The Use of Mixed Models for the Analysis of Mediated Data with Time-Dependent Predictors

Table 3

Performance of unrestricted structural equation model (USEM) and unrestricted and time interaction linear mixed models (UMM and TIMM, resp.) when true underlying effects are small for early time points and small to moderate for late time points.

Simulated data scenarios			USEM			TIMM			UMM
Time point	Effect size	Sample size	Bias (%)	Coverage probability (%)	Power (%)	Bias (%)	Coverage probability (%)	Power (%)	Bias (%)	Coverage probability (%)	Power (%)
𝑡1	0.05	350	16	95	8	−50	93	6	16	96	7
𝑡2	0.05	350	9.4	94	8	51	94	19	8.6	94	8
𝑡3	0.05	350	7.4	94	9	153	75	56	4.9	95	8
𝑡4	0.25	350	−0.6	94	54	−29	81	76	−0.09	94	54
𝑡5	0.25	350	−0.4	94	48	−8.9	94	73	−0.5	93	48
𝑡6	0.25	350	−0.08	93	40	11	93	66	−1.0	94	38
𝑡1	0.05*	350	−4.0	94	8	−71	94	5	−6.3	95	7
𝑡2	0.05*	350	−9.6	96	7	38	94	15	−9.8	95	6
𝑡3	0.05*	350	−1.4	95	8	146	78	49	1.3	95	7
𝑡4	0.25*	350	2.9	95	55	−29	81	70	2.6	94	54
𝑡5	0.25*	350	2.2	95	49	−7.4	94	71	1.6	94	48
𝑡6	0.25*	350	0.4	95	36	14	94	66	−0.5	95	36
𝑡1	0.05**	350	10	95	7	−60	94	6	8.7	95	7
𝑡2	0.05**	350	−14	93	7	44	95	18	−14	93	7
𝑡3	0.05**	350	11	94	8	148	75	56	12	94	9
𝑡4	0.25**	350	−0.4	95	58	−29	81	79	−0.3	95	55
𝑡5	0.25**	350	0.0	96	50	−8.6	95	77	0.2	96	48
𝑡6	0.25**	350	−0.2	96	37	12	95	70	−2.6	96	36
𝑡1	0.05	100	−25	94	7	−26	94	6	−69	93	6
𝑡2	0.05	100	8.8	94	6	7.2	93	6	36	94	9
𝑡3	0.05	100	10	96	5	14	95	5	141	90	20
𝑡4	0.25	100	−2.0	94	20	−2.2	93	20	−31	90	30
𝑡5	0.25	100	−3.8	94	17	−3.2	94	17	−9.8	95	29
𝑡6	0.25	100	−2.5	94	16	−2.2	94	16	11	95	26
𝑡1	0.05	200	8.2	95	7	−60	95	5	7.7	95	7
𝑡2	0.05	200	1.2	95	7	45	95	13	0.4	95	6
𝑡3	0.05	200	−7.8	95	7	150	83	34	−9.2	95	6
𝑡4	0.25	200	4.0	96	38	−29	97	52	4.1	95	36
𝑡5	0.25	200	−3.0	95	28	−8.1	95	50	−2.6	95	28
𝑡6	0.25	200	−0.7	94	24	13	95	45	−1.3	94	25
𝑡1	0.05	400	41	95	8	−65	94	5	2.7	95	7
𝑡2	0.05	400	−3.2	94	7	41	94	19	−4.7	97	6
𝑡3	0.05	400	−0.2	95	9	146	74	58	−2.3	96	7
𝑡4	0.25	400	−1.3	95	60	−30	76	80	−1.7	95	58
𝑡5	0.25	400	1.2	95	54	−8.6	95	79	1.0	94	53
𝑡6	0.25	400	−0.5	96	43	12	95	73	−1.9	96	40
𝑡1	0.05	400	−6	95	7	52	94	14	−7	95	7
𝑡2	0.05	400	4	97	6	−33	95	8	3	97	7
𝑡3	0.05	400	2	95	8	−119	82	5	5	95	7
𝑡4	−0.11	400	0.4	95	17	−52	83	14	0.9	95	17
𝑡5	−0.11	400	2.5	95	17	−13	95	23	4	95	17
𝑡6	−0.11	400	1	95	13	26	94	26	2	95	13

Based on 1000 simulated datasets.
Results are from simulated data with total effects equally distributed between direct and indirect effects, except where indicated.
*Total effect is primarily direct.
**Total effect is primarily indirect.