Genomic SEM is a two-stage Structural Equation Modelling approach. In the first stage, a genetic covariance matrix (S) and its associated sampling covariance matrix (VS) are estimated with a multivariate version of LD Score regression (LDSC). S consists of heritabilities on the diagonal and genetic covariances (co-heritabilities) on the off-diagonal. V consists of squared standard errors of S on the diagonal and sampling covariances on the off-diagonal, which capture dependencies between estimating errors that will arise in situations such as participant sample overlap across GWAS phenotypes. In the second stage, a structural equation model is fit to S by optimizing a fit function that minimizes the discrepancy between the model-implied genetic covariance matrix (Σ(θ)) and S, weighted by the elements within V. We use the diagonally weighted least squares (WLS) fit function described in Grotzinger et al.13: FWLS(θ)=(s−σ(θ))′DS−1(s−σ(θ)) where S and Σ(θ) have been half-vectorized to produce s and σ(θ), respectively, and DS is VS with its off-diagonal elements set to 0. The sampling covariance matrix of the stage 2, Genomic SEM parameter estimates (Vθ) are obtained using a sandwich
