To verify that the null distribution for QSNP is χ2 distributed, a set of simulations specified a generating population in which the direct effects of the SNP on the indicators were entirely mediated through the common factor. Each simulation included 1,000 datasets, with N = 100,000 completely overlapping participants per dataset. All simulated datasets were analyzed using both WLS and ML. We examined three models with F = 1 factor, and k = 4, 5, or 6 phenotypes. Supplementary Table 21 presents descriptive statistics for QSNP. Using a genome-wide significance threshold, in all cases the false discovery rate for QSNP was 0, and the power to detect a SNP effect on the common factor was 1. Both WLS and ML estimation produced mean estimates of QSNP that were approximately equal to the df of the corresponding model. Supplementary Figure 34 depicts the null sampling distributions of QSNP estimated using WLS or ML. Supplementary Figure 35 plots QSNP from these two estimation methods against χ2 distributions and against one another. These results indicate that both estimation methods produce results that are approximately χ2 distributed.
