The Use of Mixed Models for the Analysis of Mediated Data with Time-Dependent Predictors
Table 2
Performance of SEM and linear mixed model assuming delayed effects of main independent variable when true underlying effects are small for early time points and small to moderate for late time points.
Simulated data scenarios
Delayed effect SEM
Naive delayed effect LMM
Full delayed effect LMM
Time point
Effect size
Sample size
Bias (%)
Coverage probability (%)
Power (%)
Bias (%)
Coverage probability (%)
Power (%)
Bias (%)
Coverage probability (%)
Power (%)
0.05
350
10
95
13
390
23
53
9.6
95
13
0.25
350
−0.1
95
83
109
9
100
−0.3
94
82
0.05*
350
−4.2
95
11
522
6
82
−5.0
95
10
0.25*
350
1.7
95
83
144
0.8
100
1.4
94
82
0.05**
350
2.2
94
11
−234
61
17
2.2
94
12
0.25**
350
−0.7
95
85
633
48
100
−0.7
96
84
0.05
100
−0.2
94
8
−397
68
20
−0.9
94
7
0.25
100
−2.9
94
34
107
58
92
−2.5
94
32
0.05
200
0.2
95
10
−396
45
34
-0.9
95
9
0.25
200
0.8
95
63
109
28
99
0.7
96
61
0.05
400
0.2
94
14
−400
17
60
−1.4
94
12
0.25
400
8.0
96
88
109
6
100
−0.8
94
86
0.05
350
4.2
96
11
−684
0.2
97
4.1
96
9
0.5
350
0.5
95
100
98
0
100
0.09
95
100
0.05
400
0.4
95
11
−148
80
6
0.6
95
10
−0.11
400
1.5
95
30
−90
74
6
2
95
30
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.
