Table A1 (available in online Appendix) shows the mean (±standard error) of the raw score for the SxAnxDep scale as a function of sex, age and reporter. Higher rates of symptoms were seen for females versus males and for self-report versus parental report. Symptoms increased with age in females whereas for males they declined through adolescence and then increased in young adulthood. shows the correlations between self-reports and parental reports of SxAnxDep within and across time. At ages 13–14, 17–18 and 19–20, the correlations in self- and parental ratings of SxAnxDep varied across a narrow range from +0.33 to +0.35. In adjacent waves, the within-rater correlations for self- and parental ratings were similar, ranging from +0.47 to +0.57 and decline monotonically with increasing passage of time. The cross-time cross-rater correlations were lower and, for adjacent assessment periods, ranged from +0.18 to +0.30.
Correlations for symptoms of anxiety and depression as a function of age and reporter (self versus parent)
Our model fitting began with a full model including both quantitative and qualitative sex effects (model I in ). We first attempted to simplify this model by dropping the quantitative sex effects (model II), which markedly improved the model fit as indexed by the BIC. Of note, in this model, the genetic correlations between males and females in model II were estimated at +1.00, 0.72, 0.71 and 0.55 at ages 8–9, 13–14, 16–7 and 19–20 respectively. This intriguing pattern, sugestive of declining similarity of genetic risk factors for SxAnxDep in males and females, is explored in more detail below. Next, we rigorously tested for these qualitative sex effects in model III. Despite the suggestive pattern of estimates, the model fit improved when all genetic correlations were constrained to 1.00.
Model fitting results: a multi-rater developmental model for symptoms of anxiety and depression
Our goal was then to determine which of the paths in the model III were required to explain the pattern of correlations between and within twin pairs within and across time. To facilitate this effort, in model IV, we constrained the measurement portion of our model to the estimates obtained in model III (Table A2, online). All subsequent models modify only the genetic and environmental influences on the latent measures of SxAnxDep (T1 to T4). We compare the resultant fit to that obtained by model IV.
In models V, VI, VII and VIII, we constrained to zero the shared environmental or C effects at times 4, 3, 2 and 1. The model fit, as reflected by the BIC, improved with each step. Next, we constrained to zero the unique environmental or E effects at times 4, 3 and 2 in models IX, X and XI respectively. The fit further improved in models IX and X (), but setting to zero the E effects at time 2 results in a substantial deterioration in the BIC. Finally, in model XII, we constrained to zero the genetic effects at time 4. This also caused the model fit to deteriorate, thereby indicating that model X was our best-fit model.
Parameter estimates for this model, along with 95% confidence intervals, are shown in and results for the genetic factors illustrated in . Seven results are noteworthy. First, shared environmental factors did not contribute to the rater-independent latent SxAnxDep scores. Second, genetic factors played a strong role in influencing symptoms of SxAnxDep as indexed by self- and parent ratings. Heritability was estimated at 72, 89, 84 and 79% for times 1, 2, 3 and 4 respectively.
Parameter estimates and 95% confidence intervals for the best-fit model (model X) for symptoms of anxiety and depression (T1 to T4)a
Fig. 2 The proportion of total variance in symptoms of anxiety and depression (SxAnxDep) accounted for by genetic factors through development. The y axis represents the total phenotypic variance so the sum of all the factors equals the total heritability. The (more ...)
Third, consistent with the predictions of the ‘developmentally dynamic’ hypothesis, we found evidence for genetic innovation in genetic factors 2, 3 and 4. That is, in addition to the temporally stable genetic influences that begin at ages 8–9, as illustrated in , the model demonstrated substantial new genetic influences on SxAnxDep emerging at each of the three subsequent ages: 13–14, 16–17 and 19–20. Fourth, we also saw strong evidence for genetic attenuation. The first genetic factor accounted for 72% of the variance in our latent measures of SxAnxDep at ages 8–9 but declines steeply in influence, and by ages 19–20 accounted for only 12% of that variance. A less dramatic but similar decline is seen for factor 2. The attenuation of these genetic factors is not likely to result from chance factors as the parameter estimates in the youngest and oldest age periods have non-overlapping confidence intervals.
Fifth, unique environmental factors accounted for 28, 11, 16 and 21% of the variance in SxAnxDep as reported by both parent and child. The effects of the first unique environmental factor attenuated sharply over time. By contrast, the impact of the second unique environmental factor grew over time, suggesting that some environmental experiences not shared with twins between the ages of 8–9 and 13–14 have an enduring impact on SxAnxDep. Sixth, at each of the three time-points when we had reports from both parent and child, the λP path was higher than the λS path, suggesting that parental ratings were contributing more strongly to the latent index of anxiety and depression than was self-report. Seventh, parameter estimates for the reporter-specific parent- and self-report factors for SxAnxDep are shown in Table A2 (online). Examining rater-specific effects unique to parents, estimates of shared environment substantially exceeded that for genetic effects whereas for the rater-specific factors unique to the twins, the reverse pattern was seen.
Although our global analyses did not support the presence of qualitative sex effects, model II showed intriguing evidence suggestive of declining genetic correlations between males and females with development. Given our prior interest in this question, and the low power for detecting qualitative sex effects even with samples of our size (Prescott & Gottesman, 1993
), we pursued this issue further in an exploratory manner. Our best-fit model X produced a –2 log likelihood value of 31893.6 with 12 557 degrees of freedom. This model constrained the genetic correlation (ra
) in males and females to equal unity across all four ages. If we added to this model a single parameter, a linear decline in ra
across age, the –2 log likelihood improved by 1.1 units and estimated ra
was equal to 1.00, +0.90, +0.80 and +0.70 at ages 8–9, 13–14, 16–17 and 19–20 respectively. The fit by BIC was moderately worse than that seen for the best-fit model (Δ 8.4 units) and the fit by Akaike’s Information Criterion (AIC; Akaike, 1987
), another widely used and validated fit index for structural modeling (Williams & Holahan, 1994
), was slightly worse (Δ 0.9 units).
To determine whether this effect was seen in both parental and twin reports, we examined the ratio of correlations in SxAnxDep scores in opposite- to same-sex DZ twins. With parental ratings, this ratio was 1.50, 1.14, 0.88 and 0.64 respectively across the four waves from ages 8–9 to 19–20. Using self-ratings, this ratio, from ages 13–14 to 19–20 was 0.85, 0.62 and 0.62 respectively.