We conducted a series of simulations to further validate the calibration of Genomic SEM for multivariate GWAS in the specific context of the analyses presented here. For each simulation, we used Genomic SEM to estimate factor-specific SNP effects and factor-specific indices of heterogeneity, as indexed by QSNP13. QSNP indexes violation of the null hypothesis that the SNP acts on the individual disorders entirely via the factor on which they load (Fig. 2; see Methods). As expected, simulation results revealed that the power to detect multivariate SNP effects and QSNP decreased and increased, respectively, as population SNP effects increasingly deviated from those implied by the factor structure (Supplementary Figs. 25-28 and Supplementary Table 11). These simulations additionally illustrated that that SNP effects on factors, as estimated with Genomic SEM, are not simply the reflection of the most high-powered univariate GWAS that defines the factor, that there is null signal when the population of SNP effects is set to 0, and that power for QSNP is particularly high when there are directionally discordant SNP effects across the factor indicators.
