79	1	0.05156
16	16372	16478	-8170	16340	0.7968	4	0.9389
26	16375	16548	-8161	16323	16.83	10	0.07811

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)	-0.5625	0.1596	-3.524	13676	0.0004259	-1.011	-0.1145
fixed	NA	poly(age, 3, raw = TRUE)1	0.0273	0.01529	1.786	13553	0.07411	-0.01561	0.07021
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002583	0.0004491	-0.5752	13371	0.5652	-0.001519	0.001002
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000008022	0.000004131	-0.1942	13199	0.846	-0.0000124	0.00001079
fixed	NA	male	0.06076	0.0169	3.596	13854	0.0003241	0.01333	0.1082
fixed	NA	sibling_count3	-0.02089	0.03345	-0.6245	10670	0.5323	-0.1148	0.07301
fixed	NA	sibling_count4	0.03056	0.03436	0.8896	9679	0.3737	-0.06588	0.127
fixed	NA	sibling_count5	0.007767	0.03558	0.2183	8553	0.8272	-0.0921	0.1076
fixed	NA	sibling_count>5	0.005771	0.02805	0.2058	9766	0.837	-0.07295	0.0845
ran_pars	mother_pidlink	sd__(Intercept)	0.2511	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9667	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)	-0.5602	0.1596	-3.509	13678	0.0004505	-1.008	-0.1121
fixed	NA	birth_order	0.004807	0.003507	1.371	11206	0.1704	-0.005036	0.01465
fixed	NA	poly(age, 3, raw = TRUE)1	0.02588	0.01532	1.689	13536	0.09117	-0.01712	0.06888
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002084	0.0004506	-0.4624	13310	0.6438	-0.001473	0.001056
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001256	0.000004144	-0.303	13116	0.7619	-0.00001289	0.00001038
fixed	NA	male	0.06062	0.0169	3.588	13853	0.0003345	0.01319	0.108
fixed	NA	sibling_count3	-0.0221	0.03346	-0.6604	10683	0.509	-0.116	0.07183
fixed	NA	sibling_count4	0.02712	0.03445	0.7873	9736	0.4311	-0.06957	0.1238
fixed	NA	sibling_count5	0.001865	0.03584	0.05204	8652	0.9585	-0.09873	0.1025
fixed	NA	sibling_count>5	-0.01264	0.03109	-0.4065	10700	0.6844	-0.09992	0.07464
ran_pars	mother_pidlink	sd__(Intercept)	0.251	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9667	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)	-0.5594	0.1601	-3.495	13681	0.0004758	-1.009	-0.1101
fixed	NA	poly(age, 3, raw = TRUE)1	0.02613	0.01533	1.705	13547	0.0882	-0.01689	0.06916
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002155	0.0004507	-0.4782	13321	0.6325	-0.001481	0.00105
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001198	0.000004146	-0.2889	13117	0.7727	-0.00001283	0.00001044
fixed	NA	male	0.0607	0.0169	3.592	13849	0.0003293	0.01326	0.1081
fixed	NA	sibling_count3	-0.01916	0.03398	-0.5638	11024	0.5729	-0.1145	0.07623
fixed	NA	sibling_count4	0.02892	0.03552	0.814	10472	0.4156	-0.07079	0.1286
fixed	NA	sibling_count5	0.007183	0.03737	0.1922	9652	0.8476	-0.09771	0.1121
fixed	NA	sibling_count>5	-0.01117	0.03282	-0.3404	11853	0.7335	-0.1033	0.08095
fixed	NA	birth_order_nonlinear2	0.008944	0.0247	0.3622	12790	0.7172	-0.06038	0.07827
fixed	NA	birth_order_nonlinear3	-0.002557	0.02915	-0.08772	12675	0.9301	-0.08439	0.07928
fixed	NA	birth_order_nonlinear4	0.02067	0.0332	0.6226	12782	0.5336	-0.07252	0.1139
fixed	NA	birth_order_nonlinear5	-0.001727	0.03775	-0.04573	12862	0.9635	-0.1077	0.1042
fixed	NA	birth_order_nonlinear>5	0.04206	0.03104	1.355	13911	0.1753	-0.04506	0.1292
ran_pars	mother_pidlink	sd__(Intercept)	0.251	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9668	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)	-0.5441	0.1607	-3.384	13685	0.0007151	-0.9953	-0.09283
fixed	NA	poly(age, 3, raw = TRUE)1	0.0261	0.01533	1.703	13541	0.08864	-0.01693	0.06913
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002053	0.0004508	-0.4555	13310	0.6487	-0.001471	0.00106
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001373	0.000004146	-0.331	13098	0.7406	-0.00001301	0.00001027
fixed	NA	male	0.06108	0.0169	3.615	13836	0.0003019	0.01365	0.1085
fixed	NA	count_birth_order2/2	-0.03887	0.048	-0.8099	12577	0.418	-0.1736	0.09586
fixed	NA	count_birth_order1/3	-0.02833	0.04506	-0.6288	13856	0.5295	-0.1548	0.09816
fixed	NA	count_birth_order2/3	0.003943	0.05039	0.07825	13880	0.9376	-0.1375	0.1454
fixed	NA	count_birth_order3/3	-0.1023	0.05645	-1.812	13899	0.07	-0.2607	0.05616
fixed	NA	count_birth_order1/4	0.0002992	0.05146	0.005815	13883	0.9954	-0.1442	0.1447
fixed	NA	count_birth_order2/4	0.0164	0.05412	0.3031	13889	0.7618	-0.1355	0.1683
fixed	NA	count_birth_order3/4	-0.02745	0.05881	-0.4668	13900	0.6406	-0.1925	0.1376
fixed	NA	count_birth_order4/4	0.09601	0.06227	1.542	13907	0.1231	-0.07878	0.2708
fixed	NA	count_birth_order1/5	0.03871	0.0584	0.6629	13900	0.5074	-0.1252	0.2026
fixed	NA	count_birth_order2/5	-0.03562	0.06143	-0.5797	13907	0.5621	-0.2081	0.1368
fixed	NA	count_birth_order3/5	-0.03819	0.06306	-0.6057	13908	0.5448	-0.2152	0.1388
fixed	NA	count_birth_order4/5	-0.01414	0.0668	-0.2117	13910	0.8323	-0.2017	0.1734
fixed	NA	count_birth_order5/5	0.01126	0.06829	0.1649	13910	0.869	-0.1804	0.203
fixed	NA	count_birth_order1/>5	-0.08303	0.04717	-1.76	13908	0.07837	-0.2154	0.04937
fixed	NA	count_birth_order2/>5	-0.001421	0.04866	-0.02921	13910	0.9767	-0.138	0.1352
fixed	NA	count_birth_order3/>5	0.03321	0.04767	0.6967	13910	0.486	-0.1006	0.167
fixed	NA	count_birth_order4/>5	-0.02795	0.04671	-0.5984	13910	0.5496	-0.1591	0.1032
fixed	NA	count_birth_order5/>5	-0.03953	0.04706	-0.8398	13909	0.401	-0.1716	0.09258
fixed	NA	count_birth_order>5/>5	0.0126	0.03651	0.3452	12680	0.73	-0.08988	0.1151
ran_pars	mother_pidlink	sd__(Intercept)	0.2528	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9662	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)
11	39479	39562	-19728	39457	NA	NA	NA
12	39479	39569	-19727	39455	1.881	1	0.1702
16	39486	39607	-19727	39454	0.9485	4	0.9175
26	39492	39688	-19720	39440	13.71	10	0.1865

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)	-0.645	0.4388	-1.47	5911	0.1416	-1.877	0.5867
fixed	NA	poly(age, 3, raw = TRUE)1	0.03354	0.04978	0.6737	5914	0.5005	-0.1062	0.1733
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003367	0.001776	-0.1896	5915	0.8496	-0.005323	0.004649
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000005582	0.00002011	-0.02776	5914	0.9779	-0.00005701	0.00005589
fixed	NA	male	0.05795	0.02567	2.258	5886	0.024	-0.0141	0.13
fixed	NA	sibling_count3	-0.04282	0.03968	-1.079	4538	0.2805	-0.1542	0.06856
fixed	NA	sibling_count4	-0.05145	0.04258	-1.208	3962	0.227	-0.171	0.06806
fixed	NA	sibling_count5	0.007037	0.04843	0.1453	3482	0.8845	-0.1289	0.143
fixed	NA	sibling_count>5	-0.05468	0.04243	-1.288	3192	0.1977	-0.1738	0.06444
ran_pars	mother_pidlink	sd__(Intercept)	0.2632	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9527	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)	-0.6472	0.4389	-1.475	5910	0.1404	-1.879	0.5847
fixed	NA	birth_order	0.002615	0.00843	0.3102	5637	0.7564	-0.02105	0.02628
fixed	NA	poly(age, 3, raw = TRUE)1	0.03343	0.04979	0.6715	5913	0.5019	-0.1063	0.1732
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003375	0.001776	-0.19	5914	0.8493	-0.005324	0.004649
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000004477	0.00002011	-0.02226	5913	0.9822	-0.00005691	0.00005601
fixed	NA	male	0.05784	0.02567	2.253	5885	0.02429	-0.01422	0.1299
fixed	NA	sibling_count3	-0.04408	0.03989	-1.105	4540	0.2692	-0.1561	0.06789
fixed	NA	sibling_count4	-0.05442	0.04364	-1.247	3959	0.2125	-0.1769	0.06809
fixed	NA	sibling_count5	0.002162	0.05092	0.04246	3544	0.9661	-0.1408	0.1451
fixed	NA	sibling_count>5	-0.06446	0.05288	-1.219	3698	0.2229	-0.2129	0.08397
ran_pars	mother_pidlink	sd__(Intercept)	0.2632	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9528	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)	-0.6237	0.4395	-1.419	5907	0.1559	-1.857	0.6101
fixed	NA	poly(age, 3, raw = TRUE)1	0.03241	0.04982	0.6507	5909	0.5153	-0.1074	0.1722
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002935	0.001777	-0.1651	5910	0.8689	-0.005283	0.004696
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001054	0.00002013	-0.05235	5909	0.9583	-0.00005756	0.00005545
fixed	NA	male	0.05752	0.02568	2.24	5880	0.02512	-0.01455	0.1296
fixed	NA	sibling_count3	-0.03331	0.04077	-0.8171	4729	0.4139	-0.1477	0.08112
fixed	NA	sibling_count4	-0.05023	0.04547	-1.105	4313	0.2693	-0.1779	0.0774
fixed	NA	sibling_count5	-0.003593	0.05371	-0.06689	4020	0.9467	-0.1543	0.1472
fixed	NA	sibling_count>5	-0.05582	0.05457	-1.023	4005	0.3064	-0.209	0.09736
fixed	NA	birth_order_nonlinear2	-0.03669	0.03347	-1.096	5072	0.2731	-0.1306	0.05727
fixed	NA	birth_order_nonlinear3	-0.04412	0.04123	-1.07	5315	0.2846	-0.1599	0.07161
fixed	NA	birth_order_nonlinear4	0.02951	0.05091	0.5796	5468	0.5622	-0.1134	0.1724
fixed	NA	birth_order_nonlinear5	0.03323	0.06362	0.5224	5383	0.6014	-0.1453	0.2118
fixed	NA	birth_order_nonlinear>5	-0.03071	0.06333	-0.485	5903	0.6277	-0.2085	0.147
ran_pars	mother_pidlink	sd__(Intercept)	0.263	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9529	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)	-0.6322	0.4405	-1.435	5898	0.1513	-1.869	0.6043
fixed	NA	poly(age, 3, raw = TRUE)1	0.03344	0.04993	0.6699	5899	0.503	-0.1067	0.1736
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003295	0.001782	-0.1849	5900	0.8533	-0.005331	0.004672
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000006666	0.00002018	-0.03303	5899	0.9737	-0.00005732	0.00005598
fixed	NA	male	0.05848	0.0257	2.276	5870	0.02291	-0.01366	0.1306
fixed	NA	count_birth_order2/2	-0.03959	0.06047	-0.6547	5235	0.5127	-0.2093	0.1302
fixed	NA	count_birth_order1/3	-0.02909	0.05298	-0.5491	5890	0.5829	-0.1778	0.1196
fixed	NA	count_birth_order2/3	-0.05869	0.05791	-1.014	5898	0.3108	-0.2212	0.1038
fixed	NA	count_birth_order3/3	-0.1059	0.06475	-1.636	5900	0.102	-0.2877	0.07586
fixed	NA	count_birth_order1/4	-0.06212	0.06478	-0.9589	5893	0.3377	-0.244	0.1197
fixed	NA	count_birth_order2/4	-0.1076	0.06708	-1.603	5900	0.1089	-0.2959	0.08075
fixed	NA	count_birth_order3/4	-0.0601	0.07093	-0.8474	5898	0.3968	-0.2592	0.139
fixed	NA	count_birth_order4/4	-0.0189	0.07374	-0.2563	5897	0.7978	-0.2259	0.1881
fixed	NA	count_birth_order1/5	0.04298	0.08804	0.4882	5900	0.6255	-0.2042	0.2901
fixed	NA	count_birth_order2/5	-0.101	0.09431	-1.071	5895	0.2844	-0.3657	0.1638
fixed	NA	count_birth_order3/5	-0.02089	0.08841	-0.2363	5893	0.8132	-0.269	0.2273
fixed	NA	count_birth_order4/5	-0.05274	0.08515	-0.6193	5895	0.5357	-0.2918	0.1863
fixed	NA	count_birth_order5/5	0.08936	0.08862	1.008	5890	0.3134	-0.1594	0.3381
fixed	NA	count_birth_order1/>5	-0.1027	0.08735	-1.176	5900	0.2398	-0.3479	0.1425
fixed	NA	count_birth_order2/>5	-0.0403	0.08651	-0.4659	5900	0.6413	-0.2831	0.2025
fixed	NA	count_birth_order3/>5	-0.1274	0.08669	-1.47	5892	0.1417	-0.3707	0.1159
fixed	NA	count_birth_order4/>5	0.03782	0.08169	0.463	5889	0.6434	-0.1915	0.2671
fixed	NA	count_birth_order5/>5	-0.0659	0.0772	-0.8536	5888	0.3934	-0.2826	0.1508
fixed	NA	count_birth_order>5/>5	-0.08752	0.05776	-1.515	5299	0.1298	-0.2497	0.07461
ran_pars	mother_pidlink	sd__(Intercept)	0.2633	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9531	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)
11	16672	16745	-8325	16650	NA	NA	NA
12	16673	16754	-8325	16649	0.09659	1	0.756
16	16677	16784	-8323	16645	3.955	4	0.4121
26	16692	16866	-8320	16640	5.719	10	0.8383

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)	-0.6188	0.4369	-1.416	5962	0.1568	-1.845	0.6077
fixed	NA	poly(age, 3, raw = TRUE)1	0.03119	0.04959	0.629	5965	0.5294	-0.108	0.1704
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002451	0.00177	-0.1385	5966	0.8899	-0.005213	0.004723
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001585	0.00002004	-0.07908	5965	0.937	-0.00005784	0.00005467
fixed	NA	male	0.05768	0.02554	2.259	5937	0.02392	-0.014	0.1294
fixed	NA	sibling_count3	-0.05156	0.04288	-1.202	4705	0.2292	-0.1719	0.0688
fixed	NA	sibling_count4	-0.02386	0.04507	-0.5294	4273	0.5965	-0.1504	0.1026
fixed	NA	sibling_count5	-0.03461	0.04805	-0.7203	3794	0.4714	-0.1695	0.1003
fixed	NA	sibling_count>5	-0.0736	0.04215	-1.746	3867	0.08084	-0.1919	0.04471
ran_pars	mother_pidlink	sd__(Intercept)	0.2616	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.952	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)	-0.6268	0.437	-1.434	5961	0.1515	-1.853	0.5998
fixed	NA	birth_order	0.007124	0.007328	0.9722	5363	0.331	-0.01345	0.02769
fixed	NA	poly(age, 3, raw = TRUE)1	0.03115	0.04959	0.6282	5964	0.5299	-0.1081	0.1704
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002563	0.00177	-0.1448	5965	0.8849	-0.005224	0.004712
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001183	0.00002005	-0.05902	5964	0.9529	-0.00005745	0.00005508
fixed	NA	male	0.05745	0.02554	2.249	5936	0.02452	-0.01424	0.1291
fixed	NA	sibling_count3	-0.05498	0.04302	-1.278	4700	0.2013	-0.1757	0.06579
fixed	NA	sibling_count4	-0.03161	0.04577	-0.6907	4250	0.4898	-0.1601	0.09686
fixed	NA	sibling_count5	-0.04685	0.04967	-0.9433	3789	0.3456	-0.1863	0.09257
fixed	NA	sibling_count>5	-0.0996	0.04991	-1.995	4129	0.04606	-0.2397	0.04051
ran_pars	mother_pidlink	sd__(Intercept)	0.2614	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9521	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)	-0.6006	0.4376	-1.373	5959	0.1699	-1.829	0.6277
fixed	NA	poly(age, 3, raw = TRUE)1	0.03018	0.04962	0.6083	5960	0.543	-0.1091	0.1695
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002201	0.001771	-0.1243	5961	0.9011	-0.005192	0.004751
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001571	0.00002006	-0.07831	5960	0.9376	-0.00005789	0.00005474
fixed	NA	male	0.05734	0.02555	2.244	5932	0.02485	-0.01438	0.1291
fixed	NA	sibling_count3	-0.04586	0.04386	-1.046	4857	0.2958	-0.169	0.07725
fixed	NA	sibling_count4	-0.0244	0.04748	-0.5138	4553	0.6074	-0.1577	0.1089
fixed	NA	sibling_count5	-0.04551	0.05221	-0.8717	4217	0.3834	-0.1921	0.101
fixed	NA	sibling_count>5	-0.1009	0.05158	-1.957	4460	0.05039	-0.2457	0.04383
fixed	NA	birth_order_nonlinear2	-0.02657	0.03404	-0.7807	5209	0.435	-0.1221	0.06897
fixed	NA	birth_order_nonlinear3	-0.02837	0.04103	-0.6913	5442	0.4894	-0.1435	0.08681
fixed	NA	birth_order_nonlinear4	0.01991	0.04932	0.4036	5589	0.6865	-0.1185	0.1583
fixed	NA	birth_order_nonlinear5	0.04047	0.06051	0.6688	5572	0.5036	-0.1294	0.2103
fixed	NA	birth_order_nonlinear>5	0.04104	0.05641	0.7276	5905	0.4669	-0.1173	0.1994
ran_pars	mother_pidlink	sd__(Intercept)	0.2608	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9524	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)	-0.6018	0.4385	-1.372	5949	0.1701	-1.833	0.6293
fixed	NA	poly(age, 3, raw = TRUE)1	0.03204	0.04971	0.6445	5950	0.5193	-0.1075	0.1716
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002896	0.001775	-0.1632	5951	0.8704	-0.005271	0.004692
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000007273	0.0000201	-0.03618	5949	0.9711	-0.00005716	0.00005571
fixed	NA	male	0.05762	0.02557	2.253	5922	0.0243	-0.01417	0.1294
fixed	NA	count_birth_order2/2	-0.07001	0.0661	-1.059	5348	0.2896	-0.2556	0.1155
fixed	NA	count_birth_order1/3	-0.05588	0.05731	-0.9752	5941	0.3295	-0.2167	0.105
fixed	NA	count_birth_order2/3	-0.06772	0.06217	-1.089	5949	0.2761	-0.2422	0.1068
fixed	NA	count_birth_order3/3	-0.127	0.07	-1.814	5951	0.06968	-0.3235	0.06949
fixed	NA	count_birth_order1/4	-0.05227	0.06778	-0.7711	5945	0.4407	-0.2425	0.138
fixed	NA	count_birth_order2/4	-0.04976	0.06909	-0.7201	5950	0.4715	-0.2437	0.1442
fixed	NA	count_birth_order3/4	-0.07543	0.07588	-0.9941	5949	0.3202	-0.2884	0.1376
fixed	NA	count_birth_order4/4	-0.01413	0.07823	-0.1806	5949	0.8567	-0.2337	0.2055
fixed	NA	count_birth_order1/5	-0.03582	0.08047	-0.4451	5950	0.6562	-0.2617	0.1901
fixed	NA	count_birth_order2/5	-0.1593	0.08648	-1.842	5949	0.06554	-0.402	0.08347
fixed	NA	count_birth_order3/5	-0.03115	0.08411	-0.3704	5948	0.7111	-0.2673	0.205
fixed	NA	count_birth_order4/5	-0.06292	0.0872	-0.7215	5943	0.4706	-0.3077	0.1819
fixed	NA	count_birth_order5/5	-0.0179	0.08745	-0.2047	5941	0.8378	-0.2634	0.2276
fixed	NA	count_birth_order1/>5	-0.1703	0.07649	-2.227	5948	0.02598	-0.385	0.04436
fixed	NA	count_birth_order2/>5	-0.1037	0.07995	-1.297	5951	0.1948	-0.3281	0.1208
fixed	NA	count_birth_order3/>5	-0.1335	0.07845	-1.701	5947	0.08891	-0.3537	0.08674
fixed	NA	count_birth_order4/>5	-0.08556	0.07552	-1.133	5945	0.2573	-0.2975	0.1264
fixed	NA	count_birth_order5/>5	-0.07678	0.07763	-0.989	5935	0.3227	-0.2947	0.1411
fixed	NA	count_birth_order>5/>5	-0.07471	0.05656	-1.321	5447	0.1866	-0.2335	0.08405
ran_pars	mother_pidlink	sd__(Intercept)	0.2602	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9531	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)
11	16802	16876	-8390	16780	NA	NA	NA
12	16803	16884	-8390	16779	0.9475	1	0.3304
16	16810	16917	-8389	16778	1.889	4	0.7562
26	16825	17000	-8387	16773	4.132	10	0.9412

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)	-0.5969	0.4431	-1.347	5793	0.178	-1.841	0.647
fixed	NA	poly(age, 3, raw = TRUE)1	0.02716	0.0503	0.5399	5795	0.5893	-0.114	0.1683
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00008155	0.001795	-0.04543	5796	0.9638	-0.00512	0.004957
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003671	0.00002033	-0.1805	5794	0.8567	-0.00006075	0.00005341
fixed	NA	male	0.0572	0.02589	2.21	5769	0.02718	-0.01547	0.1299
fixed	NA	sibling_count3	-0.04753	0.03907	-1.217	4416	0.2238	-0.1572	0.06213
fixed	NA	sibling_count4	-0.06009	0.04218	-1.425	3862	0.1544	-0.1785	0.05832
fixed	NA	sibling_count5	0.04759	0.04945	0.9624	3265	0.3359	-0.09122	0.1864
fixed	NA	sibling_count>5	-0.0633	0.04274	-1.481	2989	0.1387	-0.1833	0.05668
ran_pars	mother_pidlink	sd__(Intercept)	0.2586	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9519	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)	-0.5982	0.4432	-1.35	5792	0.1771	-1.842	0.6459
fixed	NA	birth_order	0.001925	0.008673	0.222	5563	0.8243	-0.02242	0.02627
fixed	NA	poly(age, 3, raw = TRUE)1	0.02705	0.0503	0.5377	5794	0.5908	-0.1142	0.1682
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00008128	0.001795	-0.04528	5795	0.9639	-0.00512	0.004958
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003598	0.00002034	-0.1769	5793	0.8596	-0.00006069	0.00005349
fixed	NA	male	0.05715	0.02589	2.207	5768	0.02732	-0.01552	0.1298
fixed	NA	sibling_count3	-0.04846	0.03929	-1.233	4416	0.2176	-0.1588	0.06184
fixed	NA	sibling_count4	-0.06225	0.04329	-1.438	3871	0.1505	-0.1838	0.05927
fixed	NA	sibling_count5	0.04417	0.05181	0.8525	3330	0.394	-0.1013	0.1896
fixed	NA	sibling_count>5	-0.07045	0.05352	-1.316	3599	0.1881	-0.2207	0.07977
ran_pars	mother_pidlink	sd__(Intercept)	0.2587	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9519	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)	-0.5775	0.4438	-1.301	5789	0.1932	-1.823	0.6683
fixed	NA	poly(age, 3, raw = TRUE)1	0.02592	0.05033	0.515	5791	0.6066	-0.1154	0.1672
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00003914	0.001796	-0.02179	5791	0.9826	-0.005081	0.005003
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004064	0.00002035	-0.1997	5789	0.8417	-0.0000612	0.00005307
fixed	NA	male	0.0566	0.0259	2.186	5763	0.02888	-0.01609	0.1293
fixed	NA	sibling_count3	-0.03684	0.0402	-0.9166	4608	0.3594	-0.1497	0.076
fixed	NA	sibling_count4	-0.05666	0.04517	-1.254	4225	0.2098	-0.1835	0.07015
fixed	NA	sibling_count5	0.04475	0.0544	0.8225	3754	0.4108	-0.108	0.1975
fixed	NA	sibling_count>5	-0.06844	0.05532	-1.237	3922	0.2161	-0.2237	0.08684
fixed	NA	birth_order_nonlinear2	-0.02562	0.03336	-0.768	4955	0.4425	-0.1193	0.06802
fixed	NA	birth_order_nonlinear3	-0.04947	0.0412	-1.201	5175	0.2299	-0.1651	0.06617
fixed	NA	birth_order_nonlinear4	0.0286	0.05233	0.5465	5341	0.5847	-0.1183	0.1755
fixed	NA	birth_order_nonlinear5	0.007749	0.06629	0.1169	5277	0.9069	-0.1783	0.1938
fixed	NA	birth_order_nonlinear>5	-0.00116	0.06527	-0.01777	5789	0.9858	-0.1844	0.1821
ran_pars	mother_pidlink	sd__(Intercept)	0.2588	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.952	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)	-0.5521	0.4449	-1.241	5780	0.2147	-1.801	0.6967
fixed	NA	poly(age, 3, raw = TRUE)1	0.02312	0.05045	0.4584	5781	0.6467	-0.1185	0.1647
fixed	NA	poly(age, 3, raw = TRUE)2	0.00006625	0.001801	0.03679	5781	0.9707	-0.004988	0.005121
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000005314	0.00002041	-0.2604	5779	0.7945	-0.0000626	0.00005197
fixed	NA	male	0.05695	0.02592	2.197	5752	0.02805	-0.01581	0.1297
fixed	NA	count_birth_order2/2	-0.03262	0.05883	-0.5544	5086	0.5793	-0.1978	0.1325
fixed	NA	count_birth_order1/3	-0.03163	0.05223	-0.6057	5770	0.5448	-0.1782	0.115
fixed	NA	count_birth_order2/3	-0.05113	0.05778	-0.885	5780	0.3762	-0.2133	0.111
fixed	NA	count_birth_order3/3	-0.1218	0.0635	-1.918	5780	0.05516	-0.3	0.05645
fixed	NA	count_birth_order1/4	-0.07897	0.06499	-1.215	5777	0.2244	-0.2614	0.1035
fixed	NA	count_birth_order2/4	-0.1058	0.06687	-1.583	5781	0.1135	-0.2935	0.08185
fixed	NA	count_birth_order3/4	-0.07093	0.07008	-1.012	5777	0.3115	-0.2676	0.1258
fixed	NA	count_birth_order4/4	-0.01687	0.07408	-0.2277	5775	0.8199	-0.2248	0.1911
fixed	NA	count_birth_order1/5	0.05054	0.08768	0.5764	5781	0.5644	-0.1956	0.2967
fixed	NA	count_birth_order2/5	-0.01504	0.09697	-0.1551	5776	0.8767	-0.2872	0.2572
fixed	NA	count_birth_order3/5	-0.0003237	0.09252	-0.003499	5773	0.9972	-0.26	0.2594
fixed	NA	count_birth_order4/5	-0.02	0.08914	-0.2244	5775	0.8225	-0.2702	0.2302
fixed	NA	count_birth_order5/5	0.1681	0.09472	1.774	5771	0.07608	-0.09783	0.4339
fixed	NA	count_birth_order1/>5	-0.0804	0.08927	-0.9006	5781	0.3679	-0.331	0.1702
fixed	NA	count_birth_order2/>5	-0.05915	0.08855	-0.668	5780	0.5042	-0.3077	0.1894
fixed	NA	count_birth_order3/>5	-0.1176	0.08777	-1.34	5772	0.1802	-0.364	0.1287
fixed	NA	count_birth_order4/>5	0.02036	0.08587	0.2372	5765	0.8125	-0.2207	0.2614
fixed	NA	count_birth_order5/>5	-0.1374	0.07891	-1.741	5767	0.08173	-0.3589	0.08412
fixed	NA	count_birth_order>5/>5	-0.07222	0.05867	-1.231	5114	0.2184	-0.2369	0.09246
ran_pars	mother_pidlink	sd__(Intercept)	0.2592	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9522	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)
11	16314	16387	-8146	16292	NA	NA	NA
12	16316	16396	-8146	16292	0.0492	1	0.8245
16	16321	16428	-8144	16289	2.826	4	0.5874
26	16334	16508	-8141	16282	6.65	10	0.758

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)	0.4167	0.1589	2.623	13709	0.008727	-0.02924	0.8626
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03942	0.01522	-2.59	13601	0.009601	-0.08214	0.003299
fixed	NA	poly(age, 3, raw = TRUE)2	0.001142	0.0004473	2.552	13428	0.01072	-0.000114	0.002397
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001113	0.000004115	-2.705	13257	0.006832	-0.00002269	0.0000004185
fixed	NA	male	0.1705	0.01678	10.16	13815	3.517e-24	0.1234	0.2177
fixed	NA	sibling_count3	-0.0164	0.03344	-0.4905	10579	0.6238	-0.1103	0.07746
fixed	NA	sibling_count4	-0.04541	0.03438	-1.321	9628	0.1866	-0.1419	0.05109
fixed	NA	sibling_count5	-0.004679	0.03564	-0.1313	8559	0.8956	-0.1047	0.09537
fixed	NA	sibling_count>5	-0.07108	0.02806	-2.533	9722	0.01132	-0.1498	0.007688
ran_pars	mother_pidlink	sd__(Intercept)	0.2818	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9529	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)	0.4136	0.1588	2.604	13710	0.009231	-0.03229	0.8595
fixed	NA	birth_order	-0.006737	0.003501	-1.924	11701	0.05434	-0.01657	0.003091
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03742	0.01525	-2.453	13584	0.01416	-0.08023	0.005394
fixed	NA	poly(age, 3, raw = TRUE)2	0.001071	0.0004488	2.386	13368	0.01707	-0.0001891	0.00233
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001049	0.000004129	-2.54	13175	0.0111	-0.00002208	0.000001103
fixed	NA	male	0.1707	0.01678	10.18	13814	3.116e-24	0.1236	0.2178
fixed	NA	sibling_count3	-0.01476	0.03344	-0.4413	10591	0.659	-0.1086	0.07912
fixed	NA	sibling_count4	-0.04063	0.03446	-1.179	9685	0.2384	-0.1374	0.0561
fixed	NA	sibling_count5	0.003553	0.03589	0.099	8660	0.9211	-0.0972	0.1043
fixed	NA	sibling_count>5	-0.04537	0.03107	-1.46	10694	0.1443	-0.1326	0.04186
ran_pars	mother_pidlink	sd__(Intercept)	0.2814	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9529	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)	0.4067	0.1593	2.554	13713	0.01067	-0.04038	0.8538
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03765	0.01526	-2.467	13594	0.01362	-0.08047	0.005181
fixed	NA	poly(age, 3, raw = TRUE)2	0.001092	0.0004489	2.432	13379	0.01501	-0.0001681	0.002352
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001079	0.00000413	-2.613	13175	0.008993	-0.00002238	0.0000008026
fixed	NA	male	0.1708	0.01678	10.18	13810	3.101e-24	0.1237	0.2179
fixed	NA	sibling_count3	-0.004799	0.03395	-0.1414	10928	0.8876	-0.1001	0.09049
fixed	NA	sibling_count4	-0.02479	0.0355	-0.6983	10404	0.485	-0.1245	0.07487
fixed	NA	sibling_count5	0.01456	0.03739	0.3894	9631	0.697	-0.09039	0.1195
fixed	NA	sibling_count>5	-0.04095	0.03276	-1.25	11805	0.2113	-0.1329	0.051
fixed	NA	birth_order_nonlinear2	-0.01379	0.02447	-0.5636	12763	0.5731	-0.08249	0.0549
fixed	NA	birth_order_nonlinear3	-0.0592	0.02888	-2.049	12620	0.04044	-0.1403	0.02188
fixed	NA	birth_order_nonlinear4	-0.05691	0.0329	-1.73	12710	0.08366	-0.1493	0.03543
fixed	NA	birth_order_nonlinear5	-0.007878	0.03741	-0.2106	12776	0.8332	-0.1129	0.09714
fixed	NA	birth_order_nonlinear>5	-0.04945	0.03085	-1.603	13920	0.109	-0.136	0.03715
ran_pars	mother_pidlink	sd__(Intercept)	0.2817	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9528	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)	0.4334	0.16	2.709	13713	0.006754	-0.01566	0.8824
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03779	0.01526	-2.477	13585	0.01327	-0.08063	0.00504
fixed	NA	poly(age, 3, raw = TRUE)2	0.001099	0.0004489	2.448	13365	0.01439	-0.0001613	0.002359
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001087	0.000004131	-2.633	13155	0.008485	-0.00002247	0.0000007208
fixed	NA	male	0.1706	0.01678	10.16	13800	3.581e-24	0.1234	0.2177
fixed	NA	count_birth_order2/2	-0.08334	0.04757	-1.752	12613	0.0798	-0.2169	0.05019
fixed	NA	count_birth_order1/3	-0.0571	0.04482	-1.274	13832	0.2027	-0.1829	0.06871
fixed	NA	count_birth_order2/3	-0.02348	0.05011	-0.4685	13867	0.6394	-0.1641	0.1172
fixed	NA	count_birth_order3/3	-0.0652	0.05612	-1.162	13895	0.2454	-0.2227	0.09234
fixed	NA	count_birth_order1/4	-0.07077	0.05117	-1.383	13871	0.1667	-0.2144	0.07288
fixed	NA	count_birth_order2/4	-0.009176	0.05382	-0.1705	13881	0.8646	-0.1602	0.1419
fixed	NA	count_birth_order3/4	-0.1791	0.05847	-3.062	13898	0.002201	-0.3432	-0.01492
fixed	NA	count_birth_order4/4	-0.07479	0.0619	-1.208	13906	0.227	-0.2485	0.09897
fixed	NA	count_birth_order1/5	0.0005729	0.05806	0.009867	13896	0.9921	-0.1624	0.1636
fixed	NA	count_birth_order2/5	-0.06346	0.06107	-1.039	13905	0.2988	-0.2349	0.108
fixed	NA	count_birth_order3/5	-0.07172	0.06269	-1.144	13908	0.2526	-0.2477	0.1042
fixed	NA	count_birth_order4/5	-0.02146	0.0664	-0.3232	13910	0.7465	-0.2079	0.1649
fixed	NA	count_birth_order5/5	-0.03514	0.06788	-0.5177	13910	0.6046	-0.2257	0.1554
fixed	NA	count_birth_order1/>5	-0.06634	0.04689	-1.415	13909	0.1571	-0.198	0.06527
fixed	NA	count_birth_order2/>5	-0.07713	0.04836	-1.595	13910	0.1108	-0.2129	0.05863
fixed	NA	count_birth_order3/>5	-0.1038	0.04738	-2.19	13910	0.02853	-0.2368	0.02923
fixed	NA	count_birth_order4/>5	-0.1541	0.04643	-3.319	13910	0.0009054	-0.2845	-0.02378
fixed	NA	count_birth_order5/>5	-0.06927	0.04678	-1.481	13909	0.1387	-0.2006	0.06204
fixed	NA	count_birth_order>5/>5	-0.1164	0.0364	-3.198	12676	0.001387	-0.2186	-0.01423
ran_pars	mother_pidlink	sd__(Intercept)	0.2812	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.953	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)
11	39311	39394	-19645	39289	NA	NA	NA
12	39310	39400	-19643	39286	3.706	1	0.05421
16	39315	39435	-19641	39283	3.124	4	0.5373
26	39324	39521	-19636	39272	10.07	10	0.4341

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)	-0.833	0.4144	-2.01	5898	0.04449	-1.996	0.3304
fixed	NA	poly(age, 3, raw = TRUE)1	0.1105	0.04703	2.349	5903	0.01885	-0.02153	0.2425
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004051	0.001678	-2.414	5908	0.01581	-0.008761	0.0006597
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004751	0.000019	2.5	5911	0.01245	-0.000005835	0.0001008
fixed	NA	male	0.1386	0.02423	5.719	5858	0.00000001124	0.07055	0.2066
fixed	NA	sibling_count3	-0.09714	0.03779	-2.571	4467	0.01018	-0.2032	0.008928
fixed	NA	sibling_count4	-0.08943	0.04063	-2.201	3920	0.02778	-0.2035	0.02462
fixed	NA	sibling_count5	-0.1136	0.04629	-2.453	3478	0.01421	-0.2435	0.01638
fixed	NA	sibling_count>5	-0.1441	0.04061	-3.548	3230	0.0003942	-0.2581	-0.03008
ran_pars	mother_pidlink	sd__(Intercept)	0.2961	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8871	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)	-0.8361	0.4145	-2.017	5897	0.04374	-2	0.3275
fixed	NA	birth_order	0.003801	0.007987	0.4758	5757	0.6342	-0.01862	0.02622
fixed	NA	poly(age, 3, raw = TRUE)1	0.1103	0.04703	2.345	5902	0.01904	-0.02171	0.2423
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004051	0.001678	-2.414	5907	0.01581	-0.008762	0.0006597
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004766	0.00001901	2.507	5910	0.01219	-0.000005693	0.000101
fixed	NA	male	0.1384	0.02423	5.711	5858	0.00000001176	0.07038	0.2064
fixed	NA	sibling_count3	-0.09898	0.03799	-2.606	4471	0.009196	-0.2056	0.007644
fixed	NA	sibling_count4	-0.09377	0.04164	-2.252	3925	0.02438	-0.2107	0.02312
fixed	NA	sibling_count5	-0.1207	0.04866	-2.481	3554	0.01317	-0.2573	0.01589
fixed	NA	sibling_count>5	-0.1583	0.0505	-3.136	3749	0.001727	-0.3001	-0.0166
ran_pars	mother_pidlink	sd__(Intercept)	0.296	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8872	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)	-0.8633	0.4151	-2.08	5897	0.03758	-2.028	0.3018
fixed	NA	poly(age, 3, raw = TRUE)1	0.113	0.04705	2.402	5900	0.01634	-0.01906	0.2451
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00414	0.001679	-2.466	5904	0.01369	-0.008853	0.0005725
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000485	0.00001902	2.55	5907	0.01079	-0.000004881	0.0001019
fixed	NA	male	0.1388	0.02423	5.727	5852	0.00000001074	0.07074	0.2068
fixed	NA	sibling_count3	-0.0928	0.03879	-2.392	4656	0.01677	-0.2017	0.01608
fixed	NA	sibling_count4	-0.09456	0.04332	-2.183	4267	0.02912	-0.2162	0.02706
fixed	NA	sibling_count5	-0.1389	0.05122	-2.712	4011	0.006717	-0.2827	0.00487
fixed	NA	sibling_count>5	-0.146	0.05205	-2.806	4036	0.005043	-0.2921	0.00006495
fixed	NA	birth_order_nonlinear2	0.02394	0.03144	0.7614	5006	0.4465	-0.06432	0.1122
fixed	NA	birth_order_nonlinear3	-0.01775	0.03877	-0.4578	5241	0.6471	-0.1266	0.09107
fixed	NA	birth_order_nonlinear4	0.05292	0.0479	1.105	5396	0.2693	-0.08154	0.1874
fixed	NA	birth_order_nonlinear5	0.106	0.05983	1.771	5286	0.07654	-0.06196	0.274
fixed	NA	birth_order_nonlinear>5	-0.03825	0.05984	-0.6391	5909	0.5228	-0.2062	0.1297
ran_pars	mother_pidlink	sd__(Intercept)	0.2962	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8869	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)	-0.8675	0.416	-2.085	5888	0.03708	-2.035	0.3002
fixed	NA	poly(age, 3, raw = TRUE)1	0.1149	0.04715	2.436	5890	0.01486	-0.01747	0.2472
fixed	NA	poly(age, 3, raw = TRUE)2	-0.004197	0.001683	-2.494	5894	0.01267	-0.00892	0.0005273
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004901	0.00001906	2.571	5897	0.01018	-0.000004509	0.0001025
fixed	NA	male	0.1395	0.02425	5.752	5842	0.000000009252	0.07142	0.2076
fixed	NA	count_birth_order2/2	-0.01995	0.05685	-0.351	5213	0.7256	-0.1795	0.1396
fixed	NA	count_birth_order1/3	-0.137	0.05008	-2.736	5880	0.00623	-0.2776	0.003537
fixed	NA	count_birth_order2/3	-0.07656	0.05472	-1.399	5896	0.1619	-0.2302	0.07705
fixed	NA	count_birth_order3/3	-0.0773	0.06117	-1.264	5900	0.2064	-0.249	0.09441
fixed	NA	count_birth_order1/4	-0.07394	0.06123	-1.208	5891	0.2273	-0.2458	0.09794
fixed	NA	count_birth_order2/4	-0.1317	0.06338	-2.078	5900	0.03775	-0.3096	0.04621
fixed	NA	count_birth_order3/4	-0.1464	0.06698	-2.186	5897	0.02884	-0.3345	0.04158
fixed	NA	count_birth_order4/4	-0.02691	0.06964	-0.3864	5895	0.6992	-0.2224	0.1686
fixed	NA	count_birth_order1/5	-0.1685	0.08317	-2.026	5900	0.0428	-0.402	0.06496
fixed	NA	count_birth_order2/5	-0.05147	0.08905	-0.578	5889	0.5633	-0.3014	0.1985
fixed	NA	count_birth_order3/5	-0.2027	0.08347	-2.428	5888	0.01521	-0.437	0.03163
fixed	NA	count_birth_order4/5	-0.1164	0.08041	-1.448	5892	0.1476	-0.3422	0.1093
fixed	NA	count_birth_order5/5	-0.05156	0.08367	-0.6162	5884	0.5378	-0.2864	0.1833
fixed	NA	count_birth_order1/>5	-0.1743	0.08252	-2.112	5899	0.03475	-0.4059	0.05737
fixed	NA	count_birth_order2/>5	-0.06251	0.0817	-0.7651	5894	0.4442	-0.2919	0.1668
fixed	NA	count_birth_order3/>5	-0.2153	0.08185	-2.631	5879	0.008545	-0.4451	0.01444
fixed	NA	count_birth_order4/>5	-0.1316	0.07712	-1.707	5875	0.08787	-0.3481	0.08483
fixed	NA	count_birth_order5/>5	-0.0526	0.07288	-0.7217	5876	0.4705	-0.2572	0.152
fixed	NA	count_birth_order>5/>5	-0.1993	0.05481	-3.636	5364	0.0002797	-0.3531	-0.04543
ran_pars	mother_pidlink	sd__(Intercept)	0.2959	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8872	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)
11	16002	16076	-7990	15980	NA	NA	NA
12	16004	16084	-7990	15980	0.2274	1	0.6335
16	16005	16112	-7986	15973	7.314	4	0.1202
26	16018	16192	-7983	15966	6.635	10	0.7594

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)	-0.7636	0.4132	-1.848	5950	0.06468	-1.924	0.3964
fixed	NA	poly(age, 3, raw = TRUE)1	0.1043	0.04691	2.224	5954	0.02621	-0.02736	0.236
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003837	0.001674	-2.292	5959	0.02196	-0.008537	0.0008629
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004507	0.00001896	2.376	5962	0.01751	-0.000008165	0.0000983
fixed	NA	male	0.1403	0.02414	5.814	5908	0.000000006409	0.07258	0.2081
fixed	NA	sibling_count3	-0.1248	0.04088	-3.052	4624	0.002283	-0.2395	-0.01003
fixed	NA	sibling_count4	-0.1013	0.04303	-2.354	4207	0.01864	-0.2221	0.01951
fixed	NA	sibling_count5	-0.1191	0.04596	-2.592	3760	0.009571	-0.2481	0.00987
fixed	NA	sibling_count>5	-0.134	0.0403	-3.325	3858	0.0008931	-0.2471	-0.02087
ran_pars	mother_pidlink	sd__(Intercept)	0.2966	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8872	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)	-0.7645	0.4133	-1.85	5949	0.06442	-1.925	0.3957
fixed	NA	birth_order	0.0008314	0.006965	0.1194	5559	0.905	-0.01872	0.02038
fixed	NA	poly(age, 3, raw = TRUE)1	0.1043	0.04691	2.223	5953	0.02623	-0.02738	0.236
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003838	0.001674	-2.292	5957	0.02193	-0.008539	0.0008622
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004511	0.00001897	2.378	5961	0.01743	-0.000008134	0.00009836
fixed	NA	male	0.1403	0.02414	5.812	5907	0.000000006484	0.07255	0.2081
fixed	NA	sibling_count3	-0.1252	0.04102	-3.052	4621	0.002288	-0.2403	-0.01004
fixed	NA	sibling_count4	-0.1022	0.04371	-2.338	4193	0.01943	-0.2249	0.0205
fixed	NA	sibling_count5	-0.1206	0.04751	-2.538	3769	0.0112	-0.2539	0.0128
fixed	NA	sibling_count>5	-0.137	0.04768	-2.874	4144	0.004076	-0.2709	-0.003186
ran_pars	mother_pidlink	sd__(Intercept)	0.2967	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8873	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)	-0.7658	0.4139	-1.85	5949	0.06431	-1.928	0.3959
fixed	NA	poly(age, 3, raw = TRUE)1	0.1043	0.04693	2.221	5951	0.02636	-0.02749	0.236
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00383	0.001675	-2.286	5955	0.02228	-0.008533	0.0008726
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000449	0.00001898	2.366	5958	0.01803	-0.00000838	0.00009818
fixed	NA	male	0.1403	0.02414	5.81	5902	0.000000006563	0.07251	0.2081
fixed	NA	sibling_count3	-0.1194	0.04179	-2.857	4777	0.00429	-0.2367	-0.002104
fixed	NA	sibling_count4	-0.1057	0.04529	-2.333	4488	0.0197	-0.2328	0.02148
fixed	NA	sibling_count5	-0.1304	0.04986	-2.614	4182	0.008972	-0.2703	0.009608
fixed	NA	sibling_count>5	-0.126	0.04921	-2.561	4450	0.01046	-0.2642	0.0121
fixed	NA	birth_order_nonlinear2	0.006196	0.03202	0.1935	5140	0.8466	-0.0837	0.09609
fixed	NA	birth_order_nonlinear3	-0.02327	0.03865	-0.6022	5366	0.547	-0.1318	0.08521
fixed	NA	birth_order_nonlinear4	0.05037	0.04648	1.084	5519	0.2785	-0.08011	0.1809
fixed	NA	birth_order_nonlinear5	0.04243	0.05703	0.744	5482	0.4569	-0.1176	0.2025
fixed	NA	birth_order_nonlinear>5	-0.04304	0.05343	-0.8055	5943	0.4206	-0.193	0.1069
ran_pars	mother_pidlink	sd__(Intercept)	0.2968	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8872	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)	-0.7433	0.4145	-1.793	5939	0.073	-1.907	0.4203
fixed	NA	poly(age, 3, raw = TRUE)1	0.1031	0.04699	2.194	5941	0.02827	-0.02881	0.235
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003777	0.001678	-2.251	5944	0.02442	-0.008487	0.0009329
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004418	0.00001901	2.324	5948	0.02016	-0.000009185	0.00009755
fixed	NA	male	0.1401	0.02415	5.801	5891	0.000000006922	0.07232	0.2079
fixed	NA	count_birth_order2/2	-0.03849	0.0622	-0.6188	5328	0.5361	-0.2131	0.1361
fixed	NA	count_birth_order1/3	-0.1582	0.05423	-2.917	5931	0.003545	-0.3104	-0.005976
fixed	NA	count_birth_order2/3	-0.1277	0.05882	-2.171	5946	0.03	-0.2928	0.03743
fixed	NA	count_birth_order3/3	-0.1121	0.0662	-1.693	5951	0.09043	-0.2979	0.07372
fixed	NA	count_birth_order1/4	-0.1371	0.06414	-2.138	5942	0.03256	-0.3172	0.04291
fixed	NA	count_birth_order2/4	-0.1088	0.06536	-1.665	5950	0.09598	-0.2923	0.07464
fixed	NA	count_birth_order3/4	-0.2025	0.07174	-2.823	5948	0.004773	-0.4039	-0.001148
fixed	NA	count_birth_order4/4	0.008894	0.07396	0.1203	5948	0.9043	-0.1987	0.2165
fixed	NA	count_birth_order1/5	-0.1709	0.07612	-2.245	5950	0.0248	-0.3846	0.04277
fixed	NA	count_birth_order2/5	-0.161	0.08176	-1.969	5947	0.04903	-0.3904	0.06854
fixed	NA	count_birth_order3/5	-0.1594	0.07951	-2.004	5944	0.04509	-0.3826	0.06383
fixed	NA	count_birth_order4/5	-0.03537	0.08242	-0.4291	5936	0.6679	-0.2667	0.196
fixed	NA	count_birth_order5/5	-0.1204	0.08264	-1.457	5935	0.1453	-0.3524	0.1116
fixed	NA	count_birth_order1/>5	-0.084	0.07236	-1.161	5950	0.2457	-0.2871	0.1191
fixed	NA	count_birth_order2/>5	-0.08335	0.0756	-1.103	5947	0.2703	-0.2955	0.1289
fixed	NA	count_birth_order3/>5	-0.17	0.07416	-2.293	5939	0.02188	-0.3782	0.03811
fixed	NA	count_birth_order4/>5	-0.201	0.07138	-2.816	5937	0.004873	-0.4014	-0.0006655
fixed	NA	count_birth_order5/>5	-0.08702	0.07335	-1.186	5920	0.2355	-0.2929	0.1189
fixed	NA	count_birth_order>5/>5	-0.1847	0.05372	-3.439	5495	0.0005887	-0.3355	-0.03394
ran_pars	mother_pidlink	sd__(Intercept)	0.2977	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8869	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)
11	16143	16217	-8061	16121	NA	NA	NA
12	16145	16225	-8061	16121	0.01427	1	0.9049
16	16149	16256	-8058	16117	4.361	4	0.3594
26	16158	16332	-8053	16106	10.45	10	0.4015

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)	-0.7587	0.4191	-1.81	5780	0.07031	-1.935	0.4178
fixed	NA	poly(age, 3, raw = TRUE)1	0.1017	0.04758	2.138	5785	0.03258	-0.03184	0.2353
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003723	0.001698	-2.192	5789	0.02841	-0.00849	0.001044
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004357	0.00001924	2.264	5793	0.0236	-0.00001044	0.00009758
fixed	NA	male	0.1344	0.02447	5.493	5740	0.00000004125	0.06571	0.2031
fixed	NA	sibling_count3	-0.1099	0.03728	-2.949	4351	0.003205	-0.2146	-0.005294
fixed	NA	sibling_count4	-0.09092	0.04034	-2.254	3830	0.02428	-0.2042	0.02233
fixed	NA	sibling_count5	-0.09754	0.04741	-2.057	3285	0.03975	-0.2306	0.03555
fixed	NA	sibling_count>5	-0.1308	0.04103	-3.188	3049	0.001449	-0.246	-0.01561
ran_pars	mother_pidlink	sd__(Intercept)	0.2968	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8863	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)	-0.7619	0.4192	-1.818	5779	0.06917	-1.938	0.4147
fixed	NA	birth_order	0.004791	0.008228	0.5822	5679	0.5604	-0.01831	0.02789
fixed	NA	poly(age, 3, raw = TRUE)1	0.1014	0.04758	2.131	5784	0.03309	-0.03214	0.235
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003721	0.001698	-2.191	5788	0.02848	-0.008488	0.001046
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004374	0.00001924	2.273	5792	0.02307	-0.00001028	0.00009776
fixed	NA	male	0.1343	0.02447	5.487	5739	0.00000004254	0.06559	0.203
fixed	NA	sibling_count3	-0.1123	0.0375	-2.994	4354	0.002767	-0.2175	-0.007017
fixed	NA	sibling_count4	-0.09632	0.0414	-2.327	3848	0.02004	-0.2125	0.01989
fixed	NA	sibling_count5	-0.1061	0.04965	-2.137	3361	0.03265	-0.2455	0.03326
fixed	NA	sibling_count>5	-0.1486	0.05122	-2.902	3668	0.003734	-0.2924	-0.004849
ran_pars	mother_pidlink	sd__(Intercept)	0.2968	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8863	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)	-0.7727	0.4197	-1.841	5780	0.06568	-1.951	0.4055
fixed	NA	poly(age, 3, raw = TRUE)1	0.1028	0.0476	2.16	5782	0.0308	-0.03079	0.2364
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003761	0.001699	-2.214	5785	0.02689	-0.008531	0.001008
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004398	0.00001926	2.284	5788	0.02242	-0.00001007	0.00009803
fixed	NA	male	0.1339	0.02447	5.473	5734	0.00000004602	0.06525	0.2026
fixed	NA	sibling_count3	-0.1077	0.03832	-2.811	4541	0.004962	-0.2153	-0.000148
fixed	NA	sibling_count4	-0.1011	0.04312	-2.345	4186	0.01908	-0.2222	0.01993
fixed	NA	sibling_count5	-0.1219	0.05202	-2.344	3762	0.01913	-0.268	0.02409
fixed	NA	sibling_count>5	-0.1329	0.05286	-2.514	3966	0.01199	-0.2813	0.01551
fixed	NA	birth_order_nonlinear2	0.01259	0.03137	0.4012	4886	0.6883	-0.07547	0.1006
fixed	NA	birth_order_nonlinear3	-0.007885	0.03878	-0.2033	5100	0.8389	-0.1167	0.101
fixed	NA	birth_order_nonlinear4	0.06473	0.0493	1.313	5262	0.1892	-0.07364	0.2031
fixed	NA	birth_order_nonlinear5	0.07644	0.06242	1.225	5174	0.2208	-0.09878	0.2517
fixed	NA	birth_order_nonlinear>5	-0.03802	0.06175	-0.6156	5785	0.5382	-0.2114	0.1353
ran_pars	mother_pidlink	sd__(Intercept)	0.2956	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.8866	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)	-0.7574	0.4207	-1.8	5771	0.07189	-1.938	0.4236
fixed	NA	poly(age, 3, raw = TRUE)1	0.1027	0.04771	2.152	5772	0.0314	-0.03123	0.2366
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003749	0.001703	-2.201	5776	0.02778	-0.008531	0.001032
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004374	0.00001931	2.266	5779	0.02352	-0.00001046	0.00009794
fixed	NA	male	0.1337	0.02449	5.46	5723	0.00000004957	0.06499	0.2025
fixed	NA	count_birth_order2/2	-0.03314	0.05536	-0.5986	5061	0.5495	-0.1886	0.1223
fixed	NA	count_birth_order1/3	-0.1392	0.04945	-2.815	5760	0.004896	-0.278	-0.0003884
fixed	NA	count_birth_order2/3	-0.1234	0.05468	-2.257	5779	0.02403	-0.2769	0.03006
fixed	NA	count_birth_order3/3	-0.08378	0.06007	-1.395	5780	0.1632	-0.2524	0.08484
fixed	NA	count_birth_order1/4	-0.1067	0.06151	-1.735	5775	0.08283	-0.2794	0.06596
fixed	NA	count_birth_order2/4	-0.1168	0.06327	-1.846	5781	0.065	-0.2944	0.06083
fixed	NA	count_birth_order3/4	-0.1429	0.06628	-2.156	5776	0.0311	-0.329	0.04313
fixed	NA	count_birth_order4/4	-0.02894	0.07005	-0.4132	5772	0.6795	-0.2256	0.1677
fixed	NA	count_birth_order1/5	-0.2023	0.08297	-2.438	5781	0.0148	-0.4352	0.03062
fixed	NA	count_birth_order2/5	-0.03606	0.0917	-0.3932	5768	0.6942	-0.2934	0.2213
fixed	NA	count_birth_order3/5	-0.1885	0.08748	-2.154	5766	0.03125	-0.434	0.0571
fixed	NA	count_birth_order4/5	-0.05182	0.08429	-0.6147	5771	0.5388	-0.2884	0.1848
fixed	NA	count_birth_order5/5	-0.04479	0.08956	-0.5001	5763	0.617	-0.2962	0.2066
fixed	NA	count_birth_order1/>5	-0.1186	0.08445	-1.404	5778	0.1603	-0.3556	0.1185
fixed	NA	count_birth_order2/>5	-0.06131	0.08375	-0.7321	5774	0.4642	-0.2964	0.1738
fixed	NA	count_birth_order3/>5	-0.1921	0.08298	-2.315	5757	0.02065	-0.425	0.04083
fixed	NA	count_birth_order4/>5	-0.1344	0.08117	-1.656	5743	0.09781	-0.3622	0.09344
fixed	NA	count_birth_order5/>5	-0.08222	0.0746	-1.102	5753	0.2704	-0.2916	0.1272
fixed	NA	count_birth_order>5/>5	-0.1868	0.05579	-3.349	5198	0.000818	-0.3434	-0.03021
ran_pars	mother_pidlink	sd__(Intercept)	0.2954	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.887	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)
11	15673	15746	-7826	15651	NA	NA	NA
12	15675	15755	-7825	15651	0.3398	1	0.5599
16	15678	15785	-7823	15646	4.718	4	0.3175
26	15692	15865	-7820	15640	6.553	10	0.7669

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)	1.147	0.1737	6.604	11994	0.0000000000418	0.6596	1.635
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09252	0.01678	-5.513	11800	0.00000003595	-0.1396	-0.04541
fixed	NA	poly(age, 3, raw = TRUE)2	0.002406	0.0004989	4.822	11527	0.000001438	0.001005	0.003806
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001908	0.000004653	-4.1	11257	0.00004163	-0.00003214	-0.000006015
fixed	NA	male	-0.2332	0.01776	-13.13	12290	3.886e-39	-0.283	-0.1834
fixed	NA	sibling_count3	0.003204	0.03507	0.09136	9926	0.9272	-0.09525	0.1017
fixed	NA	sibling_count4	0.004187	0.03594	0.1165	9135	0.9073	-0.09671	0.1051
fixed	NA	sibling_count5	-0.008956	0.03722	-0.2406	8113	0.8098	-0.1134	0.09551
fixed	NA	sibling_count>5	0.04878	0.02933	1.663	9175	0.09638	-0.03356	0.1311
ran_pars	mother_pidlink	sd__(Intercept)	0.2501	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9575	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	0.1738	6.615	11995	0.00000000003867	0.6617	1.637
fixed	NA	birth_order	0.002926	0.003685	0.794	10092	0.4272	-0.007419	0.01327
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09344	0.01682	-5.555	11775	0.00000002835	-0.1407	-0.04622
fixed	NA	poly(age, 3, raw = TRUE)2	0.002438	0.0005005	4.871	11459	0.000001126	0.001033	0.003843
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001937	0.000004668	-4.15	11169	0.00003342	-0.00003248	-0.000006271
fixed	NA	male	-0.2333	0.01776	-13.14	12289	3.698e-39	-0.2831	-0.1834
fixed	NA	sibling_count3	0.002364	0.03509	0.06739	9936	0.9463	-0.09613	0.1009
fixed	NA	sibling_count4	0.002011	0.03604	0.05579	9175	0.9555	-0.09916	0.1032
fixed	NA	sibling_count5	-0.01272	0.03751	-0.3391	8187	0.7346	-0.118	0.09258
fixed	NA	sibling_count>5	0.03741	0.03264	1.146	9887	0.2517	-0.0542	0.129
ran_pars	mother_pidlink	sd__(Intercept)	0.2494	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9577	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)	1.134	0.1743	6.508	11992	0.00000000007936	0.645	1.623
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09246	0.01683	-5.495	11783	0.00000003986	-0.1397	-0.04523
fixed	NA	poly(age, 3, raw = TRUE)2	0.002401	0.0005007	4.795	11465	0.000001648	0.0009953	0.003806
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001898	0.00000467	-4.064	11162	0.00004865	-0.00003208	-0.000005868
fixed	NA	male	-0.2334	0.01776	-13.14	12284	3.363e-39	-0.2832	-0.1835
fixed	NA	sibling_count3	0.00682	0.03566	0.1912	10217	0.8484	-0.09329	0.1069
fixed	NA	sibling_count4	0.006205	0.03719	0.1669	9772	0.8675	-0.09818	0.1106
fixed	NA	sibling_count5	-0.01895	0.03919	-0.4834	9054	0.6288	-0.129	0.09107
fixed	NA	sibling_count>5	0.04327	0.03453	1.253	10833	0.2102	-0.05366	0.1402
fixed	NA	birth_order_nonlinear2	0.03422	0.02611	1.311	11515	0.1899	-0.03906	0.1075
fixed	NA	birth_order_nonlinear3	-0.005286	0.0307	-0.1722	11400	0.8633	-0.09145	0.08088
fixed	NA	birth_order_nonlinear4	0.015	0.03513	0.4268	11505	0.6695	-0.08362	0.1136
fixed	NA	birth_order_nonlinear5	0.08311	0.03947	2.106	11550	0.03526	-0.02769	0.1939
fixed	NA	birth_order_nonlinear>5	0.009131	0.03275	0.2789	12349	0.7804	-0.08279	0.101
ran_pars	mother_pidlink	sd__(Intercept)	0.2505	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9573	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)	1.152	0.175	6.581	11987	0.00000000004863	0.6604	1.643
fixed	NA	poly(age, 3, raw = TRUE)1	-0.09299	0.01682	-5.528	11770	0.00000003299	-0.1402	-0.04577
fixed	NA	poly(age, 3, raw = TRUE)2	0.002411	0.0005005	4.817	11443	0.000001478	0.001006	0.003816
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001901	0.000004669	-4.072	11131	0.00004694	-0.00003212	-0.000005906
fixed	NA	male	-0.2341	0.01775	-13.19	12273	1.866e-39	-0.2839	-0.1843
fixed	NA	count_birth_order2/2	0.005908	0.05039	0.1173	11387	0.9067	-0.1355	0.1473
fixed	NA	count_birth_order1/3	-0.04965	0.04725	-1.051	12312	0.2934	-0.1823	0.08299
fixed	NA	count_birth_order2/3	0.02964	0.05332	0.5559	12329	0.5783	-0.12	0.1793
fixed	NA	count_birth_order3/3	0.08396	0.05874	1.429	12340	0.1529	-0.08092	0.2488
fixed	NA	count_birth_order1/4	0.05371	0.05395	0.9955	12331	0.3195	-0.09773	0.2051
fixed	NA	count_birth_order2/4	-0.01678	0.05658	-0.2965	12334	0.7668	-0.1756	0.1421
fixed	NA	count_birth_order3/4	-0.09029	0.06134	-1.472	12344	0.141	-0.2625	0.08188
fixed	NA	count_birth_order4/4	0.07955	0.06589	1.207	12346	0.2273	-0.1054	0.2645
fixed	NA	count_birth_order1/5	-0.02778	0.062	-0.4482	12343	0.654	-0.2018	0.1462
fixed	NA	count_birth_order2/5	0.04518	0.06404	0.7054	12345	0.4806	-0.1346	0.225
fixed	NA	count_birth_order3/5	0.01774	0.06616	0.2682	12347	0.7886	-0.168	0.2034
fixed	NA	count_birth_order4/5	-0.1898	0.06999	-2.712	12347	0.006689	-0.3863	0.006622
fixed	NA	count_birth_order5/5	0.1188	0.07047	1.686	12347	0.09189	-0.07903	0.3166
fixed	NA	count_birth_order1/>5	0.02633	0.04975	0.5293	12347	0.5966	-0.1133	0.166
fixed	NA	count_birth_order2/>5	0.1002	0.05139	1.949	12346	0.05127	-0.04407	0.2444
fixed	NA	count_birth_order3/>5	-0.006486	0.05003	-0.1296	12346	0.8968	-0.1469	0.1339
fixed	NA	count_birth_order4/>5	0.0823	0.049	1.68	12347	0.09304	-0.05524	0.2198
fixed	NA	count_birth_order5/>5	0.09391	0.04895	1.919	12346	0.05505	-0.04348	0.2313
fixed	NA	count_birth_order>5/>5	0.04251	0.03807	1.116	11430	0.2642	-0.06437	0.1494
ran_pars	mother_pidlink	sd__(Intercept)	0.2503	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9567	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)
11	34828	34909	-17403	34806	NA	NA	NA
12	34829	34918	-17403	34805	0.6324	1	0.4265
16	34831	34949	-17399	34799	6.352	4	0.1743
26	34825	35018	-17386	34773	25.71	10	0.004149

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)	1.577	0.4493	3.51	5320	0.000452	0.3158	2.838
fixed	NA	poly(age, 3, raw = TRUE)1	-0.134	0.05105	-2.626	5322	0.008665	-0.2773	0.009243
fixed	NA	poly(age, 3, raw = TRUE)2	0.003493	0.001825	1.914	5323	0.05565	-0.001629	0.008614
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002836	0.0000207	-1.37	5324	0.1708	-0.00008648	0.00002975
fixed	NA	male	-0.2542	0.02616	-9.717	5298	3.894e-22	-0.3276	-0.1808
fixed	NA	sibling_count3	-0.01637	0.04026	-0.4067	4232	0.6843	-0.1294	0.09664
fixed	NA	sibling_count4	0.01001	0.04325	0.2314	3736	0.817	-0.1114	0.1314
fixed	NA	sibling_count5	0.02769	0.04899	0.5652	3337	0.5719	-0.1098	0.1652
fixed	NA	sibling_count>5	0.1299	0.04299	3.021	3120	0.002542	0.009186	0.2506
ran_pars	mother_pidlink	sd__(Intercept)	0.2518	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9226	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)	1.58	0.4494	3.516	5319	0.0004423	0.3185	2.841
fixed	NA	birth_order	-0.003278	0.008588	-0.3817	5089	0.7027	-0.02738	0.02083
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1339	0.05105	-2.624	5321	0.008728	-0.2772	0.009369
fixed	NA	poly(age, 3, raw = TRUE)2	0.003494	0.001825	1.915	5322	0.05557	-0.001628	0.008616
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000285	0.00002071	-1.376	5323	0.1688	-0.00008663	0.00002963
fixed	NA	male	-0.2541	0.02616	-9.71	5297	4.156e-22	-0.3275	-0.1806
fixed	NA	sibling_count3	-0.01474	0.04049	-0.3641	4234	0.7158	-0.1284	0.09891
fixed	NA	sibling_count4	0.01385	0.0444	0.3118	3736	0.7552	-0.1108	0.1385
fixed	NA	sibling_count5	0.03389	0.05161	0.6566	3384	0.5115	-0.111	0.1788
fixed	NA	sibling_count>5	0.1424	0.05406	2.634	3552	0.00848	-0.009364	0.2941
ran_pars	mother_pidlink	sd__(Intercept)	0.2515	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9228	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)	1.557	0.4502	3.459	5316	0.0005455	0.2937	2.821
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1325	0.05109	-2.593	5317	0.009537	-0.2759	0.01093
fixed	NA	poly(age, 3, raw = TRUE)2	0.003436	0.001826	1.881	5319	0.05999	-0.001691	0.008563
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002774	0.00002073	-1.338	5319	0.1808	-0.00008593	0.00003045
fixed	NA	male	-0.2537	0.02617	-9.693	5292	4.897e-22	-0.3271	-0.1802
fixed	NA	sibling_count3	-0.02883	0.04149	-0.6949	4391	0.4872	-0.1453	0.08763
fixed	NA	sibling_count4	0.003924	0.04641	0.08454	4052	0.9326	-0.1264	0.1342
fixed	NA	sibling_count5	0.01893	0.05466	0.3463	3814	0.7291	-0.1345	0.1724
fixed	NA	sibling_count>5	0.1267	0.05591	2.266	3862	0.02349	-0.03024	0.2836
fixed	NA	birth_order_nonlinear2	0.01925	0.03437	0.5601	4676	0.5755	-0.07722	0.1157
fixed	NA	birth_order_nonlinear3	0.05381	0.04222	1.274	4855	0.2026	-0.06472	0.1723
fixed	NA	birth_order_nonlinear4	-0.02119	0.05203	-0.4073	4967	0.6838	-0.1672	0.1248
fixed	NA	birth_order_nonlinear5	0.03094	0.0651	0.4752	4899	0.6346	-0.1518	0.2137
fixed	NA	birth_order_nonlinear>5	-0.00119	0.06463	-0.01842	5316	0.9853	-0.1826	0.1802
ran_pars	mother_pidlink	sd__(Intercept)	0.2539	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9223	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)	1.526	0.4507	3.385	5306	0.0007173	0.2604	2.791
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1286	0.05114	-2.514	5307	0.01198	-0.2721	0.015
fixed	NA	poly(age, 3, raw = TRUE)2	0.003327	0.001828	1.82	5308	0.06888	-0.001805	0.008458
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002686	0.00002075	-1.294	5309	0.1956	-0.00008511	0.00003139
fixed	NA	male	-0.2536	0.02619	-9.683	5280	5.417e-22	-0.3271	-0.1801
fixed	NA	count_birth_order2/2	-0.008658	0.06139	-0.141	4803	0.8879	-0.181	0.1637
fixed	NA	count_birth_order1/3	-0.1013	0.05393	-1.878	5302	0.06041	-0.2527	0.05009
fixed	NA	count_birth_order2/3	0.01465	0.05898	0.2484	5308	0.8039	-0.1509	0.1802
fixed	NA	count_birth_order3/3	0.08765	0.06512	1.346	5309	0.1783	-0.09513	0.2704
fixed	NA	count_birth_order1/4	0.05273	0.06664	0.7913	5305	0.4288	-0.1343	0.2398
fixed	NA	count_birth_order2/4	-0.01304	0.06801	-0.1917	5309	0.848	-0.204	0.1779
fixed	NA	count_birth_order3/4	-0.04041	0.07259	-0.5568	5306	0.5777	-0.2442	0.1633
fixed	NA	count_birth_order4/4	0.02005	0.07383	0.2715	5306	0.786	-0.1872	0.2273
fixed	NA	count_birth_order1/5	0.1057	0.08996	1.175	5309	0.2401	-0.1468	0.3582
fixed	NA	count_birth_order2/5	-0.01872	0.09657	-0.1939	5304	0.8463	-0.2898	0.2524
fixed	NA	count_birth_order3/5	0.02719	0.0897	0.3031	5301	0.7618	-0.2246	0.279
fixed	NA	count_birth_order4/5	0.0244	0.08554	0.2853	5305	0.7754	-0.2157	0.2645
fixed	NA	count_birth_order5/5	-0.02271	0.08904	-0.2551	5301	0.7987	-0.2726	0.2272
fixed	NA	count_birth_order1/>5	0.1101	0.09201	1.197	5309	0.2315	-0.1482	0.3684
fixed	NA	count_birth_order2/>5	0.1728	0.08828	1.957	5308	0.05037	-0.07502	0.4206
fixed	NA	count_birth_order3/>5	0.1931	0.08797	2.195	5304	0.0282	-0.05383	0.44
fixed	NA	count_birth_order4/>5	-0.004091	0.08442	-0.04846	5298	0.9614	-0.2411	0.2329
fixed	NA	count_birth_order5/>5	0.1929	0.07866	2.452	5297	0.01425	-0.02796	0.4137
fixed	NA	count_birth_order>5/>5	0.1152	0.05806	1.985	4842	0.04723	-0.04774	0.2782
ran_pars	mother_pidlink	sd__(Intercept)	0.2554	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9215	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)
11	14660	14732	-7319	14638	NA	NA	NA
12	14661	14740	-7319	14637	0.1468	1	0.7016
16	14667	14772	-7317	14635	2.604	4	0.6262
26	14672	14844	-7310	14620	14.37	10	0.1569

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)	1.549	0.4478	3.46	5369	0.0005442	0.2924	2.806
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1301	0.05091	-2.555	5371	0.01064	-0.273	0.01282
fixed	NA	poly(age, 3, raw = TRUE)2	0.003384	0.00182	1.859	5372	0.06307	-0.001725	0.008493
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002719	0.00002066	-1.316	5373	0.1882	-0.00008517	0.0000308
fixed	NA	male	-0.2574	0.02605	-9.882	5346	7.785e-23	-0.3305	-0.1843
fixed	NA	sibling_count3	-0.03451	0.04357	-0.792	4369	0.4284	-0.1568	0.0878
fixed	NA	sibling_count4	-0.03854	0.04574	-0.8425	3984	0.3995	-0.1669	0.08985
fixed	NA	sibling_count5	0.02241	0.04858	0.4612	3611	0.6447	-0.114	0.1588
fixed	NA	sibling_count>5	0.0725	0.04271	1.697	3685	0.08972	-0.0474	0.1924
ran_pars	mother_pidlink	sd__(Intercept)	0.2535	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9221	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)	1.545	0.4479	3.45	5368	0.0005658	0.2878	2.802
fixed	NA	birth_order	0.003578	0.007458	0.4798	4894	0.6314	-0.01736	0.02451
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1301	0.05091	-2.555	5370	0.01065	-0.273	0.01284
fixed	NA	poly(age, 3, raw = TRUE)2	0.003378	0.00182	1.856	5371	0.06357	-0.001732	0.008487
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002699	0.00002066	-1.306	5372	0.1916	-0.00008499	0.00003102
fixed	NA	male	-0.2575	0.02605	-9.886	5345	7.537e-23	-0.3307	-0.1844
fixed	NA	sibling_count3	-0.03628	0.04373	-0.8296	4365	0.4068	-0.159	0.08648
fixed	NA	sibling_count4	-0.04254	0.0465	-0.9149	3969	0.3603	-0.1731	0.08798
fixed	NA	sibling_count5	0.01616	0.0503	0.3213	3609	0.748	-0.125	0.1574
fixed	NA	sibling_count>5	0.0592	0.05092	1.163	3896	0.245	-0.08372	0.2021
ran_pars	mother_pidlink	sd__(Intercept)	0.2537	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9222	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)	1.522	0.4487	3.392	5366	0.0006988	0.2625	2.781
fixed	NA	poly(age, 3, raw = TRUE)1	-0.128	0.05094	-2.513	5367	0.01201	-0.271	0.015
fixed	NA	poly(age, 3, raw = TRUE)2	0.003294	0.001822	1.808	5368	0.07066	-0.00182	0.008407
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002588	0.00002068	-1.252	5368	0.2108	-0.00008393	0.00003217
fixed	NA	male	-0.2576	0.02605	-9.888	5340	7.394e-23	-0.3307	-0.1844
fixed	NA	sibling_count3	-0.05732	0.04465	-1.284	4491	0.1994	-0.1827	0.06803
fixed	NA	sibling_count4	-0.06546	0.04836	-1.354	4231	0.1759	-0.2012	0.07029
fixed	NA	sibling_count5	-0.0008842	0.05303	-0.01667	3990	0.9867	-0.1497	0.148
fixed	NA	sibling_count>5	0.0348	0.05268	0.6606	4203	0.5089	-0.1131	0.1827
fixed	NA	birth_order_nonlinear2	0.03458	0.03489	0.9911	4780	0.3217	-0.06336	0.1325
fixed	NA	birth_order_nonlinear3	0.09857	0.04209	2.342	4959	0.01921	-0.01957	0.2167
fixed	NA	birth_order_nonlinear4	0.0352	0.05032	0.6995	5072	0.4843	-0.1061	0.1765
fixed	NA	birth_order_nonlinear5	0.003997	0.06168	0.06481	5041	0.9483	-0.1691	0.1771
fixed	NA	birth_order_nonlinear>5	0.07155	0.05752	1.244	5334	0.2136	-0.08993	0.233
ran_pars	mother_pidlink	sd__(Intercept)	0.2558	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9214	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)	1.49	0.4492	3.317	5356	0.0009158	0.2291	2.751
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1225	0.05098	-2.404	5356	0.01627	-0.2656	0.02057
fixed	NA	poly(age, 3, raw = TRUE)2	0.003108	0.001823	1.705	5357	0.08829	-0.002009	0.008225
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002392	0.0000207	-1.156	5358	0.2478	-0.00008202	0.00003418
fixed	NA	male	-0.2572	0.02606	-9.871	5329	8.746e-23	-0.3304	-0.1841
fixed	NA	count_birth_order2/2	-0.01902	0.06687	-0.2844	4888	0.7761	-0.2067	0.1687
fixed	NA	count_birth_order1/3	-0.1438	0.05846	-2.46	5351	0.01392	-0.3079	0.02028
fixed	NA	count_birth_order2/3	0.003974	0.06319	0.0629	5356	0.9498	-0.1734	0.1813
fixed	NA	count_birth_order3/3	0.08898	0.0708	1.257	5358	0.2089	-0.1098	0.2877
fixed	NA	count_birth_order1/4	-0.01275	0.06936	-0.1838	5355	0.8541	-0.2074	0.1819
fixed	NA	count_birth_order2/4	-0.1237	0.07019	-1.762	5358	0.07817	-0.3207	0.07337
fixed	NA	count_birth_order3/4	-0.04247	0.07755	-0.5477	5356	0.5839	-0.2601	0.1752
fixed	NA	count_birth_order4/4	0.01075	0.07811	0.1376	5356	0.8905	-0.2085	0.23
fixed	NA	count_birth_order1/5	0.01399	0.08174	0.1712	5358	0.8641	-0.2154	0.2434
fixed	NA	count_birth_order2/5	0.009527	0.08838	0.1078	5356	0.9142	-0.2386	0.2576
fixed	NA	count_birth_order3/5	0.1061	0.08479	1.251	5354	0.211	-0.1319	0.3441
fixed	NA	count_birth_order4/5	0.02947	0.08793	0.3351	5351	0.7375	-0.2174	0.2763
fixed	NA	count_birth_order5/5	-0.0916	0.08745	-1.047	5349	0.295	-0.3371	0.1539
fixed	NA	count_birth_order1/>5	0.001461	0.07901	0.01849	5357	0.9852	-0.2203	0.2233
fixed	NA	count_birth_order2/>5	0.1332	0.08149	1.635	5357	0.1021	-0.0955	0.362
fixed	NA	count_birth_order3/>5	0.06555	0.08021	0.8172	5354	0.4139	-0.1596	0.2907
fixed	NA	count_birth_order4/>5	-0.01491	0.07757	-0.1922	5351	0.8476	-0.2326	0.2028
fixed	NA	count_birth_order5/>5	0.07852	0.07906	0.9931	5342	0.3207	-0.1434	0.3004
fixed	NA	count_birth_order>5/>5	0.08841	0.05687	1.555	4983	0.1201	-0.07122	0.248
ran_pars	mother_pidlink	sd__(Intercept)	0.2571	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9206	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)
11	14794	14866	-7386	14772	NA	NA	NA
12	14796	14875	-7386	14772	0.2304	1	0.6312
16	14797	14903	-7383	14765	6.297	4	0.178
26	14802	14973	-7375	14750	15.5	10	0.1149

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)	1.476	0.455	3.243	5219	0.00119	0.1984	2.753
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1219	0.05172	-2.358	5221	0.01842	-0.2671	0.02323
fixed	NA	poly(age, 3, raw = TRUE)2	0.003027	0.00185	1.637	5222	0.1018	-0.002165	0.008219
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002277	0.00002101	-1.084	5223	0.2784	-0.00008173	0.00003619
fixed	NA	male	-0.259	0.02642	-9.801	5196	1.743e-22	-0.3331	-0.1848
fixed	NA	sibling_count3	-0.01595	0.03977	-0.4011	4134	0.6884	-0.1276	0.09568
fixed	NA	sibling_count4	0.002577	0.04305	0.05986	3673	0.9523	-0.1183	0.1234
fixed	NA	sibling_count5	0.06957	0.05029	1.383	3182	0.1666	-0.07159	0.2107
fixed	NA	sibling_count>5	0.1304	0.04352	2.997	2969	0.002745	0.008285	0.2526
ran_pars	mother_pidlink	sd__(Intercept)	0.255	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.922	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)	1.477	0.4551	3.246	5218	0.001177	0.1999	2.755
fixed	NA	birth_order	-0.002007	0.008824	-0.2275	5012	0.8201	-0.02678	0.02276
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1219	0.05173	-2.356	5220	0.01851	-0.2671	0.02333
fixed	NA	poly(age, 3, raw = TRUE)2	0.003028	0.00185	1.637	5221	0.1017	-0.002165	0.00822
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002285	0.00002101	-1.088	5222	0.2768	-0.00008183	0.00003612
fixed	NA	male	-0.2589	0.02643	-9.798	5195	1.79e-22	-0.3331	-0.1847
fixed	NA	sibling_count3	-0.01493	0.04002	-0.3731	4132	0.7091	-0.1273	0.09741
fixed	NA	sibling_count4	0.004905	0.04426	0.1108	3679	0.9118	-0.1193	0.1291
fixed	NA	sibling_count5	0.0732	0.05277	1.387	3230	0.1655	-0.07492	0.2213
fixed	NA	sibling_count>5	0.1381	0.0549	2.515	3487	0.01196	-0.01605	0.2922
ran_pars	mother_pidlink	sd__(Intercept)	0.2549	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9221	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)	1.46	0.4559	3.203	5215	0.00137	0.1803	2.74
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1207	0.05177	-2.332	5217	0.01975	-0.266	0.0246
fixed	NA	poly(age, 3, raw = TRUE)2	0.002979	0.001851	1.609	5217	0.1077	-0.002218	0.008176
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002217	0.00002103	-1.054	5218	0.2918	-0.0000812	0.00003686
fixed	NA	male	-0.2584	0.02643	-9.775	5190	2.242e-22	-0.3326	-0.1842
fixed	NA	sibling_count3	-0.02704	0.04106	-0.6587	4293	0.5101	-0.1423	0.0882
fixed	NA	sibling_count4	-0.002276	0.04631	-0.04916	3991	0.9608	-0.1323	0.1277
fixed	NA	sibling_count5	0.06283	0.0556	1.13	3618	0.2585	-0.09323	0.2189
fixed	NA	sibling_count>5	0.1202	0.05686	2.113	3802	0.03465	-0.03945	0.2798
fixed	NA	birth_order_nonlinear2	0.01531	0.03429	0.4465	4577	0.6553	-0.08093	0.1115
fixed	NA	birth_order_nonlinear3	0.04702	0.04216	1.115	4732	0.2647	-0.07132	0.1654
fixed	NA	birth_order_nonlinear4	-0.02296	0.05335	-0.4304	4862	0.6669	-0.1727	0.1268
fixed	NA	birth_order_nonlinear5	0.02594	0.06801	0.3815	4794	0.7029	-0.165	0.2168
fixed	NA	birth_order_nonlinear>5	0.01797	0.0667	0.2694	5217	0.7877	-0.1693	0.2052
ran_pars	mother_pidlink	sd__(Intercept)	0.2571	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9217	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)	1.418	0.4564	3.108	5205	0.001896	0.1372	2.699
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1144	0.05181	-2.207	5206	0.02734	-0.2598	0.03107
fixed	NA	poly(age, 3, raw = TRUE)2	0.002775	0.001853	1.497	5207	0.1343	-0.002427	0.007976
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002013	0.00002105	-0.9565	5208	0.3388	-0.00007922	0.00003895
fixed	NA	male	-0.2579	0.02644	-9.756	5178	2.713e-22	-0.3322	-0.1837
fixed	NA	count_birth_order2/2	-0.03894	0.05986	-0.6506	4693	0.5154	-0.207	0.1291
fixed	NA	count_birth_order1/3	-0.1122	0.05335	-2.103	5200	0.03548	-0.262	0.03754
fixed	NA	count_birth_order2/3	-0.005963	0.05896	-0.1011	5208	0.9194	-0.1715	0.1595
fixed	NA	count_birth_order3/3	0.0912	0.06371	1.432	5207	0.1523	-0.08763	0.27
fixed	NA	count_birth_order1/4	0.0365	0.06697	0.5451	5206	0.5857	-0.1515	0.2245
fixed	NA	count_birth_order2/4	0.00438	0.06821	0.06421	5208	0.9488	-0.1871	0.1959
fixed	NA	count_birth_order3/4	-0.08139	0.07209	-1.129	5203	0.259	-0.2838	0.121
fixed	NA	count_birth_order4/4	-0.01876	0.07401	-0.2534	5202	0.7999	-0.2265	0.189
fixed	NA	count_birth_order1/5	0.1228	0.09013	1.362	5208	0.1733	-0.1303	0.3758
fixed	NA	count_birth_order2/5	0.01063	0.09959	0.1067	5202	0.915	-0.2689	0.2902
fixed	NA	count_birth_order3/5	0.05929	0.09337	0.6351	5199	0.5254	-0.2028	0.3214
fixed	NA	count_birth_order4/5	0.09376	0.09014	1.04	5203	0.2983	-0.1593	0.3468
fixed	NA	count_birth_order5/5	-0.02808	0.09563	-0.2937	5199	0.769	-0.2965	0.2404
fixed	NA	count_birth_order1/>5	0.08835	0.09431	0.9368	5207	0.3489	-0.1764	0.3531
fixed	NA	count_birth_order2/>5	0.1599	0.09032	1.771	5206	0.07668	-0.0936	0.4134
fixed	NA	count_birth_order3/>5	0.1489	0.08977	1.659	5200	0.09721	-0.1031	0.4009
fixed	NA	count_birth_order4/>5	-0.02845	0.0881	-0.3229	5193	0.7468	-0.2757	0.2188
fixed	NA	count_birth_order5/>5	0.1909	0.08075	2.365	5193	0.01809	-0.03573	0.4176
fixed	NA	count_birth_order>5/>5	0.119	0.05923	2.01	4696	0.0445	-0.04721	0.2853
ran_pars	mother_pidlink	sd__(Intercept)	0.2591	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9205	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)
11	14385	14457	-7181	14363	NA	NA	NA
12	14386	14465	-7181	14362	0.05235	1	0.819
16	14392	14497	-7180	14360	2.057	4	0.7253
26	14395	14565	-7171	14343	17.69	10	0.06035

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)	0.3885	0.1683	2.309	12765	0.02098	-0.08389	0.861
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02493	0.01621	-1.537	12562	0.1242	-0.07044	0.02058
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007458	0.0004805	1.552	12293	0.1206	-0.0006029	0.002095
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000007326	0.000004462	-1.642	12042	0.1007	-0.00001985	0.000005199
fixed	NA	male	-0.1892	0.01731	-10.93	13119	1.054e-27	-0.2378	-0.1406
fixed	NA	sibling_count3	-0.02192	0.03395	-0.6458	10321	0.5184	-0.1172	0.07337
fixed	NA	sibling_count4	-0.00809	0.03496	-0.2314	9498	0.817	-0.1062	0.09005
fixed	NA	sibling_count5	-0.03174	0.03599	-0.8819	8323	0.3779	-0.1328	0.06929
fixed	NA	sibling_count>5	-0.04519	0.0285	-1.586	9488	0.1129	-0.1252	0.03481
ran_pars	mother_pidlink	sd__(Intercept)	0.2164	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.969	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)	0.3874	0.1683	2.301	12768	0.02139	-0.08514	0.8599
fixed	NA	birth_order	-0.001201	0.003596	-0.3339	10334	0.7384	-0.0113	0.008894
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02453	0.01626	-1.509	12531	0.1314	-0.07017	0.02111
fixed	NA	poly(age, 3, raw = TRUE)2	0.000732	0.0004823	1.518	12211	0.1291	-0.0006218	0.002086
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000072	0.000004478	-1.608	11938	0.1079	-0.00001977	0.00000537
fixed	NA	male	-0.1892	0.01731	-10.93	13118	1.098e-27	-0.2377	-0.1406
fixed	NA	sibling_count3	-0.02161	0.03396	-0.6363	10335	0.5246	-0.1169	0.07372
fixed	NA	sibling_count4	-0.007222	0.03506	-0.206	9548	0.8368	-0.1056	0.09119
fixed	NA	sibling_count5	-0.03024	0.03627	-0.8337	8416	0.4045	-0.1321	0.07158
fixed	NA	sibling_count>5	-0.04059	0.03166	-1.282	10305	0.1999	-0.1295	0.04829
ran_pars	mother_pidlink	sd__(Intercept)	0.2165	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.969	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)	0.3921	0.1689	2.321	12768	0.02028	-0.082	0.8661
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02604	0.01627	-1.601	12546	0.1095	-0.0717	0.01962
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007753	0.0004825	1.607	12226	0.1081	-0.000579	0.00213
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000007514	0.00000448	-1.677	11940	0.09356	-0.00002009	0.000005063
fixed	NA	male	-0.1895	0.01731	-10.95	13113	9.203e-28	-0.238	-0.1409
fixed	NA	sibling_count3	-0.03004	0.0345	-0.8706	10641	0.384	-0.1269	0.06681
fixed	NA	sibling_count4	-0.01974	0.03616	-0.546	10203	0.5851	-0.1212	0.08175
fixed	NA	sibling_count5	-0.04581	0.0379	-1.209	9357	0.2268	-0.1522	0.06057
fixed	NA	sibling_count>5	-0.06451	0.03346	-1.928	11369	0.05388	-0.1584	0.02941
fixed	NA	birth_order_nonlinear2	0.01757	0.02529	0.6947	12145	0.4873	-0.05343	0.08857
fixed	NA	birth_order_nonlinear3	0.04294	0.02996	1.433	12111	0.1519	-0.04117	0.127
fixed	NA	birth_order_nonlinear4	0.02767	0.03418	0.8097	12211	0.4182	-0.06827	0.1236
fixed	NA	birth_order_nonlinear5	0.0263	0.03854	0.6825	12265	0.4949	-0.08188	0.1345
fixed	NA	birth_order_nonlinear>5	0.03267	0.03179	1.028	13117	0.3041	-0.05657	0.1219
ran_pars	mother_pidlink	sd__(Intercept)	0.217	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.969	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)	0.4261	0.1695	2.513	12765	0.01197	-0.04979	0.9021
fixed	NA	poly(age, 3, raw = TRUE)1	-0.02658	0.01626	-1.635	12534	0.1022	-0.07222	0.01907
fixed	NA	poly(age, 3, raw = TRUE)2	0.0007872	0.0004824	1.632	12206	0.1027	-0.0005668	0.002141
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000757	0.00000448	-1.69	11909	0.09112	-0.00002015	0.000005006
fixed	NA	male	-0.1896	0.0173	-10.96	13103	8.252e-28	-0.2381	-0.141
fixed	NA	count_birth_order2/2	-0.05705	0.04918	-1.16	11911	0.246	-0.1951	0.08099
fixed	NA	count_birth_order1/3	-0.1249	0.04595	-2.718	13109	0.006575	-0.2539	0.004088
fixed	NA	count_birth_order2/3	0.0004879	0.05123	0.009525	13120	0.9924	-0.1433	0.1443
fixed	NA	count_birth_order3/3	0.06406	0.05765	1.111	13131	0.2665	-0.09777	0.2259
fixed	NA	count_birth_order1/4	0.03162	0.05249	0.6024	13122	0.547	-0.1157	0.179
fixed	NA	count_birth_order2/4	-0.04005	0.05544	-0.7225	13125	0.47	-0.1957	0.1156
fixed	NA	count_birth_order3/4	-0.1284	0.06086	-2.109	13132	0.03494	-0.2992	0.04246
fixed	NA	count_birth_order4/4	-0.001447	0.06385	-0.02266	13134	0.9819	-0.1807	0.1778
fixed	NA	count_birth_order1/5	-0.1393	0.05994	-2.324	13132	0.02014	-0.3076	0.02895
fixed	NA	count_birth_order2/5	-0.06536	0.06223	-1.05	13134	0.2936	-0.24	0.1093
fixed	NA	count_birth_order3/5	0.00197	0.06385	0.03086	13135	0.9754	-0.1773	0.1812
fixed	NA	count_birth_order4/5	-0.05504	0.06836	-0.8053	13136	0.4207	-0.2469	0.1368
fixed	NA	count_birth_order5/5	0.03196	0.06921	0.4618	13136	0.6442	-0.1623	0.2262
fixed	NA	count_birth_order1/>5	-0.08178	0.04827	-1.694	13134	0.09023	-0.2173	0.05371
fixed	NA	count_birth_order2/>5	-0.05255	0.04983	-1.055	13136	0.2917	-0.1924	0.08733
fixed	NA	count_birth_order3/>5	-0.04667	0.04888	-0.9549	13136	0.3396	-0.1839	0.09053
fixed	NA	count_birth_order4/>5	-0.06846	0.04795	-1.428	13136	0.1534	-0.2031	0.06614
fixed	NA	count_birth_order5/>5	-0.09239	0.04793	-1.928	13136	0.0539	-0.2269	0.04214
fixed	NA	count_birth_order>5/>5	-0.05918	0.03721	-1.591	12080	0.1117	-0.1636	0.04525
ran_pars	mother_pidlink	sd__(Intercept)	0.2169	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9685	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)
11	37149	37232	-18564	37127	NA	NA	NA
12	37151	37241	-18564	37127	0.1115	1	0.7384
16	37157	37277	-18562	37125	2.188	4	0.7013
26	37153	37348	-18550	37101	23.98	10	0.007645

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)	1.049	0.4283	2.45	5592	0.01433	-0.1531	2.251
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0891	0.04851	-1.837	5584	0.06632	-0.2253	0.04708
fixed	NA	poly(age, 3, raw = TRUE)2	0.002848	0.001728	1.648	5571	0.09949	-0.002004	0.007699
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000287	0.00001954	-1.469	5551	0.1419	-0.00008354	0.00002614
fixed	NA	male	-0.2247	0.02515	-8.938	5596	5.295e-19	-0.2953	-0.1542
fixed	NA	sibling_count3	-0.07825	0.03816	-2.051	4405	0.04037	-0.1854	0.02887
fixed	NA	sibling_count4	-0.02742	0.04083	-0.6716	3811	0.5019	-0.142	0.08719
fixed	NA	sibling_count5	-0.05557	0.04624	-1.202	3280	0.2295	-0.1854	0.07422
fixed	NA	sibling_count>5	-0.01853	0.04043	-0.4583	2939	0.6468	-0.132	0.09495
ran_pars	mother_pidlink	sd__(Intercept)	0.1238	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9313	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)	1.052	0.4284	2.455	5591	0.01413	-0.151	2.254
fixed	NA	birth_order	-0.00229	0.008256	-0.2774	5083	0.7815	-0.02547	0.02089
fixed	NA	poly(age, 3, raw = TRUE)1	-0.08908	0.04852	-1.836	5583	0.0664	-0.2253	0.04711
fixed	NA	poly(age, 3, raw = TRUE)2	0.002851	0.001729	1.649	5570	0.09911	-0.002001	0.007703
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002882	0.00001954	-1.475	5550	0.1403	-0.00008368	0.00002604
fixed	NA	male	-0.2247	0.02515	-8.934	5595	5.493e-19	-0.2953	-0.1541
fixed	NA	sibling_count3	-0.07714	0.03837	-2.011	4401	0.04443	-0.1848	0.03056
fixed	NA	sibling_count4	-0.02485	0.04188	-0.5933	3796	0.553	-0.1424	0.0927
fixed	NA	sibling_count5	-0.05135	0.04868	-1.055	3318	0.2916	-0.188	0.08531
fixed	NA	sibling_count>5	-0.01003	0.05071	-0.1979	3400	0.8431	-0.1524	0.1323
ran_pars	mother_pidlink	sd__(Intercept)	0.1234	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9315	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)	1.026	0.429	2.391	5586	0.01685	-0.1786	2.23
fixed	NA	poly(age, 3, raw = TRUE)1	-0.08819	0.04855	-1.816	5578	0.06936	-0.2245	0.04809
fixed	NA	poly(age, 3, raw = TRUE)2	0.002811	0.00173	1.625	5564	0.1042	-0.002045	0.007667
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002829	0.00001956	-1.446	5544	0.1482	-0.00008319	0.00002662
fixed	NA	male	-0.2244	0.02515	-8.92	5591	6.231e-19	-0.295	-0.1538
fixed	NA	sibling_count3	-0.08624	0.03928	-2.196	4582	0.02817	-0.1965	0.02402
fixed	NA	sibling_count4	-0.03939	0.04378	-0.8997	4151	0.3683	-0.1623	0.08349
fixed	NA	sibling_count5	-0.05825	0.05154	-1.13	3794	0.2585	-0.2029	0.08644
fixed	NA	sibling_count>5	-0.0163	0.0524	-0.311	3709	0.7558	-0.1634	0.1308
fixed	NA	birth_order_nonlinear2	0.04954	0.03309	1.497	4885	0.1344	-0.04333	0.1424
fixed	NA	birth_order_nonlinear3	0.03766	0.04077	0.9236	5141	0.3557	-0.07679	0.1521
fixed	NA	birth_order_nonlinear4	0.03502	0.05007	0.6993	5284	0.4844	-0.1055	0.1756
fixed	NA	birth_order_nonlinear5	-0.02212	0.06288	-0.3517	5282	0.7251	-0.1986	0.1544
fixed	NA	birth_order_nonlinear>5	0.01008	0.06199	0.1626	5498	0.8709	-0.1639	0.1841
ran_pars	mother_pidlink	sd__(Intercept)	0.1225	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9316	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)	0.9659	0.4297	2.248	5576	0.02463	-0.2403	2.172
fixed	NA	poly(age, 3, raw = TRUE)1	-0.08106	0.04864	-1.667	5569	0.09563	-0.2176	0.05546
fixed	NA	poly(age, 3, raw = TRUE)2	0.002578	0.001733	1.487	5555	0.137	-0.002287	0.007443
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002589	0.0000196	-1.321	5535	0.1866	-0.00008091	0.00002913
fixed	NA	male	-0.2227	0.02516	-8.853	5581	1.127e-18	-0.2934	-0.1521
fixed	NA	count_birth_order2/2	0.02637	0.05933	0.4445	4955	0.6567	-0.1402	0.1929
fixed	NA	count_birth_order1/3	-0.1491	0.05167	-2.885	5580	0.003932	-0.2941	-0.004016
fixed	NA	count_birth_order2/3	-0.006833	0.05633	-0.1213	5581	0.9035	-0.165	0.1513
fixed	NA	count_birth_order3/3	-0.005061	0.06322	-0.08006	5581	0.9362	-0.1825	0.1724
fixed	NA	count_birth_order1/4	0.007126	0.06334	0.1125	5579	0.9104	-0.1707	0.1849
fixed	NA	count_birth_order2/4	-0.03101	0.06571	-0.4719	5581	0.637	-0.2155	0.1534
fixed	NA	count_birth_order3/4	-0.07549	0.06934	-1.089	5580	0.2763	-0.2701	0.1191
fixed	NA	count_birth_order4/4	0.02371	0.07167	0.3308	5580	0.7408	-0.1775	0.2249
fixed	NA	count_birth_order1/5	0.0343	0.08707	0.3939	5581	0.6936	-0.2101	0.2787
fixed	NA	count_birth_order2/5	-0.1382	0.0915	-1.511	5581	0.1309	-0.3951	0.1186
fixed	NA	count_birth_order3/5	0.06142	0.08583	0.7156	5580	0.4743	-0.1795	0.3024
fixed	NA	count_birth_order4/5	-0.08468	0.08257	-1.025	5580	0.3052	-0.3165	0.1471
fixed	NA	count_birth_order5/5	-0.1152	0.08712	-1.322	5578	0.1861	-0.3597	0.1293
fixed	NA	count_birth_order1/>5	-0.05294	0.08612	-0.6147	5566	0.5388	-0.2947	0.1888
fixed	NA	count_birth_order2/>5	0.1103	0.08418	1.31	5572	0.1902	-0.126	0.3466
fixed	NA	count_birth_order3/>5	-0.07246	0.08492	-0.8532	5580	0.3936	-0.3108	0.1659
fixed	NA	count_birth_order4/>5	0.01143	0.07976	0.1433	5581	0.8861	-0.2125	0.2353
fixed	NA	count_birth_order5/>5	-0.02858	0.07532	-0.3794	5581	0.7044	-0.24	0.1828
fixed	NA	count_birth_order>5/>5	-0.01489	0.05589	-0.2664	4859	0.7899	-0.1718	0.142
ran_pars	mother_pidlink	sd__(Intercept)	0.1247	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9309	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)
11	15219	15292	-7598	15197	NA	NA	NA
12	15221	15300	-7598	15197	0.07815	1	0.7798
16	15226	15332	-7597	15194	3.215	4	0.5226
26	15230	15403	-7589	15178	15.45	10	0.1164

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)	1.028	0.4272	2.407	5644	0.01612	-0.171	2.228
fixed	NA	poly(age, 3, raw = TRUE)1	-0.08594	0.04842	-1.775	5635	0.07593	-0.2218	0.04996
fixed	NA	poly(age, 3, raw = TRUE)2	0.00276	0.001725	1.6	5621	0.1098	-0.002083	0.007603
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002778	0.00001951	-1.424	5600	0.1544	-0.00008253	0.00002697
fixed	NA	male	-0.2282	0.02506	-9.107	5648	1.154e-19	-0.2986	-0.1579
fixed	NA	sibling_count3	-0.09326	0.04133	-2.256	4563	0.0241	-0.2093	0.02276
fixed	NA	sibling_count4	-0.05237	0.04336	-1.208	4110	0.2272	-0.1741	0.06934
fixed	NA	sibling_count5	-0.05936	0.04608	-1.288	3599	0.1978	-0.1887	0.06999
fixed	NA	sibling_count>5	-0.04957	0.04042	-1.226	3618	0.2201	-0.163	0.06388
ran_pars	mother_pidlink	sd__(Intercept)	0.1245	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9322	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)	1.03	0.4274	2.41	5642	0.016	-0.1698	2.229
fixed	NA	birth_order	-0.00116	0.007178	-0.1616	4714	0.8716	-0.02131	0.01899
fixed	NA	poly(age, 3, raw = TRUE)1	-0.08597	0.04842	-1.775	5634	0.07587	-0.2219	0.04995
fixed	NA	poly(age, 3, raw = TRUE)2	0.002763	0.001726	1.601	5620	0.1094	-0.002081	0.007606
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002786	0.00001951	-1.428	5598	0.1534	-0.00008263	0.00002691
fixed	NA	male	-0.2282	0.02506	-9.105	5647	1.174e-19	-0.2985	-0.1578
fixed	NA	sibling_count3	-0.0927	0.04148	-2.235	4555	0.02546	-0.2091	0.02372
fixed	NA	sibling_count4	-0.05113	0.04404	-1.161	4077	0.2456	-0.1747	0.07248
fixed	NA	sibling_count5	-0.0574	0.04767	-1.204	3578	0.2286	-0.1912	0.07641
fixed	NA	sibling_count>5	-0.04536	0.04809	-0.9432	3823	0.3456	-0.1803	0.08963
ran_pars	mother_pidlink	sd__(Intercept)	0.1245	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)	1.002	0.4279	2.342	5637	0.01922	-0.199	2.203
fixed	NA	poly(age, 3, raw = TRUE)1	-0.08492	0.04844	-1.753	5629	0.07965	-0.2209	0.05106
fixed	NA	poly(age, 3, raw = TRUE)2	0.002714	0.001726	1.572	5615	0.116	-0.002132	0.00756
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002717	0.00001952	-1.391	5593	0.1641	-0.00008197	0.00002764
fixed	NA	male	-0.228	0.02506	-9.096	5643	1.274e-19	-0.2983	-0.1576
fixed	NA	sibling_count3	-0.1039	0.04233	-2.456	4702	0.0141	-0.2228	0.01487
fixed	NA	sibling_count4	-0.06911	0.04576	-1.51	4366	0.131	-0.1976	0.05934
fixed	NA	sibling_count5	-0.0629	0.05026	-1.251	4013	0.2108	-0.204	0.07818
fixed	NA	sibling_count>5	-0.05826	0.04978	-1.17	4167	0.2419	-0.198	0.08147
fixed	NA	birth_order_nonlinear2	0.05573	0.03362	1.657	5001	0.0975	-0.03866	0.1501
fixed	NA	birth_order_nonlinear3	0.04984	0.04063	1.227	5251	0.2201	-0.06422	0.1639
fixed	NA	birth_order_nonlinear4	0.04656	0.04858	0.9584	5395	0.3379	-0.0898	0.1829
fixed	NA	birth_order_nonlinear5	-0.03878	0.05997	-0.6466	5413	0.5179	-0.2071	0.1296
fixed	NA	birth_order_nonlinear>5	0.0368	0.05516	0.667	5458	0.5048	-0.1181	0.1916
ran_pars	mother_pidlink	sd__(Intercept)	0.1244	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)	0.9712	0.4283	2.267	5626	0.0234	-0.2311	2.174
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0814	0.04848	-1.679	5618	0.09319	-0.2175	0.05468
fixed	NA	poly(age, 3, raw = TRUE)2	0.002602	0.001728	1.506	5603	0.1321	-0.002248	0.007453
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002605	0.00001954	-1.333	5581	0.1826	-0.00008091	0.00002881
fixed	NA	male	-0.2291	0.02507	-9.14	5633	8.554e-20	-0.2995	-0.1587
fixed	NA	count_birth_order2/2	0.04849	0.06493	0.7467	5044	0.4553	-0.1338	0.2308
fixed	NA	count_birth_order1/3	-0.1679	0.05589	-3.005	5632	0.002671	-0.3248	-0.01104
fixed	NA	count_birth_order2/3	-0.02805	0.06057	-0.4631	5633	0.6433	-0.1981	0.142
fixed	NA	count_birth_order3/3	0.0296	0.06842	0.4325	5633	0.6654	-0.1625	0.2217
fixed	NA	count_birth_order1/4	-0.005126	0.06627	-0.07735	5632	0.9383	-0.1911	0.1809
fixed	NA	count_birth_order2/4	-0.04986	0.06714	-0.7426	5633	0.4578	-0.2383	0.1386
fixed	NA	count_birth_order3/4	-0.1197	0.07463	-1.605	5632	0.1086	-0.3292	0.08974
fixed	NA	count_birth_order4/4	0.02688	0.07657	0.3511	5632	0.7256	-0.1881	0.2418
fixed	NA	count_birth_order1/5	-0.0005703	0.07891	-0.007228	5632	0.9942	-0.2221	0.2209
fixed	NA	count_birth_order2/5	-0.06387	0.08439	-0.7568	5633	0.4492	-0.3007	0.173
fixed	NA	count_birth_order3/5	0.05279	0.08275	0.6379	5633	0.5236	-0.1795	0.2851
fixed	NA	count_birth_order4/5	-0.1065	0.08431	-1.264	5632	0.2064	-0.3432	0.1301
fixed	NA	count_birth_order5/5	-0.1147	0.08589	-1.335	5630	0.1818	-0.3558	0.1264
fixed	NA	count_birth_order1/>5	-0.06879	0.07534	-0.9131	5623	0.3613	-0.2803	0.1427
fixed	NA	count_birth_order2/>5	0.04887	0.07825	0.6245	5628	0.5323	-0.1708	0.2685
fixed	NA	count_birth_order3/>5	-0.07751	0.07663	-1.011	5633	0.3119	-0.2926	0.1376
fixed	NA	count_birth_order4/>5	-0.0007247	0.07385	-0.009813	5633	0.9922	-0.208	0.2066
fixed	NA	count_birth_order5/>5	-0.09299	0.07634	-1.218	5632	0.2232	-0.3073	0.1213
fixed	NA	count_birth_order>5/>5	-0.02458	0.0547	-0.4494	5065	0.6532	-0.1781	0.129
ran_pars	mother_pidlink	sd__(Intercept)	0.1213	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9321	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)
11	15371	15444	-7675	15349	NA	NA	NA
12	15373	15453	-7675	15349	0.02676	1	0.8701
16	15376	15482	-7672	15344	5.218	4	0.2657
26	15381	15553	-7664	15329	15.32	10	0.1209

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)	0.9132	0.4324	2.112	5480	0.03473	-0.3005	2.127
fixed	NA	poly(age, 3, raw = TRUE)1	-0.07301	0.049	-1.49	5472	0.1363	-0.2106	0.06455
fixed	NA	poly(age, 3, raw = TRUE)2	0.002181	0.001747	1.249	5459	0.2119	-0.002722	0.007084
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002022	0.00001976	-1.023	5440	0.3062	-0.00007567	0.00003524
fixed	NA	male	-0.2238	0.02536	-8.828	5483	1.413e-18	-0.295	-0.1527
fixed	NA	sibling_count3	-0.04656	0.03761	-1.238	4289	0.2158	-0.1521	0.05901
fixed	NA	sibling_count4	-0.01363	0.04054	-0.3363	3717	0.7367	-0.1274	0.1002
fixed	NA	sibling_count5	0.001808	0.04729	0.03824	3067	0.9695	-0.1309	0.1345
fixed	NA	sibling_count>5	-0.01265	0.04078	-0.3103	2754	0.7564	-0.1271	0.1018
ran_pars	mother_pidlink	sd__(Intercept)	0.1348	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9277	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)	0.9127	0.4325	2.111	5479	0.03486	-0.3012	2.127
fixed	NA	birth_order	0.000456	0.008519	0.05353	5095	0.9573	-0.02346	0.02437
fixed	NA	poly(age, 3, raw = TRUE)1	-0.07302	0.04901	-1.49	5471	0.1363	-0.2106	0.06455
fixed	NA	poly(age, 3, raw = TRUE)2	0.00218	0.001747	1.248	5458	0.212	-0.002723	0.007084
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00002019	0.00001976	-1.022	5439	0.3069	-0.00007567	0.00003528
fixed	NA	male	-0.2238	0.02536	-8.827	5482	1.422e-18	-0.295	-0.1527
fixed	NA	sibling_count3	-0.04678	0.03784	-1.236	4284	0.2164	-0.153	0.05943
fixed	NA	sibling_count4	-0.01414	0.04163	-0.3396	3716	0.7342	-0.131	0.1027
fixed	NA	sibling_count5	0.001006	0.04962	0.02027	3118	0.9838	-0.1383	0.1403
fixed	NA	sibling_count>5	-0.01433	0.05143	-0.2786	3317	0.7806	-0.1587	0.13
ran_pars	mother_pidlink	sd__(Intercept)	0.1351	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9278	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)	0.8882	0.433	2.051	5473	0.04029	-0.3272	2.104
fixed	NA	poly(age, 3, raw = TRUE)1	-0.07193	0.04904	-1.467	5466	0.1425	-0.2096	0.06572
fixed	NA	poly(age, 3, raw = TRUE)2	0.002137	0.001748	1.222	5453	0.2216	-0.00277	0.007043
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001967	0.00001978	-0.9946	5434	0.32	-0.00007519	0.00003584
fixed	NA	male	-0.2233	0.02537	-8.805	5478	1.733e-18	-0.2945	-0.1521
fixed	NA	sibling_count3	-0.0543	0.03876	-1.401	4466	0.1613	-0.1631	0.05451
fixed	NA	sibling_count4	-0.02342	0.04356	-0.5376	4064	0.5909	-0.1457	0.09886
fixed	NA	sibling_count5	-0.001756	0.05226	-0.0336	3536	0.9732	-0.1485	0.1449
fixed	NA	sibling_count>5	-0.016	0.05321	-0.3006	3640	0.7637	-0.1654	0.1334
fixed	NA	birth_order_nonlinear2	0.04845	0.03294	1.471	4775	0.1414	-0.04401	0.1409
fixed	NA	birth_order_nonlinear3	0.03917	0.04067	0.9632	5008	0.3355	-0.07498	0.1533
fixed	NA	birth_order_nonlinear4	0.02205	0.05151	0.428	5165	0.6687	-0.1226	0.1666
fixed	NA	birth_order_nonlinear5	-0.004136	0.06549	-0.06317	5179	0.9496	-0.188	0.1797
fixed	NA	birth_order_nonlinear>5	0.02085	0.06395	0.3261	5437	0.7444	-0.1586	0.2004
ran_pars	mother_pidlink	sd__(Intercept)	0.1348	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9279	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)	0.831	0.4338	1.915	5463	0.0555	-0.3869	2.049
fixed	NA	poly(age, 3, raw = TRUE)1	-0.06428	0.04913	-1.308	5456	0.1909	-0.2022	0.07365
fixed	NA	poly(age, 3, raw = TRUE)2	0.001883	0.001752	1.075	5443	0.2825	-0.003034	0.0068
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001703	0.00001982	-0.8592	5423	0.3903	-0.00007268	0.00003861
fixed	NA	male	-0.2212	0.02538	-8.718	5468	3.705e-18	-0.2925	-0.15
fixed	NA	count_birth_order2/2	0.005957	0.0577	0.1032	4832	0.9178	-0.156	0.1679
fixed	NA	count_birth_order1/3	-0.1323	0.0509	-2.599	5466	0.009377	-0.2752	0.01059
fixed	NA	count_birth_order2/3	0.01953	0.0563	0.3468	5468	0.7287	-0.1385	0.1775
fixed	NA	count_birth_order3/3	0.03569	0.06196	0.576	5467	0.5646	-0.1382	0.2096
fixed	NA	count_birth_order1/4	0.02198	0.06356	0.3458	5466	0.7295	-0.1564	0.2004
fixed	NA	count_birth_order2/4	-0.01268	0.06554	-0.1935	5468	0.8466	-0.1967	0.1713
fixed	NA	count_birth_order3/4	-0.0643	0.06839	-0.9402	5467	0.3472	-0.2563	0.1277
fixed	NA	count_birth_order4/4	0.001813	0.07231	0.02506	5466	0.98	-0.2012	0.2048
fixed	NA	count_birth_order1/5	0.08837	0.08671	1.019	5467	0.3082	-0.155	0.3318
fixed	NA	count_birth_order2/5	-0.07422	0.0942	-0.7878	5468	0.4308	-0.3386	0.1902
fixed	NA	count_birth_order3/5	0.06378	0.08976	0.7106	5467	0.4774	-0.1882	0.3157
fixed	NA	count_birth_order4/5	-0.01829	0.08662	-0.2112	5467	0.8327	-0.2614	0.2248
fixed	NA	count_birth_order5/5	-0.06024	0.09297	-0.6479	5465	0.5171	-0.3212	0.2007
fixed	NA	count_birth_order1/>5	-0.07076	0.08852	-0.7993	5458	0.4241	-0.3192	0.1777
fixed	NA	count_birth_order2/>5	0.09919	0.08581	1.156	5461	0.2478	-0.1417	0.3401
fixed	NA	count_birth_order3/>5	-0.06262	0.08586	-0.7294	5468	0.4658	-0.3036	0.1784
fixed	NA	count_birth_order4/>5	-0.01431	0.08371	-0.1709	5468	0.8643	-0.2493	0.2207
fixed	NA	count_birth_order5/>5	-0.01093	0.07712	-0.1418	5468	0.8872	-0.2274	0.2055
fixed	NA	count_birth_order>5/>5	-0.01065	0.05681	-0.1875	4727	0.8513	-0.1701	0.1488
ran_pars	mother_pidlink	sd__(Intercept)	0.1365	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9273	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)
11	14888	14961	-7433	14866	NA	NA	NA
12	14890	14970	-7433	14866	0.002696	1	0.9586
16	14896	15001	-7432	14864	2.661	4	0.6161
26	14901	15073	-7424	14849	14.83	10	0.1385

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)	-2.688	0.1288	-20.87	13921	2.79e-95	-3.05	-2.327
fixed	NA	poly(age, 3, raw = TRUE)1	0.2633	0.01224	21.51	13740	5.722e-101	0.2289	0.2977
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006974	0.0003591	-19.42	13831	6.417e-83	-0.007982	-0.005966
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005177	0.000003294	15.71	13961	3.555e-55	0.00004252	0.00006102
fixed	NA	male	-0.02813	0.013	-2.163	11845	0.03054	-0.06464	0.008371
fixed	NA	sibling_count3	0.07051	0.03368	2.093	8872	0.03634	-0.02403	0.1651
fixed	NA	sibling_count4	0.0338	0.03529	0.9576	8520	0.3383	-0.06527	0.1329
fixed	NA	sibling_count5	0.02754	0.0374	0.7364	8186	0.4615	-0.07745	0.1325
fixed	NA	sibling_count>5	-0.2199	0.02876	-7.648	8601	2.267e-14	-0.3007	-0.1392
ran_pars	mother_pidlink	sd__(Intercept)	0.6782	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6413	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)	-2.696	0.1288	-20.93	13940	8.407e-96	-3.058	-2.335
fixed	NA	birth_order	0.006501	0.002997	2.169	14329	0.03007	-0.001911	0.01491
fixed	NA	poly(age, 3, raw = TRUE)1	0.2614	0.01227	21.3	13729	4.864e-99	0.2269	0.2958
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006884	0.0003615	-19.04	13901	7.772e-80	-0.007898	-0.005869
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005089	0.00000332	15.33	14047	1.298e-52	0.00004157	0.00006021
fixed	NA	male	-0.0283	0.013	-2.177	11831	0.02948	-0.06479	0.008187
fixed	NA	sibling_count3	0.07026	0.0337	2.085	8864	0.03708	-0.02433	0.1649
fixed	NA	sibling_count4	0.0308	0.03534	0.8716	8552	0.3835	-0.0684	0.13
fixed	NA	sibling_count5	0.02083	0.03755	0.5546	8274	0.5792	-0.08457	0.1262
fixed	NA	sibling_count>5	-0.2435	0.03076	-7.917	9687	2.696e-15	-0.3298	-0.1572
ran_pars	mother_pidlink	sd__(Intercept)	0.6792	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6407	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)	-2.665	0.1291	-20.64	13948	3.079e-93	-3.027	-2.302
fixed	NA	poly(age, 3, raw = TRUE)1	0.2613	0.01227	21.31	13731	3.994e-99	0.2269	0.2958
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006871	0.0003613	-19.02	13893	1.177e-79	-0.007885	-0.005857
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005046	0.000003321	15.2	14054	9.485e-52	0.00004114	0.00005979
fixed	NA	male	-0.02841	0.01299	-2.188	11817	0.02869	-0.06486	0.008038
fixed	NA	sibling_count3	0.08287	0.03392	2.443	9053	0.01458	-0.01234	0.1781
fixed	NA	sibling_count4	0.05735	0.0358	1.602	8918	0.1092	-0.04315	0.1579
fixed	NA	sibling_count5	0.05175	0.03825	1.353	8753	0.1761	-0.05563	0.1591
fixed	NA	sibling_count>5	-0.2166	0.03162	-6.85	10296	7.805e-12	-0.3054	-0.1278
fixed	NA	birth_order_nonlinear2	-0.04969	0.01841	-2.698	11706	0.006979	-0.1014	0.002002
fixed	NA	birth_order_nonlinear3	-0.07061	0.02142	-3.296	11239	0.000984	-0.1308	-0.01047
fixed	NA	birth_order_nonlinear4	-0.08076	0.02452	-3.293	11322	0.0009945	-0.1496	-0.01192
fixed	NA	birth_order_nonlinear5	-0.02921	0.02787	-1.048	11274	0.2946	-0.1074	0.04902
fixed	NA	birth_order_nonlinear>5	0.0102	0.02471	0.4128	13717	0.6797	-0.05916	0.07956
ran_pars	mother_pidlink	sd__(Intercept)	0.6799	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6398	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	0.1297	-20.47	13969	8.124e-92	-3.019	-2.291
fixed	NA	poly(age, 3, raw = TRUE)1	0.261	0.01227	21.27	13739	8.457e-99	0.2266	0.2955
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006856	0.0003615	-18.96	13907	3.426e-79	-0.007871	-0.005841
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005029	0.000003325	15.12	14075	2.806e-51	0.00004096	0.00005963
fixed	NA	male	-0.02811	0.01299	-2.165	11808	0.03043	-0.06457	0.008342
fixed	NA	count_birth_order2/2	-0.07379	0.03615	-2.041	12452	0.04125	-0.1753	0.02768
fixed	NA	count_birth_order1/3	0.07773	0.03991	1.948	12462	0.05148	-0.0343	0.1898
fixed	NA	count_birth_order2/3	0.01959	0.04385	0.4469	13398	0.655	-0.1035	0.1427
fixed	NA	count_birth_order3/3	0.004158	0.04807	0.08651	14043	0.9311	-0.1308	0.1391
fixed	NA	count_birth_order1/4	0.03963	0.04447	0.8911	13169	0.3729	-0.0852	0.1645
fixed	NA	count_birth_order2/4	-0.01847	0.04706	-0.3925	13682	0.6947	-0.1506	0.1136
fixed	NA	count_birth_order3/4	-0.003081	0.0501	-0.0615	14157	0.951	-0.1437	0.1376
fixed	NA	count_birth_order4/4	-0.006753	0.05219	-0.1294	14271	0.8971	-0.1533	0.1398
fixed	NA	count_birth_order1/5	0.03106	0.05016	0.6191	13791	0.5359	-0.1098	0.1719
fixed	NA	count_birth_order2/5	0.004568	0.05248	0.08705	14111	0.9306	-0.1427	0.1519
fixed	NA	count_birth_order3/5	-0.09389	0.05304	-1.77	14194	0.07675	-0.2428	0.05501
fixed	NA	count_birth_order4/5	-0.04342	0.05613	-0.7736	14397	0.4392	-0.201	0.1141
fixed	NA	count_birth_order5/5	0.1147	0.0571	2.008	14418	0.04461	-0.0456	0.275
fixed	NA	count_birth_order1/>5	-0.2286	0.0397	-5.758	14136	0.000000008705	-0.34	-0.1171
fixed	NA	count_birth_order2/>5	-0.2492	0.04077	-6.112	14318	0.000000001011	-0.3637	-0.1347
fixed	NA	count_birth_order3/>5	-0.2759	0.03996	-6.904	14268	5.255e-12	-0.388	-0.1637
fixed	NA	count_birth_order4/>5	-0.3126	0.03947	-7.919	14200	2.578e-15	-0.4234	-0.2018
fixed	NA	count_birth_order5/>5	-0.2873	0.03954	-7.266	14231	3.898e-13	-0.3983	-0.1763
fixed	NA	count_birth_order>5/>5	-0.2149	0.03384	-6.349	11606	0.0000000002245	-0.3099	-0.1199
ran_pars	mother_pidlink	sd__(Intercept)	0.6799	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.6397	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)
11	36298	36381	-18138	36276	NA	NA	NA
12	36295	36386	-18136	36271	4.685	1	0.03043
16	36281	36402	-18125	36249	22.33	4	0.0001724
26	36288	36485	-18118	36236	13.46	10	0.1991

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)	-6.736	0.309	-21.8	5587	3.473e-101	-7.603	-5.869
fixed	NA	poly(age, 3, raw = TRUE)1	0.7187	0.03506	20.5	5537	4.764e-90	0.6203	0.8171
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02238	0.001252	-17.87	5503	1.784e-69	-0.0259	-0.01886
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002241	0.0000142	15.78	5486	6.934e-55	0.0001843	0.000264
fixed	NA	male	-0.07737	0.0178	-4.347	5339	0.00001407	-0.1273	-0.02741
fixed	NA	sibling_count3	0.01365	0.03226	0.423	4384	0.6723	-0.07692	0.1042
fixed	NA	sibling_count4	-0.08132	0.03529	-2.304	4151	0.02126	-0.1804	0.01775
fixed	NA	sibling_count5	-0.1649	0.04105	-4.017	4003	0.0000599	-0.2802	-0.04969
fixed	NA	sibling_count>5	-0.3901	0.03602	-10.83	3979	5.93e-27	-0.4912	-0.289
ran_pars	mother_pidlink	sd__(Intercept)	0.5155	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5677	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)	-6.749	0.3088	-21.86	5584	1.094e-101	-7.616	-5.882
fixed	NA	birth_order	0.01624	0.006102	2.662	5956	0.007783	-0.0008834	0.03337
fixed	NA	poly(age, 3, raw = TRUE)1	0.7172	0.03504	20.47	5534	8.325e-90	0.6188	0.8155
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02234	0.001251	-17.85	5501	2.566e-69	-0.02585	-0.01882
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002243	0.00001419	15.81	5480	4.538e-55	0.0001845	0.0002642
fixed	NA	male	-0.07822	0.01779	-4.398	5334	0.00001114	-0.1281	-0.0283
fixed	NA	sibling_count3	0.004941	0.03243	0.1524	4398	0.8789	-0.0861	0.09598
fixed	NA	sibling_count4	-0.1021	0.03616	-2.824	4189	0.004758	-0.2036	-0.0006304
fixed	NA	sibling_count5	-0.198	0.04291	-4.615	4127	0.000004046	-0.3185	-0.07759
fixed	NA	sibling_count>5	-0.4559	0.04371	-10.43	4521	3.489e-25	-0.5786	-0.3332
ran_pars	mother_pidlink	sd__(Intercept)	0.5166	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5667	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)	-6.665	0.3096	-21.53	5634	7.32e-99	-7.533	-5.796
fixed	NA	poly(age, 3, raw = TRUE)1	0.712	0.03506	20.31	5568	1.623e-88	0.6136	0.8105
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02217	0.001252	-17.71	5526	2.665e-68	-0.02568	-0.01865
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002228	0.00001419	15.69	5497	2.469e-54	0.0001829	0.0002626
fixed	NA	male	-0.07857	0.01776	-4.425	5329	0.000009827	-0.1284	-0.02873
fixed	NA	sibling_count3	0.005269	0.03283	0.1605	4535	0.8725	-0.0869	0.09743
fixed	NA	sibling_count4	-0.1132	0.03708	-3.054	4416	0.002272	-0.2173	-0.009156
fixed	NA	sibling_count5	-0.2355	0.04429	-5.317	4415	0.0000001104	-0.3598	-0.1112
fixed	NA	sibling_count>5	-0.4792	0.04459	-10.74	4663	1.282e-26	-0.6043	-0.354
fixed	NA	birth_order_nonlinear2	-0.05353	0.02201	-2.433	4629	0.01503	-0.1153	0.008243
fixed	NA	birth_order_nonlinear3	0.02796	0.02736	1.022	4813	0.307	-0.04886	0.1048
fixed	NA	birth_order_nonlinear4	0.0843	0.03424	2.462	5002	0.01385	-0.01182	0.1804
fixed	NA	birth_order_nonlinear5	0.1608	0.04246	3.786	4749	0.0001547	0.04158	0.2799
fixed	NA	birth_order_nonlinear>5	0.07327	0.04454	1.645	5665	0.1	-0.05175	0.1983
ran_pars	mother_pidlink	sd__(Intercept)	0.5157	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5657	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)	-6.676	0.3105	-21.5	5642	1.325e-98	-7.548	-5.804
fixed	NA	poly(age, 3, raw = TRUE)1	0.713	0.03516	20.28	5568	2.752e-88	0.6143	0.8117
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02222	0.001256	-17.69	5528	3.405e-68	-0.02574	-0.01869
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002235	0.00001424	15.69	5502	2.59e-54	0.0001835	0.0002634
fixed	NA	male	-0.07799	0.01778	-4.386	5320	0.00001175	-0.1279	-0.02808
fixed	NA	count_birth_order2/2	-0.03586	0.04032	-0.8893	5082	0.3739	-0.149	0.07733
fixed	NA	count_birth_order1/3	0.03154	0.03934	0.8017	5865	0.4228	-0.0789	0.142
fixed	NA	count_birth_order2/3	-0.06423	0.04233	-1.517	6060	0.1292	-0.183	0.05459
fixed	NA	count_birth_order3/3	0.02724	0.04677	0.5824	6126	0.5603	-0.1041	0.1585
fixed	NA	count_birth_order1/4	-0.1151	0.0475	-2.423	6050	0.01543	-0.2484	0.01825
fixed	NA	count_birth_order2/4	-0.1695	0.04852	-3.495	6118	0.0004782	-0.3057	-0.03336
fixed	NA	count_birth_order3/4	-0.0516	0.05091	-1.014	6126	0.3108	-0.1945	0.09131
fixed	NA	count_birth_order4/4	-0.03001	0.05286	-0.5676	6123	0.5703	-0.1784	0.1184
fixed	NA	count_birth_order1/5	-0.2277	0.06389	-3.564	6130	0.0003685	-0.407	-0.04834
fixed	NA	count_birth_order2/5	-0.2326	0.06767	-3.437	6029	0.0005926	-0.4225	-0.04262
fixed	NA	count_birth_order3/5	-0.2085	0.06323	-3.297	6079	0.0009821	-0.386	-0.03099
fixed	NA	count_birth_order4/5	-0.1802	0.06188	-2.912	6108	0.003603	-0.3539	-0.006502
fixed	NA	count_birth_order5/5	-0.06835	0.06392	-1.069	6073	0.285	-0.2478	0.1111
fixed	NA	count_birth_order1/>5	-0.5118	0.06239	-8.204	6045	2.818e-16	-0.6869	-0.3367
fixed	NA	count_birth_order2/>5	-0.5145	0.06185	-8.319	6010	1.09e-16	-0.6881	-0.3409
fixed	NA	count_birth_order3/>5	-0.4626	0.0607	-7.622	5958	2.895e-14	-0.633	-0.2922
fixed	NA	count_birth_order4/>5	-0.351	0.05758	-6.095	5998	0.000000001159	-0.5126	-0.1893
fixed	NA	count_birth_order5/>5	-0.3139	0.05473	-5.734	6037	0.00000001026	-0.4675	-0.1602
fixed	NA	count_birth_order>5/>5	-0.3993	0.04395	-9.085	5818	1.393e-19	-0.5227	-0.2759
ran_pars	mother_pidlink	sd__(Intercept)	0.5154	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5662	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)
11	13603	13677	-6790	13581	NA	NA	NA
12	13598	13678	-6787	13574	7.074	1	0.007821
16	13581	13688	-6774	13549	24.75	4	0.00005645
26	13596	13771	-6772	13544	4.93	10	0.8958

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)	-6.746	0.3083	-21.88	5626	6.385e-102	-7.612	-5.881
fixed	NA	poly(age, 3, raw = TRUE)1	0.7193	0.035	20.55	5570	1.483e-90	0.6211	0.8176
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02245	0.00125	-17.96	5534	3.827e-70	-0.02596	-0.01894
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002249	0.00001418	15.85	5516	2.161e-55	0.000185	0.0002647
fixed	NA	male	-0.07773	0.01774	-4.381	5374	0.00001204	-0.1275	-0.02793
fixed	NA	sibling_count3	0.0339	0.03494	0.9704	4519	0.3319	-0.06417	0.132
fixed	NA	sibling_count4	-0.03127	0.03721	-0.8404	4323	0.4007	-0.1357	0.07318
fixed	NA	sibling_count5	-0.08928	0.04042	-2.209	4164	0.02724	-0.2027	0.02418
fixed	NA	sibling_count>5	-0.2673	0.03522	-7.589	4304	3.939e-14	-0.3662	-0.1684
ran_pars	mother_pidlink	sd__(Intercept)	0.5206	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5663	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)	-6.75	0.3084	-21.89	5623	5.425e-102	-7.615	-5.884
fixed	NA	birth_order	0.003115	0.005405	0.5763	6116	0.5644	-0.01206	0.01829
fixed	NA	poly(age, 3, raw = TRUE)1	0.7191	0.035	20.55	5567	1.658e-90	0.6209	0.8174
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02245	0.00125	-17.96	5531	4.071e-70	-0.02596	-0.01894
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002249	0.00001418	15.86	5510	1.976e-55	0.0001851	0.0002647
fixed	NA	male	-0.07789	0.01774	-4.39	5370	0.00001157	-0.1277	-0.02808
fixed	NA	sibling_count3	0.03222	0.03507	0.9189	4519	0.3582	-0.06621	0.1307
fixed	NA	sibling_count4	-0.03509	0.0378	-0.9283	4329	0.3533	-0.1412	0.07102
fixed	NA	sibling_count5	-0.09522	0.04172	-2.282	4209	0.02253	-0.2123	0.0219
fixed	NA	sibling_count>5	-0.2794	0.04103	-6.809	4662	0.00000000001107	-0.3946	-0.1642
ran_pars	mother_pidlink	sd__(Intercept)	0.521	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5661	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)	-6.671	0.3092	-21.57	5670	2.942e-99	-7.539	-5.803
fixed	NA	poly(age, 3, raw = TRUE)1	0.7127	0.03503	20.34	5600	7.838e-89	0.6144	0.8111
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02222	0.001251	-17.76	5557	1.068e-68	-0.02573	-0.01871
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002226	0.00001419	15.68	5529	2.803e-54	0.0001828	0.0002624
fixed	NA	male	-0.07837	0.01773	-4.421	5366	0.00001003	-0.1281	-0.02861
fixed	NA	sibling_count3	0.03597	0.03548	1.014	4641	0.3107	-0.06361	0.1356
fixed	NA	sibling_count4	-0.03978	0.0387	-1.028	4536	0.304	-0.1484	0.06884
fixed	NA	sibling_count5	-0.1169	0.04304	-2.716	4476	0.006635	-0.2377	0.003922
fixed	NA	sibling_count>5	-0.2918	0.04193	-6.96	4804	3.865e-12	-0.4095	-0.1741
fixed	NA	birth_order_nonlinear2	-0.05895	0.02256	-2.613	4743	0.008999	-0.1223	0.004373
fixed	NA	birth_order_nonlinear3	-0.01423	0.0274	-0.5195	4898	0.6034	-0.09113	0.06267
fixed	NA	birth_order_nonlinear4	0.03769	0.03338	1.129	5125	0.2589	-0.05601	0.1314
fixed	NA	birth_order_nonlinear5	0.0732	0.04067	1.8	4937	0.07195	-0.04096	0.1874
fixed	NA	birth_order_nonlinear>5	-0.01079	0.04033	-0.2675	5891	0.7891	-0.124	0.1024
ran_pars	mother_pidlink	sd__(Intercept)	0.5208	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5654	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)	-6.652	0.3102	-21.44	5684	3.797e-98	-7.523	-5.781
fixed	NA	poly(age, 3, raw = TRUE)1	0.7099	0.03512	20.22	5604	8.757e-88	0.6114	0.8085
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02212	0.001255	-17.63	5564	9.955e-68	-0.02564	-0.01859
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002213	0.00001423	15.55	5538	2.102e-53	0.0001814	0.0002613
fixed	NA	male	-0.07904	0.01775	-4.453	5361	0.000008631	-0.1289	-0.02922
fixed	NA	count_birth_order2/2	-0.04672	0.0446	-1.048	5245	0.2949	-0.1719	0.07847
fixed	NA	count_birth_order1/3	0.05622	0.04275	1.315	5928	0.1886	-0.06378	0.1762
fixed	NA	count_birth_order2/3	-0.05503	0.04603	-1.196	6113	0.2319	-0.1842	0.07417
fixed	NA	count_birth_order3/3	0.04289	0.05079	0.8444	6182	0.3985	-0.09968	0.1855
fixed	NA	count_birth_order1/4	-0.07165	0.04984	-1.438	6098	0.1506	-0.2115	0.06824
fixed	NA	count_birth_order2/4	-0.05084	0.05034	-1.01	6159	0.3125	-0.1921	0.09046
fixed	NA	count_birth_order3/4	-0.06351	0.0545	-1.165	6177	0.2439	-0.2165	0.08946
fixed	NA	count_birth_order4/4	0.009664	0.0564	0.1713	6178	0.864	-0.1487	0.168
fixed	NA	count_birth_order1/5	-0.1223	0.05889	-2.077	6177	0.03787	-0.2876	0.04301
fixed	NA	count_birth_order2/5	-0.1555	0.06209	-2.504	6151	0.0123	-0.3298	0.01881
fixed	NA	count_birth_order3/5	-0.1429	0.06084	-2.349	6157	0.01888	-0.3137	0.02789
fixed	NA	count_birth_order4/5	-0.09629	0.06301	-1.528	6126	0.1265	-0.2732	0.08058
fixed	NA	count_birth_order5/5	-0.007981	0.06277	-0.1271	6133	0.8988	-0.1842	0.1682
fixed	NA	count_birth_order1/>5	-0.2597	0.05562	-4.669	6186	0.000003092	-0.4158	-0.1036
fixed	NA	count_birth_order2/>5	-0.3699	0.05726	-6.461	6112	0.0000000001124	-0.5307	-0.2092
fixed	NA	count_birth_order3/>5	-0.2976	0.05583	-5.33	6101	0.0000001018	-0.4543	-0.1408
fixed	NA	count_birth_order4/>5	-0.2436	0.05381	-4.526	6131	0.000006113	-0.3946	-0.09252
fixed	NA	count_birth_order5/>5	-0.2379	0.05508	-4.318	6043	0.00001598	-0.3925	-0.08324
fixed	NA	count_birth_order>5/>5	-0.2999	0.04319	-6.943	5904	4.247e-12	-0.4211	-0.1786
ran_pars	mother_pidlink	sd__(Intercept)	0.52	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5661	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)
11	13753	13827	-6866	13731	NA	NA	NA
12	13755	13836	-6865	13731	0.3298	1	0.5658
16	13747	13855	-6857	13715	16.17	4	0.002799
26	13760	13935	-6854	13708	6.573	10	0.765

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)	-6.758	0.313	-21.59	5471	2.78e-99	-7.636	-5.879
fixed	NA	poly(age, 3, raw = TRUE)1	0.7212	0.03553	20.3	5420	2.406e-88	0.6215	0.8209
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02248	0.001269	-17.72	5381	2.687e-68	-0.02605	-0.01892
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002253	0.0000144	15.65	5360	5.372e-54	0.0001849	0.0002658
fixed	NA	male	-0.07967	0.018	-4.426	5233	0.000009789	-0.1302	-0.02914
fixed	NA	sibling_count3	0.007354	0.03188	0.2306	4375	0.8176	-0.08215	0.09685
fixed	NA	sibling_count4	-0.06524	0.03511	-1.858	4170	0.0632	-0.1638	0.03331
fixed	NA	sibling_count5	-0.1584	0.04224	-3.75	3939	0.000179	-0.277	-0.03986
fixed	NA	sibling_count>5	-0.3751	0.03659	-10.25	3915	2.328e-24	-0.4778	-0.2724
ran_pars	mother_pidlink	sd__(Intercept)	0.5174	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.568	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)	-6.769	0.3128	-21.64	5468	1.04e-99	-7.647	-5.891
fixed	NA	birth_order	0.01578	0.006262	2.52	5789	0.01177	-0.001798	0.03336
fixed	NA	poly(age, 3, raw = TRUE)1	0.7196	0.03551	20.26	5418	4.494e-88	0.62	0.8193
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02244	0.001268	-17.69	5380	3.945e-68	-0.026	-0.01888
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002255	0.00001439	15.67	5355	3.656e-54	0.0001852	0.0002659
fixed	NA	male	-0.08017	0.01799	-4.457	5229	0.000008468	-0.1307	-0.02969
fixed	NA	sibling_count3	-0.001263	0.03207	-0.03938	4387	0.9686	-0.09128	0.08876
fixed	NA	sibling_count4	-0.08503	0.03598	-2.363	4216	0.01815	-0.186	0.01596
fixed	NA	sibling_count5	-0.1895	0.04401	-4.305	4050	0.00001708	-0.313	-0.06594
fixed	NA	sibling_count>5	-0.4382	0.04436	-9.88	4498	8.654e-23	-0.5628	-0.3137
ran_pars	mother_pidlink	sd__(Intercept)	0.5182	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5672	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)	-6.674	0.3137	-21.28	5520	1.223e-96	-7.555	-5.794
fixed	NA	poly(age, 3, raw = TRUE)1	0.7136	0.03554	20.08	5452	1.376e-86	0.6138	0.8134
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02225	0.001269	-17.53	5405	5.569e-67	-0.02581	-0.01868
fixed	NA	poly(age, 3, raw = TRUE)3	0.0002238	0.00001439	15.55	5372	2.431e-53	0.0001834	0.0002642
fixed	NA	male	-0.08054	0.01796	-4.484	5223	0.000007469	-0.131	-0.03012
fixed	NA	sibling_count3	0.00008121	0.03249	0.002499	4521	0.998	-0.09113	0.09129
fixed	NA	sibling_count4	-0.09508	0.03694	-2.574	4436	0.01008	-0.1988	0.008603
fixed	NA	sibling_count5	-0.2215	0.04531	-4.888	4307	0.000001055	-0.3486	-0.09428
fixed	NA	sibling_count>5	-0.4607	0.04527	-10.18	4652	4.53e-24	-0.5878	-0.3336
fixed	NA	birth_order_nonlinear2	-0.05633	0.02197	-2.563	4526	0.0104	-0.118	0.005353
fixed	NA	birth_order_nonlinear3	0.01674	0.0274	0.611	4708	0.5412	-0.06017	0.09365
fixed	NA	birth_order_nonlinear4	0.08775	0.03516	2.496	4842	0.0126	-0.01094	0.1864
fixed	NA	birth_order_nonlinear5	0.1372	0.04421	3.105	4611	0.001917	0.01315	0.2613
fixed	NA	birth_order_nonlinear>5	0.07675	0.04577	1.677	5462	0.09364	-0.05173	0.2052
ran_pars	mother_pidlink	sd__(Intercept)	0.5176	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5664	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)	-6.684	0.3148	-21.24	5529	2.889e-96	-7.568	-5.801
fixed	NA	poly(age, 3, raw = TRUE)1	0.7138	0.03565	20.02	5456	4.073e-86	0.6137	0.8139
fixed	NA	poly(age, 3, raw = TRUE)2	-0.02226	0.001273	-17.48	5412	1.261e-66	-0.02584	-0.01869
fixed	NA	poly(age, 3, raw = TRUE)3	0.000224	0.00001445	15.5	5382	4.495e-53	0.0001835	0.0002646
fixed	NA	male	-0.07992	0.01799	-4.444	5212	0.000009023	-0.1304	-0.02944
fixed	NA	count_birth_order2/2	-0.02734	0.03915	-0.6983	4900	0.4851	-0.1372	0.08256
fixed	NA	count_birth_order1/3	0.03303	0.03893	0.8485	5773	0.3962	-0.07625	0.1423
fixed	NA	count_birth_order2/3	-0.06894	0.04228	-1.63	5973	0.1031	-0.1876	0.04975
fixed	NA	count_birth_order3/3	0.008928	0.04599	0.1941	6010	0.8461	-0.1202	0.138
fixed	NA	count_birth_order1/4	-0.09519	0.04764	-1.998	5963	0.04577	-0.2289	0.03855
fixed	NA	count_birth_order2/4	-0.1545	0.04852	-3.184	6008	0.001461	-0.2907	-0.01828
fixed	NA	count_birth_order3/4	-0.0412	0.05053	-0.8153	5999	0.415	-0.183	0.1006
fixed	NA	count_birth_order4/4	0.003472	0.05308	0.06542	5983	0.9478	-0.1455	0.1525
fixed	NA	count_birth_order1/5	-0.2173	0.06431	-3.379	6011	0.0007323	-0.3978	-0.03678
fixed	NA	count_birth_order2/5	-0.2431	0.06969	-3.489	5887	0.0004888	-0.4388	-0.04751
fixed	NA	count_birth_order3/5	-0.1786	0.06617	-2.699	5938	0.006983	-0.3643	0.007176
fixed	NA	count_birth_order4/5	-0.1625	0.06474	-2.509	5975	0.01212	-0.3442	0.01927
fixed	NA	count_birth_order5/5	-0.06279	0.06813	-0.9216	5918	0.3568	-0.254	0.1285
fixed	NA	count_birth_order1/>5	-0.4742	0.06382	-7.43	5906	1.239e-13	-0.6534	-0.2951
fixed	NA	count_birth_order2/>5	-0.4845	0.06341	-7.64	5868	2.529e-14	-0.6625	-0.3065
fixed	NA	count_birth_order3/>5	-0.4592	0.06144	-7.474	5834	8.937e-14	-0.6316	-0.2867
fixed	NA	count_birth_order4/>5	-0.3303	0.06021	-5.486	5791	0.00000004288	-0.4993	-0.1613
fixed	NA	count_birth_order5/>5	-0.3212	0.05599	-5.737	5896	0.00000001014	-0.4784	-0.164
fixed	NA	count_birth_order>5/>5	-0.3735	0.04488	-8.322	5726	1.074e-16	-0.4995	-0.2475
ran_pars	mother_pidlink	sd__(Intercept)	0.5172	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.5669	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)
11	13356	13430	-6667	13334	NA	NA	NA
12	13352	13432	-6664	13328	6.342	1	0.01179
16	13338	13446	-6653	13306	21.48	4	0.0002543
26	13353	13528	-6651	13301	4.93	10	0.8958

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)
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)	-0.0359	0.07117	-0.5044	7512	0.614	-0.2357	0.1639
fixed	NA	poly(age, 3, raw = TRUE)1	0.005098	0.008201	0.6217	7522	0.5342	-0.01792	0.02812
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001344	0.0002977	-0.4516	7530	0.6516	-0.0009701	0.0007012
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001175	0.00000341	0.3446	7535	0.7304	-0.000008396	0.00001075
fixed	NA	male	0.01183	0.004139	2.857	7537	0.004287	0.0002072	0.02344
fixed	NA	sibling_count3	-0.004516	0.007623	-0.5924	6593	0.5536	-0.02591	0.01688
fixed	NA	sibling_count4	0.002375	0.007854	0.3024	6299	0.7623	-0.01967	0.02442
fixed	NA	sibling_count5	0.0005693	0.008131	0.07002	5736	0.9442	-0.02225	0.02339
fixed	NA	sibling_count>5	0.01343	0.006512	2.062	6104	0.03929	-0.004854	0.0317
ran_pars	mother_pidlink	sd__(Intercept)	0.03164	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1769	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)	-0.03567	0.07116	-0.5013	7511	0.6162	-0.2354	0.1641
fixed	NA	birth_order	0.001618	0.000855	1.893	5735	0.05844	-0.0007817	0.004018
fixed	NA	poly(age, 3, raw = TRUE)1	0.004764	0.008202	0.5809	7522	0.5613	-0.01826	0.02779
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001223	0.0002977	-0.4107	7530	0.6813	-0.000958	0.0007134
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001066	0.00000341	0.3126	7535	0.7546	-0.000008505	0.00001064
fixed	NA	male	0.01187	0.004138	2.869	7536	0.00413	0.0002562	0.02349
fixed	NA	sibling_count3	-0.005119	0.007628	-0.6711	6594	0.5022	-0.02653	0.01629
fixed	NA	sibling_count4	0.0008348	0.007895	0.1057	6293	0.9158	-0.02133	0.023
fixed	NA	sibling_count5	-0.001974	0.008239	-0.2396	5702	0.8107	-0.0251	0.02115
fixed	NA	sibling_count>5	0.005909	0.007626	0.7748	5985	0.4385	-0.0155	0.02732
ran_pars	mother_pidlink	sd__(Intercept)	0.03155	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1769	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)	-0.03677	0.07132	-0.5155	7517	0.6062	-0.237	0.1634
fixed	NA	poly(age, 3, raw = TRUE)1	0.005009	0.008207	0.6103	7523	0.5417	-0.01803	0.02805
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001286	0.000298	-0.4316	7530	0.6661	-0.000965	0.0007078
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000011	0.000003412	0.3224	7533	0.7471	-0.000008478	0.00001068
fixed	NA	male	0.01198	0.00414	2.893	7532	0.003828	0.0003554	0.0236
fixed	NA	sibling_count3	-0.004969	0.007769	-0.6396	6710	0.5225	-0.02678	0.01684
fixed	NA	sibling_count4	0.004068	0.008262	0.4924	6577	0.6225	-0.01912	0.02726
fixed	NA	sibling_count5	0.001791	0.008784	0.2039	6146	0.8385	-0.02287	0.02645
fixed	NA	sibling_count>5	0.009914	0.008273	1.198	6603	0.2309	-0.01331	0.03314
fixed	NA	birth_order_nonlinear2	0.002091	0.006096	0.3431	7040	0.7316	-0.01502	0.0192
fixed	NA	birth_order_nonlinear3	0.002502	0.007308	0.3424	7206	0.732	-0.01801	0.02302
fixed	NA	birth_order_nonlinear4	-0.01034	0.008412	-1.229	7298	0.2192	-0.03395	0.01328
fixed	NA	birth_order_nonlinear5	0.001859	0.009411	0.1975	7399	0.8434	-0.02456	0.02828
fixed	NA	birth_order_nonlinear>5	0.009152	0.007986	1.146	7375	0.2518	-0.01327	0.03157
ran_pars	mother_pidlink	sd__(Intercept)	0.03137	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1769	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)	-0.04214	0.07141	-0.5902	7507	0.5551	-0.2426	0.1583
fixed	NA	poly(age, 3, raw = TRUE)1	0.005408	0.008208	0.6588	7513	0.51	-0.01763	0.02845
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001434	0.000298	-0.4811	7520	0.6305	-0.0009798	0.0006931
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001267	0.000003413	0.3713	7523	0.7104	-0.000008313	0.00001085
fixed	NA	male	0.01215	0.00414	2.935	7522	0.003347	0.0005293	0.02377
fixed	NA	count_birth_order2/2	0.007844	0.0116	0.6762	7052	0.4989	-0.02472	0.0404
fixed	NA	count_birth_order1/3	0.001005	0.01024	0.09822	7525	0.9218	-0.02773	0.02974
fixed	NA	count_birth_order2/3	-0.003272	0.01139	-0.2873	7527	0.7739	-0.03524	0.0287
fixed	NA	count_birth_order3/3	-0.005575	0.01312	-0.425	7527	0.6709	-0.0424	0.03125
fixed	NA	count_birth_order1/4	0.006385	0.01209	0.5281	7527	0.5974	-0.02755	0.04032
fixed	NA	count_birth_order2/4	0.01971	0.01252	1.574	7527	0.1155	-0.01544	0.05486
fixed	NA	count_birth_order3/4	-0.01251	0.01353	-0.9247	7527	0.3552	-0.05049	0.02547
fixed	NA	count_birth_order4/4	0.002527	0.01402	0.1803	7527	0.8569	-0.03682	0.04188
fixed	NA	count_birth_order1/5	-0.008057	0.01393	-0.5784	7527	0.563	-0.04716	0.03105
fixed	NA	count_birth_order2/5	0.008299	0.01493	0.5557	7526	0.5784	-0.03362	0.05022
fixed	NA	count_birth_order3/5	0.01165	0.01465	0.795	7526	0.4266	-0.02948	0.05278
fixed	NA	count_birth_order4/5	0.004803	0.01549	0.3101	7526	0.7565	-0.03868	0.04829
fixed	NA	count_birth_order5/5	0.001672	0.01482	0.1128	7526	0.9102	-0.03992	0.04327
fixed	NA	count_birth_order1/>5	0.01773	0.01285	1.38	7527	0.1677	-0.01834	0.0538
fixed	NA	count_birth_order2/>5	-0.001829	0.01301	-0.1406	7527	0.8882	-0.03835	0.03469
fixed	NA	count_birth_order3/>5	0.03193	0.01249	2.557	7527	0.01058	-0.003125	0.06698
fixed	NA	count_birth_order4/>5	-0.007931	0.01181	-0.6717	7526	0.5018	-0.04107	0.02521
fixed	NA	count_birth_order5/>5	0.0157	0.01134	1.385	7526	0.1662	-0.01613	0.04754
fixed	NA	count_birth_order>5/>5	0.02106	0.008272	2.546	7238	0.01092	-0.002161	0.04428
ran_pars	mother_pidlink	sd__(Intercept)	0.0319	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1768	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)
11	-4483	-4407	2252	-4505	NA	NA	NA
12	-4485	-4401	2254	-4509	3.587	1	0.05823
16	-4478	-4367	2255	-4510	1.743	4	0.7829
26	-4472	-4292	2262	-4524	13.98	10	0.1738

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)	-0.1442	0.1069	-1.349	3962	0.1776	-0.4443	0.156
fixed	NA	poly(age, 3, raw = TRUE)1	0.01976	0.01294	1.527	3962	0.1269	-0.01656	0.05608
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007469	0.0004952	-1.508	3962	0.1316	-0.002137	0.0006432
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009176	0.000005979	1.535	3962	0.1249	-0.000007608	0.00002596
fixed	NA	male	0.006646	0.005295	1.255	3962	0.2095	-0.008216	0.02151
fixed	NA	sibling_count3	-0.003274	0.007264	-0.4507	3962	0.6522	-0.02366	0.01712
fixed	NA	sibling_count4	-0.004942	0.008107	-0.6095	3962	0.5422	-0.0277	0.01782
fixed	NA	sibling_count5	0.002172	0.009593	0.2265	3962	0.8209	-0.02475	0.0291
fixed	NA	sibling_count>5	0.02326	0.00863	2.696	3962	0.007056	-0.0009618	0.04749
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1667	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)	-0.145	0.107	-1.355	3961	0.1754	-0.4454	0.1553
fixed	NA	birth_order	0.0004245	0.001896	0.2238	3961	0.8229	-0.004899	0.005748
fixed	NA	poly(age, 3, raw = TRUE)1	0.0198	0.01294	1.53	3961	0.1262	-0.01653	0.05612
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007491	0.0004954	-1.512	3961	0.1306	-0.00214	0.0006415
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009215	0.000005983	1.54	3961	0.1236	-0.000007578	0.00002601
fixed	NA	male	0.006655	0.005296	1.257	3961	0.2089	-0.00821	0.02152
fixed	NA	sibling_count3	-0.003473	0.007319	-0.4746	3961	0.6351	-0.02402	0.01707
fixed	NA	sibling_count4	-0.005406	0.008369	-0.6459	3961	0.5184	-0.0289	0.01809
fixed	NA	sibling_count5	0.001394	0.0102	0.1366	3961	0.8914	-0.02725	0.03004
fixed	NA	sibling_count>5	0.02152	0.01163	1.85	3961	0.0644	-0.01113	0.05417
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1667	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)	-0.1453	0.1071	-1.356	3957	0.175	-0.446	0.1554
fixed	NA	poly(age, 3, raw = TRUE)1	0.0198	0.01295	1.529	3957	0.1263	-0.01655	0.05615
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007478	0.0004957	-1.509	3957	0.1315	-0.002139	0.0006435
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009187	0.000005986	1.535	3957	0.125	-0.000007617	0.00002599
fixed	NA	male	0.006736	0.005298	1.271	3957	0.2037	-0.008136	0.02161
fixed	NA	sibling_count3	-0.003312	0.007538	-0.4394	3957	0.6604	-0.02447	0.01785
fixed	NA	sibling_count4	-0.000942	0.008859	-0.1063	3957	0.9153	-0.02581	0.02393
fixed	NA	sibling_count5	0.007974	0.01095	0.7286	3957	0.4663	-0.02275	0.0387
fixed	NA	sibling_count>5	0.02341	0.01232	1.9	3957	0.05752	-0.01118	0.058
fixed	NA	birth_order_nonlinear2	0.001382	0.006812	0.2029	3957	0.8392	-0.01774	0.0205
fixed	NA	birth_order_nonlinear3	0.0001446	0.008687	0.01664	3957	0.9867	-0.02424	0.02453
fixed	NA	birth_order_nonlinear4	-0.01699	0.01116	-1.523	3957	0.128	-0.04831	0.01433
fixed	NA	birth_order_nonlinear5	-0.007998	0.01468	-0.5448	3957	0.5859	-0.04921	0.03321
fixed	NA	birth_order_nonlinear>5	0.007723	0.01497	0.5159	3957	0.606	-0.0343	0.04975
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1667	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)	-0.143	0.1073	-1.332	3947	0.1828	-0.4442	0.1582
fixed	NA	poly(age, 3, raw = TRUE)1	0.0197	0.01297	1.519	3947	0.1289	-0.01671	0.05612
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007376	0.0004966	-1.485	3947	0.1375	-0.002132	0.0006564
fixed	NA	poly(age, 3, raw = TRUE)3	0.000008982	0.000005999	1.497	3947	0.1344	-0.000007858	0.00002582
fixed	NA	male	0.006549	0.005306	1.234	3947	0.2172	-0.008345	0.02144
fixed	NA	count_birth_order2/2	-0.006425	0.01127	-0.5701	3947	0.5686	-0.03806	0.02521
fixed	NA	count_birth_order1/3	-0.01274	0.009904	-1.286	3947	0.1985	-0.04054	0.01506
fixed	NA	count_birth_order2/3	0.001926	0.01084	0.1776	3947	0.859	-0.02852	0.03237
fixed	NA	count_birth_order3/3	-0.001935	0.01213	-0.1595	3947	0.8733	-0.036	0.03213
fixed	NA	count_birth_order1/4	-0.000406	0.01319	-0.03077	3947	0.9755	-0.03744	0.03663
fixed	NA	count_birth_order2/4	0.002909	0.01367	0.2127	3947	0.8315	-0.03548	0.04129
fixed	NA	count_birth_order3/4	-0.01698	0.0144	-1.179	3947	0.2386	-0.05741	0.02346
fixed	NA	count_birth_order4/4	-0.01695	0.01423	-1.19	3947	0.2339	-0.0569	0.02301
fixed	NA	count_birth_order1/5	0.005682	0.01916	0.2965	3947	0.7668	-0.04811	0.05947
fixed	NA	count_birth_order2/5	-0.001842	0.02077	-0.08868	3947	0.9293	-0.06015	0.05647
fixed	NA	count_birth_order3/5	0.004445	0.01888	0.2354	3947	0.8139	-0.04857	0.05746
fixed	NA	count_birth_order4/5	-0.0002872	0.01775	-0.01618	3947	0.9871	-0.05011	0.04954
fixed	NA	count_birth_order5/5	-0.007808	0.01825	-0.4279	3947	0.6687	-0.05902	0.04341
fixed	NA	count_birth_order1/>5	0.04048	0.02442	1.658	3947	0.09748	-0.02807	0.109
fixed	NA	count_birth_order2/>5	0.003233	0.02367	0.1366	3947	0.8913	-0.0632	0.06967
fixed	NA	count_birth_order3/>5	0.04167	0.02177	1.914	3947	0.05566	-0.01943	0.1028
fixed	NA	count_birth_order4/>5	-0.01883	0.0199	-0.9464	3947	0.344	-0.07469	0.03702
fixed	NA	count_birth_order5/>5	0.01747	0.01754	0.9955	3947	0.3195	-0.03178	0.06672
fixed	NA	count_birth_order>5/>5	0.02843	0.01179	2.412	3947	0.01592	-0.004659	0.06152
ran_pars	mother_pidlink	sd__(Intercept)	0.0000000083	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1668	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)
11	-2946	-2877	1484	-2968	NA	NA	NA
12	-2944	-2869	1484	-2968	0.05022	1	0.8227
16	-2940	-2840	1486	-2972	4.006	4	0.4052
26	-2929	-2765	1490	-2981	8.27	10	0.6024

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)	-0.1486	0.1065	-1.395	4006	0.1631	-0.4475	0.1504
fixed	NA	poly(age, 3, raw = TRUE)1	0.02007	0.01288	1.558	4006	0.1193	-0.01609	0.05624
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007564	0.0004933	-1.533	4006	0.1253	-0.002141	0.0006283
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009311	0.000005958	1.563	4006	0.1182	-0.000007413	0.00002604
fixed	NA	male	0.006283	0.005263	1.194	4006	0.2326	-0.00849	0.02106
fixed	NA	sibling_count3	0.00281	0.007829	0.3589	4006	0.7197	-0.01917	0.02479
fixed	NA	sibling_count4	-0.005559	0.008443	-0.6585	4006	0.5103	-0.02926	0.01814
fixed	NA	sibling_count5	-0.005294	0.009292	-0.5697	4006	0.5689	-0.03138	0.02079
fixed	NA	sibling_count>5	0.01816	0.008216	2.21	4006	0.02715	-0.004904	0.04122
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1666	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)	-0.1523	0.1065	-1.429	4005	0.153	-0.4513	0.1468
fixed	NA	birth_order	0.001729	0.001583	1.092	4005	0.2748	-0.002715	0.006174
fixed	NA	poly(age, 3, raw = TRUE)1	0.02027	0.01289	1.573	4005	0.1157	-0.0159	0.05644
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007663	0.0004934	-1.553	4005	0.1205	-0.002151	0.0006187
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009479	0.00000596	1.59	4005	0.1118	-0.000007251	0.00002621
fixed	NA	male	0.006291	0.005263	1.195	4005	0.232	-0.008482	0.02106
fixed	NA	sibling_count3	0.00197	0.007866	0.2504	4005	0.8023	-0.02011	0.02405
fixed	NA	sibling_count4	-0.007413	0.008611	-0.8609	4005	0.3894	-0.03159	0.01676
fixed	NA	sibling_count5	-0.008217	0.00967	-0.8498	4005	0.3955	-0.03536	0.01893
fixed	NA	sibling_count>5	0.01149	0.01024	1.122	4005	0.2619	-0.01725	0.04023
ran_pars	mother_pidlink	sd__(Intercept)	0.000000003507	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1666	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)	-0.1515	0.1067	-1.42	4001	0.1556	-0.4509	0.1479
fixed	NA	poly(age, 3, raw = TRUE)1	0.02036	0.0129	1.579	4001	0.1145	-0.01584	0.05656
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007676	0.0004938	-1.554	4001	0.1202	-0.002154	0.0006187
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009457	0.000005966	1.585	4001	0.113	-0.000007289	0.0000262
fixed	NA	male	0.006342	0.005267	1.204	4001	0.2286	-0.008443	0.02113
fixed	NA	sibling_count3	0.002582	0.008089	0.3193	4001	0.7495	-0.02012	0.02529
fixed	NA	sibling_count4	-0.004501	0.009063	-0.4966	4001	0.6195	-0.02994	0.02094
fixed	NA	sibling_count5	-0.003395	0.01036	-0.3278	4001	0.7431	-0.03247	0.02568
fixed	NA	sibling_count>5	0.01573	0.01075	1.464	4001	0.1433	-0.01444	0.04591
fixed	NA	birth_order_nonlinear2	0.001636	0.006938	0.2358	4001	0.8136	-0.01784	0.02111
fixed	NA	birth_order_nonlinear3	0.0009229	0.008591	0.1074	4001	0.9145	-0.02319	0.02504
fixed	NA	birth_order_nonlinear4	-0.005306	0.01049	-0.506	4001	0.6129	-0.03474	0.02413
fixed	NA	birth_order_nonlinear5	-0.003994	0.0136	-0.2938	4001	0.7689	-0.04216	0.03417
fixed	NA	birth_order_nonlinear>5	0.009254	0.0127	0.7289	4001	0.4661	-0.02639	0.0449
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1666	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)	-0.1472	0.1069	-1.377	3991	0.1684	-0.4471	0.1528
fixed	NA	poly(age, 3, raw = TRUE)1	0.02004	0.01292	1.552	3991	0.1208	-0.01621	0.05629
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000755	0.0004946	-1.527	3991	0.1269	-0.002143	0.0006333
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009301	0.000005975	1.557	3991	0.1196	-0.000007469	0.00002607
fixed	NA	male	0.006449	0.005273	1.223	3991	0.2214	-0.008353	0.02125
fixed	NA	count_birth_order2/2	-0.003815	0.01228	-0.3108	3991	0.756	-0.03827	0.03064
fixed	NA	count_birth_order1/3	-0.003669	0.01069	-0.3433	3991	0.7314	-0.03367	0.02633
fixed	NA	count_birth_order2/3	0.007273	0.0116	0.6268	3991	0.5308	-0.0253	0.03984
fixed	NA	count_birth_order3/3	0.003067	0.01296	0.2366	3991	0.813	-0.03332	0.03945
fixed	NA	count_birth_order1/4	0.0007049	0.01346	0.05236	3991	0.9582	-0.03708	0.03849
fixed	NA	count_birth_order2/4	0.001997	0.01358	0.147	3991	0.8831	-0.03612	0.04011
fixed	NA	count_birth_order3/4	-0.02048	0.01513	-1.354	3991	0.1759	-0.06296	0.02199
fixed	NA	count_birth_order4/4	-0.01489	0.01471	-1.012	3991	0.3116	-0.05618	0.0264
fixed	NA	count_birth_order1/5	-0.01108	0.01672	-0.6626	3991	0.5076	-0.05802	0.03586
fixed	NA	count_birth_order2/5	-0.005183	0.01899	-0.2729	3991	0.7849	-0.05849	0.04812
fixed	NA	count_birth_order3/5	-0.008834	0.01738	-0.5082	3991	0.6113	-0.05763	0.03996
fixed	NA	count_birth_order4/5	-0.008066	0.0178	-0.4531	3991	0.6505	-0.05804	0.04191
fixed	NA	count_birth_order5/5	0.0008635	0.01743	0.04954	3991	0.9605	-0.04806	0.04979
fixed	NA	count_birth_order1/>5	0.0153	0.01781	0.8591	3991	0.3903	-0.03469	0.06529
fixed	NA	count_birth_order2/>5	-0.006775	0.01984	-0.3415	3991	0.7328	-0.06247	0.04892
fixed	NA	count_birth_order3/>5	0.04067	0.01842	2.208	3991	0.02731	-0.01104	0.09237
fixed	NA	count_birth_order4/>5	0.01091	0.01658	0.6578	3991	0.5107	-0.03564	0.05745
fixed	NA	count_birth_order5/>5	-0.0003145	0.01759	-0.01788	3991	0.9857	-0.0497	0.04907
fixed	NA	count_birth_order>5/>5	0.02317	0.01124	2.062	3991	0.03928	-0.008374	0.05472
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1667	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)
11	-2986	-2917	1504	-3008	NA	NA	NA
12	-2985	-2910	1505	-3009	1.196	1	0.2742
16	-2977	-2877	1505	-3009	0.2612	4	0.9922
26	-2965	-2802	1509	-3017	7.849	10	0.6436

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)	-0.1524	0.1069	-1.425	3877	0.1543	-0.4526	0.1478
fixed	NA	poly(age, 3, raw = TRUE)1	0.02052	0.01293	1.587	3877	0.1127	-0.01578	0.05682
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007638	0.0004946	-1.544	3877	0.1226	-0.002152	0.0006246
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000093	0.000005968	1.558	3877	0.1193	-0.000007453	0.00002605
fixed	NA	male	0.004826	0.005319	0.9073	3877	0.3643	-0.0101	0.01976
fixed	NA	sibling_count3	-0.001595	0.00716	-0.2227	3877	0.8238	-0.02169	0.0185
fixed	NA	sibling_count4	-0.007724	0.008028	-0.9621	3877	0.3361	-0.03026	0.01481
fixed	NA	sibling_count5	0.002436	0.009835	0.2477	3877	0.8044	-0.02517	0.03004
fixed	NA	sibling_count>5	0.02079	0.008775	2.37	3877	0.01786	-0.003839	0.04542
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1656	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)	-0.1561	0.107	-1.459	3876	0.1447	-0.4565	0.1443
fixed	NA	birth_order	0.002012	0.001944	1.035	3876	0.3008	-0.003445	0.00747
fixed	NA	poly(age, 3, raw = TRUE)1	0.02069	0.01293	1.599	3876	0.1098	-0.01562	0.05699
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007734	0.0004947	-1.563	3876	0.118	-0.002162	0.0006152
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000948	0.000005971	1.588	3876	0.1124	-0.00000728	0.00002624
fixed	NA	male	0.004883	0.005319	0.9181	3876	0.3586	-0.01005	0.01981
fixed	NA	sibling_count3	-0.002519	0.007215	-0.3492	3876	0.727	-0.02277	0.01773
fixed	NA	sibling_count4	-0.00991	0.008301	-1.194	3876	0.2327	-0.03321	0.01339
fixed	NA	sibling_count5	-0.001106	0.01041	-0.1062	3876	0.9154	-0.03034	0.02812
fixed	NA	sibling_count>5	0.01253	0.01187	1.056	3876	0.2912	-0.02078	0.04583
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1656	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)	-0.1555	0.1071	-1.451	3872	0.1468	-0.4562	0.1452
fixed	NA	poly(age, 3, raw = TRUE)1	0.02077	0.01294	1.605	3872	0.1087	-0.01556	0.0571
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007756	0.000495	-1.567	3872	0.1173	-0.002165	0.000614
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009493	0.000005975	1.589	3872	0.1122	-0.00000728	0.00002627
fixed	NA	male	0.004933	0.005323	0.9269	3872	0.3541	-0.01001	0.01987
fixed	NA	sibling_count3	-0.002476	0.007436	-0.333	3872	0.7391	-0.02335	0.0184
fixed	NA	sibling_count4	-0.006352	0.008807	-0.7213	3872	0.4707	-0.03107	0.01837
fixed	NA	sibling_count5	0.005045	0.01113	0.4534	3872	0.6503	-0.02619	0.03628
fixed	NA	sibling_count>5	0.0149	0.01266	1.177	3872	0.2394	-0.02064	0.05044
fixed	NA	birth_order_nonlinear2	0.003457	0.006762	0.5112	3872	0.6092	-0.01553	0.02244
fixed	NA	birth_order_nonlinear3	0.004017	0.008668	0.4635	3872	0.6431	-0.02031	0.02835
fixed	NA	birth_order_nonlinear4	-0.009119	0.01146	-0.7957	3872	0.4263	-0.04129	0.02305
fixed	NA	birth_order_nonlinear5	-0.003768	0.0153	-0.2462	3872	0.8055	-0.04673	0.03919
fixed	NA	birth_order_nonlinear>5	0.01701	0.01547	1.1	3872	0.2716	-0.02642	0.06045
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1656	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)	-0.1605	0.1074	-1.495	3862	0.1351	-0.462	0.141
fixed	NA	poly(age, 3, raw = TRUE)1	0.02159	0.01297	1.664	3862	0.09624	-0.01483	0.05801
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0008016	0.0004963	-1.615	3862	0.1064	-0.002195	0.0005916
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009745	0.000005992	1.626	3862	0.104	-0.000007075	0.00002656
fixed	NA	male	0.005014	0.005333	0.9402	3862	0.3472	-0.009956	0.01998
fixed	NA	count_birth_order2/2	-0.004404	0.0109	-0.404	3862	0.6862	-0.035	0.02619
fixed	NA	count_birth_order1/3	-0.01262	0.009776	-1.291	3862	0.1968	-0.04006	0.01482
fixed	NA	count_birth_order2/3	0.003637	0.01089	0.334	3862	0.7384	-0.02693	0.03421
fixed	NA	count_birth_order3/3	0.005645	0.01197	0.4714	3862	0.6374	-0.02797	0.03926
fixed	NA	count_birth_order1/4	-0.004056	0.01325	-0.3062	3862	0.7595	-0.04124	0.03313
fixed	NA	count_birth_order2/4	-0.001733	0.01367	-0.1268	3862	0.8991	-0.0401	0.03663
fixed	NA	count_birth_order3/4	-0.01717	0.01406	-1.222	3862	0.222	-0.05662	0.02229
fixed	NA	count_birth_order4/4	-0.01619	0.01435	-1.128	3862	0.2594	-0.05646	0.02409
fixed	NA	count_birth_order1/5	0.006246	0.01912	0.3266	3862	0.744	-0.04743	0.05992
fixed	NA	count_birth_order2/5	0.0009551	0.02176	0.04389	3862	0.965	-0.06014	0.06205
fixed	NA	count_birth_order3/5	0.009442	0.01987	0.4752	3862	0.6347	-0.04634	0.06522
fixed	NA	count_birth_order4/5	0.003884	0.01857	0.2091	3862	0.8344	-0.04826	0.05602
fixed	NA	count_birth_order5/5	-0.01661	0.0193	-0.8607	3862	0.3895	-0.0708	0.03757
fixed	NA	count_birth_order1/>5	0.02319	0.02464	0.9411	3862	0.3467	-0.04598	0.09237
fixed	NA	count_birth_order2/>5	0.005438	0.02432	0.2236	3862	0.8231	-0.06283	0.0737
fixed	NA	count_birth_order3/>5	0.01683	0.02315	0.7271	3862	0.4672	-0.04815	0.0818
fixed	NA	count_birth_order4/>5	-0.01712	0.02153	-0.7949	3862	0.4267	-0.07756	0.04333
fixed	NA	count_birth_order5/>5	0.02131	0.01811	1.177	3862	0.2393	-0.02952	0.07214
fixed	NA	count_birth_order>5/>5	0.02908	0.01199	2.425	3862	0.01534	-0.004578	0.06273
ran_pars	mother_pidlink	sd__(Intercept)	0.000000004709	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1657	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)
11	-2935	-2866	1478	-2957	NA	NA	NA
12	-2934	-2859	1479	-2958	1.074	1	0.3001
16	-2928	-2828	1480	-2960	2.375	4	0.6672
26	-2915	-2752	1483	-2967	6.831	10	0.7413

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)	-0.07964	0.08885	-0.8964	7460	0.3701	-0.3291	0.1698
fixed	NA	poly(age, 3, raw = TRUE)1	0.00962	0.01022	0.9411	7478	0.3467	-0.01907	0.03831
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003134	0.0003703	-0.8464	7496	0.3974	-0.001353	0.000726
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004026	0.00000423	0.9519	7508	0.3412	-0.000007846	0.0000159
fixed	NA	male	0.03192	0.005231	6.103	7480	0.000000001094	0.01724	0.04661
fixed	NA	sibling_count3	-0.008452	0.009849	-0.8582	6513	0.3908	-0.0361	0.01919
fixed	NA	sibling_count4	0.00381	0.01018	0.3744	6259	0.7081	-0.02475	0.03237
fixed	NA	sibling_count5	0.01119	0.01059	1.057	5819	0.2907	-0.01853	0.0409
fixed	NA	sibling_count>5	0.03482	0.008449	4.122	6134	0.00003812	0.01111	0.05854
ran_pars	mother_pidlink	sd__(Intercept)	0.08269	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2132	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)	-0.07986	0.08885	-0.8988	7460	0.3688	-0.3293	0.1696
fixed	NA	birth_order	0.0009563	0.001108	0.8631	6682	0.3881	-0.002154	0.004066
fixed	NA	poly(age, 3, raw = TRUE)1	0.009444	0.01022	0.9236	7477	0.3557	-0.01926	0.03815
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003064	0.0003704	-0.8273	7496	0.4081	-0.001346	0.0007332
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003962	0.00000423	0.9364	7509	0.3491	-0.000007913	0.00001584
fixed	NA	male	0.03195	0.005231	6.108	7479	0.000000001057	0.01727	0.04664
fixed	NA	sibling_count3	-0.008806	0.009856	-0.8934	6515	0.3717	-0.03647	0.01886
fixed	NA	sibling_count4	0.002898	0.01023	0.2833	6262	0.777	-0.02582	0.03161
fixed	NA	sibling_count5	0.009665	0.01073	0.9007	5807	0.3678	-0.02046	0.03979
fixed	NA	sibling_count>5	0.03038	0.009896	3.069	6192	0.002154	0.002597	0.05816
ran_pars	mother_pidlink	sd__(Intercept)	0.08257	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2133	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)	-0.0841	0.08913	-0.9436	7479	0.3454	-0.3343	0.1661
fixed	NA	poly(age, 3, raw = TRUE)1	0.009802	0.01024	0.9574	7489	0.3384	-0.01894	0.03854
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003176	0.0003709	-0.8565	7504	0.3918	-0.001359	0.0007234
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004062	0.000004236	0.9589	7514	0.3376	-0.000007828	0.00001595
fixed	NA	male	0.03209	0.005232	6.133	7475	0.000000000905	0.0174	0.04678
fixed	NA	sibling_count3	-0.008324	0.01002	-0.8303	6630	0.4064	-0.03646	0.01982
fixed	NA	sibling_count4	0.006027	0.01067	0.5647	6544	0.5723	-0.02393	0.03599
fixed	NA	sibling_count5	0.01112	0.01139	0.9759	6225	0.3291	-0.02086	0.04309
fixed	NA	sibling_count>5	0.0318	0.01067	2.979	6720	0.002901	0.001837	0.06175
fixed	NA	birth_order_nonlinear2	0.006231	0.007625	0.8172	6954	0.4139	-0.01517	0.02763
fixed	NA	birth_order_nonlinear3	0.0001958	0.009161	0.02138	7069	0.9829	-0.02552	0.02591
fixed	NA	birth_order_nonlinear4	-0.008989	0.01056	-0.8511	7141	0.3947	-0.03864	0.02066
fixed	NA	birth_order_nonlinear5	0.01249	0.01183	1.056	7243	0.2911	-0.02071	0.04569
fixed	NA	birth_order_nonlinear>5	0.007857	0.01017	0.7724	7531	0.4399	-0.0207	0.03641
ran_pars	mother_pidlink	sd__(Intercept)	0.08259	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2133	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)	-0.08246	0.08926	-0.9238	7472	0.3556	-0.333	0.1681
fixed	NA	poly(age, 3, raw = TRUE)1	0.009748	0.01024	0.952	7480	0.3412	-0.019	0.03849
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003177	0.000371	-0.8564	7495	0.3918	-0.001359	0.0007237
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004095	0.000004238	0.9664	7505	0.3339	-0.0000078	0.00001599
fixed	NA	male	0.03227	0.005234	6.167	7465	0.0000000007337	0.01758	0.04697
fixed	NA	count_birth_order2/2	0.00326	0.01454	0.2242	7097	0.8226	-0.03755	0.04407
fixed	NA	count_birth_order1/3	-0.004176	0.013	-0.3212	7516	0.748	-0.04067	0.03232
fixed	NA	count_birth_order2/3	0.0007817	0.01446	0.05408	7534	0.9569	-0.0398	0.04136
fixed	NA	count_birth_order3/3	-0.02654	0.01664	-1.595	7537	0.1108	-0.07326	0.02017
fixed	NA	count_birth_order1/4	0.001379	0.01533	0.08991	7533	0.9284	-0.04167	0.04442
fixed	NA	count_birth_order2/4	0.01607	0.01589	1.011	7537	0.3118	-0.02853	0.06068
fixed	NA	count_birth_order3/4	0.001507	0.01716	0.08783	7536	0.93	-0.04666	0.04968
fixed	NA	count_birth_order4/4	-0.00101	0.01778	-0.05678	7537	0.9547	-0.05093	0.04891
fixed	NA	count_birth_order1/5	0.02121	0.01767	1.2	7537	0.2302	-0.0284	0.07082
fixed	NA	count_birth_order2/5	0.008517	0.01889	0.451	7527	0.652	-0.0445	0.06153
fixed	NA	count_birth_order3/5	-0.004503	0.01857	-0.2426	7523	0.8084	-0.05662	0.04761
fixed	NA	count_birth_order4/5	0.01404	0.01963	0.7155	7522	0.4743	-0.04106	0.06914
fixed	NA	count_birth_order5/5	0.02075	0.01878	1.105	7533	0.2694	-0.03198	0.07347
fixed	NA	count_birth_order1/>5	0.01348	0.01626	0.829	7520	0.4071	-0.03217	0.05914
fixed	NA	count_birth_order2/>5	0.03364	0.01647	2.043	7520	0.0411	-0.01258	0.07987
fixed	NA	count_birth_order3/>5	0.05796	0.0158	3.669	7510	0.0002454	0.01361	0.1023
fixed	NA	count_birth_order4/>5	0.01383	0.01495	0.9249	7514	0.355	-0.02814	0.05581
fixed	NA	count_birth_order5/>5	0.04418	0.01434	3.08	7522	0.00208	0.00391	0.08444
fixed	NA	count_birth_order>5/>5	0.03869	0.01059	3.654	7264	0.0002602	0.008965	0.0684
ran_pars	mother_pidlink	sd__(Intercept)	0.08253	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2133	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)
11	-891.6	-815.4	456.8	-913.6	NA	NA	NA
12	-890.4	-807.2	457.2	-914.4	0.7467	1	0.3875
16	-885.9	-775	458.9	-917.9	3.481	4	0.4807
26	-877	-696.8	464.5	-929	11.14	10	0.3467

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)	0.01121	0.12	0.09338	3918	0.9256	-0.3257	0.3481
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0008552	0.01454	-0.05884	3928	0.9531	-0.04166	0.03995
fixed	NA	poly(age, 3, raw = TRUE)2	0.0000577	0.0005569	0.1036	3939	0.9175	-0.001506	0.001621
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001182	0.000006732	-0.1755	3949	0.8607	-0.00002008	0.00001772
fixed	NA	male	0.02491	0.005955	4.183	3935	0.00002942	0.008193	0.04163
fixed	NA	sibling_count3	0.003041	0.008421	0.3611	3312	0.718	-0.0206	0.02668
fixed	NA	sibling_count4	0.02978	0.00946	3.148	3099	0.001658	0.003228	0.05634
fixed	NA	sibling_count5	0.02227	0.01122	1.984	3015	0.04733	-0.009237	0.05378
fixed	NA	sibling_count>5	0.0533	0.01018	5.234	2763	0.0000001787	0.02472	0.08189
ran_pars	mother_pidlink	sd__(Intercept)	0.07007	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.175	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)	0.01518	0.1201	0.1263	3920	0.8995	-0.322	0.3524
fixed	NA	birth_order	-0.001798	0.002186	-0.8224	3737	0.4109	-0.007934	0.004338
fixed	NA	poly(age, 3, raw = TRUE)1	-0.001049	0.01454	-0.07217	3928	0.9425	-0.04186	0.03976
fixed	NA	poly(age, 3, raw = TRUE)2	0.00006671	0.000557	0.1198	3939	0.9047	-0.001497	0.00163
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001341	0.000006735	-0.1991	3948	0.8422	-0.00002025	0.00001756
fixed	NA	male	0.02488	0.005956	4.178	3934	0.00003003	0.008165	0.0416
fixed	NA	sibling_count3	0.003896	0.008485	0.4591	3310	0.6462	-0.01992	0.02771
fixed	NA	sibling_count4	0.03179	0.00977	3.254	3089	0.001151	0.004366	0.05921
fixed	NA	sibling_count5	0.02563	0.01194	2.146	3024	0.03197	-0.007897	0.05915
fixed	NA	sibling_count>5	0.0608	0.01367	4.448	2965	0.000008989	0.02243	0.09918
ran_pars	mother_pidlink	sd__(Intercept)	0.07	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1751	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)	0.01003	0.1203	0.0834	3922	0.9335	-0.3277	0.3478
fixed	NA	poly(age, 3, raw = TRUE)1	-0.00082	0.01455	-0.05634	3928	0.9551	-0.04168	0.04004
fixed	NA	poly(age, 3, raw = TRUE)2	0.00005832	0.0005576	0.1046	3937	0.9167	-0.001507	0.001624
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001221	0.000006742	-0.181	3946	0.8563	-0.00002015	0.0000177
fixed	NA	male	0.02492	0.00596	4.182	3930	0.00002952	0.008195	0.04165
fixed	NA	sibling_count3	0.002344	0.008719	0.2688	3405	0.7881	-0.02213	0.02682
fixed	NA	sibling_count4	0.03282	0.0103	3.186	3262	0.001456	0.003905	0.06173
fixed	NA	sibling_count5	0.02701	0.01274	2.121	3255	0.03402	-0.008741	0.06276
fixed	NA	sibling_count>5	0.05584	0.01442	3.871	3144	0.0001104	0.01535	0.09633
fixed	NA	birth_order_nonlinear2	0.001738	0.007499	0.2318	3389	0.8167	-0.01931	0.02279
fixed	NA	birth_order_nonlinear3	0.003074	0.009668	0.318	3735	0.7505	-0.02406	0.03021
fixed	NA	birth_order_nonlinear4	-0.01505	0.01247	-1.206	3836	0.2277	-0.05006	0.01996
fixed	NA	birth_order_nonlinear5	-0.007201	0.01644	-0.4379	3861	0.6615	-0.05336	0.03896
fixed	NA	birth_order_nonlinear>5	0.001383	0.0171	0.0809	3914	0.9355	-0.04662	0.04939
ran_pars	mother_pidlink	sd__(Intercept)	0.07028	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.175	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)	0.02475	0.1206	0.2052	3914	0.8374	-0.3137	0.3632
fixed	NA	poly(age, 3, raw = TRUE)1	-0.002739	0.01459	-0.1878	3919	0.851	-0.04368	0.0382
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001345	0.0005589	0.2407	3928	0.8098	-0.001434	0.001703
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002188	0.000006758	-0.3238	3937	0.7461	-0.00002116	0.00001678
fixed	NA	male	0.02456	0.005969	4.114	3919	0.00003972	0.0078	0.04131
fixed	NA	count_birth_order2/2	0.004317	0.01246	0.3465	3562	0.729	-0.03066	0.03929
fixed	NA	count_birth_order1/3	0.003408	0.01118	0.3048	3945	0.7605	-0.02798	0.03479
fixed	NA	count_birth_order2/3	0.006332	0.01223	0.5179	3947	0.6046	-0.02799	0.04065
fixed	NA	count_birth_order3/3	0.004064	0.01367	0.2972	3947	0.7663	-0.03432	0.04245
fixed	NA	count_birth_order1/4	0.03974	0.01488	2.671	3948	0.007602	-0.00203	0.08151
fixed	NA	count_birth_order2/4	0.02834	0.0154	1.84	3940	0.0659	-0.0149	0.07158
fixed	NA	count_birth_order3/4	0.02931	0.01621	1.808	3933	0.07065	-0.01619	0.07482
fixed	NA	count_birth_order4/4	0.02599	0.01604	1.62	3947	0.1053	-0.01904	0.07102
fixed	NA	count_birth_order1/5	0.00689	0.0216	0.319	3946	0.7498	-0.05374	0.06753
fixed	NA	count_birth_order2/5	0.03487	0.02336	1.492	3913	0.1357	-0.03071	0.1004
fixed	NA	count_birth_order3/5	0.0276	0.02126	1.298	3931	0.1943	-0.03208	0.08728
fixed	NA	count_birth_order4/5	0.01066	0.01998	0.5339	3932	0.5935	-0.04541	0.06674
fixed	NA	count_birth_order5/5	0.04122	0.02055	2.006	3943	0.04496	-0.01647	0.09892
fixed	NA	count_birth_order1/>5	0.07669	0.02748	2.791	3897	0.005277	-0.000436	0.1538
fixed	NA	count_birth_order2/>5	0.05725	0.02663	2.15	3898	0.03161	-0.01749	0.132
fixed	NA	count_birth_order3/>5	0.09302	0.02448	3.799	3898	0.0001475	0.02429	0.1617
fixed	NA	count_birth_order4/>5	0.02899	0.02237	1.296	3894	0.1949	-0.03379	0.09178
fixed	NA	count_birth_order5/>5	0.0316	0.01974	1.601	3915	0.1094	-0.0238	0.087
fixed	NA	count_birth_order>5/>5	0.05784	0.01354	4.272	3737	0.00001987	0.01983	0.09585
ran_pars	mother_pidlink	sd__(Intercept)	0.07014	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1751	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)
11	-1991	-1922	1007	-2013	NA	NA	NA
12	-1990	-1915	1007	-2014	0.6787	1	0.41
16	-1984	-1883	1008	-2016	1.76	4	0.7799
26	-1971	-1808	1012	-2023	7.601	10	0.6677

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)	0.0002828	0.1195	0.002366	3962	0.9981	-0.3352	0.3358
fixed	NA	poly(age, 3, raw = TRUE)1	0.0006424	0.01447	0.04439	3972	0.9646	-0.03998	0.04127
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000002017	0.0005547	-0.003637	3983	0.9971	-0.001559	0.001555
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000003936	0.000006707	-0.05869	3993	0.9532	-0.00001922	0.00001843
fixed	NA	male	0.02545	0.005918	4.3	3978	0.00001749	0.008835	0.04206
fixed	NA	sibling_count3	-0.002779	0.009064	-0.3066	3402	0.7592	-0.02822	0.02267
fixed	NA	sibling_count4	0.02307	0.009816	2.35	3263	0.01884	-0.004487	0.05062
fixed	NA	sibling_count5	0.02523	0.01087	2.321	3044	0.02033	-0.005278	0.05573
fixed	NA	sibling_count>5	0.03975	0.009611	4.136	3090	0.00003634	0.01277	0.06673
ran_pars	mother_pidlink	sd__(Intercept)	0.07022	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1748	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)	0.001055	0.1196	0.008822	3964	0.993	-0.3347	0.3368
fixed	NA	birth_order	-0.0003297	0.001834	-0.1797	3665	0.8574	-0.005479	0.004819
fixed	NA	poly(age, 3, raw = TRUE)1	0.000602	0.01448	0.04159	3972	0.9668	-0.04003	0.04124
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0000002517	0.0005548	-0.0004536	3982	0.9996	-0.001558	0.001557
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000000423	0.00000671	-0.06305	3992	0.9497	-0.00001926	0.00001841
fixed	NA	male	0.02545	0.005918	4.299	3977	0.00001753	0.008833	0.04206
fixed	NA	sibling_count3	-0.002616	0.009111	-0.2872	3397	0.774	-0.02819	0.02296
fixed	NA	sibling_count4	0.02343	0.01002	2.338	3242	0.01946	-0.004702	0.05156
fixed	NA	sibling_count5	0.02579	0.01132	2.279	3035	0.02273	-0.005975	0.05756
fixed	NA	sibling_count>5	0.04103	0.01196	3.43	3190	0.0006104	0.007455	0.0746
ran_pars	mother_pidlink	sd__(Intercept)	0.07023	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1748	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)	-0.00532	0.1198	-0.04442	3966	0.9646	-0.3415	0.3309
fixed	NA	poly(age, 3, raw = TRUE)1	0.00107	0.01449	0.07384	3972	0.9411	-0.0396	0.04174
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00001789	0.0005553	-0.03221	3981	0.9743	-0.001577	0.001541
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000001971	0.000006716	-0.02934	3990	0.9766	-0.00001905	0.00001865
fixed	NA	male	0.02563	0.005921	4.329	3973	0.00001537	0.00901	0.04225
fixed	NA	sibling_count3	-0.002255	0.009346	-0.2413	3477	0.8093	-0.02849	0.02398
fixed	NA	sibling_count4	0.0258	0.0105	2.456	3383	0.0141	-0.003687	0.05529
fixed	NA	sibling_count5	0.02825	0.01205	2.344	3245	0.01913	-0.005579	0.06208
fixed	NA	sibling_count>5	0.03817	0.01249	3.057	3382	0.002253	0.003122	0.07322
fixed	NA	birth_order_nonlinear2	0.00555	0.007641	0.7263	3474	0.4677	-0.0159	0.027
fixed	NA	birth_order_nonlinear3	-0.002217	0.009564	-0.2318	3800	0.8167	-0.02906	0.02463
fixed	NA	birth_order_nonlinear4	-0.008889	0.01172	-0.7585	3890	0.4482	-0.04179	0.02401
fixed	NA	birth_order_nonlinear5	0.00004574	0.01522	0.003004	3917	0.9976	-0.04269	0.04278
fixed	NA	birth_order_nonlinear>5	0.01021	0.01449	0.7042	3945	0.4813	-0.03048	0.05089
ran_pars	mother_pidlink	sd__(Intercept)	0.07045	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1747	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)	0.001061	0.12	0.008841	3959	0.9929	-0.3359	0.338
fixed	NA	poly(age, 3, raw = TRUE)1	0.0001726	0.01452	0.01189	3964	0.9905	-0.04058	0.04092
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001582	0.0005564	0.02843	3972	0.9773	-0.001546	0.001578
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000005898	0.000006729	-0.08766	3981	0.9302	-0.00001948	0.0000183
fixed	NA	male	0.02548	0.005931	4.297	3964	0.00001775	0.008835	0.04213
fixed	NA	count_birth_order2/2	0.008978	0.01357	0.6614	3612	0.5084	-0.02913	0.04708
fixed	NA	count_birth_order1/3	0.003922	0.01206	0.3251	3989	0.7451	-0.02994	0.03779
fixed	NA	count_birth_order2/3	0.0002864	0.01308	0.02189	3992	0.9825	-0.03643	0.037
fixed	NA	count_birth_order3/3	-0.007098	0.01461	-0.4859	3991	0.6271	-0.0481	0.03391
fixed	NA	count_birth_order1/4	0.02279	0.01518	1.501	3992	0.1335	-0.01984	0.06541
fixed	NA	count_birth_order2/4	0.02978	0.0153	1.946	3990	0.0517	-0.01317	0.07274
fixed	NA	count_birth_order3/4	0.01887	0.01703	1.108	3977	0.2679	-0.02893	0.06667
fixed	NA	count_birth_order4/4	0.03166	0.01658	1.91	3992	0.05627	-0.01488	0.0782
fixed	NA	count_birth_order1/5	0.03335	0.01886	1.768	3992	0.07708	-0.01959	0.08628
fixed	NA	count_birth_order2/5	0.04802	0.02126	2.259	3953	0.02394	-0.01165	0.1077
fixed	NA	count_birth_order3/5	0.02118	0.01957	1.083	3976	0.279	-0.03374	0.07611
fixed	NA	count_birth_order4/5	0.01393	0.02002	0.6957	3966	0.4867	-0.04227	0.07012
fixed	NA	count_birth_order5/5	0.02655	0.01963	1.353	3986	0.1762	-0.02854	0.08164
fixed	NA	count_birth_order1/>5	0.02823	0.02007	1.407	3985	0.1596	-0.02811	0.08456
fixed	NA	count_birth_order2/>5	0.0452	0.02232	2.025	3953	0.04292	-0.01745	0.1079
fixed	NA	count_birth_order3/>5	0.06224	0.02072	3.003	3965	0.002687	0.004069	0.1204
fixed	NA	count_birth_order4/>5	0.01788	0.01865	0.9585	3966	0.3379	-0.03448	0.07023
fixed	NA	count_birth_order5/>5	0.04218	0.01978	2.132	3960	0.03305	-0.01335	0.09772
fixed	NA	count_birth_order>5/>5	0.04944	0.01289	3.835	3796	0.0001278	0.01325	0.08564
ran_pars	mother_pidlink	sd__(Intercept)	0.0702	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1749	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)
11	-2022	-1953	1022	-2044	NA	NA	NA
12	-2020	-1945	1022	-2044	0.03257	1	0.8568
16	-2015	-1914	1023	-2047	2.509	4	0.6429
26	-2000	-1837	1026	-2052	5.464	10	0.8581

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)	0.01789	0.1209	0.148	3834	0.8823	-0.3214	0.3572
fixed	NA	poly(age, 3, raw = TRUE)1	-0.001561	0.01463	-0.1067	3844	0.9151	-0.04263	0.0395
fixed	NA	poly(age, 3, raw = TRUE)2	0.00008934	0.0005601	0.1595	3855	0.8733	-0.001483	0.001661
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001613	0.000006766	-0.2384	3865	0.8116	-0.00002061	0.00001738
fixed	NA	male	0.02612	0.006023	4.337	3849	0.0000148	0.009216	0.04303
fixed	NA	sibling_count3	0.0007046	0.008364	0.08425	3225	0.9329	-0.02277	0.02418
fixed	NA	sibling_count4	0.021	0.009442	2.224	3009	0.02622	-0.005504	0.0475
fixed	NA	sibling_count5	0.02668	0.01162	2.295	2866	0.02181	-0.005952	0.0593
fixed	NA	sibling_count>5	0.05476	0.01044	5.245	2673	0.0000001689	0.02545	0.08406
ran_pars	mother_pidlink	sd__(Intercept)	0.07021	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1751	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)	0.02227	0.121	0.1841	3836	0.8539	-0.3173	0.3618
fixed	NA	birth_order	-0.002079	0.00225	-0.9241	3712	0.3555	-0.008395	0.004236
fixed	NA	poly(age, 3, raw = TRUE)1	-0.001768	0.01463	-0.1208	3844	0.9039	-0.04284	0.0393
fixed	NA	poly(age, 3, raw = TRUE)2	0.00009948	0.0005602	0.1776	3854	0.8591	-0.001473	0.001672
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001796	0.000006769	-0.2653	3864	0.7908	-0.0000208	0.0000172
fixed	NA	male	0.02607	0.006024	4.328	3848	0.0000154	0.009164	0.04298
fixed	NA	sibling_count3	0.001673	0.008429	0.1985	3222	0.8426	-0.02199	0.02533
fixed	NA	sibling_count4	0.02331	0.009766	2.387	3005	0.01707	-0.004107	0.05072
fixed	NA	sibling_count5	0.03041	0.0123	2.471	2887	0.01352	-0.00413	0.06494
fixed	NA	sibling_count>5	0.06342	0.01403	4.52	2945	0.000006415	0.02404	0.1028
ran_pars	mother_pidlink	sd__(Intercept)	0.07014	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1751	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)	0.0182	0.1212	0.1502	3840	0.8806	-0.3219	0.3583
fixed	NA	poly(age, 3, raw = TRUE)1	-0.001587	0.01465	-0.1083	3844	0.9137	-0.0427	0.03953
fixed	NA	poly(age, 3, raw = TRUE)2	0.00009018	0.0005608	0.1608	3853	0.8722	-0.001484	0.001664
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001632	0.000006776	-0.2409	3861	0.8097	-0.00002065	0.00001739
fixed	NA	male	0.02602	0.006028	4.317	3843	0.00001621	0.009102	0.04294
fixed	NA	sibling_count3	0.000491	0.008668	0.05664	3313	0.9548	-0.02384	0.02482
fixed	NA	sibling_count4	0.02332	0.01032	2.261	3182	0.02385	-0.005636	0.05228
fixed	NA	sibling_count5	0.03303	0.01308	2.526	3101	0.01159	-0.003676	0.06974
fixed	NA	sibling_count>5	0.0583	0.01491	3.911	3135	0.00009367	0.01646	0.1001
fixed	NA	birth_order_nonlinear2	0.0002169	0.007492	0.02895	3300	0.9769	-0.02081	0.02125
fixed	NA	birth_order_nonlinear3	0.001036	0.009708	0.1067	3644	0.915	-0.02621	0.02829
fixed	NA	birth_order_nonlinear4	-0.01089	0.01288	-0.8453	3728	0.398	-0.04706	0.02528
fixed	NA	birth_order_nonlinear5	-0.019	0.01726	-1.101	3772	0.271	-0.06743	0.02944
fixed	NA	birth_order_nonlinear>5	0.001732	0.01775	0.09756	3854	0.9223	-0.0481	0.05156
ran_pars	mother_pidlink	sd__(Intercept)	0.07048	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.175	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)	0.03478	0.1215	0.2863	3832	0.7747	-0.3063	0.3758
fixed	NA	poly(age, 3, raw = TRUE)1	-0.003973	0.01469	-0.2706	3836	0.7867	-0.0452	0.03725
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001861	0.0005623	0.3309	3845	0.7407	-0.001392	0.001764
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002854	0.000006796	-0.4199	3853	0.6746	-0.00002193	0.00001622
fixed	NA	male	0.02537	0.006038	4.202	3832	0.00002704	0.008423	0.04232
fixed	NA	count_birth_order2/2	0.007706	0.01212	0.6361	3449	0.5248	-0.0263	0.04172
fixed	NA	count_birth_order1/3	0.004014	0.01111	0.3613	3859	0.7179	-0.02717	0.0352
fixed	NA	count_birth_order2/3	0.003202	0.01236	0.2591	3862	0.7956	-0.03148	0.03789
fixed	NA	count_birth_order3/3	0.002463	0.01358	0.1813	3862	0.8561	-0.03566	0.04059
fixed	NA	count_birth_order1/4	0.03037	0.01504	2.02	3862	0.04345	-0.01183	0.07258
fixed	NA	count_birth_order2/4	0.02255	0.0155	1.455	3854	0.1457	-0.02095	0.06604
fixed	NA	count_birth_order3/4	0.0205	0.01592	1.287	3849	0.198	-0.0242	0.0652
fixed	NA	count_birth_order4/4	0.02008	0.01627	1.234	3859	0.2172	-0.02559	0.06575
fixed	NA	count_birth_order1/5	0.01887	0.0217	0.8697	3859	0.3845	-0.04203	0.07977
fixed	NA	count_birth_order2/5	0.03535	0.02463	1.435	3818	0.1513	-0.03379	0.1045
fixed	NA	count_birth_order3/5	0.03267	0.02251	1.451	3842	0.1468	-0.03052	0.09586
fixed	NA	count_birth_order4/5	0.02488	0.02104	1.183	3842	0.2369	-0.03416	0.08393
fixed	NA	count_birth_order5/5	0.03749	0.02189	1.713	3857	0.08683	-0.02395	0.09892
fixed	NA	count_birth_order1/>5	0.09729	0.02792	3.485	3822	0.0004973	0.01893	0.1757
fixed	NA	count_birth_order2/>5	0.04167	0.02754	1.513	3818	0.1303	-0.03564	0.119
fixed	NA	count_birth_order3/>5	0.09556	0.0262	3.647	3808	0.0002685	0.02202	0.1691
fixed	NA	count_birth_order4/>5	0.03713	0.02435	1.525	3789	0.1273	-0.03121	0.1055
fixed	NA	count_birth_order5/>5	0.02453	0.0205	1.197	3829	0.2316	-0.03302	0.08208
fixed	NA	count_birth_order>5/>5	0.06231	0.01387	4.493	3647	0.000007249	0.02338	0.1012
ran_pars	mother_pidlink	sd__(Intercept)	0.07055	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.175	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)
11	-1946	-1877	984.1	-1968	NA	NA	NA
12	-1945	-1870	984.5	-1969	0.857	1	0.3546
16	-1938	-1838	985.2	-1970	1.428	4	0.8393
26	-1927	-1764	989.3	-1979	8.208	10	0.6085

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)	0.9681	0.01706	56.76	14640	0	0.9203	1.016
fixed	NA	poly(age, 3, raw = TRUE)1	0.002032	0.001622	1.253	14591	0.2102	-0.00252	0.006584
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002256	0.00004725	-0.4774	14484	0.6331	-0.0001552	0.0001101
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000005908	0.0000004301	-1.374	14359	0.1696	-0.000001798	0.0000006165
fixed	NA	male	0.0045	0.00183	2.459	14526	0.01393	-0.0006361	0.009636
fixed	NA	sibling_count3	-0.0003612	0.00372	-0.09709	11178	0.9227	-0.0108	0.01008
fixed	NA	sibling_count4	-0.0006508	0.003832	-0.1698	10302	0.8651	-0.01141	0.01011
fixed	NA	sibling_count5	0.003564	0.004005	0.8899	9432	0.3735	-0.007677	0.0148
fixed	NA	sibling_count>5	-0.003767	0.003134	-1.202	10431	0.2294	-0.01256	0.00503
ran_pars	mother_pidlink	sd__(Intercept)	0.04	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1049	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)	0.9682	0.01706	56.77	14641	0	0.9204	1.016
fixed	NA	birth_order	0.0003991	0.0003879	1.029	13583	0.3036	-0.0006898	0.001488
fixed	NA	poly(age, 3, raw = TRUE)1	0.001915	0.001626	1.178	14583	0.2388	-0.002648	0.006478
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00001828	0.00004743	-0.3854	14442	0.7	-0.0001514	0.0001149
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000006301	0.0000004318	-1.459	14297	0.1445	-0.000001842	0.000000582
fixed	NA	male	0.00449	0.00183	2.454	14525	0.01415	-0.0006463	0.009625
fixed	NA	sibling_count3	-0.0004555	0.003722	-0.1224	11194	0.9026	-0.0109	0.009991
fixed	NA	sibling_count4	-0.0009254	0.003842	-0.2409	10369	0.8096	-0.01171	0.009858
fixed	NA	sibling_count5	0.003088	0.004032	0.7659	9548	0.4438	-0.008229	0.0144
fixed	NA	sibling_count>5	-0.005271	0.003458	-1.524	11502	0.1275	-0.01498	0.004436
ran_pars	mother_pidlink	sd__(Intercept)	0.04003	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1049	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)	0.9654	0.0171	56.47	14641	0	0.9174	1.013
fixed	NA	poly(age, 3, raw = TRUE)1	0.001958	0.001626	1.204	14586	0.2286	-0.002606	0.006521
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002171	0.00004743	-0.4577	14447	0.6472	-0.0001549	0.0001114
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000000577	0.0000004318	-1.336	14293	0.1815	-0.000001789	0.0000006352
fixed	NA	male	0.004508	0.001829	2.464	14520	0.01373	-0.0006267	0.009642
fixed	NA	sibling_count3	-0.0008396	0.003773	-0.2226	11526	0.8239	-0.01143	0.00975
fixed	NA	sibling_count4	-0.001915	0.003947	-0.4851	11041	0.6276	-0.01299	0.009165
fixed	NA	sibling_count5	0.002337	0.004181	0.5589	10434	0.5762	-0.0094	0.01407
fixed	NA	sibling_count>5	-0.005684	0.003629	-1.566	12497	0.1174	-0.01587	0.004504
fixed	NA	birth_order_nonlinear2	0.009478	0.002651	3.576	13546	0.0003508	0.002037	0.01692
fixed	NA	birth_order_nonlinear3	0.004998	0.00312	1.602	13356	0.1092	-0.003761	0.01376
fixed	NA	birth_order_nonlinear4	0.00704	0.003569	1.972	13457	0.0486	-0.002979	0.01706
fixed	NA	birth_order_nonlinear5	0.00423	0.00406	1.042	13457	0.2975	-0.007167	0.01563
fixed	NA	birth_order_nonlinear>5	0.006468	0.003369	1.92	14708	0.0549	-0.002989	0.01593
ran_pars	mother_pidlink	sd__(Intercept)	0.04003	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1049	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)	0.9637	0.01717	56.11	14637	0	0.9155	1.012
fixed	NA	poly(age, 3, raw = TRUE)1	0.001951	0.001626	1.2	14577	0.2303	-0.002614	0.006516
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00002194	0.00004745	-0.4624	14434	0.6438	-0.0001551	0.0001113
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000005714	0.0000004321	-1.322	14273	0.1861	-0.000001784	0.0000006415
fixed	NA	male	0.004513	0.00183	2.466	14510	0.01367	-0.0006237	0.00965
fixed	NA	count_birth_order2/2	0.01457	0.005155	2.826	13469	0.004716	0.00009923	0.02904
fixed	NA	count_birth_order1/3	0.003496	0.004912	0.7117	14558	0.4767	-0.01029	0.01729
fixed	NA	count_birth_order2/3	0.006761	0.005492	1.231	14632	0.2184	-0.008656	0.02218
fixed	NA	count_birth_order3/3	0.006183	0.006121	1.01	14690	0.3125	-0.011	0.02337
fixed	NA	count_birth_order1/4	-0.001403	0.00556	-0.2522	14635	0.8009	-0.01701	0.01421
fixed	NA	count_birth_order2/4	0.00841	0.005915	1.422	14664	0.1552	-0.008195	0.02501
fixed	NA	count_birth_order3/4	0.007888	0.006414	1.23	14703	0.2188	-0.01012	0.02589
fixed	NA	count_birth_order4/4	0.00767	0.006728	1.14	14715	0.2542	-0.01121	0.02655
fixed	NA	count_birth_order1/5	0.003475	0.006362	0.5463	14690	0.5849	-0.01438	0.02133
fixed	NA	count_birth_order2/5	0.0146	0.006711	2.175	14711	0.02966	-0.004243	0.03343
fixed	NA	count_birth_order3/5	0.009876	0.006864	1.439	14717	0.1502	-0.009391	0.02914
fixed	NA	count_birth_order4/5	0.01004	0.007349	1.367	14725	0.1717	-0.01058	0.03067
fixed	NA	count_birth_order5/5	0.00893	0.007486	1.193	14725	0.2329	-0.01208	0.02994
fixed	NA	count_birth_order1/>5	-0.002407	0.005119	-0.4702	14721	0.6382	-0.01678	0.01196
fixed	NA	count_birth_order2/>5	0.006208	0.005288	1.174	14725	0.2405	-0.008637	0.02105
fixed	NA	count_birth_order3/>5	-0.0006546	0.005174	-0.1265	14725	0.8993	-0.01518	0.01387
fixed	NA	count_birth_order4/>5	0.003439	0.005098	0.6747	14725	0.4999	-0.01087	0.01775
fixed	NA	count_birth_order5/>5	0.0002875	0.005118	0.05618	14725	0.9552	-0.01408	0.01465
fixed	NA	count_birth_order>5/>5	0.002677	0.00402	0.6661	13473	0.5054	-0.008606	0.01396
ran_pars	mother_pidlink	sd__(Intercept)	0.04003	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1049	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)
11	-22818	-22735	11420	-22840	NA	NA	NA
12	-22817	-22726	11421	-22841	1.058	1	0.3037
16	-22822	-22701	11427	-22854	12.65	4	0.01311
26	-22805	-22608	11429	-22857	3.176	10	0.977

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)	1.011	0.02852	35.46	6237	4.527e-251	0.9311	1.091
fixed	NA	poly(age, 3, raw = TRUE)1	-0.001947	0.003235	-0.6018	6237	0.5473	-0.01103	0.007135
fixed	NA	poly(age, 3, raw = TRUE)2	0.0000824	0.0001155	0.7134	6237	0.4756	-0.0002418	0.0004066
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001031	0.000001309	-0.7881	6237	0.4307	-0.000004706	0.000002643
fixed	NA	male	0.0001955	0.001662	0.1176	6237	0.9064	-0.00447	0.004861
fixed	NA	sibling_count3	-0.0003751	0.002516	-0.1491	6237	0.8815	-0.007438	0.006688
fixed	NA	sibling_count4	-0.001316	0.002683	-0.4904	6237	0.6238	-0.008847	0.006216
fixed	NA	sibling_count5	-0.003354	0.003057	-1.097	6237	0.2725	-0.01193	0.005225
fixed	NA	sibling_count>5	-0.006361	0.002651	-2.399	6237	0.01645	-0.0138	0.001081
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.0656	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)	1.012	0.02852	35.48	6236	2.299e-251	0.9318	1.092
fixed	NA	birth_order	-0.0007748	0.00054	-1.435	6236	0.1514	-0.002291	0.0007411
fixed	NA	poly(age, 3, raw = TRUE)1	-0.001931	0.003235	-0.5969	6236	0.5506	-0.01101	0.00715
fixed	NA	poly(age, 3, raw = TRUE)2	0.00008326	0.0001155	0.7209	6236	0.471	-0.0002409	0.0004075
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000107	0.000001309	-0.8174	6236	0.4137	-0.000004745	0.000002604
fixed	NA	male	0.0002228	0.001662	0.1341	6236	0.8933	-0.004442	0.004888
fixed	NA	sibling_count3	0.00000391	0.00253	0.001546	6236	0.9988	-0.007098	0.007105
fixed	NA	sibling_count4	-0.0004532	0.002749	-0.1648	6236	0.8691	-0.008171	0.007264
fixed	NA	sibling_count5	-0.001941	0.003211	-0.6046	6236	0.5455	-0.01095	0.007072
fixed	NA	sibling_count>5	-0.003485	0.003324	-1.048	6236	0.2945	-0.01282	0.005846
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.0656	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)	1.015	0.02855	35.54	6232	4.212e-252	0.9347	1.095
fixed	NA	poly(age, 3, raw = TRUE)1	-0.002183	0.003236	-0.6745	6232	0.5	-0.01127	0.006901
fixed	NA	poly(age, 3, raw = TRUE)2	0.00009152	0.0001155	0.7921	6232	0.4284	-0.0002328	0.0004159
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001145	0.00000131	-0.8742	6232	0.382	-0.000004822	0.000002532
fixed	NA	male	0.0001161	0.001662	0.06984	6232	0.9443	-0.004549	0.004781
fixed	NA	sibling_count3	-0.0003986	0.00259	-0.1539	6232	0.8777	-0.00767	0.006873
fixed	NA	sibling_count4	-0.00217	0.002874	-0.7549	6232	0.4503	-0.01024	0.005898
fixed	NA	sibling_count5	-0.00477	0.0034	-1.403	6232	0.1607	-0.01431	0.004774
fixed	NA	sibling_count>5	-0.006043	0.003442	-1.756	6232	0.07922	-0.0157	0.003619
fixed	NA	birth_order_nonlinear2	-0.005037	0.002194	-2.296	6232	0.02171	-0.01119	0.001121
fixed	NA	birth_order_nonlinear3	-0.0001685	0.002691	-0.06262	6232	0.9501	-0.007723	0.007386
fixed	NA	birth_order_nonlinear4	0.002693	0.003327	0.8095	6232	0.4183	-0.006646	0.01203
fixed	NA	birth_order_nonlinear5	0.0002744	0.004181	0.06563	6232	0.9477	-0.01146	0.01201
fixed	NA	birth_order_nonlinear>5	-0.004911	0.00408	-1.204	6232	0.2287	-0.01636	0.00654
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.06558	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)	1.014	0.02858	35.49	6222	2.077e-251	0.9342	1.095
fixed	NA	poly(age, 3, raw = TRUE)1	-0.00219	0.00324	-0.6758	6222	0.4992	-0.01128	0.006905
fixed	NA	poly(age, 3, raw = TRUE)2	0.00009155	0.0001157	0.7913	6222	0.4288	-0.0002332	0.0004163
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001146	0.000001312	-0.8737	6222	0.3823	-0.000004828	0.000002536
fixed	NA	male	0.0001459	0.001662	0.08779	6222	0.93	-0.004519	0.004811
fixed	NA	count_birth_order2/2	-0.003615	0.003935	-0.9188	6222	0.3582	-0.01466	0.007429
fixed	NA	count_birth_order1/3	-0.0004489	0.003422	-0.1312	6222	0.8956	-0.01006	0.009158
fixed	NA	count_birth_order2/3	-0.004972	0.003731	-1.333	6222	0.1827	-0.01544	0.005501
fixed	NA	count_birth_order3/3	0.0009987	0.004173	0.2393	6222	0.8108	-0.01071	0.01271
fixed	NA	count_birth_order1/4	-0.001972	0.004172	-0.4727	6222	0.6365	-0.01368	0.009738
fixed	NA	count_birth_order2/4	-0.005412	0.004322	-1.252	6222	0.2105	-0.01754	0.00672
fixed	NA	count_birth_order3/4	0.000761	0.00458	0.1662	6222	0.868	-0.0121	0.01362
fixed	NA	count_birth_order4/4	-0.003091	0.004762	-0.6492	6222	0.5163	-0.01646	0.01027
fixed	NA	count_birth_order1/5	-0.005454	0.005692	-0.9582	6222	0.338	-0.02143	0.01052
fixed	NA	count_birth_order2/5	-0.02171	0.006134	-3.539	6222	0.0004039	-0.03893	-0.004492
fixed	NA	count_birth_order3/5	0.0004959	0.00569	0.08716	6222	0.9305	-0.01548	0.01647
fixed	NA	count_birth_order4/5	0.0006201	0.005594	0.1109	6222	0.9117	-0.01508	0.01632
fixed	NA	count_birth_order5/5	0.0007406	0.005808	0.1275	6222	0.8985	-0.01556	0.01704
fixed	NA	count_birth_order1/>5	0.0007324	0.00565	0.1296	6222	0.8969	-0.01513	0.01659
fixed	NA	count_birth_order2/>5	-0.005395	0.005634	-0.9577	6222	0.3383	-0.02121	0.01042
fixed	NA	count_birth_order3/>5	-0.01633	0.005546	-2.945	6222	0.003237	-0.0319	-0.0007676
fixed	NA	count_birth_order4/>5	0.0004021	0.005225	0.07696	6222	0.9387	-0.01426	0.01507
fixed	NA	count_birth_order5/>5	-0.00845	0.005	-1.69	6222	0.09108	-0.02248	0.005585
fixed	NA	count_birth_order>5/>5	-0.01044	0.003679	-2.838	6222	0.004558	-0.02077	-0.0001129
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.06554	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)
11	-16291	-16217	8157	-16313	NA	NA	NA
12	-16291	-16210	8158	-16315	2.061	1	0.1511
16	-16291	-16183	8161	-16323	7.77	4	0.1004
26	-16288	-16113	8170	-16340	16.98	10	0.07483

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)	1.012	0.02829	35.76	6295	4.227e-255	0.9322	1.091
fixed	NA	poly(age, 3, raw = TRUE)1	-0.001995	0.003211	-0.6213	6295	0.5344	-0.01101	0.007019
fixed	NA	poly(age, 3, raw = TRUE)2	0.00008284	0.0001147	0.7224	6295	0.4701	-0.0002391	0.0004047
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001035	0.0000013	-0.7966	6295	0.4257	-0.000004684	0.000002613
fixed	NA	male	0.0001628	0.001648	0.09879	6295	0.9213	-0.004463	0.004788
fixed	NA	sibling_count3	-0.0002068	0.002719	-0.07605	6295	0.9394	-0.00784	0.007427
fixed	NA	sibling_count4	-0.00003864	0.002839	-0.01361	6295	0.9891	-0.008008	0.007931
fixed	NA	sibling_count5	-0.001917	0.003027	-0.6333	6295	0.5266	-0.01041	0.006579
fixed	NA	sibling_count>5	-0.00446	0.002648	-1.684	6295	0.09219	-0.01189	0.002974
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.06532	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)	1.012	0.02829	35.78	6294	2.301e-255	0.9329	1.092
fixed	NA	birth_order	-0.0006005	0.0004664	-1.288	6294	0.1979	-0.00191	0.0007086
fixed	NA	poly(age, 3, raw = TRUE)1	-0.002002	0.003211	-0.6233	6294	0.5331	-0.01102	0.007012
fixed	NA	poly(age, 3, raw = TRUE)2	0.00008416	0.0001147	0.7339	6294	0.463	-0.0002377	0.000406
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001072	0.0000013	-0.8247	6294	0.4096	-0.000004721	0.000002577
fixed	NA	male	0.000178	0.001648	0.108	6294	0.914	-0.004447	0.004803
fixed	NA	sibling_count3	0.00008331	0.002729	0.03053	6294	0.9756	-0.007576	0.007743
fixed	NA	sibling_count4	0.0006008	0.002882	0.2085	6294	0.8349	-0.007489	0.008691
fixed	NA	sibling_count5	-0.0009089	0.003126	-0.2907	6294	0.7713	-0.009684	0.007867
fixed	NA	sibling_count>5	-0.002282	0.003142	-0.7263	6294	0.4677	-0.0111	0.006538
ran_pars	mother_pidlink	sd__(Intercept)	0.000000001071	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.06532	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)	1.015	0.02832	35.85	6290	2.461e-256	0.9359	1.095
fixed	NA	poly(age, 3, raw = TRUE)1	-0.002241	0.003211	-0.6979	6290	0.4853	-0.01126	0.006773
fixed	NA	poly(age, 3, raw = TRUE)2	0.00009272	0.0001147	0.8084	6290	0.4189	-0.0002292	0.0004147
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001162	0.0000013	-0.8934	6290	0.3717	-0.000004812	0.000002488
fixed	NA	male	0.00009342	0.001647	0.05671	6290	0.9548	-0.004531	0.004718
fixed	NA	sibling_count3	-0.0001752	0.002785	-0.06292	6290	0.9498	-0.007992	0.007642
fixed	NA	sibling_count4	-0.0005815	0.002996	-0.1941	6290	0.8461	-0.008991	0.007828
fixed	NA	sibling_count5	-0.003249	0.003294	-0.9863	6290	0.324	-0.0125	0.005998
fixed	NA	sibling_count>5	-0.003948	0.003257	-1.212	6290	0.2254	-0.01309	0.005193
fixed	NA	birth_order_nonlinear2	-0.005297	0.00222	-2.386	6290	0.01706	-0.01153	0.0009346
fixed	NA	birth_order_nonlinear3	-0.0005044	0.002664	-0.1893	6290	0.8498	-0.007982	0.006974
fixed	NA	birth_order_nonlinear4	0.001782	0.003203	0.5562	6290	0.5781	-0.00721	0.01077
fixed	NA	birth_order_nonlinear5	0.001802	0.003933	0.4582	6290	0.6468	-0.009237	0.01284
fixed	NA	birth_order_nonlinear>5	-0.005815	0.003619	-1.607	6290	0.1082	-0.01597	0.004344
ran_pars	mother_pidlink	sd__(Intercept)	0.0000000003181	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.06529	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)	1.015	0.02836	35.79	6280	2.026e-255	0.9353	1.095
fixed	NA	poly(age, 3, raw = TRUE)1	-0.002231	0.003215	-0.694	6280	0.4877	-0.01126	0.006793
fixed	NA	poly(age, 3, raw = TRUE)2	0.00009229	0.0001148	0.8037	6280	0.4216	-0.0002301	0.0004146
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001156	0.000001302	-0.8876	6280	0.3748	-0.000004811	0.0000025
fixed	NA	male	0.0001064	0.001648	0.06454	6280	0.9485	-0.004519	0.004732
fixed	NA	count_birth_order2/2	-0.004276	0.004292	-0.9963	6280	0.3191	-0.01632	0.007771
fixed	NA	count_birth_order1/3	-0.0003683	0.003692	-0.09976	6280	0.9205	-0.01073	0.009996
fixed	NA	count_birth_order2/3	-0.00554	0.004017	-1.379	6280	0.168	-0.01682	0.005737
fixed	NA	count_birth_order3/3	0.001302	0.004497	0.2896	6280	0.7722	-0.01132	0.01392
fixed	NA	count_birth_order1/4	-0.001762	0.004341	-0.406	6280	0.6848	-0.01395	0.01042
fixed	NA	count_birth_order2/4	-0.001991	0.004433	-0.4491	6280	0.6534	-0.01443	0.01045
fixed	NA	count_birth_order3/4	0.0011	0.004877	0.2256	6280	0.8215	-0.01259	0.01479
fixed	NA	count_birth_order4/4	-0.003243	0.005046	-0.6427	6280	0.5204	-0.01741	0.01092
fixed	NA	count_birth_order1/5	-0.003534	0.005172	-0.6833	6280	0.4945	-0.01805	0.01098
fixed	NA	count_birth_order2/5	-0.01611	0.005572	-2.891	6280	0.003849	-0.03175	-0.0004697
fixed	NA	count_birth_order3/5	0.0009379	0.005428	0.1728	6280	0.8628	-0.0143	0.01618
fixed	NA	count_birth_order4/5	0.001	0.005696	0.1756	6280	0.8606	-0.01499	0.01699
fixed	NA	count_birth_order5/5	0.001112	0.005673	0.196	6280	0.8446	-0.01481	0.01704
fixed	NA	count_birth_order1/>5	0.001216	0.00493	0.2466	6280	0.8052	-0.01262	0.01505
fixed	NA	count_birth_order2/>5	-0.008076	0.005152	-1.568	6280	0.117	-0.02254	0.006385
fixed	NA	count_birth_order3/>5	-0.01154	0.005022	-2.297	6280	0.02165	-0.02564	0.002561
fixed	NA	count_birth_order4/>5	0.0009338	0.004821	0.1937	6280	0.8464	-0.0126	0.01447
fixed	NA	count_birth_order5/>5	-0.003345	0.00499	-0.6702	6280	0.5028	-0.01735	0.01066
fixed	NA	count_birth_order>5/>5	-0.009414	0.003609	-2.609	6280	0.00911	-0.01954	0.0007156
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.06528	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)
11	-16498	-16423	8260	-16520	NA	NA	NA
12	-16497	-16416	8261	-16521	1.66	1	0.1976
16	-16499	-16391	8266	-16531	9.831	4	0.04338
26	-16491	-16315	8271	-16543	11.8	10	0.2989

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)	1.018	0.02859	35.61	6115	1.509e-252	0.9377	1.098
fixed	NA	poly(age, 3, raw = TRUE)1	-0.00255	0.003245	-0.7858	6115	0.432	-0.01166	0.006559
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001017	0.0001159	0.8777	6115	0.3801	-0.0002236	0.000427
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000123	0.000001314	-0.936	6115	0.3493	-0.000004918	0.000002458
fixed	NA	male	-0.00009463	0.001664	-0.05687	6115	0.9546	-0.004765	0.004576
fixed	NA	sibling_count3	-0.001208	0.00246	-0.4911	6115	0.6234	-0.008115	0.005698
fixed	NA	sibling_count4	-0.003839	0.002643	-1.452	6115	0.1464	-0.01126	0.00358
fixed	NA	sibling_count5	-0.003218	0.003094	-1.04	6115	0.2983	-0.0119	0.005466
fixed	NA	sibling_count>5	-0.006981	0.002649	-2.636	6115	0.008414	-0.01442	0.0004534
ran_pars	mother_pidlink	sd__(Intercept)	0.0000000004397	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.06502	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)	1.019	0.02859	35.62	6114	9.457e-253	0.9382	1.099
fixed	NA	birth_order	-0.0006737	0.0005522	-1.22	6114	0.2225	-0.002224	0.0008763
fixed	NA	poly(age, 3, raw = TRUE)1	-0.002525	0.003245	-0.778	6114	0.4366	-0.01163	0.006584
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001021	0.0001159	0.8812	6114	0.3782	-0.0002231	0.0004274
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000126	0.000001314	-0.9586	6114	0.3378	-0.000004948	0.000002429
fixed	NA	male	-0.0000827	0.001664	-0.0497	6114	0.9604	-0.004753	0.004588
fixed	NA	sibling_count3	-0.0008808	0.002475	-0.3559	6114	0.7219	-0.007828	0.006067
fixed	NA	sibling_count4	-0.0031	0.002712	-1.143	6114	0.253	-0.01071	0.004512
fixed	NA	sibling_count5	-0.002043	0.00324	-0.6306	6114	0.5284	-0.01114	0.007051
fixed	NA	sibling_count>5	-0.004499	0.00334	-1.347	6114	0.178	-0.01387	0.004876
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.06501	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)	1.021	0.02862	35.68	6110	1.688e-253	0.941	1.102
fixed	NA	poly(age, 3, raw = TRUE)1	-0.002776	0.003246	-0.8553	6110	0.3924	-0.01189	0.006335
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001105	0.0001159	0.9533	6110	0.3405	-0.0002149	0.0004359
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001342	0.000001315	-1.021	6110	0.3075	-0.000005032	0.000002349
fixed	NA	male	-0.0001589	0.001664	-0.0955	6110	0.9239	-0.004829	0.004511
fixed	NA	sibling_count3	-0.001365	0.002536	-0.5382	6110	0.5905	-0.008485	0.005755
fixed	NA	sibling_count4	-0.004754	0.002838	-1.675	6110	0.09402	-0.01272	0.003214
fixed	NA	sibling_count5	-0.003792	0.003416	-1.11	6110	0.267	-0.01338	0.005797
fixed	NA	sibling_count>5	-0.006122	0.003464	-1.768	6110	0.07718	-0.01584	0.0036
fixed	NA	birth_order_nonlinear2	-0.004324	0.002171	-1.992	6110	0.04639	-0.01042	0.001769
fixed	NA	birth_order_nonlinear3	0.0001426	0.002671	0.05338	6110	0.9574	-0.007355	0.00764
fixed	NA	birth_order_nonlinear4	0.00281	0.003394	0.828	6110	0.4077	-0.006717	0.01234
fixed	NA	birth_order_nonlinear5	-0.004068	0.004315	-0.9426	6110	0.3459	-0.01618	0.008045
fixed	NA	birth_order_nonlinear>5	-0.004234	0.004176	-1.014	6110	0.3107	-0.01596	0.007488
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.065	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)	1.021	0.02867	35.61	6100	1.551e-252	0.9404	1.101
fixed	NA	poly(age, 3, raw = TRUE)1	-0.002721	0.003251	-0.8371	6100	0.4026	-0.01185	0.006403
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001088	0.0001161	0.9369	6100	0.3489	-0.0002171	0.0004347
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001325	0.000001317	-1.006	6100	0.3146	-0.000005021	0.000002372
fixed	NA	male	-0.00008317	0.001664	-0.04997	6100	0.9601	-0.004755	0.004589
fixed	NA	count_birth_order2/2	-0.004503	0.003796	-1.186	6100	0.2356	-0.01516	0.006153
fixed	NA	count_birth_order1/3	-0.001611	0.003351	-0.4808	6100	0.6307	-0.01102	0.007796
fixed	NA	count_birth_order2/3	-0.00631	0.0037	-1.705	6100	0.0882	-0.0167	0.004077
fixed	NA	count_birth_order3/3	-0.0002261	0.004069	-0.05556	6100	0.9557	-0.01165	0.01119
fixed	NA	count_birth_order1/4	-0.008884	0.004156	-2.137	6100	0.0326	-0.02055	0.002783
fixed	NA	count_birth_order2/4	-0.006667	0.004294	-1.552	6100	0.1206	-0.01872	0.005387
fixed	NA	count_birth_order3/4	-0.0003684	0.004503	-0.08182	6100	0.9348	-0.01301	0.01227
fixed	NA	count_birth_order4/4	-0.004377	0.004758	-0.9199	6100	0.3576	-0.01773	0.008978
fixed	NA	count_birth_order1/5	-0.0004467	0.005644	-0.07915	6100	0.9369	-0.01629	0.0154
fixed	NA	count_birth_order2/5	-0.01668	0.006279	-2.656	6100	0.00793	-0.0343	0.0009487
fixed	NA	count_birth_order3/5	-0.0006599	0.005896	-0.1119	6100	0.9109	-0.01721	0.01589
fixed	NA	count_birth_order4/5	-0.000488	0.0058	-0.08414	6100	0.9329	-0.01677	0.01579
fixed	NA	count_birth_order5/5	-0.008039	0.006139	-1.309	6100	0.1904	-0.02527	0.009193
fixed	NA	count_birth_order1/>5	-0.0002868	0.005746	-0.04992	6100	0.9602	-0.01642	0.01584
fixed	NA	count_birth_order2/>5	-0.006855	0.005725	-1.197	6100	0.2312	-0.02293	0.009216
fixed	NA	count_birth_order3/>5	-0.01792	0.005558	-3.225	6100	0.001268	-0.03352	-0.002321
fixed	NA	count_birth_order4/>5	-0.0006839	0.005444	-0.1256	6100	0.9	-0.01597	0.0146
fixed	NA	count_birth_order5/>5	-0.0102	0.005072	-2.011	6100	0.04438	-0.02443	0.004038
fixed	NA	count_birth_order>5/>5	-0.01043	0.003711	-2.812	6100	0.004944	-0.02085	-0.00001732
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.06498	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)
11	-16083	-16009	8052	-16105	NA	NA	NA
12	-16082	-16002	8053	-16106	1.491	1	0.2221
16	-16081	-15974	8057	-16113	6.603	4	0.1584
26	-16075	-15901	8064	-16127	14.38	10	0.1565

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)	-2.166	0.3787	-5.72	5937	0.00000001118	-3.23	-1.103
fixed	NA	poly(age, 3, raw = TRUE)1	0.1631	0.03571	4.567	5923	0.00000505	0.06284	0.2633
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003976	0.001063	-3.739	5911	0.0001865	-0.00696	-0.0009909
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003055	0.00001006	3.036	5906	0.002407	0.000002305	0.00005879
fixed	NA	male	0.1388	0.02631	5.276	5982	0.0000001363	0.06498	0.2127
fixed	NA	sibling_count3	0.1019	0.05214	1.954	4767	0.05082	-0.0445	0.2482
fixed	NA	sibling_count4	0.05405	0.05208	1.038	4546	0.2994	-0.09213	0.2002
fixed	NA	sibling_count5	0.05158	0.05423	0.9512	4306	0.3415	-0.1006	0.2038
fixed	NA	sibling_count>5	-0.003651	0.04276	-0.08539	4670	0.932	-0.1237	0.1164
ran_pars	mother_pidlink	sd__(Intercept)	0.2708	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.95	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)	-2.15	0.3789	-5.675	5935	0.00000001457	-3.213	-1.086
fixed	NA	birth_order	0.007971	0.005175	1.54	4824	0.1235	-0.006554	0.0225
fixed	NA	poly(age, 3, raw = TRUE)1	0.1595	0.03578	4.457	5913	0.000008464	0.05903	0.2599
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003854	0.001066	-3.615	5893	0.0003034	-0.006846	-0.0008609
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000294	0.00001009	2.914	5885	0.003576	0.000001084	0.00005772
fixed	NA	male	0.1384	0.02631	5.26	5981	0.0000001487	0.06455	0.2123
fixed	NA	sibling_count3	0.0995	0.05217	1.907	4769	0.05654	-0.04694	0.2459
fixed	NA	sibling_count4	0.04798	0.05223	0.9185	4568	0.3584	-0.09865	0.1946
fixed	NA	sibling_count5	0.04152	0.05463	0.7601	4344	0.4472	-0.1118	0.1949
fixed	NA	sibling_count>5	-0.03363	0.04698	-0.7158	4986	0.4741	-0.1655	0.09824
ran_pars	mother_pidlink	sd__(Intercept)	0.2729	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9493	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)	-2.148	0.3795	-5.66	5928	0.00000001586	-3.213	-1.083
fixed	NA	poly(age, 3, raw = TRUE)1	0.1602	0.03579	4.475	5909	0.000007783	0.0597	0.2606
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003894	0.001067	-3.65	5888	0.0002643	-0.006889	-0.0008995
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002995	0.0000101	2.965	5877	0.003036	0.000001599	0.0000583
fixed	NA	male	0.1388	0.02631	5.274	5977	0.0000001381	0.06492	0.2127
fixed	NA	sibling_count3	0.09578	0.05293	1.809	4894	0.07044	-0.0528	0.2444
fixed	NA	sibling_count4	0.03642	0.05393	0.6753	4841	0.4995	-0.115	0.1878
fixed	NA	sibling_count5	0.01732	0.05692	0.3043	4717	0.7609	-0.1425	0.1771
fixed	NA	sibling_count>5	-0.04504	0.0495	-0.9098	5352	0.3629	-0.184	0.09391
fixed	NA	birth_order_nonlinear2	0.02294	0.03805	0.6028	5545	0.5467	-0.08387	0.1297
fixed	NA	birth_order_nonlinear3	0.03579	0.04407	0.8122	5531	0.4167	-0.0879	0.1595
fixed	NA	birth_order_nonlinear4	0.07121	0.04928	1.445	5595	0.1485	-0.06711	0.2095
fixed	NA	birth_order_nonlinear5	0.1192	0.05594	2.131	5583	0.03312	-0.03781	0.2762
fixed	NA	birth_order_nonlinear>5	0.0531	0.04599	1.155	5960	0.2483	-0.07601	0.1822
ran_pars	mother_pidlink	sd__(Intercept)	0.2737	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9492	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)	-2.12	0.3809	-5.565	5920	0.0000000274	-3.189	-1.05
fixed	NA	poly(age, 3, raw = TRUE)1	0.1581	0.03585	4.409	5898	0.00001057	0.05743	0.2587
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00382	0.001069	-3.574	5875	0.0003546	-0.00682	-0.0008196
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002915	0.00001012	2.88	5862	0.003988	0.0000007407	0.00005757
fixed	NA	male	0.1379	0.02635	5.235	5967	0.0000001702	0.06398	0.2119
fixed	NA	count_birth_order2/2	-0.006871	0.07714	-0.08907	5560	0.929	-0.2234	0.2097
fixed	NA	count_birth_order1/3	0.1024	0.06942	1.475	5953	0.1403	-0.09247	0.2972
fixed	NA	count_birth_order2/3	0.08335	0.0791	1.054	5964	0.292	-0.1387	0.3054
fixed	NA	count_birth_order3/3	0.1205	0.08859	1.361	5968	0.1737	-0.1281	0.3692
fixed	NA	count_birth_order1/4	0.06485	0.07708	0.8413	5962	0.4002	-0.1515	0.2812
fixed	NA	count_birth_order2/4	0.08698	0.08249	1.054	5964	0.2917	-0.1446	0.3185
fixed	NA	count_birth_order3/4	-0.04521	0.08657	-0.5222	5967	0.6016	-0.2882	0.1978
fixed	NA	count_birth_order4/4	0.108	0.09454	1.142	5968	0.2535	-0.1574	0.3733
fixed	NA	count_birth_order1/5	-0.03409	0.08715	-0.3912	5966	0.6956	-0.2787	0.2105
fixed	NA	count_birth_order2/5	0.1125	0.09623	1.169	5967	0.2425	-0.1576	0.3826
fixed	NA	count_birth_order3/5	0.05178	0.09796	0.5285	5967	0.5971	-0.2232	0.3268
fixed	NA	count_birth_order4/5	0.03552	0.09973	0.3561	5964	0.7218	-0.2444	0.3155
fixed	NA	count_birth_order5/5	0.1267	0.1031	1.229	5966	0.2192	-0.1627	0.4161
fixed	NA	count_birth_order1/>5	-0.09157	0.06947	-1.318	5968	0.1875	-0.2866	0.1034
fixed	NA	count_birth_order2/>5	-0.06085	0.07256	-0.8386	5966	0.4017	-0.2645	0.1428
fixed	NA	count_birth_order3/>5	0.0349	0.07161	0.4874	5965	0.626	-0.1661	0.2359
fixed	NA	count_birth_order4/>5	0.02553	0.06944	0.3677	5968	0.7131	-0.1694	0.2204
fixed	NA	count_birth_order5/>5	0.06345	0.07022	0.9035	5965	0.3663	-0.1337	0.2606
fixed	NA	count_birth_order>5/>5	-0.002149	0.05532	-0.03884	5572	0.969	-0.1574	0.1531
ran_pars	mother_pidlink	sd__(Intercept)	0.2764	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9487	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)
11	16856	16930	-8417	16834	NA	NA	NA
12	16856	16936	-8416	16832	2.37	1	0.1237
16	16861	16968	-8415	16829	2.788	4	0.5939
26	16875	17049	-8411	16823	6.743	10	0.7495

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)	-2.967	0.8516	-3.484	2520	0.0005031	-5.357	-0.5762
fixed	NA	poly(age, 3, raw = TRUE)1	0.24	0.09033	2.656	2522	0.007946	-0.0136	0.4935
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00612	0.003071	-1.993	2524	0.0464	-0.01474	0.002501
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005134	0.00003351	1.532	2526	0.1256	-0.00004272	0.0001454
fixed	NA	male	0.1734	0.03918	4.426	2528	0.00001003	0.06341	0.2833
fixed	NA	sibling_count3	0.05539	0.06069	0.9127	2127	0.3615	-0.115	0.2257
fixed	NA	sibling_count4	-0.05519	0.06241	-0.8843	1977	0.3766	-0.2304	0.12
fixed	NA	sibling_count5	-0.1223	0.07112	-1.72	1841	0.08567	-0.3219	0.07733
fixed	NA	sibling_count>5	-0.1055	0.06141	-1.718	1733	0.08605	-0.2778	0.0669
ran_pars	mother_pidlink	sd__(Intercept)	0.1431	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9554	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)	-2.949	0.851	-3.465	2520	0.0005386	-5.338	-0.5601
fixed	NA	birth_order	0.02897	0.01228	2.359	2271	0.01839	-0.005497	0.06345
fixed	NA	poly(age, 3, raw = TRUE)1	0.2348	0.09028	2.601	2521	0.009363	-0.01865	0.4882
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005999	0.003069	-1.955	2523	0.05071	-0.01461	0.002615
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005109	0.00003348	1.526	2525	0.1272	-0.00004289	0.0001451
fixed	NA	male	0.1711	0.03915	4.371	2528	0.00001286	0.06124	0.2811
fixed	NA	sibling_count3	0.04128	0.06096	0.6772	2126	0.4983	-0.1298	0.2124
fixed	NA	sibling_count4	-0.08726	0.06386	-1.367	1980	0.1719	-0.2665	0.09198
fixed	NA	sibling_count5	-0.1757	0.07463	-2.355	1843	0.01865	-0.3852	0.03376
fixed	NA	sibling_count>5	-0.2097	0.07565	-2.772	1785	0.005637	-0.422	0.002683
ran_pars	mother_pidlink	sd__(Intercept)	0.1526	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9531	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)	-2.933	0.8519	-3.443	2516	0.0005837	-5.325	-0.5421
fixed	NA	poly(age, 3, raw = TRUE)1	0.2365	0.09037	2.617	2518	0.008922	-0.01717	0.4902
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006059	0.003072	-1.972	2520	0.04867	-0.01468	0.002564
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000517	0.00003351	1.543	2522	0.123	-0.00004237	0.0001458
fixed	NA	male	0.1724	0.03916	4.402	2524	0.00001117	0.06247	0.2823
fixed	NA	sibling_count3	0.02577	0.06226	0.4139	2185	0.679	-0.149	0.2005
fixed	NA	sibling_count4	-0.1117	0.06659	-1.678	2118	0.09355	-0.2986	0.0752
fixed	NA	sibling_count5	-0.1958	0.07894	-2.48	2016	0.01321	-0.4174	0.02579
fixed	NA	sibling_count>5	-0.2197	0.07809	-2.813	1897	0.004958	-0.4389	-0.0004703
fixed	NA	birth_order_nonlinear2	0.02232	0.05137	0.4345	2297	0.664	-0.1219	0.1665
fixed	NA	birth_order_nonlinear3	0.1267	0.06161	2.057	2378	0.03981	-0.04622	0.2997
fixed	NA	birth_order_nonlinear4	0.1321	0.07471	1.769	2427	0.07707	-0.07757	0.3418
fixed	NA	birth_order_nonlinear5	0.0958	0.09391	1.02	2472	0.3078	-0.1678	0.3594
fixed	NA	birth_order_nonlinear>5	0.1847	0.09213	2.004	2440	0.04515	-0.07396	0.4433
ran_pars	mother_pidlink	sd__(Intercept)	0.1585	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9525	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)	-2.924	0.8537	-3.424	2506	0.000626	-5.32	-0.5271
fixed	NA	poly(age, 3, raw = TRUE)1	0.2359	0.09068	2.601	2508	0.009348	-0.01868	0.4904
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006003	0.003083	-1.947	2510	0.05162	-0.01466	0.002651
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005074	0.00003364	1.508	2512	0.1316	-0.00004369	0.0001452
fixed	NA	male	0.1682	0.03928	4.281	2515	0.00001927	0.05791	0.2784
fixed	NA	count_birth_order2/2	-0.01186	0.09694	-0.1223	2306	0.9027	-0.284	0.2603
fixed	NA	count_birth_order1/3	0.002427	0.08014	0.03029	2517	0.9758	-0.2225	0.2274
fixed	NA	count_birth_order2/3	0.08795	0.09083	0.9683	2517	0.333	-0.167	0.3429
fixed	NA	count_birth_order3/3	0.09969	0.1004	0.9929	2516	0.3208	-0.1821	0.3815
fixed	NA	count_birth_order1/4	-0.193	0.09389	-2.056	2517	0.03989	-0.4566	0.07052
fixed	NA	count_birth_order2/4	-0.03204	0.09714	-0.3299	2517	0.7415	-0.3047	0.2406
fixed	NA	count_birth_order3/4	0.05193	0.1026	0.5059	2516	0.6129	-0.2362	0.34
fixed	NA	count_birth_order4/4	-0.03512	0.11	-0.3193	2516	0.7495	-0.3439	0.2736
fixed	NA	count_birth_order1/5	-0.0734	0.127	-0.5779	2517	0.5634	-0.4299	0.2831
fixed	NA	count_birth_order2/5	-0.2006	0.1483	-1.353	2516	0.1762	-0.6169	0.2156
fixed	NA	count_birth_order3/5	-0.1334	0.1329	-1.003	2517	0.3158	-0.5065	0.2398
fixed	NA	count_birth_order4/5	-0.06657	0.1264	-0.5265	2516	0.5986	-0.4214	0.2883
fixed	NA	count_birth_order5/5	-0.2006	0.1302	-1.54	2516	0.1236	-0.5662	0.165
fixed	NA	count_birth_order1/>5	-0.204	0.1252	-1.629	2514	0.1034	-0.5555	0.1475
fixed	NA	count_birth_order2/>5	-0.4087	0.1263	-3.236	2516	0.001229	-0.7632	-0.05415
fixed	NA	count_birth_order3/>5	-0.06434	0.1266	-0.5081	2517	0.6115	-0.4198	0.2911
fixed	NA	count_birth_order4/>5	-0.05434	0.1165	-0.4663	2517	0.641	-0.3815	0.2728
fixed	NA	count_birth_order5/>5	-0.07096	0.1149	-0.6177	2516	0.5368	-0.3934	0.2515
fixed	NA	count_birth_order>5/>5	-0.04591	0.08527	-0.5384	2356	0.5904	-0.2853	0.1934
ran_pars	mother_pidlink	sd__(Intercept)	0.1652	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9515	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)
11	7048	7112	-3513	7026	NA	NA	NA
12	7045	7115	-3510	7021	5.566	1	0.01831
16	7051	7144	-3509	7019	1.971	4	0.741
26	7061	7213	-3505	7009	9.311	10	0.5029

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)	-3.021	0.8508	-3.551	2536	0.0003903	-5.409	-0.6332
fixed	NA	poly(age, 3, raw = TRUE)1	0.2478	0.09033	2.744	2537	0.006121	-0.005736	0.5014
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006428	0.003071	-2.093	2540	0.03643	-0.01505	0.002192
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005481	0.00003351	1.636	2541	0.102	-0.00003925	0.0001489
fixed	NA	male	0.1666	0.03915	4.256	2545	0.00002155	0.05673	0.2765
fixed	NA	sibling_count3	0.03445	0.06704	0.5139	2194	0.6074	-0.1537	0.2226
fixed	NA	sibling_count4	0.00218	0.06772	0.03219	2086	0.9743	-0.1879	0.1923
fixed	NA	sibling_count5	-0.1056	0.0713	-1.481	1944	0.1387	-0.3058	0.09454
fixed	NA	sibling_count>5	-0.08992	0.06331	-1.42	2003	0.1557	-0.2676	0.0878
ran_pars	mother_pidlink	sd__(Intercept)	0.1499	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9564	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)	-3.016	0.8506	-3.546	2535	0.0003985	-5.403	-0.6284
fixed	NA	birth_order	0.01776	0.01074	1.653	2211	0.09839	-0.01239	0.04792
fixed	NA	poly(age, 3, raw = TRUE)1	0.2451	0.09032	2.714	2537	0.006698	-0.008426	0.4986
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006365	0.00307	-2.073	2539	0.03828	-0.01498	0.002254
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005472	0.0000335	1.633	2541	0.1025	-0.00003932	0.0001488
fixed	NA	male	0.1651	0.03914	4.218	2544	0.00002552	0.05523	0.275
fixed	NA	sibling_count3	0.0256	0.06726	0.3806	2191	0.7036	-0.1632	0.2144
fixed	NA	sibling_count4	-0.01668	0.06869	-0.2428	2080	0.8082	-0.2095	0.1761
fixed	NA	sibling_count5	-0.1356	0.07361	-1.842	1940	0.06558	-0.3422	0.07101
fixed	NA	sibling_count>5	-0.1524	0.07377	-2.066	1993	0.039	-0.3594	0.0547
ran_pars	mother_pidlink	sd__(Intercept)	0.1605	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9544	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)	-3.025	0.8511	-3.555	2531	0.0003854	-5.414	-0.6363
fixed	NA	poly(age, 3, raw = TRUE)1	0.247	0.09037	2.733	2533	0.006314	-0.006665	0.5007
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006441	0.003072	-2.097	2536	0.03612	-0.01506	0.002182
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005564	0.00003352	1.66	2538	0.09702	-0.00003844	0.0001497
fixed	NA	male	0.1661	0.03914	4.244	2541	0.00002278	0.05623	0.276
fixed	NA	sibling_count3	0.005788	0.06854	0.08445	2232	0.9327	-0.1866	0.1982
fixed	NA	sibling_count4	-0.05279	0.07109	-0.7426	2178	0.4578	-0.2523	0.1468
fixed	NA	sibling_count5	-0.167	0.07725	-2.161	2080	0.03079	-0.3838	0.04989
fixed	NA	sibling_count>5	-0.1714	0.07608	-2.254	2088	0.02433	-0.385	0.04211
fixed	NA	birth_order_nonlinear2	0.05834	0.0521	1.12	2328	0.263	-0.08792	0.2046
fixed	NA	birth_order_nonlinear3	0.1224	0.06201	1.974	2428	0.04852	-0.05167	0.2965
fixed	NA	birth_order_nonlinear4	0.1577	0.07258	2.173	2452	0.02989	-0.04603	0.3614
fixed	NA	birth_order_nonlinear5	0.07475	0.08919	0.8381	2485	0.4021	-0.1756	0.3251
fixed	NA	birth_order_nonlinear>5	0.1222	0.08292	1.473	2441	0.1409	-0.1106	0.3549
ran_pars	mother_pidlink	sd__(Intercept)	0.1634	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9539	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)	-3.005	0.8535	-3.521	2521	0.0004373	-5.401	-0.6095
fixed	NA	poly(age, 3, raw = TRUE)1	0.2466	0.09072	2.718	2523	0.006617	-0.008097	0.5012
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006401	0.003084	-2.075	2525	0.03805	-0.01506	0.002256
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005498	0.00003365	1.634	2527	0.1024	-0.00003948	0.0001495
fixed	NA	male	0.1643	0.03928	4.183	2531	0.00002976	0.05404	0.2745
fixed	NA	count_birth_order2/2	-0.01229	0.1097	-0.112	2369	0.9108	-0.3202	0.2956
fixed	NA	count_birth_order1/3	-0.03131	0.08855	-0.3535	2533	0.7237	-0.2799	0.2173
fixed	NA	count_birth_order2/3	0.1016	0.09821	1.035	2533	0.3009	-0.1741	0.3773
fixed	NA	count_birth_order3/3	0.054	0.1103	0.4897	2533	0.6244	-0.2556	0.3636
fixed	NA	count_birth_order1/4	-0.1062	0.09942	-1.068	2533	0.2857	-0.3852	0.1729
fixed	NA	count_birth_order2/4	0.06707	0.1002	0.6692	2533	0.5034	-0.2143	0.3484
fixed	NA	count_birth_order3/4	0.02235	0.1126	0.1984	2533	0.8427	-0.2938	0.3385
fixed	NA	count_birth_order4/4	0.02293	0.1206	0.19	2532	0.8493	-0.3157	0.3616
fixed	NA	count_birth_order1/5	-0.1291	0.116	-1.113	2533	0.2659	-0.4547	0.1965
fixed	NA	count_birth_order2/5	-0.1532	0.1278	-1.199	2532	0.2307	-0.5118	0.2055
fixed	NA	count_birth_order3/5	-0.05305	0.1277	-0.4155	2532	0.6778	-0.4115	0.3054
fixed	NA	count_birth_order4/5	-0.03084	0.1287	-0.2395	2531	0.8107	-0.3922	0.3306
fixed	NA	count_birth_order5/5	-0.1853	0.1282	-1.446	2532	0.1484	-0.5452	0.1746
fixed	NA	count_birth_order1/>5	-0.2191	0.1105	-1.984	2530	0.04737	-0.5292	0.09091
fixed	NA	count_birth_order2/>5	-0.2885	0.1175	-2.456	2532	0.01411	-0.6183	0.04121
fixed	NA	count_birth_order3/>5	0.006948	0.1182	0.05879	2533	0.9531	-0.3248	0.3387
fixed	NA	count_birth_order4/>5	0.008072	0.1093	0.07383	2533	0.9411	-0.2988	0.315
fixed	NA	count_birth_order5/>5	-0.06426	0.1169	-0.5495	2531	0.5827	-0.3925	0.264
fixed	NA	count_birth_order>5/>5	-0.07115	0.08545	-0.8326	2414	0.4051	-0.311	0.1687
ran_pars	mother_pidlink	sd__(Intercept)	0.1732	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9527	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)
11	7103	7167	-3541	7081	NA	NA	NA
12	7102	7173	-3539	7078	2.723	1	0.0989
16	7106	7200	-3537	7074	3.99	4	0.4074
26	7119	7271	-3533	7067	7.706	10	0.6575

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)	-2.95	0.8647	-3.411	2471	0.0006572	-5.377	-0.5224
fixed	NA	poly(age, 3, raw = TRUE)1	0.2362	0.09172	2.575	2473	0.01007	-0.02125	0.4937
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005959	0.003116	-1.912	2475	0.05597	-0.01471	0.002789
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004927	0.00003398	1.45	2477	0.1472	-0.00004612	0.0001446
fixed	NA	male	0.1752	0.03992	4.388	2480	0.00001193	0.06311	0.2872
fixed	NA	sibling_count3	0.04336	0.06038	0.7181	2078	0.4728	-0.1261	0.2129
fixed	NA	sibling_count4	-0.08107	0.06277	-1.292	1918	0.1967	-0.2573	0.09513
fixed	NA	sibling_count5	-0.09708	0.07355	-1.32	1726	0.187	-0.3035	0.1094
fixed	NA	sibling_count>5	-0.08266	0.06241	-1.324	1639	0.1855	-0.2578	0.09252
ran_pars	mother_pidlink	sd__(Intercept)	0.15	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9632	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)	-2.931	0.8643	-3.391	2470	0.0007075	-5.357	-0.5047
fixed	NA	birth_order	0.02467	0.01273	1.938	2248	0.05277	-0.01107	0.06042
fixed	NA	poly(age, 3, raw = TRUE)1	0.2313	0.09171	2.523	2471	0.01171	-0.02609	0.4888
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005839	0.003115	-1.874	2474	0.061	-0.01458	0.002906
fixed	NA	poly(age, 3, raw = TRUE)3	0.00004885	0.00003396	1.438	2476	0.1505	-0.00004649	0.0001442
fixed	NA	male	0.1739	0.03991	4.357	2480	0.0000137	0.06187	0.2859
fixed	NA	sibling_count3	0.03093	0.06071	0.5095	2075	0.6105	-0.1395	0.2014
fixed	NA	sibling_count4	-0.108	0.06429	-1.68	1925	0.09304	-0.2885	0.07243
fixed	NA	sibling_count5	-0.1412	0.07701	-1.834	1734	0.06688	-0.3574	0.07497
fixed	NA	sibling_count>5	-0.1711	0.07736	-2.212	1731	0.02708	-0.3883	0.04601
ran_pars	mother_pidlink	sd__(Intercept)	0.1571	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9616	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)	-2.945	0.8651	-3.404	2466	0.0006738	-5.374	-0.5167
fixed	NA	poly(age, 3, raw = TRUE)1	0.2361	0.09179	2.573	2468	0.01015	-0.02152	0.4938
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006009	0.003118	-1.927	2470	0.05408	-0.01476	0.002744
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000507	0.000034	1.491	2473	0.136	-0.00004473	0.0001461
fixed	NA	male	0.1757	0.03993	4.402	2476	0.00001119	0.06367	0.2878
fixed	NA	sibling_count3	0.009872	0.06207	0.159	2135	0.8737	-0.1644	0.1841
fixed	NA	sibling_count4	-0.1259	0.06698	-1.88	2064	0.06029	-0.3139	0.06211
fixed	NA	sibling_count5	-0.1521	0.08111	-1.875	1911	0.0609	-0.3798	0.07557
fixed	NA	sibling_count>5	-0.1838	0.07992	-2.3	1849	0.02158	-0.4081	0.04056
fixed	NA	birth_order_nonlinear2	0.01217	0.05179	0.235	2249	0.8142	-0.1332	0.1576
fixed	NA	birth_order_nonlinear3	0.1384	0.0622	2.225	2331	0.02614	-0.03617	0.313
fixed	NA	birth_order_nonlinear4	0.05726	0.07794	0.7346	2369	0.4626	-0.1615	0.276
fixed	NA	birth_order_nonlinear5	0.07804	0.09835	0.7935	2397	0.4276	-0.198	0.3541
fixed	NA	birth_order_nonlinear>5	0.1773	0.09559	1.855	2387	0.0637	-0.09099	0.4457
ran_pars	mother_pidlink	sd__(Intercept)	0.1621	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9608	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)	-2.969	0.8669	-3.426	2456	0.0006237	-5.403	-0.5361
fixed	NA	poly(age, 3, raw = TRUE)1	0.2408	0.09211	2.615	2458	0.008989	-0.01773	0.4994
fixed	NA	poly(age, 3, raw = TRUE)2	-0.006135	0.003129	-1.96	2460	0.05006	-0.01492	0.002649
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005172	0.00003412	1.516	2462	0.1298	-0.00004407	0.0001475
fixed	NA	male	0.1726	0.04006	4.308	2466	0.00001712	0.06013	0.285
fixed	NA	count_birth_order2/2	-0.07046	0.09561	-0.7369	2240	0.4613	-0.3388	0.1979
fixed	NA	count_birth_order1/3	-0.04347	0.08004	-0.5431	2467	0.5871	-0.2681	0.1812
fixed	NA	count_birth_order2/3	0.06615	0.09109	0.7262	2468	0.4678	-0.1895	0.3218
fixed	NA	count_birth_order3/3	0.08534	0.09871	0.8646	2466	0.3874	-0.1917	0.3624
fixed	NA	count_birth_order1/4	-0.2178	0.09523	-2.287	2468	0.0223	-0.4851	0.04955
fixed	NA	count_birth_order2/4	-0.0797	0.09775	-0.8153	2468	0.415	-0.3541	0.1947
fixed	NA	count_birth_order3/4	0.04818	0.1035	0.4657	2468	0.6415	-0.2423	0.3386
fixed	NA	count_birth_order4/4	-0.1601	0.1133	-1.414	2467	0.1575	-0.478	0.1578
fixed	NA	count_birth_order1/5	-0.08318	0.1309	-0.6352	2468	0.5253	-0.4507	0.2844
fixed	NA	count_birth_order2/5	-0.1651	0.1522	-1.085	2468	0.2782	-0.5923	0.2622
fixed	NA	count_birth_order3/5	-0.09123	0.1405	-0.6492	2468	0.5163	-0.4857	0.3032
fixed	NA	count_birth_order4/5	-0.1192	0.1345	-0.8861	2467	0.3756	-0.4966	0.2583
fixed	NA	count_birth_order5/5	-0.1676	0.1392	-1.204	2467	0.2288	-0.5584	0.2232
fixed	NA	count_birth_order1/>5	-0.1719	0.1281	-1.342	2465	0.1799	-0.5314	0.1877
fixed	NA	count_birth_order2/>5	-0.3917	0.1323	-2.961	2468	0.003096	-0.763	-0.02036
fixed	NA	count_birth_order3/>5	-0.06893	0.1285	-0.5364	2468	0.5917	-0.4296	0.2918
fixed	NA	count_birth_order4/>5	-0.07846	0.1223	-0.6416	2467	0.5212	-0.4217	0.2648
fixed	NA	count_birth_order5/>5	-0.08894	0.1182	-0.7525	2467	0.4518	-0.4207	0.2428
fixed	NA	count_birth_order>5/>5	-0.03323	0.08726	-0.3809	2282	0.7033	-0.2782	0.2117
ran_pars	mother_pidlink	sd__(Intercept)	0.1651	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9606	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)
11	6958	7022	-3468	6936	NA	NA	NA
12	6956	7026	-3466	6932	3.756	1	0.05262
16	6960	7053	-3464	6928	3.587	4	0.4648
26	6971	7123	-3460	6919	8.955	10	0.5364

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)	-3.932	0.3808	-10.33	5912	8.56e-25	-5.001	-2.864
fixed	NA	poly(age, 3, raw = TRUE)1	0.3021	0.03594	8.408	5904	5.174e-17	0.2013	0.403
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007364	0.001071	-6.873	5897	6.923e-12	-0.01037	-0.004357
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005769	0.00001015	5.683	5892	0.00000001388	0.00002919	0.00008618
fixed	NA	male	0.1267	0.02642	4.798	5923	0.000001641	0.0526	0.2009
fixed	NA	sibling_count3	0.0766	0.05286	1.449	4789	0.1474	-0.07179	0.225
fixed	NA	sibling_count4	0.04296	0.05286	0.8128	4611	0.4164	-0.1054	0.1913
fixed	NA	sibling_count5	0.03471	0.05503	0.6307	4424	0.5282	-0.1198	0.1892
fixed	NA	sibling_count>5	-0.04989	0.04336	-1.151	4726	0.2499	-0.1716	0.07181
ran_pars	mother_pidlink	sd__(Intercept)	0.341	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9299	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)	-3.925	0.3809	-10.3	5910	1.092e-24	-4.994	-2.856
fixed	NA	birth_order	0.003522	0.005228	0.6737	5269	0.5005	-0.01115	0.0182
fixed	NA	poly(age, 3, raw = TRUE)1	0.3005	0.03602	8.344	5897	8.887e-17	0.1994	0.4016
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007309	0.001075	-6.801	5882	0.00000000001145	-0.01033	-0.004292
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005716	0.00001018	5.614	5875	0.00000002067	0.00002858	0.00008574
fixed	NA	male	0.1265	0.02642	4.789	5922	0.000001716	0.05237	0.2007
fixed	NA	sibling_count3	0.07559	0.05289	1.429	4793	0.153	-0.07288	0.2241
fixed	NA	sibling_count4	0.0403	0.05301	0.7601	4635	0.4472	-0.1085	0.1891
fixed	NA	sibling_count5	0.03033	0.05542	0.5472	4465	0.5842	-0.1252	0.1859
fixed	NA	sibling_count>5	-0.06306	0.04756	-1.326	5053	0.1849	-0.1966	0.07045
ran_pars	mother_pidlink	sd__(Intercept)	0.3417	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9298	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)	-3.911	0.3816	-10.25	5903	1.929e-24	-4.982	-2.84
fixed	NA	poly(age, 3, raw = TRUE)1	0.3	0.03603	8.327	5892	1.021e-16	0.1989	0.4012
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007284	0.001075	-6.773	5876	0.00000000001386	-0.0103	-0.004265
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005682	0.0000102	5.573	5867	0.00000002613	0.0000282	0.00008544
fixed	NA	male	0.1269	0.02642	4.801	5919	0.000001614	0.0527	0.201
fixed	NA	sibling_count3	0.08191	0.05362	1.528	4907	0.1267	-0.0686	0.2324
fixed	NA	sibling_count4	0.04998	0.05468	0.9141	4884	0.3607	-0.1035	0.2035
fixed	NA	sibling_count5	0.02631	0.05763	0.4565	4795	0.6481	-0.1355	0.1881
fixed	NA	sibling_count>5	-0.06185	0.05001	-1.237	5369	0.2162	-0.2022	0.07853
fixed	NA	birth_order_nonlinear2	-0.0194	0.03805	-0.5098	5505	0.6102	-0.1262	0.08742
fixed	NA	birth_order_nonlinear3	-0.0268	0.04408	-0.608	5472	0.5432	-0.1505	0.09694
fixed	NA	birth_order_nonlinear4	-0.01244	0.04932	-0.2522	5521	0.8009	-0.1509	0.126
fixed	NA	birth_order_nonlinear5	0.07847	0.05601	1.401	5489	0.1613	-0.07875	0.2357
fixed	NA	birth_order_nonlinear>5	0.006064	0.04625	0.1311	5931	0.8957	-0.1238	0.1359
ran_pars	mother_pidlink	sd__(Intercept)	0.3407	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9302	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)	-3.899	0.3829	-10.18	5894	3.712e-24	-4.974	-2.824
fixed	NA	poly(age, 3, raw = TRUE)1	0.2982	0.03608	8.265	5881	1.717e-16	0.1969	0.3995
fixed	NA	poly(age, 3, raw = TRUE)2	-0.007207	0.001077	-6.691	5864	0.00000000002416	-0.01023	-0.004184
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005593	0.00001021	5.476	5853	0.00000004539	0.00002726	0.0000846
fixed	NA	male	0.1262	0.02645	4.771	5909	0.00000188	0.05193	0.2004
fixed	NA	count_birth_order2/2	-0.02015	0.07713	-0.2613	5573	0.7939	-0.2367	0.1964
fixed	NA	count_birth_order1/3	0.09485	0.06972	1.36	5895	0.1738	-0.1009	0.2906
fixed	NA	count_birth_order2/3	0.03908	0.0799	0.4891	5916	0.6248	-0.1852	0.2634
fixed	NA	count_birth_order3/3	0.05765	0.08899	0.6479	5921	0.5171	-0.1921	0.3074
fixed	NA	count_birth_order1/4	0.1217	0.07784	1.563	5912	0.118	-0.09681	0.3402
fixed	NA	count_birth_order2/4	0.02243	0.08287	0.2707	5916	0.7866	-0.2102	0.2551
fixed	NA	count_birth_order3/4	-0.07628	0.08696	-0.8772	5920	0.3804	-0.3204	0.1678
fixed	NA	count_birth_order4/4	0.04495	0.09473	0.4745	5921	0.6352	-0.221	0.3109
fixed	NA	count_birth_order1/5	0.07361	0.08756	0.8407	5918	0.4006	-0.1722	0.3194
fixed	NA	count_birth_order2/5	0.0388	0.09613	0.4036	5920	0.6865	-0.231	0.3086
fixed	NA	count_birth_order3/5	0.03883	0.09843	0.3945	5919	0.6932	-0.2375	0.3151
fixed	NA	count_birth_order4/5	-0.1091	0.1005	-1.086	5914	0.2777	-0.3912	0.173
fixed	NA	count_birth_order5/5	0.07412	0.1036	0.7154	5915	0.4744	-0.2167	0.365
fixed	NA	count_birth_order1/>5	-0.1477	0.06989	-2.113	5921	0.03468	-0.3438	0.04854
fixed	NA	count_birth_order2/>5	-0.07679	0.07276	-1.055	5917	0.2913	-0.281	0.1274
fixed	NA	count_birth_order3/>5	-0.05401	0.072	-0.7501	5915	0.4532	-0.2561	0.1481
fixed	NA	count_birth_order4/>5	-0.0383	0.0698	-0.5487	5920	0.5832	-0.2342	0.1576
fixed	NA	count_birth_order5/>5	0.02497	0.07063	0.3535	5915	0.7237	-0.1733	0.2232
fixed	NA	count_birth_order>5/>5	-0.05612	0.05586	-1.005	5575	0.3152	-0.2129	0.1007
ran_pars	mother_pidlink	sd__(Intercept)	0.3415	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9299	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)
11	16736	16809	-8357	16714	NA	NA	NA
12	16737	16818	-8357	16713	0.4529	1	0.501
16	16742	16849	-8355	16710	3.397	4	0.4938
26	16752	16926	-8350	16700	10.14	10	0.4285

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)	-5.457	0.8887	-6.141	2513	0.0000000009516	-7.952	-2.963
fixed	NA	poly(age, 3, raw = TRUE)1	0.4617	0.0944	4.891	2515	0.000001066	0.1967	0.7267
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01258	0.003215	-3.911	2516	0.00009423	-0.0216	-0.003551
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001155	0.00003516	3.286	2517	0.001031	0.00001684	0.0002142
fixed	NA	male	0.17	0.04053	4.196	2517	0.00002814	0.05628	0.2838
fixed	NA	sibling_count3	0.03386	0.06327	0.5352	2061	0.5926	-0.1437	0.2115
fixed	NA	sibling_count4	-0.04681	0.06518	-0.7182	1914	0.4727	-0.2298	0.1361
fixed	NA	sibling_count5	-0.1543	0.07425	-2.078	1798	0.03787	-0.3627	0.05415
fixed	NA	sibling_count>5	-0.1823	0.0642	-2.84	1712	0.004566	-0.3625	-0.002109
ran_pars	mother_pidlink	sd__(Intercept)	0.2543	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9641	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)	-5.45	0.8887	-6.133	2512	0.000000001	-7.945	-2.956
fixed	NA	birth_order	0.01116	0.01275	0.8758	2332	0.3812	-0.02462	0.04695
fixed	NA	poly(age, 3, raw = TRUE)1	0.4598	0.09444	4.869	2513	0.000001194	0.1947	0.7249
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01253	0.003216	-3.897	2515	0.0001001	-0.02156	-0.003504
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001155	0.00003516	3.284	2516	0.001038	0.00001677	0.0002142
fixed	NA	male	0.1691	0.04054	4.171	2516	0.00003137	0.05529	0.2829
fixed	NA	sibling_count3	0.02843	0.06359	0.4472	2061	0.6548	-0.1501	0.2069
fixed	NA	sibling_count4	-0.05926	0.06673	-0.8881	1922	0.3746	-0.2466	0.128
fixed	NA	sibling_count5	-0.175	0.07795	-2.245	1808	0.02487	-0.3938	0.04379
fixed	NA	sibling_count>5	-0.2227	0.07907	-2.817	1791	0.004904	-0.4447	-0.0007727
ran_pars	mother_pidlink	sd__(Intercept)	0.2562	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9637	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)	-5.411	0.8892	-6.085	2508	0.000000001346	-7.907	-2.915
fixed	NA	poly(age, 3, raw = TRUE)1	0.4567	0.09448	4.833	2510	0.000001423	0.1914	0.7219
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01242	0.003218	-3.861	2511	0.0001157	-0.02146	-0.003392
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001143	0.00003518	3.248	2512	0.001179	0.0000155	0.000213
fixed	NA	male	0.1692	0.04053	4.174	2512	0.00003095	0.0554	0.2829
fixed	NA	sibling_count3	0.01621	0.06489	0.2498	2123	0.8027	-0.1659	0.1984
fixed	NA	sibling_count4	-0.08453	0.06948	-1.216	2061	0.2239	-0.2796	0.1105
fixed	NA	sibling_count5	-0.1747	0.08228	-2.123	1980	0.03385	-0.4057	0.05625
fixed	NA	sibling_count>5	-0.2263	0.08151	-2.777	1904	0.005541	-0.4551	0.002451
fixed	NA	birth_order_nonlinear2	0.01137	0.05292	0.2149	2230	0.8299	-0.1372	0.1599
fixed	NA	birth_order_nonlinear3	0.07625	0.06357	1.199	2315	0.2305	-0.1022	0.2547
fixed	NA	birth_order_nonlinear4	0.101	0.07699	1.311	2364	0.1899	-0.1152	0.3171
fixed	NA	birth_order_nonlinear5	-0.07953	0.09654	-0.8238	2417	0.4101	-0.3505	0.1915
fixed	NA	birth_order_nonlinear>5	0.09209	0.09551	0.9642	2473	0.335	-0.176	0.3602
ran_pars	mother_pidlink	sd__(Intercept)	0.262	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.962	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)	-5.375	0.8908	-6.033	2498	0.000000001844	-7.875	-2.874
fixed	NA	poly(age, 3, raw = TRUE)1	0.4507	0.09477	4.756	2499	0.000002085	0.1847	0.7167
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01218	0.003228	-3.774	2501	0.0001641	-0.02124	-0.003123
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001113	0.0000353	3.153	2502	0.001636	0.00001221	0.0002104
fixed	NA	male	0.1628	0.04062	4.007	2502	0.00006336	0.04874	0.2768
fixed	NA	count_birth_order2/2	0.05057	0.0999	0.5062	2260	0.6128	-0.2298	0.331
fixed	NA	count_birth_order1/3	0.008137	0.08297	0.09806	2501	0.9219	-0.2248	0.241
fixed	NA	count_birth_order2/3	0.11	0.09415	1.168	2502	0.2428	-0.1543	0.3743
fixed	NA	count_birth_order3/3	0.05356	0.1036	0.5168	2500	0.6054	-0.2374	0.3445
fixed	NA	count_birth_order1/4	-0.09397	0.09738	-0.965	2502	0.3347	-0.3673	0.1794
fixed	NA	count_birth_order2/4	-0.06464	0.1005	-0.6428	2502	0.5204	-0.3469	0.2176
fixed	NA	count_birth_order3/4	0.04913	0.1063	0.4623	2500	0.6439	-0.2492	0.3474
fixed	NA	count_birth_order4/4	0.0121	0.1135	0.1066	2498	0.9151	-0.3065	0.3308
fixed	NA	count_birth_order1/5	-0.008234	0.1311	-0.06281	2502	0.9499	-0.3763	0.3598
fixed	NA	count_birth_order2/5	-0.1178	0.153	-0.7701	2497	0.4413	-0.5473	0.3116
fixed	NA	count_birth_order3/5	-0.1788	0.1381	-1.295	2500	0.1955	-0.5664	0.2088
fixed	NA	count_birth_order4/5	-0.04439	0.1305	-0.3402	2498	0.7337	-0.4106	0.3218
fixed	NA	count_birth_order5/5	-0.3668	0.1344	-2.729	2499	0.0064	-0.744	0.01051
fixed	NA	count_birth_order1/>5	-0.1898	0.1294	-1.467	2502	0.1424	-0.553	0.1733
fixed	NA	count_birth_order2/>5	-0.4359	0.1304	-3.343	2501	0.0008405	-0.8019	-0.06991
fixed	NA	count_birth_order3/>5	-0.0447	0.1321	-0.3384	2501	0.7351	-0.4155	0.3261
fixed	NA	count_birth_order4/>5	-0.1088	0.1208	-0.9012	2496	0.3676	-0.4478	0.2301
fixed	NA	count_birth_order5/>5	-0.2063	0.1181	-1.747	2494	0.08069	-0.5377	0.1251
fixed	NA	count_birth_order>5/>5	-0.122	0.0885	-1.378	2360	0.1682	-0.3704	0.1264
ran_pars	mother_pidlink	sd__(Intercept)	0.2591	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9626	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)
11	7164	7228	-3571	7142	NA	NA	NA
12	7165	7235	-3570	7141	0.7669	1	0.3812
16	7168	7261	-3568	7136	4.699	4	0.3195
26	7177	7329	-3563	7125	10.95	10	0.3616

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)	-5.441	0.8839	-6.156	2529	0.0000000008662	-7.922	-2.96
fixed	NA	poly(age, 3, raw = TRUE)1	0.4605	0.09398	4.9	2530	0.000001019	0.1967	0.7243
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01255	0.003201	-3.921	2532	0.00009034	-0.02154	-0.003568
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001153	0.00003501	3.292	2533	0.001008	0.00001698	0.0002135
fixed	NA	male	0.1649	0.04032	4.089	2533	0.00004466	0.05169	0.278
fixed	NA	sibling_count3	0.03006	0.06953	0.4324	2134	0.6655	-0.1651	0.2252
fixed	NA	sibling_count4	0.01484	0.07034	0.2109	2025	0.833	-0.1826	0.2123
fixed	NA	sibling_count5	-0.1237	0.07397	-1.673	1900	0.09451	-0.3314	0.0839
fixed	NA	sibling_count>5	-0.153	0.06571	-2.328	1970	0.02003	-0.3374	0.0315
ran_pars	mother_pidlink	sd__(Intercept)	0.2542	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.962	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)	-5.441	0.884	-6.154	2528	0.0000000008751	-7.922	-2.959
fixed	NA	birth_order	0.001754	0.01111	0.158	2270	0.8745	-0.02942	0.03293
fixed	NA	poly(age, 3, raw = TRUE)1	0.4603	0.09402	4.896	2529	0.000001042	0.1964	0.7242
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01255	0.003202	-3.919	2531	0.00009134	-0.02154	-0.00356
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001153	0.00003501	3.292	2532	0.001009	0.00001697	0.0002135
fixed	NA	male	0.1647	0.04034	4.083	2532	0.00004582	0.05147	0.2779
fixed	NA	sibling_count3	0.02918	0.06976	0.4183	2132	0.6757	-0.1666	0.225
fixed	NA	sibling_count4	0.01296	0.07136	0.1816	2021	0.8559	-0.1874	0.2133
fixed	NA	sibling_count5	-0.1267	0.07636	-1.66	1899	0.09714	-0.3411	0.08761
fixed	NA	sibling_count>5	-0.1591	0.07655	-2.079	1976	0.03775	-0.374	0.05573
ran_pars	mother_pidlink	sd__(Intercept)	0.2551	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9619	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)	-5.442	0.8838	-6.157	2524	0.0000000008593	-7.923	-2.961
fixed	NA	poly(age, 3, raw = TRUE)1	0.4599	0.09399	4.893	2526	0.000001054	0.1961	0.7238
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01254	0.003201	-3.916	2527	0.00009242	-0.02152	-0.00355
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001151	0.000035	3.289	2528	0.001018	0.00001688	0.0002134
fixed	NA	male	0.1643	0.0403	4.077	2528	0.00004697	0.05119	0.2774
fixed	NA	sibling_count3	0.009383	0.07102	0.1321	2177	0.8949	-0.19	0.2087
fixed	NA	sibling_count4	-0.0289	0.07374	-0.3919	2122	0.6952	-0.2359	0.1781
fixed	NA	sibling_count5	-0.1455	0.07999	-1.819	2042	0.06907	-0.37	0.07904
fixed	NA	sibling_count>5	-0.1811	0.07882	-2.297	2072	0.02169	-0.4023	0.04016
fixed	NA	birth_order_nonlinear2	0.02068	0.05343	0.3871	2271	0.6987	-0.1293	0.1707
fixed	NA	birth_order_nonlinear3	0.09024	0.06368	1.417	2376	0.1566	-0.08851	0.269
fixed	NA	birth_order_nonlinear4	0.1398	0.07445	1.878	2396	0.06046	-0.06915	0.3488
fixed	NA	birth_order_nonlinear5	-0.1024	0.0914	-1.121	2434	0.2625	-0.359	0.1541
fixed	NA	birth_order_nonlinear>5	0.03478	0.08567	0.406	2463	0.6847	-0.2057	0.2753
ran_pars	mother_pidlink	sd__(Intercept)	0.2586	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9602	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)	-5.453	0.8868	-6.149	2513	0.0000000009035	-7.942	-2.964
fixed	NA	poly(age, 3, raw = TRUE)1	0.4599	0.09439	4.873	2515	0.00000117	0.195	0.7249
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01251	0.003215	-3.89	2517	0.0001027	-0.02153	-0.003483
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001146	0.00003516	3.259	2518	0.001133	0.0000159	0.0002133
fixed	NA	male	0.1614	0.04046	3.989	2518	0.00006832	0.04781	0.2749
fixed	NA	count_birth_order2/2	0.03684	0.1127	0.327	2336	0.7437	-0.2794	0.3531
fixed	NA	count_birth_order1/3	-0.01654	0.09127	-0.1812	2517	0.8562	-0.2727	0.2397
fixed	NA	count_birth_order2/3	0.1026	0.1014	1.012	2518	0.3117	-0.182	0.3871
fixed	NA	count_birth_order3/3	0.07168	0.1133	0.6325	2517	0.5271	-0.2465	0.3898
fixed	NA	count_birth_order1/4	0.000209	0.1026	0.002036	2518	0.9984	-0.2879	0.2883
fixed	NA	count_birth_order2/4	0.01402	0.1032	0.1358	2518	0.892	-0.2758	0.3038
fixed	NA	count_birth_order3/4	0.02956	0.1166	0.2536	2516	0.7998	-0.2977	0.3568
fixed	NA	count_birth_order4/4	0.08172	0.124	0.6593	2514	0.5098	-0.2662	0.4297
fixed	NA	count_birth_order1/5	-0.07394	0.1193	-0.6201	2518	0.5353	-0.4087	0.2608
fixed	NA	count_birth_order2/5	-0.1639	0.1313	-1.249	2515	0.2118	-0.5324	0.2045
fixed	NA	count_birth_order3/5	-0.01559	0.1312	-0.1188	2515	0.9054	-0.3838	0.3526
fixed	NA	count_birth_order4/5	0.03078	0.1323	0.2328	2512	0.816	-0.3405	0.402
fixed	NA	count_birth_order5/5	-0.3571	0.1317	-2.712	2514	0.006743	-0.7269	0.01258
fixed	NA	count_birth_order1/>5	-0.1954	0.1136	-1.72	2517	0.08555	-0.5144	0.1235
fixed	NA	count_birth_order2/>5	-0.2732	0.1208	-2.263	2518	0.02375	-0.6122	0.06575
fixed	NA	count_birth_order3/>5	-0.03812	0.122	-0.3126	2517	0.7546	-0.3805	0.3043
fixed	NA	count_birth_order4/>5	-0.03309	0.1126	-0.2937	2516	0.769	-0.3493	0.2831
fixed	NA	count_birth_order5/>5	-0.1922	0.1201	-1.6	2510	0.1097	-0.5295	0.145
fixed	NA	count_birth_order>5/>5	-0.1421	0.08825	-1.61	2406	0.1075	-0.3898	0.1056
ran_pars	mother_pidlink	sd__(Intercept)	0.2591	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9609	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)
11	7198	7262	-3588	7176	NA	NA	NA
12	7200	7270	-3588	7176	0.02429	1	0.8761
16	7200	7293	-3584	7168	8.315	4	0.08069
26	7214	7366	-3581	7162	5.651	10	0.8437

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)	-5.422	0.9015	-6.014	2464	0.000000002078	-7.952	-2.891
fixed	NA	poly(age, 3, raw = TRUE)1	0.4572	0.09577	4.773	2465	0.000001918	0.1883	0.726
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01237	0.00326	-3.794	2467	0.0001518	-0.02152	-0.003218
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001128	0.00003563	3.166	2468	0.001565	0.00001278	0.0002128
fixed	NA	male	0.1739	0.04126	4.215	2468	0.00002588	0.0581	0.2898
fixed	NA	sibling_count3	-0.003189	0.06289	-0.05071	2016	0.9596	-0.1797	0.1733
fixed	NA	sibling_count4	-0.1003	0.06552	-1.53	1856	0.1261	-0.2842	0.08365
fixed	NA	sibling_count5	-0.1661	0.07676	-2.164	1689	0.03057	-0.3816	0.04933
fixed	NA	sibling_count>5	-0.1681	0.06519	-2.579	1623	0.009992	-0.3511	0.01486
ran_pars	mother_pidlink	sd__(Intercept)	0.2569	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)	-5.415	0.9017	-6.005	2463	0.000000002191	-7.946	-2.884
fixed	NA	birth_order	0.008665	0.0132	0.6563	2305	0.5117	-0.0284	0.04573
fixed	NA	poly(age, 3, raw = TRUE)1	0.4554	0.09582	4.753	2464	0.000002122	0.1864	0.7244
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01233	0.003261	-3.78	2466	0.0001607	-0.02148	-0.003172
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001127	0.00003563	3.161	2467	0.001589	0.00001263	0.0002127
fixed	NA	male	0.1734	0.04128	4.2	2467	0.00002758	0.05752	0.2892
fixed	NA	sibling_count3	-0.007568	0.06326	-0.1196	2014	0.9048	-0.1851	0.17
fixed	NA	sibling_count4	-0.1098	0.06712	-1.635	1867	0.1021	-0.2982	0.07863
fixed	NA	sibling_count5	-0.1818	0.08039	-2.261	1703	0.02388	-0.4074	0.04389
fixed	NA	sibling_count>5	-0.1994	0.08076	-2.469	1739	0.01365	-0.4261	0.02731
ran_pars	mother_pidlink	sd__(Intercept)	0.2582	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9718	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)	-5.41	0.9024	-5.996	2459	0.000000002325	-7.943	-2.877
fixed	NA	poly(age, 3, raw = TRUE)1	0.4563	0.09589	4.759	2461	0.00000206	0.1872	0.7255
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01236	0.003263	-3.788	2462	0.0001554	-0.02152	-0.003202
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001131	0.00003566	3.171	2463	0.001537	0.00001299	0.0002132
fixed	NA	male	0.174	0.04128	4.214	2463	0.00002595	0.0581	0.2899
fixed	NA	sibling_count3	-0.02677	0.06466	-0.4139	2076	0.679	-0.2083	0.1547
fixed	NA	sibling_count4	-0.1287	0.06985	-1.842	2007	0.06558	-0.3247	0.06738
fixed	NA	sibling_count5	-0.1758	0.08455	-2.079	1877	0.03777	-0.4131	0.06157
fixed	NA	sibling_count>5	-0.2091	0.08338	-2.508	1859	0.01222	-0.4432	0.02492
fixed	NA	birth_order_nonlinear2	-0.0007985	0.0533	-0.01498	2180	0.988	-0.1504	0.1488
fixed	NA	birth_order_nonlinear3	0.09794	0.06412	1.528	2269	0.1268	-0.08203	0.2779
fixed	NA	birth_order_nonlinear4	0.0248	0.08029	0.3089	2301	0.7574	-0.2006	0.2502
fixed	NA	birth_order_nonlinear5	-0.07846	0.1009	-0.7773	2332	0.4371	-0.3618	0.2049
fixed	NA	birth_order_nonlinear>5	0.1007	0.09905	1.016	2422	0.3097	-0.1774	0.3787
ran_pars	mother_pidlink	sd__(Intercept)	0.2667	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.9694	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)	-5.398	0.9042	-5.97	2448	0.000000002716	-7.937	-2.86
fixed	NA	poly(age, 3, raw = TRUE)1	0.4538	0.09623	4.715	2450	0.000002547	0.1836	0.7239
fixed	NA	poly(age, 3, raw = TRUE)2	-0.01223	0.003276	-3.734	2452	0.0001926	-0.02143	-0.003037
fixed	NA	poly(age, 3, raw = TRUE)3	0.0001112	0.0000358	3.106	2452	0.001917	0.00001071	0.0002117
fixed	NA	male	0.1673	0.04143	4.04	2453	0.0000552	0.05106	0.2836
fixed	NA	count_birth_order2/2	0.01444	0.09844	0.1467	2189	0.8834	-0.2619	0.2908
fixed	NA	count_birth_order1/3	-0.06221	0.08283	-0.751	2451	0.4527	-0.2947	0.1703
fixed	NA	count_birth_order2/3	0.07763	0.09437	0.8226	2453	0.4108	-0.1873	0.3425
fixed	NA	count_birth_order3/3	0.03025	0.1018	0.297	2450	0.7665	-0.2556	0.3161
fixed	NA	count_birth_order1/4	-0.1345	0.09873	-1.362	2453	0.1734	-0.4116	0.1427
fixed	NA	count_birth_order2/4	-0.1646	0.1011	-1.628	2453	0.1037	-0.4485	0.1193
fixed	NA	count_birth_order3/4	0.02741	0.1071	0.2559	2451	0.798	-0.2732	0.328
fixed	NA	count_birth_order4/4	-0.08879	0.1173	-0.757	2448	0.4491	-0.418	0.2405
fixed	NA	count_birth_order1/5	-0.002286	0.1351	-0.01692	2453	0.9865	-0.3816	0.377
fixed	NA	count_birth_order2/5	-0.1884	0.157	-1.2	2449	0.2301	-0.629	0.2522
fixed	NA	count_birth_order3/5	-0.1273	0.146	-0.8719	2451	0.3833	-0.5373	0.2826
fixed	NA	count_birth_order4/5	-0.2074	0.1387	-1.496	2448	0.1349	-0.5967	0.1819
fixed	NA	count_birth_order5/5	-0.3175	0.1436	-2.211	2450	0.02713	-0.7205	0.08559
fixed	NA	count_birth_order1/>5	-0.1604	0.1323	-1.212	2453	0.2256	-0.5317	0.211
fixed	NA	count_birth_order2/>5	-0.3924	0.1365	-2.875	2451	0.004072	-0.7756	-0.009305
fixed	NA	count_birth_order3/>5	-0.06706	0.134	-0.5004	2452	0.6169	-0.4432	0.3091
fixed	NA	count_birth_order4/>5	-0.1438	0.1262	-1.14	2447	0.2543	-0.498	0.2103
fixed	NA	count_birth_order5/>5	-0.2396	0.1213	-1.974	2444	0.04845	-0.5802	0.101
fixed	NA	count_birth_order>5/>5	-0.1037	0.09056	-1.145	2291	0.2523	-0.3579	0.1505
ran_pars	mother_pidlink	sd__(Intercept)	0.261	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_genes_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
11	7066	7130	-3522	7044	NA	NA	NA
12	7067	7137	-3522	7043	0.4305	1	0.5117
16	7070	7163	-3519	7038	4.865	4	0.3014
26	7082	7233	-3515	7030	8.758	10	0.5552

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)	-0.2665	0.095	-2.805	9917	0.005038	-0.5331	0.000174
fixed	NA	poly(age, 3, raw = TRUE)1	0.02362	0.008521	2.772	9866	0.005576	-0.0002959	0.04754
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001646	0.0002393	-0.6879	9765	0.4915	-0.0008364	0.0005071
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000002153	0.000002126	-0.1013	9648	0.9193	-0.000006183	0.000005753
fixed	NA	male	-0.002977	0.008766	-0.3396	9989	0.7342	-0.02758	0.02163
fixed	NA	sibling_count3	-0.02246	0.01828	-1.229	7683	0.2192	-0.07376	0.02885
fixed	NA	sibling_count4	-0.01987	0.01844	-1.077	7310	0.2813	-0.07162	0.03189
fixed	NA	sibling_count5	-0.01023	0.01921	-0.5326	6871	0.5944	-0.06417	0.0437
fixed	NA	sibling_count>5	0.01732	0.0149	1.162	7571	0.2452	-0.0245	0.05913
ran_pars	mother_pidlink	sd__(Intercept)	0.1531	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4098	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)	-0.2668	0.09499	-2.809	9915	0.004984	-0.5335	-0.0001598
fixed	NA	birth_order	0.002029	0.001784	1.137	9196	0.2556	-0.00298	0.007038
fixed	NA	poly(age, 3, raw = TRUE)1	0.02307	0.008535	2.703	9857	0.006891	-0.0008909	0.04703
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001441	0.00024	-0.6006	9731	0.5481	-0.0008177	0.0005295
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000004013	0.000002132	-0.1882	9599	0.8507	-0.000006387	0.000005584
fixed	NA	male	-0.003007	0.008766	-0.3431	9989	0.7315	-0.02761	0.0216
fixed	NA	sibling_count3	-0.023	0.01828	-1.258	7695	0.2084	-0.07432	0.02832
fixed	NA	sibling_count4	-0.0211	0.01847	-1.143	7356	0.2532	-0.07295	0.03074
fixed	NA	sibling_count5	-0.01241	0.01931	-0.6426	6958	0.5205	-0.06661	0.04179
fixed	NA	sibling_count>5	0.01022	0.01615	0.6328	8281	0.5269	-0.03512	0.05556
ran_pars	mother_pidlink	sd__(Intercept)	0.1529	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4098	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)	-0.2752	0.09511	-2.893	9918	0.003821	-0.5422	-0.008203
fixed	NA	poly(age, 3, raw = TRUE)1	0.02319	0.008541	2.715	9858	0.006636	-0.0007847	0.04716
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001598	0.0002401	-0.6657	9735	0.5056	-0.0008336	0.0005141
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000001582	0.000002133	-0.07415	9600	0.9409	-0.000006145	0.000005829
fixed	NA	male	-0.003111	0.008765	-0.3549	9984	0.7227	-0.02771	0.02149
fixed	NA	sibling_count3	-0.02462	0.01855	-1.327	7932	0.1844	-0.07669	0.02745
fixed	NA	sibling_count4	-0.02199	0.01896	-1.16	7793	0.2461	-0.07521	0.03123
fixed	NA	sibling_count5	-0.01296	0.01996	-0.6493	7524	0.5162	-0.06899	0.04307
fixed	NA	sibling_count>5	0.01309	0.01691	0.7741	8865	0.4389	-0.03438	0.06055
fixed	NA	birth_order_nonlinear2	0.03823	0.01276	2.997	9348	0.002737	0.002419	0.07405
fixed	NA	birth_order_nonlinear3	0.01961	0.01483	1.322	9199	0.1861	-0.02202	0.06123
fixed	NA	birth_order_nonlinear4	0.0146	0.01665	0.877	9276	0.3805	-0.03214	0.06135
fixed	NA	birth_order_nonlinear5	0.01968	0.01874	1.05	9304	0.2936	-0.03291	0.07227
fixed	NA	birth_order_nonlinear>5	0.02218	0.01558	1.423	10079	0.1546	-0.02156	0.06591
ran_pars	mother_pidlink	sd__(Intercept)	0.1529	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4097	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)	-0.2834	0.09546	-2.969	9918	0.002995	-0.5514	-0.01546
fixed	NA	poly(age, 3, raw = TRUE)1	0.02291	0.008548	2.68	9849	0.007384	-0.00109	0.0469
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001582	0.0002402	-0.6585	9723	0.5102	-0.0008324	0.0005161
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000000111	0.000002134	-0.052	9586	0.9585	-0.000006101	0.000005879
fixed	NA	male	-0.003372	0.008769	-0.3845	9975	0.7006	-0.02799	0.02124
fixed	NA	count_birth_order2/2	0.07421	0.02534	2.928	9275	0.003418	0.003069	0.1453
fixed	NA	count_birth_order1/3	-0.02418	0.02456	-0.9844	9991	0.3249	-0.09311	0.04476
fixed	NA	count_birth_order2/3	0.03323	0.02722	1.221	10030	0.2221	-0.04317	0.1096
fixed	NA	count_birth_order3/3	0.02459	0.02989	0.8229	10053	0.4106	-0.0593	0.1085
fixed	NA	count_birth_order1/4	0.01501	0.0269	0.5579	10031	0.5769	-0.0605	0.09051
fixed	NA	count_birth_order2/4	0.005201	0.02884	0.1804	10046	0.8569	-0.07575	0.08616
fixed	NA	count_birth_order3/4	-0.005191	0.03075	-0.1688	10061	0.8659	-0.0915	0.08111
fixed	NA	count_birth_order4/4	0.01914	0.03266	0.5862	10066	0.5578	-0.07253	0.1108
fixed	NA	count_birth_order1/5	0.009117	0.03054	0.2985	10059	0.7653	-0.07661	0.09484
fixed	NA	count_birth_order2/5	0.04643	0.03238	1.434	10065	0.1517	-0.04447	0.1373
fixed	NA	count_birth_order3/5	0.03461	0.03409	1.015	10069	0.31	-0.06108	0.1303
fixed	NA	count_birth_order4/5	-0.01429	0.03583	-0.3989	10068	0.69	-0.1149	0.08627
fixed	NA	count_birth_order5/5	0.0102	0.03582	0.2846	10071	0.7759	-0.09036	0.1107
fixed	NA	count_birth_order1/>5	0.03492	0.02352	1.485	10069	0.1377	-0.03111	0.1009
fixed	NA	count_birth_order2/>5	0.05428	0.02449	2.216	10071	0.02672	-0.01448	0.123
fixed	NA	count_birth_order3/>5	0.04115	0.02413	1.705	10071	0.0882	-0.02659	0.1089
fixed	NA	count_birth_order4/>5	0.04521	0.0237	1.907	10070	0.05649	-0.02132	0.1117
fixed	NA	count_birth_order5/>5	0.04958	0.02396	2.069	10071	0.03857	-0.01769	0.1168
fixed	NA	count_birth_order>5/>5	0.04898	0.01941	2.523	9318	0.01164	-0.005507	0.1035
ran_pars	mother_pidlink	sd__(Intercept)	0.153	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4097	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)
11	11871	11950	-5924	11849	NA	NA	NA
12	11871	11958	-5924	11847	1.295	1	0.2552
16	11872	11987	-5920	11840	7.919	4	0.0946
26	11883	12071	-5916	11831	8.217	10	0.6077

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)	0.9428	0.2612	3.609	3819	0.0003116	0.2094	1.676
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1058	0.02805	-3.773	3817	0.0001635	-0.1846	-0.02711
fixed	NA	poly(age, 3, raw = TRUE)2	0.004147	0.0009623	4.309	3815	0.00001678	0.001446	0.006848
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004614	0.00001056	-4.368	3814	0.00001288	-0.0000758	-0.00001649
fixed	NA	male	-0.02367	0.01315	-1.8	3785	0.0719	-0.06057	0.01324
fixed	NA	sibling_count3	0.01552	0.02194	0.7075	3125	0.4793	-0.04606	0.0771
fixed	NA	sibling_count4	-0.02907	0.02271	-1.28	2946	0.2007	-0.09282	0.03469
fixed	NA	sibling_count5	0.03856	0.02531	1.524	2677	0.1277	-0.03248	0.1096
fixed	NA	sibling_count>5	0.04773	0.02198	2.172	2660	0.02998	-0.01397	0.1094
ran_pars	mother_pidlink	sd__(Intercept)	0.1578	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3721	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)	0.9413	0.2613	3.602	3819	0.0003195	0.2078	1.675
fixed	NA	birth_order	-0.001447	0.004107	-0.3524	3766	0.7246	-0.01298	0.01008
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1055	0.02807	-3.759	3817	0.0001733	-0.1843	-0.02671
fixed	NA	poly(age, 3, raw = TRUE)2	0.004138	0.0009626	4.299	3815	0.00001761	0.001436	0.00684
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004611	0.00001057	-4.364	3813	0.00001308	-0.00007577	-0.00001645
fixed	NA	male	-0.02362	0.01315	-1.796	3783	0.07252	-0.06052	0.01329
fixed	NA	sibling_count3	0.01627	0.02204	0.7382	3124	0.4605	-0.04561	0.07815
fixed	NA	sibling_count4	-0.02744	0.02318	-1.184	2948	0.2365	-0.09251	0.03762
fixed	NA	sibling_count5	0.0412	0.02642	1.559	2723	0.119	-0.03296	0.1154
fixed	NA	sibling_count>5	0.05295	0.02654	1.995	2828	0.04609	-0.02154	0.1274
ran_pars	mother_pidlink	sd__(Intercept)	0.1582	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.372	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)	0.9329	0.2617	3.565	3815	0.0003682	0.1984	1.667
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1051	0.02809	-3.742	3812	0.0001852	-0.184	-0.02627
fixed	NA	poly(age, 3, raw = TRUE)2	0.004127	0.0009634	4.283	3810	0.00001887	0.001422	0.006831
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004607	0.00001058	-4.355	3808	0.00001363	-0.00007576	-0.00001638
fixed	NA	male	-0.02352	0.01315	-1.788	3779	0.07392	-0.06044	0.01341
fixed	NA	sibling_count3	0.0156	0.02247	0.6942	3214	0.4876	-0.04747	0.07867
fixed	NA	sibling_count4	-0.02767	0.02398	-1.154	3114	0.2487	-0.09499	0.03965
fixed	NA	sibling_count5	0.04284	0.02763	1.55	2963	0.1212	-0.03472	0.1204
fixed	NA	sibling_count>5	0.0613	0.02722	2.252	2955	0.02438	-0.0151	0.1377
fixed	NA	birth_order_nonlinear2	0.01025	0.01727	0.5934	3368	0.553	-0.03824	0.05874
fixed	NA	birth_order_nonlinear3	0.001374	0.02033	0.06759	3441	0.9461	-0.0557	0.05845
fixed	NA	birth_order_nonlinear4	-0.002639	0.02479	-0.1065	3498	0.9152	-0.07221	0.06693
fixed	NA	birth_order_nonlinear5	-0.008891	0.03048	-0.2917	3505	0.7706	-0.09446	0.07668
fixed	NA	birth_order_nonlinear>5	-0.02557	0.03043	-0.8404	3817	0.4007	-0.111	0.05985
ran_pars	mother_pidlink	sd__(Intercept)	0.1581	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3722	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)	0.9316	0.2628	3.545	3805	0.000397	0.194	1.669
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1065	0.02821	-3.774	3803	0.0001631	-0.1856	-0.02728
fixed	NA	poly(age, 3, raw = TRUE)2	0.004174	0.0009678	4.313	3801	0.00001652	0.001457	0.006891
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004658	0.00001063	-4.383	3800	0.000012	-0.00007642	-0.00001675
fixed	NA	male	-0.02415	0.01318	-1.832	3769	0.067	-0.06115	0.01285
fixed	NA	count_birth_order2/2	0.05231	0.0336	1.557	3475	0.1196	-0.04201	0.1466
fixed	NA	count_birth_order1/3	0.03981	0.02861	1.392	3792	0.1641	-0.04049	0.1201
fixed	NA	count_birth_order2/3	0.03881	0.03176	1.222	3805	0.2218	-0.05034	0.128
fixed	NA	count_birth_order3/3	0.01045	0.03434	0.3044	3807	0.7609	-0.08594	0.1068
fixed	NA	count_birth_order1/4	-0.008259	0.03285	-0.2514	3802	0.8015	-0.1005	0.08395
fixed	NA	count_birth_order2/4	-0.02985	0.03453	-0.8646	3807	0.3873	-0.1268	0.06706
fixed	NA	count_birth_order3/4	-0.01272	0.0362	-0.3513	3804	0.7254	-0.1143	0.08889
fixed	NA	count_birth_order4/4	0.008705	0.03839	0.2267	3801	0.8206	-0.09907	0.1165
fixed	NA	count_birth_order1/5	0.05321	0.04307	1.235	3807	0.2168	-0.06769	0.1741
fixed	NA	count_birth_order2/5	0.07654	0.04684	1.634	3790	0.1023	-0.05495	0.208
fixed	NA	count_birth_order3/5	0.06749	0.04389	1.538	3795	0.1242	-0.05572	0.1907
fixed	NA	count_birth_order4/5	0.05473	0.04269	1.282	3794	0.1999	-0.06511	0.1746
fixed	NA	count_birth_order5/5	0.02978	0.04476	0.6652	3789	0.506	-0.09587	0.1554
fixed	NA	count_birth_order1/>5	0.07785	0.04095	1.901	3804	0.05738	-0.0371	0.1928
fixed	NA	count_birth_order2/>5	0.07465	0.04131	1.807	3792	0.07084	-0.04131	0.1906
fixed	NA	count_birth_order3/>5	0.09799	0.04038	2.426	3787	0.01529	-0.01537	0.2113
fixed	NA	count_birth_order4/>5	0.04506	0.03922	1.149	3779	0.2506	-0.06502	0.1551
fixed	NA	count_birth_order5/>5	0.07709	0.03782	2.038	3785	0.0416	-0.02908	0.1832
fixed	NA	count_birth_order>5/>5	0.04905	0.0296	1.657	3670	0.09751	-0.03402	0.1321
ran_pars	mother_pidlink	sd__(Intercept)	0.1579	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3725	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)
11	3908	3977	-1943	3886	NA	NA	NA
12	3910	3985	-1943	3886	0.122	1	0.7269
16	3917	4017	-1942	3885	1.352	4	0.8525
26	3931	4094	-1940	3879	5.638	10	0.8447

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)	0.917	0.2603	3.523	3846	0.0004316	0.1864	1.648
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1019	0.02798	-3.642	3843	0.0002737	-0.1804	-0.02337
fixed	NA	poly(age, 3, raw = TRUE)2	0.004027	0.0009598	4.196	3841	0.00002782	0.001333	0.006722
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004496	0.00001054	-4.266	3840	0.00002039	-0.00007455	-0.00001538
fixed	NA	male	-0.02421	0.01311	-1.847	3810	0.06483	-0.06101	0.01259
fixed	NA	sibling_count3	-0.006695	0.02405	-0.2784	3201	0.7807	-0.0742	0.06081
fixed	NA	sibling_count4	-0.03614	0.02428	-1.489	3079	0.1366	-0.1043	0.032
fixed	NA	sibling_count5	-0.008562	0.02563	-0.3341	2892	0.7383	-0.0805	0.06337
fixed	NA	sibling_count>5	0.0278	0.02245	1.238	2968	0.2157	-0.03522	0.09082
ran_pars	mother_pidlink	sd__(Intercept)	0.1587	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.372	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)	0.9174	0.2603	3.524	3845	0.0004304	0.1866	1.648
fixed	NA	birth_order	0.0004435	0.003628	0.1222	3719	0.9027	-0.009742	0.01063
fixed	NA	poly(age, 3, raw = TRUE)1	-0.102	0.02799	-3.644	3843	0.0002721	-0.1806	-0.02342
fixed	NA	poly(age, 3, raw = TRUE)2	0.00403	0.0009601	4.197	3841	0.00002769	0.001334	0.006725
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004497	0.00001054	-4.266	3839	0.0000204	-0.00007456	-0.00001538
fixed	NA	male	-0.02422	0.01311	-1.848	3809	0.06474	-0.06103	0.01258
fixed	NA	sibling_count3	-0.006931	0.02413	-0.2872	3197	0.7739	-0.07466	0.0608
fixed	NA	sibling_count4	-0.03661	0.02457	-1.49	3071	0.1364	-0.1056	0.03237
fixed	NA	sibling_count5	-0.009323	0.02638	-0.3534	2901	0.7238	-0.08337	0.06472
fixed	NA	sibling_count>5	0.02623	0.02589	1.013	3022	0.311	-0.04644	0.09889
ran_pars	mother_pidlink	sd__(Intercept)	0.1587	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3721	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)	0.9044	0.2607	3.47	3841	0.0005271	0.1727	1.636
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1011	0.02801	-3.608	3839	0.0003122	-0.1797	-0.02244
fixed	NA	poly(age, 3, raw = TRUE)2	0.003996	0.0009609	4.159	3836	0.00003269	0.001299	0.006694
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004462	0.00001055	-4.229	3835	0.00002404	-0.00007425	-0.000015
fixed	NA	male	-0.02403	0.01312	-1.832	3804	0.06702	-0.06085	0.01279
fixed	NA	sibling_count3	-0.01015	0.02454	-0.4134	3267	0.6793	-0.07903	0.05874
fixed	NA	sibling_count4	-0.03844	0.02528	-1.521	3196	0.1284	-0.1094	0.03252
fixed	NA	sibling_count5	-0.008874	0.02749	-0.3228	3097	0.7469	-0.08604	0.06829
fixed	NA	sibling_count>5	0.02904	0.02661	1.091	3148	0.2752	-0.04564	0.1037
fixed	NA	birth_order_nonlinear2	0.01753	0.01751	1.001	3422	0.3169	-0.03163	0.06668
fixed	NA	birth_order_nonlinear3	0.01558	0.02045	0.7616	3503	0.4464	-0.04184	0.07299
fixed	NA	birth_order_nonlinear4	-0.00005851	0.0242	-0.002418	3563	0.9981	-0.06799	0.06787
fixed	NA	birth_order_nonlinear5	-0.002062	0.02949	-0.06994	3572	0.9442	-0.08484	0.08071
fixed	NA	birth_order_nonlinear>5	0.002764	0.02752	0.1004	3836	0.92	-0.07449	0.08002
ran_pars	mother_pidlink	sd__(Intercept)	0.1585	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3722	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)	0.904	0.2612	3.46	3831	0.0005452	0.1707	1.637
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1033	0.02807	-3.68	3829	0.0002365	-0.1821	-0.0245
fixed	NA	poly(age, 3, raw = TRUE)2	0.004077	0.0009634	4.233	3828	0.00002364	0.001373	0.006782
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004555	0.00001058	-4.305	3827	0.00001715	-0.00007526	-0.00001585
fixed	NA	male	-0.02482	0.01313	-1.89	3795	0.05884	-0.06169	0.01205
fixed	NA	count_birth_order2/2	0.07947	0.03699	2.148	3581	0.03176	-0.02437	0.1833
fixed	NA	count_birth_order1/3	0.02032	0.0316	0.643	3818	0.5202	-0.06838	0.109
fixed	NA	count_birth_order2/3	0.04303	0.03437	1.252	3830	0.2107	-0.05345	0.1395
fixed	NA	count_birth_order3/3	-0.015	0.03778	-0.3971	3833	0.6913	-0.121	0.09104
fixed	NA	count_birth_order1/4	0.005795	0.03435	0.1687	3825	0.866	-0.09063	0.1022
fixed	NA	count_birth_order2/4	-0.0307	0.03584	-0.8566	3832	0.3917	-0.1313	0.0699
fixed	NA	count_birth_order3/4	-0.0108	0.03917	-0.2758	3830	0.7827	-0.1207	0.09914
fixed	NA	count_birth_order4/4	-0.006404	0.04181	-0.1532	3827	0.8783	-0.1238	0.111
fixed	NA	count_birth_order1/5	0.01609	0.04117	0.3908	3833	0.6959	-0.09947	0.1316
fixed	NA	count_birth_order2/5	0.01692	0.04276	0.3957	3831	0.6924	-0.1031	0.1369
fixed	NA	count_birth_order3/5	0.01622	0.04352	0.3728	3825	0.7093	-0.1059	0.1384
fixed	NA	count_birth_order4/5	0.01776	0.04424	0.4013	3818	0.6882	-0.1064	0.1419
fixed	NA	count_birth_order5/5	0.02105	0.04457	0.4723	3817	0.6367	-0.104	0.1461
fixed	NA	count_birth_order1/>5	0.03557	0.03723	0.9554	3832	0.3394	-0.06894	0.1401
fixed	NA	count_birth_order2/>5	0.04765	0.03933	1.211	3824	0.2258	-0.06276	0.1581
fixed	NA	count_birth_order3/>5	0.1171	0.03789	3.092	3824	0.002004	0.01079	0.2235
fixed	NA	count_birth_order4/>5	0.03739	0.03695	1.012	3821	0.3117	-0.06634	0.1411
fixed	NA	count_birth_order5/>5	0.03913	0.03908	1.001	3808	0.3167	-0.07056	0.1488
fixed	NA	count_birth_order>5/>5	0.05174	0.02961	1.747	3707	0.08067	-0.03138	0.1349
ran_pars	mother_pidlink	sd__(Intercept)	0.1582	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3723	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)
11	3939	4008	-1958	3917	NA	NA	NA
12	3941	4016	-1958	3917	0.01549	1	0.901
16	3947	4047	-1958	3915	1.543	4	0.8189
26	3955	4118	-1952	3903	11.8	10	0.2988

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)	0.9712	0.2646	3.67	3751	0.0002462	0.2283	1.714
fixed	NA	poly(age, 3, raw = TRUE)1	-0.11	0.02846	-3.864	3749	0.0001135	-0.1898	-0.03008
fixed	NA	poly(age, 3, raw = TRUE)2	0.004334	0.0009771	4.435	3746	0.000009468	0.001591	0.007076
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004871	0.00001074	-4.536	3745	0.000005926	-0.00007886	-0.00001856
fixed	NA	male	-0.02276	0.0133	-1.711	3715	0.08719	-0.0601	0.01458
fixed	NA	sibling_count3	0.02252	0.02157	1.044	3069	0.2966	-0.03803	0.08307
fixed	NA	sibling_count4	-0.02657	0.02265	-1.173	2884	0.2409	-0.09016	0.03702
fixed	NA	sibling_count5	0.03133	0.02594	1.208	2547	0.2273	-0.04149	0.1042
fixed	NA	sibling_count>5	0.04105	0.02217	1.852	2545	0.06416	-0.02117	0.1033
ran_pars	mother_pidlink	sd__(Intercept)	0.16	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3726	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)	0.9698	0.2647	3.663	3751	0.0002524	0.2267	1.713
fixed	NA	birth_order	-0.001067	0.004238	-0.2517	3715	0.8013	-0.01296	0.01083
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1097	0.02848	-3.851	3749	0.0001198	-0.1896	-0.02972
fixed	NA	poly(age, 3, raw = TRUE)2	0.004326	0.0009776	4.425	3747	0.000009919	0.001582	0.00707
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004867	0.00001074	-4.531	3745	0.000006041	-0.00007883	-0.00001852
fixed	NA	male	-0.02275	0.0133	-1.71	3713	0.0874	-0.06009	0.0146
fixed	NA	sibling_count3	0.02308	0.02169	1.064	3067	0.2874	-0.03781	0.08397
fixed	NA	sibling_count4	-0.02539	0.02314	-1.097	2891	0.2725	-0.09034	0.03955
fixed	NA	sibling_count5	0.03322	0.02704	1.229	2589	0.2193	-0.04268	0.1091
fixed	NA	sibling_count>5	0.0449	0.02695	1.666	2763	0.09583	-0.03075	0.1205
ran_pars	mother_pidlink	sd__(Intercept)	0.1602	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3725	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)	0.9616	0.2651	3.628	3747	0.0002899	0.2175	1.706
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1091	0.0285	-3.828	3744	0.0001314	-0.1891	-0.02909
fixed	NA	poly(age, 3, raw = TRUE)2	0.00431	0.0009784	4.405	3742	0.00001088	0.001563	0.007056
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004859	0.00001075	-4.519	3740	0.000006417	-0.00007877	-0.0000184
fixed	NA	male	-0.02281	0.01331	-1.713	3710	0.08675	-0.06018	0.01456
fixed	NA	sibling_count3	0.02313	0.02213	1.045	3157	0.296	-0.039	0.08526
fixed	NA	sibling_count4	-0.02585	0.02394	-1.08	3054	0.2803	-0.09306	0.04136
fixed	NA	sibling_count5	0.03196	0.02818	1.134	2816	0.2569	-0.04715	0.1111
fixed	NA	sibling_count>5	0.05248	0.02768	1.896	2897	0.05807	-0.02522	0.1302
fixed	NA	birth_order_nonlinear2	0.004606	0.01724	0.2672	3285	0.7893	-0.04378	0.05299
fixed	NA	birth_order_nonlinear3	-0.001029	0.02041	-0.0504	3362	0.9598	-0.05831	0.05626
fixed	NA	birth_order_nonlinear4	0.001722	0.02559	0.06727	3422	0.9464	-0.07012	0.07357
fixed	NA	birth_order_nonlinear5	0.003465	0.03152	0.1099	3399	0.9125	-0.08503	0.09196
fixed	NA	birth_order_nonlinear>5	-0.02943	0.03147	-0.9352	3747	0.3498	-0.1178	0.05891
ran_pars	mother_pidlink	sd__(Intercept)	0.1602	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3727	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)	0.9503	0.266	3.573	3737	0.000358	0.2036	1.697
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1092	0.0286	-3.819	3735	0.0001361	-0.1895	-0.02895
fixed	NA	poly(age, 3, raw = TRUE)2	0.004316	0.0009823	4.394	3733	0.00001143	0.001559	0.007073
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004867	0.0000108	-4.507	3732	0.000006766	-0.00007898	-0.00001836
fixed	NA	male	-0.0234	0.01334	-1.754	3699	0.07946	-0.06083	0.01404
fixed	NA	count_birth_order2/2	0.0426	0.03271	1.302	3378	0.193	-0.04923	0.1344
fixed	NA	count_birth_order1/3	0.04535	0.0282	1.608	3724	0.1078	-0.0338	0.1245
fixed	NA	count_birth_order2/3	0.04406	0.03134	1.406	3738	0.1598	-0.0439	0.132
fixed	NA	count_birth_order3/3	0.01164	0.03353	0.3472	3738	0.7285	-0.08249	0.1058
fixed	NA	count_birth_order1/4	-0.008358	0.03305	-0.2528	3736	0.8004	-0.1011	0.08443
fixed	NA	count_birth_order2/4	-0.04096	0.03452	-1.187	3739	0.2355	-0.1379	0.05594
fixed	NA	count_birth_order3/4	-0.01007	0.03618	-0.2784	3735	0.7807	-0.1116	0.09147
fixed	NA	count_birth_order4/4	0.02124	0.03901	0.5443	3731	0.5862	-0.08827	0.1307
fixed	NA	count_birth_order1/5	0.0574	0.04322	1.328	3739	0.1842	-0.06392	0.1787
fixed	NA	count_birth_order2/5	0.07243	0.04845	1.495	3715	0.1351	-0.06358	0.2084
fixed	NA	count_birth_order3/5	0.0487	0.04642	1.049	3719	0.2941	-0.08159	0.179
fixed	NA	count_birth_order4/5	0.03821	0.04477	0.8534	3722	0.3935	-0.08747	0.1639
fixed	NA	count_birth_order5/5	0.0122	0.04712	0.2589	3717	0.7957	-0.1201	0.1445
fixed	NA	count_birth_order1/>5	0.05652	0.0421	1.342	3735	0.1795	-0.06166	0.1747
fixed	NA	count_birth_order2/>5	0.05222	0.04261	1.225	3719	0.2205	-0.06739	0.1718
fixed	NA	count_birth_order3/>5	0.09224	0.04079	2.261	3719	0.02382	-0.02227	0.2067
fixed	NA	count_birth_order4/>5	0.03775	0.04057	0.9304	3703	0.3522	-0.07614	0.1516
fixed	NA	count_birth_order5/>5	0.0893	0.0384	2.326	3713	0.02009	-0.01849	0.1971
fixed	NA	count_birth_order>5/>5	0.0354	0.0301	1.176	3588	0.2396	-0.04908	0.1199
ran_pars	mother_pidlink	sd__(Intercept)	0.1598	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3729	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)
11	3861	3930	-1919	3839	NA	NA	NA
12	3863	3938	-1919	3839	0.06169	1	0.8038
16	3870	3969	-1919	3838	1.332	4	0.856
26	3882	4044	-1915	3830	8.08	10	0.6211

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)	0.06852	0.03525	1.944	9844	0.05195	-0.03043	0.1675
fixed	NA	poly(age, 3, raw = TRUE)1	-0.004585	0.003161	-1.45	9771	0.147	-0.01346	0.004289
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001275	0.00008876	1.437	9635	0.1508	-0.0001216	0.0003767
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000009703	0.0000007884	-1.231	9480	0.2185	-0.000003184	0.000001243
fixed	NA	male	0.0003999	0.003258	0.1228	9985	0.9023	-0.008744	0.009544
fixed	NA	sibling_count3	-0.00296	0.006763	-0.4378	7181	0.6616	-0.02194	0.01602
fixed	NA	sibling_count4	0.005901	0.00682	0.8653	6742	0.3869	-0.01324	0.02504
fixed	NA	sibling_count5	-0.002795	0.007104	-0.3935	6243	0.694	-0.02274	0.01714
fixed	NA	sibling_count>5	0.008566	0.005512	1.554	7041	0.1202	-0.006905	0.02404
ran_pars	mother_pidlink	sd__(Intercept)	0.05392	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)	0.06862	0.03525	1.947	9843	0.05159	-0.03032	0.1676
fixed	NA	birth_order	-0.0009169	0.0006614	-1.386	8785	0.1657	-0.002773	0.0009396
fixed	NA	poly(age, 3, raw = TRUE)1	-0.004333	0.003167	-1.368	9760	0.1712	-0.01322	0.004555
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001183	0.00008901	1.329	9591	0.1837	-0.0001315	0.0003682
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000008869	0.0000007907	-1.122	9419	0.262	-0.000003107	0.000001333
fixed	NA	male	0.0004145	0.003257	0.1273	9983	0.8987	-0.008729	0.009558
fixed	NA	sibling_count3	-0.00271	0.006766	-0.4005	7190	0.6888	-0.0217	0.01628
fixed	NA	sibling_count4	0.006467	0.006833	0.9464	6790	0.344	-0.01271	0.02565
fixed	NA	sibling_count5	-0.001804	0.007141	-0.2526	6335	0.8006	-0.02185	0.01824
fixed	NA	sibling_count>5	0.01179	0.005981	1.971	7847	0.04878	-0.005001	0.02858
ran_pars	mother_pidlink	sd__(Intercept)	0.05405	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)	0.0684	0.03531	1.937	9847	0.05273	-0.0307	0.1675
fixed	NA	poly(age, 3, raw = TRUE)1	-0.004322	0.00317	-1.364	9763	0.1727	-0.01322	0.004576
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001208	0.00008907	1.357	9596	0.1749	-0.0001292	0.0003709
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000009306	0.0000007912	-1.176	9420	0.2396	-0.000003152	0.00000129
fixed	NA	male	0.0004062	0.003258	0.1247	9979	0.9008	-0.008739	0.009552
fixed	NA	sibling_count3	-0.002613	0.006868	-0.3805	7465	0.7036	-0.02189	0.01667
fixed	NA	sibling_count4	0.007246	0.007019	1.032	7292	0.302	-0.01246	0.02695
fixed	NA	sibling_count5	-0.001002	0.007388	-0.1356	6974	0.8921	-0.02174	0.01974
fixed	NA	sibling_count>5	0.01129	0.006267	1.801	8560	0.07178	-0.006306	0.02888
fixed	NA	birth_order_nonlinear2	-0.00616	0.004749	-1.297	9156	0.1946	-0.01949	0.007169
fixed	NA	birth_order_nonlinear3	-0.003442	0.00552	-0.6236	8982	0.5329	-0.01894	0.01205
fixed	NA	birth_order_nonlinear4	-0.008114	0.006198	-1.309	9085	0.1905	-0.02551	0.009284
fixed	NA	birth_order_nonlinear5	-0.006216	0.006973	-0.8915	9127	0.3727	-0.02579	0.01336
fixed	NA	birth_order_nonlinear>5	-0.006247	0.005788	-1.079	10081	0.2805	-0.02249	0.01
ran_pars	mother_pidlink	sd__(Intercept)	0.05398	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1531	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)	0.07183	0.03542	2.028	9850	0.0426	-0.0276	0.1713
fixed	NA	poly(age, 3, raw = TRUE)1	-0.004317	0.003172	-1.361	9752	0.1735	-0.01322	0.004586
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001217	0.0000891	1.366	9583	0.1721	-0.0001284	0.0003718
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000009483	0.0000007913	-1.198	9403	0.2308	-0.00000317	0.000001273
fixed	NA	male	0.0003518	0.003259	0.1079	9970	0.914	-0.008797	0.0095
fixed	NA	count_birth_order2/2	-0.01611	0.009432	-1.708	9035	0.08768	-0.04258	0.01037
fixed	NA	count_birth_order1/3	-0.007027	0.009116	-0.7708	9982	0.4408	-0.03262	0.01856
fixed	NA	count_birth_order2/3	-0.006682	0.0101	-0.6613	10024	0.5084	-0.03505	0.02168
fixed	NA	count_birth_order3/3	-0.01617	0.0111	-1.457	10049	0.1452	-0.04732	0.01498
fixed	NA	count_birth_order1/4	-0.007734	0.009987	-0.7744	10027	0.4387	-0.03577	0.0203
fixed	NA	count_birth_order2/4	-0.003666	0.01071	-0.3423	10042	0.7321	-0.03372	0.02639
fixed	NA	count_birth_order3/4	0.01068	0.01142	0.935	10059	0.3498	-0.02137	0.04272
fixed	NA	count_birth_order4/4	0.00423	0.01213	0.3488	10064	0.7273	-0.02981	0.03827
fixed	NA	count_birth_order1/5	0.002099	0.01134	0.1851	10058	0.8531	-0.02973	0.03393
fixed	NA	count_birth_order2/5	-0.01472	0.01203	-1.224	10064	0.2208	-0.04848	0.01903
fixed	NA	count_birth_order3/5	-0.02292	0.01266	-1.81	10069	0.07029	-0.05845	0.01262
fixed	NA	count_birth_order4/5	0.003402	0.01331	0.2556	10069	0.7982	-0.03395	0.04076
fixed	NA	count_birth_order5/5	-0.01578	0.0133	-1.186	10071	0.2356	-0.05313	0.02156
fixed	NA	count_birth_order1/>5	0.007944	0.008735	0.9094	10069	0.3632	-0.01658	0.03246
fixed	NA	count_birth_order2/>5	0.004563	0.009098	0.5016	10071	0.616	-0.02097	0.0301
fixed	NA	count_birth_order3/>5	0.007596	0.008963	0.8475	10071	0.3967	-0.01756	0.03275
fixed	NA	count_birth_order4/>5	-0.008504	0.008802	-0.9661	10070	0.334	-0.03321	0.0162
fixed	NA	count_birth_order5/>5	0.002768	0.008901	0.311	10071	0.7558	-0.02222	0.02775
fixed	NA	count_birth_order>5/>5	0.001264	0.007196	0.1757	9110	0.8605	-0.01894	0.02146
ran_pars	mother_pidlink	sd__(Intercept)	0.05386	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1531	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)
11	-8128	-8049	4075	-8150	NA	NA	NA
12	-8128	-8041	4076	-8152	1.92	1	0.1659
16	-8121	-8005	4076	-8153	0.7708	4	0.9423
26	-8114	-7926	4083	-8166	13.04	10	0.2216

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)	0.01952	0.07867	0.2481	3803	0.804	-0.2013	0.2404
fixed	NA	poly(age, 3, raw = TRUE)1	0.001255	0.008445	0.1486	3791	0.8819	-0.02245	0.02496
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001097	0.0002896	-0.3787	3781	0.7049	-0.0009227	0.0007033
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001805	0.000003179	0.5676	3774	0.5703	-0.00000712	0.00001073
fixed	NA	male	0.003915	0.003952	0.9909	3702	0.3218	-0.007177	0.01501
fixed	NA	sibling_count3	-0.005883	0.006687	-0.8798	2731	0.3791	-0.02465	0.01289
fixed	NA	sibling_count4	0.0002679	0.006935	0.03863	2527	0.9692	-0.0192	0.01974
fixed	NA	sibling_count5	-0.007085	0.007746	-0.9147	2239	0.3605	-0.02883	0.01466
fixed	NA	sibling_count>5	0.01689	0.006728	2.51	2229	0.01213	-0.001997	0.03578
ran_pars	mother_pidlink	sd__(Intercept)	0.05521	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1091	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)	0.02063	0.07869	0.2622	3804	0.7932	-0.2003	0.2415
fixed	NA	birth_order	0.0009961	0.001241	0.803	3794	0.422	-0.002486	0.004478
fixed	NA	poly(age, 3, raw = TRUE)1	0.001006	0.008451	0.119	3795	0.9053	-0.02272	0.02473
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001032	0.0002898	-0.3563	3784	0.7216	-0.0009166	0.0007101
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001779	0.00000318	0.5595	3775	0.5759	-0.000007146	0.0000107
fixed	NA	male	0.003886	0.003952	0.9833	3702	0.3255	-0.007208	0.01498
fixed	NA	sibling_count3	-0.006403	0.006718	-0.953	2736	0.3407	-0.02526	0.01246
fixed	NA	sibling_count4	-0.0008584	0.007075	-0.1213	2539	0.9034	-0.02072	0.019
fixed	NA	sibling_count5	-0.008934	0.00808	-1.106	2304	0.269	-0.03162	0.01375
fixed	NA	sibling_count>5	0.01326	0.008107	1.635	2458	0.1022	-0.009501	0.03601
ran_pars	mother_pidlink	sd__(Intercept)	0.05515	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1091	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)	0.02295	0.07878	0.2913	3800	0.7709	-0.1982	0.2441
fixed	NA	poly(age, 3, raw = TRUE)1	0.0008336	0.008454	0.0986	3788	0.9215	-0.0229	0.02456
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0000993	0.0002899	-0.3425	3777	0.732	-0.0009131	0.0007145
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001774	0.000003182	0.5574	3768	0.5773	-0.000007159	0.00001071
fixed	NA	male	0.003896	0.003953	0.9856	3697	0.3244	-0.0072	0.01499
fixed	NA	sibling_count3	-0.005982	0.006841	-0.8744	2856	0.382	-0.02519	0.01322
fixed	NA	sibling_count4	-0.0002267	0.007308	-0.03102	2746	0.9753	-0.02074	0.02029
fixed	NA	sibling_count5	-0.00734	0.008432	-0.8706	2585	0.3841	-0.03101	0.01633
fixed	NA	sibling_count>5	0.01131	0.008306	1.361	2609	0.1736	-0.01201	0.03462
fixed	NA	birth_order_nonlinear2	0.002468	0.005159	0.4784	3041	0.6324	-0.01201	0.01695
fixed	NA	birth_order_nonlinear3	0.0001147	0.006077	0.01887	3134	0.9849	-0.01694	0.01717
fixed	NA	birth_order_nonlinear4	0.001705	0.007413	0.23	3210	0.8181	-0.0191	0.02251
fixed	NA	birth_order_nonlinear5	-0.0005972	0.009118	-0.06549	3207	0.9478	-0.02619	0.025
fixed	NA	birth_order_nonlinear>5	0.0157	0.009163	1.713	3794	0.0868	-0.01002	0.04141
ran_pars	mother_pidlink	sd__(Intercept)	0.05527	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1091	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)	0.02181	0.07903	0.276	3792	0.7826	-0.2	0.2436
fixed	NA	poly(age, 3, raw = TRUE)1	0.001327	0.008482	0.1565	3782	0.8756	-0.02248	0.02514
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001173	0.0002909	-0.4032	3773	0.6868	-0.000934	0.0006994
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000199	0.000003194	0.6231	3766	0.5333	-0.000006976	0.00001096
fixed	NA	male	0.003913	0.003957	0.989	3692	0.3227	-0.007193	0.01502
fixed	NA	count_birth_order2/2	-0.007885	0.01004	-0.785	3256	0.4325	-0.03608	0.02031
fixed	NA	count_birth_order1/3	-0.01161	0.008624	-1.346	3766	0.1784	-0.03582	0.0126
fixed	NA	count_birth_order2/3	-0.009642	0.009564	-1.008	3802	0.3134	-0.03649	0.0172
fixed	NA	count_birth_order3/3	-0.001103	0.01033	-0.1067	3807	0.915	-0.03011	0.02791
fixed	NA	count_birth_order1/4	0.001448	0.009895	0.1463	3796	0.8837	-0.02633	0.02922
fixed	NA	count_birth_order2/4	-0.001238	0.01039	-0.1191	3807	0.9052	-0.03041	0.02793
fixed	NA	count_birth_order3/4	-0.0139	0.01089	-1.277	3798	0.2019	-0.04446	0.01666
fixed	NA	count_birth_order4/4	0.002229	0.01154	0.1931	3792	0.8469	-0.03018	0.03464
fixed	NA	count_birth_order1/5	-0.009352	0.01296	-0.7215	3806	0.4706	-0.04573	0.02703
fixed	NA	count_birth_order2/5	-0.01508	0.01408	-1.071	3760	0.2842	-0.05459	0.02443
fixed	NA	count_birth_order3/5	-0.01413	0.01319	-1.071	3774	0.2844	-0.05115	0.0229
fixed	NA	count_birth_order4/5	0.002559	0.01283	0.1994	3773	0.842	-0.03346	0.03858
fixed	NA	count_birth_order5/5	-0.01591	0.01345	-1.183	3763	0.2371	-0.05366	0.02185
fixed	NA	count_birth_order1/>5	-0.00645	0.01232	-0.5237	3793	0.6005	-0.04102	0.02812
fixed	NA	count_birth_order2/>5	0.03205	0.01241	2.582	3757	0.00986	-0.002793	0.06689
fixed	NA	count_birth_order3/>5	0.01239	0.01213	1.022	3748	0.3071	-0.02166	0.04645
fixed	NA	count_birth_order4/>5	-0.003848	0.01178	-0.3267	3732	0.7439	-0.03691	0.02921
fixed	NA	count_birth_order5/>5	0.01032	0.01136	0.9085	3749	0.3637	-0.02157	0.04222
fixed	NA	count_birth_order>5/>5	0.02363	0.008944	2.642	3613	0.008276	-0.001476	0.04874
ran_pars	mother_pidlink	sd__(Intercept)	0.05466	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1093	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)
11	-5280	-5211	2651	-5302	NA	NA	NA
12	-5279	-5203	2651	-5303	0.6479	1	0.4209
16	-5274	-5174	2653	-5306	3.207	4	0.5238
26	-5268	-5106	2660	-5320	14.78	10	0.1402

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)	0.01131	0.0782	0.1446	3830	0.885	-0.2082	0.2308
fixed	NA	poly(age, 3, raw = TRUE)1	0.002056	0.008402	0.2447	3819	0.8067	-0.02153	0.02564
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001338	0.0002882	-0.4642	3809	0.6425	-0.0009428	0.0006753
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002068	0.000003165	0.6536	3802	0.5134	-0.000006815	0.00001095
fixed	NA	male	0.003961	0.003931	1.007	3729	0.3138	-0.007075	0.015
fixed	NA	sibling_count3	-0.003733	0.007306	-0.5109	2825	0.6094	-0.02424	0.01677
fixed	NA	sibling_count4	-0.002881	0.007382	-0.3903	2681	0.6964	-0.0236	0.01784
fixed	NA	sibling_count5	-0.005224	0.007806	-0.6693	2471	0.5034	-0.02714	0.01669
fixed	NA	sibling_count>5	0.00942	0.006833	1.379	2566	0.1682	-0.009761	0.0286
ran_pars	mother_pidlink	sd__(Intercept)	0.05499	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1089	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)	0.01302	0.07819	0.1665	3831	0.8678	-0.2065	0.2325
fixed	NA	birth_order	0.001766	0.001094	1.613	3737	0.1068	-0.001307	0.004838
fixed	NA	poly(age, 3, raw = TRUE)1	0.001647	0.008404	0.1959	3822	0.8447	-0.02194	0.02524
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001235	0.0002882	-0.4285	3812	0.6683	-0.0009326	0.0006856
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002037	0.000003164	0.6439	3803	0.5197	-0.000006845	0.00001092
fixed	NA	male	0.003919	0.003931	0.997	3730	0.3188	-0.007115	0.01495
fixed	NA	sibling_count3	-0.004682	0.007326	-0.6391	2826	0.5228	-0.02525	0.01588
fixed	NA	sibling_count4	-0.004751	0.007469	-0.6361	2677	0.5248	-0.02572	0.01622
fixed	NA	sibling_count5	-0.00828	0.008028	-1.031	2492	0.3025	-0.03082	0.01426
fixed	NA	sibling_count>5	0.00311	0.00787	0.3951	2663	0.6928	-0.01898	0.0252
ran_pars	mother_pidlink	sd__(Intercept)	0.0548	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.109	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)	0.01294	0.07828	0.1654	3828	0.8687	-0.2068	0.2327
fixed	NA	poly(age, 3, raw = TRUE)1	0.001859	0.008409	0.2211	3817	0.825	-0.02174	0.02546
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001321	0.0002884	-0.4581	3807	0.6469	-0.0009418	0.0006775
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000215	0.000003167	0.6788	3799	0.4973	-0.00000674	0.00001104
fixed	NA	male	0.003953	0.003932	1.005	3726	0.3148	-0.007085	0.01499
fixed	NA	sibling_count3	-0.003594	0.007444	-0.4828	2922	0.6293	-0.02449	0.0173
fixed	NA	sibling_count4	-0.002937	0.007673	-0.3828	2839	0.7019	-0.02447	0.0186
fixed	NA	sibling_count5	-0.006432	0.008351	-0.7703	2731	0.4412	-0.02987	0.01701
fixed	NA	sibling_count>5	0.00298	0.008078	0.3689	2818	0.7122	-0.0197	0.02565
fixed	NA	birth_order_nonlinear2	0.002136	0.005222	0.409	3118	0.6826	-0.01252	0.01679
fixed	NA	birth_order_nonlinear3	-0.001164	0.006104	-0.1907	3223	0.8488	-0.0183	0.01597
fixed	NA	birth_order_nonlinear4	0.0004516	0.007227	0.06249	3307	0.9502	-0.01983	0.02074
fixed	NA	birth_order_nonlinear5	0.006838	0.008807	0.7765	3312	0.4375	-0.01788	0.03156
fixed	NA	birth_order_nonlinear>5	0.01633	0.008275	1.974	3843	0.0485	-0.006897	0.03956
ran_pars	mother_pidlink	sd__(Intercept)	0.05469	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1091	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)	0.01009	0.07847	0.1286	3820	0.8977	-0.2102	0.2304
fixed	NA	poly(age, 3, raw = TRUE)1	0.002548	0.008429	0.3022	3811	0.7625	-0.02111	0.02621
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001574	0.0002892	-0.5441	3803	0.5864	-0.0009693	0.0006545
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002441	0.000003177	0.7684	3797	0.4423	-0.000006476	0.00001136
fixed	NA	male	0.003936	0.003938	0.9995	3720	0.3176	-0.007119	0.01499
fixed	NA	count_birth_order2/2	-0.007212	0.01106	-0.6522	3418	0.5143	-0.03825	0.02383
fixed	NA	count_birth_order1/3	-0.008172	0.009511	-0.8592	3794	0.3903	-0.03487	0.01853
fixed	NA	count_birth_order2/3	-0.009063	0.01034	-0.8768	3825	0.3807	-0.03808	0.01995
fixed	NA	count_birth_order3/3	0.001455	0.01135	0.1282	3833	0.898	-0.03042	0.03333
fixed	NA	count_birth_order1/4	0.0004717	0.01034	0.04564	3814	0.9636	-0.02854	0.02948
fixed	NA	count_birth_order2/4	-0.007483	0.01077	-0.6945	3832	0.4874	-0.03773	0.02276
fixed	NA	count_birth_order3/4	-0.01528	0.01176	-1.298	3826	0.1942	-0.0483	0.01775
fixed	NA	count_birth_order4/4	-0.001979	0.01256	-0.1576	3818	0.8748	-0.03722	0.03326
fixed	NA	count_birth_order1/5	-0.01023	0.01238	-0.8266	3833	0.4085	-0.04497	0.02451
fixed	NA	count_birth_order2/5	-0.007519	0.01284	-0.5854	3826	0.5583	-0.04357	0.02853
fixed	NA	count_birth_order3/5	-0.0147	0.01307	-1.125	3812	0.2606	-0.05138	0.02198
fixed	NA	count_birth_order4/5	0.00125	0.01328	0.09417	3794	0.925	-0.03602	0.03852
fixed	NA	count_birth_order5/5	-0.007193	0.01338	-0.5377	3795	0.5908	-0.04474	0.03035
fixed	NA	count_birth_order1/>5	-0.0104	0.01119	-0.9288	3833	0.3531	-0.04181	0.02102
fixed	NA	count_birth_order2/>5	0.02034	0.01181	1.723	3804	0.08504	-0.01281	0.05349
fixed	NA	count_birth_order3/>5	-0.0001227	0.01137	-0.01078	3808	0.9914	-0.03205	0.03181
fixed	NA	count_birth_order4/>5	-0.007947	0.01109	-0.7164	3803	0.4738	-0.03908	0.02319
fixed	NA	count_birth_order5/>5	0.009955	0.01172	0.8491	3772	0.3959	-0.02295	0.04286
fixed	NA	count_birth_order>5/>5	0.01644	0.008933	1.84	3643	0.06586	-0.008639	0.04151
ran_pars	mother_pidlink	sd__(Intercept)	0.05419	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1092	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)
11	-5331	-5262	2676	-5353	NA	NA	NA
12	-5332	-5256	2678	-5356	2.611	1	0.1061
16	-5326	-5226	2679	-5358	2.522	4	0.6408
26	-5318	-5155	2685	-5370	11.59	10	0.3135

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)	-0.001325	0.07952	-0.01666	3737	0.9867	-0.2246	0.2219
fixed	NA	poly(age, 3, raw = TRUE)1	0.003218	0.008549	0.3765	3726	0.7066	-0.02078	0.02722
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001742	0.0002935	-0.5934	3716	0.5529	-0.0009979	0.0006496
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000248	0.000003225	0.7689	3709	0.442	-0.000006574	0.00001153
fixed	NA	male	0.003577	0.003991	0.8963	3640	0.3702	-0.007625	0.01478
fixed	NA	sibling_count3	-0.003884	0.006553	-0.5927	2720	0.5534	-0.02228	0.01451
fixed	NA	sibling_count4	0.002849	0.006893	0.4133	2508	0.6794	-0.0165	0.0222
fixed	NA	sibling_count5	-0.00005811	0.007916	-0.007341	2150	0.9941	-0.02228	0.02216
fixed	NA	sibling_count>5	0.01903	0.006764	2.814	2154	0.004938	0.00004676	0.03802
ran_pars	mother_pidlink	sd__(Intercept)	0.05496	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1093	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)	-0.0002167	0.07955	-0.002724	3738	0.9978	-0.2235	0.2231
fixed	NA	birth_order	0.000822	0.001276	0.644	3738	0.5196	-0.002761	0.004405
fixed	NA	poly(age, 3, raw = TRUE)1	0.002991	0.008557	0.3496	3729	0.7267	-0.02103	0.02701
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001681	0.0002936	-0.5724	3719	0.5671	-0.0009924	0.0006562
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000245	0.000003226	0.7596	3710	0.4475	-0.000006605	0.00001151
fixed	NA	male	0.003571	0.003991	0.8946	3640	0.371	-0.007633	0.01477
fixed	NA	sibling_count3	-0.004323	0.006588	-0.6561	2722	0.5118	-0.02282	0.01417
fixed	NA	sibling_count4	0.001934	0.007037	0.2748	2524	0.7835	-0.01782	0.02169
fixed	NA	sibling_count5	-0.001542	0.008244	-0.187	2206	0.8517	-0.02468	0.0216
fixed	NA	sibling_count>5	0.01604	0.008204	1.955	2429	0.05067	-0.006988	0.03907
ran_pars	mother_pidlink	sd__(Intercept)	0.05492	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1093	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)	0.004456	0.07962	0.05596	3734	0.9554	-0.219	0.228
fixed	NA	poly(age, 3, raw = TRUE)1	0.002493	0.008558	0.2913	3723	0.7708	-0.02153	0.02652
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001531	0.0002937	-0.5212	3713	0.6023	-0.0009776	0.0006714
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002327	0.000003228	0.721	3705	0.4709	-0.000006733	0.00001139
fixed	NA	male	0.00353	0.003992	0.8844	3637	0.3766	-0.007675	0.01474
fixed	NA	sibling_count3	-0.003619	0.006713	-0.5391	2841	0.5898	-0.02246	0.01522
fixed	NA	sibling_count4	0.001897	0.007268	0.261	2725	0.7941	-0.01851	0.0223
fixed	NA	sibling_count5	-0.0000944	0.008571	-0.01101	2461	0.9912	-0.02415	0.02397
fixed	NA	sibling_count>5	0.01416	0.008412	1.684	2583	0.09233	-0.009448	0.03778
fixed	NA	birth_order_nonlinear2	0.003759	0.00514	0.7312	2983	0.4647	-0.01067	0.01819
fixed	NA	birth_order_nonlinear3	-0.001207	0.00609	-0.1982	3082	0.8429	-0.0183	0.01589
fixed	NA	birth_order_nonlinear4	0.006397	0.007642	0.837	3157	0.4027	-0.01506	0.02785
fixed	NA	birth_order_nonlinear5	-0.004586	0.009411	-0.4873	3113	0.6261	-0.031	0.02183
fixed	NA	birth_order_nonlinear>5	0.01514	0.009452	1.602	3721	0.1093	-0.01139	0.04167
ran_pars	mother_pidlink	sd__(Intercept)	0.05481	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1094	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)	0.001525	0.07984	0.0191	3727	0.9848	-0.2226	0.2257
fixed	NA	poly(age, 3, raw = TRUE)1	0.003193	0.008584	0.372	3717	0.7099	-0.0209	0.02729
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001795	0.0002947	-0.6092	3709	0.5424	-0.001007	0.0006477
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002647	0.000003239	0.817	3702	0.414	-0.000006447	0.00001174
fixed	NA	male	0.003806	0.003996	0.9523	3629	0.341	-0.007412	0.01502
fixed	NA	count_birth_order2/2	-0.00583	0.009763	-0.5971	3160	0.5505	-0.03324	0.02158
fixed	NA	count_birth_order1/3	-0.008914	0.008482	-1.051	3703	0.2933	-0.03272	0.01489
fixed	NA	count_birth_order2/3	-0.006944	0.009415	-0.7375	3738	0.4609	-0.03337	0.01949
fixed	NA	count_birth_order3/3	0.001039	0.01007	0.1032	3738	0.9178	-0.02723	0.0293
fixed	NA	count_birth_order1/4	0.005042	0.009935	0.5075	3732	0.6118	-0.02284	0.03293
fixed	NA	count_birth_order2/4	0.001827	0.01037	0.1762	3738	0.8602	-0.02728	0.03093
fixed	NA	count_birth_order3/4	-0.01081	0.01086	-0.9954	3729	0.3196	-0.04129	0.01967
fixed	NA	count_birth_order4/4	0.005862	0.01171	0.5008	3719	0.6165	-0.02699	0.03872
fixed	NA	count_birth_order1/5	-0.005219	0.01298	-0.4021	3739	0.6877	-0.04165	0.03122
fixed	NA	count_birth_order2/5	-0.001872	0.01453	-0.1289	3679	0.8975	-0.04265	0.03891
fixed	NA	count_birth_order3/5	-0.009697	0.01392	-0.6966	3689	0.4861	-0.04877	0.02938
fixed	NA	count_birth_order4/5	0.01645	0.01343	1.225	3699	0.2207	-0.02124	0.05414
fixed	NA	count_birth_order5/5	-0.01244	0.01413	-0.8801	3688	0.3789	-0.0521	0.02723
fixed	NA	count_birth_order1/>5	-0.003465	0.01264	-0.2742	3722	0.7839	-0.03893	0.032
fixed	NA	count_birth_order2/>5	0.03849	0.01278	3.012	3682	0.00261	0.002623	0.07436
fixed	NA	count_birth_order3/>5	0.01002	0.01223	0.8194	3686	0.4126	-0.02432	0.04436
fixed	NA	count_birth_order4/>5	0.006257	0.01216	0.5146	3651	0.6069	-0.02788	0.04039
fixed	NA	count_birth_order5/>5	0.009081	0.01151	0.7888	3678	0.4303	-0.02324	0.0414
fixed	NA	count_birth_order>5/>5	0.02622	0.009074	2.889	3535	0.003887	0.0007449	0.05169
ran_pars	mother_pidlink	sd__(Intercept)	0.05436	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1095	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)
11	-5181	-5113	2602	-5203	NA	NA	NA
12	-5180	-5105	2602	-5204	0.4171	1	0.5184
16	-5177	-5077	2604	-5209	4.736	4	0.3155
26	-5171	-5009	2611	-5223	14.04	10	0.171

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)	0.2572	0.05886	4.37	9890	0.00001256	0.09198	0.4224
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01623	0.00528	-3.074	9831	0.002114	-0.03105	-0.001412
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003827	0.0001483	2.581	9715	0.009866	-0.00003352	0.0007989
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002755	0.000001317	-2.092	9579	0.03649	-0.000006453	0.0000009423
fixed	NA	male	0.06204	0.00543	11.43	9970	4.752e-30	0.0468	0.07729
fixed	NA	sibling_count3	0.002887	0.01133	0.2549	7371	0.7988	-0.02891	0.03469
fixed	NA	sibling_count4	-0.006908	0.01143	-0.6044	6971	0.5456	-0.03899	0.02517
fixed	NA	sibling_count5	-0.001617	0.01191	-0.1358	6507	0.892	-0.03505	0.03182
fixed	NA	sibling_count>5	-0.007001	0.009233	-0.7582	7251	0.4483	-0.03292	0.01892
ran_pars	mother_pidlink	sd__(Intercept)	0.09542	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2537	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)	0.2572	0.05886	4.37	9889	0.00001255	0.09199	0.4224
fixed	NA	birth_order	-0.0001545	0.001106	-0.1397	9078	0.8889	-0.003259	0.00295
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01619	0.005289	-3.061	9821	0.002211	-0.03103	-0.001344
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003811	0.0001487	2.563	9676	0.0104	-0.0000363	0.0007985
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002741	0.000001321	-2.075	9523	0.03805	-0.00000645	0.0000009678
fixed	NA	male	0.06205	0.00543	11.43	9968	4.761e-30	0.0468	0.07729
fixed	NA	sibling_count3	0.002928	0.01133	0.2583	7381	0.7962	-0.02888	0.03474
fixed	NA	sibling_count4	-0.006814	0.01145	-0.5951	7017	0.5518	-0.03895	0.02533
fixed	NA	sibling_count5	-0.00145	0.01197	-0.1212	6596	0.9036	-0.03505	0.03215
fixed	NA	sibling_count>5	-0.00646	0.01001	-0.6453	8025	0.5187	-0.03456	0.02164
ran_pars	mother_pidlink	sd__(Intercept)	0.09546	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2537	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)	0.2574	0.05896	4.367	9892	0.00001275	0.09194	0.4229
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0162	0.005294	-3.06	9823	0.002222	-0.03106	-0.001338
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003819	0.0001488	2.567	9680	0.01028	-0.00003575	0.0007996
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002754	0.000001322	-2.083	9524	0.0373	-0.000006465	0.0000009577
fixed	NA	male	0.06205	0.005432	11.42	9965	4.87e-30	0.04681	0.0773
fixed	NA	sibling_count3	0.003057	0.0115	0.2658	7639	0.7904	-0.02923	0.03534
fixed	NA	sibling_count4	-0.006794	0.01176	-0.578	7490	0.5633	-0.03979	0.0262
fixed	NA	sibling_count5	-0.0008552	0.01238	-0.0691	7200	0.9449	-0.0356	0.03389
fixed	NA	sibling_count>5	-0.006345	0.01048	-0.6053	8677	0.545	-0.03577	0.02308
fixed	NA	birth_order_nonlinear2	-0.00146	0.007906	-0.1847	9227	0.8535	-0.02365	0.02073
fixed	NA	birth_order_nonlinear3	-0.001161	0.009188	-0.1263	9055	0.8995	-0.02695	0.02463
fixed	NA	birth_order_nonlinear4	-0.0003736	0.01032	-0.03621	9142	0.9711	-0.02934	0.02859
fixed	NA	birth_order_nonlinear5	-0.004592	0.01161	-0.3955	9173	0.6925	-0.03718	0.02799
fixed	NA	birth_order_nonlinear>5	-0.0009382	0.009655	-0.09716	10078	0.9226	-0.02804	0.02617
ran_pars	mother_pidlink	sd__(Intercept)	0.09536	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2537	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)	0.2538	0.05915	4.291	9894	0.00001795	0.08778	0.4198
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01604	0.005297	-3.028	9813	0.002465	-0.03091	-0.001173
fixed	NA	poly(age, 3, raw = TRUE)2	0.000377	0.0001488	2.533	9667	0.01133	-0.00004083	0.0007948
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000002706	0.000001322	-2.046	9508	0.04074	-0.000006418	0.000001006
fixed	NA	male	0.06207	0.005433	11.42	9955	4.852e-30	0.04682	0.07732
fixed	NA	count_birth_order2/2	0.004305	0.0157	0.2742	9148	0.7839	-0.03976	0.04837
fixed	NA	count_birth_order1/3	0.008432	0.01522	0.5541	9975	0.5795	-0.03428	0.05115
fixed	NA	count_birth_order2/3	0.00825	0.01686	0.4892	10021	0.6247	-0.03909	0.05559
fixed	NA	count_birth_order3/3	-0.008015	0.01852	-0.4328	10049	0.6652	-0.06	0.04397
fixed	NA	count_birth_order1/4	-0.0248	0.01667	-1.488	10023	0.1368	-0.07159	0.02198
fixed	NA	count_birth_order2/4	0.007322	0.01787	0.4098	10041	0.682	-0.04284	0.05748
fixed	NA	count_birth_order3/4	0.01171	0.01905	0.6149	10059	0.5386	-0.04176	0.06519
fixed	NA	count_birth_order4/4	-0.009058	0.02023	-0.4477	10065	0.6544	-0.06586	0.04774
fixed	NA	count_birth_order1/5	-0.01351	0.01892	-0.7138	10057	0.4754	-0.06662	0.03961
fixed	NA	count_birth_order2/5	-0.01094	0.02006	-0.5453	10064	0.5856	-0.06726	0.04538
fixed	NA	count_birth_order3/5	0.02642	0.02112	1.251	10069	0.2109	-0.03286	0.08571
fixed	NA	count_birth_order4/5	0.01116	0.0222	0.5028	10068	0.6151	-0.05115	0.07347
fixed	NA	count_birth_order5/5	-0.006309	0.02219	-0.2843	10071	0.7762	-0.06861	0.05599
fixed	NA	count_birth_order1/>5	0.01452	0.01457	0.9961	10069	0.3192	-0.02639	0.05543
fixed	NA	count_birth_order2/>5	-0.01502	0.01518	-0.9897	10071	0.3224	-0.05762	0.02758
fixed	NA	count_birth_order3/>5	-0.01649	0.01495	-1.103	10071	0.2701	-0.05846	0.02548
fixed	NA	count_birth_order4/>5	-0.005982	0.01468	-0.4074	10070	0.6837	-0.0472	0.03524
fixed	NA	count_birth_order5/>5	-0.007781	0.01485	-0.524	10071	0.6003	-0.04946	0.0339
fixed	NA	count_birth_order>5/>5	-0.005229	0.01203	-0.4346	9195	0.6638	-0.039	0.02854
ran_pars	mother_pidlink	sd__(Intercept)	0.09533	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2537	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)
11	2203	2282	-1090	2181	NA	NA	NA
12	2205	2291	-1090	2181	0.01918	1	0.8899
16	2213	2328	-1090	2181	0.1667	4	0.9967
26	2218	2406	-1083	2166	14.27	10	0.1609

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)	0.5278	0.1723	3.064	3822	0.002199	0.04427	1.011
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04411	0.0185	-2.385	3822	0.01715	-0.09604	0.007814
fixed	NA	poly(age, 3, raw = TRUE)2	0.00134	0.0006347	2.111	3822	0.03487	-0.000442	0.003121
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001395	0.000006968	-2.001	3822	0.04541	-0.0000335	0.000005613
fixed	NA	male	0.04766	0.008681	5.49	3804	0.00000004281	0.02329	0.07202
fixed	NA	sibling_count3	-0.005651	0.01432	-0.3946	3064	0.6932	-0.04585	0.03455
fixed	NA	sibling_count4	0.009222	0.0148	0.6229	2846	0.5334	-0.03233	0.05078
fixed	NA	sibling_count5	-0.01576	0.01645	-0.9578	2523	0.3383	-0.06194	0.03043
fixed	NA	sibling_count>5	0.02188	0.01429	1.531	2492	0.1258	-0.01823	0.06199
ran_pars	mother_pidlink	sd__(Intercept)	0.08695	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)	0.5268	0.1723	3.058	3821	0.002247	0.04316	1.01
fixed	NA	birth_order	-0.00116	0.002699	-0.4297	3683	0.6675	-0.008735	0.006416
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04386	0.01851	-2.37	3821	0.01785	-0.09582	0.008095
fixed	NA	poly(age, 3, raw = TRUE)2	0.001333	0.0006349	2.1	3821	0.03576	-0.0004486	0.003116
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001393	0.000006969	-1.999	3821	0.04569	-0.00003349	0.000005631
fixed	NA	male	0.04769	0.008682	5.493	3802	0.00000004207	0.02332	0.07206
fixed	NA	sibling_count3	-0.005053	0.01439	-0.3512	3064	0.7255	-0.04545	0.03534
fixed	NA	sibling_count4	0.01051	0.01511	0.6959	2846	0.4865	-0.03189	0.05292
fixed	NA	sibling_count5	-0.01363	0.01718	-0.7934	2567	0.4276	-0.06187	0.0346
fixed	NA	sibling_count>5	0.02605	0.01727	1.508	2653	0.1316	-0.02244	0.07454
ran_pars	mother_pidlink	sd__(Intercept)	0.08704	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2512	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)	0.5254	0.1725	3.046	3817	0.002338	0.04115	1.01
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0439	0.01852	-2.37	3817	0.01782	-0.09589	0.008089
fixed	NA	poly(age, 3, raw = TRUE)2	0.001338	0.0006353	2.106	3817	0.03531	-0.0004457	0.003121
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001404	0.000006975	-2.013	3817	0.04416	-0.00003362	0.000005537
fixed	NA	male	0.04763	0.008685	5.484	3798	0.00000004422	0.02325	0.07201
fixed	NA	sibling_count3	-0.001229	0.01468	-0.08376	3161	0.9333	-0.04243	0.03997
fixed	NA	sibling_count4	0.01619	0.01565	1.035	3031	0.3009	-0.02774	0.06013
fixed	NA	sibling_count5	-0.00553	0.01801	-0.3071	2835	0.7588	-0.05608	0.04502
fixed	NA	sibling_count>5	0.03521	0.01774	1.985	2798	0.04725	-0.01458	0.08499
fixed	NA	birth_order_nonlinear2	0.0003386	0.01147	0.02952	3348	0.9764	-0.03186	0.03253
fixed	NA	birth_order_nonlinear3	-0.01783	0.01349	-1.322	3441	0.1864	-0.05569	0.02004
fixed	NA	birth_order_nonlinear4	-0.01307	0.01643	-0.7954	3512	0.4264	-0.0592	0.03306
fixed	NA	birth_order_nonlinear5	-0.01722	0.02021	-0.8518	3529	0.3944	-0.07394	0.03951
fixed	NA	birth_order_nonlinear>5	-0.01704	0.02005	-0.8501	3809	0.3953	-0.07332	0.03924
ran_pars	mother_pidlink	sd__(Intercept)	0.08715	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2512	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)	0.5537	0.1731	3.199	3807	0.00139	0.06784	1.04
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04629	0.01858	-2.491	3807	0.01279	-0.09845	0.005878
fixed	NA	poly(age, 3, raw = TRUE)2	0.001425	0.0006377	2.234	3807	0.02552	-0.0003652	0.003215
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001505	0.000007003	-2.15	3807	0.03163	-0.00003471	0.000004602
fixed	NA	male	0.04776	0.008695	5.492	3788	0.00000004224	0.02335	0.07216
fixed	NA	count_birth_order2/2	-0.02316	0.02227	-1.04	3430	0.2985	-0.08567	0.03935
fixed	NA	count_birth_order1/3	-0.01659	0.01882	-0.8817	3797	0.378	-0.06942	0.03623
fixed	NA	count_birth_order2/3	0.002044	0.02091	0.09778	3806	0.9221	-0.05664	0.06073
fixed	NA	count_birth_order3/3	-0.0255	0.02262	-1.127	3807	0.2596	-0.08898	0.03799
fixed	NA	count_birth_order1/4	-0.0171	0.02162	-0.7912	3804	0.4289	-0.07779	0.04358
fixed	NA	count_birth_order2/4	0.01951	0.02274	0.858	3807	0.391	-0.04431	0.08333
fixed	NA	count_birth_order3/4	0.004401	0.02385	0.1845	3805	0.8536	-0.06255	0.07135
fixed	NA	count_birth_order4/4	0.006849	0.0253	0.2707	3803	0.7866	-0.06417	0.07787
fixed	NA	count_birth_order1/5	-0.0173	0.02837	-0.6099	3807	0.5419	-0.09693	0.06232
fixed	NA	count_birth_order2/5	-0.008308	0.03089	-0.269	3797	0.7879	-0.095	0.07839
fixed	NA	count_birth_order3/5	-0.03295	0.02893	-1.139	3799	0.2549	-0.1142	0.04827
fixed	NA	count_birth_order4/5	-0.03155	0.02815	-1.121	3798	0.2624	-0.1106	0.04746
fixed	NA	count_birth_order5/5	-0.02164	0.02952	-0.7332	3794	0.4635	-0.1045	0.06121
fixed	NA	count_birth_order1/>5	0.07584	0.02698	2.811	3807	0.00496	0.0001135	0.1516
fixed	NA	count_birth_order2/>5	0.01185	0.02723	0.4352	3801	0.6634	-0.06459	0.0883
fixed	NA	count_birth_order3/>5	-0.007979	0.02663	-0.2996	3796	0.7645	-0.08273	0.06677
fixed	NA	count_birth_order4/>5	0.007473	0.02587	0.2889	3790	0.7727	-0.06513	0.08008
fixed	NA	count_birth_order5/>5	0.004793	0.02494	0.1922	3793	0.8476	-0.06522	0.0748
fixed	NA	count_birth_order>5/>5	0.01042	0.01941	0.5368	3614	0.5915	-0.04407	0.0649
ran_pars	mother_pidlink	sd__(Intercept)	0.08705	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2512	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)
11	715.1	783.9	-346.6	693.1	NA	NA	NA
12	716.9	791.9	-346.5	692.9	0.1845	1	0.6675
16	722.4	822.4	-345.2	690.4	2.501	4	0.6444
26	731	893.5	-339.5	679	11.45	10	0.3232

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)	0.5216	0.1714	3.044	3848	0.00235	0.04061	1.003
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04348	0.01842	-2.36	3848	0.01831	-0.09518	0.008228
fixed	NA	poly(age, 3, raw = TRUE)2	0.001321	0.0006321	2.09	3848	0.03669	-0.0004533	0.003095
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001375	0.000006941	-1.98	3848	0.04774	-0.00003323	0.000005739
fixed	NA	male	0.04835	0.008643	5.595	3829	0.00000002367	0.02409	0.07262
fixed	NA	sibling_count3	-0.01324	0.01568	-0.8443	3150	0.3986	-0.05725	0.03078
fixed	NA	sibling_count4	-0.005395	0.01581	-0.3412	3004	0.7329	-0.04977	0.03898
fixed	NA	sibling_count5	0.008151	0.01666	0.4892	2775	0.6247	-0.03862	0.05492
fixed	NA	sibling_count>5	0.01342	0.01461	0.9192	2856	0.3581	-0.02757	0.05442
ran_pars	mother_pidlink	sd__(Intercept)	0.08703	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)	0.5211	0.1714	3.041	3847	0.002376	0.04004	1.002
fixed	NA	birth_order	-0.0006892	0.002377	-0.2899	3595	0.7719	-0.007362	0.005984
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04334	0.01843	-2.352	3847	0.01873	-0.09507	0.008387
fixed	NA	poly(age, 3, raw = TRUE)2	0.001318	0.0006322	2.084	3847	0.03719	-0.0004569	0.003093
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001374	0.000006942	-1.979	3847	0.04784	-0.00003323	0.000005745
fixed	NA	male	0.04837	0.008644	5.596	3828	0.00000002354	0.0241	0.07264
fixed	NA	sibling_count3	-0.01288	0.01573	-0.8184	3146	0.4132	-0.05704	0.03129
fixed	NA	sibling_count4	-0.004677	0.016	-0.2923	2994	0.7701	-0.0496	0.04025
fixed	NA	sibling_count5	0.00933	0.01715	0.544	2782	0.5865	-0.03882	0.05748
fixed	NA	sibling_count>5	0.01586	0.01685	0.9413	2895	0.3466	-0.03144	0.06315
ran_pars	mother_pidlink	sd__(Intercept)	0.0871	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2509	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)	0.5174	0.1715	3.017	3843	0.002572	0.03597	0.9988
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04304	0.01843	-2.335	3843	0.01959	-0.09478	0.008697
fixed	NA	poly(age, 3, raw = TRUE)2	0.001309	0.0006324	2.069	3843	0.0386	-0.0004667	0.003084
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000137	0.000006945	-1.973	3843	0.04859	-0.0000332	0.000005794
fixed	NA	male	0.04827	0.008643	5.585	3823	0.000000025	0.02401	0.07254
fixed	NA	sibling_count3	-0.008033	0.01601	-0.5018	3218	0.6158	-0.05297	0.03691
fixed	NA	sibling_count4	0.004259	0.01648	0.2584	3129	0.7961	-0.042	0.05052
fixed	NA	sibling_count5	0.01848	0.01791	1.032	2998	0.3021	-0.03178	0.06874
fixed	NA	sibling_count>5	0.02776	0.01734	1.602	3038	0.1094	-0.0209	0.07643
fixed	NA	birth_order_nonlinear2	0.001952	0.0116	0.1683	3403	0.8663	-0.03061	0.03451
fixed	NA	birth_order_nonlinear3	-0.02108	0.01354	-1.558	3505	0.1194	-0.05908	0.01691
fixed	NA	birth_order_nonlinear4	-0.0265	0.01601	-1.655	3578	0.09792	-0.07142	0.01843
fixed	NA	birth_order_nonlinear5	-0.002944	0.0195	-0.151	3594	0.88	-0.05768	0.05179
fixed	NA	birth_order_nonlinear>5	-0.01788	0.01808	-0.989	3809	0.3227	-0.06864	0.03287
ran_pars	mother_pidlink	sd__(Intercept)	0.08779	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2506	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)	0.5206	0.1719	3.028	3833	0.002478	0.03799	1.003
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04292	0.01848	-2.323	3833	0.02023	-0.09478	0.008943
fixed	NA	poly(age, 3, raw = TRUE)2	0.00131	0.0006341	2.066	3833	0.03888	-0.0004698	0.00309
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001377	0.000006966	-1.977	3833	0.04816	-0.00003332	0.000005785
fixed	NA	male	0.04851	0.008658	5.603	3814	0.00000002261	0.0242	0.07281
fixed	NA	count_birth_order2/2	-0.0166	0.02448	-0.6779	3541	0.4979	-0.08531	0.05212
fixed	NA	count_birth_order1/3	-0.02012	0.02077	-0.9688	3824	0.3327	-0.07841	0.03818
fixed	NA	count_birth_order2/3	-0.003152	0.0226	-0.1394	3831	0.8891	-0.0666	0.06029
fixed	NA	count_birth_order3/3	-0.03641	0.02486	-1.465	3833	0.1431	-0.1062	0.03337
fixed	NA	count_birth_order1/4	-0.02499	0.02258	-1.107	3828	0.2685	-0.08839	0.0384
fixed	NA	count_birth_order2/4	0.008599	0.02357	0.3648	3833	0.7153	-0.05757	0.07477
fixed	NA	count_birth_order3/4	-0.01663	0.02578	-0.6451	3831	0.5189	-0.08901	0.05574
fixed	NA	count_birth_order4/4	-0.006556	0.02753	-0.2381	3829	0.8118	-0.08384	0.07072
fixed	NA	count_birth_order1/5	0.01083	0.02708	0.3998	3833	0.6893	-0.0652	0.08685
fixed	NA	count_birth_order2/5	0.01599	0.02815	0.5683	3832	0.5699	-0.06301	0.095
fixed	NA	count_birth_order3/5	0.01195	0.02866	0.417	3828	0.6767	-0.06849	0.09239
fixed	NA	count_birth_order4/5	-0.01794	0.02915	-0.6154	3823	0.5383	-0.09975	0.06388
fixed	NA	count_birth_order5/5	-0.01009	0.02936	-0.3437	3822	0.7311	-0.09251	0.07232
fixed	NA	count_birth_order1/>5	0.04959	0.02449	2.025	3831	0.04292	-0.01915	0.1183
fixed	NA	count_birth_order2/>5	0.01055	0.0259	0.4072	3830	0.6838	-0.06216	0.08326
fixed	NA	count_birth_order3/>5	-0.01746	0.02495	-0.6998	3829	0.4841	-0.0875	0.05258
fixed	NA	count_birth_order4/>5	-0.01776	0.02434	-0.7295	3826	0.4657	-0.08608	0.05057
fixed	NA	count_birth_order5/>5	0.03147	0.02575	1.222	3817	0.2217	-0.04081	0.1038
fixed	NA	count_birth_order>5/>5	0.00355	0.01941	0.1829	3667	0.8549	-0.05092	0.05802
ran_pars	mother_pidlink	sd__(Intercept)	0.08629	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_preg_factor, …

Df	AIC	BIC	logLik	deviance	Chisq	Chi Df	Pr(>Chisq)
11	711.8	780.7	-344.9	689.8	NA	NA	NA
12	713.7	788.8	-344.9	689.7	0.08395	1	0.772
16	716.2	816.4	-342.1	684.2	5.493	4	0.2404
26	726.6	889.3	-337.3	674.6	9.669	10	0.47

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)	0.5159	0.1741	2.964	3754	0.003058	0.02728	1.004
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04311	0.01872	-2.303	3754	0.02134	-0.09566	0.009439
fixed	NA	poly(age, 3, raw = TRUE)2	0.001318	0.0006429	2.05	3754	0.04042	-0.0004865	0.003123
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001381	0.000007066	-1.955	3754	0.05066	-0.00003365	0.00000602
fixed	NA	male	0.04962	0.008764	5.662	3736	0.00000001612	0.02502	0.07422
fixed	NA	sibling_count3	-0.007423	0.01403	-0.5289	3020	0.5969	-0.04682	0.03197
fixed	NA	sibling_count4	0.003436	0.01471	0.2335	2796	0.8154	-0.03786	0.04473
fixed	NA	sibling_count5	-0.02066	0.01679	-1.23	2393	0.2187	-0.06779	0.02647
fixed	NA	sibling_count>5	0.02131	0.01435	1.485	2381	0.1376	-0.01896	0.06159
ran_pars	mother_pidlink	sd__(Intercept)	0.08655	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2514	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)	0.5148	0.1741	2.956	3753	0.003131	0.02602	1.003
fixed	NA	birth_order	-0.0009926	0.002778	-0.3573	3637	0.7209	-0.008791	0.006805
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04287	0.01874	-2.288	3753	0.02219	-0.09546	0.009723
fixed	NA	poly(age, 3, raw = TRUE)2	0.001312	0.0006432	2.04	3753	0.04146	-0.0004936	0.003117
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001379	0.000007067	-1.951	3753	0.05111	-0.00003363	0.000006048
fixed	NA	male	0.04963	0.008765	5.662	3735	0.00000001612	0.02502	0.07423
fixed	NA	sibling_count3	-0.006901	0.01411	-0.4891	3018	0.6248	-0.04651	0.03271
fixed	NA	sibling_count4	0.004525	0.01502	0.3012	2801	0.7633	-0.03765	0.0467
fixed	NA	sibling_count5	-0.01889	0.01751	-1.079	2434	0.2806	-0.06803	0.03025
fixed	NA	sibling_count>5	0.02488	0.01747	1.424	2596	0.1547	-0.02418	0.07393
ran_pars	mother_pidlink	sd__(Intercept)	0.08661	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2514	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)	0.5132	0.1743	2.944	3749	0.003264	0.02381	1.003
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04284	0.01875	-2.285	3749	0.02236	-0.09546	0.009784
fixed	NA	poly(age, 3, raw = TRUE)2	0.001315	0.0006437	2.044	3749	0.04106	-0.0004914	0.003122
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001392	0.000007074	-1.968	3749	0.04918	-0.00003378	0.000005938
fixed	NA	male	0.04953	0.00877	5.648	3731	0.00000001749	0.02491	0.07414
fixed	NA	sibling_count3	-0.004327	0.01441	-0.3003	3115	0.764	-0.04478	0.03612
fixed	NA	sibling_count4	0.009017	0.01557	0.5791	2982	0.5626	-0.03469	0.05272
fixed	NA	sibling_count5	-0.01119	0.01828	-0.6119	2684	0.5407	-0.06251	0.04013
fixed	NA	sibling_count>5	0.0347	0.01797	1.931	2747	0.0536	-0.01574	0.08513
fixed	NA	birth_order_nonlinear2	-0.001036	0.01143	-0.09066	3280	0.9278	-0.03312	0.03104
fixed	NA	birth_order_nonlinear3	-0.01195	0.01352	-0.8841	3375	0.3767	-0.0499	0.02599
fixed	NA	birth_order_nonlinear4	-0.01326	0.01694	-0.7827	3451	0.4339	-0.06081	0.03429
fixed	NA	birth_order_nonlinear5	-0.02167	0.02087	-1.038	3436	0.2992	-0.08026	0.03692
fixed	NA	birth_order_nonlinear>5	-0.01784	0.02069	-0.8624	3743	0.3885	-0.07592	0.04023
ran_pars	mother_pidlink	sd__(Intercept)	0.08642	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2516	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)	0.5353	0.1748	3.062	3739	0.002214	0.04459	1.026
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04495	0.0188	-2.391	3739	0.01685	-0.09773	0.007822
fixed	NA	poly(age, 3, raw = TRUE)2	0.001394	0.0006457	2.158	3739	0.03097	-0.0004189	0.003206
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001485	0.000007099	-2.092	3739	0.03653	-0.00003478	0.000005077
fixed	NA	male	0.04938	0.00878	5.625	3720	0.00000001994	0.02474	0.07403
fixed	NA	count_birth_order2/2	-0.0126	0.02165	-0.5819	3342	0.5607	-0.07338	0.04818
fixed	NA	count_birth_order1/3	-0.0158	0.01851	-0.8535	3730	0.3934	-0.06774	0.03615
fixed	NA	count_birth_order2/3	0.0005413	0.02059	0.02629	3739	0.979	-0.05725	0.05833
fixed	NA	count_birth_order3/3	-0.01806	0.02204	-0.8195	3738	0.4125	-0.07993	0.04381
fixed	NA	count_birth_order1/4	-0.01388	0.02171	-0.6392	3736	0.5227	-0.0748	0.04705
fixed	NA	count_birth_order2/4	0.01046	0.02269	0.461	3739	0.6448	-0.05323	0.07414
fixed	NA	count_birth_order3/4	0.00654	0.02379	0.275	3736	0.7834	-0.06023	0.07331
fixed	NA	count_birth_order4/4	-0.001575	0.02566	-0.06138	3734	0.9511	-0.07359	0.07044
fixed	NA	count_birth_order1/5	-0.02303	0.0284	-0.811	3739	0.4174	-0.1027	0.05668
fixed	NA	count_birth_order2/5	0.007691	0.03189	0.2412	3726	0.8094	-0.08181	0.0972
fixed	NA	count_birth_order3/5	-0.03383	0.03054	-1.108	3727	0.2681	-0.1196	0.0519
fixed	NA	count_birth_order4/5	-0.04271	0.02946	-1.45	3728	0.1471	-0.1254	0.03997
fixed	NA	count_birth_order5/5	-0.02514	0.03101	-0.8108	3725	0.4176	-0.1122	0.0619
fixed	NA	count_birth_order1/>5	0.08574	0.02768	3.098	3739	0.001963	0.008051	0.1634
fixed	NA	count_birth_order2/>5	-0.0053	0.02803	-0.189	3732	0.8501	-0.08399	0.07339
fixed	NA	count_birth_order3/>5	0.003049	0.02684	0.1136	3730	0.9096	-0.07229	0.07839
fixed	NA	count_birth_order4/>5	0.02215	0.02671	0.8294	3719	0.407	-0.05282	0.09713
fixed	NA	count_birth_order5/>5	0.00261	0.02527	0.1033	3724	0.9178	-0.06833	0.07355
fixed	NA	count_birth_order>5/>5	0.01287	0.01968	0.6538	3521	0.5133	-0.04237	0.06811
ran_pars	mother_pidlink	sd__(Intercept)	0.08667	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2514	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)
11	705.5	774	-341.7	683.5	NA	NA	NA
12	707.4	782.2	-341.7	683.4	0.1277	1	0.7209
16	713.6	813.3	-340.8	681.6	1.778	4	0.7765
26	721	883.1	-334.5	669	12.58	10	0.2478

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)	-0.1944	0.05324	-3.651	10007	0.0002623	-0.3438	-0.04494
fixed	NA	poly(age, 3, raw = TRUE)1	0.01928	0.004779	4.034	9983	0.00005525	0.005864	0.03269
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0004177	0.0001344	-3.108	9909	0.001891	-0.000795	-0.00004042
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002971	0.000001196	2.484	9809	0.013	-0.000000386	0.000006329
fixed	NA	male	-0.02151	0.004853	-4.432	9733	0.000009455	-0.03513	-0.007885
fixed	NA	sibling_count3	0.008502	0.01049	0.8108	7091	0.4175	-0.02093	0.03794
fixed	NA	sibling_count4	0.01057	0.0106	0.9964	6790	0.3191	-0.0192	0.04033
fixed	NA	sibling_count5	0.01661	0.01108	1.498	6417	0.1341	-0.01451	0.04772
fixed	NA	sibling_count>5	-0.009424	0.008552	-1.102	7030	0.2705	-0.03343	0.01458
ran_pars	mother_pidlink	sd__(Intercept)	0.1135	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2183	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)	-0.1943	0.05324	-3.649	10004	0.0002645	-0.3437	-0.04483
fixed	NA	birth_order	-0.0002719	0.001006	-0.2703	9789	0.787	-0.003096	0.002553
fixed	NA	poly(age, 3, raw = TRUE)1	0.01936	0.004788	4.043	9976	0.00005323	0.005916	0.03279
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0004207	0.0001349	-3.119	9878	0.001818	-0.0007992	-0.00004211
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002999	0.0000012	2.498	9760	0.0125	-0.0000003708	0.000006368
fixed	NA	male	-0.02151	0.004854	-4.431	9732	0.000009492	-0.03513	-0.007881
fixed	NA	sibling_count3	0.008566	0.01049	0.8168	7098	0.4141	-0.02087	0.03801
fixed	NA	sibling_count4	0.01072	0.01062	1.009	6834	0.3128	-0.01909	0.04053
fixed	NA	sibling_count5	0.01689	0.01113	1.517	6506	0.1293	-0.01436	0.04813
fixed	NA	sibling_count>5	-0.008494	0.00922	-0.9212	7868	0.357	-0.03437	0.01739
ran_pars	mother_pidlink	sd__(Intercept)	0.1135	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2183	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)	-0.1934	0.0533	-3.628	10005	0.0002868	-0.343	-0.04377
fixed	NA	poly(age, 3, raw = TRUE)1	0.01971	0.004791	4.115	9976	0.00003905	0.006266	0.03316
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0004282	0.0001349	-3.175	9880	0.001505	-0.0008069	-0.00004958
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003015	0.000001201	2.511	9759	0.01205	-0.0000003553	0.000006385
fixed	NA	male	-0.02147	0.004854	-4.424	9730	0.000009815	-0.03509	-0.007846
fixed	NA	sibling_count3	0.01191	0.01062	1.121	7339	0.2621	-0.0179	0.04173
fixed	NA	sibling_count4	0.01411	0.01086	1.299	7266	0.194	-0.01638	0.04461
fixed	NA	sibling_count5	0.02163	0.01146	1.888	7047	0.05907	-0.01053	0.0538
fixed	NA	sibling_count>5	-0.002547	0.009608	-0.2651	8468	0.7909	-0.02952	0.02442
fixed	NA	birth_order_nonlinear2	-0.01229	0.007011	-1.753	9053	0.07964	-0.03197	0.00739
fixed	NA	birth_order_nonlinear3	-0.01874	0.008133	-2.304	8783	0.02124	-0.04157	0.004091
fixed	NA	birth_order_nonlinear4	-0.00766	0.009138	-0.8382	8836	0.4019	-0.03331	0.01799
fixed	NA	birth_order_nonlinear5	-0.01681	0.01028	-1.634	8828	0.1022	-0.04567	0.01206
fixed	NA	birth_order_nonlinear>5	-0.0144	0.008664	-1.662	10000	0.09648	-0.03872	0.009918
ran_pars	mother_pidlink	sd__(Intercept)	0.1133	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2184	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)	-0.1926	0.05348	-3.602	10001	0.000317	-0.3428	-0.04253
fixed	NA	poly(age, 3, raw = TRUE)1	0.0199	0.004794	4.151	9966	0.00003341	0.006442	0.03336
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0004295	0.000135	-3.182	9868	0.001467	-0.0008084	-0.00005062
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002987	0.000001201	2.486	9744	0.01292	-0.0000003851	0.000006359
fixed	NA	male	-0.02117	0.004856	-4.36	9719	0.00001315	-0.0348	-0.00754
fixed	NA	count_birth_order2/2	-0.0235	0.01393	-1.687	9168	0.09155	-0.06259	0.01559
fixed	NA	count_birth_order1/3	0.02031	0.01377	1.475	9837	0.1403	-0.01834	0.05896
fixed	NA	count_birth_order2/3	-0.01708	0.01523	-1.121	9957	0.2623	-0.05984	0.02568
fixed	NA	count_birth_order3/3	-0.01838	0.0167	-1.101	10031	0.2711	-0.06527	0.0285
fixed	NA	count_birth_order1/4	0.009319	0.01506	0.6189	9952	0.536	-0.03294	0.05158
fixed	NA	count_birth_order2/4	0.01105	0.01613	0.685	10007	0.4934	-0.03422	0.05631
fixed	NA	count_birth_order3/4	-0.0106	0.01717	-0.6175	10050	0.5369	-0.0588	0.0376
fixed	NA	count_birth_order4/4	-0.01459	0.01822	-0.8008	10065	0.4233	-0.06575	0.03656
fixed	NA	count_birth_order1/5	0.01084	0.01706	0.6352	10034	0.5253	-0.03706	0.05873
fixed	NA	count_birth_order2/5	-0.002587	0.01808	-0.1431	10054	0.8862	-0.05333	0.04816
fixed	NA	count_birth_order3/5	0.01388	0.01901	0.7301	10069	0.4653	-0.03949	0.06725
fixed	NA	count_birth_order4/5	0.006791	0.01995	0.3404	10060	0.7335	-0.0492	0.06278
fixed	NA	count_birth_order5/5	0.006184	0.01996	0.3098	10070	0.7567	-0.04985	0.06222
fixed	NA	count_birth_order1/>5	-0.01924	0.01312	-1.466	10065	0.1427	-0.05608	0.0176
fixed	NA	count_birth_order2/>5	-0.01011	0.01365	-0.7407	10071	0.4589	-0.04843	0.02821
fixed	NA	count_birth_order3/>5	-0.027	0.01345	-2.008	10071	0.0447	-0.06475	0.01075
fixed	NA	count_birth_order4/>5	-0.007687	0.01322	-0.5815	10068	0.5609	-0.04479	0.02942
fixed	NA	count_birth_order5/>5	-0.02553	0.01336	-1.911	10071	0.05601	-0.06302	0.01197
fixed	NA	count_birth_order>5/>5	-0.02128	0.01098	-1.938	9079	0.0526	-0.0521	0.009537
ran_pars	mother_pidlink	sd__(Intercept)	0.1134	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2183	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)
11	72.34	151.8	-25.17	50.34	NA	NA	NA
12	74.27	160.9	-25.13	50.27	0.0738	1	0.7859
16	75.28	190.8	-21.64	43.28	6.987	4	0.1366
26	84.51	272.2	-16.26	32.51	10.77	10	0.3758

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)	-0.867	0.1698	-5.107	3812	0.0000003439	-1.344	-0.3904
fixed	NA	poly(age, 3, raw = TRUE)1	0.09225	0.01822	5.062	3805	0.0000004346	0.0411	0.1434
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002883	0.000625	-4.613	3799	0.000004102	-0.004638	-0.001129
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003017	0.000006861	4.397	3796	0.00001128	0.00001091	0.00004943
fixed	NA	male	-0.02578	0.008528	-3.023	3756	0.002518	-0.04972	-0.001844
fixed	NA	sibling_count3	0.007785	0.01443	0.5395	3139	0.5896	-0.03272	0.0483
fixed	NA	sibling_count4	0.004312	0.01497	0.2881	2988	0.7733	-0.0377	0.04632
fixed	NA	sibling_count5	0.003921	0.01672	0.2346	2759	0.8146	-0.043	0.05084
fixed	NA	sibling_count>5	-0.0358	0.01452	-2.465	2751	0.01375	-0.07655	0.004962
ran_pars	mother_pidlink	sd__(Intercept)	0.1191	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2355	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)	-0.871	0.1698	-5.13	3812	0.0000003048	-1.348	-0.3944
fixed	NA	birth_order	-0.003387	0.002677	-1.265	3806	0.2059	-0.0109	0.004127
fixed	NA	poly(age, 3, raw = TRUE)1	0.09312	0.01824	5.106	3807	0.0000003445	0.04193	0.1443
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002906	0.0006253	-4.648	3801	0.000003473	-0.004661	-0.001151
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003026	0.000006861	4.411	3796	0.0000106	0.000011	0.00004952
fixed	NA	male	-0.02566	0.008528	-3.009	3755	0.002635	-0.0496	-0.001726
fixed	NA	sibling_count3	0.009541	0.01449	0.6583	3140	0.5104	-0.03114	0.05023
fixed	NA	sibling_count4	0.008137	0.01526	0.5331	2993	0.594	-0.03471	0.05098
fixed	NA	sibling_count5	0.0102	0.01743	0.5852	2808	0.5585	-0.03873	0.05913
fixed	NA	sibling_count>5	-0.02346	0.01749	-1.341	2930	0.1799	-0.07255	0.02563
ran_pars	mother_pidlink	sd__(Intercept)	0.1187	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2356	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)	-0.8585	0.17	-5.05	3808	0.0000004629	-1.336	-0.3813
fixed	NA	poly(age, 3, raw = TRUE)1	0.09185	0.01824	5.034	3801	0.0000005013	0.04064	0.1431
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002859	0.0006256	-4.571	3795	0.000005014	-0.004615	-0.001103
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002975	0.000006867	4.332	3790	0.00001513	0.00001047	0.00004902
fixed	NA	male	-0.02605	0.00853	-3.054	3750	0.002274	-0.04999	-0.002106
fixed	NA	sibling_count3	0.01138	0.01476	0.7712	3220	0.4407	-0.03005	0.05282
fixed	NA	sibling_count4	0.007978	0.01577	0.506	3141	0.6129	-0.03628	0.05224
fixed	NA	sibling_count5	0.01	0.01819	0.5499	3023	0.5824	-0.04106	0.06107
fixed	NA	sibling_count>5	-0.02489	0.01792	-1.389	3040	0.165	-0.07519	0.02541
fixed	NA	birth_order_nonlinear2	-0.01938	0.01113	-1.741	3347	0.08182	-0.05064	0.01187
fixed	NA	birth_order_nonlinear3	-0.01584	0.01312	-1.207	3408	0.2273	-0.05265	0.02098
fixed	NA	birth_order_nonlinear4	-0.004245	0.016	-0.2654	3457	0.7908	-0.04915	0.04066
fixed	NA	birth_order_nonlinear5	-0.02336	0.01968	-1.187	3456	0.2353	-0.07859	0.03188
fixed	NA	birth_order_nonlinear>5	-0.02327	0.01977	-1.177	3805	0.2392	-0.07878	0.03223
ran_pars	mother_pidlink	sd__(Intercept)	0.1191	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2355	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)	-0.837	0.1707	-4.905	3798	0.0000009749	-1.316	-0.358
fixed	NA	poly(age, 3, raw = TRUE)1	0.08981	0.01832	4.903	3792	0.0000009818	0.03839	0.1412
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00279	0.0006283	-4.441	3787	0.000009204	-0.004554	-0.001027
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002901	0.000006898	4.205	3783	0.00002671	0.000009644	0.00004837
fixed	NA	male	-0.02647	0.008544	-3.098	3740	0.001965	-0.05045	-0.002483
fixed	NA	count_birth_order2/2	-0.02663	0.02168	-1.228	3480	0.2194	-0.0875	0.03423
fixed	NA	count_birth_order1/3	0.0166	0.01863	0.8912	3784	0.3729	-0.03569	0.06889
fixed	NA	count_birth_order2/3	-0.01654	0.02066	-0.8007	3804	0.4234	-0.07452	0.04144
fixed	NA	count_birth_order3/3	-0.01347	0.02232	-0.6033	3807	0.5463	-0.07611	0.04918
fixed	NA	count_birth_order1/4	-0.01372	0.02137	-0.6419	3801	0.521	-0.07371	0.04627
fixed	NA	count_birth_order2/4	0.01028	0.02244	0.4582	3807	0.6468	-0.05271	0.07328
fixed	NA	count_birth_order3/4	0.003243	0.02351	0.1379	3802	0.8903	-0.06275	0.06924
fixed	NA	count_birth_order4/4	-0.01605	0.02493	-0.644	3798	0.5196	-0.08604	0.05393
fixed	NA	count_birth_order1/5	0.01175	0.02799	0.4196	3807	0.6748	-0.06683	0.09032
fixed	NA	count_birth_order2/5	-0.03345	0.03039	-1.101	3781	0.2711	-0.1188	0.05186
fixed	NA	count_birth_order3/5	-0.03181	0.02849	-1.116	3789	0.2643	-0.1118	0.04816
fixed	NA	count_birth_order4/5	0.02514	0.02771	0.9072	3788	0.3644	-0.05264	0.1029
fixed	NA	count_birth_order5/5	-0.000456	0.02904	-0.0157	3782	0.9875	-0.08198	0.08107
fixed	NA	count_birth_order1/>5	-0.02476	0.0266	-0.9311	3799	0.3519	-0.09942	0.04989
fixed	NA	count_birth_order2/>5	-0.04955	0.0268	-1.849	3778	0.0646	-0.1248	0.02569
fixed	NA	count_birth_order3/>5	-0.03274	0.0262	-1.25	3773	0.2114	-0.1063	0.0408
fixed	NA	count_birth_order4/>5	-0.03021	0.02543	-1.188	3764	0.2349	-0.1016	0.04118
fixed	NA	count_birth_order5/>5	-0.06004	0.02453	-2.447	3774	0.01444	-0.1289	0.00883
fixed	NA	count_birth_order>5/>5	-0.05057	0.01932	-2.617	3698	0.008898	-0.1048	0.003665
ran_pars	mother_pidlink	sd__(Intercept)	0.1189	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2356	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)
11	613.9	682.6	-295.9	591.9	NA	NA	NA
12	614.3	689.3	-295.1	590.3	1.606	1	0.205
16	619.3	719.3	-293.7	587.3	2.942	4	0.5676
26	630.8	793.3	-289.4	578.8	8.559	10	0.5744

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)	-0.8577	0.1687	-5.085	3839	0.0000003845	-1.331	-0.3842
fixed	NA	poly(age, 3, raw = TRUE)1	0.09078	0.01812	5.01	3832	0.0000005698	0.03992	0.1417
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002845	0.0006216	-4.577	3827	0.000004868	-0.00459	-0.0011
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002981	0.000006826	4.367	3824	0.0000129	0.00001065	0.00004897
fixed	NA	male	-0.02579	0.008479	-3.041	3783	0.002372	-0.04959	-0.001986
fixed	NA	sibling_count3	0.01011	0.01575	0.6416	3214	0.5212	-0.03411	0.05433
fixed	NA	sibling_count4	0.02064	0.01592	1.297	3111	0.1948	-0.02404	0.06533
fixed	NA	sibling_count5	0.01602	0.01683	0.9516	2952	0.3414	-0.03123	0.06326
fixed	NA	sibling_count>5	-0.01717	0.01473	-1.166	3024	0.2439	-0.05853	0.02419
ran_pars	mother_pidlink	sd__(Intercept)	0.1183	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2351	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)	-0.8617	0.1686	-5.11	3838	0.0000003384	-1.335	-0.3883
fixed	NA	birth_order	-0.004012	0.00236	-1.7	3785	0.08927	-0.01064	0.002614
fixed	NA	poly(age, 3, raw = TRUE)1	0.09173	0.01813	5.061	3833	0.0000004377	0.04085	0.1426
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002869	0.0006217	-4.615	3828	0.000004057	-0.004614	-0.001124
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002989	0.000006824	4.379	3823	0.00001222	0.00001073	0.00004904
fixed	NA	male	-0.02568	0.008478	-3.029	3783	0.002473	-0.04947	-0.001879
fixed	NA	sibling_count3	0.01227	0.0158	0.7764	3213	0.4376	-0.03208	0.05661
fixed	NA	sibling_count4	0.0249	0.01611	1.546	3106	0.1223	-0.02031	0.0701
fixed	NA	sibling_count5	0.02296	0.01731	1.327	2966	0.1848	-0.02563	0.07156
fixed	NA	sibling_count>5	-0.002852	0.01697	-0.168	3094	0.8666	-0.05049	0.04478
ran_pars	mother_pidlink	sd__(Intercept)	0.1179	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2352	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)	-0.844	0.1687	-5.003	3834	0.0000005912	-1.318	-0.3704
fixed	NA	poly(age, 3, raw = TRUE)1	0.08976	0.01812	4.953	3828	0.0000007618	0.03889	0.1406
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0028	0.0006216	-4.503	3823	0.000006884	-0.004545	-0.001055
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002914	0.000006826	4.268	3819	0.00002016	0.000009976	0.0000483
fixed	NA	male	-0.02612	0.008475	-3.082	3777	0.002072	-0.04991	-0.002329
fixed	NA	sibling_count3	0.01501	0.01605	0.9355	3276	0.3496	-0.03003	0.06006
fixed	NA	sibling_count4	0.02489	0.01654	1.505	3218	0.1324	-0.02153	0.07132
fixed	NA	sibling_count5	0.02825	0.018	1.569	3141	0.1167	-0.02228	0.07878
fixed	NA	sibling_count>5	-0.003534	0.01741	-0.203	3203	0.8392	-0.05241	0.04534
fixed	NA	birth_order_nonlinear2	-0.0175	0.01125	-1.555	3407	0.1201	-0.04909	0.01409
fixed	NA	birth_order_nonlinear3	-0.02054	0.01315	-1.561	3475	0.1186	-0.05746	0.01639
fixed	NA	birth_order_nonlinear4	-0.001737	0.01557	-0.1115	3528	0.9112	-0.04545	0.04198
fixed	NA	birth_order_nonlinear5	-0.05317	0.01898	-2.802	3531	0.005109	-0.1064	0.00009916
fixed	NA	birth_order_nonlinear>5	-0.02094	0.01784	-1.174	3843	0.2404	-0.071	0.02912
ran_pars	mother_pidlink	sd__(Intercept)	0.1181	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.235	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)	-0.8285	0.1689	-4.904	3825	0.0000009789	-1.303	-0.3543
fixed	NA	poly(age, 3, raw = TRUE)1	0.0882	0.01815	4.86	3819	0.000001221	0.03726	0.1391
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002742	0.0006227	-4.404	3814	0.00001092	-0.00449	-0.0009944
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002847	0.000006839	4.163	3811	0.00003204	0.000009277	0.00004767
fixed	NA	male	-0.0269	0.008477	-3.173	3766	0.001521	-0.0507	-0.003103
fixed	NA	count_birth_order2/2	-0.0224	0.0238	-0.9412	3591	0.3466	-0.08919	0.0444
fixed	NA	count_birth_order1/3	0.02072	0.02048	1.012	3810	0.3118	-0.03678	0.07822
fixed	NA	count_birth_order2/3	-0.01094	0.02226	-0.4914	3829	0.6232	-0.07342	0.05155
fixed	NA	count_birth_order3/3	-0.01167	0.02445	-0.4772	3833	0.6333	-0.08029	0.05696
fixed	NA	count_birth_order1/4	0.01157	0.02226	0.5198	3822	0.6032	-0.05091	0.07405
fixed	NA	count_birth_order2/4	0.0485	0.0232	2.09	3832	0.03664	-0.01663	0.1136
fixed	NA	count_birth_order3/4	-0.008379	0.02533	-0.3308	3829	0.7408	-0.07948	0.06273
fixed	NA	count_birth_order4/4	-0.0125	0.02703	-0.4624	3824	0.6438	-0.08838	0.06338
fixed	NA	count_birth_order1/5	0.03036	0.02665	1.139	3833	0.2546	-0.04444	0.1052
fixed	NA	count_birth_order2/5	-0.02963	0.02765	-1.071	3829	0.2841	-0.1073	0.048
fixed	NA	count_birth_order3/5	-0.007984	0.02813	-0.2838	3821	0.7766	-0.08695	0.07098
fixed	NA	count_birth_order4/5	0.07203	0.02859	2.52	3810	0.01179	-0.008218	0.1523
fixed	NA	count_birth_order5/5	-0.01908	0.0288	-0.6625	3811	0.5077	-0.09991	0.06175
fixed	NA	count_birth_order1/>5	-0.007641	0.0241	-0.317	3833	0.7512	-0.0753	0.06001
fixed	NA	count_birth_order2/>5	-0.03434	0.02542	-1.351	3816	0.1769	-0.1057	0.03702
fixed	NA	count_birth_order3/>5	-0.002912	0.02449	-0.1189	3819	0.9054	-0.07165	0.06583
fixed	NA	count_birth_order4/>5	-0.01136	0.02388	-0.4756	3816	0.6344	-0.07839	0.05568
fixed	NA	count_birth_order5/>5	-0.0629	0.02524	-2.492	3797	0.01274	-0.1337	0.00795
fixed	NA	count_birth_order>5/>5	-0.02624	0.01925	-1.364	3727	0.1728	-0.08026	0.02778
ran_pars	mother_pidlink	sd__(Intercept)	0.1185	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2345	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)
11	598.1	666.9	-288	576.1	NA	NA	NA
12	597.2	672.3	-286.6	573.2	2.897	1	0.08874
16	597.7	697.8	-282.8	565.7	7.516	4	0.111
26	599.1	761.8	-273.5	547.1	18.6	10	0.04565

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)	-0.8904	0.1716	-5.188	3745	0.0000002242	-1.372	-0.4086
fixed	NA	poly(age, 3, raw = TRUE)1	0.09498	0.01845	5.148	3738	0.0000002773	0.04319	0.1468
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002992	0.0006334	-4.723	3733	0.000002406	-0.00477	-0.001214
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003151	0.000006961	4.527	3729	0.000006182	0.00001197	0.00005105
fixed	NA	male	-0.02612	0.008613	-3.032	3689	0.002444	-0.05029	-0.00194
fixed	NA	sibling_count3	0.005929	0.01414	0.4193	3084	0.675	-0.03376	0.04562
fixed	NA	sibling_count4	0.01116	0.01487	0.7506	2923	0.453	-0.03058	0.05291
fixed	NA	sibling_count5	0.009306	0.01708	0.5449	2630	0.5858	-0.03863	0.05724
fixed	NA	sibling_count>5	-0.03426	0.01459	-2.347	2633	0.01898	-0.07522	0.006707
ran_pars	mother_pidlink	sd__(Intercept)	0.1183	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.236	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)	-0.8946	0.1717	-5.211	3745	0.0000001976	-1.377	-0.4128
fixed	NA	birth_order	-0.003066	0.002754	-1.113	3744	0.2657	-0.0108	0.004665
fixed	NA	poly(age, 3, raw = TRUE)1	0.09584	0.01847	5.19	3740	0.0000002215	0.04401	0.1477
fixed	NA	poly(age, 3, raw = TRUE)2	-0.003015	0.0006337	-4.757	3734	0.000002036	-0.004794	-0.001236
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003162	0.000006962	4.543	3729	0.000005734	0.00001208	0.00005116
fixed	NA	male	-0.02608	0.008613	-3.028	3688	0.002477	-0.05026	-0.001905
fixed	NA	sibling_count3	0.007558	0.01421	0.5318	3083	0.5949	-0.03234	0.04745
fixed	NA	sibling_count4	0.01457	0.01518	0.9599	2933	0.3372	-0.02804	0.05718
fixed	NA	sibling_count5	0.01484	0.01778	0.8345	2674	0.4041	-0.03508	0.06475
fixed	NA	sibling_count>5	-0.02312	0.0177	-1.306	2857	0.1916	-0.07279	0.02656
ran_pars	mother_pidlink	sd__(Intercept)	0.118	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2361	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)	-0.8848	0.1719	-5.148	3740	0.0000002768	-1.367	-0.4024
fixed	NA	poly(age, 3, raw = TRUE)1	0.0948	0.01847	5.132	3734	0.000000302	0.04295	0.1467
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002977	0.0006341	-4.695	3728	0.00000276	-0.004757	-0.001197
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003121	0.000006968	4.48	3724	0.000007692	0.00001166	0.00005077
fixed	NA	male	-0.0264	0.008617	-3.063	3684	0.002205	-0.05059	-0.002208
fixed	NA	sibling_count3	0.009706	0.01449	0.6698	3166	0.503	-0.03097	0.05038
fixed	NA	sibling_count4	0.01476	0.01569	0.9406	3081	0.347	-0.02928	0.05879
fixed	NA	sibling_count5	0.01424	0.0185	0.7696	2879	0.4416	-0.03769	0.06617
fixed	NA	sibling_count>5	-0.02438	0.01816	-1.343	2974	0.1795	-0.07534	0.02659
fixed	NA	birth_order_nonlinear2	-0.01562	0.0111	-1.408	3266	0.1593	-0.04677	0.01553
fixed	NA	birth_order_nonlinear3	-0.01657	0.01315	-1.26	3333	0.2076	-0.05348	0.02034
fixed	NA	birth_order_nonlinear4	-0.002065	0.0165	-0.1252	3384	0.9004	-0.04838	0.04425
fixed	NA	birth_order_nonlinear5	-0.0181	0.02032	-0.891	3355	0.373	-0.07513	0.03893
fixed	NA	birth_order_nonlinear>5	-0.02136	0.0204	-1.047	3733	0.2952	-0.07863	0.03591
ran_pars	mother_pidlink	sd__(Intercept)	0.1181	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2362	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)	-0.8625	0.1725	-5	3731	0.0000005999	-1.347	-0.3783
fixed	NA	poly(age, 3, raw = TRUE)1	0.09284	0.01855	5.006	3726	0.0000005806	0.04079	0.1449
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002912	0.0006367	-4.574	3720	0.000004938	-0.0047	-0.001125
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003055	0.000006999	4.365	3716	0.00001303	0.00001091	0.0000502
fixed	NA	male	-0.02659	0.008634	-3.08	3673	0.002085	-0.05083	-0.002357
fixed	NA	count_birth_order2/2	-0.02698	0.02109	-1.28	3379	0.2008	-0.08617	0.03221
fixed	NA	count_birth_order1/3	0.01649	0.01833	0.8995	3717	0.3685	-0.03496	0.06793
fixed	NA	count_birth_order2/3	-0.01704	0.02034	-0.8376	3738	0.4023	-0.07415	0.04007
fixed	NA	count_birth_order3/3	-0.02125	0.02176	-0.9768	3738	0.3287	-0.08232	0.03982
fixed	NA	count_birth_order1/4	-0.01368	0.02147	-0.6371	3735	0.5241	-0.07393	0.04658
fixed	NA	count_birth_order2/4	0.0192	0.0224	0.857	3739	0.3915	-0.04368	0.08208
fixed	NA	count_birth_order3/4	0.004533	0.02346	0.1932	3733	0.8468	-0.06132	0.07038
fixed	NA	count_birth_order4/4	0.003269	0.02529	0.1293	3727	0.8972	-0.06772	0.07426
fixed	NA	count_birth_order1/5	0.00178	0.02805	0.06347	3739	0.9494	-0.07694	0.0805
fixed	NA	count_birth_order2/5	-0.01452	0.03139	-0.4625	3703	0.6437	-0.1026	0.07359
fixed	NA	count_birth_order3/5	-0.009643	0.03007	-0.3207	3709	0.7485	-0.09405	0.07477
fixed	NA	count_birth_order4/5	0.02184	0.02901	0.753	3715	0.4515	-0.05959	0.1033
fixed	NA	count_birth_order5/5	0.0006849	0.03053	0.02243	3709	0.9821	-0.08501	0.08638
fixed	NA	count_birth_order1/>5	-0.02163	0.0273	-0.7922	3729	0.4283	-0.09826	0.05501
fixed	NA	count_birth_order2/>5	-0.04792	0.0276	-1.736	3705	0.08268	-0.1254	0.02957
fixed	NA	count_birth_order3/>5	-0.03897	0.02643	-1.474	3707	0.1405	-0.1132	0.03522
fixed	NA	count_birth_order4/>5	-0.03379	0.02627	-1.286	3686	0.1985	-0.1075	0.03996
fixed	NA	count_birth_order5/>5	-0.05096	0.02487	-2.049	3703	0.04053	-0.1208	0.01885
fixed	NA	count_birth_order>5/>5	-0.0495	0.01961	-2.524	3619	0.01165	-0.1045	0.005553
ran_pars	mother_pidlink	sd__(Intercept)	0.1183	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2362	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)
11	608.1	676.7	-293	586.1	NA	NA	NA
12	608.8	683.6	-292.4	584.8	1.244	1	0.2646
16	614.6	714.3	-291.3	582.6	2.283	4	0.6838
26	627.7	789.7	-287.8	575.7	6.885	10	0.7363

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)	-0.02918	0.1054	-0.2769	9991	0.7819	-0.325	0.2667
fixed	NA	poly(age, 3, raw = TRUE)1	0.05562	0.00946	5.88	9962	0.000000004244	0.02907	0.08218
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001725	0.000266	-6.484	9882	0.00000000009364	-0.002471	-0.000978
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001406	0.000002366	5.941	9777	0.00000000293	0.000007416	0.0000207
fixed	NA	male	0.05526	0.00963	5.738	9792	0.000000009848	0.02823	0.08229
fixed	NA	sibling_count3	0.0003855	0.02066	0.01865	7198	0.9851	-0.05762	0.05839
fixed	NA	sibling_count4	-0.008148	0.02089	-0.39	6885	0.6965	-0.06679	0.05049
fixed	NA	sibling_count5	-0.02683	0.02182	-1.229	6500	0.2191	-0.08809	0.03444
fixed	NA	sibling_count>5	-0.0556	0.01685	-3.3	7129	0.000973	-0.1029	-0.008301
ran_pars	mother_pidlink	sd__(Intercept)	0.2157	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4361	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)	-0.02842	0.1054	-0.2697	9988	0.7874	-0.3243	0.2674
fixed	NA	birth_order	-0.002304	0.00199	-1.158	9712	0.247	-0.007891	0.003283
fixed	NA	poly(age, 3, raw = TRUE)1	0.05627	0.009476	5.938	9955	0.000000002977	0.02967	0.08287
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00175	0.0002668	-6.556	9850	0.00000000005792	-0.002499	-0.001
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001429	0.000002374	6.017	9728	0.000000001842	0.000007622	0.00002095
fixed	NA	male	0.05529	0.00963	5.741	9792	0.000000009677	0.02826	0.08232
fixed	NA	sibling_count3	0.0009427	0.02067	0.04561	7210	0.9636	-0.05707	0.05896
fixed	NA	sibling_count4	-0.006841	0.02092	-0.327	6933	0.7436	-0.06556	0.05188
fixed	NA	sibling_count5	-0.02445	0.02192	-1.116	6593	0.2646	-0.08598	0.03707
fixed	NA	sibling_count>5	-0.04769	0.01819	-2.622	7951	0.008757	-0.09873	0.003364
ran_pars	mother_pidlink	sd__(Intercept)	0.2156	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4362	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)	-0.02558	0.1055	-0.2424	9990	0.8085	-0.3218	0.2707
fixed	NA	poly(age, 3, raw = TRUE)1	0.0563	0.009484	5.937	9955	0.000000003009	0.02968	0.08292
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001739	0.000267	-6.513	9853	0.00000000007739	-0.002488	-0.0009893
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001409	0.000002375	5.932	9727	0.000000003098	0.000007423	0.00002076
fixed	NA	male	0.0553	0.009632	5.741	9789	0.000000009688	0.02826	0.08233
fixed	NA	sibling_count3	0.003277	0.02094	0.1565	7452	0.8756	-0.05551	0.06206
fixed	NA	sibling_count4	-0.003538	0.02142	-0.1652	7368	0.8688	-0.06366	0.05659
fixed	NA	sibling_count5	-0.02212	0.02258	-0.9795	7141	0.3274	-0.08552	0.04127
fixed	NA	sibling_count>5	-0.04829	0.01897	-2.546	8548	0.01092	-0.1015	0.004958
fixed	NA	birth_order_nonlinear2	-0.02808	0.01393	-2.016	9115	0.04385	-0.06718	0.01102
fixed	NA	birth_order_nonlinear3	-0.02067	0.01617	-1.278	8868	0.2011	-0.06605	0.02471
fixed	NA	birth_order_nonlinear4	-0.02172	0.01816	-1.196	8925	0.2318	-0.0727	0.02926
fixed	NA	birth_order_nonlinear5	-0.01489	0.02044	-0.7284	8924	0.4664	-0.07225	0.04248
fixed	NA	birth_order_nonlinear>5	-0.02235	0.01718	-1.301	10022	0.1932	-0.07058	0.02587
ran_pars	mother_pidlink	sd__(Intercept)	0.2154	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4363	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)	-0.02217	0.1059	-0.2094	9987	0.8342	-0.3195	0.2751
fixed	NA	poly(age, 3, raw = TRUE)1	0.05677	0.009494	5.98	9946	0.00000000231	0.03012	0.08342
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001744	0.0002672	-6.528	9842	0.00000000006976	-0.002494	-0.0009943
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001406	0.000002377	5.916	9714	0.000000003415	0.00000739	0.00002074
fixed	NA	male	0.05551	0.009637	5.76	9778	0.000000008674	0.02846	0.08256
fixed	NA	count_birth_order2/2	-0.05724	0.02767	-2.068	9195	0.03862	-0.1349	0.02044
fixed	NA	count_birth_order1/3	0.0003303	0.02726	0.01212	9871	0.9903	-0.07618	0.07684
fixed	NA	count_birth_order2/3	-0.03185	0.03017	-1.056	9973	0.2911	-0.1165	0.05283
fixed	NA	count_birth_order3/3	-0.04859	0.03309	-1.469	10036	0.142	-0.1415	0.04428
fixed	NA	count_birth_order1/4	-0.005195	0.02981	-0.1743	9970	0.8617	-0.08888	0.07849
fixed	NA	count_birth_order2/4	-0.03899	0.03194	-1.221	10016	0.2222	-0.1286	0.05067
fixed	NA	count_birth_order3/4	-0.0355	0.03402	-1.043	10052	0.2968	-0.131	0.05999
fixed	NA	count_birth_order4/4	-0.0587	0.03611	-1.626	10065	0.1041	-0.1601	0.04266
fixed	NA	count_birth_order1/5	-0.02741	0.0338	-0.8109	10040	0.4174	-0.1223	0.06747
fixed	NA	count_birth_order2/5	-0.06241	0.03582	-1.742	10057	0.08148	-0.163	0.03814
fixed	NA	count_birth_order3/5	-0.07078	0.03768	-1.879	10069	0.06033	-0.1765	0.03498
fixed	NA	count_birth_order4/5	-0.03619	0.03954	-0.9152	10062	0.3601	-0.1472	0.07481
fixed	NA	count_birth_order5/5	-0.0552	0.03957	-1.395	10070	0.163	-0.1663	0.05587
fixed	NA	count_birth_order1/>5	-0.08694	0.026	-3.343	10066	0.000831	-0.1599	-0.01394
fixed	NA	count_birth_order2/>5	-0.07812	0.02706	-2.887	10071	0.003892	-0.1541	-0.002175
fixed	NA	count_birth_order3/>5	-0.06474	0.02665	-2.429	10071	0.01516	-0.1396	0.01008
fixed	NA	count_birth_order4/>5	-0.07889	0.0262	-3.012	10069	0.002605	-0.1524	-0.00536
fixed	NA	count_birth_order5/>5	-0.07251	0.02647	-2.739	10071	0.006175	-0.1468	0.001803
fixed	NA	count_birth_order>5/>5	-0.08181	0.0217	-3.77	9130	0.0001646	-0.1427	-0.02089
ran_pars	mother_pidlink	sd__(Intercept)	0.2159	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4362	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)
11	13876	13956	-6927	13854	NA	NA	NA
12	13877	13964	-6927	13853	1.343	1	0.2466
16	13882	13997	-6925	13850	3.301	4	0.5088
26	13895	14083	-6922	13843	6.494	10	0.7722

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)	-2.026	0.3156	-6.419	3807	0.0000000001543	-2.912	-1.14
fixed	NA	poly(age, 3, raw = TRUE)1	0.2738	0.03387	8.083	3798	8.427e-16	0.1787	0.3689
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008982	0.001162	-7.732	3789	1.346e-14	-0.01224	-0.005721
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009119	0.00001275	7.151	3784	1.026e-12	0.0000554	0.000127
fixed	NA	male	0.03804	0.01584	2.401	3733	0.01642	-0.006441	0.08251
fixed	NA	sibling_count3	-0.03885	0.0269	-1.444	3023	0.1488	-0.1144	0.03666
fixed	NA	sibling_count4	-0.03699	0.02791	-1.325	2860	0.1852	-0.1153	0.04135
fixed	NA	sibling_count5	-0.07355	0.03119	-2.358	2618	0.01842	-0.1611	0.01399
fixed	NA	sibling_count>5	-0.1243	0.02709	-4.59	2611	0.000004649	-0.2004	-0.04829
ran_pars	mother_pidlink	sd__(Intercept)	0.2278	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4351	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)	-2.023	0.3157	-6.408	3807	0.0000000001656	-2.909	-1.137
fixed	NA	birth_order	0.002475	0.00498	0.4971	3809	0.6192	-0.0115	0.01645
fixed	NA	poly(age, 3, raw = TRUE)1	0.2732	0.0339	8.058	3800	1.032e-15	0.178	0.3683
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008966	0.001162	-7.714	3791	1.549e-14	-0.01223	-0.005703
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009112	0.00001275	7.145	3784	1.076e-12	0.00005532	0.0001269
fixed	NA	male	0.03797	0.01585	2.396	3731	0.01663	-0.006516	0.08245
fixed	NA	sibling_count3	-0.04015	0.02703	-1.485	3026	0.1376	-0.116	0.03573
fixed	NA	sibling_count4	-0.0398	0.02848	-1.398	2869	0.1624	-0.1197	0.04014
fixed	NA	sibling_count5	-0.07815	0.03254	-2.402	2675	0.01638	-0.1695	0.01318
fixed	NA	sibling_count>5	-0.1334	0.03264	-4.087	2813	0.00004497	-0.225	-0.04177
ran_pars	mother_pidlink	sd__(Intercept)	0.228	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4351	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)	-2.027	0.3161	-6.411	3803	0.0000000001622	-2.914	-1.139
fixed	NA	poly(age, 3, raw = TRUE)1	0.2741	0.03392	8.08	3794	8.631e-16	0.1789	0.3693
fixed	NA	poly(age, 3, raw = TRUE)2	-0.009001	0.001163	-7.739	3786	1.281e-14	-0.01227	-0.005736
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009161	0.00001277	7.176	3779	8.608e-13	0.00005577	0.0001274
fixed	NA	male	0.0381	0.01585	2.403	3728	0.0163	-0.006404	0.0826
fixed	NA	sibling_count3	-0.03972	0.02752	-1.443	3119	0.149	-0.117	0.03752
fixed	NA	sibling_count4	-0.03822	0.0294	-1.3	3034	0.1937	-0.1207	0.0443
fixed	NA	sibling_count5	-0.08413	0.03393	-2.48	2908	0.0132	-0.1794	0.0111
fixed	NA	sibling_count>5	-0.1433	0.03342	-4.287	2932	0.00001866	-0.2371	-0.04947
fixed	NA	birth_order_nonlinear2	-0.00469	0.02067	-0.2269	3256	0.8205	-0.06271	0.05333
fixed	NA	birth_order_nonlinear3	0.002097	0.02435	0.08612	3324	0.9314	-0.06625	0.07045
fixed	NA	birth_order_nonlinear4	-0.001416	0.0297	-0.04766	3380	0.962	-0.0848	0.08197
fixed	NA	birth_order_nonlinear5	0.04611	0.03654	1.262	3376	0.207	-0.05645	0.1487
fixed	NA	birth_order_nonlinear>5	0.0272	0.03676	0.7398	3797	0.4595	-0.076	0.1304
ran_pars	mother_pidlink	sd__(Intercept)	0.2275	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4354	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)	-2.078	0.3173	-6.548	3794	0.00000000006596	-2.969	-1.187
fixed	NA	poly(age, 3, raw = TRUE)1	0.2796	0.03406	8.211	3785	2.978e-16	0.184	0.3752
fixed	NA	poly(age, 3, raw = TRUE)2	-0.009203	0.001168	-7.879	3777	4.295e-15	-0.01248	-0.005924
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009392	0.00001282	7.324	3771	2.933e-13	0.00005792	0.0001299
fixed	NA	male	0.03892	0.01588	2.451	3717	0.01428	-0.005648	0.0835
fixed	NA	count_birth_order2/2	0.005079	0.04026	0.1262	3419	0.8996	-0.1079	0.1181
fixed	NA	count_birth_order1/3	-0.02901	0.03467	-0.8367	3776	0.4028	-0.1263	0.0683
fixed	NA	count_birth_order2/3	-0.04598	0.03843	-1.197	3803	0.2315	-0.1539	0.06188
fixed	NA	count_birth_order3/3	-0.0427	0.04151	-1.029	3807	0.3037	-0.1592	0.07382
fixed	NA	count_birth_order1/4	-0.01582	0.03976	-0.3978	3799	0.6908	-0.1274	0.09579
fixed	NA	count_birth_order2/4	-0.03676	0.04174	-0.8806	3807	0.3786	-0.1539	0.08042
fixed	NA	count_birth_order3/4	-0.02532	0.04372	-0.579	3801	0.5626	-0.1481	0.09742
fixed	NA	count_birth_order4/4	-0.08068	0.04636	-1.74	3796	0.08189	-0.2108	0.04945
fixed	NA	count_birth_order1/5	-0.07601	0.05206	-1.46	3806	0.1444	-0.2221	0.07013
fixed	NA	count_birth_order2/5	-0.1138	0.05651	-2.014	3772	0.04407	-0.2724	0.04481
fixed	NA	count_birth_order3/5	-0.03707	0.05297	-0.6999	3783	0.4841	-0.1857	0.1116
fixed	NA	count_birth_order4/5	-0.1023	0.05152	-1.986	3782	0.04706	-0.2469	0.04228
fixed	NA	count_birth_order5/5	-0.03525	0.054	-0.6528	3774	0.5139	-0.1868	0.1163
fixed	NA	count_birth_order1/>5	-0.1897	0.04946	-3.835	3795	0.0001275	-0.3285	-0.05085
fixed	NA	count_birth_order2/>5	-0.13	0.04983	-2.609	3768	0.009127	-0.2699	0.009887
fixed	NA	count_birth_order3/>5	-0.1686	0.0487	-3.462	3762	0.0005426	-0.3053	-0.03189
fixed	NA	count_birth_order4/>5	-0.08096	0.04728	-1.712	3751	0.08691	-0.2137	0.05175
fixed	NA	count_birth_order5/>5	-0.09381	0.04561	-2.057	3764	0.03978	-0.2218	0.03422
fixed	NA	count_birth_order>5/>5	-0.1121	0.03598	-3.115	3683	0.001852	-0.2131	-0.01109
ran_pars	mother_pidlink	sd__(Intercept)	0.2282	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4353	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)
11	5366	5435	-2672	5344	NA	NA	NA
12	5368	5443	-2672	5344	0.2466	1	0.6195
16	5374	5474	-2671	5342	2.082	4	0.7207
26	5386	5549	-2667	5334	8.045	10	0.6245

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)	-2.018	0.3145	-6.417	3833	0.000000000156	-2.901	-1.135
fixed	NA	poly(age, 3, raw = TRUE)1	0.272	0.03379	8.048	3824	1.113e-15	0.1771	0.3668
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008924	0.001159	-7.699	3815	1.737e-14	-0.01218	-0.00567
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009054	0.00001273	7.114	3810	1.339e-12	0.00005481	0.0001263
fixed	NA	male	0.03847	0.0158	2.434	3757	0.01497	-0.005892	0.08283
fixed	NA	sibling_count3	-0.01225	0.02948	-0.4156	3097	0.6777	-0.09501	0.0705
fixed	NA	sibling_count4	-0.02102	0.0298	-0.7053	2984	0.4807	-0.1047	0.06263
fixed	NA	sibling_count5	-0.04856	0.03152	-1.541	2814	0.1235	-0.137	0.03992
fixed	NA	sibling_count>5	-0.09925	0.02759	-3.598	2894	0.0003267	-0.1767	-0.02181
ran_pars	mother_pidlink	sd__(Intercept)	0.2287	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4351	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)	-2.02	0.3146	-6.42	3833	0.0000000001529	-2.903	-1.137
fixed	NA	birth_order	-0.001348	0.004409	-0.3058	3789	0.7598	-0.01372	0.01103
fixed	NA	poly(age, 3, raw = TRUE)1	0.2723	0.03381	8.053	3825	1.07e-15	0.1774	0.3672
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008932	0.00116	-7.703	3817	1.681e-14	-0.01219	-0.005677
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009057	0.00001273	7.115	3810	1.328e-12	0.00005484	0.0001263
fixed	NA	male	0.0385	0.01581	2.436	3756	0.01491	-0.00587	0.08287
fixed	NA	sibling_count3	-0.01153	0.02958	-0.3896	3095	0.6968	-0.09456	0.07151
fixed	NA	sibling_count4	-0.01958	0.03017	-0.6491	2979	0.5163	-0.1043	0.0651
fixed	NA	sibling_count5	-0.04622	0.03244	-1.425	2831	0.1543	-0.1373	0.04483
fixed	NA	sibling_count>5	-0.09442	0.03179	-2.971	2978	0.002996	-0.1836	-0.0052
ran_pars	mother_pidlink	sd__(Intercept)	0.2286	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4352	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)	-2.011	0.315	-6.386	3829	0.0000000001908	-2.896	-1.127
fixed	NA	poly(age, 3, raw = TRUE)1	0.2716	0.03383	8.03	3820	1.288e-15	0.1767	0.3666
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008913	0.00116	-7.682	3812	1.985e-14	-0.01217	-0.005656
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009045	0.00001274	7.1	3806	1.486e-12	0.00005469	0.0001262
fixed	NA	male	0.03842	0.01581	2.43	3752	0.01514	-0.005961	0.08281
fixed	NA	sibling_count3	-0.01008	0.03005	-0.3354	3170	0.7373	-0.09443	0.07427
fixed	NA	sibling_count4	-0.01969	0.03098	-0.6358	3108	0.525	-0.1066	0.06725
fixed	NA	sibling_count5	-0.05592	0.03372	-1.658	3026	0.09734	-0.1506	0.03873
fixed	NA	sibling_count>5	-0.103	0.03261	-3.158	3100	0.001604	-0.1945	-0.01144
fixed	NA	birth_order_nonlinear2	-0.01341	0.02097	-0.6398	3314	0.5224	-0.07227	0.04544
fixed	NA	birth_order_nonlinear3	-0.01003	0.02451	-0.409	3391	0.6826	-0.07883	0.05878
fixed	NA	birth_order_nonlinear4	0.000195	0.02903	0.006718	3451	0.9946	-0.08129	0.08168
fixed	NA	birth_order_nonlinear5	0.04181	0.03537	1.182	3453	0.2373	-0.05749	0.1411
fixed	NA	birth_order_nonlinear>5	-0.009151	0.0333	-0.2748	3842	0.7835	-0.1026	0.08434
ran_pars	mother_pidlink	sd__(Intercept)	0.228	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4355	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)	-2.009	0.3158	-6.363	3820	0.000000000221	-2.896	-1.123
fixed	NA	poly(age, 3, raw = TRUE)1	0.2733	0.03392	8.058	3811	1.029e-15	0.1781	0.3685
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008987	0.001164	-7.723	3804	1.445e-14	-0.01225	-0.00572
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009141	0.00001278	7.153	3798	1.015e-12	0.00005554	0.0001273
fixed	NA	male	0.03913	0.01584	2.471	3740	0.01353	-0.005325	0.08358
fixed	NA	count_birth_order2/2	-0.05345	0.04441	-1.204	3543	0.2288	-0.1781	0.07121
fixed	NA	count_birth_order1/3	-0.01953	0.03832	-0.5096	3802	0.6104	-0.1271	0.08804
fixed	NA	count_birth_order2/3	-0.04084	0.04163	-0.981	3827	0.3266	-0.1577	0.07601
fixed	NA	count_birth_order3/3	-0.03316	0.04571	-0.7255	3833	0.4682	-0.1615	0.09515
fixed	NA	count_birth_order1/4	-0.04812	0.04163	-1.156	3819	0.2478	-0.165	0.06874
fixed	NA	count_birth_order2/4	-0.03541	0.04338	-0.8163	3832	0.4144	-0.1572	0.08636
fixed	NA	count_birth_order3/4	-0.01073	0.04735	-0.2265	3827	0.8208	-0.1436	0.1222
fixed	NA	count_birth_order4/4	-0.05686	0.05053	-1.125	3821	0.2605	-0.1987	0.08496
fixed	NA	count_birth_order1/5	-0.04768	0.04983	-0.9569	3833	0.3387	-0.1875	0.09218
fixed	NA	count_birth_order2/5	-0.08619	0.05169	-1.667	3827	0.09552	-0.2313	0.05891
fixed	NA	count_birth_order3/5	-0.05817	0.05257	-1.106	3816	0.2686	-0.2057	0.08941
fixed	NA	count_birth_order4/5	-0.129	0.05342	-2.416	3803	0.01575	-0.279	0.0209
fixed	NA	count_birth_order5/5	-0.009836	0.05381	-0.1828	3804	0.855	-0.1609	0.1412
fixed	NA	count_birth_order1/>5	-0.1407	0.04506	-3.123	3833	0.001805	-0.2672	-0.01423
fixed	NA	count_birth_order2/>5	-0.1041	0.04751	-2.191	3809	0.02852	-0.2375	0.02927
fixed	NA	count_birth_order3/>5	-0.1657	0.04577	-3.621	3813	0.0002976	-0.2942	-0.03724
fixed	NA	count_birth_order4/>5	-0.06336	0.04463	-1.42	3810	0.1558	-0.1886	0.06191
fixed	NA	count_birth_order5/>5	-0.08578	0.04716	-1.819	3786	0.06897	-0.2182	0.04658
fixed	NA	count_birth_order>5/>5	-0.1241	0.03602	-3.446	3709	0.000575	-0.2253	-0.02302
ran_pars	mother_pidlink	sd__(Intercept)	0.2294	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.435	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)
11	5409	5477	-2693	5387	NA	NA	NA
12	5410	5486	-2693	5386	0.09448	1	0.7586
16	5416	5516	-2692	5384	2.809	4	0.5902
26	5426	5589	-2687	5374	9.447	10	0.4903

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)	-1.997	0.3192	-6.256	3740	0.0000000004382	-2.893	-1.101
fixed	NA	poly(age, 3, raw = TRUE)1	0.2714	0.03431	7.912	3731	3.319e-15	0.1751	0.3677
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008929	0.001178	-7.582	3723	4.27e-14	-0.01223	-0.005623
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009099	0.00001294	7.031	3717	2.431e-12	0.00005466	0.0001273
fixed	NA	male	0.0349	0.01601	2.18	3667	0.02929	-0.01003	0.07984
fixed	NA	sibling_count3	-0.04555	0.02637	-1.727	2984	0.08422	-0.1196	0.02848
fixed	NA	sibling_count4	-0.04056	0.02775	-1.462	2813	0.144	-0.1185	0.03733
fixed	NA	sibling_count5	-0.0787	0.03189	-2.468	2508	0.01366	-0.1682	0.01082
fixed	NA	sibling_count>5	-0.1247	0.02725	-4.577	2512	0.000004941	-0.2012	-0.04824
ran_pars	mother_pidlink	sd__(Intercept)	0.227	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.436	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)	-1.994	0.3193	-6.245	3740	0.0000000004712	-2.89	-1.098
fixed	NA	birth_order	0.002076	0.005125	0.405	3747	0.6855	-0.01231	0.01646
fixed	NA	poly(age, 3, raw = TRUE)1	0.2708	0.03434	7.887	3733	4.043e-15	0.1744	0.3672
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008913	0.001178	-7.564	3725	4.911e-14	-0.01222	-0.005605
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009091	0.00001294	7.023	3718	2.568e-12	0.00005457	0.0001272
fixed	NA	male	0.03489	0.01601	2.18	3665	0.02936	-0.01005	0.07983
fixed	NA	sibling_count3	-0.04667	0.02652	-1.76	2985	0.07857	-0.1211	0.02778
fixed	NA	sibling_count4	-0.04288	0.02834	-1.513	2826	0.1303	-0.1224	0.03666
fixed	NA	sibling_count5	-0.08244	0.03322	-2.482	2558	0.01313	-0.1757	0.0108
fixed	NA	sibling_count>5	-0.1323	0.03304	-4.004	2758	0.00006399	-0.225	-0.03954
ran_pars	mother_pidlink	sd__(Intercept)	0.2272	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.436	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)	-1.999	0.3196	-6.253	3736	0.0000000004491	-2.896	-1.101
fixed	NA	poly(age, 3, raw = TRUE)1	0.2719	0.03435	7.916	3727	3.207e-15	0.1755	0.3684
fixed	NA	poly(age, 3, raw = TRUE)2	-0.008956	0.001179	-7.596	3719	3.842e-14	-0.01226	-0.005646
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000915	0.00001295	7.063	3712	1.939e-12	0.00005513	0.0001279
fixed	NA	male	0.03526	0.01602	2.201	3662	0.02777	-0.0097	0.08022
fixed	NA	sibling_count3	-0.04768	0.02702	-1.764	3078	0.0778	-0.1235	0.02818
fixed	NA	sibling_count4	-0.04006	0.02926	-1.369	2989	0.1712	-0.1222	0.04209
fixed	NA	sibling_count5	-0.08599	0.03453	-2.49	2776	0.01282	-0.1829	0.01093
fixed	NA	sibling_count>5	-0.1441	0.03388	-4.252	2884	0.00002183	-0.2392	-0.04896
fixed	NA	birth_order_nonlinear2	-0.008968	0.02059	-0.4354	3181	0.6633	-0.06678	0.04884
fixed	NA	birth_order_nonlinear3	0.006384	0.02441	0.2616	3255	0.7936	-0.06212	0.07489
fixed	NA	birth_order_nonlinear4	-0.01746	0.03063	-0.5702	3310	0.5686	-0.1034	0.06851
fixed	NA	birth_order_nonlinear5	0.03934	0.03771	1.043	3275	0.297	-0.06652	0.1452
fixed	NA	birth_order_nonlinear>5	0.03292	0.03794	0.8678	3723	0.3856	-0.07357	0.1394
ran_pars	mother_pidlink	sd__(Intercept)	0.2269	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4362	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)	-2.036	0.3208	-6.347	3727	0.0000000002462	-2.937	-1.136
fixed	NA	poly(age, 3, raw = TRUE)1	0.2765	0.03449	8.018	3719	1.432e-15	0.1797	0.3733
fixed	NA	poly(age, 3, raw = TRUE)2	-0.009123	0.001184	-7.705	3712	1.662e-14	-0.01245	-0.0058
fixed	NA	poly(age, 3, raw = TRUE)3	0.00009344	0.00001301	7.18	3706	8.36e-13	0.00005691	0.00013
fixed	NA	male	0.03622	0.01605	2.257	3650	0.02404	-0.008821	0.08127
fixed	NA	count_birth_order2/2	-0.01423	0.03915	-0.3636	3319	0.7162	-0.1241	0.09566
fixed	NA	count_birth_order1/3	-0.04654	0.03411	-1.364	3711	0.1726	-0.1423	0.04922
fixed	NA	count_birth_order2/3	-0.06353	0.03785	-1.678	3738	0.09334	-0.1698	0.04272
fixed	NA	count_birth_order3/3	-0.04164	0.04047	-1.029	3738	0.3036	-0.1552	0.07196
fixed	NA	count_birth_order1/4	-0.02181	0.03994	-0.546	3734	0.5851	-0.1339	0.09031
fixed	NA	count_birth_order2/4	-0.03984	0.04167	-0.9562	3739	0.339	-0.1568	0.07713
fixed	NA	count_birth_order3/4	-0.03702	0.04363	-0.8485	3731	0.3962	-0.1595	0.08545
fixed	NA	count_birth_order4/4	-0.1064	0.04703	-2.262	3723	0.02376	-0.2384	0.02564
fixed	NA	count_birth_order1/5	-0.08905	0.05217	-1.707	3739	0.08791	-0.2355	0.05739
fixed	NA	count_birth_order2/5	-0.1309	0.05835	-2.243	3692	0.02498	-0.2947	0.03293
fixed	NA	count_birth_order3/5	-0.04651	0.05591	-0.8318	3700	0.4056	-0.2035	0.1104
fixed	NA	count_birth_order4/5	-0.1053	0.05394	-1.953	3708	0.0509	-0.2568	0.04607
fixed	NA	count_birth_order5/5	-0.04859	0.05676	-0.856	3700	0.392	-0.2079	0.1107
fixed	NA	count_birth_order1/>5	-0.1966	0.05077	-3.873	3724	0.0001093	-0.3391	-0.05413
fixed	NA	count_birth_order2/>5	-0.1305	0.05132	-2.542	3694	0.01106	-0.2745	0.0136
fixed	NA	count_birth_order3/>5	-0.1642	0.04914	-3.341	3697	0.0008435	-0.3021	-0.02623
fixed	NA	count_birth_order4/>5	-0.1132	0.04884	-2.318	3671	0.02048	-0.2503	0.02386
fixed	NA	count_birth_order5/>5	-0.1064	0.04624	-2.302	3692	0.0214	-0.2362	0.02336
fixed	NA	count_birth_order>5/>5	-0.112	0.03652	-3.067	3606	0.002177	-0.2145	-0.009499
ran_pars	mother_pidlink	sd__(Intercept)	0.2272	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4363	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)
11	5279	5348	-2629	5257	NA	NA	NA
12	5281	5356	-2628	5257	0.1631	1	0.6863
16	5286	5386	-2627	5254	2.91	4	0.573
26	5299	5461	-2624	5247	6.613	10	0.7614

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)	-0.2665	0.095	-2.805	9917	0.005038	-0.5331	0.000174
fixed	NA	poly(age, 3, raw = TRUE)1	0.02362	0.008521	2.772	9866	0.005576	-0.0002959	0.04754
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001646	0.0002393	-0.6879	9765	0.4915	-0.0008364	0.0005071
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000002153	0.000002126	-0.1013	9648	0.9193	-0.000006183	0.000005753
fixed	NA	male	-0.002977	0.008766	-0.3396	9989	0.7342	-0.02758	0.02163
fixed	NA	sibling_count3	-0.02246	0.01828	-1.229	7683	0.2192	-0.07376	0.02885
fixed	NA	sibling_count4	-0.01987	0.01844	-1.077	7310	0.2813	-0.07162	0.03189
fixed	NA	sibling_count5	-0.01023	0.01921	-0.5326	6871	0.5944	-0.06417	0.0437
fixed	NA	sibling_count>5	0.01732	0.0149	1.162	7571	0.2452	-0.0245	0.05913
ran_pars	mother_pidlink	sd__(Intercept)	0.1531	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4098	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)	-0.2668	0.09499	-2.809	9915	0.004984	-0.5335	-0.0001598
fixed	NA	birth_order	0.002029	0.001784	1.137	9196	0.2556	-0.00298	0.007038
fixed	NA	poly(age, 3, raw = TRUE)1	0.02307	0.008535	2.703	9857	0.006891	-0.0008909	0.04703
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001441	0.00024	-0.6006	9731	0.5481	-0.0008177	0.0005295
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000004013	0.000002132	-0.1882	9599	0.8507	-0.000006387	0.000005584
fixed	NA	male	-0.003007	0.008766	-0.3431	9989	0.7315	-0.02761	0.0216
fixed	NA	sibling_count3	-0.023	0.01828	-1.258	7695	0.2084	-0.07432	0.02832
fixed	NA	sibling_count4	-0.0211	0.01847	-1.143	7356	0.2532	-0.07295	0.03074
fixed	NA	sibling_count5	-0.01241	0.01931	-0.6426	6958	0.5205	-0.06661	0.04179
fixed	NA	sibling_count>5	0.01022	0.01615	0.6328	8281	0.5269	-0.03512	0.05556
ran_pars	mother_pidlink	sd__(Intercept)	0.1529	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4098	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)	-0.2752	0.09511	-2.893	9918	0.003821	-0.5422	-0.008203
fixed	NA	poly(age, 3, raw = TRUE)1	0.02319	0.008541	2.715	9858	0.006636	-0.0007847	0.04716
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001598	0.0002401	-0.6657	9735	0.5056	-0.0008336	0.0005141
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000001582	0.000002133	-0.07415	9600	0.9409	-0.000006145	0.000005829
fixed	NA	male	-0.003111	0.008765	-0.3549	9984	0.7227	-0.02771	0.02149
fixed	NA	sibling_count3	-0.02462	0.01855	-1.327	7932	0.1844	-0.07669	0.02745
fixed	NA	sibling_count4	-0.02199	0.01896	-1.16	7793	0.2461	-0.07521	0.03123
fixed	NA	sibling_count5	-0.01296	0.01996	-0.6493	7524	0.5162	-0.06899	0.04307
fixed	NA	sibling_count>5	0.01309	0.01691	0.7741	8865	0.4389	-0.03438	0.06055
fixed	NA	birth_order_nonlinear2	0.03823	0.01276	2.997	9348	0.002737	0.002419	0.07405
fixed	NA	birth_order_nonlinear3	0.01961	0.01483	1.322	9199	0.1861	-0.02202	0.06123
fixed	NA	birth_order_nonlinear4	0.0146	0.01665	0.877	9276	0.3805	-0.03214	0.06135
fixed	NA	birth_order_nonlinear5	0.01968	0.01874	1.05	9304	0.2936	-0.03291	0.07227
fixed	NA	birth_order_nonlinear>5	0.02218	0.01558	1.423	10079	0.1546	-0.02156	0.06591
ran_pars	mother_pidlink	sd__(Intercept)	0.1529	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4097	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)	-0.2834	0.09546	-2.969	9918	0.002995	-0.5514	-0.01546
fixed	NA	poly(age, 3, raw = TRUE)1	0.02291	0.008548	2.68	9849	0.007384	-0.00109	0.0469
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0001582	0.0002402	-0.6585	9723	0.5102	-0.0008324	0.0005161
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000000111	0.000002134	-0.052	9586	0.9585	-0.000006101	0.000005879
fixed	NA	male	-0.003372	0.008769	-0.3845	9975	0.7006	-0.02799	0.02124
fixed	NA	count_birth_order2/2	0.07421	0.02534	2.928	9275	0.003418	0.003069	0.1453
fixed	NA	count_birth_order1/3	-0.02418	0.02456	-0.9844	9991	0.3249	-0.09311	0.04476
fixed	NA	count_birth_order2/3	0.03323	0.02722	1.221	10030	0.2221	-0.04317	0.1096
fixed	NA	count_birth_order3/3	0.02459	0.02989	0.8229	10053	0.4106	-0.0593	0.1085
fixed	NA	count_birth_order1/4	0.01501	0.0269	0.5579	10031	0.5769	-0.0605	0.09051
fixed	NA	count_birth_order2/4	0.005201	0.02884	0.1804	10046	0.8569	-0.07575	0.08616
fixed	NA	count_birth_order3/4	-0.005191	0.03075	-0.1688	10061	0.8659	-0.0915	0.08111
fixed	NA	count_birth_order4/4	0.01914	0.03266	0.5862	10066	0.5578	-0.07253	0.1108
fixed	NA	count_birth_order1/5	0.009117	0.03054	0.2985	10059	0.7653	-0.07661	0.09484
fixed	NA	count_birth_order2/5	0.04643	0.03238	1.434	10065	0.1517	-0.04447	0.1373
fixed	NA	count_birth_order3/5	0.03461	0.03409	1.015	10069	0.31	-0.06108	0.1303
fixed	NA	count_birth_order4/5	-0.01429	0.03583	-0.3989	10068	0.69	-0.1149	0.08627
fixed	NA	count_birth_order5/5	0.0102	0.03582	0.2846	10071	0.7759	-0.09036	0.1107
fixed	NA	count_birth_order1/>5	0.03492	0.02352	1.485	10069	0.1377	-0.03111	0.1009
fixed	NA	count_birth_order2/>5	0.05428	0.02449	2.216	10071	0.02672	-0.01448	0.123
fixed	NA	count_birth_order3/>5	0.04115	0.02413	1.705	10071	0.0882	-0.02659	0.1089
fixed	NA	count_birth_order4/>5	0.04521	0.0237	1.907	10070	0.05649	-0.02132	0.1117
fixed	NA	count_birth_order5/>5	0.04958	0.02396	2.069	10071	0.03857	-0.01769	0.1168
fixed	NA	count_birth_order>5/>5	0.04898	0.01941	2.523	9318	0.01164	-0.005507	0.1035
ran_pars	mother_pidlink	sd__(Intercept)	0.153	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4097	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)
11	11871	11950	-5924	11849	NA	NA	NA
12	11871	11958	-5924	11847	1.295	1	0.2552
16	11872	11987	-5920	11840	7.919	4	0.0946
26	11883	12071	-5916	11831	8.217	10	0.6077

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)	0.9428	0.2612	3.609	3819	0.0003116	0.2094	1.676
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1058	0.02805	-3.773	3817	0.0001635	-0.1846	-0.02711
fixed	NA	poly(age, 3, raw = TRUE)2	0.004147	0.0009623	4.309	3815	0.00001678	0.001446	0.006848
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004614	0.00001056	-4.368	3814	0.00001288	-0.0000758	-0.00001649
fixed	NA	male	-0.02367	0.01315	-1.8	3785	0.0719	-0.06057	0.01324
fixed	NA	sibling_count3	0.01552	0.02194	0.7075	3125	0.4793	-0.04606	0.0771
fixed	NA	sibling_count4	-0.02907	0.02271	-1.28	2946	0.2007	-0.09282	0.03469
fixed	NA	sibling_count5	0.03856	0.02531	1.524	2677	0.1277	-0.03248	0.1096
fixed	NA	sibling_count>5	0.04773	0.02198	2.172	2660	0.02998	-0.01397	0.1094
ran_pars	mother_pidlink	sd__(Intercept)	0.1578	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3721	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)	0.9413	0.2613	3.602	3819	0.0003195	0.2078	1.675
fixed	NA	birth_order	-0.001447	0.004107	-0.3524	3766	0.7246	-0.01298	0.01008
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1055	0.02807	-3.759	3817	0.0001733	-0.1843	-0.02671
fixed	NA	poly(age, 3, raw = TRUE)2	0.004138	0.0009626	4.299	3815	0.00001761	0.001436	0.00684
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004611	0.00001057	-4.364	3813	0.00001308	-0.00007577	-0.00001645
fixed	NA	male	-0.02362	0.01315	-1.796	3783	0.07252	-0.06052	0.01329
fixed	NA	sibling_count3	0.01627	0.02204	0.7382	3124	0.4605	-0.04561	0.07815
fixed	NA	sibling_count4	-0.02744	0.02318	-1.184	2948	0.2365	-0.09251	0.03762
fixed	NA	sibling_count5	0.0412	0.02642	1.559	2723	0.119	-0.03296	0.1154
fixed	NA	sibling_count>5	0.05295	0.02654	1.995	2828	0.04609	-0.02154	0.1274
ran_pars	mother_pidlink	sd__(Intercept)	0.1582	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.372	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)	0.9329	0.2617	3.565	3815	0.0003682	0.1984	1.667
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1051	0.02809	-3.742	3812	0.0001852	-0.184	-0.02627
fixed	NA	poly(age, 3, raw = TRUE)2	0.004127	0.0009634	4.283	3810	0.00001887	0.001422	0.006831
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004607	0.00001058	-4.355	3808	0.00001363	-0.00007576	-0.00001638
fixed	NA	male	-0.02352	0.01315	-1.788	3779	0.07392	-0.06044	0.01341
fixed	NA	sibling_count3	0.0156	0.02247	0.6942	3214	0.4876	-0.04747	0.07867
fixed	NA	sibling_count4	-0.02767	0.02398	-1.154	3114	0.2487	-0.09499	0.03965
fixed	NA	sibling_count5	0.04284	0.02763	1.55	2963	0.1212	-0.03472	0.1204
fixed	NA	sibling_count>5	0.0613	0.02722	2.252	2955	0.02438	-0.0151	0.1377
fixed	NA	birth_order_nonlinear2	0.01025	0.01727	0.5934	3368	0.553	-0.03824	0.05874
fixed	NA	birth_order_nonlinear3	0.001374	0.02033	0.06759	3441	0.9461	-0.0557	0.05845
fixed	NA	birth_order_nonlinear4	-0.002639	0.02479	-0.1065	3498	0.9152	-0.07221	0.06693
fixed	NA	birth_order_nonlinear5	-0.008891	0.03048	-0.2917	3505	0.7706	-0.09446	0.07668
fixed	NA	birth_order_nonlinear>5	-0.02557	0.03043	-0.8404	3817	0.4007	-0.111	0.05985
ran_pars	mother_pidlink	sd__(Intercept)	0.1581	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3722	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)	0.9316	0.2628	3.545	3805	0.000397	0.194	1.669
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1065	0.02821	-3.774	3803	0.0001631	-0.1856	-0.02728
fixed	NA	poly(age, 3, raw = TRUE)2	0.004174	0.0009678	4.313	3801	0.00001652	0.001457	0.006891
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004658	0.00001063	-4.383	3800	0.000012	-0.00007642	-0.00001675
fixed	NA	male	-0.02415	0.01318	-1.832	3769	0.067	-0.06115	0.01285
fixed	NA	count_birth_order2/2	0.05231	0.0336	1.557	3475	0.1196	-0.04201	0.1466
fixed	NA	count_birth_order1/3	0.03981	0.02861	1.392	3792	0.1641	-0.04049	0.1201
fixed	NA	count_birth_order2/3	0.03881	0.03176	1.222	3805	0.2218	-0.05034	0.128
fixed	NA	count_birth_order3/3	0.01045	0.03434	0.3044	3807	0.7609	-0.08594	0.1068
fixed	NA	count_birth_order1/4	-0.008259	0.03285	-0.2514	3802	0.8015	-0.1005	0.08395
fixed	NA	count_birth_order2/4	-0.02985	0.03453	-0.8646	3807	0.3873	-0.1268	0.06706
fixed	NA	count_birth_order3/4	-0.01272	0.0362	-0.3513	3804	0.7254	-0.1143	0.08889
fixed	NA	count_birth_order4/4	0.008705	0.03839	0.2267	3801	0.8206	-0.09907	0.1165
fixed	NA	count_birth_order1/5	0.05321	0.04307	1.235	3807	0.2168	-0.06769	0.1741
fixed	NA	count_birth_order2/5	0.07654	0.04684	1.634	3790	0.1023	-0.05495	0.208
fixed	NA	count_birth_order3/5	0.06749	0.04389	1.538	3795	0.1242	-0.05572	0.1907
fixed	NA	count_birth_order4/5	0.05473	0.04269	1.282	3794	0.1999	-0.06511	0.1746
fixed	NA	count_birth_order5/5	0.02978	0.04476	0.6652	3789	0.506	-0.09587	0.1554
fixed	NA	count_birth_order1/>5	0.07785	0.04095	1.901	3804	0.05738	-0.0371	0.1928
fixed	NA	count_birth_order2/>5	0.07465	0.04131	1.807	3792	0.07084	-0.04131	0.1906
fixed	NA	count_birth_order3/>5	0.09799	0.04038	2.426	3787	0.01529	-0.01537	0.2113
fixed	NA	count_birth_order4/>5	0.04506	0.03922	1.149	3779	0.2506	-0.06502	0.1551
fixed	NA	count_birth_order5/>5	0.07709	0.03782	2.038	3785	0.0416	-0.02908	0.1832
fixed	NA	count_birth_order>5/>5	0.04905	0.0296	1.657	3670	0.09751	-0.03402	0.1321
ran_pars	mother_pidlink	sd__(Intercept)	0.1579	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3725	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)
11	3908	3977	-1943	3886	NA	NA	NA
12	3910	3985	-1943	3886	0.122	1	0.7269
16	3917	4017	-1942	3885	1.352	4	0.8525
26	3931	4094	-1940	3879	5.638	10	0.8447

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)	0.917	0.2603	3.523	3846	0.0004316	0.1864	1.648
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1019	0.02798	-3.642	3843	0.0002737	-0.1804	-0.02337
fixed	NA	poly(age, 3, raw = TRUE)2	0.004027	0.0009598	4.196	3841	0.00002782	0.001333	0.006722
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004496	0.00001054	-4.266	3840	0.00002039	-0.00007455	-0.00001538
fixed	NA	male	-0.02421	0.01311	-1.847	3810	0.06483	-0.06101	0.01259
fixed	NA	sibling_count3	-0.006695	0.02405	-0.2784	3201	0.7807	-0.0742	0.06081
fixed	NA	sibling_count4	-0.03614	0.02428	-1.489	3079	0.1366	-0.1043	0.032
fixed	NA	sibling_count5	-0.008562	0.02563	-0.3341	2892	0.7383	-0.0805	0.06337
fixed	NA	sibling_count>5	0.0278	0.02245	1.238	2968	0.2157	-0.03522	0.09082
ran_pars	mother_pidlink	sd__(Intercept)	0.1587	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.372	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)	0.9174	0.2603	3.524	3845	0.0004304	0.1866	1.648
fixed	NA	birth_order	0.0004435	0.003628	0.1222	3719	0.9027	-0.009742	0.01063
fixed	NA	poly(age, 3, raw = TRUE)1	-0.102	0.02799	-3.644	3843	0.0002721	-0.1806	-0.02342
fixed	NA	poly(age, 3, raw = TRUE)2	0.00403	0.0009601	4.197	3841	0.00002769	0.001334	0.006725
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004497	0.00001054	-4.266	3839	0.0000204	-0.00007456	-0.00001538
fixed	NA	male	-0.02422	0.01311	-1.848	3809	0.06474	-0.06103	0.01258
fixed	NA	sibling_count3	-0.006931	0.02413	-0.2872	3197	0.7739	-0.07466	0.0608
fixed	NA	sibling_count4	-0.03661	0.02457	-1.49	3071	0.1364	-0.1056	0.03237
fixed	NA	sibling_count5	-0.009323	0.02638	-0.3534	2901	0.7238	-0.08337	0.06472
fixed	NA	sibling_count>5	0.02623	0.02589	1.013	3022	0.311	-0.04644	0.09889
ran_pars	mother_pidlink	sd__(Intercept)	0.1587	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3721	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)	0.9044	0.2607	3.47	3841	0.0005271	0.1727	1.636
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1011	0.02801	-3.608	3839	0.0003122	-0.1797	-0.02244
fixed	NA	poly(age, 3, raw = TRUE)2	0.003996	0.0009609	4.159	3836	0.00003269	0.001299	0.006694
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004462	0.00001055	-4.229	3835	0.00002404	-0.00007425	-0.000015
fixed	NA	male	-0.02403	0.01312	-1.832	3804	0.06702	-0.06085	0.01279
fixed	NA	sibling_count3	-0.01015	0.02454	-0.4134	3267	0.6793	-0.07903	0.05874
fixed	NA	sibling_count4	-0.03844	0.02528	-1.521	3196	0.1284	-0.1094	0.03252
fixed	NA	sibling_count5	-0.008874	0.02749	-0.3228	3097	0.7469	-0.08604	0.06829
fixed	NA	sibling_count>5	0.02904	0.02661	1.091	3148	0.2752	-0.04564	0.1037
fixed	NA	birth_order_nonlinear2	0.01753	0.01751	1.001	3422	0.3169	-0.03163	0.06668
fixed	NA	birth_order_nonlinear3	0.01558	0.02045	0.7616	3503	0.4464	-0.04184	0.07299
fixed	NA	birth_order_nonlinear4	-0.00005851	0.0242	-0.002418	3563	0.9981	-0.06799	0.06787
fixed	NA	birth_order_nonlinear5	-0.002062	0.02949	-0.06994	3572	0.9442	-0.08484	0.08071
fixed	NA	birth_order_nonlinear>5	0.002764	0.02752	0.1004	3836	0.92	-0.07449	0.08002
ran_pars	mother_pidlink	sd__(Intercept)	0.1585	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3722	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)	0.904	0.2612	3.46	3831	0.0005452	0.1707	1.637
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1033	0.02807	-3.68	3829	0.0002365	-0.1821	-0.0245
fixed	NA	poly(age, 3, raw = TRUE)2	0.004077	0.0009634	4.233	3828	0.00002364	0.001373	0.006782
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004555	0.00001058	-4.305	3827	0.00001715	-0.00007526	-0.00001585
fixed	NA	male	-0.02482	0.01313	-1.89	3795	0.05884	-0.06169	0.01205
fixed	NA	count_birth_order2/2	0.07947	0.03699	2.148	3581	0.03176	-0.02437	0.1833
fixed	NA	count_birth_order1/3	0.02032	0.0316	0.643	3818	0.5202	-0.06838	0.109
fixed	NA	count_birth_order2/3	0.04303	0.03437	1.252	3830	0.2107	-0.05345	0.1395
fixed	NA	count_birth_order3/3	-0.015	0.03778	-0.3971	3833	0.6913	-0.121	0.09104
fixed	NA	count_birth_order1/4	0.005795	0.03435	0.1687	3825	0.866	-0.09063	0.1022
fixed	NA	count_birth_order2/4	-0.0307	0.03584	-0.8566	3832	0.3917	-0.1313	0.0699
fixed	NA	count_birth_order3/4	-0.0108	0.03917	-0.2758	3830	0.7827	-0.1207	0.09914
fixed	NA	count_birth_order4/4	-0.006404	0.04181	-0.1532	3827	0.8783	-0.1238	0.111
fixed	NA	count_birth_order1/5	0.01609	0.04117	0.3908	3833	0.6959	-0.09947	0.1316
fixed	NA	count_birth_order2/5	0.01692	0.04276	0.3957	3831	0.6924	-0.1031	0.1369
fixed	NA	count_birth_order3/5	0.01622	0.04352	0.3728	3825	0.7093	-0.1059	0.1384
fixed	NA	count_birth_order4/5	0.01776	0.04424	0.4013	3818	0.6882	-0.1064	0.1419
fixed	NA	count_birth_order5/5	0.02105	0.04457	0.4723	3817	0.6367	-0.104	0.1461
fixed	NA	count_birth_order1/>5	0.03557	0.03723	0.9554	3832	0.3394	-0.06894	0.1401
fixed	NA	count_birth_order2/>5	0.04765	0.03933	1.211	3824	0.2258	-0.06276	0.1581
fixed	NA	count_birth_order3/>5	0.1171	0.03789	3.092	3824	0.002004	0.01079	0.2235
fixed	NA	count_birth_order4/>5	0.03739	0.03695	1.012	3821	0.3117	-0.06634	0.1411
fixed	NA	count_birth_order5/>5	0.03913	0.03908	1.001	3808	0.3167	-0.07056	0.1488
fixed	NA	count_birth_order>5/>5	0.05174	0.02961	1.747	3707	0.08067	-0.03138	0.1349
ran_pars	mother_pidlink	sd__(Intercept)	0.1582	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3723	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)
11	3939	4008	-1958	3917	NA	NA	NA
12	3941	4016	-1958	3917	0.01549	1	0.901
16	3947	4047	-1958	3915	1.543	4	0.8189
26	3955	4118	-1952	3903	11.8	10	0.2988

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)	0.9712	0.2646	3.67	3751	0.0002462	0.2283	1.714
fixed	NA	poly(age, 3, raw = TRUE)1	-0.11	0.02846	-3.864	3749	0.0001135	-0.1898	-0.03008
fixed	NA	poly(age, 3, raw = TRUE)2	0.004334	0.0009771	4.435	3746	0.000009468	0.001591	0.007076
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004871	0.00001074	-4.536	3745	0.000005926	-0.00007886	-0.00001856
fixed	NA	male	-0.02276	0.0133	-1.711	3715	0.08719	-0.0601	0.01458
fixed	NA	sibling_count3	0.02252	0.02157	1.044	3069	0.2966	-0.03803	0.08307
fixed	NA	sibling_count4	-0.02657	0.02265	-1.173	2884	0.2409	-0.09016	0.03702
fixed	NA	sibling_count5	0.03133	0.02594	1.208	2547	0.2273	-0.04149	0.1042
fixed	NA	sibling_count>5	0.04105	0.02217	1.852	2545	0.06416	-0.02117	0.1033
ran_pars	mother_pidlink	sd__(Intercept)	0.16	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3726	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)	0.9698	0.2647	3.663	3751	0.0002524	0.2267	1.713
fixed	NA	birth_order	-0.001067	0.004238	-0.2517	3715	0.8013	-0.01296	0.01083
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1097	0.02848	-3.851	3749	0.0001198	-0.1896	-0.02972
fixed	NA	poly(age, 3, raw = TRUE)2	0.004326	0.0009776	4.425	3747	0.000009919	0.001582	0.00707
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004867	0.00001074	-4.531	3745	0.000006041	-0.00007883	-0.00001852
fixed	NA	male	-0.02275	0.0133	-1.71	3713	0.0874	-0.06009	0.0146
fixed	NA	sibling_count3	0.02308	0.02169	1.064	3067	0.2874	-0.03781	0.08397
fixed	NA	sibling_count4	-0.02539	0.02314	-1.097	2891	0.2725	-0.09034	0.03955
fixed	NA	sibling_count5	0.03322	0.02704	1.229	2589	0.2193	-0.04268	0.1091
fixed	NA	sibling_count>5	0.0449	0.02695	1.666	2763	0.09583	-0.03075	0.1205
ran_pars	mother_pidlink	sd__(Intercept)	0.1602	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3725	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)	0.9616	0.2651	3.628	3747	0.0002899	0.2175	1.706
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1091	0.0285	-3.828	3744	0.0001314	-0.1891	-0.02909
fixed	NA	poly(age, 3, raw = TRUE)2	0.00431	0.0009784	4.405	3742	0.00001088	0.001563	0.007056
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004859	0.00001075	-4.519	3740	0.000006417	-0.00007877	-0.0000184
fixed	NA	male	-0.02281	0.01331	-1.713	3710	0.08675	-0.06018	0.01456
fixed	NA	sibling_count3	0.02313	0.02213	1.045	3157	0.296	-0.039	0.08526
fixed	NA	sibling_count4	-0.02585	0.02394	-1.08	3054	0.2803	-0.09306	0.04136
fixed	NA	sibling_count5	0.03196	0.02818	1.134	2816	0.2569	-0.04715	0.1111
fixed	NA	sibling_count>5	0.05248	0.02768	1.896	2897	0.05807	-0.02522	0.1302
fixed	NA	birth_order_nonlinear2	0.004606	0.01724	0.2672	3285	0.7893	-0.04378	0.05299
fixed	NA	birth_order_nonlinear3	-0.001029	0.02041	-0.0504	3362	0.9598	-0.05831	0.05626
fixed	NA	birth_order_nonlinear4	0.001722	0.02559	0.06727	3422	0.9464	-0.07012	0.07357
fixed	NA	birth_order_nonlinear5	0.003465	0.03152	0.1099	3399	0.9125	-0.08503	0.09196
fixed	NA	birth_order_nonlinear>5	-0.02943	0.03147	-0.9352	3747	0.3498	-0.1178	0.05891
ran_pars	mother_pidlink	sd__(Intercept)	0.1602	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3727	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)	0.9503	0.266	3.573	3737	0.000358	0.2036	1.697
fixed	NA	poly(age, 3, raw = TRUE)1	-0.1092	0.0286	-3.819	3735	0.0001361	-0.1895	-0.02895
fixed	NA	poly(age, 3, raw = TRUE)2	0.004316	0.0009823	4.394	3733	0.00001143	0.001559	0.007073
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00004867	0.0000108	-4.507	3732	0.000006766	-0.00007898	-0.00001836
fixed	NA	male	-0.0234	0.01334	-1.754	3699	0.07946	-0.06083	0.01404
fixed	NA	count_birth_order2/2	0.0426	0.03271	1.302	3378	0.193	-0.04923	0.1344
fixed	NA	count_birth_order1/3	0.04535	0.0282	1.608	3724	0.1078	-0.0338	0.1245
fixed	NA	count_birth_order2/3	0.04406	0.03134	1.406	3738	0.1598	-0.0439	0.132
fixed	NA	count_birth_order3/3	0.01164	0.03353	0.3472	3738	0.7285	-0.08249	0.1058
fixed	NA	count_birth_order1/4	-0.008358	0.03305	-0.2528	3736	0.8004	-0.1011	0.08443
fixed	NA	count_birth_order2/4	-0.04096	0.03452	-1.187	3739	0.2355	-0.1379	0.05594
fixed	NA	count_birth_order3/4	-0.01007	0.03618	-0.2784	3735	0.7807	-0.1116	0.09147
fixed	NA	count_birth_order4/4	0.02124	0.03901	0.5443	3731	0.5862	-0.08827	0.1307
fixed	NA	count_birth_order1/5	0.0574	0.04322	1.328	3739	0.1842	-0.06392	0.1787
fixed	NA	count_birth_order2/5	0.07243	0.04845	1.495	3715	0.1351	-0.06358	0.2084
fixed	NA	count_birth_order3/5	0.0487	0.04642	1.049	3719	0.2941	-0.08159	0.179
fixed	NA	count_birth_order4/5	0.03821	0.04477	0.8534	3722	0.3935	-0.08747	0.1639
fixed	NA	count_birth_order5/5	0.0122	0.04712	0.2589	3717	0.7957	-0.1201	0.1445
fixed	NA	count_birth_order1/>5	0.05652	0.0421	1.342	3735	0.1795	-0.06166	0.1747
fixed	NA	count_birth_order2/>5	0.05222	0.04261	1.225	3719	0.2205	-0.06739	0.1718
fixed	NA	count_birth_order3/>5	0.09224	0.04079	2.261	3719	0.02382	-0.02227	0.2067
fixed	NA	count_birth_order4/>5	0.03775	0.04057	0.9304	3703	0.3522	-0.07614	0.1516
fixed	NA	count_birth_order5/>5	0.0893	0.0384	2.326	3713	0.02009	-0.01849	0.1971
fixed	NA	count_birth_order>5/>5	0.0354	0.0301	1.176	3588	0.2396	-0.04908	0.1199
ran_pars	mother_pidlink	sd__(Intercept)	0.1598	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3729	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)
11	3861	3930	-1919	3839	NA	NA	NA
12	3863	3938	-1919	3839	0.06169	1	0.8038
16	3870	3969	-1919	3838	1.332	4	0.856
26	3882	4044	-1915	3830	8.08	10	0.6211

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)	1.174	0.06645	17.66	9941	8.86e-69	0.9873	1.36
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0784	0.005963	-13.15	9896	3.758e-39	-0.09513	-0.06166
fixed	NA	poly(age, 3, raw = TRUE)2	0.001808	0.0001676	10.79	9796	5.516e-27	0.001337	0.002278
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001311	0.00000149	-8.799	9672	1.618e-18	-0.00001729	-0.000008926
fixed	NA	male	-0.09204	0.006103	-15.08	9888	7.898e-51	-0.1092	-0.07491
fixed	NA	sibling_count3	0.01356	0.0129	1.051	7256	0.2933	-0.02266	0.04978
fixed	NA	sibling_count4	0.01864	0.01303	1.43	6899	0.1527	-0.01794	0.05521
fixed	NA	sibling_count5	0.02536	0.0136	1.865	6474	0.06216	-0.0128	0.06353
fixed	NA	sibling_count>5	0.04657	0.01052	4.427	7163	0.000009694	0.01704	0.07609
ran_pars	mother_pidlink	sd__(Intercept)	0.1222	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2808	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)	1.173	0.06645	17.66	9939	9.994e-69	0.9867	1.36
fixed	NA	birth_order	0.002099	0.001252	1.676	9439	0.09368	-0.001416	0.005614
fixed	NA	poly(age, 3, raw = TRUE)1	-0.07898	0.005973	-13.22	9888	1.392e-39	-0.09575	-0.06221
fixed	NA	poly(age, 3, raw = TRUE)2	0.00183	0.0001681	10.89	9761	1.907e-27	0.001358	0.002301
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001331	0.000001494	-8.905	9619	6.278e-19	-0.0000175	-0.000009113
fixed	NA	male	-0.09207	0.006102	-15.09	9887	7.137e-51	-0.1092	-0.07494
fixed	NA	sibling_count3	0.01303	0.01291	1.009	7267	0.3129	-0.0232	0.04925
fixed	NA	sibling_count4	0.0174	0.01305	1.333	6947	0.1825	-0.01923	0.05403
fixed	NA	sibling_count5	0.02316	0.01366	1.695	6567	0.09009	-0.01519	0.0615
fixed	NA	sibling_count>5	0.03929	0.01138	3.453	7970	0.0005576	0.007349	0.07123
ran_pars	mother_pidlink	sd__(Intercept)	0.1223	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2807	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)	1.178	0.06653	17.71	9941	3.766e-69	0.9917	1.365
fixed	NA	poly(age, 3, raw = TRUE)1	-0.07952	0.005977	-13.3	9889	4.805e-40	-0.09629	-0.06274
fixed	NA	poly(age, 3, raw = TRUE)2	0.001839	0.0001681	10.94	9763	1.056e-27	0.001367	0.002311
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001332	0.000001495	-8.914	9618	5.821e-19	-0.00001752	-0.000009128
fixed	NA	male	-0.09203	0.006102	-15.08	9885	7.813e-51	-0.1092	-0.0749
fixed	NA	sibling_count3	0.008595	0.01308	0.657	7520	0.5112	-0.02813	0.04532
fixed	NA	sibling_count4	0.01064	0.01338	0.7952	7404	0.4265	-0.02691	0.04818
fixed	NA	sibling_count5	0.01522	0.01409	1.08	7145	0.2802	-0.02434	0.05479
fixed	NA	sibling_count>5	0.0316	0.01189	2.658	8599	0.007882	-0.001775	0.06497
fixed	NA	birth_order_nonlinear2	0.01122	0.008852	1.268	9164	0.2048	-0.01362	0.03607
fixed	NA	birth_order_nonlinear3	0.02609	0.01028	2.537	8952	0.01118	-0.002772	0.05495
fixed	NA	birth_order_nonlinear4	0.02517	0.01155	2.179	9025	0.02934	-0.00725	0.05758
fixed	NA	birth_order_nonlinear5	0.02458	0.01299	1.892	9039	0.05854	-0.01189	0.06106
fixed	NA	birth_order_nonlinear>5	0.0255	0.01086	2.347	10058	0.01895	-0.004999	0.056
ran_pars	mother_pidlink	sd__(Intercept)	0.122	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2808	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)	1.183	0.06675	17.73	9940	3.009e-69	0.996	1.371
fixed	NA	poly(age, 3, raw = TRUE)1	-0.08008	0.005981	-13.39	9878	1.561e-40	-0.09687	-0.0633
fixed	NA	poly(age, 3, raw = TRUE)2	0.00185	0.0001682	11	9751	5.56e-28	0.001378	0.002322
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001336	0.000001495	-8.938	9603	4.688e-19	-0.00001756	-0.000009168
fixed	NA	male	-0.09221	0.006105	-15.1	9876	5.625e-51	-0.1093	-0.07507
fixed	NA	count_birth_order2/2	0.01891	0.01758	1.076	9167	0.2821	-0.03044	0.06826
fixed	NA	count_birth_order1/3	0.001989	0.01717	0.1158	9928	0.9078	-0.04621	0.05018
fixed	NA	count_birth_order2/3	0.01413	0.01902	0.7428	9999	0.4576	-0.03925	0.06751
fixed	NA	count_birth_order3/3	0.06725	0.02087	3.222	10042	0.001278	0.008659	0.1258
fixed	NA	count_birth_order1/4	0.01351	0.01879	0.7191	9999	0.4721	-0.03924	0.06627
fixed	NA	count_birth_order2/4	0.0194	0.02014	0.9631	10029	0.3355	-0.03715	0.07595
fixed	NA	count_birth_order3/4	0.02846	0.02147	1.326	10055	0.1849	-0.0318	0.08872
fixed	NA	count_birth_order4/4	0.06085	0.0228	2.67	10065	0.007608	-0.003134	0.1248
fixed	NA	count_birth_order1/5	0.0184	0.02132	0.8626	10049	0.3884	-0.04146	0.07826
fixed	NA	count_birth_order2/5	0.04596	0.02261	2.033	10061	0.04208	-0.0175	0.1094
fixed	NA	count_birth_order3/5	0.02026	0.02379	0.8517	10069	0.3944	-0.04652	0.08704
fixed	NA	count_birth_order4/5	0.0333	0.02499	1.333	10065	0.1826	-0.03683	0.1034
fixed	NA	count_birth_order5/5	0.059	0.02499	2.361	10071	0.01826	-0.01116	0.1291
fixed	NA	count_birth_order1/>5	0.04611	0.01642	2.809	10068	0.004985	0.0000257	0.09219
fixed	NA	count_birth_order2/>5	0.04523	0.01709	2.647	10071	0.008138	-0.002738	0.0932
fixed	NA	count_birth_order3/>5	0.0602	0.01683	3.576	10071	0.0003509	0.01294	0.1075
fixed	NA	count_birth_order4/>5	0.05521	0.01654	3.338	10070	0.0008472	0.008781	0.1016
fixed	NA	count_birth_order5/>5	0.05467	0.01672	3.27	10071	0.001081	0.007733	0.1016
fixed	NA	count_birth_order>5/>5	0.06034	0.01362	4.429	9159	0.000009559	0.0221	0.09857
ran_pars	mother_pidlink	sd__(Intercept)	0.1218	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2808	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)
11	4606	4686	-2292	4584	NA	NA	NA
12	4605	4692	-2291	4581	2.811	1	0.09361
16	4607	4722	-2287	4575	6.69	4	0.1532
26	4616	4804	-2282	4564	10.22	10	0.4212

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)	2.442	0.188	12.99	3820	8.801e-38	1.914	2.97
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2215	0.02019	-10.97	3818	1.353e-27	-0.2782	-0.1648
fixed	NA	poly(age, 3, raw = TRUE)2	0.006628	0.0006926	9.57	3816	1.861e-21	0.004684	0.008572
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00006461	0.000007603	-8.497	3815	2.749e-17	-0.00008595	-0.00004326
fixed	NA	male	-0.03876	0.009466	-4.095	3775	0.00004316	-0.06533	-0.01219
fixed	NA	sibling_count3	0.02684	0.01573	1.706	2806	0.08803	-0.01731	0.07099
fixed	NA	sibling_count4	0.05053	0.01628	3.105	2567	0.001926	0.004844	0.09622
fixed	NA	sibling_count5	0.05469	0.01812	3.018	2230	0.00257	0.00383	0.1055
fixed	NA	sibling_count>5	0.07393	0.01574	4.699	2206	0.000002782	0.02976	0.1181
ran_pars	mother_pidlink	sd__(Intercept)	0.1072	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2701	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)	2.445	0.188	13	3819	7.481e-38	1.917	2.972
fixed	NA	birth_order	0.003024	0.002952	1.024	3702	0.3058	-0.005263	0.01131
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2222	0.0202	-11	3818	1.01e-27	-0.2789	-0.1655
fixed	NA	poly(age, 3, raw = TRUE)2	0.006644	0.0006927	9.591	3816	1.524e-21	0.0047	0.008589
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00006465	0.000007603	-8.503	3814	2.61e-17	-0.000086	-0.00004331
fixed	NA	male	-0.03886	0.009466	-4.105	3774	0.00004124	-0.06543	-0.01229
fixed	NA	sibling_count3	0.02528	0.0158	1.6	2809	0.1098	-0.01908	0.06964
fixed	NA	sibling_count4	0.04716	0.01661	2.839	2573	0.004559	0.0005333	0.09378
fixed	NA	sibling_count5	0.04914	0.01892	2.598	2286	0.009449	-0.003963	0.1022
fixed	NA	sibling_count>5	0.06302	0.01901	3.315	2401	0.0009284	0.009665	0.1164
ran_pars	mother_pidlink	sd__(Intercept)	0.1075	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.27	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)	2.444	0.1882	12.99	3816	9.112e-38	1.916	2.972
fixed	NA	poly(age, 3, raw = TRUE)1	-0.222	0.0202	-10.99	3813	1.111e-27	-0.2787	-0.1653
fixed	NA	poly(age, 3, raw = TRUE)2	0.006638	0.000693	9.578	3811	1.727e-21	0.004692	0.008583
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00006456	0.000007608	-8.486	3810	3.025e-17	-0.00008592	-0.00004321
fixed	NA	male	-0.03863	0.009467	-4.08	3770	0.00004587	-0.0652	-0.01206
fixed	NA	sibling_count3	0.01909	0.0161	1.186	2927	0.2358	-0.02611	0.06429
fixed	NA	sibling_count4	0.03957	0.01718	2.303	2784	0.02133	-0.008652	0.0878
fixed	NA	sibling_count5	0.0444	0.01979	2.244	2577	0.0249	-0.01114	0.09994
fixed	NA	sibling_count>5	0.05921	0.01949	3.038	2555	0.002407	0.004499	0.1139
fixed	NA	birth_order_nonlinear2	0.01273	0.01246	1.022	3150	0.3071	-0.02224	0.04769
fixed	NA	birth_order_nonlinear3	0.03267	0.01466	2.229	3261	0.02589	-0.008476	0.07382
fixed	NA	birth_order_nonlinear4	0.02027	0.01786	1.135	3349	0.2566	-0.02988	0.07042
fixed	NA	birth_order_nonlinear5	0.004018	0.02197	0.1828	3364	0.8549	-0.05766	0.06569
fixed	NA	birth_order_nonlinear>5	0.02633	0.02188	1.203	3816	0.2289	-0.03509	0.08776
ran_pars	mother_pidlink	sd__(Intercept)	0.107	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2701	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)	2.448	0.1889	12.96	3806	1.237e-37	1.918	2.979
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2223	0.02028	-10.96	3804	1.461e-27	-0.2793	-0.1654
fixed	NA	poly(age, 3, raw = TRUE)2	0.006654	0.0006958	9.563	3802	1.98e-21	0.004701	0.008607
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00006481	0.00000764	-8.483	3801	3.098e-17	-0.00008626	-0.00004337
fixed	NA	male	-0.03842	0.00948	-4.053	3760	0.00005165	-0.06503	-0.01181
fixed	NA	count_birth_order2/2	0.003413	0.02421	0.141	3296	0.8879	-0.06454	0.07136
fixed	NA	count_birth_order1/3	0.0001465	0.02055	0.007127	3787	0.9943	-0.05754	0.05784
fixed	NA	count_birth_order2/3	0.03307	0.02282	1.449	3804	0.1474	-0.03099	0.09713
fixed	NA	count_birth_order3/3	0.07378	0.02468	2.99	3807	0.002811	0.004507	0.1431
fixed	NA	count_birth_order1/4	0.05301	0.0236	2.246	3800	0.02477	-0.01324	0.1193
fixed	NA	count_birth_order2/4	0.03648	0.02481	1.47	3807	0.1416	-0.03317	0.1061
fixed	NA	count_birth_order3/4	0.04578	0.02602	1.759	3802	0.07861	-0.02726	0.1188
fixed	NA	count_birth_order4/4	0.07534	0.0276	2.73	3799	0.006371	-0.002139	0.1528
fixed	NA	count_birth_order1/5	0.03696	0.03096	1.194	3807	0.2325	-0.04993	0.1239
fixed	NA	count_birth_order2/5	0.09427	0.03368	2.799	3785	0.005157	-0.0002813	0.1888
fixed	NA	count_birth_order3/5	0.05057	0.03156	1.602	3791	0.1092	-0.03802	0.1391
fixed	NA	count_birth_order4/5	0.0572	0.0307	1.863	3789	0.06249	-0.02897	0.1434
fixed	NA	count_birth_order5/5	0.04417	0.03219	1.372	3782	0.17	-0.04618	0.1345
fixed	NA	count_birth_order1/>5	0.06705	0.02944	2.278	3805	0.02279	-0.01558	0.1497
fixed	NA	count_birth_order2/>5	0.06292	0.0297	2.118	3789	0.03421	-0.02045	0.1463
fixed	NA	count_birth_order3/>5	0.101	0.02904	3.479	3781	0.0005098	0.0195	0.1825
fixed	NA	count_birth_order4/>5	0.06068	0.0282	2.152	3770	0.03149	-0.01848	0.1398
fixed	NA	count_birth_order5/>5	0.06101	0.0272	2.243	3777	0.02493	-0.01533	0.1374
fixed	NA	count_birth_order>5/>5	0.08233	0.02124	3.876	3573	0.0001079	0.02271	0.142
ran_pars	mother_pidlink	sd__(Intercept)	0.107	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2701	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)
11	1386	1455	-682.2	1364	NA	NA	NA
12	1387	1462	-681.6	1363	1.048	1	0.3059
16	1390	1490	-679.2	1358	4.901	4	0.2976
26	1401	1563	-674.3	1349	9.699	10	0.4672

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)	2.464	0.1878	13.13	3846	1.562e-38	1.937	2.991
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2235	0.02018	-11.07	3844	4.507e-28	-0.2801	-0.1668
fixed	NA	poly(age, 3, raw = TRUE)2	0.00669	0.0006925	9.661	3842	7.831e-22	0.004746	0.008633
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000652	0.000007604	-8.574	3841	1.426e-17	-0.00008654	-0.00004385
fixed	NA	male	-0.03937	0.009461	-4.161	3798	0.00003233	-0.06593	-0.01281
fixed	NA	sibling_count3	0.02618	0.01729	1.514	2889	0.13	-0.02235	0.07471
fixed	NA	sibling_count4	0.0433	0.01744	2.482	2722	0.01313	-0.005673	0.09226
fixed	NA	sibling_count5	0.03684	0.01841	2.001	2475	0.04545	-0.01483	0.0885
fixed	NA	sibling_count>5	0.06644	0.01613	4.12	2570	0.00003915	0.02117	0.1117
ran_pars	mother_pidlink	sd__(Intercept)	0.1083	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2705	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)	2.468	0.1877	13.14	3845	1.231e-38	1.941	2.994
fixed	NA	birth_order	0.004248	0.002612	1.626	3598	0.104	-0.003085	0.01158
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2243	0.02018	-11.11	3844	2.88e-28	-0.281	-0.1677
fixed	NA	poly(age, 3, raw = TRUE)2	0.00671	0.0006924	9.691	3842	5.88e-22	0.004766	0.008654
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00006523	0.000007602	-8.581	3840	1.35e-17	-0.00008657	-0.00004389
fixed	NA	male	-0.03948	0.009459	-4.174	3797	0.00003061	-0.06603	-0.01293
fixed	NA	sibling_count3	0.02393	0.01734	1.38	2888	0.1678	-0.02476	0.07261
fixed	NA	sibling_count4	0.03886	0.01766	2.201	2716	0.02784	-0.01071	0.08842
fixed	NA	sibling_count5	0.02956	0.01894	1.561	2491	0.1188	-0.02361	0.08273
fixed	NA	sibling_count>5	0.05138	0.0186	2.763	2636	0.005763	-0.000815	0.1036
ran_pars	mother_pidlink	sd__(Intercept)	0.1085	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2704	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)	2.458	0.1878	13.09	3842	2.526e-38	1.931	2.986
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2232	0.02018	-11.06	3839	5.342e-28	-0.2798	-0.1665
fixed	NA	poly(age, 3, raw = TRUE)2	0.006673	0.0006925	9.636	3837	9.933e-22	0.004729	0.008617
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00006486	0.000007605	-8.528	3836	2.115e-17	-0.00008621	-0.00004351
fixed	NA	male	-0.03913	0.009457	-4.137	3792	0.00003588	-0.06568	-0.01258
fixed	NA	sibling_count3	0.01657	0.01763	0.9395	2980	0.3476	-0.03293	0.06607
fixed	NA	sibling_count4	0.0298	0.01816	1.641	2879	0.101	-0.02118	0.08078
fixed	NA	sibling_count5	0.02269	0.01975	1.149	2739	0.2505	-0.03273	0.07812
fixed	NA	sibling_count>5	0.04598	0.01911	2.406	2800	0.01621	-0.007671	0.09963
fixed	NA	birth_order_nonlinear2	0.01053	0.01265	0.8323	3205	0.4053	-0.02497	0.04602
fixed	NA	birth_order_nonlinear3	0.03994	0.01477	2.705	3330	0.00687	-0.00151	0.08139
fixed	NA	birth_order_nonlinear4	0.02845	0.01747	1.629	3422	0.1035	-0.02059	0.07748
fixed	NA	birth_order_nonlinear5	0.009549	0.02128	0.4487	3438	0.6537	-0.0502	0.0693
fixed	NA	birth_order_nonlinear>5	0.03222	0.01982	1.625	3824	0.1042	-0.02343	0.08787
ran_pars	mother_pidlink	sd__(Intercept)	0.1088	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2702	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)	2.444	0.1881	12.99	3832	8.715e-38	1.916	2.972
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2221	0.02022	-10.99	3831	1.132e-27	-0.2789	-0.1654
fixed	NA	poly(age, 3, raw = TRUE)2	0.00664	0.0006938	9.571	3829	1.845e-21	0.004693	0.008588
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00006454	0.000007622	-8.468	3829	3.5e-17	-0.00008594	-0.00004315
fixed	NA	male	-0.03836	0.009465	-4.052	3785	0.0000517	-0.06492	-0.01179
fixed	NA	count_birth_order2/2	0.02215	0.02669	0.83	3435	0.4066	-0.05277	0.09708
fixed	NA	count_birth_order1/3	0.00529	0.02274	0.2326	3813	0.8161	-0.05855	0.06913
fixed	NA	count_birth_order2/3	0.02414	0.02474	0.9755	3829	0.3294	-0.04532	0.09359
fixed	NA	count_birth_order3/3	0.09777	0.0272	3.594	3833	0.0003298	0.02141	0.1741
fixed	NA	count_birth_order1/4	0.05529	0.02473	2.236	3822	0.0254	-0.01412	0.1247
fixed	NA	count_birth_order2/4	0.01373	0.0258	0.5321	3832	0.5947	-0.0587	0.08616
fixed	NA	count_birth_order3/4	0.06335	0.02821	2.246	3829	0.02477	-0.01583	0.1425
fixed	NA	count_birth_order4/4	0.08211	0.03012	2.727	3825	0.006428	-0.002422	0.1666
fixed	NA	count_birth_order1/5	0.001284	0.02964	0.04333	3833	0.9654	-0.08192	0.08449
fixed	NA	count_birth_order2/5	0.08761	0.03079	2.845	3830	0.004462	0.001176	0.1741
fixed	NA	count_birth_order3/5	0.05313	0.03135	1.695	3822	0.09017	-0.03486	0.1411
fixed	NA	count_birth_order4/5	0.05656	0.03187	1.775	3812	0.07603	-0.0329	0.146
fixed	NA	count_birth_order5/5	0.02284	0.03211	0.7115	3811	0.4768	-0.06728	0.113
fixed	NA	count_birth_order1/>5	0.07247	0.0268	2.704	3831	0.006889	-0.002771	0.1477
fixed	NA	count_birth_order2/>5	0.06204	0.02833	2.19	3822	0.02862	-0.0175	0.1416
fixed	NA	count_birth_order3/>5	0.07122	0.02729	2.61	3822	0.009099	-0.005387	0.1478
fixed	NA	count_birth_order4/>5	0.06325	0.02662	2.376	3817	0.01754	-0.01147	0.138
fixed	NA	count_birth_order5/>5	0.06806	0.02816	2.417	3800	0.01568	-0.01097	0.1471
fixed	NA	count_birth_order>5/>5	0.08184	0.02129	3.844	3621	0.0001233	0.02207	0.1416
ran_pars	mother_pidlink	sd__(Intercept)	0.1072	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2705	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)
11	1418	1487	-697.9	1396	NA	NA	NA
12	1417	1492	-696.5	1393	2.648	1	0.1037
16	1419	1519	-693.4	1387	6.263	4	0.1804
26	1422	1585	-685	1370	16.78	10	0.07945

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)	2.439	0.1895	12.87	3753	3.812e-37	1.907	2.971
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2205	0.02038	-10.82	3751	6.611e-27	-0.2777	-0.1633
fixed	NA	poly(age, 3, raw = TRUE)2	0.006576	0.0006996	9.4	3749	9.213e-21	0.004613	0.00854
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00006393	0.00000769	-8.314	3749	1.276e-16	-0.00008552	-0.00004235
fixed	NA	male	-0.03783	0.009531	-3.97	3710	0.00007337	-0.06459	-0.01108
fixed	NA	sibling_count3	0.02853	0.01537	1.857	2784	0.06348	-0.01461	0.07167
fixed	NA	sibling_count4	0.04803	0.01613	2.978	2538	0.002924	0.002765	0.0933
fixed	NA	sibling_count5	0.06003	0.01844	3.255	2121	0.001151	0.008265	0.1118
fixed	NA	sibling_count>5	0.07782	0.01576	4.938	2115	0.0000008509	0.03358	0.122
ran_pars	mother_pidlink	sd__(Intercept)	0.1061	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2697	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)	2.442	0.1895	12.89	3752	3.213e-37	1.91	2.974
fixed	NA	birth_order	0.002716	0.003029	0.8965	3658	0.37	-0.005788	0.01122
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2212	0.02039	-10.85	3751	5.051e-27	-0.2784	-0.164
fixed	NA	poly(age, 3, raw = TRUE)2	0.006594	0.0006999	9.421	3749	7.577e-21	0.004629	0.008559
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00006401	0.00000769	-8.323	3748	1.187e-16	-0.00008559	-0.00004242
fixed	NA	male	-0.03786	0.009531	-3.972	3709	0.00007249	-0.06461	-0.01111
fixed	NA	sibling_count3	0.0271	0.01545	1.754	2785	0.07958	-0.01628	0.07048
fixed	NA	sibling_count4	0.04504	0.01647	2.735	2549	0.006286	-0.00119	0.09127
fixed	NA	sibling_count5	0.05519	0.01922	2.871	2171	0.00413	0.001232	0.1092
fixed	NA	sibling_count>5	0.06803	0.01917	3.548	2363	0.0003953	0.01421	0.1219
ran_pars	mother_pidlink	sd__(Intercept)	0.1063	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2697	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)	2.443	0.1897	12.88	3748	3.528e-37	1.911	2.975
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2215	0.02039	-10.86	3747	4.502e-27	-0.2787	-0.1642
fixed	NA	poly(age, 3, raw = TRUE)2	0.006599	0.0007002	9.425	3745	7.293e-21	0.004634	0.008565
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00006404	0.000007695	-8.322	3744	1.202e-16	-0.00008564	-0.00004244
fixed	NA	male	-0.03763	0.009533	-3.948	3706	0.00008039	-0.06439	-0.01087
fixed	NA	sibling_count3	0.02229	0.01576	1.415	2903	0.1573	-0.02194	0.06653
fixed	NA	sibling_count4	0.03807	0.01704	2.234	2756	0.02555	-0.009763	0.0859
fixed	NA	sibling_count5	0.05204	0.02004	2.598	2436	0.009446	-0.004197	0.1083
fixed	NA	sibling_count>5	0.06606	0.01968	3.356	2524	0.0008029	0.0108	0.1213
fixed	NA	birth_order_nonlinear2	0.01948	0.01238	1.573	3092	0.1157	-0.01527	0.05423
fixed	NA	birth_order_nonlinear3	0.027	0.01465	1.843	3206	0.06546	-0.01413	0.06812
fixed	NA	birth_order_nonlinear4	0.02471	0.01837	1.345	3298	0.1786	-0.02685	0.07627
fixed	NA	birth_order_nonlinear5	0.001399	0.02263	0.06181	3271	0.9507	-0.06212	0.06491
fixed	NA	birth_order_nonlinear>5	0.02411	0.02252	1.071	3749	0.2843	-0.03909	0.08732
ran_pars	mother_pidlink	sd__(Intercept)	0.1055	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2699	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)	2.451	0.1904	12.87	3739	3.825e-37	1.916	2.985
fixed	NA	poly(age, 3, raw = TRUE)1	-0.2225	0.02047	-10.87	3738	4.073e-27	-0.28	-0.1651
fixed	NA	poly(age, 3, raw = TRUE)2	0.006642	0.0007031	9.448	3736	5.925e-21	0.004669	0.008616
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00006459	0.000007729	-8.357	3736	8.95e-17	-0.00008629	-0.0000429
fixed	NA	male	-0.03784	0.009553	-3.961	3697	0.00007597	-0.06466	-0.01103
fixed	NA	count_birth_order2/2	0.01989	0.0235	0.8465	3208	0.3973	-0.04606	0.08584
fixed	NA	count_birth_order1/3	0.008942	0.02016	0.4434	3721	0.6575	-0.04766	0.06554
fixed	NA	count_birth_order2/3	0.04507	0.02242	2.01	3738	0.04446	-0.01786	0.108
fixed	NA	count_birth_order3/3	0.07044	0.024	2.935	3738	0.003353	0.003077	0.1378
fixed	NA	count_birth_order1/4	0.05241	0.02364	2.217	3735	0.0267	-0.01396	0.1188
fixed	NA	count_birth_order2/4	0.04846	0.0247	1.962	3739	0.04989	-0.02089	0.1178
fixed	NA	count_birth_order3/4	0.04797	0.02589	1.852	3734	0.06404	-0.02472	0.1207
fixed	NA	count_birth_order4/4	0.07353	0.02793	2.633	3730	0.008497	-0.004858	0.1519
fixed	NA	count_birth_order1/5	0.05752	0.03092	1.86	3739	0.06296	-0.02928	0.1443
fixed	NA	count_birth_order2/5	0.07077	0.0347	2.04	3712	0.04146	-0.02663	0.1682
fixed	NA	count_birth_order3/5	0.05268	0.03324	1.585	3715	0.1131	-0.04062	0.146
fixed	NA	count_birth_order4/5	0.07725	0.03206	2.41	3719	0.01601	-0.01274	0.1672
fixed	NA	count_birth_order5/5	0.07412	0.03375	2.196	3713	0.02812	-0.02061	0.1688
fixed	NA	count_birth_order1/>5	0.07883	0.03014	2.616	3737	0.008934	-0.005758	0.1634
fixed	NA	count_birth_order2/>5	0.09488	0.03051	3.11	3720	0.001888	0.009231	0.1805
fixed	NA	count_birth_order3/>5	0.1004	0.02921	3.436	3718	0.0005975	0.01836	0.1824
fixed	NA	count_birth_order4/>5	0.07875	0.02906	2.71	3698	0.006766	-0.002829	0.1603
fixed	NA	count_birth_order5/>5	0.05546	0.0275	2.017	3709	0.04379	-0.02173	0.1327
fixed	NA	count_birth_order>5/>5	0.09005	0.02148	4.192	3478	0.00002835	0.02975	0.1504
ran_pars	mother_pidlink	sd__(Intercept)	0.1046	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2704	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)
11	1344	1413	-661	1322	NA	NA	NA
12	1345	1420	-660.6	1321	0.8029	1	0.3702
16	1348	1448	-658.2	1316	4.708	4	0.3186
26	1362	1524	-655.2	1310	6.094	10	0.8073

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)	0.1306	0.0897	1.456	9664	0.1455	-0.1212	0.3824
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0008862	0.008036	-0.1103	9640	0.9122	-0.02344	0.02167
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001282	0.0002255	0.5685	9572	0.5697	-0.0005048	0.0007612
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001381	0.000002002	-0.6899	9480	0.4903	-0.000007	0.000004238
fixed	NA	male	0.02977	0.008213	3.624	9475	0.0002912	0.006712	0.05282
fixed	NA	sibling_count3	0.00264	0.01767	0.1494	7173	0.8813	-0.04697	0.05225
fixed	NA	sibling_count4	0.0012	0.01789	0.06708	6867	0.9465	-0.04901	0.05141
fixed	NA	sibling_count5	0.00142	0.01864	0.07615	6516	0.9393	-0.05092	0.05376
fixed	NA	sibling_count>5	0.01776	0.01442	1.232	7097	0.2182	-0.02273	0.05825
ran_pars	mother_pidlink	sd__(Intercept)	0.1829	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3648	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)	0.1302	0.0897	1.451	9662	0.1468	-0.1216	0.3819
fixed	NA	birth_order	0.001497	0.001692	0.8848	9436	0.3763	-0.003252	0.006245
fixed	NA	poly(age, 3, raw = TRUE)1	-0.001315	0.008051	-0.1634	9633	0.8702	-0.02391	0.02128
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001445	0.0002262	0.6385	9544	0.5231	-0.0004906	0.0007795
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000153	0.000002009	-0.7617	9437	0.4462	-0.000007169	0.000004109
fixed	NA	male	0.02974	0.008213	3.621	9475	0.0002953	0.006683	0.05279
fixed	NA	sibling_count3	0.0023	0.01768	0.1301	7182	0.8965	-0.04732	0.05192
fixed	NA	sibling_count4	0.0003682	0.01791	0.02055	6909	0.9836	-0.04991	0.05065
fixed	NA	sibling_count5	-0.00009096	0.01872	-0.004859	6600	0.9961	-0.05264	0.05246
fixed	NA	sibling_count>5	0.01263	0.01555	0.812	7848	0.4168	-0.03102	0.05627
ran_pars	mother_pidlink	sd__(Intercept)	0.1827	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3649	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)	0.1386	0.08983	1.543	9663	0.1228	-0.1135	0.3908
fixed	NA	poly(age, 3, raw = TRUE)1	-0.001996	0.008057	-0.2477	9634	0.8044	-0.02461	0.02062
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001671	0.0002264	0.7384	9546	0.4603	-0.0004682	0.0008025
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001733	0.00000201	-0.8621	9437	0.3887	-0.000007374	0.000003909
fixed	NA	male	0.02977	0.008214	3.624	9471	0.0002917	0.00671	0.05283
fixed	NA	sibling_count3	0.002077	0.01791	0.116	7398	0.9076	-0.04819	0.05234
fixed	NA	sibling_count4	-0.003051	0.01834	-0.1663	7312	0.8679	-0.05454	0.04844
fixed	NA	sibling_count5	-0.00412	0.01928	-0.2137	7101	0.8308	-0.05824	0.05
fixed	NA	sibling_count>5	0.004782	0.01621	0.295	8382	0.768	-0.04073	0.05029
fixed	NA	birth_order_nonlinear2	-0.004716	0.01189	-0.3967	8886	0.6916	-0.03809	0.02866
fixed	NA	birth_order_nonlinear3	0.003489	0.01378	0.2532	8648	0.8001	-0.03519	0.04217
fixed	NA	birth_order_nonlinear4	0.02163	0.0155	1.396	8674	0.1628	-0.02188	0.06514
fixed	NA	birth_order_nonlinear5	0.0108	0.01742	0.6202	8681	0.5351	-0.03809	0.05969
fixed	NA	birth_order_nonlinear>5	0.02094	0.01463	1.431	9684	0.1524	-0.02013	0.06202
ran_pars	mother_pidlink	sd__(Intercept)	0.1826	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3649	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)	0.1623	0.09007	1.802	9660	0.07158	-0.09052	0.4151
fixed	NA	poly(age, 3, raw = TRUE)1	-0.00313	0.008058	-0.3884	9626	0.6977	-0.02575	0.01949
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001942	0.0002263	0.8581	9537	0.3909	-0.0004411	0.0008295
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001913	0.000002009	-0.9523	9426	0.341	-0.000007553	0.000003726
fixed	NA	male	0.02973	0.00821	3.622	9459	0.0002944	0.006687	0.05278
fixed	NA	count_birth_order2/2	-0.03256	0.02366	-1.376	8968	0.1687	-0.09897	0.03385
fixed	NA	count_birth_order1/3	-0.02768	0.02327	-1.19	9551	0.2342	-0.093	0.03764
fixed	NA	count_birth_order2/3	-0.02653	0.02583	-1.027	9645	0.3044	-0.09905	0.04598
fixed	NA	count_birth_order3/3	0.05159	0.02831	1.822	9700	0.06848	-0.02789	0.1311
fixed	NA	count_birth_order1/4	-0.02445	0.02556	-0.9567	9644	0.3388	-0.09619	0.04729
fixed	NA	count_birth_order2/4	-0.04134	0.02739	-1.509	9682	0.1312	-0.1182	0.03554
fixed	NA	count_birth_order3/4	0.03614	0.02885	1.253	9710	0.2103	-0.04483	0.1171
fixed	NA	count_birth_order4/4	0.007561	0.03102	0.2438	9727	0.8074	-0.07951	0.09463
fixed	NA	count_birth_order1/5	-0.01458	0.02876	-0.507	9703	0.6122	-0.09532	0.06616
fixed	NA	count_birth_order2/5	-0.001386	0.03052	-0.04544	9717	0.9638	-0.08704	0.08427
fixed	NA	count_birth_order3/5	-0.04137	0.03206	-1.29	9729	0.197	-0.1314	0.04864
fixed	NA	count_birth_order4/5	0.04476	0.03378	1.325	9718	0.1852	-0.05006	0.1396
fixed	NA	count_birth_order5/5	-0.02623	0.03388	-0.7743	9728	0.4388	-0.1213	0.06888
fixed	NA	count_birth_order1/>5	0.006506	0.02222	0.2929	9726	0.7696	-0.05585	0.06887
fixed	NA	count_birth_order2/>5	0.02085	0.02307	0.9039	9730	0.3661	-0.0439	0.0856
fixed	NA	count_birth_order3/>5	-0.04021	0.02283	-1.761	9730	0.07819	-0.1043	0.02387
fixed	NA	count_birth_order4/>5	0.007129	0.02239	0.3185	9729	0.7501	-0.05571	0.06997
fixed	NA	count_birth_order5/>5	0.01262	0.02261	0.5581	9730	0.5768	-0.05085	0.07609
fixed	NA	count_birth_order>5/>5	0.01603	0.01858	0.8625	8912	0.3885	-0.03613	0.06818
ran_pars	mother_pidlink	sd__(Intercept)	0.1828	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3644	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)
11	9969	10049	-4974	9947	NA	NA	NA
12	9971	10057	-4973	9947	0.7849	1	0.3756
16	9975	10090	-4972	9943	3.619	4	0.4601
26	9966	10153	-4957	9914	28.92	10	0.001283

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)	0.2048	0.2492	0.8218	3657	0.4112	-0.4947	0.9043
fixed	NA	poly(age, 3, raw = TRUE)1	-0.006416	0.02672	-0.2401	3652	0.8102	-0.08142	0.06859
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002029	0.0009152	0.2217	3647	0.8246	-0.002366	0.002772
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000112	0.00001003	-0.1116	3645	0.9111	-0.00002928	0.00002704
fixed	NA	male	0.01815	0.01255	1.446	3607	0.1482	-0.01708	0.05338
fixed	NA	sibling_count3	-0.01727	0.02117	-0.8156	2932	0.4148	-0.07668	0.04215
fixed	NA	sibling_count4	-0.006193	0.02193	-0.2825	2756	0.7776	-0.06774	0.05536
fixed	NA	sibling_count5	0.005548	0.02456	0.2259	2497	0.8213	-0.06339	0.07449
fixed	NA	sibling_count>5	0.01615	0.02122	0.7613	2490	0.4466	-0.0434	0.07571
ran_pars	mother_pidlink	sd__(Intercept)	0.1644	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3417	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)	0.2093	0.2493	0.8396	3657	0.4012	-0.4904	0.909
fixed	NA	birth_order	0.003167	0.003924	0.8071	3633	0.4197	-0.007847	0.01418
fixed	NA	poly(age, 3, raw = TRUE)1	-0.007299	0.02674	-0.2729	3653	0.7849	-0.08237	0.06777
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002263	0.0009157	0.2472	3649	0.8048	-0.002344	0.002797
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001234	0.00001003	-0.123	3645	0.9021	-0.0000294	0.00002693
fixed	NA	male	0.01803	0.01255	1.437	3606	0.1509	-0.0172	0.05326
fixed	NA	sibling_count3	-0.01886	0.02126	-0.8871	2935	0.3751	-0.07854	0.04082
fixed	NA	sibling_count4	-0.009734	0.02236	-0.4353	2762	0.6634	-0.07251	0.05304
fixed	NA	sibling_count5	-0.00025	0.02559	-0.009769	2546	0.9922	-0.07208	0.07158
fixed	NA	sibling_count>5	0.004629	0.02557	0.181	2664	0.8564	-0.06715	0.07641
ran_pars	mother_pidlink	sd__(Intercept)	0.1644	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3417	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)	0.2063	0.2494	0.8274	3653	0.4081	-0.4936	0.9063
fixed	NA	poly(age, 3, raw = TRUE)1	-0.007303	0.02673	-0.2732	3648	0.7847	-0.08234	0.06773
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002221	0.0009154	0.2426	3643	0.8083	-0.002347	0.002792
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001135	0.00001003	-0.1131	3640	0.91	-0.0000293	0.00002703
fixed	NA	male	0.01846	0.01255	1.471	3602	0.1413	-0.01676	0.05369
fixed	NA	sibling_count3	-0.02808	0.02162	-1.299	3024	0.1941	-0.08877	0.03261
fixed	NA	sibling_count4	-0.02	0.02309	-0.8659	2927	0.3866	-0.08482	0.04483
fixed	NA	sibling_count5	-0.004471	0.02665	-0.1678	2779	0.8668	-0.07929	0.07035
fixed	NA	sibling_count>5	-0.002136	0.02617	-0.08163	2795	0.9349	-0.07559	0.07131
fixed	NA	birth_order_nonlinear2	0.02484	0.01643	1.512	3174	0.1308	-0.02129	0.07097
fixed	NA	birth_order_nonlinear3	0.04716	0.01931	2.443	3215	0.01463	-0.007032	0.1014
fixed	NA	birth_order_nonlinear4	0.02073	0.02359	0.8784	3261	0.3798	-0.0455	0.08696
fixed	NA	birth_order_nonlinear5	-0.005032	0.02894	-0.1739	3254	0.862	-0.08627	0.07621
fixed	NA	birth_order_nonlinear>5	0.04153	0.02893	1.435	3654	0.1513	-0.03969	0.1227
ran_pars	mother_pidlink	sd__(Intercept)	0.164	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3417	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)	0.1737	0.2502	0.6943	3645	0.4875	-0.5286	0.8761
fixed	NA	poly(age, 3, raw = TRUE)1	-0.003514	0.02683	-0.131	3640	0.8958	-0.07882	0.07179
fixed	NA	poly(age, 3, raw = TRUE)2	0.00007322	0.000919	0.07967	3637	0.9365	-0.002506	0.002653
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000006975	0.00001008	0.06922	3635	0.9448	-0.00002758	0.00002898
fixed	NA	male	0.01881	0.01256	1.498	3595	0.1343	-0.01644	0.05407
fixed	NA	count_birth_order2/2	0.03164	0.03213	0.9849	3281	0.3247	-0.05854	0.1218
fixed	NA	count_birth_order1/3	-0.007422	0.02734	-0.2715	3628	0.7861	-0.08417	0.06932
fixed	NA	count_birth_order2/3	-0.0317	0.03035	-1.045	3646	0.2962	-0.1169	0.05348
fixed	NA	count_birth_order3/3	0.0254	0.03301	0.7693	3650	0.4417	-0.06727	0.1181
fixed	NA	count_birth_order1/4	-0.0155	0.03133	-0.4946	3644	0.6209	-0.1034	0.07244
fixed	NA	count_birth_order2/4	0.009061	0.03316	0.2732	3650	0.7847	-0.08402	0.1021
fixed	NA	count_birth_order3/4	0.05157	0.03435	1.501	3646	0.1334	-0.04485	0.148
fixed	NA	count_birth_order4/4	-0.02999	0.03675	-0.8159	3641	0.4146	-0.1331	0.07318
fixed	NA	count_birth_order1/5	-0.007561	0.0412	-0.1835	3650	0.8544	-0.1232	0.1081
fixed	NA	count_birth_order2/5	-0.0012	0.04434	-0.02707	3629	0.9784	-0.1257	0.1233
fixed	NA	count_birth_order3/5	0.04731	0.04215	1.123	3631	0.2617	-0.07099	0.1656
fixed	NA	count_birth_order4/5	0.05736	0.0411	1.396	3628	0.1629	-0.05802	0.1727
fixed	NA	count_birth_order5/5	-0.02381	0.04323	-0.5508	3619	0.5818	-0.1452	0.09754
fixed	NA	count_birth_order1/>5	-0.0458	0.03899	-1.175	3642	0.2403	-0.1552	0.06365
fixed	NA	count_birth_order2/>5	0.09322	0.03922	2.377	3618	0.01752	-0.01688	0.2033
fixed	NA	count_birth_order3/>5	0.01043	0.03826	0.2726	3617	0.7851	-0.09698	0.1178
fixed	NA	count_birth_order4/>5	0.02492	0.03743	0.6657	3604	0.5056	-0.08015	0.13
fixed	NA	count_birth_order5/>5	0.005131	0.03579	0.1434	3618	0.886	-0.09534	0.1056
fixed	NA	count_birth_order>5/>5	0.0424	0.02827	1.5	3520	0.1338	-0.03697	0.1218
ran_pars	mother_pidlink	sd__(Intercept)	0.1621	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3422	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)
11	3263	3332	-1621	3241	NA	NA	NA
12	3265	3339	-1620	3241	0.6535	1	0.4189
16	3265	3364	-1616	3233	7.902	4	0.09525
26	3271	3432	-1609	3219	14.38	10	0.1564

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)	0.2	0.248	0.8065	3681	0.42	-0.4961	0.8961
fixed	NA	poly(age, 3, raw = TRUE)1	-0.005978	0.02661	-0.2246	3676	0.8223	-0.08068	0.06873
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001901	0.0009118	0.2085	3672	0.8349	-0.002369	0.002749
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000009767	0.000009998	-0.09769	3670	0.9222	-0.00002904	0.00002709
fixed	NA	male	0.01874	0.0125	1.499	3631	0.134	-0.01635	0.05383
fixed	NA	sibling_count3	-0.02278	0.02317	-0.9834	3000	0.3255	-0.08781	0.04225
fixed	NA	sibling_count4	-0.004367	0.02342	-0.1865	2881	0.8521	-0.07011	0.06138
fixed	NA	sibling_count5	0.004279	0.02475	0.1729	2716	0.8627	-0.06519	0.07375
fixed	NA	sibling_count>5	0.009765	0.02168	0.4505	2770	0.6524	-0.05108	0.07061
ran_pars	mother_pidlink	sd__(Intercept)	0.1641	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3415	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)	0.2047	0.248	0.8255	3681	0.4092	-0.4915	0.9009
fixed	NA	birth_order	0.003732	0.00347	1.076	3595	0.2822	-0.006008	0.01347
fixed	NA	poly(age, 3, raw = TRUE)1	-0.006952	0.02663	-0.2611	3677	0.794	-0.0817	0.0678
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002152	0.0009121	0.236	3673	0.8134	-0.002345	0.002775
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000108	0.000009998	-0.108	3670	0.914	-0.00002914	0.00002699
fixed	NA	male	0.0186	0.0125	1.488	3631	0.1369	-0.01649	0.05369
fixed	NA	sibling_count3	-0.0247	0.02323	-1.063	2999	0.2879	-0.08991	0.04052
fixed	NA	sibling_count4	-0.008205	0.02369	-0.3464	2875	0.7291	-0.0747	0.05829
fixed	NA	sibling_count5	-0.002088	0.02545	-0.08207	2728	0.9346	-0.07351	0.06934
fixed	NA	sibling_count>5	-0.003568	0.02497	-0.1429	2834	0.8864	-0.07366	0.06653
ran_pars	mother_pidlink	sd__(Intercept)	0.1639	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3416	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)	0.196	0.2482	0.7895	3677	0.4298	-0.5007	0.8927
fixed	NA	poly(age, 3, raw = TRUE)1	-0.006367	0.02663	-0.2391	3672	0.811	-0.08112	0.06838
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001927	0.0009122	0.2113	3668	0.8327	-0.002368	0.002753
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000008051	0.00001	-0.0805	3666	0.9358	-0.00002888	0.00002727
fixed	NA	male	0.01888	0.0125	1.51	3627	0.131	-0.01621	0.05397
fixed	NA	sibling_count3	-0.03091	0.02358	-1.311	3070	0.19	-0.09711	0.03528
fixed	NA	sibling_count4	-0.01824	0.02432	-0.7502	2998	0.4532	-0.0865	0.05002
fixed	NA	sibling_count5	-0.008351	0.02645	-0.3157	2922	0.7522	-0.0826	0.0659
fixed	NA	sibling_count>5	-0.00879	0.02563	-0.343	2966	0.7316	-0.08072	0.06314
fixed	NA	birth_order_nonlinear2	0.02643	0.01663	1.589	3225	0.1121	-0.02025	0.07311
fixed	NA	birth_order_nonlinear3	0.03556	0.01942	1.831	3283	0.06718	-0.01895	0.09008
fixed	NA	birth_order_nonlinear4	0.04224	0.02305	1.833	3350	0.06695	-0.02246	0.1069
fixed	NA	birth_order_nonlinear5	0.00225	0.02807	0.08016	3328	0.9361	-0.07653	0.08103
fixed	NA	birth_order_nonlinear>5	0.03512	0.02623	1.339	3683	0.1806	-0.0385	0.1087
ran_pars	mother_pidlink	sd__(Intercept)	0.1636	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3417	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)	0.1632	0.2485	0.6567	3669	0.5114	-0.5344	0.8609
fixed	NA	poly(age, 3, raw = TRUE)1	-0.002079	0.02667	-0.07794	3665	0.9379	-0.07695	0.07279
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001812	0.000914	0.01983	3662	0.9842	-0.002548	0.002584
fixed	NA	poly(age, 3, raw = TRUE)3	0.000001353	0.00001002	0.135	3660	0.8926	-0.00002679	0.00002949
fixed	NA	male	0.01964	0.01251	1.57	3619	0.1165	-0.01547	0.05475
fixed	NA	count_birth_order2/2	0.02775	0.03526	0.7871	3393	0.4313	-0.07122	0.1267
fixed	NA	count_birth_order1/3	-0.01368	0.03019	-0.453	3652	0.6506	-0.09843	0.07108
fixed	NA	count_birth_order2/3	-0.02855	0.03284	-0.8694	3669	0.3847	-0.1207	0.06364
fixed	NA	count_birth_order3/3	0.007524	0.03635	0.207	3674	0.836	-0.09451	0.1096
fixed	NA	count_birth_order1/4	-0.02249	0.03274	-0.6868	3664	0.4923	-0.1144	0.06942
fixed	NA	count_birth_order2/4	-0.01115	0.03446	-0.3235	3673	0.7463	-0.1079	0.08557
fixed	NA	count_birth_order3/4	0.08672	0.03724	2.328	3671	0.01994	-0.01782	0.1913
fixed	NA	count_birth_order4/4	-0.01743	0.04042	-0.4312	3664	0.6663	-0.1309	0.09603
fixed	NA	count_birth_order1/5	0.01313	0.03952	0.3322	3674	0.7397	-0.09781	0.1241
fixed	NA	count_birth_order2/5	0.02348	0.04048	0.58	3672	0.562	-0.09014	0.1371
fixed	NA	count_birth_order3/5	0.01464	0.0416	0.3519	3662	0.7249	-0.1021	0.1314
fixed	NA	count_birth_order4/5	0.04861	0.04232	1.149	3654	0.2508	-0.07019	0.1674
fixed	NA	count_birth_order5/5	-0.036	0.04295	-0.8381	3648	0.402	-0.1566	0.08458
fixed	NA	count_birth_order1/>5	-0.04299	0.03567	-1.205	3674	0.2282	-0.1431	0.05713
fixed	NA	count_birth_order2/>5	0.07643	0.03759	2.034	3656	0.04207	-0.02907	0.1819
fixed	NA	count_birth_order3/>5	-0.02567	0.03621	-0.7089	3659	0.4785	-0.1273	0.07598
fixed	NA	count_birth_order4/>5	0.05458	0.03517	1.552	3657	0.1208	-0.04414	0.1533
fixed	NA	count_birth_order5/>5	0.0148	0.03721	0.3979	3638	0.6907	-0.08963	0.1192
fixed	NA	count_birth_order>5/>5	0.0284	0.02839	1	3552	0.3172	-0.0513	0.1081
ran_pars	mother_pidlink	sd__(Intercept)	0.1614	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.342	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)
11	3280	3348	-1629	3258	NA	NA	NA
12	3280	3355	-1628	3256	1.161	1	0.2813
16	3283	3382	-1625	3251	5.449	4	0.2443
26	3282	3444	-1615	3230	20.81	10	0.02245

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)	0.1848	0.2525	0.732	3593	0.4642	-0.524	0.8936
fixed	NA	poly(age, 3, raw = TRUE)1	-0.004672	0.02712	-0.1723	3587	0.8632	-0.0808	0.07145
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001606	0.0009297	0.1727	3583	0.8629	-0.002449	0.00277
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000009046	0.0000102	-0.08866	3580	0.9294	-0.00002955	0.00002774
fixed	NA	male	0.01747	0.01271	1.375	3541	0.1691	-0.01819	0.05314
fixed	NA	sibling_count3	-0.006028	0.0208	-0.2897	2884	0.772	-0.06442	0.05237
fixed	NA	sibling_count4	-0.008332	0.02186	-0.3811	2715	0.7031	-0.0697	0.05303
fixed	NA	sibling_count5	0.00707	0.02522	0.2804	2382	0.7792	-0.06371	0.07785
fixed	NA	sibling_count>5	0.01936	0.02141	0.9043	2398	0.3659	-0.04074	0.07947
ran_pars	mother_pidlink	sd__(Intercept)	0.1663	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3423	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)	0.1905	0.2526	0.7539	3593	0.4509	-0.5186	0.8995
fixed	NA	birth_order	0.003283	0.004052	0.81	3583	0.418	-0.008093	0.01466
fixed	NA	poly(age, 3, raw = TRUE)1	-0.005701	0.02715	-0.21	3589	0.8337	-0.08191	0.07051
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001888	0.0009304	0.2029	3584	0.8392	-0.002423	0.0028
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001065	0.00001021	-0.1043	3581	0.9169	-0.00002971	0.00002758
fixed	NA	male	0.01743	0.01271	1.372	3540	0.1701	-0.01823	0.0531
fixed	NA	sibling_count3	-0.007723	0.02091	-0.3694	2886	0.7119	-0.06642	0.05097
fixed	NA	sibling_count4	-0.01195	0.02231	-0.5356	2727	0.5922	-0.07459	0.05068
fixed	NA	sibling_count5	0.00124	0.02622	0.04729	2426	0.9623	-0.07237	0.07485
fixed	NA	sibling_count>5	0.007432	0.02599	0.2859	2621	0.7749	-0.06552	0.08039
ran_pars	mother_pidlink	sd__(Intercept)	0.1663	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3424	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)	0.1896	0.2527	0.7506	3589	0.453	-0.5196	0.8988
fixed	NA	poly(age, 3, raw = TRUE)1	-0.006112	0.02713	-0.2253	3584	0.8218	-0.08227	0.07005
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001968	0.0009299	0.2116	3579	0.8324	-0.002414	0.002807
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001088	0.0000102	-0.1067	3576	0.9151	-0.00002973	0.00002755
fixed	NA	male	0.01806	0.0127	1.422	3538	0.1551	-0.01759	0.05372
fixed	NA	sibling_count3	-0.01698	0.02128	-0.7977	2977	0.4251	-0.07671	0.04276
fixed	NA	sibling_count4	-0.0222	0.02304	-0.9634	2889	0.3354	-0.08688	0.04248
fixed	NA	sibling_count5	-0.001415	0.0272	-0.052	2640	0.9585	-0.07778	0.07495
fixed	NA	sibling_count>5	0.001559	0.02661	0.0586	2758	0.9533	-0.07314	0.07626
fixed	NA	birth_order_nonlinear2	0.03129	0.0164	1.908	3101	0.05647	-0.01474	0.07733
fixed	NA	birth_order_nonlinear3	0.04782	0.01938	2.467	3148	0.01367	-0.006586	0.1022
fixed	NA	birth_order_nonlinear4	0.02218	0.02437	0.9103	3189	0.3627	-0.04621	0.09058
fixed	NA	birth_order_nonlinear5	-0.006486	0.03001	-0.2161	3153	0.8289	-0.09074	0.07777
fixed	NA	birth_order_nonlinear>5	0.04426	0.02993	1.479	3584	0.1393	-0.03975	0.1283
ran_pars	mother_pidlink	sd__(Intercept)	0.1653	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3425	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)	0.1681	0.2535	0.663	3581	0.5074	-0.5436	0.8798
fixed	NA	poly(age, 3, raw = TRUE)1	-0.003336	0.02724	-0.1225	3577	0.9025	-0.07979	0.07312
fixed	NA	poly(age, 3, raw = TRUE)2	0.0000858	0.0009339	0.09188	3574	0.9268	-0.002536	0.002707
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000002996	0.00001025	0.02923	3572	0.9767	-0.00002847	0.00002907
fixed	NA	male	0.01896	0.01272	1.49	3530	0.1362	-0.01675	0.05467
fixed	NA	count_birth_order2/2	0.02905	0.03134	0.9271	3202	0.354	-0.05891	0.117
fixed	NA	count_birth_order1/3	-0.002032	0.02696	-0.07537	3564	0.9399	-0.07771	0.07364
fixed	NA	count_birth_order2/3	-0.007826	0.02992	-0.2615	3584	0.7937	-0.09183	0.07617
fixed	NA	count_birth_order3/3	0.02743	0.03219	0.8522	3585	0.3942	-0.06292	0.1178
fixed	NA	count_birth_order1/4	-0.02844	0.03159	-0.9001	3582	0.3681	-0.1171	0.06025
fixed	NA	count_birth_order2/4	0.01055	0.03314	0.3183	3586	0.7503	-0.08247	0.1036
fixed	NA	count_birth_order3/4	0.05262	0.03435	1.532	3581	0.1257	-0.04381	0.1491
fixed	NA	count_birth_order4/4	-0.02922	0.0373	-0.7834	3574	0.4334	-0.1339	0.07549
fixed	NA	count_birth_order1/5	-0.005244	0.04125	-0.1271	3586	0.8989	-0.121	0.1106
fixed	NA	count_birth_order2/5	0.01438	0.04592	0.3131	3554	0.7542	-0.1145	0.1433
fixed	NA	count_birth_order3/5	0.03522	0.04477	0.7867	3553	0.4315	-0.09046	0.1609
fixed	NA	count_birth_order4/5	0.06448	0.04311	1.496	3558	0.1348	-0.05652	0.1855
fixed	NA	count_birth_order5/5	-0.02928	0.04577	-0.6397	3549	0.5224	-0.1577	0.09919
fixed	NA	count_birth_order1/>5	-0.03966	0.04016	-0.9875	3576	0.3235	-0.1524	0.07308
fixed	NA	count_birth_order2/>5	0.09011	0.04053	2.224	3547	0.02624	-0.02365	0.2039
fixed	NA	count_birth_order3/>5	0.02288	0.0387	0.5913	3555	0.5544	-0.08575	0.1315
fixed	NA	count_birth_order4/>5	0.02081	0.03882	0.5362	3528	0.5919	-0.08815	0.1298
fixed	NA	count_birth_order5/>5	0.005412	0.03647	0.1484	3550	0.882	-0.09696	0.1078
fixed	NA	count_birth_order>5/>5	0.04579	0.02876	1.592	3444	0.1114	-0.03493	0.1265
ran_pars	mother_pidlink	sd__(Intercept)	0.1631	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3434	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)
11	3231	3300	-1605	3209	NA	NA	NA
12	3233	3307	-1604	3209	0.6582	1	0.4172
16	3232	3331	-1600	3200	8.947	4	0.06245
26	3241	3402	-1595	3189	10.51	10	0.3971

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)	-0.00014	0.007992	-0.01751	9745	0.986	-0.02257	0.02229
fixed	NA	poly(age, 3, raw = TRUE)1	0.0001646	0.0007143	0.2304	9745	0.8178	-0.001841	0.00217
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000005987	0.00001998	-0.2997	9745	0.7644	-0.00006206	0.00005009
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000005958	0.0000001767	0.3371	9745	0.736	-0.0000004365	0.0000005557
fixed	NA	male	0.001437	0.0007496	1.917	9745	0.05521	-0.0006668	0.003542
fixed	NA	sibling_count3	-0.001779	0.001507	-1.18	9745	0.2379	-0.006009	0.002452
fixed	NA	sibling_count4	0.0006745	0.001514	0.4455	9745	0.656	-0.003576	0.004925
fixed	NA	sibling_count5	-0.0008865	0.001566	-0.5663	9745	0.5712	-0.005281	0.003508
fixed	NA	sibling_count>5	-0.0004652	0.001227	-0.3793	9745	0.7045	-0.003908	0.002978
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03649	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)	-0.0001227	0.007992	-0.01535	9744	0.9878	-0.02256	0.02231
fixed	NA	birth_order	0.00008633	0.0001468	0.5883	9744	0.5564	-0.0003256	0.0004983
fixed	NA	poly(age, 3, raw = TRUE)1	0.0001414	0.0007155	0.1976	9744	0.8433	-0.001867	0.00215
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00000519	0.00002002	-0.2592	9744	0.7955	-0.00006139	0.00005101
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000005258	0.0000001771	0.2968	9744	0.7666	-0.0000004446	0.0000005498
fixed	NA	male	0.001435	0.0007497	1.914	9744	0.05564	-0.0006694	0.003539
fixed	NA	sibling_count3	-0.001804	0.001508	-1.197	9744	0.2315	-0.006037	0.002428
fixed	NA	sibling_count4	0.000616	0.001517	0.4059	9744	0.6848	-0.003644	0.004875
fixed	NA	sibling_count5	-0.0009842	0.001574	-0.6252	9744	0.5319	-0.005404	0.003435
fixed	NA	sibling_count>5	-0.0007791	0.001338	-0.5825	9744	0.5603	-0.004534	0.002976
ran_pars	mother_pidlink	sd__(Intercept)	0.000000003213	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03649	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)	-0.0006085	0.008007	-0.07599	9740	0.9394	-0.02308	0.02187
fixed	NA	poly(age, 3, raw = TRUE)1	0.0002089	0.0007162	0.2916	9740	0.7706	-0.001802	0.002219
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000007051	0.00002004	-0.3519	9740	0.7249	-0.0000633	0.0000492
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000006636	0.0000001772	0.3744	9740	0.7081	-0.0000004312	0.0000005639
fixed	NA	male	0.00143	0.0007498	1.907	9740	0.05657	-0.000675	0.003534
fixed	NA	sibling_count3	-0.001577	0.001534	-1.028	9740	0.3039	-0.005882	0.002728
fixed	NA	sibling_count4	0.001223	0.001566	0.7812	9740	0.4347	-0.003173	0.005619
fixed	NA	sibling_count5	-0.0005539	0.001638	-0.3382	9740	0.7352	-0.005152	0.004044
fixed	NA	sibling_count>5	-0.00006166	0.00141	-0.04372	9740	0.9651	-0.00402	0.003897
fixed	NA	birth_order_nonlinear2	-0.00004771	0.001109	-0.04303	9740	0.9657	-0.00316	0.003065
fixed	NA	birth_order_nonlinear3	-0.0008901	0.001289	-0.6904	9740	0.4899	-0.004509	0.002729
fixed	NA	birth_order_nonlinear4	-0.002	0.001448	-1.382	9740	0.1671	-0.006064	0.002063
fixed	NA	birth_order_nonlinear5	0.000813	0.001625	0.5004	9740	0.6168	-0.003748	0.005374
fixed	NA	birth_order_nonlinear>5	-0.0004879	0.001322	-0.369	9740	0.7121	-0.004199	0.003223
ran_pars	mother_pidlink	sd__(Intercept)	0.000000004815	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03649	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)	-0.001129	0.00804	-0.1404	9730	0.8883	-0.0237	0.02144
fixed	NA	poly(age, 3, raw = TRUE)1	0.0002277	0.0007171	0.3175	9730	0.7509	-0.001785	0.002241
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000007642	0.00002005	-0.3811	9730	0.7032	-0.00006394	0.00004865
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000007203	0.0000001773	0.4062	9730	0.6846	-0.0000004258	0.0000005699
fixed	NA	male	0.001399	0.0007502	1.865	9730	0.06222	-0.0007068	0.003505
fixed	NA	count_birth_order2/2	0.0008908	0.002215	0.4021	9730	0.6876	-0.005328	0.00711
fixed	NA	count_birth_order1/3	-0.001422	0.002092	-0.6798	9730	0.4966	-0.007293	0.00445
fixed	NA	count_birth_order2/3	-0.001456	0.002328	-0.6254	9730	0.5317	-0.007989	0.005078
fixed	NA	count_birth_order3/3	-0.001499	0.002556	-0.5867	9730	0.5574	-0.008673	0.005674
fixed	NA	count_birth_order1/4	0.003658	0.002303	1.588	9730	0.1122	-0.002807	0.01012
fixed	NA	count_birth_order2/4	0.001647	0.00247	0.6669	9730	0.5048	-0.005286	0.008581
fixed	NA	count_birth_order3/4	-0.001469	0.002605	-0.5637	9730	0.573	-0.008782	0.005845
fixed	NA	count_birth_order4/4	-0.001533	0.002805	-0.5465	9730	0.5847	-0.009406	0.006341
fixed	NA	count_birth_order1/5	-0.001484	0.002599	-0.5709	9730	0.5681	-0.008778	0.005811
fixed	NA	count_birth_order2/5	0.00277	0.002759	1.004	9730	0.3154	-0.004974	0.01051
fixed	NA	count_birth_order3/5	-0.001468	0.002903	-0.5055	9730	0.6132	-0.009617	0.006682
fixed	NA	count_birth_order4/5	-0.001597	0.003066	-0.521	9730	0.6023	-0.0102	0.007008
fixed	NA	count_birth_order5/5	-0.001528	0.00307	-0.4976	9730	0.6188	-0.01015	0.00709
fixed	NA	count_birth_order1/>5	0.0001466	0.00201	0.07294	9730	0.9419	-0.005496	0.00579
fixed	NA	count_birth_order2/>5	-0.001418	0.00209	-0.6783	9730	0.4976	-0.007286	0.00445
fixed	NA	count_birth_order3/>5	0.0002647	0.002069	0.1279	9730	0.8982	-0.005544	0.006073
fixed	NA	count_birth_order4/>5	-0.001477	0.002027	-0.729	9730	0.466	-0.007166	0.004212
fixed	NA	count_birth_order5/>5	0.001744	0.002049	0.8512	9730	0.3947	-0.004008	0.007496
fixed	NA	count_birth_order>5/>5	-0.0001939	0.001632	-0.1188	9730	0.9054	-0.004776	0.004388
ran_pars	mother_pidlink	sd__(Intercept)	0.000000002354	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03649	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)
11	-36894	-36815	18458	-36916	NA	NA	NA
12	-36892	-36806	18458	-36916	0.3464	1	0.5562
16	-36887	-36772	18460	-36919	3.056	4	0.5484
26	-36874	-36687	18463	-36926	7.077	10	0.7181

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)	-0.01904	0.02438	-0.7808	3665	0.4349	-0.08748	0.0494
fixed	NA	poly(age, 3, raw = TRUE)1	0.00222	0.002615	0.8488	3665	0.3961	-0.005121	0.00956
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00006986	0.00008957	-0.7799	3665	0.4355	-0.0003213	0.0001816
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000006769	0.0000009816	0.6896	3665	0.4905	-0.000002078	0.000003432
fixed	NA	male	0.001275	0.001234	1.033	3665	0.3016	-0.002189	0.00474
fixed	NA	sibling_count3	-0.002135	0.001996	-1.07	3665	0.2848	-0.007738	0.003468
fixed	NA	sibling_count4	-0.003247	0.002052	-1.582	3665	0.1136	-0.009006	0.002513
fixed	NA	sibling_count5	-0.001205	0.002273	-0.5304	3665	0.5958	-0.007585	0.005174
fixed	NA	sibling_count>5	-0.002255	0.00196	-1.15	3665	0.2501	-0.007758	0.003248
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03688	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)	-0.01893	0.02439	-0.7762	3664	0.4377	-0.08739	0.04953
fixed	NA	birth_order	0.0001139	0.0003773	0.302	3664	0.7627	-0.000945	0.001173
fixed	NA	poly(age, 3, raw = TRUE)1	0.002195	0.002617	0.839	3664	0.4015	-0.00515	0.00954
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00006929	0.0000896	-0.7733	3664	0.4394	-0.0003208	0.0001822
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000006754	0.0000009817	0.688	3664	0.4915	-0.00000208	0.000003431
fixed	NA	male	0.001271	0.001235	1.029	3664	0.3035	-0.002195	0.004736
fixed	NA	sibling_count3	-0.002192	0.002005	-1.093	3664	0.2744	-0.007819	0.003436
fixed	NA	sibling_count4	-0.00337	0.002092	-1.611	3664	0.1073	-0.009244	0.002503
fixed	NA	sibling_count5	-0.001409	0.002371	-0.5944	3664	0.5523	-0.008065	0.005246
fixed	NA	sibling_count>5	-0.00266	0.002374	-1.12	3664	0.2627	-0.009324	0.004005
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03689	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)	-0.01804	0.0244	-0.7394	3660	0.4597	-0.08654	0.05046
fixed	NA	poly(age, 3, raw = TRUE)1	0.002198	0.002617	0.8399	3660	0.401	-0.005147	0.009543
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00006814	0.00008961	-0.7603	3660	0.4471	-0.0003197	0.0001834
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000006483	0.0000009821	0.6601	3660	0.5092	-0.000002108	0.000003405
fixed	NA	male	0.001222	0.001235	0.9901	3660	0.3222	-0.002243	0.004688
fixed	NA	sibling_count3	-0.001531	0.002047	-0.7481	3660	0.4545	-0.007276	0.004214
fixed	NA	sibling_count4	-0.002233	0.002175	-1.027	3660	0.3047	-0.008339	0.003873
fixed	NA	sibling_count5	0.0001622	0.002493	0.06504	3660	0.9481	-0.006837	0.007161
fixed	NA	sibling_count>5	-0.001611	0.002443	-0.6594	3660	0.5097	-0.00847	0.005248
fixed	NA	birth_order_nonlinear2	-0.003122	0.001656	-1.886	3660	0.05944	-0.007771	0.001526
fixed	NA	birth_order_nonlinear3	-0.002794	0.00194	-1.44	3660	0.15	-0.00824	0.002652
fixed	NA	birth_order_nonlinear4	-0.003035	0.002365	-1.284	3660	0.1994	-0.009674	0.003603
fixed	NA	birth_order_nonlinear5	-0.003377	0.002899	-1.165	3660	0.2441	-0.01151	0.00476
fixed	NA	birth_order_nonlinear>5	-0.0000936	0.002817	-0.03323	3660	0.9735	-0.008	0.007813
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03688	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)	-0.01888	0.02451	-0.7703	3650	0.4412	-0.08768	0.04992
fixed	NA	poly(age, 3, raw = TRUE)1	0.002348	0.002629	0.8932	3650	0.3718	-0.00503	0.009726
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00007276	0.00009004	-0.8081	3650	0.4191	-0.0003255	0.00018
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000006932	0.0000009869	0.7024	3650	0.4825	-0.000002077	0.000003463
fixed	NA	male	0.001217	0.001237	0.9839	3650	0.3252	-0.002256	0.00469
fixed	NA	count_birth_order2/2	-0.005185	0.003234	-1.603	3650	0.1089	-0.01426	0.003892
fixed	NA	count_birth_order1/3	-0.002396	0.002674	-0.8963	3650	0.3702	-0.009901	0.005109
fixed	NA	count_birth_order2/3	-0.005014	0.002973	-1.687	3650	0.09177	-0.01336	0.003331
fixed	NA	count_birth_order3/3	-0.005052	0.00324	-1.559	3650	0.119	-0.01415	0.004044
fixed	NA	count_birth_order1/4	-0.004789	0.003067	-1.561	3650	0.1185	-0.0134	0.003821
fixed	NA	count_birth_order2/4	-0.004976	0.003253	-1.529	3650	0.1262	-0.01411	0.004156
fixed	NA	count_birth_order3/4	-0.004932	0.003375	-1.461	3650	0.144	-0.0144	0.004542
fixed	NA	count_birth_order4/4	-0.005233	0.003613	-1.448	3650	0.1476	-0.01537	0.004909
fixed	NA	count_birth_order1/5	0.004607	0.004041	1.14	3650	0.2544	-0.006737	0.01595
fixed	NA	count_birth_order2/5	-0.004763	0.004362	-1.092	3650	0.2749	-0.01701	0.007481
fixed	NA	count_birth_order3/5	-0.004893	0.004147	-1.18	3650	0.2381	-0.01653	0.006748
fixed	NA	count_birth_order4/5	-0.005202	0.004046	-1.286	3650	0.1987	-0.01656	0.006156
fixed	NA	count_birth_order5/5	-0.005179	0.004259	-1.216	3650	0.2241	-0.01713	0.006777
fixed	NA	count_birth_order1/>5	-0.004681	0.003823	-1.224	3650	0.2209	-0.01541	0.006051
fixed	NA	count_birth_order2/>5	-0.00473	0.003857	-1.226	3650	0.2201	-0.01556	0.006096
fixed	NA	count_birth_order3/>5	-0.004821	0.003765	-1.28	3650	0.2006	-0.01539	0.005749
fixed	NA	count_birth_order4/>5	-0.004809	0.003688	-1.304	3650	0.1923	-0.01516	0.005542
fixed	NA	count_birth_order5/>5	-0.004901	0.003524	-1.391	3650	0.1644	-0.01479	0.004992
fixed	NA	count_birth_order>5/>5	-0.002395	0.002722	-0.8798	3650	0.379	-0.01003	0.005246
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03691	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)
11	-13809	-13741	6916	-13831	NA	NA	NA
12	-13807	-13733	6916	-13831	0.09146	1	0.7623
16	-13805	-13705	6918	-13837	5.574	4	0.2333
26	-13790	-13628	6921	-13842	4.71	10	0.9097

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)	-0.01904	0.02419	-0.7868	3689	0.4314	-0.08695	0.04888
fixed	NA	poly(age, 3, raw = TRUE)1	0.002273	0.002597	0.875	3689	0.3816	-0.005018	0.009564
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00007096	0.00008898	-0.7975	3689	0.4252	-0.0003207	0.0001788
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000006852	0.0000009753	0.7025	3689	0.4824	-0.000002053	0.000003423
fixed	NA	male	0.001309	0.001226	1.067	3689	0.2859	-0.002133	0.00475
fixed	NA	sibling_count3	-0.002695	0.002183	-1.235	3689	0.217	-0.008822	0.003432
fixed	NA	sibling_count4	-0.004092	0.002196	-1.864	3689	0.0624	-0.01026	0.00207
fixed	NA	sibling_count5	-0.002261	0.002303	-0.9815	3689	0.3264	-0.008727	0.004205
fixed	NA	sibling_count>5	-0.00326	0.00202	-1.614	3689	0.1067	-0.008932	0.002411
ran_pars	mother_pidlink	sd__(Intercept)	0.000000000423	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03676	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)	-0.01896	0.0242	-0.7833	3688	0.4335	-0.08688	0.04897
fixed	NA	birth_order	0.0001029	0.0003309	0.3109	3688	0.7559	-0.0008261	0.001032
fixed	NA	poly(age, 3, raw = TRUE)1	0.002253	0.002598	0.8669	3688	0.386	-0.005041	0.009547
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00007051	0.000089	-0.7923	3688	0.4282	-0.0003203	0.0001793
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000006846	0.0000009754	0.7018	3688	0.4828	-0.000002053	0.000003423
fixed	NA	male	0.001304	0.001226	1.064	3688	0.2876	-0.002138	0.004747
fixed	NA	sibling_count3	-0.002747	0.002189	-1.255	3688	0.2097	-0.008892	0.003399
fixed	NA	sibling_count4	-0.004195	0.00222	-1.889	3688	0.05893	-0.01043	0.002038
fixed	NA	sibling_count5	-0.002432	0.002369	-1.027	3688	0.3046	-0.009082	0.004217
fixed	NA	sibling_count>5	-0.003621	0.00233	-1.554	3688	0.1202	-0.01016	0.002919
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03676	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)	-0.01787	0.02422	-0.7379	3684	0.4606	-0.08584	0.05011
fixed	NA	poly(age, 3, raw = TRUE)1	0.002244	0.002599	0.8634	3684	0.388	-0.005051	0.009539
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00006906	0.00008903	-0.7757	3684	0.438	-0.000319	0.0001808
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000006551	0.0000009758	0.6713	3684	0.5021	-0.000002084	0.000003394
fixed	NA	male	0.001255	0.001226	1.023	3684	0.3063	-0.002188	0.004697
fixed	NA	sibling_count3	-0.002103	0.002228	-0.944	3684	0.3452	-0.008358	0.004151
fixed	NA	sibling_count4	-0.003207	0.00229	-1.4	3684	0.1615	-0.009635	0.003221
fixed	NA	sibling_count5	-0.001055	0.002481	-0.4253	3684	0.6706	-0.008019	0.005909
fixed	NA	sibling_count>5	-0.002713	0.002404	-1.129	3684	0.2591	-0.00946	0.004034
fixed	NA	birth_order_nonlinear2	-0.003291	0.001669	-1.972	3684	0.04873	-0.007976	0.001394
fixed	NA	birth_order_nonlinear3	-0.002759	0.001942	-1.42	3684	0.1556	-0.008211	0.002694
fixed	NA	birth_order_nonlinear4	-0.002861	0.002297	-1.245	3684	0.213	-0.009309	0.003587
fixed	NA	birth_order_nonlinear5	-0.003159	0.002798	-1.129	3684	0.2588	-0.01101	0.004694
fixed	NA	birth_order_nonlinear>5	-0.00035	0.002537	-0.1379	3684	0.8903	-0.007472	0.006772
ran_pars	mother_pidlink	sd__(Intercept)	0.0000000005529	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03675	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)	-0.01698	0.02429	-0.6991	3674	0.4845	-0.08518	0.05121
fixed	NA	poly(age, 3, raw = TRUE)1	0.00227	0.002608	0.8703	3674	0.3842	-0.00505	0.00959
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0000702	0.00008935	-0.7857	3674	0.4321	-0.000321	0.0001806
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000006703	0.0000009796	0.6843	3674	0.4939	-0.000002079	0.00000342
fixed	NA	male	0.001227	0.001229	0.9981	3674	0.3183	-0.002224	0.004678
fixed	NA	count_birth_order2/2	-0.006385	0.00353	-1.809	3674	0.07059	-0.01629	0.003525
fixed	NA	count_birth_order1/3	-0.003068	0.002946	-1.041	3674	0.2979	-0.01134	0.005203
fixed	NA	count_birth_order2/3	-0.006267	0.00321	-1.952	3674	0.051	-0.01528	0.002745
fixed	NA	count_birth_order3/3	-0.006277	0.003561	-1.763	3674	0.07802	-0.01627	0.003718
fixed	NA	count_birth_order1/4	-0.006116	0.003198	-1.913	3674	0.05587	-0.01509	0.00286
fixed	NA	count_birth_order2/4	-0.006265	0.003371	-1.859	3674	0.06317	-0.01573	0.003197
fixed	NA	count_birth_order3/4	-0.006214	0.003651	-1.702	3674	0.08881	-0.01646	0.004033
fixed	NA	count_birth_order4/4	-0.006527	0.003966	-1.646	3674	0.09987	-0.01766	0.004605
fixed	NA	count_birth_order1/5	0.001582	0.003866	0.4093	3674	0.6824	-0.009271	0.01244
fixed	NA	count_birth_order2/5	-0.006089	0.003966	-1.535	3674	0.1248	-0.01722	0.005043
fixed	NA	count_birth_order3/5	-0.006068	0.004082	-1.486	3674	0.1372	-0.01753	0.005391
fixed	NA	count_birth_order4/5	-0.006315	0.004157	-1.519	3674	0.1288	-0.01798	0.005354
fixed	NA	count_birth_order5/5	-0.006395	0.004222	-1.515	3674	0.1299	-0.01825	0.005455
fixed	NA	count_birth_order1/>5	-0.00598	0.003485	-1.716	3674	0.08623	-0.01576	0.003802
fixed	NA	count_birth_order2/>5	-0.006117	0.003686	-1.66	3674	0.09705	-0.01646	0.004228
fixed	NA	count_birth_order3/>5	-0.006069	0.003552	-1.709	3674	0.08763	-0.01604	0.003902
fixed	NA	count_birth_order4/>5	-0.006211	0.003452	-1.799	3674	0.07209	-0.0159	0.00348
fixed	NA	count_birth_order5/>5	-0.006157	0.003658	-1.683	3674	0.09237	-0.01642	0.004109
fixed	NA	count_birth_order>5/>5	-0.004098	0.002734	-1.499	3674	0.134	-0.01177	0.003576
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03678	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)
11	-13925	-13856	6973	-13947	NA	NA	NA
12	-13923	-13848	6973	-13947	0.09692	1	0.7556
16	-13920	-13821	6976	-13952	5.536	4	0.2366
26	-13904	-13743	6978	-13956	4.304	10	0.9326

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)	-0.02014	0.02484	-0.8108	3601	0.4176	-0.08985	0.04958
fixed	NA	poly(age, 3, raw = TRUE)1	0.002324	0.002668	0.871	3601	0.3838	-0.005166	0.009813
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00007334	0.00009147	-0.8018	3601	0.4227	-0.0003301	0.0001834
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000007122	0.000001003	0.7098	3601	0.4779	-0.000002105	0.000003529
fixed	NA	male	0.001306	0.001257	1.039	3601	0.2987	-0.002221	0.004833
fixed	NA	sibling_count3	-0.002062	0.001971	-1.046	3601	0.2955	-0.007594	0.00347
fixed	NA	sibling_count4	-0.003122	0.002055	-1.52	3601	0.1287	-0.00889	0.002646
fixed	NA	sibling_count5	-0.0008557	0.002335	-0.3665	3601	0.714	-0.00741	0.005698
fixed	NA	sibling_count>5	-0.002037	0.001982	-1.028	3601	0.3042	-0.0076	0.003527
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03721	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)	-0.01997	0.02484	-0.804	3600	0.4215	-0.08971	0.04977
fixed	NA	birth_order	0.0001248	0.0003922	0.3183	3600	0.7503	-0.0009761	0.001226
fixed	NA	poly(age, 3, raw = TRUE)1	0.002292	0.00267	0.8585	3600	0.3907	-0.005203	0.009788
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00007255	0.00009151	-0.7927	3600	0.428	-0.0003294	0.0001843
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000007088	0.000001004	0.7062	3600	0.4801	-0.000002109	0.000003526
fixed	NA	male	0.001304	0.001257	1.038	3600	0.2994	-0.002224	0.004832
fixed	NA	sibling_count3	-0.002125	0.001981	-1.073	3600	0.2834	-0.007685	0.003435
fixed	NA	sibling_count4	-0.003256	0.002098	-1.552	3600	0.1207	-0.009145	0.002632
fixed	NA	sibling_count5	-0.001071	0.002431	-0.4406	3600	0.6596	-0.007896	0.005754
fixed	NA	sibling_count>5	-0.00248	0.002422	-1.024	3600	0.3061	-0.00928	0.00432
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03721	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)	-0.01926	0.02486	-0.7748	3596	0.4385	-0.08904	0.05052
fixed	NA	poly(age, 3, raw = TRUE)1	0.002317	0.00267	0.8677	3596	0.3856	-0.005178	0.009812
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00007222	0.00009152	-0.7891	3596	0.4301	-0.0003291	0.0001847
fixed	NA	poly(age, 3, raw = TRUE)3	0.000000692	0.000001004	0.6892	3596	0.4907	-0.000002126	0.00000351
fixed	NA	male	0.001266	0.001257	1.008	3596	0.3137	-0.002262	0.004794
fixed	NA	sibling_count3	-0.00148	0.002025	-0.7309	3596	0.4649	-0.007163	0.004203
fixed	NA	sibling_count4	-0.002126	0.002182	-0.9744	3596	0.3299	-0.008251	0.003999
fixed	NA	sibling_count5	0.0004233	0.002547	0.1662	3596	0.868	-0.006726	0.007573
fixed	NA	sibling_count>5	-0.001472	0.002497	-0.5893	3596	0.5557	-0.008482	0.005538
fixed	NA	birth_order_nonlinear2	-0.003103	0.001663	-1.866	3596	0.06216	-0.007772	0.001566
fixed	NA	birth_order_nonlinear3	-0.002762	0.00196	-1.409	3596	0.1589	-0.008263	0.00274
fixed	NA	birth_order_nonlinear4	-0.003046	0.002457	-1.239	3596	0.2152	-0.009943	0.003852
fixed	NA	birth_order_nonlinear5	-0.003403	0.003029	-1.123	3596	0.2613	-0.0119	0.005099
fixed	NA	birth_order_nonlinear>5	0.00008479	0.002932	0.02891	3596	0.9769	-0.008147	0.008316
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03721	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)	-0.01999	0.02495	-0.8009	3586	0.4232	-0.09004	0.05006
fixed	NA	poly(age, 3, raw = TRUE)1	0.002455	0.002681	0.9155	3586	0.36	-0.005072	0.009981
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00007656	0.00009193	-0.8328	3586	0.405	-0.0003346	0.0001815
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000007349	0.000001009	0.7286	3586	0.4663	-0.000002097	0.000003566
fixed	NA	male	0.00125	0.001259	0.9929	3586	0.3208	-0.002285	0.004786
fixed	NA	count_birth_order2/2	-0.004988	0.003173	-1.572	3586	0.116	-0.01389	0.003918
fixed	NA	count_birth_order1/3	-0.002318	0.002649	-0.8749	3586	0.3817	-0.009754	0.005119
fixed	NA	count_birth_order2/3	-0.00488	0.002948	-1.655	3586	0.09796	-0.01315	0.003395
fixed	NA	count_birth_order3/3	-0.004906	0.003177	-1.544	3586	0.1226	-0.01382	0.004012
fixed	NA	count_birth_order1/4	-0.004633	0.00311	-1.49	3586	0.1363	-0.01336	0.004095
fixed	NA	count_birth_order2/4	-0.004836	0.003269	-1.479	3586	0.1392	-0.01401	0.00434
fixed	NA	count_birth_order3/4	-0.004774	0.003394	-1.407	3586	0.1596	-0.0143	0.004752
fixed	NA	count_birth_order4/4	-0.005074	0.003687	-1.376	3586	0.1689	-0.01542	0.005276
fixed	NA	count_birth_order1/5	0.00475	0.004066	1.168	3586	0.2427	-0.006662	0.01616
fixed	NA	count_birth_order2/5	-0.004579	0.004544	-1.008	3586	0.3136	-0.01734	0.008176
fixed	NA	count_birth_order3/5	-0.004708	0.004432	-1.062	3586	0.2882	-0.01715	0.007733
fixed	NA	count_birth_order4/5	-0.005011	0.004267	-1.174	3586	0.2403	-0.01699	0.006967
fixed	NA	count_birth_order5/5	-0.005039	0.004533	-1.111	3586	0.2665	-0.01776	0.007687
fixed	NA	count_birth_order1/>5	-0.004509	0.003959	-1.139	3586	0.2548	-0.01562	0.006604
fixed	NA	count_birth_order2/>5	-0.004502	0.004007	-1.124	3586	0.2613	-0.01575	0.006746
fixed	NA	count_birth_order3/>5	-0.00464	0.003827	-1.212	3586	0.2255	-0.01538	0.006103
fixed	NA	count_birth_order4/>5	-0.00463	0.003846	-1.204	3586	0.2287	-0.01543	0.006166
fixed	NA	count_birth_order5/>5	-0.00472	0.003611	-1.307	3586	0.1912	-0.01486	0.005415
fixed	NA	count_birth_order>5/>5	-0.002027	0.002777	-0.7299	3586	0.4655	-0.009823	0.005769
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.03723	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)
11	-13505	-13437	6763	-13527	NA	NA	NA
12	-13503	-13429	6763	-13527	0.1016	1	0.75
16	-13500	-13401	6766	-13532	5.511	4	0.2388
26	-13485	-13324	6768	-13537	4.409	10	0.927

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)	0.01323	0.0289	0.4577	9429	0.6472	-0.0679	0.09435
fixed	NA	poly(age, 3, raw = TRUE)1	0.0002009	0.002584	0.07776	9336	0.938	-0.007053	0.007455
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001341	0.0000723	0.1854	9207	0.8529	-0.0001895	0.0002163
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000002622	0.0000006399	-0.4098	9080	0.682	-0.000002058	0.000001534
fixed	NA	male	0.00005814	0.002704	0.02151	9745	0.9828	-0.007531	0.007647
fixed	NA	sibling_count3	-0.006514	0.005475	-1.19	7729	0.2342	-0.02188	0.008854
fixed	NA	sibling_count4	0.000643	0.005507	0.1168	7189	0.9071	-0.01482	0.0161
fixed	NA	sibling_count5	-0.01138	0.005702	-1.996	6635	0.04598	-0.02739	0.004625
fixed	NA	sibling_count>5	-0.007491	0.004458	-1.68	7477	0.09295	-0.02001	0.005024
ran_pars	mother_pidlink	sd__(Intercept)	0.02111	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1299	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)	0.01323	0.0289	0.4578	9428	0.6471	-0.0679	0.09436
fixed	NA	birth_order	0.00004661	0.0005342	0.08725	7243	0.9305	-0.001453	0.001546
fixed	NA	poly(age, 3, raw = TRUE)1	0.0001884	0.002588	0.07278	9324	0.942	-0.007077	0.007454
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001385	0.00007248	0.191	9168	0.8485	-0.0001896	0.0002173
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000002661	0.0000006415	-0.4149	9029	0.6783	-0.000002067	0.000001534
fixed	NA	male	0.00005681	0.002704	0.02101	9744	0.9832	-0.007533	0.007647
fixed	NA	sibling_count3	-0.006527	0.005477	-1.192	7738	0.2334	-0.0219	0.008848
fixed	NA	sibling_count4	0.000612	0.005519	0.1109	7229	0.9117	-0.01488	0.0161
fixed	NA	sibling_count5	-0.01143	0.005733	-1.994	6708	0.04618	-0.02753	0.004661
fixed	NA	sibling_count>5	-0.007659	0.004856	-1.577	8054	0.1148	-0.02129	0.005971
ran_pars	mother_pidlink	sd__(Intercept)	0.02113	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1299	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)	0.01097	0.02895	0.3791	9435	0.7047	-0.07029	0.09224
fixed	NA	poly(age, 3, raw = TRUE)1	0.0002738	0.002591	0.1057	9329	0.9159	-0.006999	0.007547
fixed	NA	poly(age, 3, raw = TRUE)2	0.000009056	0.00007253	0.1249	9175	0.9006	-0.0001945	0.0002126
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000002072	0.0000006418	-0.3228	9033	0.7469	-0.000002009	0.000001594
fixed	NA	male	0.00005961	0.002704	0.02205	9740	0.9824	-0.007531	0.00765
fixed	NA	sibling_count3	-0.006954	0.005568	-1.249	7978	0.2117	-0.02258	0.008675
fixed	NA	sibling_count4	0.0003152	0.00569	0.0554	7705	0.9558	-0.01566	0.01629
fixed	NA	sibling_count5	-0.01083	0.005956	-1.819	7339	0.069	-0.02755	0.005886
fixed	NA	sibling_count>5	-0.005929	0.005111	-1.16	8707	0.2461	-0.02027	0.008417
fixed	NA	birth_order_nonlinear2	0.006418	0.003984	1.611	9149	0.1073	-0.004766	0.0176
fixed	NA	birth_order_nonlinear3	0.003461	0.004631	0.7474	9088	0.4549	-0.009538	0.01646
fixed	NA	birth_order_nonlinear4	0.001524	0.005203	0.2928	9196	0.7696	-0.01308	0.01613
fixed	NA	birth_order_nonlinear5	-0.002664	0.005841	-0.456	9273	0.6484	-0.01906	0.01373
fixed	NA	birth_order_nonlinear>5	-0.0001668	0.004776	-0.03492	9649	0.9721	-0.01357	0.01324
ran_pars	mother_pidlink	sd__(Intercept)	0.02114	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1299	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)	0.008777	0.02906	0.302	9441	0.7627	-0.0728	0.09035
fixed	NA	poly(age, 3, raw = TRUE)1	0.0003881	0.002593	0.1496	9319	0.8811	-0.006892	0.007668
fixed	NA	poly(age, 3, raw = TRUE)2	0.000006036	0.00007257	0.08317	9164	0.9337	-0.0001977	0.0002097
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000001841	0.0000006421	-0.2867	9020	0.7743	-0.000001986	0.000001618
fixed	NA	male	-0.0001087	0.002705	-0.04017	9730	0.968	-0.007702	0.007485
fixed	NA	count_birth_order2/2	0.009253	0.00795	1.164	8855	0.2445	-0.01306	0.03157
fixed	NA	count_birth_order1/3	-0.002485	0.007543	-0.3295	9723	0.7418	-0.02366	0.01869
fixed	NA	count_birth_order2/3	-0.003798	0.008393	-0.4525	9726	0.6509	-0.02736	0.01976
fixed	NA	count_birth_order3/3	-0.003063	0.009215	-0.3324	9726	0.7396	-0.02893	0.02281
fixed	NA	count_birth_order1/4	-0.006877	0.008305	-0.8281	9727	0.4076	-0.03019	0.01643
fixed	NA	count_birth_order2/4	0.02091	0.008908	2.347	9725	0.01892	-0.004094	0.04591
fixed	NA	count_birth_order3/4	0.001834	0.009395	0.1952	9726	0.8452	-0.02454	0.02821
fixed	NA	count_birth_order4/4	0.002255	0.01012	0.2229	9725	0.8236	-0.02614	0.03065
fixed	NA	count_birth_order1/5	-0.005294	0.009369	-0.5651	9729	0.572	-0.03159	0.02101
fixed	NA	count_birth_order2/5	-0.01186	0.009948	-1.192	9729	0.2334	-0.03978	0.01607
fixed	NA	count_birth_order3/5	-0.01047	0.01047	-1	9729	0.3173	-0.03985	0.01891
fixed	NA	count_birth_order4/5	0.008094	0.01105	0.7322	9730	0.4641	-0.02293	0.03912
fixed	NA	count_birth_order5/5	-0.01984	0.01107	-1.793	9729	0.07308	-0.05092	0.01123
fixed	NA	count_birth_order1/>5	-0.003349	0.007249	-0.462	9729	0.6441	-0.0237	0.017
fixed	NA	count_birth_order2/>5	-0.0008831	0.007537	-0.1172	9730	0.9067	-0.02204	0.02027
fixed	NA	count_birth_order3/>5	0.001765	0.007461	0.2366	9730	0.813	-0.01918	0.02271
fixed	NA	count_birth_order4/>5	-0.00785	0.007308	-1.074	9729	0.2827	-0.02836	0.01266
fixed	NA	count_birth_order5/>5	-0.005377	0.007388	-0.7278	9730	0.4667	-0.02612	0.01536
fixed	NA	count_birth_order>5/>5	-0.005087	0.005909	-0.861	9032	0.3893	-0.02167	0.0115
ran_pars	mother_pidlink	sd__(Intercept)	0.02122	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1299	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)
11	-11872	-11793	5947	-11894	NA	NA	NA
12	-11870	-11783	5947	-11894	0.007754	1	0.9298
16	-11866	-11751	5949	-11898	4.007	4	0.405
26	-11858	-11671	5955	-11910	12.21	10	0.271

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)	-0.06892	0.08321	-0.8282	3661	0.4076	-0.3025	0.1647
fixed	NA	poly(age, 3, raw = TRUE)1	0.009208	0.008926	1.032	3660	0.3023	-0.01585	0.03426
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003094	0.0003058	-1.012	3659	0.3117	-0.001168	0.0005489
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003375	0.000003352	1.007	3657	0.314	-0.000006033	0.00001278
fixed	NA	male	-0.003225	0.004207	-0.7666	3664	0.4434	-0.01503	0.008584
fixed	NA	sibling_count3	-0.004733	0.006873	-0.6886	3135	0.4911	-0.02403	0.01456
fixed	NA	sibling_count4	0.0002426	0.007083	0.03425	2921	0.9727	-0.01964	0.02013
fixed	NA	sibling_count5	-0.003574	0.007875	-0.4539	2600	0.65	-0.02568	0.01853
fixed	NA	sibling_count>5	0.000262	0.006798	0.03854	2552	0.9693	-0.01882	0.01935
ran_pars	mother_pidlink	sd__(Intercept)	0.02884	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1224	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)	-0.0693	0.08324	-0.8326	3659	0.4051	-0.3029	0.1643
fixed	NA	birth_order	-0.0003813	0.001296	-0.2942	3433	0.7686	-0.00402	0.003257
fixed	NA	poly(age, 3, raw = TRUE)1	0.009293	0.008932	1.04	3659	0.2982	-0.01578	0.03436
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003114	0.0003059	-1.018	3658	0.3087	-0.00117	0.0005472
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003381	0.000003352	1.009	3656	0.3132	-0.000006029	0.00001279
fixed	NA	male	-0.00321	0.004208	-0.7627	3663	0.4457	-0.01502	0.008602
fixed	NA	sibling_count3	-0.004544	0.006904	-0.6581	3134	0.5105	-0.02392	0.01484
fixed	NA	sibling_count4	0.0006594	0.007225	0.09126	2915	0.9273	-0.01962	0.02094
fixed	NA	sibling_count5	-0.002889	0.008215	-0.3516	2625	0.7251	-0.02595	0.02017
fixed	NA	sibling_count>5	0.001623	0.008225	0.1974	2655	0.8435	-0.02146	0.02471
ran_pars	mother_pidlink	sd__(Intercept)	0.02889	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1224	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)	-0.07098	0.08333	-0.8518	3655	0.3944	-0.3049	0.1629
fixed	NA	poly(age, 3, raw = TRUE)1	0.00929	0.008936	1.04	3655	0.2986	-0.01579	0.03437
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003122	0.0003061	-1.02	3654	0.3078	-0.001171	0.000547
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003395	0.000003355	1.012	3653	0.3116	-0.000006022	0.00001281
fixed	NA	male	-0.003165	0.00421	-0.7517	3659	0.4523	-0.01498	0.008654
fixed	NA	sibling_count3	-0.00357	0.007046	-0.5067	3210	0.6124	-0.02335	0.01621
fixed	NA	sibling_count4	0.002033	0.007502	0.271	3076	0.7864	-0.01902	0.02309
fixed	NA	sibling_count5	-0.001211	0.00862	-0.1405	2875	0.8883	-0.02541	0.02299
fixed	NA	sibling_count>5	0.003208	0.008457	0.3793	2803	0.7045	-0.02053	0.02695
fixed	NA	birth_order_nonlinear2	0.004487	0.005605	0.8006	3363	0.4234	-0.01125	0.02022
fixed	NA	birth_order_nonlinear3	-0.004523	0.006574	-0.688	3425	0.4915	-0.02297	0.01393
fixed	NA	birth_order_nonlinear4	-0.001963	0.00802	-0.2447	3480	0.8067	-0.02448	0.02055
fixed	NA	birth_order_nonlinear5	-0.001521	0.009835	-0.1547	3497	0.8771	-0.02913	0.02609
fixed	NA	birth_order_nonlinear>5	-0.002346	0.009645	-0.2432	3610	0.8078	-0.02942	0.02473
ran_pars	mother_pidlink	sd__(Intercept)	0.02914	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1224	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)	-0.07149	0.08369	-0.8543	3645	0.393	-0.3064	0.1634
fixed	NA	poly(age, 3, raw = TRUE)1	0.009321	0.008976	1.038	3645	0.2992	-0.01588	0.03452
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000314	0.0003075	-1.021	3644	0.3074	-0.001177	0.0005493
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003412	0.000003372	1.012	3642	0.3117	-0.000006053	0.00001288
fixed	NA	male	-0.002905	0.004218	-0.6887	3649	0.4911	-0.01475	0.008936
fixed	NA	count_birth_order2/2	0.005885	0.01094	0.5379	3367	0.5907	-0.02483	0.0366
fixed	NA	count_birth_order1/3	-0.004307	0.009118	-0.4724	3648	0.6367	-0.0299	0.02129
fixed	NA	count_birth_order2/3	0.001187	0.01014	0.1171	3650	0.9068	-0.02727	0.02965
fixed	NA	count_birth_order3/3	-0.005007	0.01105	-0.4533	3650	0.6504	-0.03601	0.026
fixed	NA	count_birth_order1/4	0.0067	0.01046	0.6405	3649	0.5219	-0.02267	0.03607
fixed	NA	count_birth_order2/4	0.005103	0.01109	0.4601	3650	0.6455	-0.02603	0.03624
fixed	NA	count_birth_order3/4	0.001785	0.0115	0.1551	3649	0.8767	-0.03051	0.03408
fixed	NA	count_birth_order4/4	-0.008181	0.01232	-0.6643	3649	0.5065	-0.04275	0.02639
fixed	NA	count_birth_order1/5	-0.005837	0.01378	-0.4236	3650	0.6719	-0.04452	0.03285
fixed	NA	count_birth_order2/5	0.01789	0.01487	1.203	3649	0.2291	-0.02385	0.05963
fixed	NA	count_birth_order3/5	-0.01558	0.01414	-1.102	3648	0.2705	-0.05526	0.0241
fixed	NA	count_birth_order4/5	-0.006235	0.01379	-0.4522	3647	0.6512	-0.04494	0.03247
fixed	NA	count_birth_order5/5	0.005751	0.01451	0.3963	3646	0.6919	-0.03499	0.04649
fixed	NA	count_birth_order1/>5	0.005701	0.01305	0.4368	3648	0.6623	-0.03093	0.04233
fixed	NA	count_birth_order2/>5	0.0003942	0.01316	0.02996	3650	0.9761	-0.03654	0.03733
fixed	NA	count_birth_order3/>5	-0.001544	0.01284	-0.1203	3649	0.9043	-0.03759	0.0345
fixed	NA	count_birth_order4/>5	0.01352	0.01257	1.076	3647	0.2821	-0.02176	0.04881
fixed	NA	count_birth_order5/>5	-0.002532	0.01201	-0.2108	3648	0.8331	-0.03626	0.03119
fixed	NA	count_birth_order>5/>5	0.001374	0.009344	0.147	3463	0.8831	-0.02485	0.0276
ran_pars	mother_pidlink	sd__(Intercept)	0.02937	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1224	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)
11	-4799	-4731	2410	-4821	NA	NA	NA
12	-4797	-4723	2411	-4821	0.08637	1	0.7688
16	-4791	-4692	2411	-4823	1.815	4	0.7697
26	-4777	-4615	2414	-4829	5.762	10	0.8349

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)	-0.07294	0.08327	-0.8759	3684	0.3811	-0.3067	0.1608
fixed	NA	poly(age, 3, raw = TRUE)1	0.009914	0.00894	1.109	3684	0.2676	-0.01518	0.03501
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003348	0.0003063	-1.093	3683	0.2745	-0.001195	0.0005251
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003659	0.000003359	1.089	3680	0.276	-0.000005769	0.00001309
fixed	NA	male	-0.003755	0.004214	-0.8909	3688	0.373	-0.01558	0.008075
fixed	NA	sibling_count3	-0.005675	0.007576	-0.7491	3192	0.4538	-0.02694	0.01559
fixed	NA	sibling_count4	-0.005706	0.007633	-0.7476	3051	0.4548	-0.02713	0.01572
fixed	NA	sibling_count5	-0.00168	0.008027	-0.2093	2841	0.8342	-0.02421	0.02085
fixed	NA	sibling_count>5	-0.00157	0.007039	-0.2231	2877	0.8235	-0.02133	0.01819
ran_pars	mother_pidlink	sd__(Intercept)	0.02896	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.123	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)	-0.07311	0.08329	-0.8777	3683	0.3801	-0.3069	0.1607
fixed	NA	birth_order	-0.0002085	0.001148	-0.1815	3335	0.856	-0.003432	0.003015
fixed	NA	poly(age, 3, raw = TRUE)1	0.009956	0.008945	1.113	3682	0.2658	-0.01515	0.03506
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003358	0.0003064	-1.096	3681	0.2733	-0.001196	0.0005244
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000366	0.000003359	1.09	3679	0.2759	-0.000005769	0.00001309
fixed	NA	male	-0.003746	0.004215	-0.8887	3687	0.3742	-0.01558	0.008086
fixed	NA	sibling_count3	-0.005571	0.007599	-0.7331	3188	0.4636	-0.0269	0.01576
fixed	NA	sibling_count4	-0.005497	0.007721	-0.7119	3038	0.4766	-0.02717	0.01618
fixed	NA	sibling_count5	-0.001332	0.008257	-0.1613	2837	0.8719	-0.02451	0.02184
fixed	NA	sibling_count>5	-0.0008368	0.008118	-0.1031	2879	0.9179	-0.02362	0.02195
ran_pars	mother_pidlink	sd__(Intercept)	0.02901	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1231	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)	-0.07406	0.08335	-0.8886	3679	0.3743	-0.308	0.1599
fixed	NA	poly(age, 3, raw = TRUE)1	0.009711	0.008946	1.086	3679	0.2778	-0.0154	0.03482
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0003301	0.0003065	-1.077	3678	0.2815	-0.001191	0.0005302
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003623	0.000003361	1.078	3676	0.281	-0.00000581	0.00001306
fixed	NA	male	-0.003724	0.004215	-0.8835	3683	0.377	-0.01556	0.008108
fixed	NA	sibling_count3	-0.005213	0.00773	-0.6743	3246	0.5001	-0.02691	0.01649
fixed	NA	sibling_count4	-0.005691	0.007954	-0.7155	3154	0.4744	-0.02802	0.01664
fixed	NA	sibling_count5	-0.0003466	0.008631	-0.04016	3035	0.968	-0.02457	0.02388
fixed	NA	sibling_count>5	0.0007911	0.008365	0.09457	3023	0.9247	-0.02269	0.02427
fixed	NA	birth_order_nonlinear2	0.011	0.005694	1.933	3397	0.05337	-0.00498	0.02699
fixed	NA	birth_order_nonlinear3	-0.001224	0.006636	-0.1845	3474	0.8536	-0.01985	0.0174
fixed	NA	birth_order_nonlinear4	0.005638	0.007857	0.7176	3538	0.4731	-0.01642	0.02769
fixed	NA	birth_order_nonlinear5	-0.003972	0.009571	-0.415	3542	0.6782	-0.03084	0.02289
fixed	NA	birth_order_nonlinear>5	-0.00001819	0.008764	-0.002076	3603	0.9983	-0.02462	0.02458
ran_pars	mother_pidlink	sd__(Intercept)	0.0295	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1229	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)	-0.06463	0.08354	-0.7736	3669	0.4392	-0.2991	0.1699
fixed	NA	poly(age, 3, raw = TRUE)1	0.008684	0.008969	0.9682	3669	0.333	-0.01649	0.03386
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002926	0.0003074	-0.9519	3667	0.3412	-0.001155	0.0005702
fixed	NA	poly(age, 3, raw = TRUE)3	0.000003186	0.000003371	0.9452	3665	0.3446	-0.000006276	0.00001265
fixed	NA	male	-0.003631	0.004221	-0.8603	3672	0.3897	-0.01548	0.008218
fixed	NA	count_birth_order2/2	0.009313	0.01203	0.7738	3441	0.4391	-0.02447	0.04309
fixed	NA	count_birth_order1/3	-0.01236	0.01012	-1.221	3672	0.2222	-0.04077	0.01605
fixed	NA	count_birth_order2/3	0.0116	0.01102	1.052	3673	0.2927	-0.01935	0.04255
fixed	NA	count_birth_order3/3	-0.003213	0.01222	-0.2628	3674	0.7927	-0.03752	0.0311
fixed	NA	count_birth_order1/4	-0.01075	0.01098	-0.9789	3672	0.3277	-0.04159	0.02008
fixed	NA	count_birth_order2/4	0.01045	0.01158	0.9025	3674	0.3668	-0.02205	0.04294
fixed	NA	count_birth_order3/4	-0.002847	0.01253	-0.2271	3674	0.8203	-0.03802	0.03233
fixed	NA	count_birth_order4/4	-0.007088	0.01361	-0.5207	3673	0.6026	-0.0453	0.03113
fixed	NA	count_birth_order1/5	0.01516	0.01328	1.141	3674	0.2538	-0.02212	0.05243
fixed	NA	count_birth_order2/5	0.008984	0.01362	0.6598	3674	0.5094	-0.02924	0.04721
fixed	NA	count_birth_order3/5	-0.01683	0.01401	-1.201	3673	0.2298	-0.05617	0.0225
fixed	NA	count_birth_order4/5	-0.007029	0.01427	-0.4927	3672	0.6223	-0.04708	0.03302
fixed	NA	count_birth_order5/5	0.003691	0.01449	0.2548	3670	0.7989	-0.03697	0.04436
fixed	NA	count_birth_order1/>5	0.004812	0.01198	0.4017	3671	0.6879	-0.02881	0.03843
fixed	NA	count_birth_order2/>5	-0.003156	0.01266	-0.2493	3674	0.8032	-0.03869	0.03238
fixed	NA	count_birth_order3/>5	0.0007469	0.0122	0.06123	3674	0.9512	-0.03349	0.03499
fixed	NA	count_birth_order4/>5	0.01669	0.01185	1.408	3673	0.1592	-0.01658	0.04995
fixed	NA	count_birth_order5/>5	-0.009497	0.01255	-0.7565	3670	0.4494	-0.04473	0.02574
fixed	NA	count_birth_order>5/>5	0.000137	0.009443	0.01451	3530	0.9884	-0.02637	0.02664
ran_pars	mother_pidlink	sd__(Intercept)	0.03021	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1227	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)
11	-4793	-4725	2408	-4815	NA	NA	NA
12	-4791	-4717	2408	-4815	0.03277	1	0.8563
16	-4789	-4689	2410	-4821	5.725	4	0.2207
26	-4781	-4619	2416	-4833	11.8	10	0.2989

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)	-0.0498	0.0826	-0.603	3596	0.5466	-0.2817	0.182
fixed	NA	poly(age, 3, raw = TRUE)1	0.007002	0.008874	0.789	3596	0.4302	-0.01791	0.03191
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002367	0.0003043	-0.778	3594	0.4366	-0.001091	0.0006174
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002649	0.000003339	0.7933	3592	0.4277	-0.000006724	0.00001202
fixed	NA	male	-0.002382	0.004174	-0.5707	3600	0.5683	-0.0141	0.009334
fixed	NA	sibling_count3	-0.00575	0.00661	-0.8699	3113	0.3844	-0.02431	0.0128
fixed	NA	sibling_count4	0.002621	0.006909	0.3793	2913	0.7045	-0.01677	0.02202
fixed	NA	sibling_count5	-0.001736	0.007888	-0.22	2508	0.8259	-0.02388	0.02041
fixed	NA	sibling_count>5	-0.001253	0.006699	-0.187	2492	0.8517	-0.02006	0.01755
ran_pars	mother_pidlink	sd__(Intercept)	0.02772	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1205	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)	-0.04939	0.08263	-0.5978	3595	0.55	-0.2813	0.1825
fixed	NA	birth_order	0.0003003	0.001312	0.2289	3402	0.819	-0.003383	0.003984
fixed	NA	poly(age, 3, raw = TRUE)1	0.006922	0.008882	0.7793	3593	0.4358	-0.01801	0.03186
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002347	0.0003045	-0.7709	3592	0.4408	-0.001089	0.0006199
fixed	NA	poly(age, 3, raw = TRUE)3	0.00000264	0.00000334	0.7903	3590	0.4294	-0.000006736	0.00001201
fixed	NA	male	-0.002386	0.004174	-0.5716	3599	0.5676	-0.0141	0.009331
fixed	NA	sibling_count3	-0.005903	0.006644	-0.8883	3110	0.3744	-0.02455	0.01275
fixed	NA	sibling_count4	0.002296	0.007054	0.3255	2911	0.7449	-0.01751	0.0221
fixed	NA	sibling_count5	-0.002258	0.008213	-0.2749	2532	0.7834	-0.02531	0.0208
fixed	NA	sibling_count>5	-0.002324	0.008174	-0.2844	2644	0.7762	-0.02527	0.02062
ran_pars	mother_pidlink	sd__(Intercept)	0.02771	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1205	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)	-0.05159	0.08271	-0.6238	3591	0.5328	-0.2837	0.1806
fixed	NA	poly(age, 3, raw = TRUE)1	0.007037	0.008885	0.792	3590	0.4284	-0.0179	0.03198
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002395	0.0003046	-0.7862	3589	0.4318	-0.001094	0.0006156
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000027	0.000003342	0.8077	3587	0.4193	-0.000006682	0.00001208
fixed	NA	male	-0.002368	0.004176	-0.567	3595	0.5708	-0.01409	0.009354
fixed	NA	sibling_count3	-0.00439	0.006788	-0.6468	3184	0.5178	-0.02344	0.01466
fixed	NA	sibling_count4	0.00465	0.007327	0.6346	3063	0.5257	-0.01592	0.02522
fixed	NA	sibling_count5	0.00009162	0.008584	0.01067	2760	0.9915	-0.02401	0.02419
fixed	NA	sibling_count>5	-0.0008097	0.008416	-0.09621	2796	0.9234	-0.02443	0.02281
fixed	NA	birth_order_nonlinear2	0.005265	0.005486	0.9597	3320	0.3373	-0.01014	0.02067
fixed	NA	birth_order_nonlinear3	-0.005105	0.006471	-0.7888	3379	0.4303	-0.02327	0.01306
fixed	NA	birth_order_nonlinear4	-0.002657	0.008121	-0.3272	3434	0.7435	-0.02545	0.02014
fixed	NA	birth_order_nonlinear5	0.002499	0.01001	0.2497	3430	0.8029	-0.0256	0.0306
fixed	NA	birth_order_nonlinear>5	0.003725	0.009781	0.3809	3554	0.7033	-0.02373	0.03118
ran_pars	mother_pidlink	sd__(Intercept)	0.02781	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1205	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)	-0.05244	0.08302	-0.6316	3580	0.5277	-0.2855	0.1806
fixed	NA	poly(age, 3, raw = TRUE)1	0.007219	0.008922	0.8091	3579	0.4185	-0.01783	0.03226
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0002477	0.000306	-0.8097	3578	0.4182	-0.001107	0.0006111
fixed	NA	poly(age, 3, raw = TRUE)3	0.000002801	0.000003358	0.8341	3575	0.4043	-0.000006625	0.00001223
fixed	NA	male	-0.002176	0.004184	-0.5202	3585	0.603	-0.01392	0.009568
fixed	NA	count_birth_order2/2	0.004609	0.01046	0.4405	3320	0.6596	-0.02476	0.03398
fixed	NA	count_birth_order1/3	-0.004567	0.008804	-0.5187	3584	0.604	-0.02928	0.02015
fixed	NA	count_birth_order2/3	-0.002892	0.009793	-0.2953	3586	0.7678	-0.03038	0.0246
fixed	NA	count_birth_order3/3	-0.00515	0.01055	-0.4882	3586	0.6255	-0.03476	0.02446
fixed	NA	count_birth_order1/4	0.007362	0.01033	0.7125	3585	0.4762	-0.02164	0.03637
fixed	NA	count_birth_order2/4	0.01055	0.01086	0.972	3586	0.3311	-0.01993	0.04103
fixed	NA	count_birth_order3/4	0.00207	0.01127	0.1836	3585	0.8543	-0.02957	0.03371
fixed	NA	count_birth_order4/4	-0.007332	0.01224	-0.5988	3585	0.5494	-0.0417	0.02704
fixed	NA	count_birth_order1/5	-0.006338	0.01351	-0.4691	3586	0.639	-0.04426	0.03159
fixed	NA	count_birth_order2/5	0.02056	0.01509	1.362	3585	0.1732	-0.02181	0.06293
fixed	NA	count_birth_order3/5	-0.01572	0.01472	-1.068	3584	0.2855	-0.05704	0.02559
fixed	NA	count_birth_order4/5	-0.004808	0.01417	-0.3393	3583	0.7344	-0.04458	0.03496
fixed	NA	count_birth_order5/5	0.009342	0.01505	0.6207	3582	0.5349	-0.03291	0.05159
fixed	NA	count_birth_order1/>5	-0.001178	0.01317	-0.0895	3584	0.9287	-0.03814	0.03578
fixed	NA	count_birth_order2/>5	0.001312	0.01332	0.0985	3586	0.9215	-0.03607	0.0387
fixed	NA	count_birth_order3/>5	-0.009649	0.01272	-0.7588	3586	0.448	-0.04534	0.02605
fixed	NA	count_birth_order4/>5	0.007954	0.01277	0.6227	3583	0.5335	-0.0279	0.04381
fixed	NA	count_birth_order5/>5	-0.002177	0.01199	-0.1815	3584	0.856	-0.03584	0.03148
fixed	NA	count_birth_order>5/>5	0.002798	0.009292	0.3011	3378	0.7634	-0.02329	0.02888
ran_pars	mother_pidlink	sd__(Intercept)	0.02796	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1206	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)
11	-4839	-4771	2430	-4861	NA	NA	NA
12	-4837	-4762	2430	-4861	0.05301	1	0.8179
16	-4832	-4732	2432	-4864	2.872	4	0.5795
26	-4817	-4656	2434	-4869	5.404	10	0.8626

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)	-0.07441	0.09233	-0.8059	9530	0.4203	-0.3336	0.1848
fixed	NA	poly(age, 3, raw = TRUE)1	0.02539	0.008265	3.072	9465	0.002134	0.002188	0.04859
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006471	0.0002316	-2.795	9346	0.005207	-0.001297	0.000002882
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005081	0.000002052	2.476	9211	0.01331	-0.0000006795	0.00001084
fixed	NA	male	0.0594	0.008556	6.943	9661	4.073e-12	0.03539	0.08342
fixed	NA	sibling_count3	-0.007552	0.01779	-0.4245	7229	0.6712	-0.05748	0.04238
fixed	NA	sibling_count4	-0.02384	0.01795	-1.328	6797	0.1842	-0.07424	0.02655
fixed	NA	sibling_count5	-0.02626	0.01865	-1.407	6338	0.1593	-0.07862	0.02611
fixed	NA	sibling_count>5	-0.05315	0.0145	-3.664	7081	0.00025	-0.09386	-0.01243
ran_pars	mother_pidlink	sd__(Intercept)	0.1381	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3954	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)	-0.07441	0.09233	-0.8059	9528	0.4203	-0.3336	0.1848
fixed	NA	birth_order	0.0000267	0.001729	0.01544	8590	0.9877	-0.004828	0.004881
fixed	NA	poly(age, 3, raw = TRUE)1	0.02538	0.008279	3.066	9455	0.002179	0.00214	0.04862
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006469	0.0002322	-2.785	9308	0.005357	-0.001299	0.000005026
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005079	0.000002058	2.467	9156	0.01363	-0.0000006991	0.00001086
fixed	NA	male	0.0594	0.008556	6.943	9660	4.087e-12	0.03539	0.08342
fixed	NA	sibling_count3	-0.007559	0.01779	-0.4248	7240	0.671	-0.05751	0.04239
fixed	NA	sibling_count4	-0.02386	0.01799	-1.327	6843	0.1847	-0.07435	0.02663
fixed	NA	sibling_count5	-0.02628	0.01875	-1.402	6425	0.1609	-0.07891	0.02634
fixed	NA	sibling_count>5	-0.05324	0.01573	-3.386	7806	0.0007137	-0.09738	-0.009099
ran_pars	mother_pidlink	sd__(Intercept)	0.1381	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3954	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)	-0.07779	0.09248	-0.8411	9533	0.4003	-0.3374	0.1818
fixed	NA	poly(age, 3, raw = TRUE)1	0.02597	0.008287	3.134	9457	0.001729	0.002711	0.04923
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006675	0.0002324	-2.872	9313	0.004084	-0.00132	-0.00001518
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005269	0.000002059	2.558	9158	0.01053	-0.000000512	0.00001105
fixed	NA	male	0.05941	0.008557	6.943	9656	4.091e-12	0.03539	0.08343
fixed	NA	sibling_count3	-0.01047	0.01806	-0.58	7487	0.5619	-0.06116	0.04021
fixed	NA	sibling_count4	-0.02378	0.01848	-1.287	7308	0.1981	-0.07566	0.02809
fixed	NA	sibling_count5	-0.02538	0.01939	-1.309	7012	0.1906	-0.0798	0.02904
fixed	NA	sibling_count>5	-0.0482	0.01647	-2.927	8436	0.003436	-0.09444	-0.001969
fixed	NA	birth_order_nonlinear2	-0.0008122	0.01249	-0.06505	8957	0.9481	-0.03586	0.03423
fixed	NA	birth_order_nonlinear3	0.01115	0.0145	0.7694	8796	0.4417	-0.02954	0.05185
fixed	NA	birth_order_nonlinear4	-0.01657	0.0163	-1.016	8869	0.3094	-0.06233	0.02919
fixed	NA	birth_order_nonlinear5	-0.005199	0.01831	-0.2839	8915	0.7765	-0.0566	0.04621
fixed	NA	birth_order_nonlinear>5	-0.01029	0.01518	-0.6782	9740	0.4976	-0.0529	0.03231
ran_pars	mother_pidlink	sd__(Intercept)	0.1378	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3955	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)	-0.06935	0.09283	-0.7471	9535	0.455	-0.3299	0.1912
fixed	NA	poly(age, 3, raw = TRUE)1	0.02651	0.008296	3.195	9448	0.001401	0.003222	0.04979
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0006742	0.0002325	-2.899	9302	0.003748	-0.001327	-0.00002148
fixed	NA	poly(age, 3, raw = TRUE)3	0.000005249	0.00000206	2.548	9145	0.01087	-0.0000005347	0.00001103
fixed	NA	male	0.05988	0.008562	6.994	9646	2.849e-12	0.03585	0.08391
fixed	NA	count_birth_order2/2	-0.04629	0.02487	-1.861	8848	0.06278	-0.1161	0.02353
fixed	NA	count_birth_order1/3	-0.01612	0.02398	-0.6721	9657	0.5015	-0.08345	0.05121
fixed	NA	count_birth_order2/3	-0.02574	0.02667	-0.9651	9693	0.3345	-0.1006	0.04912
fixed	NA	count_birth_order3/3	-0.04184	0.02927	-1.429	9712	0.1529	-0.124	0.04032
fixed	NA	count_birth_order1/4	-0.05395	0.02639	-2.044	9695	0.04093	-0.128	0.02012
fixed	NA	count_birth_order2/4	-0.02768	0.0283	-0.978	9706	0.3281	-0.1071	0.05176
fixed	NA	count_birth_order3/4	-0.02782	0.02984	-0.9325	9718	0.3511	-0.1116	0.05593
fixed	NA	count_birth_order4/4	-0.05826	0.03211	-1.814	9726	0.06971	-0.1484	0.03189
fixed	NA	count_birth_order1/5	-0.05281	0.02975	-1.775	9720	0.07586	-0.1363	0.03069
fixed	NA	count_birth_order2/5	-0.02327	0.03158	-0.7369	9724	0.4612	-0.1119	0.06537
fixed	NA	count_birth_order3/5	-0.02847	0.03321	-0.8573	9729	0.3913	-0.1217	0.06476
fixed	NA	count_birth_order4/5	-0.09112	0.03505	-2.6	9727	0.009348	-0.1895	0.007271
fixed	NA	count_birth_order5/5	-0.03226	0.03512	-0.9184	9730	0.3584	-0.1309	0.06634
fixed	NA	count_birth_order1/>5	-0.08272	0.023	-3.596	9728	0.0003251	-0.1473	-0.01814
fixed	NA	count_birth_order2/>5	-0.06344	0.02391	-2.654	9730	0.007977	-0.1306	0.003668
fixed	NA	count_birth_order3/>5	-0.04458	0.02366	-1.884	9730	0.05959	-0.111	0.02184
fixed	NA	count_birth_order4/>5	-0.07335	0.02319	-3.163	9729	0.001565	-0.1384	-0.008259
fixed	NA	count_birth_order5/>5	-0.0759	0.02343	-3.239	9730	0.001205	-0.1417	-0.01012
fixed	NA	count_birth_order>5/>5	-0.07606	0.01898	-4.007	8923	0.00006187	-0.1293	-0.02278
ran_pars	mother_pidlink	sd__(Intercept)	0.1378	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3956	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)
11	10644	10723	-5311	10622	NA	NA	NA
12	10646	10732	-5311	10622	0.0002311	1	0.9879
16	10651	10766	-5309	10619	3.022	4	0.5542
26	10661	10848	-5305	10609	9.616	10	0.4748

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)	-0.5687	0.2886	-1.971	3661	0.04884	-1.379	0.2413
fixed	NA	poly(age, 3, raw = TRUE)1	0.0821	0.03095	2.653	3661	0.008023	-0.004781	0.169
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002522	0.00106	-2.378	3661	0.01744	-0.005498	0.0004544
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002507	0.00001162	2.157	3659	0.03108	-0.000007557	0.0000577
fixed	NA	male	0.05418	0.01459	3.715	3662	0.0002064	0.01324	0.09512
fixed	NA	sibling_count3	-0.03401	0.02387	-1.424	3039	0.1544	-0.101	0.03301
fixed	NA	sibling_count4	-0.04521	0.02461	-1.837	2803	0.06634	-0.1143	0.02388
fixed	NA	sibling_count5	-0.09774	0.02738	-3.57	2460	0.000364	-0.1746	-0.02089
fixed	NA	sibling_count>5	-0.08594	0.02364	-3.636	2414	0.0002831	-0.1523	-0.01959
ran_pars	mother_pidlink	sd__(Intercept)	0.1082	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4226	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)	-0.5687	0.2886	-1.97	3660	0.04887	-1.379	0.2415
fixed	NA	birth_order	-0.00005679	0.004499	-0.01262	3418	0.9899	-0.01269	0.01257
fixed	NA	poly(age, 3, raw = TRUE)1	0.08212	0.03097	2.651	3659	0.008057	-0.004829	0.1691
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002522	0.001061	-2.378	3659	0.01747	-0.0055	0.0004554
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002507	0.00001163	2.157	3657	0.0311	-0.000007561	0.0000577
fixed	NA	male	0.05418	0.01459	3.714	3661	0.0002069	0.01323	0.09514
fixed	NA	sibling_count3	-0.03398	0.02398	-1.417	3036	0.1566	-0.1013	0.03334
fixed	NA	sibling_count4	-0.04515	0.02511	-1.798	2796	0.07225	-0.1156	0.02533
fixed	NA	sibling_count5	-0.09764	0.02856	-3.419	2488	0.0006391	-0.1778	-0.01747
fixed	NA	sibling_count>5	-0.08574	0.02859	-2.999	2527	0.002739	-0.166	-0.005476
ran_pars	mother_pidlink	sd__(Intercept)	0.1083	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4226	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)	-0.5737	0.2889	-1.986	3656	0.04713	-1.385	0.2373
fixed	NA	poly(age, 3, raw = TRUE)1	0.08249	0.03098	2.662	3656	0.007795	-0.004485	0.1695
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002533	0.001061	-2.387	3655	0.01703	-0.005512	0.0004457
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002515	0.00001163	2.162	3654	0.03067	-0.000007502	0.00005781
fixed	NA	male	0.05423	0.01459	3.715	3657	0.0002059	0.01326	0.09519
fixed	NA	sibling_count3	-0.02672	0.02446	-1.092	3126	0.2748	-0.09537	0.04194
fixed	NA	sibling_count4	-0.03303	0.02605	-1.268	2977	0.2049	-0.1061	0.04009
fixed	NA	sibling_count5	-0.08304	0.02994	-2.773	2757	0.005585	-0.1671	0.001008
fixed	NA	sibling_count>5	-0.07479	0.02938	-2.546	2686	0.01096	-0.1573	0.007675
fixed	NA	birth_order_nonlinear2	0.004422	0.01941	0.2278	3302	0.8198	-0.05006	0.0589
fixed	NA	birth_order_nonlinear3	-0.03044	0.02277	-1.337	3372	0.1813	-0.09435	0.03346
fixed	NA	birth_order_nonlinear4	-0.02453	0.02778	-0.8831	3436	0.3772	-0.1025	0.05345
fixed	NA	birth_order_nonlinear5	-0.01353	0.03407	-0.3972	3455	0.6913	-0.1092	0.0821
fixed	NA	birth_order_nonlinear>5	-0.002097	0.03345	-0.06269	3611	0.95	-0.096	0.09181
ran_pars	mother_pidlink	sd__(Intercept)	0.1081	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4227	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)	-0.5355	0.2901	-1.846	3645	0.06495	-1.35	0.2787
fixed	NA	poly(age, 3, raw = TRUE)1	0.07959	0.03111	2.558	3645	0.01057	-0.007747	0.1669
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002426	0.001066	-2.276	3644	0.02293	-0.005418	0.0005666
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002391	0.00001169	2.046	3642	0.04087	-0.000008899	0.00005671
fixed	NA	male	0.05452	0.01462	3.73	3647	0.0001947	0.01349	0.09556
fixed	NA	count_birth_order2/2	-0.03903	0.03789	-1.03	3315	0.3031	-0.1454	0.06733
fixed	NA	count_birth_order1/3	-0.04971	0.03161	-1.573	3647	0.1158	-0.1384	0.039
fixed	NA	count_birth_order2/3	-0.01491	0.03514	-0.4244	3649	0.6713	-0.1135	0.08372
fixed	NA	count_birth_order3/3	-0.08276	0.03828	-2.162	3650	0.0307	-0.1902	0.0247
fixed	NA	count_birth_order1/4	-0.05126	0.03626	-1.414	3648	0.1576	-0.153	0.05053
fixed	NA	count_birth_order2/4	-0.05105	0.03844	-1.328	3650	0.1843	-0.159	0.05687
fixed	NA	count_birth_order3/4	-0.09079	0.03987	-2.277	3649	0.02283	-0.2027	0.02113
fixed	NA	count_birth_order4/4	-0.03882	0.04268	-0.9094	3649	0.3632	-0.1586	0.08099
fixed	NA	count_birth_order1/5	-0.1067	0.04777	-2.234	3650	0.02554	-0.2408	0.02737
fixed	NA	count_birth_order2/5	-0.08707	0.05153	-1.69	3648	0.0912	-0.2317	0.05759
fixed	NA	count_birth_order3/5	-0.1337	0.04899	-2.728	3648	0.006396	-0.2712	0.003856
fixed	NA	count_birth_order4/5	-0.1599	0.04779	-3.345	3646	0.0008298	-0.294	-0.02573
fixed	NA	count_birth_order5/5	-0.05661	0.0503	-1.126	3644	0.2604	-0.1978	0.08457
fixed	NA	count_birth_order1/>5	-0.09304	0.04523	-2.057	3648	0.03977	-0.22	0.03393
fixed	NA	count_birth_order2/>5	-0.07479	0.0456	-1.64	3650	0.101	-0.2028	0.0532
fixed	NA	count_birth_order3/>5	-0.08138	0.0445	-1.829	3648	0.06752	-0.2063	0.04353
fixed	NA	count_birth_order4/>5	-0.1182	0.04357	-2.712	3646	0.006714	-0.2404	0.004128
fixed	NA	count_birth_order5/>5	-0.1354	0.04163	-3.253	3646	0.001154	-0.2523	-0.01855
fixed	NA	count_birth_order>5/>5	-0.0913	0.03241	-2.817	3435	0.004868	-0.1823	-0.0003379
ran_pars	mother_pidlink	sd__(Intercept)	0.1074	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.423	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)
11	4337	4406	-2158	4315	NA	NA	NA
12	4339	4414	-2158	4315	0.00009047	1	0.9924
16	4344	4444	-2156	4312	2.997	4	0.5583
26	4357	4518	-2152	4305	7.716	10	0.6566

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)	-0.5662	0.2875	-1.97	3685	0.04896	-1.373	0.2407
fixed	NA	poly(age, 3, raw = TRUE)1	0.08105	0.03086	2.626	3685	0.008667	-0.005577	0.1677
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002488	0.001058	-2.353	3684	0.01867	-0.005457	0.00048
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002469	0.0000116	2.129	3682	0.03331	-0.000007861	0.00005723
fixed	NA	male	0.05379	0.01454	3.699	3686	0.0002198	0.01297	0.09462
fixed	NA	sibling_count3	-0.01975	0.0262	-0.7539	3108	0.4509	-0.09329	0.05379
fixed	NA	sibling_count4	-0.03216	0.0264	-1.218	2954	0.2233	-0.1063	0.04196
fixed	NA	sibling_count5	-0.07215	0.02778	-2.597	2729	0.00945	-0.1501	0.00583
fixed	NA	sibling_count>5	-0.07094	0.02436	-2.912	2772	0.003615	-0.1393	-0.002567
ran_pars	mother_pidlink	sd__(Intercept)	0.1094	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4225	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)	-0.5664	0.2875	-1.97	3684	0.04893	-1.373	0.2407
fixed	NA	birth_order	-0.0002095	0.00397	-0.05278	3318	0.9579	-0.01135	0.01093
fixed	NA	poly(age, 3, raw = TRUE)1	0.0811	0.03088	2.626	3683	0.008664	-0.005577	0.1678
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002489	0.001058	-2.353	3683	0.01866	-0.005459	0.0004799
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002469	0.0000116	2.129	3681	0.03332	-0.000007863	0.00005724
fixed	NA	male	0.0538	0.01455	3.699	3685	0.0002199	0.01297	0.09464
fixed	NA	sibling_count3	-0.01965	0.02628	-0.7476	3102	0.4547	-0.09341	0.05412
fixed	NA	sibling_count4	-0.03195	0.02671	-1.196	2940	0.2317	-0.1069	0.04302
fixed	NA	sibling_count5	-0.0718	0.02857	-2.513	2725	0.01204	-0.152	0.008414
fixed	NA	sibling_count>5	-0.0702	0.02809	-2.499	2777	0.01251	-0.1491	0.00865
ran_pars	mother_pidlink	sd__(Intercept)	0.1096	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4225	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)	-0.578	0.2878	-2.008	3680	0.04468	-1.386	0.2298
fixed	NA	poly(age, 3, raw = TRUE)1	0.08201	0.03089	2.655	3680	0.007962	-0.004692	0.1687
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002519	0.001058	-2.38	3680	0.01736	-0.005489	0.0004519
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002491	0.0000116	2.147	3678	0.03186	-0.000007659	0.00005749
fixed	NA	male	0.05398	0.01455	3.71	3681	0.0002105	0.01314	0.09482
fixed	NA	sibling_count3	-0.01423	0.02673	-0.5325	3168	0.5945	-0.08927	0.0608
fixed	NA	sibling_count4	-0.01948	0.02751	-0.7081	3066	0.4789	-0.09671	0.05775
fixed	NA	sibling_count5	-0.05724	0.02986	-1.917	2939	0.05532	-0.1411	0.02657
fixed	NA	sibling_count>5	-0.05202	0.02894	-1.798	2932	0.07236	-0.1333	0.02922
fixed	NA	birth_order_nonlinear2	0.01072	0.01963	0.5459	3341	0.5851	-0.04439	0.06582
fixed	NA	birth_order_nonlinear3	-0.02222	0.02288	-0.9713	3427	0.3315	-0.08645	0.042
fixed	NA	birth_order_nonlinear4	-0.03943	0.0271	-1.455	3502	0.1457	-0.1155	0.03663
fixed	NA	birth_order_nonlinear5	-0.007367	0.03301	-0.2232	3504	0.8234	-0.1	0.08529
fixed	NA	birth_order_nonlinear>5	-0.01766	0.03028	-0.5834	3604	0.5597	-0.1026	0.06732
ran_pars	mother_pidlink	sd__(Intercept)	0.1108	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4222	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)	-0.512	0.2882	-1.776	3669	0.07576	-1.321	0.2971
fixed	NA	poly(age, 3, raw = TRUE)1	0.07721	0.03094	2.495	3669	0.01263	-0.009649	0.1641
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002343	0.001061	-2.209	3668	0.02725	-0.005319	0.0006344
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002292	0.00001163	1.97	3666	0.04887	-0.000009731	0.00005556
fixed	NA	male	0.05323	0.01456	3.656	3671	0.0002601	0.01236	0.09411
fixed	NA	count_birth_order2/2	-0.06461	0.04148	-1.558	3403	0.1194	-0.1811	0.05183
fixed	NA	count_birth_order1/3	-0.0366	0.03492	-1.048	3670	0.2946	-0.1346	0.06142
fixed	NA	count_birth_order2/3	-0.01324	0.03804	-0.348	3673	0.7279	-0.12	0.09353
fixed	NA	count_birth_order3/3	-0.08953	0.04217	-2.123	3674	0.0338	-0.2079	0.02884
fixed	NA	count_birth_order1/4	-0.08289	0.0379	-2.187	3672	0.02879	-0.1893	0.02349
fixed	NA	count_birth_order2/4	0.00127	0.03994	0.03181	3674	0.9746	-0.1108	0.1134
fixed	NA	count_birth_order3/4	-0.08315	0.04323	-1.923	3673	0.05453	-0.2045	0.03821
fixed	NA	count_birth_order4/4	-0.04866	0.04696	-1.036	3672	0.3002	-0.1805	0.08316
fixed	NA	count_birth_order1/5	-0.06946	0.04581	-1.516	3674	0.1296	-0.1981	0.05914
fixed	NA	count_birth_order2/5	-0.1132	0.04698	-2.409	3674	0.01604	-0.245	0.01869
fixed	NA	count_birth_order3/5	-0.1311	0.04834	-2.712	3672	0.006716	-0.2668	0.004586
fixed	NA	count_birth_order4/5	-0.1211	0.04921	-2.46	3671	0.01395	-0.2592	0.0171
fixed	NA	count_birth_order5/5	-0.03203	0.04997	-0.641	3668	0.5216	-0.1723	0.1082
fixed	NA	count_birth_order1/>5	-0.08991	0.04133	-2.176	3670	0.02964	-0.2059	0.02609
fixed	NA	count_birth_order2/>5	-0.04979	0.04368	-1.14	3674	0.2543	-0.1724	0.0728
fixed	NA	count_birth_order3/>5	-0.04301	0.04208	-1.022	3673	0.3068	-0.1611	0.07511
fixed	NA	count_birth_order4/>5	-0.1407	0.04088	-3.442	3672	0.0005847	-0.2555	-0.02594
fixed	NA	count_birth_order5/>5	-0.1239	0.0433	-2.86	3668	0.004254	-0.2454	-0.002313
fixed	NA	count_birth_order>5/>5	-0.09545	0.0326	-2.928	3509	0.003433	-0.1869	-0.003945
ran_pars	mother_pidlink	sd__(Intercept)	0.1099	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.422	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)
11	4369	4437	-2173	4347	NA	NA	NA
12	4371	4445	-2173	4347	0.00247	1	0.9604
16	4375	4474	-2171	4343	4.144	4	0.3868
26	4378	4539	-2163	4326	16.88	10	0.07713

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)	-0.5595	0.2914	-1.92	3597	0.05495	-1.377	0.2585
fixed	NA	poly(age, 3, raw = TRUE)1	0.0817	0.03131	2.609	3597	0.009112	-0.006192	0.1696
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0025	0.001074	-2.329	3597	0.01992	-0.005514	0.0005134
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002474	0.00001178	2.1	3595	0.03583	-0.000008335	0.00005781
fixed	NA	male	0.05654	0.01472	3.841	3598	0.0001245	0.01522	0.09786
fixed	NA	sibling_count3	-0.05676	0.02338	-2.427	2984	0.01526	-0.1224	0.008876
fixed	NA	sibling_count4	-0.04937	0.02446	-2.019	2758	0.04362	-0.118	0.01928
fixed	NA	sibling_count5	-0.1102	0.02796	-3.94	2318	0.00008386	-0.1886	-0.03168
fixed	NA	sibling_count>5	-0.09375	0.02374	-3.949	2307	0.00008091	-0.1604	-0.02711
ran_pars	mother_pidlink	sd__(Intercept)	0.1108	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.422	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)	-0.5626	0.2915	-1.93	3596	0.0537	-1.381	0.2557
fixed	NA	birth_order	-0.002165	0.004637	-0.467	3394	0.6405	-0.01518	0.01085
fixed	NA	poly(age, 3, raw = TRUE)1	0.08229	0.03134	2.626	3595	0.008682	-0.00568	0.1703
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002516	0.001074	-2.342	3595	0.01924	-0.005531	0.0004997
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002481	0.00001178	2.105	3593	0.03532	-0.000008268	0.00005789
fixed	NA	male	0.05657	0.01472	3.843	3597	0.0001237	0.01525	0.0979
fixed	NA	sibling_count3	-0.05566	0.02351	-2.368	2981	0.01796	-0.1216	0.01033
fixed	NA	sibling_count4	-0.04701	0.02497	-1.882	2757	0.05988	-0.1171	0.02309
fixed	NA	sibling_count5	-0.1064	0.02911	-3.654	2347	0.0002637	-0.1881	-0.02466
fixed	NA	sibling_count>5	-0.08602	0.02896	-2.97	2481	0.003008	-0.1673	-0.004717
ran_pars	mother_pidlink	sd__(Intercept)	0.1114	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4219	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)	-0.5677	0.2918	-1.946	3592	0.05178	-1.387	0.2514
fixed	NA	poly(age, 3, raw = TRUE)1	0.08282	0.03135	2.642	3592	0.008283	-0.005181	0.1708
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002528	0.001075	-2.352	3591	0.01871	-0.005545	0.0004888
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002487	0.00001179	2.108	3590	0.03506	-0.000008238	0.00005797
fixed	NA	male	0.05634	0.01473	3.826	3593	0.0001327	0.015	0.09768
fixed	NA	sibling_count3	-0.04861	0.024	-2.025	3073	0.04297	-0.116	0.01878
fixed	NA	sibling_count4	-0.03533	0.02592	-1.363	2934	0.1731	-0.1081	0.03744
fixed	NA	sibling_count5	-0.09458	0.0304	-3.111	2597	0.001882	-0.1799	-0.009255
fixed	NA	sibling_count>5	-0.07499	0.0298	-2.517	2648	0.01191	-0.1586	0.008652
fixed	NA	birth_order_nonlinear2	-0.01061	0.01931	-0.5491	3236	0.5829	-0.06482	0.04361
fixed	NA	birth_order_nonlinear3	-0.03414	0.02279	-1.499	3306	0.1341	-0.0981	0.02982
fixed	NA	birth_order_nonlinear4	-0.03378	0.0286	-1.181	3372	0.2377	-0.1141	0.04651
fixed	NA	birth_order_nonlinear5	-0.01735	0.03526	-0.4922	3364	0.6226	-0.1163	0.08161
fixed	NA	birth_order_nonlinear>5	-0.0251	0.03452	-0.727	3560	0.4672	-0.122	0.07181
ran_pars	mother_pidlink	sd__(Intercept)	0.111	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4221	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)	-0.5353	0.2929	-1.827	3581	0.06771	-1.358	0.2869
fixed	NA	poly(age, 3, raw = TRUE)1	0.08019	0.03148	2.547	3581	0.01089	-0.008172	0.1686
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002433	0.00108	-2.254	3580	0.02427	-0.005463	0.0005972
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002378	0.00001185	2.007	3578	0.04477	-0.000009473	0.00005704
fixed	NA	male	0.0564	0.01476	3.822	3583	0.0001344	0.01498	0.09782
fixed	NA	count_birth_order2/2	-0.04001	0.03684	-1.086	3248	0.2775	-0.1434	0.06339
fixed	NA	count_birth_order1/3	-0.06363	0.03106	-2.049	3582	0.04058	-0.1508	0.02356
fixed	NA	count_birth_order2/3	-0.05555	0.03455	-1.608	3586	0.1079	-0.1525	0.04142
fixed	NA	count_birth_order3/3	-0.09984	0.03721	-2.683	3585	0.00733	-0.2043	0.004615
fixed	NA	count_birth_order1/4	-0.04157	0.03645	-1.141	3585	0.2541	-0.1439	0.06075
fixed	NA	count_birth_order2/4	-0.06433	0.0383	-1.68	3586	0.09312	-0.1718	0.04318
fixed	NA	count_birth_order3/4	-0.09248	0.03975	-2.326	3585	0.02005	-0.2041	0.0191
fixed	NA	count_birth_order4/4	-0.05644	0.04319	-1.307	3584	0.1914	-0.1777	0.06479
fixed	NA	count_birth_order1/5	-0.127	0.04766	-2.664	3586	0.007762	-0.2607	0.00683
fixed	NA	count_birth_order2/5	-0.1031	0.05323	-1.937	3583	0.05282	-0.2525	0.04631
fixed	NA	count_birth_order3/5	-0.1444	0.05191	-2.782	3582	0.005427	-0.2901	0.001288
fixed	NA	count_birth_order4/5	-0.1675	0.04997	-3.352	3581	0.0008116	-0.3077	-0.02721
fixed	NA	count_birth_order5/5	-0.06378	0.05308	-1.202	3579	0.2296	-0.2128	0.08522
fixed	NA	count_birth_order1/>5	-0.08858	0.04645	-1.907	3585	0.0566	-0.219	0.04181
fixed	NA	count_birth_order2/>5	-0.08499	0.04697	-1.809	3585	0.07048	-0.2168	0.04687
fixed	NA	count_birth_order3/>5	-0.08575	0.04485	-1.912	3584	0.05597	-0.2116	0.04015
fixed	NA	count_birth_order4/>5	-0.1208	0.04505	-2.683	3580	0.00734	-0.2473	0.005608
fixed	NA	count_birth_order5/>5	-0.1342	0.04229	-3.172	3581	0.001526	-0.2529	-0.01544
fixed	NA	count_birth_order>5/>5	-0.11	0.03283	-3.35	3344	0.0008166	-0.2021	-0.01783
ran_pars	mother_pidlink	sd__(Intercept)	0.1107	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4224	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)
11	4263	4331	-2120	4241	NA	NA	NA
12	4264	4339	-2120	4240	0.2157	1	0.6424
16	4270	4369	-2119	4238	2.603	4	0.6264
26	4284	4445	-2116	4232	5.553	10	0.8513

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)	0.5117	0.09457	5.41	9545	0.00000006439	0.2462	0.7772
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01479	0.008466	-1.747	9484	0.08064	-0.03856	0.008973
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002146	0.0002372	0.9045	9372	0.3657	-0.0004513	0.0008805
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000006725	0.000002103	-0.3198	9243	0.7491	-0.000006575	0.00000523
fixed	NA	male	-0.02311	0.008759	-2.639	9657	0.008339	-0.0477	0.001475
fixed	NA	sibling_count3	-0.006571	0.01824	-0.3603	7295	0.7186	-0.05776	0.04462
fixed	NA	sibling_count4	-0.00687	0.01841	-0.3732	6877	0.709	-0.05855	0.04481
fixed	NA	sibling_count5	0.01292	0.01913	0.6752	6430	0.4996	-0.04079	0.06662
fixed	NA	sibling_count>5	0.01186	0.01487	0.7972	7153	0.4254	-0.02989	0.0536
ran_pars	mother_pidlink	sd__(Intercept)	0.1442	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4041	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)	0.5117	0.09458	5.41	9543	0.00000006447	0.2462	0.7772
fixed	NA	birth_order	-0.0001019	0.001772	-0.05749	8686	0.9542	-0.005077	0.004873
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01476	0.008481	-1.741	9475	0.08175	-0.03857	0.009043
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002136	0.0002379	0.8976	9335	0.3694	-0.0004543	0.0008814
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000006633	0.000002109	-0.3145	9190	0.7532	-0.000006583	0.000005257
fixed	NA	male	-0.02311	0.00876	-2.638	9656	0.008349	-0.0477	0.001479
fixed	NA	sibling_count3	-0.006544	0.01824	-0.3587	7305	0.7198	-0.05776	0.04467
fixed	NA	sibling_count4	-0.006808	0.01844	-0.3691	6922	0.712	-0.05858	0.04496
fixed	NA	sibling_count5	0.01303	0.01923	0.6776	6515	0.4981	-0.04094	0.06699
fixed	NA	sibling_count>5	0.01221	0.01612	0.7577	7866	0.4487	-0.03304	0.05746
ran_pars	mother_pidlink	sd__(Intercept)	0.1442	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4041	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)	0.5096	0.09474	5.379	9548	0.00000007651	0.2437	0.7756
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01469	0.008489	-1.731	9478	0.08354	-0.03852	0.009137
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002074	0.0002381	0.8713	9341	0.3836	-0.0004609	0.0008757
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000005849	0.00000211	-0.2772	9193	0.7816	-0.000006508	0.000005338
fixed	NA	male	-0.02303	0.008761	-2.629	9652	0.008575	-0.04763	0.001559
fixed	NA	sibling_count3	-0.005231	0.01851	-0.2826	7547	0.7775	-0.0572	0.04673
fixed	NA	sibling_count4	-0.007222	0.01895	-0.3811	7377	0.7031	-0.06041	0.04597
fixed	NA	sibling_count5	0.01484	0.01988	0.7462	7091	0.4556	-0.04097	0.07064
fixed	NA	sibling_count>5	0.01629	0.01688	0.965	8476	0.3346	-0.0311	0.06368
fixed	NA	birth_order_nonlinear2	0.008384	0.01278	0.6562	8982	0.5117	-0.02748	0.04425
fixed	NA	birth_order_nonlinear3	-0.003908	0.01484	-0.2634	8821	0.7922	-0.04555	0.03774
fixed	NA	birth_order_nonlinear4	0.01104	0.01668	0.6616	8889	0.5082	-0.03579	0.05786
fixed	NA	birth_order_nonlinear5	-0.01119	0.01874	-0.5973	8932	0.5503	-0.0638	0.04141
fixed	NA	birth_order_nonlinear>5	-0.004781	0.01554	-0.3076	9740	0.7584	-0.04841	0.03885
ran_pars	mother_pidlink	sd__(Intercept)	0.1441	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4042	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)	0.4939	0.09509	5.194	9550	0.00000021	0.227	0.7608
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01421	0.008498	-1.673	9469	0.09446	-0.03807	0.009642
fixed	NA	poly(age, 3, raw = TRUE)2	0.0001951	0.0002382	0.8191	9331	0.4128	-0.0004736	0.0008639
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000000494	0.000002111	-0.234	9181	0.815	-0.00000642	0.000005432
fixed	NA	male	-0.02312	0.008766	-2.638	9642	0.008356	-0.04773	0.001483
fixed	NA	count_birth_order2/2	0.03648	0.02545	1.433	8886	0.1519	-0.03497	0.1079
fixed	NA	count_birth_order1/3	0.01974	0.02457	0.8034	9655	0.4218	-0.04922	0.08869
fixed	NA	count_birth_order2/3	0.009603	0.02731	0.3516	9692	0.7252	-0.06707	0.08628
fixed	NA	count_birth_order3/3	-0.02071	0.02998	-0.6908	9712	0.4897	-0.1049	0.06344
fixed	NA	count_birth_order1/4	0.008555	0.02702	0.3166	9694	0.7516	-0.0673	0.08441
fixed	NA	count_birth_order2/4	0.0266	0.02898	0.9179	9706	0.3587	-0.05475	0.108
fixed	NA	count_birth_order3/4	-0.03689	0.03056	-1.207	9718	0.2273	-0.1227	0.04888
fixed	NA	count_birth_order4/4	0.02723	0.03289	0.8279	9726	0.4077	-0.06509	0.1195
fixed	NA	count_birth_order1/5	0.04031	0.03046	1.323	9719	0.1858	-0.0452	0.1258
fixed	NA	count_birth_order2/5	0.02362	0.03234	0.7304	9724	0.4651	-0.06715	0.1144
fixed	NA	count_birth_order3/5	0.03578	0.03401	1.052	9729	0.2928	-0.05969	0.1313
fixed	NA	count_birth_order4/5	0.008249	0.03589	0.2298	9727	0.8182	-0.0925	0.109
fixed	NA	count_birth_order5/5	0.01433	0.03597	0.3985	9730	0.6903	-0.08663	0.1153
fixed	NA	count_birth_order1/>5	0.01689	0.02356	0.717	9728	0.4734	-0.04923	0.08302
fixed	NA	count_birth_order2/>5	0.01899	0.02448	0.7757	9730	0.4379	-0.04973	0.08772
fixed	NA	count_birth_order3/>5	0.04577	0.02423	1.889	9730	0.05895	-0.02225	0.1138
fixed	NA	count_birth_order4/>5	0.04063	0.02374	1.711	9729	0.08707	-0.02602	0.1073
fixed	NA	count_birth_order5/>5	0.01524	0.024	0.6352	9730	0.5253	-0.05212	0.0826
fixed	NA	count_birth_order>5/>5	0.02177	0.01945	1.119	8952	0.263	-0.03282	0.07637
ran_pars	mother_pidlink	sd__(Intercept)	0.1442	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4041	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)
11	11106	11186	-5542	11084	NA	NA	NA
12	11108	11195	-5542	11084	0.003397	1	0.9535
16	11114	11229	-5541	11082	2.159	4	0.7066
26	11124	11311	-5536	11072	9.91	10	0.4484

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)	0.6945	0.2861	2.428	3664	0.01524	-0.1085	1.498
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03818	0.03069	-1.244	3664	0.2135	-0.1243	0.04795
fixed	NA	poly(age, 3, raw = TRUE)2	0.001072	0.001051	1.02	3664	0.3077	-0.001878	0.004023
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001043	0.00001152	-0.9051	3664	0.3655	-0.00004278	0.00002192
fixed	NA	male	-0.01913	0.01445	-1.324	3657	0.1856	-0.0597	0.02143
fixed	NA	sibling_count3	0.001268	0.02378	0.05334	2960	0.9575	-0.06548	0.06801
fixed	NA	sibling_count4	0.02087	0.02454	0.8503	2724	0.3952	-0.04802	0.08975
fixed	NA	sibling_count5	0.02786	0.02734	1.019	2386	0.3083	-0.04889	0.1046
fixed	NA	sibling_count>5	0.01755	0.02361	0.7432	2351	0.4575	-0.04873	0.08382
ran_pars	mother_pidlink	sd__(Intercept)	0.1269	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4136	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)	0.6924	0.2862	2.42	3663	0.01558	-0.1108	1.496
fixed	NA	birth_order	-0.001776	0.004471	-0.3974	3464	0.6911	-0.01433	0.01077
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03775	0.03071	-1.229	3663	0.2191	-0.1239	0.04845
fixed	NA	poly(age, 3, raw = TRUE)2	0.001062	0.001052	1.009	3663	0.3129	-0.001891	0.004014
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001039	0.00001153	-0.9014	3663	0.3675	-0.00004274	0.00002196
fixed	NA	male	-0.01907	0.01445	-1.32	3656	0.1871	-0.05965	0.0215
fixed	NA	sibling_count3	0.002154	0.02388	0.09018	2960	0.9281	-0.06489	0.0692
fixed	NA	sibling_count4	0.02283	0.02503	0.9121	2721	0.3618	-0.04743	0.09309
fixed	NA	sibling_count5	0.03107	0.02851	1.09	2421	0.2759	-0.04896	0.1111
fixed	NA	sibling_count>5	0.02391	0.02854	0.838	2480	0.4021	-0.05619	0.104
ran_pars	mother_pidlink	sd__(Intercept)	0.1266	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4138	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)	0.7097	0.2864	2.478	3659	0.01325	-0.09416	1.514
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04004	0.03071	-1.304	3659	0.1924	-0.1262	0.04617
fixed	NA	poly(age, 3, raw = TRUE)2	0.001135	0.001052	1.079	3659	0.2808	-0.001818	0.004088
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001111	0.00001153	-0.9635	3659	0.3354	-0.00004348	0.00002126
fixed	NA	male	-0.01949	0.01446	-1.348	3651	0.1776	-0.06007	0.02109
fixed	NA	sibling_count3	0.002157	0.02435	0.08859	3053	0.9294	-0.0662	0.07051
fixed	NA	sibling_count4	0.01402	0.02595	0.5401	2906	0.5892	-0.05883	0.08687
fixed	NA	sibling_count5	0.02613	0.02986	0.875	2692	0.3817	-0.05769	0.11
fixed	NA	sibling_count>5	0.02047	0.02931	0.6984	2640	0.485	-0.0618	0.1027
fixed	NA	birth_order_nonlinear2	0.008278	0.01916	0.4321	3242	0.6657	-0.0455	0.06206
fixed	NA	birth_order_nonlinear3	-0.003106	0.02248	-0.1381	3311	0.8901	-0.06622	0.06
fixed	NA	birth_order_nonlinear4	0.0427	0.02744	1.556	3377	0.1199	-0.03434	0.1197
fixed	NA	birth_order_nonlinear5	-0.029	0.03366	-0.8614	3392	0.3891	-0.1235	0.06549
fixed	NA	birth_order_nonlinear>5	-0.005666	0.03318	-0.1707	3635	0.8644	-0.09882	0.08749
ran_pars	mother_pidlink	sd__(Intercept)	0.128	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4133	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)	0.7378	0.2875	2.566	3649	0.01033	-0.06936	1.545
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04289	0.03084	-1.391	3649	0.1644	-0.1295	0.04368
fixed	NA	poly(age, 3, raw = TRUE)2	0.001232	0.001057	1.166	3649	0.2438	-0.001734	0.004198
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001216	0.00001159	-1.05	3649	0.2939	-0.00004468	0.00002036
fixed	NA	male	-0.01952	0.01448	-1.348	3641	0.1777	-0.06017	0.02113
fixed	NA	count_birth_order2/2	0.004085	0.0374	0.1092	3277	0.913	-0.1009	0.1091
fixed	NA	count_birth_order1/3	0.01393	0.03133	0.4445	3643	0.6567	-0.07402	0.1019
fixed	NA	count_birth_order2/3	0.007459	0.03483	0.2142	3649	0.8304	-0.0903	0.1052
fixed	NA	count_birth_order3/3	-0.02574	0.03793	-0.6785	3650	0.4975	-0.1322	0.08074
fixed	NA	count_birth_order1/4	-0.01898	0.03594	-0.528	3647	0.5975	-0.1199	0.08191
fixed	NA	count_birth_order2/4	0.0258	0.0381	0.6772	3650	0.4983	-0.08114	0.1327
fixed	NA	count_birth_order3/4	0.04904	0.0395	1.241	3649	0.2145	-0.06184	0.1599
fixed	NA	count_birth_order4/4	0.05322	0.04228	1.259	3647	0.2082	-0.06547	0.1719
fixed	NA	count_birth_order1/5	0.01815	0.04733	0.3835	3650	0.7014	-0.1147	0.151
fixed	NA	count_birth_order2/5	0.08403	0.05105	1.646	3645	0.09984	-0.05927	0.2273
fixed	NA	count_birth_order3/5	-0.02305	0.04853	-0.4749	3644	0.6349	-0.1593	0.1132
fixed	NA	count_birth_order4/5	0.07164	0.04733	1.513	3642	0.1303	-0.06123	0.2045
fixed	NA	count_birth_order5/5	-0.001846	0.04981	-0.03705	3639	0.9704	-0.1417	0.138
fixed	NA	count_birth_order1/>5	0.03997	0.04483	0.8917	3650	0.3726	-0.08587	0.1658
fixed	NA	count_birth_order2/>5	-0.008876	0.04517	-0.1965	3646	0.8442	-0.1357	0.1179
fixed	NA	count_birth_order3/>5	0.03244	0.04408	0.7359	3644	0.4618	-0.0913	0.1562
fixed	NA	count_birth_order4/>5	0.06151	0.04315	1.426	3638	0.1541	-0.0596	0.1826
fixed	NA	count_birth_order5/>5	-0.01123	0.04124	-0.2723	3641	0.7854	-0.127	0.1045
fixed	NA	count_birth_order>5/>5	0.01346	0.0322	0.4178	3445	0.6761	-0.07694	0.1039
ran_pars	mother_pidlink	sd__(Intercept)	0.1285	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4133	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)
11	4272	4341	-2125	4250	NA	NA	NA
12	4274	4349	-2125	4250	0.16	1	0.6892
16	4277	4377	-2123	4245	4.804	4	0.3081
26	4290	4451	-2119	4238	7.584	10	0.6694

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)	0.6938	0.2847	2.437	3688	0.01485	-0.1053	1.493
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03908	0.03056	-1.279	3688	0.201	-0.1249	0.04671
fixed	NA	poly(age, 3, raw = TRUE)2	0.001103	0.001047	1.053	3688	0.2925	-0.001837	0.004042
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001075	0.00001148	-0.936	3688	0.3494	-0.00004298	0.00002149
fixed	NA	male	-0.01987	0.01439	-1.381	3680	0.1675	-0.06028	0.02053
fixed	NA	sibling_count3	0.02057	0.02606	0.7896	3036	0.4298	-0.05257	0.09371
fixed	NA	sibling_count4	0.01883	0.02628	0.7167	2880	0.4736	-0.05493	0.0926
fixed	NA	sibling_count5	0.02997	0.02767	1.083	2658	0.2789	-0.04771	0.1077
fixed	NA	sibling_count>5	0.02952	0.02426	1.217	2707	0.2238	-0.03858	0.09762
ran_pars	mother_pidlink	sd__(Intercept)	0.1274	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4132	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)	0.6907	0.2847	2.426	3687	0.01531	-0.1085	1.49
fixed	NA	birth_order	-0.003004	0.003942	-0.7619	3366	0.4462	-0.01407	0.008063
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0384	0.03058	-1.256	3687	0.2093	-0.1242	0.04743
fixed	NA	poly(age, 3, raw = TRUE)2	0.001086	0.001048	1.037	3687	0.2999	-0.001854	0.004027
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000107	0.00001148	-0.9316	3686	0.3516	-0.00004294	0.00002154
fixed	NA	male	-0.01978	0.0144	-1.374	3680	0.1696	-0.06018	0.02063
fixed	NA	sibling_count3	0.02208	0.02613	0.8452	3032	0.3981	-0.05126	0.09543
fixed	NA	sibling_count4	0.02188	0.02657	0.8235	2868	0.4103	-0.05271	0.09648
fixed	NA	sibling_count5	0.03503	0.02845	1.231	2658	0.2185	-0.04485	0.1149
fixed	NA	sibling_count>5	0.04012	0.02797	1.435	2725	0.1515	-0.03838	0.1186
ran_pars	mother_pidlink	sd__(Intercept)	0.1267	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4134	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)	0.7126	0.2849	2.501	3683	0.01241	-0.08707	1.512
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04117	0.03058	-1.347	3683	0.1782	-0.127	0.04466
fixed	NA	poly(age, 3, raw = TRUE)2	0.001175	0.001048	1.122	3683	0.262	-0.001765	0.004116
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001154	0.00001149	-1.005	3683	0.3151	-0.00004379	0.0000207
fixed	NA	male	-0.02032	0.01439	-1.412	3674	0.1581	-0.06072	0.02008
fixed	NA	sibling_count3	0.02206	0.02657	0.83	3100	0.4066	-0.05254	0.09665
fixed	NA	sibling_count4	0.0125	0.02736	0.4569	2998	0.6478	-0.06431	0.08931
fixed	NA	sibling_count5	0.03038	0.02971	1.023	2876	0.3066	-0.05302	0.1138
fixed	NA	sibling_count>5	0.03026	0.0288	1.051	2882	0.2935	-0.05058	0.1111
fixed	NA	birth_order_nonlinear2	0.000648	0.01936	0.03347	3286	0.9733	-0.0537	0.05499
fixed	NA	birth_order_nonlinear3	-0.006387	0.02258	-0.2829	3373	0.7773	-0.06976	0.05699
fixed	NA	birth_order_nonlinear4	0.04502	0.02675	1.683	3453	0.09249	-0.03007	0.1201
fixed	NA	birth_order_nonlinear5	-0.04231	0.03258	-1.299	3450	0.1942	-0.1338	0.04915
fixed	NA	birth_order_nonlinear>5	-0.003707	0.03001	-0.1235	3630	0.9017	-0.08794	0.08052
ran_pars	mother_pidlink	sd__(Intercept)	0.1294	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4125	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)	0.715	0.2859	2.501	3673	0.01242	-0.08738	1.517
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04177	0.03069	-1.361	3673	0.1735	-0.1279	0.04437
fixed	NA	poly(age, 3, raw = TRUE)2	0.001195	0.001052	1.137	3673	0.2558	-0.001757	0.004148
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001175	0.00001154	-1.019	3672	0.3084	-0.00004413	0.00002063
fixed	NA	male	-0.02002	0.01443	-1.387	3664	0.1655	-0.06052	0.02049
fixed	NA	count_birth_order2/2	0.0098	0.041	0.239	3377	0.8111	-0.1053	0.1249
fixed	NA	count_birth_order1/3	0.03993	0.03463	1.153	3667	0.249	-0.05729	0.1371
fixed	NA	count_birth_order2/3	0.02923	0.03772	0.7751	3672	0.4384	-0.07664	0.1351
fixed	NA	count_birth_order3/3	-0.01499	0.0418	-0.3586	3674	0.7199	-0.1323	0.1023
fixed	NA	count_birth_order1/4	0.008483	0.03758	0.2257	3670	0.8214	-0.09701	0.114
fixed	NA	count_birth_order2/4	0.00627	0.0396	0.1583	3674	0.8742	-0.1049	0.1174
fixed	NA	count_birth_order3/4	0.02997	0.04285	0.6994	3673	0.4843	-0.09032	0.1503
fixed	NA	count_birth_order4/4	0.06428	0.04654	1.381	3671	0.1673	-0.06637	0.1949
fixed	NA	count_birth_order1/5	0.008951	0.04542	0.1971	3674	0.8438	-0.1186	0.1365
fixed	NA	count_birth_order2/5	0.06832	0.04657	1.467	3674	0.1425	-0.0624	0.199
fixed	NA	count_birth_order3/5	0.02295	0.04791	0.4791	3670	0.6319	-0.1115	0.1574
fixed	NA	count_birth_order4/5	0.07555	0.04877	1.549	3667	0.1215	-0.06136	0.2125
fixed	NA	count_birth_order5/5	-0.01083	0.04952	-0.2187	3664	0.8269	-0.1498	0.1282
fixed	NA	count_birth_order1/>5	0.03972	0.04098	0.9691	3672	0.3325	-0.07532	0.1548
fixed	NA	count_birth_order2/>5	0.00776	0.04329	0.1793	3672	0.8577	-0.1138	0.1293
fixed	NA	count_birth_order3/>5	0.04269	0.04171	1.024	3671	0.3061	-0.07438	0.1598
fixed	NA	count_birth_order4/>5	0.07782	0.04052	1.921	3669	0.05486	-0.03592	0.1916
fixed	NA	count_birth_order5/>5	-0.007665	0.04291	-0.1786	3662	0.8582	-0.1281	0.1128
fixed	NA	count_birth_order>5/>5	0.02949	0.03239	0.9104	3508	0.3627	-0.06144	0.1204
ran_pars	mother_pidlink	sd__(Intercept)	0.1294	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4129	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)
11	4295	4364	-2137	4273	NA	NA	NA
12	4297	4371	-2136	4273	0.585	1	0.4444
16	4298	4398	-2133	4266	6.406	4	0.1708
26	4314	4476	-2131	4262	4.039	10	0.9455

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)	0.6847	0.2888	2.371	3600	0.0178	-0.126	1.495
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03708	0.03103	-1.195	3600	0.2322	-0.1242	0.05003
fixed	NA	poly(age, 3, raw = TRUE)2	0.001033	0.001064	0.9707	3600	0.3318	-0.001954	0.00402
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000009884	0.00001168	-0.8464	3599	0.3974	-0.00004267	0.0000229
fixed	NA	male	-0.02402	0.01458	-1.648	3593	0.09949	-0.06495	0.0169
fixed	NA	sibling_count3	0.006789	0.02327	0.2917	2910	0.7705	-0.05853	0.07211
fixed	NA	sibling_count4	0.01743	0.02436	0.7156	2681	0.4743	-0.05095	0.08582
fixed	NA	sibling_count5	0.03358	0.0279	1.204	2245	0.2289	-0.04473	0.1119
fixed	NA	sibling_count>5	0.0147	0.02369	0.6205	2243	0.535	-0.05181	0.08121
ran_pars	mother_pidlink	sd__(Intercept)	0.1271	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4135	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)	0.6811	0.2889	2.357	3598	0.01846	-0.1299	1.492
fixed	NA	birth_order	-0.002423	0.004604	-0.5263	3430	0.5987	-0.01535	0.0105
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03639	0.03106	-1.172	3598	0.2414	-0.1236	0.05079
fixed	NA	poly(age, 3, raw = TRUE)2	0.001015	0.001065	0.9533	3598	0.3405	-0.001974	0.004004
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000009793	0.00001168	-0.8384	3598	0.4018	-0.00004258	0.00002299
fixed	NA	male	-0.024	0.01458	-1.646	3592	0.09981	-0.06494	0.01693
fixed	NA	sibling_count3	0.008022	0.02339	0.343	2908	0.7317	-0.05763	0.07368
fixed	NA	sibling_count4	0.02008	0.02487	0.8073	2683	0.4196	-0.04973	0.08989
fixed	NA	sibling_count5	0.03781	0.02903	1.302	2278	0.193	-0.04369	0.1193
fixed	NA	sibling_count>5	0.02339	0.02887	0.81	2429	0.418	-0.05766	0.1044
ran_pars	mother_pidlink	sd__(Intercept)	0.1268	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4136	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)	0.6914	0.2892	2.391	3594	0.01687	-0.1204	1.503
fixed	NA	poly(age, 3, raw = TRUE)1	-0.03822	0.03107	-1.23	3595	0.2187	-0.1254	0.04899
fixed	NA	poly(age, 3, raw = TRUE)2	0.001074	0.001065	1.008	3595	0.3135	-0.001916	0.004064
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001037	0.00001169	-0.8876	3594	0.3748	-0.00004318	0.00002243
fixed	NA	male	-0.02434	0.01459	-1.669	3588	0.09526	-0.06529	0.01661
fixed	NA	sibling_count3	0.009206	0.02388	0.3855	3004	0.6999	-0.05782	0.07623
fixed	NA	sibling_count4	0.01429	0.0258	0.5538	2866	0.5798	-0.05813	0.08671
fixed	NA	sibling_count5	0.03383	0.03029	1.117	2528	0.2643	-0.05121	0.1189
fixed	NA	sibling_count>5	0.02141	0.02969	0.7211	2597	0.4709	-0.06193	0.1047
fixed	NA	birth_order_nonlinear2	0.01259	0.01907	0.6599	3177	0.5093	-0.04095	0.06613
fixed	NA	birth_order_nonlinear3	-0.008404	0.02251	-0.3733	3249	0.7089	-0.07159	0.05479
fixed	NA	birth_order_nonlinear4	0.03288	0.02827	1.163	3317	0.2448	-0.04647	0.1122
fixed	NA	birth_order_nonlinear5	-0.01862	0.03484	-0.5346	3303	0.593	-0.1164	0.07918
fixed	NA	birth_order_nonlinear>5	-0.01146	0.03423	-0.3349	3577	0.7377	-0.1076	0.08463
ran_pars	mother_pidlink	sd__(Intercept)	0.127	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4136	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)	0.7099	0.2904	2.445	3584	0.01455	-0.1053	1.525
fixed	NA	poly(age, 3, raw = TRUE)1	-0.04044	0.03121	-1.296	3584	0.1951	-0.128	0.04716
fixed	NA	poly(age, 3, raw = TRUE)2	0.001151	0.00107	1.076	3584	0.2821	-0.001853	0.004155
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00001124	0.00001175	-0.9567	3583	0.3388	-0.00004421	0.00002173
fixed	NA	male	-0.02448	0.01462	-1.675	3577	0.09408	-0.06552	0.01655
fixed	NA	count_birth_order2/2	0.01734	0.03639	0.4765	3206	0.6338	-0.08481	0.1195
fixed	NA	count_birth_order1/3	0.01849	0.03079	0.6004	3579	0.5483	-0.06795	0.1049
fixed	NA	count_birth_order2/3	0.02155	0.03424	0.6293	3585	0.5292	-0.07457	0.1177
fixed	NA	count_birth_order3/3	-0.009869	0.03687	-0.2676	3585	0.789	-0.1134	0.09364
fixed	NA	count_birth_order1/4	-0.01049	0.03613	-0.2903	3584	0.7716	-0.1119	0.09094
fixed	NA	count_birth_order2/4	0.027	0.03796	0.7113	3586	0.477	-0.07955	0.1335
fixed	NA	count_birth_order3/4	0.03907	0.03939	0.992	3584	0.3213	-0.07149	0.1496
fixed	NA	count_birth_order4/4	0.05482	0.04279	1.281	3583	0.2002	-0.06529	0.1749
fixed	NA	count_birth_order1/5	0.03448	0.04724	0.73	3586	0.4654	-0.09812	0.1671
fixed	NA	count_birth_order2/5	0.06907	0.05274	1.31	3579	0.1904	-0.07897	0.2171
fixed	NA	count_birth_order3/5	0.004936	0.05143	0.09599	3577	0.9235	-0.1394	0.1493
fixed	NA	count_birth_order4/5	0.06178	0.0495	1.248	3577	0.2121	-0.07717	0.2007
fixed	NA	count_birth_order5/5	0.02736	0.05258	0.5203	3574	0.6029	-0.1202	0.175
fixed	NA	count_birth_order1/>5	0.05413	0.04604	1.176	3586	0.2398	-0.07511	0.1834
fixed	NA	count_birth_order2/>5	0.02108	0.04654	0.4529	3582	0.6507	-0.1096	0.1517
fixed	NA	count_birth_order3/>5	0.006787	0.04444	0.1527	3581	0.8786	-0.118	0.1315
fixed	NA	count_birth_order4/>5	0.05472	0.04463	1.226	3572	0.2202	-0.07054	0.18
fixed	NA	count_birth_order5/>5	-0.00152	0.0419	-0.03627	3576	0.9711	-0.1191	0.1161
fixed	NA	count_birth_order>5/>5	0.01146	0.03262	0.3515	3348	0.7253	-0.0801	0.103
ran_pars	mother_pidlink	sd__(Intercept)	0.1273	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.4139	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)
11	4196	4264	-2087	4174	NA	NA	NA
12	4198	4272	-2087	4174	0.2797	1	0.5969
16	4203	4302	-2085	4171	3.113	4	0.5391
26	4219	4380	-2084	4167	3.496	10	0.9672

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)	-0.03035	0.03991	-0.7605	9543	0.447	-0.1424	0.08168
fixed	NA	poly(age, 3, raw = TRUE)1	0.002784	0.003572	0.7794	9482	0.4357	-0.007243	0.01281
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00004645	0.0001001	-0.4641	9372	0.6426	-0.0003274	0.0002345
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000002049	0.000000887	0.231	9246	0.8173	-0.000002285	0.000002695
fixed	NA	male	0.02971	0.0037	8.03	9672	1.089e-15	0.01932	0.04009
fixed	NA	sibling_count3	-0.0008367	0.007684	-0.1089	7398	0.9133	-0.02241	0.02073
fixed	NA	sibling_count4	0.004985	0.007755	0.6429	6978	0.5203	-0.01678	0.02675
fixed	NA	sibling_count5	0.006666	0.008057	0.8274	6531	0.408	-0.01595	0.02928
fixed	NA	sibling_count>5	0.001122	0.006266	0.179	7252	0.8579	-0.01647	0.01871
ran_pars	mother_pidlink	sd__(Intercept)	0.05891	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1712	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)	-0.03038	0.03991	-0.7613	9542	0.4465	-0.1424	0.08165
fixed	NA	birth_order	0.0005056	0.0007473	0.6765	8641	0.4987	-0.001592	0.002603
fixed	NA	poly(age, 3, raw = TRUE)1	0.002644	0.003579	0.7388	9473	0.46	-0.007401	0.01269
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00004135	0.0001004	-0.412	9336	0.6804	-0.0003231	0.0002404
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001591	0.0000008896	0.1788	9196	0.8581	-0.000002338	0.000002656
fixed	NA	male	0.0297	0.0037	8.027	9671	1.117e-15	0.01931	0.04008
fixed	NA	sibling_count3	-0.0009676	0.007687	-0.1259	7408	0.8998	-0.02254	0.02061
fixed	NA	sibling_count4	0.004674	0.007769	0.6016	7024	0.5474	-0.01713	0.02648
fixed	NA	sibling_count5	0.006127	0.008097	0.7568	6616	0.4492	-0.0166	0.02885
fixed	NA	sibling_count>5	-0.000655	0.006794	-0.09641	7942	0.9232	-0.01973	0.01842
ran_pars	mother_pidlink	sd__(Intercept)	0.05893	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1712	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)	-0.02744	0.03998	-0.6864	9547	0.4925	-0.1397	0.08478
fixed	NA	poly(age, 3, raw = TRUE)1	0.002552	0.003582	0.7125	9477	0.4762	-0.007503	0.01261
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00003768	0.0001004	-0.3752	9342	0.7076	-0.0003196	0.0002443
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001159	0.0000008902	0.1301	9199	0.8965	-0.000002383	0.000002615
fixed	NA	male	0.02973	0.0037	8.035	9666	1.047e-15	0.01934	0.04012
fixed	NA	sibling_count3	0.0002275	0.007802	0.02916	7639	0.9767	-0.02167	0.02213
fixed	NA	sibling_count4	0.004558	0.007985	0.5709	7466	0.5681	-0.01786	0.02697
fixed	NA	sibling_count5	0.00631	0.008377	0.7532	7181	0.4513	-0.0172	0.02982
fixed	NA	sibling_count>5	-0.0008504	0.007119	-0.1195	8534	0.9049	-0.02083	0.01913
fixed	NA	birth_order_nonlinear2	-0.004173	0.0054	-0.7729	9020	0.4396	-0.01933	0.01098
fixed	NA	birth_order_nonlinear3	-0.005299	0.00627	-0.8451	8872	0.3981	-0.0229	0.0123
fixed	NA	birth_order_nonlinear4	0.006777	0.00705	0.9613	8941	0.3364	-0.01301	0.02657
fixed	NA	birth_order_nonlinear5	-0.00166	0.00792	-0.2096	8985	0.834	-0.02389	0.02057
fixed	NA	birth_order_nonlinear>5	0.002234	0.006562	0.3404	9740	0.7335	-0.01619	0.02065
ran_pars	mother_pidlink	sd__(Intercept)	0.05905	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1712	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)	-0.0343	0.04011	-0.8551	9548	0.3925	-0.1469	0.0783
fixed	NA	poly(age, 3, raw = TRUE)1	0.002683	0.003585	0.7484	9467	0.4542	-0.007379	0.01275
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00004222	0.0001005	-0.4202	9331	0.6744	-0.0003243	0.0002398
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000001617	0.0000008903	0.1816	9186	0.8559	-0.000002337	0.000002661
fixed	NA	male	0.0297	0.003701	8.025	9657	1.132e-15	0.01931	0.04009
fixed	NA	count_birth_order2/2	0.01138	0.01075	1.058	8914	0.29	-0.01881	0.04157
fixed	NA	count_birth_order1/3	0.005769	0.01037	0.5566	9665	0.5778	-0.02333	0.03486
fixed	NA	count_birth_order2/3	0.01716	0.01153	1.489	9697	0.1365	-0.01519	0.04952
fixed	NA	count_birth_order3/3	-0.01888	0.01265	-1.492	9714	0.1357	-0.05439	0.01664
fixed	NA	count_birth_order1/4	0.01393	0.0114	1.222	9699	0.2218	-0.01808	0.04594
fixed	NA	count_birth_order2/4	-0.005393	0.01223	-0.441	9709	0.6592	-0.03972	0.02894
fixed	NA	count_birth_order3/4	0.009254	0.01289	0.7177	9719	0.473	-0.02694	0.04545
fixed	NA	count_birth_order4/4	0.02237	0.01388	1.612	9726	0.107	-0.01659	0.06134
fixed	NA	count_birth_order1/5	0.005794	0.01286	0.4507	9721	0.6522	-0.03029	0.04188
fixed	NA	count_birth_order2/5	0.009803	0.01365	0.7183	9725	0.4726	-0.0285	0.04811
fixed	NA	count_birth_order3/5	0.007786	0.01435	0.5424	9729	0.5876	-0.03251	0.04808
fixed	NA	count_birth_order4/5	0.01815	0.01515	1.198	9728	0.2309	-0.02437	0.06068
fixed	NA	count_birth_order5/5	0.01756	0.01518	1.157	9730	0.2473	-0.02505	0.06018
fixed	NA	count_birth_order1/>5	0.01252	0.009942	1.259	9729	0.2079	-0.01539	0.04043
fixed	NA	count_birth_order2/>5	-0.01148	0.01033	-1.111	9730	0.2666	-0.04049	0.01752
fixed	NA	count_birth_order3/>5	0.007394	0.01023	0.723	9730	0.4697	-0.02131	0.0361
fixed	NA	count_birth_order4/>5	0.01005	0.01002	1.003	9730	0.316	-0.01808	0.03818
fixed	NA	count_birth_order5/>5	0.001259	0.01013	0.1243	9730	0.9011	-0.02717	0.02969
fixed	NA	count_birth_order>5/>5	0.007163	0.0082	0.8736	8987	0.3824	-0.01585	0.03018
ran_pars	mother_pidlink	sd__(Intercept)	0.05892	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1712	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)
11	-5714	-5635	2868	-5736	NA	NA	NA
12	-5712	-5626	2868	-5736	0.4579	1	0.4986
16	-5707	-5592	2870	-5739	3.207	4	0.5238
26	-5703	-5517	2878	-5755	16.09	10	0.09704

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)	-0.0135	0.1052	-0.1283	3665	0.8979	-0.3088	0.2818
fixed	NA	poly(age, 3, raw = TRUE)1	0.0004965	0.01128	0.044	3665	0.9649	-0.03117	0.03217
fixed	NA	poly(age, 3, raw = TRUE)2	0.00002584	0.0003865	0.06685	3665	0.9467	-0.001059	0.001111
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000008291	0.000004237	-0.1957	3665	0.8449	-0.00001272	0.00001107
fixed	NA	male	0.02643	0.005311	4.977	3645	0.0000006762	0.01152	0.04134
fixed	NA	sibling_count3	0.01414	0.008772	1.612	2714	0.1071	-0.01048	0.03877
fixed	NA	sibling_count4	0.01755	0.00906	1.937	2445	0.05282	-0.00788	0.04298
fixed	NA	sibling_count5	0.004679	0.0101	0.4631	2080	0.6433	-0.02368	0.03304
fixed	NA	sibling_count>5	0.01454	0.008725	1.666	2049	0.09587	-0.009956	0.03903
ran_pars	mother_pidlink	sd__(Intercept)	0.05107	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1508	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)	-0.01511	0.1052	-0.1436	3664	0.8859	-0.3105	0.2802
fixed	NA	birth_order	-0.00126	0.001647	-0.7652	3446	0.4442	-0.005882	0.003362
fixed	NA	poly(age, 3, raw = TRUE)1	0.0008181	0.01129	0.07246	3664	0.9422	-0.03088	0.03251
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001765	0.0003867	0.04563	3664	0.9636	-0.001068	0.001103
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000007941	0.000004238	-0.1874	3664	0.8514	-0.00001269	0.0000111
fixed	NA	male	0.02649	0.005312	4.987	3643	0.0000006412	0.01158	0.0414
fixed	NA	sibling_count3	0.01478	0.008814	1.676	2712	0.09376	-0.009965	0.03952
fixed	NA	sibling_count4	0.01895	0.009244	2.05	2441	0.04051	-0.007001	0.0449
fixed	NA	sibling_count5	0.006955	0.01054	0.6599	2121	0.5094	-0.02263	0.03654
fixed	NA	sibling_count>5	0.01908	0.01055	1.809	2201	0.07064	-0.01053	0.04868
ran_pars	mother_pidlink	sd__(Intercept)	0.05147	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1506	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)	-0.01618	0.1053	-0.1537	3660	0.8779	-0.3118	0.2794
fixed	NA	poly(age, 3, raw = TRUE)1	0.00098	0.01129	0.08678	3660	0.9309	-0.03072	0.03268
fixed	NA	poly(age, 3, raw = TRUE)2	0.0000145	0.0003868	0.03749	3660	0.9701	-0.001071	0.0011
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000007877	0.00000424	-0.1858	3660	0.8526	-0.00001269	0.00001112
fixed	NA	male	0.02645	0.005314	4.978	3639	0.0000006708	0.01154	0.04137
fixed	NA	sibling_count3	0.01569	0.008983	1.747	2831	0.08078	-0.009523	0.04091
fixed	NA	sibling_count4	0.02248	0.009577	2.347	2661	0.01901	-0.004408	0.04936
fixed	NA	sibling_count5	0.01117	0.01103	1.013	2422	0.3113	-0.01978	0.04212
fixed	NA	sibling_count>5	0.02095	0.01082	1.936	2377	0.05301	-0.00943	0.05133
fixed	NA	birth_order_nonlinear2	-0.008145	0.007027	-1.159	3067	0.2466	-0.02787	0.01158
fixed	NA	birth_order_nonlinear3	-0.006853	0.008248	-0.8308	3151	0.4062	-0.03001	0.0163
fixed	NA	birth_order_nonlinear4	-0.01932	0.01007	-1.919	3235	0.0551	-0.04759	0.008946
fixed	NA	birth_order_nonlinear5	-0.01062	0.01235	-0.8596	3250	0.3901	-0.04529	0.02406
fixed	NA	birth_order_nonlinear>5	-0.007731	0.01221	-0.6332	3642	0.5266	-0.042	0.02654
ran_pars	mother_pidlink	sd__(Intercept)	0.05144	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1507	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)	-0.009966	0.1058	-0.09421	3649	0.9249	-0.3069	0.287
fixed	NA	poly(age, 3, raw = TRUE)1	0.0004782	0.01135	0.04215	3650	0.9664	-0.03137	0.03233
fixed	NA	poly(age, 3, raw = TRUE)2	0.00003556	0.0003887	0.09147	3650	0.9271	-0.001056	0.001127
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000001051	0.000004262	-0.2466	3650	0.8052	-0.00001302	0.00001091
fixed	NA	male	0.0264	0.005325	4.957	3629	0.0000007477	0.01145	0.04134
fixed	NA	count_birth_order2/2	-0.01641	0.01373	-1.195	3135	0.2321	-0.05495	0.02213
fixed	NA	count_birth_order1/3	0.00795	0.01153	0.6896	3638	0.4905	-0.02441	0.04031
fixed	NA	count_birth_order2/3	0.0165	0.01281	1.288	3648	0.1978	-0.01946	0.05247
fixed	NA	count_birth_order3/3	0.0005857	0.01395	0.04198	3650	0.9665	-0.03858	0.03975
fixed	NA	count_birth_order1/4	0.0207	0.01322	1.565	3646	0.1176	-0.01642	0.05781
fixed	NA	count_birth_order2/4	0.005796	0.01401	0.4136	3650	0.6792	-0.03354	0.04513
fixed	NA	count_birth_order3/4	0.008942	0.01453	0.6155	3648	0.5383	-0.03184	0.04972
fixed	NA	count_birth_order4/4	0.01142	0.01555	0.734	3645	0.463	-0.03224	0.05507
fixed	NA	count_birth_order1/5	0.007885	0.01741	0.4528	3650	0.6507	-0.04099	0.05676
fixed	NA	count_birth_order2/5	-0.006315	0.01877	-0.3363	3640	0.7366	-0.05901	0.04639
fixed	NA	count_birth_order3/5	0.008757	0.01785	0.4907	3639	0.6237	-0.04134	0.05885
fixed	NA	count_birth_order4/5	-0.01357	0.01741	-0.7797	3636	0.4356	-0.06243	0.03529
fixed	NA	count_birth_order5/5	-0.0001377	0.01832	-0.007518	3630	0.994	-0.05155	0.05128
fixed	NA	count_birth_order1/>5	0.02285	0.01649	1.385	3650	0.166	-0.02345	0.06914
fixed	NA	count_birth_order2/>5	0.008602	0.01661	0.5177	3640	0.6047	-0.03803	0.05524
fixed	NA	count_birth_order3/>5	0.01917	0.01621	1.182	3636	0.2371	-0.02634	0.06467
fixed	NA	count_birth_order4/>5	-0.01033	0.01587	-0.651	3626	0.5151	-0.05486	0.03421
fixed	NA	count_birth_order5/>5	0.006311	0.01516	0.4162	3632	0.6773	-0.03625	0.04888
fixed	NA	count_birth_order>5/>5	0.01036	0.01186	0.8735	3382	0.3824	-0.02294	0.04367
ran_pars	mother_pidlink	sd__(Intercept)	0.05117	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1509	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)
11	-3080	-3011	1551	-3102	NA	NA	NA
12	-3078	-3004	1551	-3102	0.5788	1	0.4468
16	-3074	-2975	1553	-3106	3.483	4	0.4804
26	-3059	-2897	1555	-3111	4.848	10	0.9011

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)	-0.01139	0.1044	-0.1092	3689	0.9131	-0.3044	0.2816
fixed	NA	poly(age, 3, raw = TRUE)1	0.0004498	0.0112	0.04014	3689	0.968	-0.031	0.0319
fixed	NA	poly(age, 3, raw = TRUE)2	0.00002628	0.000384	0.06844	3689	0.9454	-0.001051	0.001104
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000008199	0.00000421	-0.1948	3689	0.8456	-0.00001264	0.000011
fixed	NA	male	0.02609	0.005275	4.946	3670	0.0000007934	0.01128	0.0409
fixed	NA	sibling_count3	0.008191	0.009579	0.8551	2809	0.3926	-0.0187	0.03508
fixed	NA	sibling_count4	0.02248	0.009664	2.326	2627	0.02009	-0.004648	0.04961
fixed	NA	sibling_count5	-0.0006205	0.01018	-0.06093	2378	0.9514	-0.02921	0.02796
fixed	NA	sibling_count>5	0.01265	0.008926	1.417	2437	0.1567	-0.01241	0.0377
ran_pars	mother_pidlink	sd__(Intercept)	0.05052	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1503	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)	-0.01242	0.1044	-0.119	3688	0.9053	-0.3054	0.2806
fixed	NA	birth_order	-0.0009043	0.001448	-0.6243	3314	0.5324	-0.00497	0.003161
fixed	NA	poly(age, 3, raw = TRUE)1	0.0006657	0.01121	0.05938	3688	0.9527	-0.0308	0.03214
fixed	NA	poly(age, 3, raw = TRUE)2	0.00002094	0.0003841	0.05452	3688	0.9565	-0.001057	0.001099
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000008013	0.000004211	-0.1903	3688	0.8491	-0.00001262	0.00001102
fixed	NA	male	0.02613	0.005276	4.953	3668	0.0000007638	0.01132	0.04094
fixed	NA	sibling_count3	0.008654	0.00961	0.9005	2802	0.3679	-0.01832	0.03563
fixed	NA	sibling_count4	0.0234	0.009779	2.393	2611	0.01677	-0.004047	0.05085
fixed	NA	sibling_count5	0.000899	0.01048	0.08581	2380	0.9316	-0.02851	0.03031
fixed	NA	sibling_count>5	0.01586	0.0103	1.54	2467	0.1237	-0.01304	0.04475
ran_pars	mother_pidlink	sd__(Intercept)	0.05085	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1502	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)	-0.01457	0.1045	-0.1394	3684	0.8891	-0.3079	0.2787
fixed	NA	poly(age, 3, raw = TRUE)1	0.000977	0.01121	0.08712	3684	0.9306	-0.0305	0.03246
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001225	0.0003842	0.03189	3684	0.9746	-0.001066	0.001091
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000007374	0.000004213	-0.175	3684	0.8611	-0.00001256	0.00001109
fixed	NA	male	0.0261	0.005277	4.946	3663	0.0000007933	0.01128	0.04091
fixed	NA	sibling_count3	0.009587	0.00977	0.9813	2894	0.3265	-0.01784	0.03701
fixed	NA	sibling_count4	0.02691	0.01006	2.674	2774	0.007531	-0.001335	0.05516
fixed	NA	sibling_count5	0.004979	0.01093	0.4555	2635	0.6488	-0.0257	0.03566
fixed	NA	sibling_count>5	0.01859	0.01059	1.755	2650	0.07933	-0.01114	0.04833
fixed	NA	birth_order_nonlinear2	-0.006724	0.007086	-0.9489	3128	0.3428	-0.02661	0.01317
fixed	NA	birth_order_nonlinear3	-0.00603	0.008265	-0.7296	3237	0.4657	-0.02923	0.01717
fixed	NA	birth_order_nonlinear4	-0.01962	0.009795	-2.003	3342	0.04525	-0.04712	0.007875
fixed	NA	birth_order_nonlinear5	-0.008111	0.01193	-0.6798	3334	0.4967	-0.0416	0.02538
fixed	NA	birth_order_nonlinear>5	-0.007123	0.01101	-0.6469	3628	0.5178	-0.03803	0.02379
ran_pars	mother_pidlink	sd__(Intercept)	0.05104	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1502	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)	-0.01177	0.1048	-0.1123	3673	0.9106	-0.306	0.2824
fixed	NA	poly(age, 3, raw = TRUE)1	0.0009535	0.01125	0.08475	3674	0.9325	-0.03063	0.03254
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001652	0.0003856	0.04284	3674	0.9658	-0.001066	0.001099
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000000813	0.000004229	-0.1922	3674	0.8476	-0.00001268	0.00001106
fixed	NA	male	0.02624	0.005288	4.961	3653	0.0000007322	0.01139	0.04108
fixed	NA	count_birth_order2/2	-0.01773	0.01501	-1.182	3271	0.2375	-0.05985	0.02439
fixed	NA	count_birth_order1/3	-0.0005947	0.0127	-0.04683	3661	0.9626	-0.03624	0.03505
fixed	NA	count_birth_order2/3	0.01466	0.01383	1.06	3671	0.289	-0.02415	0.05348
fixed	NA	count_birth_order3/3	-0.009318	0.01532	-0.608	3674	0.5432	-0.05233	0.0337
fixed	NA	count_birth_order1/4	0.03084	0.01378	2.238	3667	0.02527	-0.007839	0.06953
fixed	NA	count_birth_order2/4	0.009355	0.01452	0.6444	3673	0.5193	-0.0314	0.05011
fixed	NA	count_birth_order3/4	0.01186	0.01571	0.7549	3672	0.4504	-0.03224	0.05595
fixed	NA	count_birth_order4/4	0.006457	0.01706	0.3785	3668	0.7051	-0.04143	0.05435
fixed	NA	count_birth_order1/5	0.0004113	0.01665	0.0247	3674	0.9803	-0.04634	0.04716
fixed	NA	count_birth_order2/5	-0.01248	0.01707	-0.731	3673	0.4648	-0.0604	0.03544
fixed	NA	count_birth_order3/5	-0.004494	0.01756	-0.2559	3667	0.798	-0.05379	0.0448
fixed	NA	count_birth_order4/5	-0.01346	0.01788	-0.753	3662	0.4515	-0.06364	0.03672
fixed	NA	count_birth_order5/5	-0.002927	0.01815	-0.1613	3657	0.8719	-0.05387	0.04801
fixed	NA	count_birth_order1/>5	0.009889	0.01503	0.6581	3671	0.5105	-0.03229	0.05207
fixed	NA	count_birth_order2/>5	0.007599	0.01587	0.4788	3669	0.6321	-0.03695	0.05214
fixed	NA	count_birth_order3/>5	0.02187	0.01529	1.43	3668	0.1527	-0.02104	0.06478
fixed	NA	count_birth_order4/>5	-0.009521	0.01485	-0.6411	3665	0.5215	-0.05121	0.03217
fixed	NA	count_birth_order5/>5	0.004109	0.01572	0.2613	3653	0.7939	-0.04003	0.04825
fixed	NA	count_birth_order>5/>5	0.00764	0.01189	0.6425	3454	0.5206	-0.02574	0.04101
ran_pars	mother_pidlink	sd__(Intercept)	0.05089	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1503	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)
11	-3126	-3058	1574	-3148	NA	NA	NA
12	-3125	-3050	1574	-3149	0.3851	1	0.5349
16	-3121	-3021	1576	-3153	3.745	4	0.4416
26	-3108	-2946	1580	-3160	6.999	10	0.7256

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)	-0.01066	0.1071	-0.09954	3601	0.9207	-0.3114	0.2901
fixed	NA	poly(age, 3, raw = TRUE)1	0.0003278	0.01151	0.02848	3601	0.9773	-0.03198	0.03264
fixed	NA	poly(age, 3, raw = TRUE)2	0.00003105	0.0003947	0.07867	3601	0.9373	-0.001077	0.001139
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000008807	0.000004332	-0.2033	3601	0.8389	-0.00001304	0.00001128
fixed	NA	male	0.02676	0.005405	4.952	3576	0.000000768	0.01159	0.04194
fixed	NA	sibling_count3	0.01389	0.008671	1.602	2619	0.1094	-0.01045	0.03823
fixed	NA	sibling_count4	0.01566	0.009086	1.723	2354	0.08493	-0.009845	0.04116
fixed	NA	sibling_count5	0.003031	0.01042	0.2908	1889	0.7712	-0.02622	0.03229
fixed	NA	sibling_count>5	0.01426	0.008852	1.611	1894	0.1074	-0.01059	0.0391
ran_pars	mother_pidlink	sd__(Intercept)	0.05302	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1516	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)	-0.01296	0.1072	-0.1209	3600	0.9038	-0.3138	0.2879
fixed	NA	birth_order	-0.001449	0.001711	-0.8467	3426	0.3972	-0.006251	0.003354
fixed	NA	poly(age, 3, raw = TRUE)1	0.00075	0.01152	0.0651	3600	0.9481	-0.03159	0.03309
fixed	NA	poly(age, 3, raw = TRUE)2	0.00001983	0.0003949	0.05021	3600	0.96	-0.001089	0.001128
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000008209	0.000004332	-0.1895	3600	0.8497	-0.00001298	0.00001134
fixed	NA	male	0.02679	0.005405	4.957	3574	0.000000749	0.01162	0.04196
fixed	NA	sibling_count3	0.01463	0.008718	1.679	2615	0.09335	-0.009838	0.03911
fixed	NA	sibling_count4	0.01724	0.009279	1.858	2358	0.06327	-0.008805	0.04329
fixed	NA	sibling_count5	0.005559	0.01085	0.5122	1928	0.6085	-0.0249	0.03602
fixed	NA	sibling_count>5	0.01948	0.01078	1.806	2110	0.07106	-0.01079	0.04975
ran_pars	mother_pidlink	sd__(Intercept)	0.05347	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1514	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)	-0.01281	0.1072	-0.1194	3596	0.9049	-0.3138	0.2882
fixed	NA	poly(age, 3, raw = TRUE)1	0.0007721	0.01152	0.06702	3596	0.9466	-0.03157	0.03311
fixed	NA	poly(age, 3, raw = TRUE)2	0.0000206	0.0003949	0.05216	3596	0.9584	-0.001088	0.001129
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000000849	0.000004334	-0.1959	3596	0.8447	-0.00001301	0.00001132
fixed	NA	male	0.02683	0.005405	4.963	3571	0.0000007255	0.01166	0.042
fixed	NA	sibling_count3	0.01413	0.008893	1.588	2740	0.1123	-0.01084	0.03909
fixed	NA	sibling_count4	0.01947	0.009615	2.025	2579	0.04293	-0.007515	0.04646
fixed	NA	sibling_count5	0.009835	0.01131	0.8699	2200	0.3845	-0.0219	0.04157
fixed	NA	sibling_count>5	0.02072	0.01108	1.871	2297	0.06154	-0.01037	0.05181
fixed	NA	birth_order_nonlinear2	-0.007982	0.007046	-1.133	2958	0.2574	-0.02776	0.0118
fixed	NA	birth_order_nonlinear3	-0.001416	0.008319	-0.1702	3049	0.8649	-0.02477	0.02193
fixed	NA	birth_order_nonlinear4	-0.02045	0.01045	-1.957	3135	0.05041	-0.04978	0.00888
fixed	NA	birth_order_nonlinear5	-0.01796	0.01288	-1.395	3107	0.1631	-0.05411	0.01819
fixed	NA	birth_order_nonlinear>5	-0.006144	0.0127	-0.4838	3588	0.6286	-0.04179	0.02951
ran_pars	mother_pidlink	sd__(Intercept)	0.0534	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1514	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)	-0.01112	0.1077	-0.1032	3586	0.9178	-0.3134	0.2912
fixed	NA	poly(age, 3, raw = TRUE)1	0.0006036	0.01157	0.05216	3586	0.9584	-0.03188	0.03309
fixed	NA	poly(age, 3, raw = TRUE)2	0.00002941	0.0003968	0.07411	3586	0.9409	-0.001085	0.001143
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000009731	0.000004356	-0.2234	3586	0.8232	-0.0000132	0.00001125
fixed	NA	male	0.02685	0.005417	4.956	3559	0.0000007513	0.01164	0.04205
fixed	NA	count_birth_order2/2	-0.01103	0.01345	-0.8202	3028	0.4122	-0.04877	0.02672
fixed	NA	count_birth_order1/3	0.007516	0.01142	0.658	3571	0.5106	-0.02455	0.03958
fixed	NA	count_birth_order2/3	0.01549	0.0127	1.22	3585	0.2225	-0.02015	0.05113
fixed	NA	count_birth_order3/3	0.009049	0.01367	0.6619	3585	0.5081	-0.02932	0.04742
fixed	NA	count_birth_order1/4	0.02297	0.0134	1.714	3582	0.08658	-0.01464	0.06059
fixed	NA	count_birth_order2/4	0.0009928	0.01407	0.07055	3586	0.9438	-0.03851	0.04049
fixed	NA	count_birth_order3/4	0.01526	0.0146	1.045	3582	0.2959	-0.02572	0.05624
fixed	NA	count_birth_order4/4	0.005978	0.01586	0.3769	3578	0.7063	-0.03854	0.0505
fixed	NA	count_birth_order1/5	0.007985	0.01752	0.4559	3586	0.6485	-0.04118	0.05715
fixed	NA	count_birth_order2/5	-0.005466	0.01954	-0.2797	3567	0.7797	-0.06032	0.04939
fixed	NA	count_birth_order3/5	0.01416	0.01906	0.7431	3564	0.4575	-0.03933	0.06765
fixed	NA	count_birth_order4/5	-0.01167	0.01834	-0.636	3566	0.5248	-0.06316	0.03982
fixed	NA	count_birth_order5/5	-0.009098	0.01948	-0.467	3558	0.6405	-0.06379	0.04559
fixed	NA	count_birth_order1/>5	0.02622	0.01707	1.536	3585	0.1246	-0.02169	0.07413
fixed	NA	count_birth_order2/>5	0.01201	0.01725	0.6963	3569	0.4863	-0.03641	0.06043
fixed	NA	count_birth_order3/>5	0.02036	0.01647	1.236	3570	0.2165	-0.02587	0.06658
fixed	NA	count_birth_order4/>5	-0.009475	0.01653	-0.573	3550	0.5667	-0.05589	0.03694
fixed	NA	count_birth_order5/>5	0.00164	0.01552	0.1056	3561	0.9159	-0.04194	0.04522
fixed	NA	count_birth_order>5/>5	0.01344	0.01213	1.108	3274	0.2679	-0.0206	0.04747
ran_pars	mother_pidlink	sd__(Intercept)	0.05348	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1516	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)
11	-2965	-2897	1493	-2987	NA	NA	NA
12	-2963	-2889	1494	-2987	0.7092	1	0.3997
16	-2960	-2861	1496	-2992	4.896	4	0.2981
26	-2944	-2783	1498	-2996	3.888	10	0.9523

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)	0.02077	0.05104	0.407	9487	0.684	-0.1225	0.164
fixed	NA	poly(age, 3, raw = TRUE)1	0.003093	0.004566	0.6775	9410	0.4981	-0.009722	0.01591
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00006539	0.0001278	-0.5117	9292	0.6089	-0.0004241	0.0002934
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000003566	0.000001132	0.3151	9167	0.7527	-0.00000282	0.000003533
fixed	NA	male	0.001089	0.004758	0.2289	9731	0.819	-0.01227	0.01444
fixed	NA	sibling_count3	-0.0007703	0.009727	-0.07919	7666	0.9369	-0.02807	0.02653
fixed	NA	sibling_count4	-0.006216	0.009798	-0.6344	7189	0.5259	-0.03372	0.02129
fixed	NA	sibling_count5	-0.01513	0.01016	-1.489	6692	0.1366	-0.04365	0.01339
fixed	NA	sibling_count>5	-0.005755	0.007926	-0.7261	7471	0.4678	-0.028	0.01649
ran_pars	mother_pidlink	sd__(Intercept)	0.05552	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2252	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)	0.02068	0.05103	0.4051	9486	0.6854	-0.1226	0.1639
fixed	NA	birth_order	-0.0014	0.0009492	-1.475	7975	0.1401	-0.004065	0.001264
fixed	NA	poly(age, 3, raw = TRUE)1	0.003478	0.004573	0.7606	9400	0.4469	-0.009358	0.01631
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00007899	0.0001281	-0.6165	9255	0.5376	-0.0004386	0.0002807
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000004777	0.000001135	0.421	9117	0.6738	-0.000002707	0.000003663
fixed	NA	male	0.001123	0.004758	0.2361	9730	0.8134	-0.01223	0.01448
fixed	NA	sibling_count3	-0.0003848	0.00973	-0.03955	7674	0.9685	-0.0277	0.02693
fixed	NA	sibling_count4	-0.005314	0.009817	-0.5413	7229	0.5883	-0.03287	0.02224
fixed	NA	sibling_count5	-0.01359	0.01021	-1.331	6767	0.1832	-0.04226	0.01507
fixed	NA	sibling_count>5	-0.0007645	0.008617	-0.08872	8078	0.9293	-0.02495	0.02342
ran_pars	mother_pidlink	sd__(Intercept)	0.0556	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2251	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)	0.01725	0.05113	0.3374	9491	0.7358	-0.1263	0.1608
fixed	NA	poly(age, 3, raw = TRUE)1	0.003601	0.004578	0.7867	9403	0.4315	-0.009249	0.01645
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00008152	0.0001282	-0.6357	9261	0.525	-0.0004415	0.0002784
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000004881	0.000001135	0.4299	9120	0.6673	-0.000002699	0.000003675
fixed	NA	male	0.001126	0.004759	0.2366	9725	0.813	-0.01223	0.01448
fixed	NA	sibling_count3	0.001311	0.009885	0.1326	7906	0.8945	-0.02644	0.02906
fixed	NA	sibling_count4	-0.003161	0.01011	-0.3127	7682	0.7545	-0.03154	0.02521
fixed	NA	sibling_count5	-0.01113	0.01059	-1.05	7359	0.2936	-0.04085	0.0186
fixed	NA	sibling_count>5	0.001919	0.009053	0.212	8684	0.8321	-0.02349	0.02733
fixed	NA	birth_order_nonlinear2	0.00005417	0.006983	0.007758	9127	0.9938	-0.01955	0.01966
fixed	NA	birth_order_nonlinear3	-0.009658	0.008114	-1.19	9035	0.234	-0.03244	0.01312
fixed	NA	birth_order_nonlinear4	-0.007049	0.00912	-0.7729	9125	0.4396	-0.03265	0.01855
fixed	NA	birth_order_nonlinear5	-0.009026	0.01024	-0.8813	9187	0.3782	-0.03777	0.01972
fixed	NA	birth_order_nonlinear>5	-0.01269	0.00842	-1.507	9711	0.1319	-0.03632	0.01095
ran_pars	mother_pidlink	sd__(Intercept)	0.05552	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2252	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)	0.01213	0.05132	0.2363	9495	0.8132	-0.1319	0.1562
fixed	NA	poly(age, 3, raw = TRUE)1	0.00332	0.004583	0.7244	9395	0.4689	-0.009544	0.01618
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00007672	0.0001283	-0.5978	9251	0.55	-0.0004369	0.0002835
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000004767	0.000001136	0.4196	9108	0.6748	-0.000002712	0.000003665
fixed	NA	male	0.001165	0.004761	0.2448	9715	0.8066	-0.0122	0.01453
fixed	NA	count_birth_order2/2	0.02407	0.01392	1.729	8918	0.08384	-0.01501	0.06315
fixed	NA	count_birth_order1/3	0.0107	0.01329	0.8051	9707	0.4208	-0.02661	0.04801
fixed	NA	count_birth_order2/3	0.002195	0.01479	0.1485	9717	0.882	-0.03931	0.0437
fixed	NA	count_birth_order3/3	0.01111	0.01623	0.6843	9722	0.4938	-0.03446	0.05668
fixed	NA	count_birth_order1/4	0.01602	0.01463	1.095	9719	0.2736	-0.02505	0.05708
fixed	NA	count_birth_order2/4	0.003873	0.01569	0.2468	9720	0.8051	-0.04018	0.04792
fixed	NA	count_birth_order3/4	-0.01074	0.01655	-0.6491	9724	0.5163	-0.0572	0.03571
fixed	NA	count_birth_order4/4	-0.006686	0.01782	-0.3752	9726	0.7075	-0.0567	0.04333
fixed	NA	count_birth_order1/5	-0.00212	0.0165	-0.1285	9727	0.8978	-0.04844	0.0442
fixed	NA	count_birth_order2/5	-0.02531	0.01752	-1.445	9728	0.1486	-0.07448	0.02387
fixed	NA	count_birth_order3/5	-0.00383	0.01843	-0.2078	9729	0.8354	-0.05557	0.04791
fixed	NA	count_birth_order4/5	-0.003889	0.01946	-0.1998	9730	0.8416	-0.05852	0.05074
fixed	NA	count_birth_order5/5	0.006752	0.0195	0.3463	9730	0.7291	-0.04798	0.06148
fixed	NA	count_birth_order1/>5	0.01512	0.01277	1.184	9729	0.2363	-0.02071	0.05095
fixed	NA	count_birth_order2/>5	0.01639	0.01327	1.235	9730	0.2168	-0.02086	0.05365
fixed	NA	count_birth_order3/>5	-0.002849	0.01314	-0.2169	9730	0.8283	-0.03973	0.03403
fixed	NA	count_birth_order4/>5	0.004882	0.01287	0.3794	9730	0.7044	-0.03124	0.04101
fixed	NA	count_birth_order5/>5	-0.002996	0.01301	-0.2303	9730	0.8179	-0.03951	0.03352
fixed	NA	count_birth_order>5/>5	-0.001484	0.01046	-0.1419	9052	0.8871	-0.03083	0.02787
ran_pars	mother_pidlink	sd__(Intercept)	0.05579	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2251	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)
11	-837.4	-758.3	429.7	-859.4	NA	NA	NA
12	-837.6	-751.3	430.8	-861.6	2.178	1	0.14
16	-830.8	-715.8	431.4	-862.8	1.23	4	0.8731
26	-820.8	-634	436.4	-872.8	10.06	10	0.4357

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)	-0.2203	0.156	-1.412	3658	0.158	-0.6581	0.2176
fixed	NA	poly(age, 3, raw = TRUE)1	0.02853	0.01673	1.705	3657	0.08823	-0.01843	0.07549
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009087	0.0005731	-1.586	3655	0.1129	-0.002517	0.0007
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009383	0.000006282	1.494	3652	0.1353	-0.000008249	0.00002702
fixed	NA	male	0.00001633	0.007889	0.00207	3665	0.9983	-0.02213	0.02216
fixed	NA	sibling_count3	-0.005898	0.01284	-0.4594	3222	0.646	-0.04194	0.03014
fixed	NA	sibling_count4	-0.01841	0.01322	-1.393	3023	0.1637	-0.05552	0.01869
fixed	NA	sibling_count5	-0.001773	0.01468	-0.1208	2716	0.9039	-0.04297	0.03943
fixed	NA	sibling_count>5	-0.007312	0.01267	-0.5772	2659	0.5639	-0.04287	0.02825
ran_pars	mother_pidlink	sd__(Intercept)	0.04285	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2318	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)	-0.2228	0.156	-1.428	3657	0.1533	-0.6607	0.2151
fixed	NA	birth_order	-0.002547	0.002424	-1.051	3411	0.2934	-0.009349	0.004256
fixed	NA	poly(age, 3, raw = TRUE)1	0.02909	0.01674	1.738	3655	0.08232	-0.0179	0.07607
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000922	0.0005732	-1.608	3653	0.1078	-0.002531	0.0006871
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009422	0.000006282	1.5	3650	0.1337	-0.000008211	0.00002705
fixed	NA	male	0.0001252	0.00789	0.01587	3664	0.9873	-0.02202	0.02227
fixed	NA	sibling_count3	-0.004632	0.01289	-0.3593	3220	0.7194	-0.04082	0.03156
fixed	NA	sibling_count4	-0.01563	0.01348	-1.16	3015	0.2462	-0.05347	0.0222
fixed	NA	sibling_count5	0.002801	0.01531	0.183	2735	0.8548	-0.04017	0.04577
fixed	NA	sibling_count>5	0.001766	0.01533	0.1152	2746	0.9083	-0.04126	0.04479
ran_pars	mother_pidlink	sd__(Intercept)	0.04259	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2319	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)	-0.2202	0.1562	-1.41	3653	0.1586	-0.6586	0.2182
fixed	NA	poly(age, 3, raw = TRUE)1	0.02881	0.01675	1.72	3652	0.08552	-0.01821	0.07582
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009102	0.0005736	-1.587	3650	0.1127	-0.00252	0.0007
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009273	0.000006287	1.475	3647	0.1403	-0.000008376	0.00002692
fixed	NA	male	-0.00008511	0.007895	-0.01078	3660	0.9914	-0.02225	0.02208
fixed	NA	sibling_count3	-0.003592	0.01316	-0.2729	3288	0.7849	-0.04054	0.03335
fixed	NA	sibling_count4	-0.01523	0.01401	-1.088	3163	0.2769	-0.05454	0.02408
fixed	NA	sibling_count5	0.001798	0.01608	0.1118	2971	0.911	-0.04334	0.04693
fixed	NA	sibling_count>5	0.00193	0.01577	0.1224	2889	0.9026	-0.04233	0.04619
fixed	NA	birth_order_nonlinear2	-0.0118	0.01054	-1.119	3420	0.2631	-0.04138	0.01779
fixed	NA	birth_order_nonlinear3	-0.01021	0.01236	-0.8264	3476	0.4087	-0.0449	0.02447
fixed	NA	birth_order_nonlinear4	-0.006922	0.01507	-0.4593	3525	0.6461	-0.04923	0.03538
fixed	NA	birth_order_nonlinear5	-0.00769	0.01848	-0.4161	3543	0.6773	-0.05956	0.04418
fixed	NA	birth_order_nonlinear>5	-0.02267	0.01806	-1.255	3592	0.2096	-0.07336	0.02803
ran_pars	mother_pidlink	sd__(Intercept)	0.04289	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)	-0.2337	0.1567	-1.491	3642	0.1359	-0.6737	0.2062
fixed	NA	poly(age, 3, raw = TRUE)1	0.03014	0.01681	1.793	3641	0.07307	-0.01705	0.07732
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009591	0.0005759	-1.665	3639	0.09591	-0.002576	0.0006574
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009839	0.000006313	1.558	3636	0.1192	-0.000007883	0.00002756
fixed	NA	male	-0.00011	0.007904	-0.01392	3650	0.9889	-0.0223	0.02208
fixed	NA	count_birth_order2/2	-0.005228	0.02055	-0.2543	3410	0.7993	-0.06292	0.05247
fixed	NA	count_birth_order1/3	-0.004104	0.01708	-0.2403	3649	0.8101	-0.05205	0.04384
fixed	NA	count_birth_order2/3	-0.03045	0.01899	-1.604	3650	0.1089	-0.08377	0.02286
fixed	NA	count_birth_order3/3	0.01606	0.0207	0.7762	3650	0.4377	-0.04203	0.07416
fixed	NA	count_birth_order1/4	-0.01085	0.0196	-0.5534	3649	0.58	-0.06585	0.04416
fixed	NA	count_birth_order2/4	-0.0261	0.02078	-1.256	3650	0.2091	-0.08443	0.03223
fixed	NA	count_birth_order3/4	-0.0325	0.02155	-1.508	3650	0.1317	-0.093	0.02801
fixed	NA	count_birth_order4/4	-0.01051	0.02308	-0.4555	3650	0.6488	-0.07528	0.05426
fixed	NA	count_birth_order1/5	0.0168	0.02582	0.6509	3650	0.5151	-0.05566	0.08927
fixed	NA	count_birth_order2/5	-0.01284	0.02786	-0.4608	3650	0.645	-0.09105	0.06537
fixed	NA	count_birth_order3/5	-0.00643	0.02649	-0.2428	3649	0.8082	-0.08078	0.06792
fixed	NA	count_birth_order4/5	0.007478	0.02584	0.2894	3649	0.7723	-0.06505	0.08001
fixed	NA	count_birth_order5/5	-0.02538	0.0272	-0.9331	3648	0.3508	-0.1017	0.05097
fixed	NA	count_birth_order1/>5	0.003552	0.02444	0.1453	3646	0.8844	-0.06505	0.07216
fixed	NA	count_birth_order2/>5	0.02602	0.02465	1.056	3650	0.2911	-0.04316	0.09521
fixed	NA	count_birth_order3/>5	-0.03433	0.02406	-1.427	3650	0.1536	-0.1019	0.0332
fixed	NA	count_birth_order4/>5	-0.02051	0.02356	-0.8706	3649	0.3841	-0.08663	0.04561
fixed	NA	count_birth_order5/>5	0.009459	0.02251	0.4202	3649	0.6744	-0.05373	0.07265
fixed	NA	count_birth_order>5/>5	-0.01853	0.01747	-1.061	3470	0.2887	-0.06756	0.03049
ran_pars	mother_pidlink	sd__(Intercept)	0.04403	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2317	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)
11	-179.5	-111.2	100.8	-201.5	NA	NA	NA
12	-178.6	-104.1	101.3	-202.6	1.109	1	0.2924
16	-171.9	-72.52	101.9	-203.9	1.257	4	0.8687
26	-163.7	-2.307	107.9	-215.7	11.87	10	0.2936

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)	-0.2294	0.1558	-1.472	3682	0.1411	-0.6668	0.208
fixed	NA	poly(age, 3, raw = TRUE)1	0.02951	0.01673	1.764	3680	0.07781	-0.01745	0.07647
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009341	0.0005732	-1.63	3678	0.1033	-0.002543	0.0006749
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009572	0.000006284	1.523	3674	0.1278	-0.000008068	0.00002721
fixed	NA	male	0.0005569	0.00789	0.07059	3689	0.9437	-0.02159	0.02271
fixed	NA	sibling_count3	-0.009068	0.01413	-0.6418	3278	0.5211	-0.04873	0.0306
fixed	NA	sibling_count4	-0.01734	0.01423	-1.218	3149	0.2231	-0.05727	0.0226
fixed	NA	sibling_count5	-0.01372	0.01495	-0.9178	2951	0.3588	-0.05569	0.02824
fixed	NA	sibling_count>5	-0.006611	0.01311	-0.5042	2978	0.6142	-0.04342	0.03019
ran_pars	mother_pidlink	sd__(Intercept)	0.04281	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2327	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)	-0.2319	0.1558	-1.488	3680	0.1368	-0.6693	0.2055
fixed	NA	birth_order	-0.003014	0.002142	-1.407	3319	0.1595	-0.009027	0.002999
fixed	NA	poly(age, 3, raw = TRUE)1	0.03012	0.01673	1.8	3678	0.07195	-0.01685	0.07709
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009479	0.0005732	-1.654	3676	0.09829	-0.002557	0.0006612
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009596	0.000006283	1.527	3673	0.1268	-0.000008042	0.00002723
fixed	NA	male	0.0006874	0.00789	0.08713	3688	0.9306	-0.02146	0.02283
fixed	NA	sibling_count3	-0.00756	0.01417	-0.5336	3275	0.5936	-0.04733	0.03221
fixed	NA	sibling_count4	-0.01432	0.01439	-0.9953	3138	0.3197	-0.0547	0.02606
fixed	NA	sibling_count5	-0.008675	0.01537	-0.5644	2944	0.5725	-0.05182	0.03447
fixed	NA	sibling_count>5	0.003984	0.01511	0.2636	2972	0.7921	-0.03844	0.04641
ran_pars	mother_pidlink	sd__(Intercept)	0.04245	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2327	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)	-0.2256	0.156	-1.446	3676	0.1483	-0.6636	0.2124
fixed	NA	poly(age, 3, raw = TRUE)1	0.02936	0.01675	1.753	3675	0.07967	-0.01765	0.07636
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009206	0.0005737	-1.605	3673	0.1087	-0.002531	0.0006898
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009293	0.00000629	1.477	3669	0.1397	-0.000008364	0.00002695
fixed	NA	male	0.0004118	0.007895	0.05216	3684	0.9584	-0.02175	0.02257
fixed	NA	sibling_count3	-0.006194	0.01442	-0.4295	3326	0.6676	-0.04667	0.03429
fixed	NA	sibling_count4	-0.01375	0.01483	-0.9267	3241	0.3541	-0.05538	0.02789
fixed	NA	sibling_count5	-0.007203	0.01608	-0.4478	3127	0.6543	-0.05235	0.03795
fixed	NA	sibling_count>5	0.004556	0.01559	0.2923	3106	0.7701	-0.0392	0.04831
fixed	NA	birth_order_nonlinear2	-0.01058	0.0107	-0.9893	3455	0.3226	-0.04061	0.01944
fixed	NA	birth_order_nonlinear3	-0.01241	0.01246	-0.9963	3523	0.3192	-0.04739	0.02256
fixed	NA	birth_order_nonlinear4	-0.007174	0.01475	-0.4865	3578	0.6266	-0.04856	0.03422
fixed	NA	birth_order_nonlinear5	-0.02097	0.01796	-1.168	3585	0.243	-0.07138	0.02944
fixed	NA	birth_order_nonlinear>5	-0.02246	0.01639	-1.371	3586	0.1706	-0.06845	0.02353
ran_pars	mother_pidlink	sd__(Intercept)	0.04251	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2328	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)	-0.2352	0.1565	-1.503	3665	0.1328	-0.6744	0.204
fixed	NA	poly(age, 3, raw = TRUE)1	0.03016	0.0168	1.796	3664	0.07262	-0.01699	0.07731
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0009527	0.0005756	-1.655	3661	0.09795	-0.002568	0.0006629
fixed	NA	poly(age, 3, raw = TRUE)3	0.000009682	0.000006311	1.534	3657	0.1251	-0.000008035	0.0000274
fixed	NA	male	0.000434	0.00791	0.05486	3674	0.9563	-0.02177	0.02264
fixed	NA	count_birth_order2/2	-0.00005066	0.02262	-0.00224	3477	0.9982	-0.06354	0.06344
fixed	NA	count_birth_order1/3	-0.008272	0.01896	-0.4363	3673	0.6626	-0.06149	0.04494
fixed	NA	count_birth_order2/3	-0.0263	0.02066	-1.273	3674	0.2029	-0.08428	0.03168
fixed	NA	count_birth_order3/3	0.01414	0.0229	0.6175	3674	0.537	-0.05015	0.07844
fixed	NA	count_birth_order1/4	-0.002246	0.02058	-0.1092	3673	0.9131	-0.06001	0.05551
fixed	NA	count_birth_order2/4	-0.03167	0.02169	-1.46	3674	0.1443	-0.09255	0.02921
fixed	NA	count_birth_order3/4	-0.02752	0.02348	-1.172	3674	0.2414	-0.09344	0.0384
fixed	NA	count_birth_order4/4	-0.008277	0.02551	-0.3244	3674	0.7456	-0.07989	0.06333
fixed	NA	count_birth_order1/5	0.0006942	0.02488	0.0279	3674	0.9777	-0.06914	0.07053
fixed	NA	count_birth_order2/5	-0.01059	0.02552	-0.4151	3674	0.6781	-0.08221	0.06103
fixed	NA	count_birth_order3/5	-0.01189	0.02626	-0.4526	3674	0.6508	-0.0856	0.06183
fixed	NA	count_birth_order4/5	-0.01932	0.02674	-0.7227	3673	0.4699	-0.09438	0.05573
fixed	NA	count_birth_order5/5	-0.02963	0.02715	-1.091	3672	0.2753	-0.1058	0.04659
fixed	NA	count_birth_order1/>5	0.01111	0.02243	0.4954	3670	0.6204	-0.05186	0.07409
fixed	NA	count_birth_order2/>5	0.02061	0.02372	0.8689	3673	0.385	-0.04597	0.08719
fixed	NA	count_birth_order3/>5	-0.02985	0.02286	-1.306	3674	0.1916	-0.09401	0.03431
fixed	NA	count_birth_order4/>5	0.000123	0.02221	0.005536	3674	0.9956	-0.06222	0.06246
fixed	NA	count_birth_order5/>5	-0.009344	0.02353	-0.3972	3673	0.6913	-0.07539	0.0567
fixed	NA	count_birth_order>5/>5	-0.01417	0.01765	-0.8029	3540	0.4221	-0.06372	0.03537
ran_pars	mother_pidlink	sd__(Intercept)	0.04262	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2328	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)
11	-155.6	-87.25	88.81	-177.6	NA	NA	NA
12	-155.6	-81.02	89.8	-179.6	1.987	1	0.1587
16	-148.5	-49.03	90.24	-180.5	0.8671	4	0.9292
26	-136.8	24.85	94.38	-188.8	8.28	10	0.6015

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)	-0.1795	0.155	-1.158	3591	0.2468	-0.6145	0.2555
fixed	NA	poly(age, 3, raw = TRUE)1	0.02407	0.01665	1.446	3589	0.1484	-0.02266	0.0708
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007797	0.0005708	-1.366	3586	0.172	-0.002382	0.0008225
fixed	NA	poly(age, 3, raw = TRUE)3	0.000008248	0.000006263	1.317	3580	0.1879	-0.000009332	0.00002583
fixed	NA	male	0.0003739	0.007836	0.04772	3601	0.9619	-0.02162	0.02237
fixed	NA	sibling_count3	-0.003764	0.01234	-0.3051	3194	0.7603	-0.03839	0.03086
fixed	NA	sibling_count4	-0.01422	0.01288	-1.105	3003	0.2694	-0.05037	0.02192
fixed	NA	sibling_count5	0.003677	0.01466	0.2508	2602	0.802	-0.03747	0.04483
fixed	NA	sibling_count>5	0.00007903	0.01245	0.006349	2567	0.9949	-0.03486	0.03502
ran_pars	mother_pidlink	sd__(Intercept)	0.03288	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2297	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)	-0.182	0.155	-1.174	3589	0.2403	-0.6171	0.2531
fixed	NA	birth_order	-0.001948	0.002453	-0.7941	3343	0.4272	-0.008835	0.004938
fixed	NA	poly(age, 3, raw = TRUE)1	0.02457	0.01666	1.474	3587	0.1405	-0.0222	0.07133
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007923	0.000571	-1.387	3583	0.1654	-0.002395	0.0008107
fixed	NA	poly(age, 3, raw = TRUE)3	0.000008303	0.000006264	1.326	3579	0.185	-0.000009279	0.00002589
fixed	NA	male	0.0004034	0.007837	0.05148	3600	0.9589	-0.02159	0.0224
fixed	NA	sibling_count3	-0.002778	0.0124	-0.2241	3191	0.8227	-0.03758	0.03202
fixed	NA	sibling_count4	-0.01213	0.01314	-0.9225	2997	0.3563	-0.04902	0.02477
fixed	NA	sibling_count5	0.007049	0.01526	0.4619	2618	0.6442	-0.03579	0.04989
fixed	NA	sibling_count>5	0.007013	0.0152	0.4613	2701	0.6446	-0.03566	0.04968
ran_pars	mother_pidlink	sd__(Intercept)	0.03272	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2297	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)	-0.18	0.1552	-1.16	3585	0.2462	-0.6156	0.2556
fixed	NA	poly(age, 3, raw = TRUE)1	0.02441	0.01667	1.464	3583	0.1433	-0.02239	0.0712
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0007846	0.0005714	-1.373	3580	0.1698	-0.002389	0.0008194
fixed	NA	poly(age, 3, raw = TRUE)3	0.000008199	0.000006269	1.308	3576	0.191	-0.000009399	0.0000258
fixed	NA	male	0.000236	0.007841	0.0301	3596	0.976	-0.02177	0.02225
fixed	NA	sibling_count3	-0.002512	0.01268	-0.1982	3257	0.8429	-0.03809	0.03307
fixed	NA	sibling_count4	-0.01313	0.01367	-0.9604	3139	0.3369	-0.0515	0.02524
fixed	NA	sibling_count5	0.004467	0.01598	0.2795	2842	0.7799	-0.04039	0.04933
fixed	NA	sibling_count>5	0.006556	0.01567	0.4184	2852	0.6757	-0.03743	0.05054
fixed	NA	birth_order_nonlinear2	-0.01101	0.01035	-1.064	3376	0.2873	-0.04005	0.01803
fixed	NA	birth_order_nonlinear3	-0.006014	0.0122	-0.4931	3431	0.622	-0.04025	0.02822
fixed	NA	birth_order_nonlinear4	-0.001251	0.0153	-0.08179	3482	0.9348	-0.04419	0.04169
fixed	NA	birth_order_nonlinear5	-0.004343	0.01886	-0.2303	3484	0.8179	-0.05727	0.04859
fixed	NA	birth_order_nonlinear>5	-0.01995	0.01833	-1.088	3521	0.2765	-0.07139	0.0315
ran_pars	mother_pidlink	sd__(Intercept)	0.03303	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2298	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)	-0.1869	0.1557	-1.201	3575	0.2299	-0.6239	0.25
fixed	NA	poly(age, 3, raw = TRUE)1	0.02514	0.01673	1.503	3572	0.1329	-0.02181	0.0721
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000813	0.0005736	-1.418	3569	0.1564	-0.002423	0.000797
fixed	NA	poly(age, 3, raw = TRUE)3	0.000008544	0.000006294	1.357	3564	0.1747	-0.000009124	0.00002621
fixed	NA	male	0.0004866	0.007851	0.06198	3586	0.9506	-0.02155	0.02253
fixed	NA	count_birth_order2/2	-0.008769	0.01971	-0.4448	3359	0.6565	-0.06411	0.04657
fixed	NA	count_birth_order1/3	-0.004317	0.01651	-0.2614	3586	0.7938	-0.05067	0.04204
fixed	NA	count_birth_order2/3	-0.02721	0.01838	-1.481	3586	0.1388	-0.07879	0.02437
fixed	NA	count_birth_order3/3	0.01517	0.0198	0.7662	3586	0.4436	-0.04041	0.07075
fixed	NA	count_birth_order1/4	-0.01353	0.01938	-0.6981	3586	0.4851	-0.06795	0.04088
fixed	NA	count_birth_order2/4	-0.02109	0.02038	-1.035	3586	0.3007	-0.07829	0.0361
fixed	NA	count_birth_order3/4	-0.02761	0.02115	-1.306	3586	0.1918	-0.08698	0.03176
fixed	NA	count_birth_order4/4	-0.003205	0.02298	-0.1395	3586	0.8891	-0.06771	0.0613
fixed	NA	count_birth_order1/5	0.01094	0.02535	0.4314	3585	0.6662	-0.06021	0.08209
fixed	NA	count_birth_order2/5	-0.01583	0.02833	-0.559	3586	0.5762	-0.09535	0.06368
fixed	NA	count_birth_order3/5	0.007652	0.02763	0.277	3586	0.7818	-0.06989	0.0852
fixed	NA	count_birth_order4/5	0.01138	0.02659	0.4279	3585	0.6688	-0.06327	0.08603
fixed	NA	count_birth_order5/5	-0.01412	0.02825	-0.4998	3585	0.6172	-0.09343	0.06519
fixed	NA	count_birth_order1/>5	0.01476	0.02469	0.5976	3580	0.5502	-0.05456	0.08407
fixed	NA	count_birth_order2/>5	0.02997	0.02499	1.199	3584	0.2305	-0.04017	0.1001
fixed	NA	count_birth_order3/>5	-0.02888	0.02386	-1.211	3586	0.2261	-0.09586	0.03809
fixed	NA	count_birth_order4/>5	-0.01081	0.02398	-0.451	3586	0.652	-0.07811	0.05649
fixed	NA	count_birth_order5/>5	0.01124	0.02251	0.4996	3586	0.6174	-0.05193	0.07442
fixed	NA	count_birth_order>5/>5	-0.01263	0.01737	-0.7269	3365	0.4673	-0.06138	0.03613
ran_pars	mother_pidlink	sd__(Intercept)	0.03417	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2296	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)
11	-290.8	-222.7	156.4	-312.8	NA	NA	NA
12	-289.4	-215.1	156.7	-313.4	0.6335	1	0.4261
16	-283	-183.9	157.5	-315	1.525	4	0.8222
26	-273	-112.1	162.5	-325	10.08	10	0.4334

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)	0.0652	0.04159	1.568	9516	0.1169	-0.05153	0.1819
fixed	NA	poly(age, 3, raw = TRUE)1	-0.003102	0.003721	-0.8336	9447	0.4045	-0.01355	0.007343
fixed	NA	poly(age, 3, raw = TRUE)2	0.00007889	0.0001042	0.7573	9338	0.4489	-0.0002135	0.0003713
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000005583	0.0000009226	-0.6052	9222	0.5451	-0.000003148	0.000002031
fixed	NA	male	-0.01246	0.003874	-3.218	9725	0.001296	-0.02334	-0.001591
fixed	NA	sibling_count3	0.008001	0.007939	1.008	7753	0.3136	-0.01428	0.03029
fixed	NA	sibling_count4	0.009834	0.008	1.229	7307	0.219	-0.01262	0.03229
fixed	NA	sibling_count5	0.02201	0.008298	2.653	6836	0.008005	-0.001281	0.04531
fixed	NA	sibling_count>5	0.01792	0.00647	2.769	7576	0.005634	-0.000245	0.03608
ran_pars	mother_pidlink	sd__(Intercept)	0.04837	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1826	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)	0.06522	0.04159	1.568	9515	0.1169	-0.05152	0.182
fixed	NA	birth_order	0.0004447	0.0007746	0.5741	8215	0.5659	-0.00173	0.002619
fixed	NA	poly(age, 3, raw = TRUE)1	-0.003224	0.003727	-0.865	9437	0.3871	-0.01369	0.007238
fixed	NA	poly(age, 3, raw = TRUE)2	0.00008323	0.0001044	0.7969	9304	0.4256	-0.00021	0.0003764
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000000597	0.0000009251	-0.6454	9175	0.5187	-0.000003194	0.000002
fixed	NA	male	-0.01247	0.003874	-3.22	9724	0.001284	-0.02335	-0.001601
fixed	NA	sibling_count3	0.007879	0.007942	0.992	7762	0.3212	-0.01442	0.03017
fixed	NA	sibling_count4	0.00955	0.008016	1.191	7347	0.2336	-0.01295	0.03205
fixed	NA	sibling_count5	0.02153	0.008341	2.581	6912	0.009879	-0.001888	0.04494
fixed	NA	sibling_count>5	0.01634	0.007032	2.323	8169	0.02019	-0.003402	0.03607
ran_pars	mother_pidlink	sd__(Intercept)	0.04838	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1826	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)	0.06535	0.04165	1.569	9519	0.1167	-0.05157	0.1823
fixed	NA	poly(age, 3, raw = TRUE)1	-0.003216	0.00373	-0.8623	9440	0.3886	-0.01369	0.007254
fixed	NA	poly(age, 3, raw = TRUE)2	0.0000849	0.0001045	0.8124	9310	0.4166	-0.0002085	0.0003783
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000006214	0.0000009255	-0.6715	9178	0.5019	-0.000003219	0.000001976
fixed	NA	male	-0.01255	0.003874	-3.241	9720	0.001196	-0.02343	-0.00168
fixed	NA	sibling_count3	0.007229	0.008066	0.8962	7983	0.3702	-0.01541	0.02987
fixed	NA	sibling_count4	0.01056	0.008249	1.28	7779	0.2006	-0.0126	0.03372
fixed	NA	sibling_count5	0.02083	0.008646	2.409	7477	0.01603	-0.003444	0.04509
fixed	NA	sibling_count>5	0.01412	0.007382	1.913	8737	0.05576	-0.006599	0.03485
fixed	NA	birth_order_nonlinear2	-0.001514	0.005678	-0.2667	9157	0.7897	-0.01745	0.01442
fixed	NA	birth_order_nonlinear3	0.003304	0.006598	0.5007	9063	0.6166	-0.01522	0.02182
fixed	NA	birth_order_nonlinear4	-0.007857	0.007416	-1.06	9143	0.2894	-0.02867	0.01296
fixed	NA	birth_order_nonlinear5	0.01102	0.008329	1.324	9198	0.1857	-0.01236	0.0344
fixed	NA	birth_order_nonlinear>5	0.007088	0.006857	1.034	9722	0.3013	-0.01216	0.02633
ran_pars	mother_pidlink	sd__(Intercept)	0.04841	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1826	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)	0.06713	0.04182	1.605	9521	0.1085	-0.05027	0.1845
fixed	NA	poly(age, 3, raw = TRUE)1	-0.003226	0.003735	-0.8637	9431	0.3878	-0.01371	0.007259
fixed	NA	poly(age, 3, raw = TRUE)2	0.00008514	0.0001046	0.8139	9299	0.4157	-0.0002085	0.0003788
fixed	NA	poly(age, 3, raw = TRUE)3	-0.0000006217	0.0000009261	-0.6713	9165	0.502	-0.000003221	0.000001978
fixed	NA	male	-0.01247	0.003877	-3.216	9710	0.001304	-0.02335	-0.001586
fixed	NA	count_birth_order2/2	-0.006295	0.01132	-0.556	8978	0.5783	-0.03808	0.02549
fixed	NA	count_birth_order1/3	0.003135	0.01083	0.2896	9704	0.7721	-0.02725	0.03352
fixed	NA	count_birth_order2/3	0.00541	0.01204	0.4493	9716	0.6533	-0.02839	0.03921
fixed	NA	count_birth_order3/3	0.01109	0.01322	0.8389	9721	0.4016	-0.02602	0.04821
fixed	NA	count_birth_order1/4	0.01225	0.01192	1.028	9718	0.3038	-0.02119	0.0457
fixed	NA	count_birth_order2/4	0.00659	0.01278	0.5156	9720	0.6062	-0.02929	0.04247
fixed	NA	count_birth_order3/4	0.01458	0.01348	1.082	9724	0.2793	-0.02325	0.05242
fixed	NA	count_birth_order4/4	-0.007248	0.01451	-0.4995	9726	0.6175	-0.04798	0.03349
fixed	NA	count_birth_order1/5	0.004284	0.01344	0.3188	9726	0.7499	-0.03344	0.04201
fixed	NA	count_birth_order2/5	0.02675	0.01427	1.875	9728	0.06086	-0.0133	0.0668
fixed	NA	count_birth_order3/5	0.0287	0.01501	1.912	9729	0.05592	-0.01344	0.07084
fixed	NA	count_birth_order4/5	0.008712	0.01585	0.5497	9730	0.5826	-0.03578	0.0532
fixed	NA	count_birth_order5/5	0.03591	0.01588	2.261	9730	0.02375	-0.008663	0.08048
fixed	NA	count_birth_order1/>5	0.0164	0.0104	1.577	9729	0.1148	-0.01279	0.04558
fixed	NA	count_birth_order2/>5	0.008682	0.01081	0.8033	9730	0.4218	-0.02166	0.03902
fixed	NA	count_birth_order3/>5	0.01101	0.0107	1.029	9730	0.3035	-0.01902	0.04104
fixed	NA	count_birth_order4/>5	0.008169	0.01048	0.7795	9730	0.4357	-0.02125	0.03759
fixed	NA	count_birth_order5/>5	0.02166	0.01059	2.044	9730	0.04096	-0.008081	0.0514
fixed	NA	count_birth_order>5/>5	0.01945	0.008525	2.281	9095	0.02255	-0.004481	0.04338
ran_pars	mother_pidlink	sd__(Intercept)	0.04833	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1826	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)
11	-4846	-4767	2434	-4868	NA	NA	NA
12	-4844	-4758	2434	-4868	0.33	1	0.5656
16	-4842	-4727	2437	-4874	5.859	4	0.2099
26	-4827	-4640	2439	-4879	4.714	10	0.9094

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)	0.147	0.1226	1.199	3656	0.2306	-0.1971	0.491
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01108	0.01315	-0.8429	3654	0.3993	-0.04798	0.02582
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003627	0.0004503	0.8054	3651	0.4207	-0.0009014	0.001627
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004015	0.000004936	-0.8135	3646	0.416	-0.00001787	0.000009839
fixed	NA	male	-0.016	0.006199	-2.581	3665	0.009896	-0.0334	0.001403
fixed	NA	sibling_count3	0.004867	0.01008	0.4826	3099	0.6294	-0.02344	0.03318
fixed	NA	sibling_count4	0.006221	0.01038	0.5992	2858	0.5491	-0.02292	0.03537
fixed	NA	sibling_count5	0.0261	0.01153	2.264	2501	0.02364	-0.006256	0.05846
fixed	NA	sibling_count>5	0.01793	0.009949	1.802	2435	0.07163	-0.009997	0.04586
ran_pars	mother_pidlink	sd__(Intercept)	0.03293	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1823	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)	0.1438	0.1225	1.173	3654	0.2408	-0.2002	0.4877
fixed	NA	birth_order	-0.00308	0.001903	-1.618	3333	0.1057	-0.008423	0.002263
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01039	0.01315	-0.7901	3652	0.4295	-0.0473	0.02652
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003461	0.0004503	0.7686	3649	0.4422	-0.0009179	0.00161
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003965	0.000004934	-0.8035	3645	0.4218	-0.00001782	0.000009887
fixed	NA	male	-0.01587	0.006198	-2.56	3664	0.01049	-0.03327	0.001528
fixed	NA	sibling_count3	0.006395	0.01013	0.6316	3105	0.5277	-0.02203	0.03482
fixed	NA	sibling_count4	0.009575	0.01058	0.9046	2858	0.3657	-0.02014	0.03929
fixed	NA	sibling_count5	0.03163	0.01202	2.632	2534	0.008551	-0.002109	0.06536
fixed	NA	sibling_count>5	0.0289	0.01203	2.401	2545	0.01641	-0.004883	0.06268
ran_pars	mother_pidlink	sd__(Intercept)	0.03253	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1823	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)	0.1472	0.1227	1.2	3650	0.2301	-0.1971	0.4915
fixed	NA	poly(age, 3, raw = TRUE)1	-0.0108	0.01315	-0.821	3648	0.4117	-0.04772	0.02612
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003645	0.0004505	0.809	3646	0.4185	-0.0009001	0.001629
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000422	0.000004938	-0.8547	3641	0.3928	-0.00001808	0.00000964
fixed	NA	male	-0.01611	0.006201	-2.598	3660	0.009409	-0.03352	0.001295
fixed	NA	sibling_count3	0.007144	0.01033	0.6914	3191	0.4894	-0.02186	0.03615
fixed	NA	sibling_count4	0.01067	0.01099	0.971	3037	0.3316	-0.02018	0.04153
fixed	NA	sibling_count5	0.03423	0.01262	2.713	2807	0.006716	-0.001192	0.06965
fixed	NA	sibling_count>5	0.03208	0.01238	2.592	2709	0.009583	-0.002657	0.06682
fixed	NA	birth_order_nonlinear2	-0.01406	0.008281	-1.698	3355	0.08955	-0.03731	0.009181
fixed	NA	birth_order_nonlinear3	-0.01005	0.009708	-1.035	3426	0.3006	-0.0373	0.0172
fixed	NA	birth_order_nonlinear4	-0.01388	0.01184	-1.172	3488	0.2412	-0.04711	0.01936
fixed	NA	birth_order_nonlinear5	-0.02517	0.01452	-1.734	3512	0.08299	-0.06592	0.01558
fixed	NA	birth_order_nonlinear>5	-0.02715	0.01418	-1.915	3567	0.05562	-0.06696	0.01266
ran_pars	mother_pidlink	sd__(Intercept)	0.03234	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1824	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)	0.1428	0.1231	1.16	3639	0.2461	-0.2028	0.4884
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01111	0.01321	-0.8416	3637	0.4001	-0.04818	0.02596
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003788	0.0004524	0.8374	3634	0.4024	-0.0008911	0.001649
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000004428	0.00000496	-0.8929	3629	0.372	-0.00001835	0.000009493
fixed	NA	male	-0.0164	0.00621	-2.64	3650	0.008318	-0.03383	0.001035
fixed	NA	count_birth_order2/2	0.006857	0.01616	0.4242	3347	0.6714	-0.03851	0.05223
fixed	NA	count_birth_order1/3	0.009847	0.01342	0.7337	3649	0.4632	-0.02782	0.04752
fixed	NA	count_birth_order2/3	-0.0002712	0.01492	-0.01818	3650	0.9855	-0.04216	0.04162
fixed	NA	count_birth_order3/3	0.01219	0.01626	0.7498	3650	0.4534	-0.03345	0.05784
fixed	NA	count_birth_order1/4	0.02105	0.0154	1.367	3649	0.1717	-0.02217	0.06427
fixed	NA	count_birth_order2/4	0.009409	0.01633	0.5762	3650	0.5645	-0.03642	0.05524
fixed	NA	count_birth_order3/4	0.0003186	0.01694	0.01881	3650	0.985	-0.04722	0.04786
fixed	NA	count_birth_order4/4	-0.001352	0.01813	-0.07459	3650	0.9405	-0.05225	0.04954
fixed	NA	count_birth_order1/5	0.04666	0.02029	2.3	3650	0.0215	-0.01028	0.1036
fixed	NA	count_birth_order2/5	0.0226	0.02189	1.032	3650	0.302	-0.03886	0.08405
fixed	NA	count_birth_order3/5	0.03762	0.02081	1.808	3649	0.07072	-0.0208	0.09605
fixed	NA	count_birth_order4/5	0.02517	0.0203	1.24	3649	0.2152	-0.03182	0.08217
fixed	NA	count_birth_order5/5	0.009177	0.02137	0.4294	3648	0.6677	-0.05081	0.06917
fixed	NA	count_birth_order1/>5	0.06168	0.0192	3.212	3643	0.001328	0.007783	0.1156
fixed	NA	count_birth_order2/>5	-0.002437	0.01937	-0.1258	3649	0.8999	-0.0568	0.05192
fixed	NA	count_birth_order3/>5	0.02147	0.0189	1.136	3650	0.256	-0.03159	0.07453
fixed	NA	count_birth_order4/>5	0.03178	0.01851	1.717	3650	0.08603	-0.02017	0.08374
fixed	NA	count_birth_order5/>5	0.01785	0.01769	1.009	3649	0.3131	-0.0318	0.0675
fixed	NA	count_birth_order>5/>5	0.01175	0.01371	0.8568	3413	0.3916	-0.02675	0.05025
ran_pars	mother_pidlink	sd__(Intercept)	0.0318	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1825	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)
11	-1951	-1883	986.6	-1973	NA	NA	NA
12	-1952	-1877	987.9	-1976	2.627	1	0.105
16	-1947	-1848	989.5	-1979	3.289	4	0.5106
26	-1936	-1774	993.8	-1988	8.507	10	0.5795

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)	0.1348	0.122	1.105	3679	0.2692	-0.2076	0.4773
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01021	0.0131	-0.7795	3677	0.4357	-0.04698	0.02656
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003311	0.0004488	0.7378	3673	0.4607	-0.0009287	0.001591
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003669	0.00000492	-0.7457	3668	0.4559	-0.00001748	0.00001014
fixed	NA	male	-0.0162	0.006178	-2.622	3689	0.008788	-0.03354	0.001146
fixed	NA	sibling_count3	0.009527	0.01106	0.8615	3170	0.389	-0.02151	0.04057
fixed	NA	sibling_count4	0.006535	0.01113	0.5869	3013	0.5573	-0.02472	0.03779
fixed	NA	sibling_count5	0.0336	0.0117	2.872	2778	0.004105	0.0007643	0.06644
fixed	NA	sibling_count>5	0.02293	0.01026	2.235	2809	0.02552	-0.005873	0.05173
ran_pars	mother_pidlink	sd__(Intercept)	0.03225	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1824	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)	0.133	0.122	1.09	3677	0.2758	-0.2095	0.4754
fixed	NA	birth_order	-0.002138	0.001677	-1.275	3214	0.2023	-0.006845	0.002568
fixed	NA	poly(age, 3, raw = TRUE)1	-0.009771	0.0131	-0.7458	3675	0.4558	-0.04655	0.02701
fixed	NA	poly(age, 3, raw = TRUE)2	0.000321	0.0004488	0.7153	3672	0.4745	-0.0009388	0.001581
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000365	0.00000492	-0.7418	3667	0.4582	-0.00001746	0.00001016
fixed	NA	male	-0.01611	0.006178	-2.607	3688	0.009167	-0.03345	0.001235
fixed	NA	sibling_count3	0.0106	0.01109	0.9557	3172	0.3393	-0.02053	0.04173
fixed	NA	sibling_count4	0.008674	0.01126	0.7704	3006	0.4411	-0.02293	0.04028
fixed	NA	sibling_count5	0.03718	0.01203	3.091	2779	0.002015	0.003415	0.07095
fixed	NA	sibling_count>5	0.03044	0.01183	2.573	2809	0.01013	-0.002767	0.06364
ran_pars	mother_pidlink	sd__(Intercept)	0.03218	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1824	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)	0.1407	0.1221	1.152	3673	0.2494	-0.2021	0.4834
fixed	NA	poly(age, 3, raw = TRUE)1	-0.01045	0.01311	-0.797	3672	0.4255	-0.04724	0.02634
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003477	0.000449	0.7743	3668	0.4388	-0.0009128	0.001608
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000398	0.000004923	-0.8085	3663	0.4189	-0.0000178	0.000009839
fixed	NA	male	-0.01637	0.006179	-2.649	3684	0.008096	-0.03372	0.0009735
fixed	NA	sibling_count3	0.01284	0.01128	1.138	3235	0.2551	-0.01883	0.04452
fixed	NA	sibling_count4	0.01034	0.0116	0.8908	3132	0.3731	-0.02224	0.04291
fixed	NA	sibling_count5	0.03911	0.01258	3.108	2993	0.001902	0.003786	0.07443
fixed	NA	sibling_count>5	0.03291	0.01219	2.699	2967	0.006998	-0.001319	0.06714
fixed	NA	birth_order_nonlinear2	-0.015	0.008375	-1.791	3394	0.07345	-0.03851	0.008513
fixed	NA	birth_order_nonlinear3	-0.01467	0.009754	-1.504	3481	0.1327	-0.04205	0.01271
fixed	NA	birth_order_nonlinear4	-0.007381	0.01154	-0.6394	3550	0.5226	-0.03978	0.02502
fixed	NA	birth_order_nonlinear5	-0.01601	0.01406	-1.138	3559	0.255	-0.05547	0.02346
fixed	NA	birth_order_nonlinear>5	-0.02288	0.01282	-1.785	3554	0.07439	-0.05888	0.01311
ran_pars	mother_pidlink	sd__(Intercept)	0.03209	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1824	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)	0.1241	0.1221	1.016	3662	0.3096	-0.2187	0.467
fixed	NA	poly(age, 3, raw = TRUE)1	-0.009842	0.01311	-0.7506	3660	0.453	-0.04665	0.02697
fixed	NA	poly(age, 3, raw = TRUE)2	0.000332	0.0004494	0.7389	3656	0.46	-0.0009293	0.001593
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003868	0.000004927	-0.785	3650	0.4325	-0.0000177	0.000009963
fixed	NA	male	-0.01598	0.006177	-2.587	3674	0.00971	-0.03332	0.001357
fixed	NA	count_birth_order2/2	0.0135	0.01767	0.7641	3428	0.4449	-0.0361	0.0631
fixed	NA	count_birth_order1/3	0.01416	0.0148	0.9565	3673	0.3389	-0.02739	0.05571
fixed	NA	count_birth_order2/3	0.00501	0.01613	0.3106	3674	0.7561	-0.04026	0.05028
fixed	NA	count_birth_order3/3	0.0268	0.01788	1.499	3674	0.134	-0.0234	0.07701
fixed	NA	count_birth_order1/4	0.04209	0.01607	2.62	3673	0.008829	-0.003005	0.08719
fixed	NA	count_birth_order2/4	0.001262	0.01694	0.07454	3674	0.9406	-0.04628	0.0488
fixed	NA	count_birth_order3/4	-0.01579	0.01834	-0.861	3674	0.3893	-0.06726	0.03569
fixed	NA	count_birth_order4/4	0.001377	0.01992	0.06911	3674	0.9449	-0.05454	0.05729
fixed	NA	count_birth_order1/5	0.01152	0.01943	0.5932	3674	0.5531	-0.043	0.06605
fixed	NA	count_birth_order2/5	0.04278	0.01992	2.147	3674	0.03184	-0.01315	0.0987
fixed	NA	count_birth_order3/5	0.05774	0.02051	2.816	3674	0.004893	0.0001778	0.1153
fixed	NA	count_birth_order4/5	0.05098	0.02088	2.441	3673	0.01467	-0.007632	0.1096
fixed	NA	count_birth_order5/5	0.03361	0.0212	1.585	3672	0.113	-0.02591	0.09313
fixed	NA	count_birth_order1/>5	0.0718	0.01752	4.099	3668	0.00004242	0.02263	0.121
fixed	NA	count_birth_order2/>5	0.00797	0.01852	0.4303	3673	0.667	-0.04402	0.05996
fixed	NA	count_birth_order3/>5	0.01289	0.01785	0.7224	3674	0.4701	-0.0372	0.06299
fixed	NA	count_birth_order4/>5	0.03653	0.01734	2.106	3674	0.03524	-0.01215	0.08521
fixed	NA	count_birth_order5/>5	0.02583	0.01837	1.406	3673	0.1599	-0.02574	0.0774
fixed	NA	count_birth_order>5/>5	0.01946	0.01378	1.412	3502	0.158	-0.01921	0.05812
ran_pars	mother_pidlink	sd__(Intercept)	0.03092	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1822	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)
11	-1965	-1897	993.5	-1987	NA	NA	NA
12	-1965	-1890	994.3	-1989	1.631	1	0.2015
16	-1961	-1861	996.3	-1993	3.928	4	0.4158
26	-1966	-1805	1009	-2018	25.91	10	0.003867

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)	0.1323	0.1239	1.068	3591	0.2857	-0.2154	0.4799
fixed	NA	poly(age, 3, raw = TRUE)1	-0.009582	0.01331	-0.72	3590	0.4715	-0.04694	0.02777
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003121	0.0004563	0.684	3587	0.494	-0.0009687	0.001593
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003541	0.000005007	-0.7072	3582	0.4795	-0.0000176	0.00001051
fixed	NA	male	-0.01515	0.006261	-2.42	3601	0.01558	-0.03272	0.002424
fixed	NA	sibling_count3	0.006555	0.009888	0.6629	3008	0.5074	-0.0212	0.03431
fixed	NA	sibling_count4	0.0103	0.01033	0.9976	2766	0.3186	-0.01869	0.0393
fixed	NA	sibling_count5	0.03153	0.01178	2.677	2297	0.007475	-0.001528	0.06459
fixed	NA	sibling_count>5	0.02033	0.01	2.032	2269	0.04224	-0.007749	0.0484
ran_pars	mother_pidlink	sd__(Intercept)	0.03537	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.182	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)	0.1282	0.1239	1.035	3589	0.3006	-0.2195	0.4759
fixed	NA	birth_order	-0.002884	0.001964	-1.469	3298	0.142	-0.008398	0.002629
fixed	NA	poly(age, 3, raw = TRUE)1	-0.008817	0.01331	-0.6622	3587	0.5079	-0.04619	0.02856
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002926	0.0004564	0.6411	3584	0.5215	-0.0009885	0.001574
fixed	NA	poly(age, 3, raw = TRUE)3	-0.00000345	0.000005006	-0.6891	3580	0.4908	-0.0000175	0.0000106
fixed	NA	male	-0.01511	0.00626	-2.414	3600	0.01585	-0.03268	0.002463
fixed	NA	sibling_count3	0.008016	0.009934	0.8069	3012	0.4198	-0.01987	0.0359
fixed	NA	sibling_count4	0.01341	0.01054	1.272	2771	0.2035	-0.01618	0.04299
fixed	NA	sibling_count5	0.03653	0.01225	2.98	2330	0.002908	0.002125	0.07093
fixed	NA	sibling_count>5	0.0306	0.0122	2.508	2442	0.01221	-0.003649	0.06486
ran_pars	mother_pidlink	sd__(Intercept)	0.03485	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1821	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)	0.1321	0.124	1.066	3585	0.2867	-0.2159	0.4802
fixed	NA	poly(age, 3, raw = TRUE)1	-0.009326	0.01332	-0.7001	3584	0.4839	-0.04672	0.02806
fixed	NA	poly(age, 3, raw = TRUE)2	0.0003124	0.0004566	0.6841	3581	0.494	-0.0009694	0.001594
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003693	0.00000501	-0.7371	3576	0.4611	-0.00001776	0.00001037
fixed	NA	male	-0.01529	0.006263	-2.441	3596	0.01471	-0.03287	0.002295
fixed	NA	sibling_count3	0.008291	0.01015	0.8167	3103	0.4142	-0.02021	0.03679
fixed	NA	sibling_count4	0.0134	0.01095	1.224	2952	0.2211	-0.01734	0.04415
fixed	NA	sibling_count5	0.03807	0.01282	2.97	2591	0.003006	0.002088	0.07405
fixed	NA	sibling_count>5	0.03212	0.01257	2.556	2617	0.01065	-0.003157	0.0674
fixed	NA	birth_order_nonlinear2	-0.01056	0.008247	-1.281	3267	0.2004	-0.03371	0.01259
fixed	NA	birth_order_nonlinear3	-0.007715	0.009724	-0.7933	3342	0.4276	-0.03501	0.01958
fixed	NA	birth_order_nonlinear4	-0.009011	0.0122	-0.7386	3412	0.4602	-0.04326	0.02524
fixed	NA	birth_order_nonlinear5	-0.02419	0.01504	-1.609	3411	0.1078	-0.06641	0.01802
fixed	NA	birth_order_nonlinear>5	-0.0218	0.01465	-1.488	3518	0.137	-0.06294	0.01934
ran_pars	mother_pidlink	sd__(Intercept)	0.03468	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1822	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)	0.121	0.1244	0.9726	3574	0.3308	-0.2282	0.4703
fixed	NA	poly(age, 3, raw = TRUE)1	-0.008724	0.01337	-0.6525	3572	0.5141	-0.04625	0.02881
fixed	NA	poly(age, 3, raw = TRUE)2	0.0002937	0.0004585	0.6407	3568	0.5218	-0.0009932	0.001581
fixed	NA	poly(age, 3, raw = TRUE)3	-0.000003527	0.000005032	-0.7009	3563	0.4834	-0.00001765	0.0000106
fixed	NA	male	-0.0155	0.006273	-2.471	3586	0.01351	-0.03311	0.002107
fixed	NA	count_birth_order2/2	0.005899	0.01572	0.3752	3261	0.7076	-0.03824	0.05003
fixed	NA	count_birth_order1/3	0.01002	0.0132	0.7592	3585	0.4478	-0.02702	0.04706
fixed	NA	count_birth_order2/3	0.004641	0.01468	0.3161	3586	0.7519	-0.03657	0.04585
fixed	NA	count_birth_order3/3	0.01141	0.01582	0.721	3585	0.4709	-0.033	0.05581
fixed	NA	count_birth_order1/4	0.02893	0.01549	1.868	3585	0.06189	-0.01455	0.07241
fixed	NA	count_birth_order2/4	0.01144	0.01628	0.7029	3586	0.4822	-0.03425	0.05714
fixed	NA	count_birth_order3/4	0.002006	0.0169	0.1187	3585	0.9055	-0.04543	0.04944
fixed	NA	count_birth_order4/4	0.0008381	0.01836	0.04565	3585	0.9636	-0.0507	0.05237
fixed	NA	count_birth_order1/5	0.04949	0.02025	2.443	3585	0.0146	-0.007367	0.1063
fixed	NA	count_birth_order2/5	0.02977	0.02263	1.316	3586	0.1884	-0.03375	0.0933
fixed	NA	count_birth_order3/5	0.04936	0.02207	2.236	3585	0.02539	-0.01259	0.1113
fixed	NA	count_birth_order4/5	0.02171	0.02125	1.022	3584	0.307	-0.03793	0.08134
fixed	NA	count_birth_order5/5	0.01596	0.02257	0.7072	3583	0.4795	-0.0474	0.07932
fixed	NA	count_birth_order1/>5	0.04549	0.01974	2.305	3580	0.02123	-0.009911	0.1009
fixed	NA	count_birth_order2/>5	0.001633	0.01997	0.08179	3585	0.9348	-0.05441	0.05768
fixed	NA	count_birth_order3/>5	0.02498	0.01907	1.31	3586	0.1903	-0.02854	0.07849
fixed	NA	count_birth_order4/>5	0.04811	0.01915	2.512	3585	0.01205	-0.005655	0.1019
fixed	NA	count_birth_order5/>5	0.01544	0.01798	0.8588	3585	0.3905	-0.03503	0.06592
fixed	NA	count_birth_order>5/>5	0.01582	0.0139	1.138	3299	0.2552	-0.0232	0.05484
ran_pars	mother_pidlink	sd__(Intercept)	0.03447	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.1823	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)
11	-1911	-1843	966.6	-1933	NA	NA	NA
12	-1911	-1837	967.7	-1935	2.166	1	0.1411
16	-1905	-1806	968.7	-1937	1.891	4	0.7558
26	-1893	-1732	972.6	-1945	7.916	10	0.637

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)	-1.03	0.0503	-20.47	14536	7.361e-92	-1.171	-0.8886
fixed	NA	poly(age, 3, raw = TRUE)1	0.08253	0.004782	17.26	14464	4.481e-66	0.0691	0.09595
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001978	0.0001393	-14.2	14316	1.824e-45	-0.002369	-0.001587
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001503	0.000001267	11.86	14149	2.761e-32	0.00001147	0.00001859
fixed	NA	male	0.6583	0.005408	121.7	14448	0	0.6431	0.6735
fixed	NA	sibling_count3	-0.01002	0.01094	-0.9159	10423	0.3597	-0.04075	0.0207
fixed	NA	sibling_count4	-0.001492	0.01126	-0.1325	9429	0.8946	-0.03311	0.03012
fixed	NA	sibling_count5	0.01039	0.01177	0.8824	8451	0.3776	-0.02265	0.04342
fixed	NA	sibling_count>5	0.01886	0.009216	2.047	9579	0.04069	-0.007005	0.04473
ran_pars	mother_pidlink	sd__(Intercept)	0.1122	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.311	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)	-1.03	0.0503	-20.48	14537	6.656e-92	-1.171	-0.8889
fixed	NA	birth_order	-0.0009195	0.001144	-0.8039	12993	0.4215	-0.00413	0.002291
fixed	NA	poly(age, 3, raw = TRUE)1	0.0828	0.004794	17.27	14453	3.558e-66	0.06934	0.09626
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001988	0.0001398	-14.22	14261	1.463e-45	-0.00238	-0.001595
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001512	0.000001272	11.88	14068	2.065e-32	0.00001155	0.00001869
fixed	NA	male	0.6583	0.005408	121.7	14447	0	0.6431	0.6735
fixed	NA	sibling_count3	-0.009801	0.01095	-0.8952	10442	0.3707	-0.04053	0.02093
fixed	NA	sibling_count4	-0.0008537	0.01129	-0.07562	9502	0.9397	-0.03255	0.03084
fixed	NA	sibling_count5	0.01149	0.01185	0.9696	8573	0.3323	-0.02177	0.04475
fixed	NA	sibling_count>5	0.02234	0.01018	2.195	10757	0.02821	-0.006234	0.05091
ran_pars	mother_pidlink	sd__(Intercept)	0.1122	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.311	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)	-1.035	0.05044	-20.52	14539	2.673e-92	-1.177	-0.8936
fixed	NA	poly(age, 3, raw = TRUE)1	0.08307	0.004796	17.32	14460	1.516e-66	0.06961	0.09653
fixed	NA	poly(age, 3, raw = TRUE)2	-0.001998	0.0001399	-14.29	14270	5.403e-46	-0.002391	-0.001606
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001522	0.000001273	11.96	14066	8.39e-33	0.00001165	0.00001879
fixed	NA	male	0.6584	0.005408	121.7	14443	0	0.6432	0.6736
fixed	NA	sibling_count3	-0.008598	0.0111	-0.7743	10829	0.4388	-0.03977	0.02257
fixed	NA	sibling_count4	-0.000003608	0.01161	-0.0003108	10265	0.9998	-0.03259	0.03258
fixed	NA	sibling_count5	0.01432	0.0123	1.164	9553	0.2443	-0.02021	0.04886
fixed	NA	sibling_count>5	0.02736	0.01069	2.558	11943	0.01054	-0.002663	0.05738
fixed	NA	birth_order_nonlinear2	0.006211	0.007852	0.791	13189	0.4289	-0.01583	0.02825
fixed	NA	birth_order_nonlinear3	-0.005846	0.009241	-0.6326	12978	0.527	-0.03178	0.02009
fixed	NA	birth_order_nonlinear4	0.0003569	0.01056	0.0338	13112	0.973	-0.02928	0.02999
fixed	NA	birth_order_nonlinear5	-0.01352	0.01202	-1.125	13128	0.2608	-0.04726	0.02022
fixed	NA	birth_order_nonlinear>5	-0.01148	0.009959	-1.153	14660	0.249	-0.03943	0.01647
ran_pars	mother_pidlink	sd__(Intercept)	0.1122	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.311	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)	-1.041	0.05065	-20.55	14538	1.64e-92	-1.183	-0.8985
fixed	NA	poly(age, 3, raw = TRUE)1	0.08302	0.004795	17.31	14451	1.774e-66	0.06956	0.09648
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002001	0.0001399	-14.31	14255	3.99e-46	-0.002394	-0.001609
fixed	NA	poly(age, 3, raw = TRUE)3	0.00001528	0.000001273	12.01	14043	4.727e-33	0.00001171	0.00001886
fixed	NA	male	0.6581	0.005408	121.7	14434	0	0.6429	0.6733
fixed	NA	count_birth_order2/2	0.02629	0.01527	1.722	13066	0.08507	-0.01656	0.06915
fixed	NA	count_birth_order1/3	-0.01405	0.0145	-0.9691	14488	0.3325	-0.05477	0.02666
fixed	NA	count_birth_order2/3	0.01445	0.01621	0.8916	14567	0.3726	-0.03105	0.05996
fixed	NA	count_birth_order3/3	0.00651	0.01806	0.3604	14630	0.7186	-0.0442	0.05722
fixed	NA	count_birth_order1/4	0.01338	0.01641	0.8149	14572	0.4151	-0.0327	0.05945
fixed	NA	count_birth_order2/4	0.006355	0.01745	0.3641	14605	0.7158	-0.04264	0.05535
fixed	NA	count_birth_order3/4	-0.001847	0.01893	-0.09757	14645	0.9223	-0.05499	0.0513
fixed	NA	count_birth_order4/4	0.01231	0.01984	0.6205	14658	0.535	-0.04338	0.068
fixed	NA	count_birth_order1/5	0.03854	0.01879	2.051	14632	0.0403	-0.01421	0.09129
fixed	NA	count_birth_order2/5	0.005322	0.01985	0.2681	14656	0.7886	-0.0504	0.06104
fixed	NA	count_birth_order3/5	0.003385	0.02026	0.167	14661	0.8673	-0.05349	0.06026
fixed	NA	count_birth_order4/5	0.05807	0.0217	2.676	14670	0.007462	-0.002847	0.119
fixed	NA	count_birth_order5/5	-0.008625	0.02211	-0.3901	14670	0.6964	-0.07069	0.05344
fixed	NA	count_birth_order1/>5	0.04767	0.01512	3.152	14665	0.001622	0.005223	0.09011
fixed	NA	count_birth_order2/>5	0.03767	0.01564	2.409	14670	0.01603	-0.006233	0.08158
fixed	NA	count_birth_order3/>5	0.02911	0.01529	1.903	14670	0.057	-0.01382	0.07204
fixed	NA	count_birth_order4/>5	0.0213	0.01504	1.417	14670	0.1566	-0.02091	0.06352
fixed	NA	count_birth_order5/>5	0.02724	0.01511	1.802	14670	0.07149	-0.01518	0.06967
fixed	NA	count_birth_order>5/>5	0.02345	0.01185	1.979	13115	0.04789	-0.009818	0.05671
ran_pars	mother_pidlink	sd__(Intercept)	0.1121	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.311	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)
11	9037	9120	-4507	9015	NA	NA	NA
12	9038	9129	-4507	9014	0.6469	1	0.4212
16	9042	9164	-4505	9010	3.709	4	0.4468
26	9046	9244	-4497	8994	16.27	10	0.09213

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)	-1.811	0.1473	-12.3	6155	2.244e-34	-2.225	-1.398
fixed	NA	poly(age, 3, raw = TRUE)1	0.175	0.01672	10.47	6159	2.005e-25	0.1281	0.222
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005302	0.0005975	-8.873	6165	9.192e-19	-0.006979	-0.003625
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005222	0.000006778	7.704	6172	1.527e-14	0.00003319	0.00007124
fixed	NA	male	0.5873	0.008561	68.6	6083	0	0.5633	0.6113
fixed	NA	sibling_count3	0.007451	0.0136	0.5479	4527	0.5838	-0.03072	0.04562
fixed	NA	sibling_count4	0.004702	0.01467	0.3206	4014	0.7486	-0.03647	0.04587
fixed	NA	sibling_count5	0.03346	0.01688	1.982	3606	0.04754	-0.01393	0.08085
fixed	NA	sibling_count>5	0.0422	0.01476	2.859	3391	0.004274	0.0007688	0.08363
ran_pars	mother_pidlink	sd__(Intercept)	0.135	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3135	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)	-1.811	0.1473	-12.29	6154	2.438e-34	-2.224	-1.397
fixed	NA	birth_order	-0.0006785	0.002855	-0.2377	6160	0.8122	-0.008693	0.007335
fixed	NA	poly(age, 3, raw = TRUE)1	0.1751	0.01672	10.47	6159	1.991e-25	0.1281	0.222
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005302	0.0005976	-8.872	6164	9.248e-19	-0.006979	-0.003624
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005219	0.000006779	7.698	6169	1.596e-14	0.00003316	0.00007122
fixed	NA	male	0.5873	0.008562	68.59	6082	0	0.5633	0.6114
fixed	NA	sibling_count3	0.007791	0.01368	0.5697	4532	0.5689	-0.0306	0.04618
fixed	NA	sibling_count4	0.005488	0.01504	0.365	4024	0.7152	-0.03672	0.0477
fixed	NA	sibling_count5	0.03474	0.01772	1.96	3697	0.05003	-0.015	0.08448
fixed	NA	sibling_count>5	0.04478	0.01832	2.445	3922	0.01454	-0.006637	0.09619
ran_pars	mother_pidlink	sd__(Intercept)	0.135	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3135	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)	-1.823	0.1476	-12.35	6162	1.218e-34	-2.238	-1.409
fixed	NA	poly(age, 3, raw = TRUE)1	0.1759	0.01674	10.5	6162	1.354e-25	0.1289	0.2229
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005327	0.0005982	-8.905	6165	6.916e-19	-0.007006	-0.003648
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005238	0.000006787	7.718	6169	1.369e-14	0.00003333	0.00007143
fixed	NA	male	0.5875	0.008564	68.6	6077	0	0.5634	0.6115
fixed	NA	sibling_count3	0.006373	0.01395	0.4567	4729	0.6479	-0.0328	0.04554
fixed	NA	sibling_count4	0.005122	0.01561	0.3282	4367	0.7428	-0.03869	0.04893
fixed	NA	sibling_count5	0.03905	0.01858	2.102	4148	0.03561	-0.0131	0.09119
fixed	NA	sibling_count>5	0.05275	0.01885	2.798	4185	0.005173	-0.0001796	0.1057
fixed	NA	birth_order_nonlinear2	0.01327	0.01101	1.205	5114	0.2282	-0.01764	0.04419
fixed	NA	birth_order_nonlinear3	0.005947	0.01359	0.4377	5359	0.6616	-0.0322	0.04409
fixed	NA	birth_order_nonlinear4	-0.002039	0.01687	-0.1209	5538	0.9038	-0.04939	0.04532
fixed	NA	birth_order_nonlinear5	-0.0184	0.02114	-0.8704	5387	0.3841	-0.07773	0.04094
fixed	NA	birth_order_nonlinear>5	-0.01167	0.02127	-0.5488	6193	0.5832	-0.07137	0.04802
ran_pars	mother_pidlink	sd__(Intercept)	0.1349	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3136	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)	-1.824	0.1479	-12.33	6156	1.65e-34	-2.239	-1.408
fixed	NA	poly(age, 3, raw = TRUE)1	0.175	0.01678	10.43	6154	2.86e-25	0.1279	0.2221
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005298	0.0005996	-8.836	6158	1.271e-18	-0.006981	-0.003615
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005206	0.000006804	7.651	6162	2.293e-14	0.00003296	0.00007116
fixed	NA	male	0.5874	0.008572	68.52	6067	0	0.5633	0.6114
fixed	NA	count_birth_order2/2	0.03734	0.01984	1.882	5368	0.05993	-0.01836	0.09304
fixed	NA	count_birth_order1/3	0.02279	0.01783	1.278	6153	0.2012	-0.02725	0.07282
fixed	NA	count_birth_order2/3	0.01879	0.01937	0.9702	6189	0.332	-0.03558	0.07317
fixed	NA	count_birth_order3/3	0.01655	0.02162	0.7655	6202	0.444	-0.04413	0.07723
fixed	NA	count_birth_order1/4	0.006185	0.0217	0.285	6184	0.7756	-0.05472	0.06709
fixed	NA	count_birth_order2/4	0.0236	0.02242	1.053	6201	0.2924	-0.03932	0.08653
fixed	NA	count_birth_order3/4	0.03506	0.02373	1.477	6197	0.1397	-0.03157	0.1017
fixed	NA	count_birth_order4/4	0.007861	0.02467	0.3187	6194	0.75	-0.06138	0.0771
fixed	NA	count_birth_order1/5	0.03545	0.0295	1.202	6202	0.2295	-0.04735	0.1182
fixed	NA	count_birth_order2/5	0.06082	0.0317	1.918	6173	0.05511	-0.02817	0.1498
fixed	NA	count_birth_order3/5	0.05973	0.02949	2.026	6181	0.04284	-0.02304	0.1425
fixed	NA	count_birth_order4/5	0.04242	0.02892	1.467	6188	0.1424	-0.03875	0.1236
fixed	NA	count_birth_order5/5	0.03742	0.02999	1.248	6173	0.2122	-0.04677	0.1216
fixed	NA	count_birth_order1/>5	0.09227	0.0293	3.149	6190	0.001644	0.01003	0.1745
fixed	NA	count_birth_order2/>5	0.06653	0.02937	2.265	6172	0.02353	-0.01591	0.149
fixed	NA	count_birth_order3/>5	0.04338	0.02873	1.51	6153	0.1311	-0.03726	0.124
fixed	NA	count_birth_order4/>5	0.06546	0.02705	2.42	6153	0.01554	-0.01046	0.1414
fixed	NA	count_birth_order5/>5	0.03659	0.02583	1.417	6155	0.1566	-0.0359	0.1091
fixed	NA	count_birth_order>5/>5	0.04926	0.01961	2.512	5699	0.01203	-0.005782	0.1043
ran_pars	mother_pidlink	sd__(Intercept)	0.1344	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3139	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)
11	4222	4296	-2100	4200	NA	NA	NA
12	4224	4304	-2100	4200	0.05593	1	0.813
16	4228	4336	-2098	4196	3.26	4	0.5153
26	4242	4417	-2095	4190	6.288	10	0.7905

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)	-1.794	0.1469	-12.21	6212	6.652e-34	-2.206	-1.381
fixed	NA	poly(age, 3, raw = TRUE)1	0.1732	0.01669	10.38	6215	5.046e-25	0.1263	0.22
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005237	0.0005964	-8.78	6221	2.085e-18	-0.006911	-0.003563
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005152	0.000006767	7.614	6228	3.051e-14	0.00003253	0.00007052
fixed	NA	male	0.5869	0.008534	68.77	6136	0	0.5629	0.6108
fixed	NA	sibling_count3	0.008936	0.01474	0.6065	4703	0.5442	-0.03243	0.0503
fixed	NA	sibling_count4	-0.001759	0.01552	-0.1134	4287	0.9098	-0.04533	0.04181
fixed	NA	sibling_count5	0.02235	0.0167	1.338	3903	0.1809	-0.02453	0.06922
fixed	NA	sibling_count>5	0.0372	0.01461	2.547	3995	0.01091	-0.003803	0.07821
ran_pars	mother_pidlink	sd__(Intercept)	0.1351	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3138	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)	-1.794	0.1469	-12.21	6211	6.894e-34	-2.206	-1.381
fixed	NA	birth_order	0.00006028	0.002496	0.02415	6060	0.9807	-0.006947	0.007068
fixed	NA	poly(age, 3, raw = TRUE)1	0.1732	0.01669	10.38	6214	5.09e-25	0.1263	0.22
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005237	0.0005965	-8.779	6219	2.097e-18	-0.006911	-0.003562
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005153	0.000006769	7.612	6226	3.089e-14	0.00003253	0.00007053
fixed	NA	male	0.5869	0.008535	68.77	6136	0	0.5629	0.6108
fixed	NA	sibling_count3	0.008906	0.01479	0.6023	4702	0.547	-0.03261	0.05042
fixed	NA	sibling_count4	-0.001826	0.01577	-0.1158	4276	0.9078	-0.04608	0.04243
fixed	NA	sibling_count5	0.02224	0.01726	1.289	3920	0.1975	-0.0262	0.07068
fixed	NA	sibling_count>5	0.03698	0.01725	2.144	4304	0.03212	-0.01144	0.0854
ran_pars	mother_pidlink	sd__(Intercept)	0.1351	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3138	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)	-1.805	0.1472	-12.26	6217	3.554e-34	-2.218	-1.392
fixed	NA	poly(age, 3, raw = TRUE)1	0.1739	0.0167	10.41	6216	3.463e-25	0.1271	0.2208
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005261	0.000597	-8.812	6219	1.579e-18	-0.006937	-0.003585
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005171	0.000006775	7.631	6224	2.67e-14	0.00003269	0.00007073
fixed	NA	male	0.5871	0.008536	68.78	6129	0	0.5631	0.611
fixed	NA	sibling_count3	0.009283	0.01506	0.6165	4865	0.5376	-0.03298	0.05155
fixed	NA	sibling_count4	-0.001904	0.01631	-0.1168	4570	0.907	-0.04767	0.04387
fixed	NA	sibling_count5	0.02286	0.01805	1.267	4314	0.2053	-0.02779	0.07352
fixed	NA	sibling_count>5	0.04524	0.01778	2.545	4581	0.01097	-0.004664	0.09514
fixed	NA	birth_order_nonlinear2	0.01394	0.01123	1.241	5253	0.2145	-0.01758	0.04546
fixed	NA	birth_order_nonlinear3	-0.0001939	0.01354	-0.01432	5491	0.9886	-0.03821	0.03782
fixed	NA	birth_order_nonlinear4	0.006623	0.01636	0.4047	5679	0.6857	-0.03931	0.05256
fixed	NA	birth_order_nonlinear5	0.004426	0.02007	0.2205	5610	0.8255	-0.05192	0.06077
fixed	NA	birth_order_nonlinear>5	-0.01611	0.01903	-0.8463	6268	0.3974	-0.06954	0.03732
ran_pars	mother_pidlink	sd__(Intercept)	0.1356	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3136	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)	-1.817	0.1475	-12.31	6212	1.901e-34	-2.231	-1.403
fixed	NA	poly(age, 3, raw = TRUE)1	0.1742	0.01673	10.41	6208	3.549e-25	0.1272	0.2212
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005268	0.0005982	-8.807	6212	1.644e-18	-0.006947	-0.003589
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005175	0.000006789	7.623	6218	2.855e-14	0.0000327	0.00007081
fixed	NA	male	0.5867	0.008543	68.68	6120	0	0.5627	0.6107
fixed	NA	count_birth_order2/2	0.04181	0.0218	1.918	5523	0.05513	-0.01937	0.103
fixed	NA	count_birth_order1/3	0.0185	0.01933	0.9574	6209	0.3384	-0.03574	0.07275
fixed	NA	count_birth_order2/3	0.0225	0.02097	1.073	6244	0.2832	-0.03636	0.08137
fixed	NA	count_birth_order3/3	0.03344	0.02342	1.428	6258	0.1534	-0.0323	0.09919
fixed	NA	count_birth_order1/4	0.0112	0.0227	0.4936	6239	0.6216	-0.05251	0.07491
fixed	NA	count_birth_order2/4	0.03426	0.02315	1.48	6254	0.1389	-0.03071	0.09923
fixed	NA	count_birth_order3/4	-0.0004727	0.02537	-0.01863	6253	0.9851	-0.07168	0.07074
fixed	NA	count_birth_order4/4	-0.00158	0.02624	-0.06022	6252	0.952	-0.07523	0.07207
fixed	NA	count_birth_order1/5	0.05073	0.02702	1.877	6256	0.06051	-0.02512	0.1266
fixed	NA	count_birth_order2/5	0.03313	0.02898	1.143	6247	0.2531	-0.04823	0.1145
fixed	NA	count_birth_order3/5	0.0241	0.02834	0.8502	6246	0.3952	-0.05546	0.1036
fixed	NA	count_birth_order4/5	0.03857	0.02958	1.304	6231	0.1924	-0.04447	0.1216
fixed	NA	count_birth_order5/5	0.03566	0.02946	1.211	6233	0.2261	-0.04702	0.1183
fixed	NA	count_birth_order1/>5	0.06043	0.02573	2.348	6258	0.01889	-0.0118	0.1327
fixed	NA	count_birth_order2/>5	0.05178	0.02694	1.922	6241	0.05471	-0.02386	0.1274
fixed	NA	count_birth_order3/>5	0.04945	0.02611	1.894	6231	0.05832	-0.02385	0.1227
fixed	NA	count_birth_order4/>5	0.07459	0.02516	2.965	6231	0.003038	0.003974	0.1452
fixed	NA	count_birth_order5/>5	0.05976	0.02593	2.305	6198	0.02122	-0.01303	0.1326
fixed	NA	count_birth_order>5/>5	0.03856	0.01928	2.001	5828	0.04548	-0.01554	0.09267
ran_pars	mother_pidlink	sd__(Intercept)	0.1352	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3139	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)
11	4271	4345	-2124	4249	NA	NA	NA
12	4273	4354	-2124	4249	0.0006262	1	0.98
16	4277	4385	-2123	4245	3.427	4	0.489
26	4291	4467	-2120	4239	6.031	10	0.8126

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)	-1.855	0.1489	-12.46	6036	3.362e-35	-2.273	-1.437
fixed	NA	poly(age, 3, raw = TRUE)1	0.1807	0.01692	10.68	6040	2.16e-26	0.1332	0.2282
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005507	0.0006047	-9.107	6044	1.135e-19	-0.007204	-0.003809
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000546	0.000006863	7.955	6051	2.117e-15	0.00003533	0.00007386
fixed	NA	male	0.5873	0.008645	67.94	5964	0	0.563	0.6116
fixed	NA	sibling_count3	0.002991	0.01342	0.2229	4438	0.8236	-0.03468	0.04066
fixed	NA	sibling_count4	-0.001225	0.01458	-0.08399	3942	0.9331	-0.04216	0.03971
fixed	NA	sibling_count5	0.01576	0.01729	0.9113	3439	0.3622	-0.03278	0.06429
fixed	NA	sibling_count>5	0.03472	0.01492	2.327	3242	0.02001	-0.007156	0.07659
ran_pars	mother_pidlink	sd__(Intercept)	0.1349	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3134	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)	-1.855	0.1489	-12.46	6035	3.47e-35	-2.274	-1.437
fixed	NA	birth_order	-0.000005794	0.002939	-0.001972	6064	0.9984	-0.008255	0.008243
fixed	NA	poly(age, 3, raw = TRUE)1	0.1807	0.01692	10.68	6039	2.189e-26	0.1332	0.2282
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005507	0.0006048	-9.106	6043	1.143e-19	-0.007205	-0.003809
fixed	NA	poly(age, 3, raw = TRUE)3	0.0000546	0.000006865	7.954	6049	2.146e-15	0.00003533	0.00007387
fixed	NA	male	0.5873	0.008646	67.93	5963	0	0.563	0.6116
fixed	NA	sibling_count3	0.002994	0.0135	0.2218	4441	0.8245	-0.0349	0.04089
fixed	NA	sibling_count4	-0.001218	0.01496	-0.08141	3964	0.9351	-0.04321	0.04078
fixed	NA	sibling_count5	0.01577	0.01809	0.8717	3528	0.3834	-0.03501	0.06654
fixed	NA	sibling_count>5	0.03474	0.01857	1.871	3867	0.06141	-0.01738	0.08686
ran_pars	mother_pidlink	sd__(Intercept)	0.1349	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3134	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)	-1.869	0.1492	-12.53	6042	1.497e-35	-2.288	-1.45
fixed	NA	poly(age, 3, raw = TRUE)1	0.1817	0.01694	10.73	6042	1.312e-26	0.1341	0.2292
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005537	0.0006053	-9.147	6044	7.824e-20	-0.007236	-0.003838
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005483	0.000006871	7.979	6048	1.751e-15	0.00003554	0.00007411
fixed	NA	male	0.5875	0.008647	67.94	5958	0	0.5632	0.6118
fixed	NA	sibling_count3	0.001975	0.01379	0.1433	4637	0.8861	-0.03672	0.04067
fixed	NA	sibling_count4	-0.0008761	0.01555	-0.05635	4304	0.9551	-0.04452	0.04277
fixed	NA	sibling_count5	0.02003	0.01889	1.06	3933	0.2891	-0.033	0.07306
fixed	NA	sibling_count>5	0.04395	0.01914	2.296	4145	0.0217	-0.009772	0.09767
fixed	NA	birth_order_nonlinear2	0.01494	0.01099	1.36	5001	0.1739	-0.0159	0.04577
fixed	NA	birth_order_nonlinear3	0.006761	0.01359	0.4976	5226	0.6188	-0.03138	0.0449
fixed	NA	birth_order_nonlinear4	-0.002179	0.01735	-0.1256	5394	0.9001	-0.05089	0.04653
fixed	NA	birth_order_nonlinear5	-0.01151	0.022	-0.5233	5266	0.6008	-0.07326	0.05023
fixed	NA	birth_order_nonlinear>5	-0.01037	0.02192	-0.4732	6052	0.6361	-0.07189	0.05115
ran_pars	mother_pidlink	sd__(Intercept)	0.135	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3134	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)	-1.866	0.1496	-12.47	6037	2.893e-35	-2.286	-1.446
fixed	NA	poly(age, 3, raw = TRUE)1	0.1803	0.01697	10.62	6035	4.043e-26	0.1326	0.2279
fixed	NA	poly(age, 3, raw = TRUE)2	-0.005484	0.0006068	-9.037	6038	2.137e-19	-0.007187	-0.00378
fixed	NA	poly(age, 3, raw = TRUE)3	0.00005418	0.00000689	7.864	6043	4.359e-15	0.00003484	0.00007352
fixed	NA	male	0.5871	0.008655	67.84	5947	0	0.5629	0.6114
fixed	NA	count_birth_order2/2	0.03855	0.01928	2	5203	0.04559	-0.01556	0.09267
fixed	NA	count_birth_order1/3	0.01712	0.0176	0.973	6032	0.3306	-0.03228	0.06653
fixed	NA	count_birth_order2/3	0.01647	0.01936	0.8508	6073	0.3949	-0.03787	0.07082
fixed	NA	count_birth_order3/3	0.01444	0.02124	0.6799	6080	0.4966	-0.04519	0.07407
fixed	NA	count_birth_order1/4	-0.006943	0.02179	-0.3187	6068	0.75	-0.06809	0.05421
fixed	NA	count_birth_order2/4	0.02816	0.02244	1.255	6080	0.2096	-0.03484	0.09116
fixed	NA	count_birth_order3/4	0.02373	0.02352	1.009	6073	0.3129	-0.04228	0.08974
fixed	NA	count_birth_order4/4	0.006673	0.02483	0.2687	6066	0.7882	-0.06303	0.07638
fixed	NA	count_birth_order1/5	0.03185	0.0295	1.08	6080	0.2803	-0.05095	0.1147
fixed	NA	count_birth_order2/5	0.02865	0.03271	0.876	6046	0.381	-0.06316	0.1205
fixed	NA	count_birth_order3/5	0.03949	0.03081	1.282	6053	0.2	-0.04699	0.126
fixed	NA	count_birth_order4/5	0.01282	0.03022	0.4241	6061	0.6715	-0.072	0.09763
fixed	NA	count_birth_order5/5	0.03525	0.03195	1.103	6043	0.2699	-0.05443	0.1249
fixed	NA	count_birth_order1/>5	0.09172	0.03002	3.055	6063	0.002259	0.007451	0.176
fixed	NA	count_birth_order2/>5	0.04846	0.0301	1.61	6045	0.1075	-0.03603	0.133
fixed	NA	count_birth_order3/>5	0.04365	0.02902	1.504	6030	0.1326	-0.03782	0.1251
fixed	NA	count_birth_order4/>5	0.05895	0.02846	2.071	6003	0.03836	-0.02094	0.1388
fixed	NA	count_birth_order5/>5	0.02874	0.0264	1.089	6027	0.2763	-0.04536	0.1029
fixed	NA	count_birth_order>5/>5	0.04156	0.01996	2.082	5549	0.03742	-0.01448	0.0976
ran_pars	mother_pidlink	sd__(Intercept)	0.1344	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.3137	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)
11	4133	4207	-2056	4111	NA	NA	NA
12	4135	4216	-2056	4111	0.0000002846	1	0.9996
16	4140	4248	-2054	4108	3.094	4	0.5423
26	4153	4327	-2050	4101	7.745	10	0.6537

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)	0.4994	0.07927	6.299	4830	0.0000000003255	0.2768	0.7219
fixed	NA	poly(age, 3, raw = TRUE)1	0.02068	0.006708	3.082	4717	0.002065	0.001848	0.03951
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005941	0.0001832	-3.243	4556	0.00119	-0.001108	-0.00007992
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004817	0.000001566	3.076	4346	0.00211	0.0000004213	0.000009212
fixed	NA	male	0.2089	0.02436	8.575	4962	1.302e-17	0.1405	0.2773
fixed	NA	sibling_count3	0.01578	0.01612	0.9789	4335	0.3277	-0.02947	0.06103
fixed	NA	sibling_count4	0.003225	0.01616	0.1996	4098	0.8418	-0.04213	0.04858
fixed	NA	sibling_count5	0.009782	0.01671	0.5853	3843	0.5583	-0.03713	0.05669
fixed	NA	sibling_count>5	0.0114	0.01314	0.8676	4225	0.3857	-0.02548	0.04827
ran_pars	mother_pidlink	sd__(Intercept)	0.03882	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2719	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)	0.4993	0.07928	6.297	4830	0.0000000003298	0.2767	0.7218
fixed	NA	birth_order	-0.0001987	0.001539	-0.1291	4029	0.8973	-0.004519	0.004121
fixed	NA	poly(age, 3, raw = TRUE)1	0.02074	0.006724	3.084	4708	0.002055	0.001861	0.03961
fixed	NA	poly(age, 3, raw = TRUE)2	-0.000596	0.0001838	-3.243	4529	0.001192	-0.001112	-0.00008008
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004833	0.000001571	3.076	4310	0.00211	0.0000004227	0.000009243
fixed	NA	male	0.2089	0.02436	8.575	4961	1.306e-17	0.1405	0.2773
fixed	NA	sibling_count3	0.01584	0.01613	0.9821	4338	0.3261	-0.02943	0.06111
fixed	NA	sibling_count4	0.003347	0.01619	0.2068	4110	0.8362	-0.04209	0.04878
fixed	NA	sibling_count5	0.009997	0.0168	0.5952	3868	0.5517	-0.03715	0.05714
fixed	NA	sibling_count>5	0.01211	0.01424	0.85	4440	0.3954	-0.02787	0.05209
ran_pars	mother_pidlink	sd__(Intercept)	0.03895	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2719	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)	0.4961	0.07939	6.249	4829	0.0000000004489	0.2732	0.7189
fixed	NA	poly(age, 3, raw = TRUE)1	0.02088	0.006727	3.104	4712	0.00192	0.001998	0.03976
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005984	0.0001838	-3.256	4539	0.001138	-0.001114	-0.00008251
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004839	0.000001571	3.081	4320	0.002075	0.0000004305	0.000009248
fixed	NA	male	0.2098	0.02437	8.608	4956	9.817e-18	0.1414	0.2782
fixed	NA	sibling_count3	0.02091	0.01643	1.272	4435	0.2033	-0.02522	0.06703
fixed	NA	sibling_count4	0.005396	0.01667	0.3237	4263	0.7462	-0.0414	0.05219
fixed	NA	sibling_count5	0.01371	0.01745	0.7858	4106	0.4321	-0.03527	0.0627
fixed	NA	sibling_count>5	0.01531	0.01499	1.021	4640	0.3071	-0.02677	0.0574
fixed	NA	birth_order_nonlinear2	0.00008096	0.01166	0.006942	4775	0.9945	-0.03266	0.03282
fixed	NA	birth_order_nonlinear3	-0.01968	0.01347	-1.462	4766	0.1439	-0.05749	0.01812
fixed	NA	birth_order_nonlinear4	0.009552	0.01505	0.6349	4843	0.5255	-0.03268	0.05178
fixed	NA	birth_order_nonlinear5	-0.01544	0.01716	-0.8998	4879	0.3683	-0.06361	0.03273
fixed	NA	birth_order_nonlinear>5	-0.002691	0.01378	-0.1952	4922	0.8452	-0.04138	0.036
ran_pars	mother_pidlink	sd__(Intercept)	0.03821	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.272	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)	0.493	0.07968	6.187	4830	0.0000000006637	0.2693	0.7166
fixed	NA	poly(age, 3, raw = TRUE)1	0.02063	0.006731	3.065	4707	0.002188	0.001737	0.03952
fixed	NA	poly(age, 3, raw = TRUE)2	-0.0005914	0.0001838	-3.217	4534	0.001303	-0.001107	-0.00007543
fixed	NA	poly(age, 3, raw = TRUE)3	0.000004788	0.00000157	3.049	4316	0.002313	0.0000003795	0.000009196
fixed	NA	male	0.2092	0.02437	8.584	4946	1.209e-17	0.1408	0.2776
fixed	NA	count_birth_order2/2	0.01447	0.02335	0.6196	4660	0.5356	-0.05109	0.08003
fixed	NA	count_birth_order1/3	0.02399	0.02313	1.037	4966	0.2998	-0.04095	0.08892
fixed	NA	count_birth_order2/3	0.03065	0.0246	1.246	4967	0.2128	-0.03839	0.09969
fixed	NA	count_birth_order3/3	0.007198	0.02658	0.2708	4966	0.7865	-0.06741	0.0818
fixed	NA	count_birth_order1/4	0.0006132	0.0246	0.02493	4967	0.9801	-0.06843	0.06966
fixed	NA	count_birth_order2/4	0.008111	0.02642	0.307	4967	0.7589	-0.06606	0.08228
fixed	NA	count_birth_order3/4	-0.001621	0.02848	-0.05692	4967	0.9546	-0.08157	0.07833
fixed	NA	count_birth_order4/4	0.03651	0.02921	1.25	4965	0.2114	-0.04548	0.1185
fixed	NA	count_birth_order1/5	0.04653	0.0274	1.698	4967	0.08951	-0.03038	0.1234
fixed	NA	count_birth_order2/5	-0.02254	0.03016	-0.7475	4967	0.4548	-0.1072	0.06211
fixed	NA	count_birth_order3/5	-0.04164	0.03144	-1.324	4967	0.1854	-0.1299	0.04662
fixed	NA	count_birth_order4/5	0.02983	0.03076	0.9699	4967	0.3321	-0.05651	0.1162
fixed	NA	count_birth_order5/5	0.06484	0.03397	1.908	4967	0.05639	-0.03053	0.1602
fixed	NA	count_birth_order1/>5	0.02421	0.02135	1.134	4967	0.2568	-0.03571	0.08414
fixed	NA	count_birth_order2/>5	0.03074	0.02247	1.368	4967	0.1713	-0.03233	0.09381
fixed	NA	count_birth_order3/>5	0.01257	0.02201	0.5714	4967	0.5678	-0.0492	0.07434
fixed	NA	count_birth_order4/>5	0.02479	0.02202	1.126	4967	0.2603	-0.03702	0.0866
fixed	NA	count_birth_order5/>5	-0.01014	0.02209	-0.4591	4967	0.6462	-0.07216	0.05187
fixed	NA	count_birth_order>5/>5	0.01887	0.01779	1.06	4766	0.289	-0.03108	0.06881
ran_pars	mother_pidlink	sd__(Intercept)	0.03823	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2719	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)
11	1276	1348	-627.1	1254	NA	NA	NA
12	1278	1356	-627.1	1254	0.01671	1	0.8972
16	1282	1386	-624.8	1250	4.631	4	0.3273
26	1288	1457	-617.9	1236	13.77	10	0.1836

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)

## 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)	-0.08365	0.2385	-0.3507	1859	0.7258	-0.7532	0.5859
fixed	NA	poly(age, 3, raw = TRUE)1	0.08334	0.02526	3.299	1859	0.0009875	0.01243	0.1542
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002847	0.0008678	-3.281	1859	0.001055	-0.005283	-0.000411
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003	0.000009506	3.156	1859	0.001628	0.000003313	0.00005668
fixed	NA	male	0.2353	0.04151	5.669	1859	0.00000001665	0.1188	0.3519
fixed	NA	sibling_count3	0.008865	0.02092	0.4238	1859	0.6717	-0.04985	0.06758
fixed	NA	sibling_count4	0.03489	0.02196	1.589	1859	0.1123	-0.02676	0.09653
fixed	NA	sibling_count5	0.02659	0.02399	1.108	1859	0.2679	-0.04075	0.09392
fixed	NA	sibling_count>5	0.03027	0.02075	1.459	1859	0.1449	-0.02799	0.08852
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2791	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)	-0.08354	0.2386	-0.3502	1856	0.7262	-0.7532	0.5861
fixed	NA	birth_order	-0.001376	0.003918	-0.3513	1710	0.7254	-0.01237	0.009622
fixed	NA	poly(age, 3, raw = TRUE)1	0.08351	0.02527	3.305	1850	0.0009685	0.01258	0.1544
fixed	NA	poly(age, 3, raw = TRUE)2	-0.00285	0.0008681	-3.283	1845	0.001046	-0.005287	-0.0004133
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002997	0.000009508	3.152	1840	0.001648	0.00000328	0.00005666
fixed	NA	male	0.2352	0.04153	5.664	1826	0.0000000171	0.1187	0.3518
fixed	NA	sibling_count3	0.009502	0.021	0.4525	1653	0.651	-0.04944	0.06845
fixed	NA	sibling_count4	0.03644	0.0224	1.626	1575	0.1041	-0.02645	0.09932
fixed	NA	sibling_count5	0.02904	0.02499	1.162	1462	0.2454	-0.0411	0.09918
fixed	NA	sibling_count>5	0.03525	0.02514	1.402	1446	0.161	-0.03531	0.1058
ran_pars	mother_pidlink	sd__(Intercept)	0.003056	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2792	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)	-0.08294	0.2389	-0.3471	1854	0.7285	-0.7537	0.5878
fixed	NA	poly(age, 3, raw = TRUE)1	0.08364	0.02531	3.305	1854	0.0009681	0.0126	0.1547
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002862	0.0008694	-3.292	1854	0.001013	-0.005303	-0.0004218
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003026	0.000009525	3.177	1854	0.001513	0.000003522	0.00005699
fixed	NA	male	0.2362	0.04156	5.683	1854	0.00000001533	0.1195	0.3528
fixed	NA	sibling_count3	0.01247	0.02145	0.5814	1854	0.561	-0.04775	0.07269
fixed	NA	sibling_count4	0.04025	0.02337	1.722	1854	0.08522	-0.02536	0.1059
fixed	NA	sibling_count5	0.0282	0.02649	1.064	1854	0.2872	-0.04616	0.1026
fixed	NA	sibling_count>5	0.02489	0.02601	0.9569	1854	0.3387	-0.04812	0.0979
fixed	NA	birth_order_nonlinear2	-0.009683	0.01749	-0.5536	1854	0.5799	-0.05877	0.03941
fixed	NA	birth_order_nonlinear3	-0.01878	0.02057	-0.9128	1854	0.3615	-0.07652	0.03897
fixed	NA	birth_order_nonlinear4	-0.01068	0.02504	-0.4265	1854	0.6698	-0.08097	0.05961
fixed	NA	birth_order_nonlinear5	0.01235	0.03151	0.3919	1854	0.6951	-0.07609	0.1008
fixed	NA	birth_order_nonlinear>5	0.01187	0.02963	0.4004	1854	0.6889	-0.07132	0.09505
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2793	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)	-0.098	0.2399	-0.4085	1844	0.683	-0.7714	0.5754
fixed	NA	poly(age, 3, raw = TRUE)1	0.08341	0.02541	3.282	1844	0.00105	0.01207	0.1547
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002855	0.0008731	-3.27	1844	0.001097	-0.005306	-0.0004039
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003018	0.000009567	3.155	1844	0.001632	0.000003328	0.00005704
fixed	NA	male	0.2385	0.04161	5.731	1844	0.00000001166	0.1217	0.3553
fixed	NA	count_birth_order2/2	0.02927	0.03273	0.8945	1844	0.3712	-0.06259	0.1211
fixed	NA	count_birth_order1/3	0.01775	0.02863	0.6201	1844	0.5353	-0.06261	0.09812
fixed	NA	count_birth_order2/3	0.0114	0.03194	0.3568	1844	0.7213	-0.07827	0.1011
fixed	NA	count_birth_order3/3	0.03532	0.03424	1.031	1844	0.3025	-0.06081	0.1314
fixed	NA	count_birth_order1/4	0.09363	0.03488	2.684	1844	0.007332	-0.004279	0.1915
fixed	NA	count_birth_order2/4	0.0124	0.03513	0.3529	1844	0.7242	-0.08622	0.111
fixed	NA	count_birth_order3/4	0.029	0.03633	0.7981	1844	0.4249	-0.07299	0.131
fixed	NA	count_birth_order4/4	0.04567	0.03891	1.174	1844	0.2407	-0.06356	0.1549
fixed	NA	count_birth_order1/5	0.06573	0.04413	1.49	1844	0.1365	-0.05813	0.1896
fixed	NA	count_birth_order2/5	0.0229	0.04788	0.4783	1844	0.6325	-0.1115	0.1573
fixed	NA	count_birth_order3/5	0.005765	0.04394	0.1312	1844	0.8956	-0.1176	0.1291
fixed	NA	count_birth_order4/5	0.06116	0.04205	1.454	1844	0.146	-0.05689	0.1792
fixed	NA	count_birth_order5/5	0.02552	0.04559	0.5598	1844	0.5757	-0.1025	0.1535
fixed	NA	count_birth_order1/>5	0.03691	0.03967	0.9304	1844	0.3523	-0.07445	0.1483
fixed	NA	count_birth_order2/>5	0.05884	0.04275	1.376	1844	0.1688	-0.06115	0.1788
fixed	NA	count_birth_order3/>5	0.004336	0.0406	0.1068	1844	0.915	-0.1096	0.1183
fixed	NA	count_birth_order4/>5	0.005484	0.03915	0.1401	1844	0.8886	-0.1044	0.1154
fixed	NA	count_birth_order5/>5	0.07248	0.03947	1.836	1844	0.06648	-0.03832	0.1833
fixed	NA	count_birth_order>5/>5	0.05185	0.02905	1.785	1844	0.07444	-0.02969	0.1334
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2794	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)
11	546.4	607.3	-262.2	524.4	NA	NA	NA
12	548.3	614.7	-262.2	524.3	0.124	1	0.7248
16	554.5	643.1	-261.3	522.5	1.784	4	0.7754
26	564.9	708.8	-256.5	512.9	9.584	10	0.4777

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)	-0.06947	0.2387	-0.291	1876	0.7711	-0.7396	0.6007
fixed	NA	poly(age, 3, raw = TRUE)1	0.08058	0.02532	3.182	1876	0.001487	0.009492	0.1517
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002747	0.0008703	-3.156	1876	0.001624	-0.00519	-0.0003039
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002892	0.000009536	3.032	1876	0.002461	0.000002148	0.00005569
fixed	NA	male	0.2456	0.04089	6.007	1876	0.000000002266	0.1308	0.3604
fixed	NA	sibling_count3	0.02061	0.02307	0.8931	1876	0.3719	-0.04416	0.08537
fixed	NA	sibling_count4	0.01468	0.02371	0.619	1876	0.536	-0.05187	0.08123
fixed	NA	sibling_count5	0.001525	0.02502	0.06093	1876	0.9514	-0.06871	0.07176
fixed	NA	sibling_count>5	0.03133	0.02169	1.444	1876	0.1489	-0.02957	0.09222
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2809	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)	-0.06945	0.2388	-0.2908	1875	0.7712	-0.7398	0.6009
fixed	NA	birth_order	0.0005249	0.003441	0.1525	1875	0.8788	-0.009134	0.01018
fixed	NA	poly(age, 3, raw = TRUE)1	0.0805	0.02533	3.177	1875	0.00151	0.009385	0.1516
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002745	0.0008706	-3.153	1875	0.001639	-0.005189	-0.0003016
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002892	0.000009539	3.032	1875	0.002463	0.000002145	0.0000557
fixed	NA	male	0.2457	0.0409	6.006	1875	0.000000002277	0.1309	0.3605
fixed	NA	sibling_count3	0.02035	0.02314	0.8797	1875	0.3791	-0.04459	0.0853
fixed	NA	sibling_count4	0.01415	0.02397	0.5904	1875	0.555	-0.05312	0.08142
fixed	NA	sibling_count5	0.0006978	0.02561	0.02725	1875	0.9783	-0.07118	0.07258
fixed	NA	sibling_count>5	0.02945	0.02495	1.18	1875	0.2381	-0.04059	0.09949
ran_pars	mother_pidlink	sd__(Intercept)	0.000000004243	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.281	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)	-0.06587	0.2393	-0.2753	1871	0.7831	-0.7376	0.6058
fixed	NA	poly(age, 3, raw = TRUE)1	0.08039	0.02539	3.166	1871	0.001568	0.009125	0.1516
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002747	0.0008723	-3.149	1871	0.001666	-0.005196	-0.0002981
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002904	0.000009559	3.038	1871	0.002412	0.000002211	0.00005587
fixed	NA	male	0.2466	0.04095	6.022	1871	0.000000002072	0.1317	0.3616
fixed	NA	sibling_count3	0.02183	0.02363	0.9241	1871	0.3555	-0.04449	0.08815
fixed	NA	sibling_count4	0.01509	0.02475	0.6096	1871	0.5422	-0.05438	0.08455
fixed	NA	sibling_count5	0.000362	0.02684	0.01349	1871	0.9892	-0.07498	0.07571
fixed	NA	sibling_count>5	0.0223	0.02591	0.8605	1871	0.3896	-0.05043	0.09502
fixed	NA	birth_order_nonlinear2	-0.005389	0.01784	-0.3021	1871	0.7626	-0.05546	0.04468
fixed	NA	birth_order_nonlinear3	-0.007488	0.0207	-0.3618	1871	0.7175	-0.06558	0.05061
fixed	NA	birth_order_nonlinear4	0.001033	0.02432	0.04248	1871	0.9661	-0.06723	0.0693
fixed	NA	birth_order_nonlinear5	0.00444	0.03014	0.1473	1871	0.8829	-0.08016	0.08904
fixed	NA	birth_order_nonlinear>5	0.0206	0.02719	0.7578	1871	0.4487	-0.05572	0.09693
ran_pars	mother_pidlink	sd__(Intercept)	0.00000008561	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2812	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)	-0.0715	0.2401	-0.2978	1861	0.7659	-0.7455	0.6025
fixed	NA	poly(age, 3, raw = TRUE)1	0.08093	0.02546	3.179	1861	0.001502	0.009471	0.1524
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002754	0.0008747	-3.148	1861	0.00167	-0.005209	-0.0002983
fixed	NA	poly(age, 3, raw = TRUE)3	0.000029	0.000009585	3.026	1861	0.002514	0.000002097	0.00005591
fixed	NA	male	0.2473	0.04103	6.026	1861	0.000000002019	0.1321	0.3625
fixed	NA	count_birth_order2/2	-0.01316	0.03653	-0.3603	1861	0.7187	-0.1157	0.08937
fixed	NA	count_birth_order1/3	0.00648	0.03199	0.2026	1861	0.8395	-0.08332	0.09628
fixed	NA	count_birth_order2/3	0.02276	0.03503	0.6497	1861	0.516	-0.07558	0.1211
fixed	NA	count_birth_order3/3	0.02057	0.03696	0.5564	1861	0.578	-0.08318	0.1243
fixed	NA	count_birth_order1/4	0.004074	0.03622	0.1125	1861	0.9105	-0.0976	0.1057
fixed	NA	count_birth_order2/4	-0.0125	0.0367	-0.3405	1861	0.7335	-0.1155	0.09052
fixed	NA	count_birth_order3/4	0.01958	0.0411	0.4763	1861	0.6339	-0.09579	0.1349
fixed	NA	count_birth_order4/4	0.03758	0.04186	0.8979	1861	0.3694	-0.07992	0.1551
fixed	NA	count_birth_order1/5	0.03448	0.0407	0.8472	1861	0.397	-0.07977	0.1487
fixed	NA	count_birth_order2/5	-0.06708	0.04668	-1.437	1861	0.1509	-0.1981	0.06395
fixed	NA	count_birth_order3/5	-0.01311	0.0456	-0.2876	1861	0.7737	-0.1411	0.1149
fixed	NA	count_birth_order4/5	0.01589	0.04613	0.3446	1861	0.7305	-0.1136	0.1454
fixed	NA	count_birth_order5/5	-0.01125	0.04681	-0.2404	1861	0.8101	-0.1426	0.1201
fixed	NA	count_birth_order1/>5	0.01485	0.03818	0.3891	1861	0.6973	-0.09232	0.122
fixed	NA	count_birth_order2/>5	0.0675	0.04056	1.664	1861	0.09626	-0.04636	0.1814
fixed	NA	count_birth_order3/>5	-0.009537	0.03866	-0.2467	1861	0.8052	-0.1181	0.099
fixed	NA	count_birth_order4/>5	-0.005476	0.03705	-0.1478	1861	0.8825	-0.1095	0.09852
fixed	NA	count_birth_order5/>5	0.03103	0.03971	0.7813	1861	0.4347	-0.08044	0.1425
fixed	NA	count_birth_order>5/>5	0.03933	0.03021	1.302	1861	0.1931	-0.04546	0.1241
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2812	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)
11	575.8	636.8	-276.9	553.8	NA	NA	NA
12	577.8	644.3	-276.9	553.8	0.02339	1	0.8784
16	584.7	673.3	-276.3	552.7	1.123	4	0.8905
26	594.9	739	-271.4	542.9	9.793	10	0.4588

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)	-0.04607	0.2413	-0.1909	1820	0.8486	-0.7234	0.6312
fixed	NA	poly(age, 3, raw = TRUE)1	0.0834	0.02552	3.267	1820	0.001105	0.01175	0.155
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002838	0.0008763	-3.239	1820	0.001221	-0.005298	-0.0003785
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002979	0.00000959	3.107	1820	0.001922	0.000002873	0.00005671
fixed	NA	male	0.2043	0.04246	4.81	1820	0.00000163	0.08506	0.3234
fixed	NA	sibling_count3	0.002244	0.02053	0.1094	1820	0.9129	-0.05537	0.05986
fixed	NA	sibling_count4	0.01715	0.02185	0.7848	1820	0.4327	-0.04418	0.07848
fixed	NA	sibling_count5	0.01547	0.02478	0.6244	1820	0.5325	-0.05409	0.08504
fixed	NA	sibling_count>5	0.01676	0.02088	0.8027	1820	0.4223	-0.04185	0.07538
ran_pars	mother_pidlink	sd__(Intercept)	0.000000003371	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2794	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)	-0.04579	0.2414	-0.1897	1819	0.8495	-0.7233	0.6317
fixed	NA	birth_order	-0.001402	0.004028	-0.3481	1819	0.7278	-0.01271	0.009905
fixed	NA	poly(age, 3, raw = TRUE)1	0.08359	0.02554	3.273	1819	0.001083	0.01191	0.1553
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002842	0.0008765	-3.242	1819	0.001209	-0.005302	-0.0003811
fixed	NA	poly(age, 3, raw = TRUE)3	0.00002977	0.000009593	3.103	1819	0.001942	0.000002843	0.0000567
fixed	NA	male	0.2039	0.04248	4.799	1819	0.000001729	0.08461	0.3231
fixed	NA	sibling_count3	0.002897	0.02062	0.1405	1819	0.8882	-0.05497	0.06077
fixed	NA	sibling_count4	0.01871	0.02231	0.8385	1819	0.4018	-0.04392	0.08133
fixed	NA	sibling_count5	0.01788	0.02573	0.6947	1819	0.4873	-0.05435	0.09011
fixed	NA	sibling_count>5	0.0218	0.02541	0.8578	1819	0.3911	-0.04954	0.09314
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2795	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)	-0.04889	0.2419	-0.2021	1815	0.8398	-0.7279	0.6301
fixed	NA	poly(age, 3, raw = TRUE)1	0.08412	0.0256	3.286	1815	0.001035	0.01227	0.156
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002866	0.0008787	-3.262	1815	0.001129	-0.005332	-0.0003994
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003016	0.000009617	3.136	1815	0.00174	0.000003163	0.00005715
fixed	NA	male	0.2047	0.04253	4.812	1815	0.000001614	0.08528	0.324
fixed	NA	sibling_count3	0.004311	0.0211	0.2044	1815	0.8381	-0.0549	0.06353
fixed	NA	sibling_count4	0.01953	0.02331	0.8379	1815	0.4022	-0.0459	0.08496
fixed	NA	sibling_count5	0.01357	0.02714	0.5	1815	0.6172	-0.06261	0.08975
fixed	NA	sibling_count>5	0.01085	0.02636	0.4114	1815	0.6808	-0.06316	0.08485
fixed	NA	birth_order_nonlinear2	-0.01028	0.01744	-0.5894	1815	0.5557	-0.05923	0.03867
fixed	NA	birth_order_nonlinear3	-0.01277	0.02068	-0.6177	1815	0.5369	-0.07082	0.04527
fixed	NA	birth_order_nonlinear4	-0.003305	0.02593	-0.1275	1815	0.8986	-0.07608	0.06947
fixed	NA	birth_order_nonlinear5	0.01257	0.03247	0.3873	1815	0.6986	-0.07856	0.1037
fixed	NA	birth_order_nonlinear>5	0.008002	0.03061	0.2614	1815	0.7938	-0.07793	0.09394
ran_pars	mother_pidlink	sd__(Intercept)	0	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2797	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)	-0.0656	0.2431	-0.2698	1805	0.7873	-0.7481	0.6169
fixed	NA	poly(age, 3, raw = TRUE)1	0.08471	0.02575	3.29	1805	0.001021	0.01244	0.157
fixed	NA	poly(age, 3, raw = TRUE)2	-0.002891	0.000884	-3.27	1805	0.001096	-0.005372	-0.0004092
fixed	NA	poly(age, 3, raw = TRUE)3	0.00003046	0.000009677	3.148	1805	0.00167	0.0000033	0.00005763
fixed	NA	male	0.2065	0.04261	4.845	1805	0.000001375	0.08684	0.3261
fixed	NA	count_birth_order2/2	0.01718	0.03204	0.5362	1805	0.5919	-0.07276	0.1071
fixed	NA	count_birth_order1/3	0.005085	0.02819	0.1804	1805	0.8569	-0.07404	0.08421
fixed	NA	count_birth_order2/3	0.0003569	0.03145	0.01135	1805	0.9909	-0.08793	0.08865
fixed	NA	count_birth_order3/3	0.02669	0.03354	0.7957	1805	0.4263	-0.06746	0.1208
fixed	NA	count_birth_order1/4	0.06555	0.0353	1.857	1805	0.06346	-0.03353	0.1646
fixed	NA	count_birth_order2/4	-0.01125	0.03483	-0.323	1805	0.7467	-0.109	0.08653
fixed	NA	count_birth_order3/4	0.01287	0.03668	0.3507	1805	0.7259	-0.09011	0.1158
fixed	NA	count_birth_order4/4	0.02968	0.03883	0.7645	1805	0.4447	-0.0793	0.1387
fixed	NA	count_birth_order1/5	0.04971	0.0441	1.127	1805	0.2598	-0.07408	0.1735
fixed	NA	count_birth_order2/5	0.02667	0.04994	0.534	1805	0.5934	-0.1135	0.1669
fixed	NA	count_birth_order3/5	-0.01025	0.04789	-0.2141	1805	0.8305	-0.1447	0.1242
fixed	NA	count_birth_order4/5	0.0333	0.04609	0.7225	1805	0.4701	-0.09607	0.1627
fixed	NA	count_birth_order5/5	0.004253	0.04725	0.09001	1805	0.9283	-0.1284	0.1369
fixed	NA	count_birth_order1/>5	0.01471	0.04019	0.3659	1805	0.7145	-0.09812	0.1275
fixed	NA	count_birth_order2/>5	0.03404	0.04497	0.757	1805	0.4491	-0.09219	0.1603
fixed	NA	count_birth_order3/>5	-0.01059	0.0404	-0.262	1805	0.7933	-0.124	0.1028
fixed	NA	count_birth_order4/>5	0.007186	0.04081	0.1761	1805	0.8603	-0.1074	0.1217
fixed	NA	count_birth_order5/>5	0.05585	0.04037	1.384	1805	0.1666	-0.05745	0.1692
fixed	NA	count_birth_order>5/>5	0.0298	0.02955	1.009	1805	0.3133	-0.05314	0.1127
ran_pars	mother_pidlink	sd__(Intercept)	0.000000002737	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.2799	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)
11	539.4	600.1	-258.7	517.4	NA	NA	NA
12	541.3	607.5	-258.7	517.3	0.1219	1	0.727
16	548.3	636.5	-258.2	516.3	0.9801	4	0.9128
26	561	704.3	-254.5	509	7.335	10	0.6935

Compare birth order specifications

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