A powerful application of Genomic SEM is to include individual SNP effects in both the genetic covariance matrix and the sampling covariance matrix, in order to estimate the effect of a given SNP on the latent genetic factor(s). If the summary statistics are composed of M different SNPs, then M models are estimated to obtain genome-wide summary statistics for the latent factor. As an example of Genomic SEM used for multivariate GWAS, we incorporated SNP effects into the p-factor and neuroticism models presented above. LD-independent hits are defined below as r2 < .1 in a 500Kb window, with the exception of a 1Mb window for chromosomes 6 and 8. 128 independent loci were genome-wide significant for the p-factor (p < 5 × 10−8; Supplementary Figures 8–10; Figure 1a, Figure 2a). Of the 128 loci, 27 independent loci were not previously identified in any of the contributing univariate GWASs (Table 1, Supplementary Table 5). Of these 27 loci, five loci were identified as either genome-wide significant or suggestive of significance (p < 1 × 10−5) in a separate, previously published GWAS
