Supplementary Table 1: Configuration and sample size for the four analyses

EFA + MI between age groups / MI within age groups – 12-18 / MI within age groups – 19-27 / MI within age groups –28-59 / Longitudinal genetic 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 / - / - / - / -
Total / 15320 / 4080 / 5814 / 3307 / 11107

Supplementary Table 2:Number of twins and siblings per age groupwith 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.

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Supplementary Table 3:Number of twins and siblings with more than one datapoint in the longitudinal genetic analyses

Twins / Brother / Sister
12-18 & 19-27 / 12-18 & 28-59 / 19-27& 28-59 / 12-18 - 28-59 / 12-18 & 19-27 / 12-18 & 28-59 / 19-27& 28-59 / 12-18 - 28-59 / 12-18 & 19-27 / 12-18 & 28-59 / 19-27& 28-59 / 12-18 - 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

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
Adolescents (ages 12 – 18):
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 / -
Young adults (ages 19 – 27):
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 / -
Adults (ages 28 – 59):
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 / -

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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 groupsin 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.

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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.

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