Genomic SEM can be employed as a tool for multivariate GWAS based on univariate summary statistics. First, the genetic covariance matrix and its associated sampling covariance matrix are expanded to include SNP effects. A Genomic SEM is then specified in which SNP effects occur at the level of a latent genetic factor defined by several phenotypes, at the level of the genetic components of each of several (potentially genetically correlated) phenotypes, or some combination of the two. The Genomic SEM is then run once per SNP (or each set of SNPs, should the user incorporate multiple SNPs into a model) to obtain its effects within the multivariate system.
