the general genetic factor and one domain-specific genetic factor. Weights for contribution of the general genetic factor were λFg,k =.70, .60, .50, .40, and .30, for correlated genotypes 1–5, respectively. Weights for the domain-specific factors were (1−λFg,k2). Phenotypes were then each constructed as the weighted linear combination of one of the correlated genotypes and domain-specific environmental factors (randomly sampled from a normal distribution with M=0, SD=1). Heritabilities for phenotypes 1-5 were set to hk2=35%, 40%, 50%, 60%, and 70%, respectively, such that the weights for the genotypes were hk2 and the weights for the environmental factors were (1−hk2). We chose these figures to stabilize the properties of the distributions across simulations at 100 replications with N~39K each. We expect that with lower SNP h2’s, the same patterns would hold, albeit at larger sample sizes. Each of the 500 phenotypes (100 sets of 5 phenotypes) was then analyzed as a univariate GWAS in PLINK56 to produce univariate GWAS summary statistics. Our multivariable LDSC function was then used to construct 100 sets of 5×5 genetic covariance matrices (S) and associated sampling covariance matrices (VS), and Genomic SEM was used to fit a one factor model to each set.
