Genome-wide association studies (GWASs) are rapidly identifying loci affecting multiple social, behavioral, and psychiatric phenotypes.1,2 Moreover, using cross-trait versions of methods such as genomic-relatedness-based restricted maximum-likelihood (GREML)3 and LD-score regression (LDSC)4 researchers have identified genetic correlations between diverse traits, e.g., age of first birth and risk of smoking,5 insomnia and psychiatric traits (e.g., schizophrenia),6 major depressive disorder and number of children,7 and educational attainment and cognitive performance.8 Widespread statistical pleiotropy appears to be the rule rather than the exception across complex traits. Although these findings are currently suggestive of constellations of phenotypes affected by shared sources of genetic liability, existing methods do not permit the causes of the observed genetic correlations to be investigated systematically. Here we introduce Genomic Structural Equation Modeling (Genomic SEM), a new method for modeling the multivariate genetic architecture of constellations of traits and incorporating genetic covariance structure into multivariate GWAS discovery. Genomic SEM is a flexible framework for formally modeling the genetic covariance structure of complex traits using GWAS summary statistics from samples of varying and potentially unknown degrees of overlap, in contrast to existing
