TABLE 4.

Estimates of Fixed Effects and Variance–Covariance Parameters From Simultaneous Modeling Mothers’ and Fathers’ Data Using MLM and SEM

	Default Error Covariance Structure						Dependent Error Covariance Structure
	MLM			SEM			MLM			SEM
Fixed Effects	Estimate	SE	p value	Estimate	SE	p value	Estimate	SE	p value	Estimate	SE	p value
Father intercept β10	117.22	1.79	< .001	117.22	1.79	< .001	117.21	1.79	< .001	117.21	1.79	< .001
Father slope β20	−2.15	1.17	0.070	−2.15	1.18	0.070	−2.12	1.16	0.071	−2.12	1.17	0.071
Difference in M vs. F intercept β30	2.09	1.56	0.182	2.09	1.56	0.180	2.09	1.56	0.181	2.09	1.56	0.179
Difference in M vs. F slope β40	−1.43	1.27	0.263	−1.43	1.28	0.265	−1.41	1.27	0.267	−1.41	1.28	0.269
Variance Components	Estimate	SE	p value	Estimate	SE	p value	Estimate	SE	p value	Estimate	SE	p value
Father intercept ${\sigma }_1^2$	345.91	52.99	< .001	345.92	52.99	< .001	346.21	53.05	< .001	346.21	53.05	< .001
Father slope ${\sigma }_2^2$	80.71	23.76	< .001	80.75	23.77	< .001	78.95	23.78	< .001	78.95	23.78	< .001
Difference in M vs. F intercept ${\sigma }_3^2$	165.19	41.03	< .001	165.20	41.03	< .001	189.82	41.34	< .001	189.80	41.34	< .001
Diff in M vs. F slope ${\sigma }_4^2$	22.91	26.61	0.195	22.93	26.61	0.195	49.72	27.44	0.035	49.72	27.44	0.035
Cov (Father intercept, Father slope) σ12	−50.83	28.32	0.073	−50.84	28.33	0.073	−50.35	28.27	0.075	−50.35	28.27	0.075
Cov (Father intercept, Difference in intercept) σ13	−114.09	36.96	< .001	−114.09	36.96	.002	−127.63	37.20	0.001	−127.64	37.21	0.001
Cov (Father intercept, Difference in slope) σ14	31.59	29.07	0.277	31.60	29.07	0.277	44.89	29.44	0.127	44.89	29.44	0.127
Cov (Father slope, Difference in intercept) σ23	12.06	24.01	0.615	12.09	24.02	0.615	21.66	24.09	0.369	21.66	24.09	0.369
Cov (Father slope, Difference in slope) σ24	−2.12	19.68	0.914	−2.14	19.68	0.913	−17.57	20.29	0.387	−17.57	20.29	0.387
Cov (Difference in intercept, Diff in slope) σ34	−16.33	28.16	0.562	−16.34	28.16	0.562	−37.33	28.56	0.191	−37.33	28.56	0.191
Level 1 residual ${\sigma }_e^2$	105.47	5.74	< .001	105.46	5.75	< .001	NA	NA	NA	NA	NA	NA
Residual variance Mother ${\sigma }_m^2$	NA	NA	NA	NA	NA	NA	108.58	8.28	< .001	108.58	8.28	< .001
Residual variance Father ${\sigma }_f^2$	NA	NA	NA	NA	NA	NA	103.36	8.11	<.001	103.36	8.11	< .001
Correlation between Mother and Father residuals ρmf	0	N/A	N/A	0	NA	NA	.170	.054	.002	.170	.054	.002

Note. M = mother; F = father; NA = not available; SE = standard error estimate. The variance tests are one-sided (H0: variance = 0 vs. Ha: variance > 0), which is the default of SAS PROC MIXED. One-sided Wald variance tests are recommended by Fitzmaurice et al. (2011) because two-sided Wald variance tests are too conservative due to the boundary issue (also see Ke & Wang, 2015). The default of Mplus is two-sided tests, so for testing the variance components, the p values in the Mplus columns are the two-sided p values from Mplus divided by 2.