Stratified Genomic SEM extends the overall Genomic SEM framework by allowing potentially different structural equation models to be fit to genetic covariance matrices estimated in different gene sets and categories. These gene sets and categories, collectively referred to as annotations, can be constructed based on a variety of sources, such as collateral gene expression data obtained from single-cell RNA sequencing. We develop a multivariate extension of Stratified LD Score Regression (S-LDSC)32 below to estimate these annotation-specific genetic covariance matrices and their associated sampling covariance matrices. We describe two types of annotation-specific genetic covariance matrices, S0 and Sτ. S0 contains estimates of genetic covariance within a specific annotation without controlling for overlap with other annotations. In other words, it is composed of the zero-order coefficients implied by the multivariate S-LDSC model. Sτ contains estimates of genetic covariance controlling for annotation overlap. In other words, it is composed of multiple regression coefficients estimated by the multivariate S-LDSC model. The distinction between S0 and Sτ directly parallels the distinction made in univariate S-LDSC32 between overall heritability explained by an annotation and the incremental
