In Stage 1, the empirical genetic covariance matrix (SLDSC) and its associated sampling covariance matrix (VSLDSC) are estimated using our multivariable extension of LDSC. SLDSC is a k × k symmetric matrix with SNP heritabilities on the diagonal and genetic covariances (σgi,gj) between phenotypes i and j off the diagonal. The genetic covariance between phenotypes i and j can be computed as the genetic correlation scaled relative to the total genetic variance of each of the two contributing phenotypes (themselves scaled to unit variances), σgi,gj=rgi,gj⋅hi2⋅hj2. Thus, the genetic covariance matrix of order k has k* = k(k+1)/2 nonredundant elements. It can be written as: SLDSC=[h12σg1,g2h22⋮⋱σg1,gkσg2,gk⋯hk2]
