Supplementary Table 1: Configuration and sample size for the four analyses
EFA + MI
MI within
MI within
MI within
Longitudinal
between
age groups
age groups
age groups
genetic
age groups
– 12-18
– 19-27
–28-59
analysis
Males from MZ twin-pairs
1366
653
890
432
1355
Males from same sex DZ twin-pairs
1044
537
717
259
1040
Females from MZ twin-pairs
2664
1051
1580
1275
2650
Females from same sex DZ twin-pairs
1654
674
1053
664
1650
Males from opposite-sex twin-pairs
1039
557
694
267
1028
Females from opposite-sex twin-pairs
1300
608
880
410
1292
Twins with unknown zygosity
379
-
-
-
-
Male siblings
922
-
-
-
809
Female siblings
1563
-
-
-
1283
Mothers
1626
-
-
-
-
Fathers
1006
-
-
-
-
Spouses of twins
526
-
-
-
-
Spouses of siblings
10
-
-
-
-
Offspring of twins
164
-
-
-
-
Offspring of siblings
57
-
-
-
-
15320
4080
5814
3307
11107
Total
1
Supplementary Table 2: Number of twins and siblings per age group with data for the longitudinal
genetic analyses
Twins
Brother
Sister
12-18
19-27
28-59
12-18
19-27
28-59
12-18
19-27
28-59
MZM
594
793
420
17
60
61
23
69
72
DZM
471
643
249
15
45
48
4
51
73
MZF
874
1419
1248
26
93
104
19
119
171
DZF
565
965
651
16
63
71
9
82
101
DOS
1015
1408
657
25
96
98
21
125
152
Separate Sibs
-
-
-
1
20
44
2
61
274
Total Twins
3519
5226
3225
-
-
-
-
-
-
Total Sibs
-
-
-
100
377
426
78
507
843
MZM/DZM = monozygotic/ dizygotic males. MZF/DZF = monozygotic/ dizygotic females. DOS =
dizygotic opposite sex twins.
2
Supplementary Table 3: Number of twins and siblings with more than one datapoint in the longitudinal genetic analyses
Twins
Brother
Sister
12-18 &
12-18 &
19-27&
12-18 -
12-18 &
12-18 &
19-27&
12-18 -
12-18 &
12-18 &
19-27&
12-18 -
19-27
28-59
28-59
28-59
19-27
28-59
28-59
28-59
19-27
28-59
28-59
28-59
MZM
187
51
68
73
0
0
14
0
2
3
14
0
DZM
146
30
65
41
0
1
11
0
0
1
11
0
MZF
194
120
159
209
2
1
23
0
3
6
36
0
DZF
145
70
120
98
2
1
17
0
3
2
16
0
DOS
302
87
143
114
0
1
20
0
4
5
36
0
Separate Sibs
-
-
-
-
0
0
0
0
0
0
3
0
Total Twins
974
358
555
535
-
-
-
-
-
-
-
-
Total Sibs
-
-
-
-
2
5
85
0
12
17
116
0
3
Supplementary Table 4: Summary of the Model Fitting Results of the MI analyses for ages 12 - 18
-2lnL
#par
df
Δχ2
Δ df
p
BIC
Effect Size
1. Full measurement invariance: no covariate effects
33320.109
52
40331
-
-
-
-138205.21
-
2. Age effects on latent variance (versus 1)
33320.057
53
40330
0.052
1
0.820
-138201.40
-.003
3. Age effects on factor loadings (versus 2)
33307.202
62
40321
12.855
9
0.169
-138173.27
-
4. Age effects on latent mean (versus 1)
33301.679
53
40330
18.43
1
< .001
-138210.59
.089
5. Age effects on thresholds (versus 4)
33261.634
62
40321
40.045
9
< .001
-138196.05
-
1. Full measurement invariance: no covariate effects
46373.794
52
57505
-
-
-
-210051.31
-
2. Age effects on latent variance (versus 1)
46373.703
53
57504
0.091
1
0.763
-210047.30
.030
3. Age effects on factor loadings (versus 2)
46364.929
62
57495
8.774
9
0.458
-210015.19
-
4. Age effects on latent mean (versus 1)
46374.521
53
57504
-0.727
1
NA
-210046.90
-.049
5. Age effects on thresholds (versus 4)
46353.477
62
57495
21.044
9
0.012
-210020.91
-
1. Full measurement invariance: no covariate effects
20215.571
52
32714
-
-
-
-116676.06
-
2. Age effects on latent variance (versus 1)
20215.824
53
32713
-0.253
1
NA
-116672.06
-.011
3. Age effects on factor loadings (versus 2)
20207.303
62
32704
8.521
9
0.483
-116641.44
-
4. Age effects on latent mean (versus 1)
20211.715
53
32713
3.856
1
0.050
-116674.11
-.042
5. Age effects on thresholds (versus 4)
20184.145
62
32704
27.57
9
0.001
-116653.02
-
Adolescents (ages 12 – 18):
Young adults (ages 19 – 27):
Adults (ages 28 – 59):
4
Supplementary Figure 1 (note: only the first, second and last of the ten items are displayed):
Configural invariance model: The 10 residual item variances are fixed at 1 in all groups, in order to estimate the
10 factor loadings freely in all groups. The unmeasured latent TP-factor is also standardized (mean = 0, variance
= 1) in all groups in order to estimate the thresholds. This model was fitted for each of the six age × sex groups
separately, as well as in a multigroup analysis of the total sample.
Metric invariance model: The factor loadings are constrained to be equal in all six groups (i.e. estimated once).
The 10 residual item variances are fixed at 1 in the first group only, in order to estimate the 10 factor loadings.
The unmeasured latent TP-factor is standardized (mean = 0, variance = 1) in all groups in order to estimate the
thresholds.
Strong factorial invariance model: The factor loadings and the thresholds of the latent responses are constrained
to be equal in all six groups (i.e. estimated once). The 10 residual item variances are fixed at 1 in the first group
only, in order to estimate the 10 factor loadings. The unmeasured latent TP-factor is standardized (mean = 0,
variance = 1) for the first group only in order to estimate the thresholds.
Strict factorial invariance model: The factor loadings and the thresholds of the latent responses are constrained
to be equal in all six groups (i.e. estimated once). The 10 residual item variances are fixed at 1 in all six groups.
The unmeasured latent TP-factor is standardized (mean = 0, variance = 1) for the first group only in order to
estimate the thresholds.
5
Supplementary Figure 2: Path diagram for the MI analyses for twins. Boxes: observed TP-items (only the first, second and last of the ten items are displayed); solid line
circles: unobserved variables (factors); broken line circles: special nodes used to estimate the covariate moderation effects; diamonds: the covariate effects (age);
triangles: unit constants for estimating means and threshold covariate effects; single-headed arrows: linear regression effects; double headed arrows: variances and
covariances. TP TW1: TP-factor for twin 1; TP TW2: TP factor for twin 2; VF: factor variance; m#: item thresholds; r#: item variances; L#: factor loadings; B: covariate
effects on the factor mean; D: covariate effects on factor variance; K#: covariate effects on item thresholds; J#: covariate effects on the factor loadings. rMZ/rDZ =
estimated factor twin correlations for monozygotic (MZ) and dizygotic (DZ) twins, r1#/r2# = twin correlations between item residuals.
6