We present additional results benchmarking Genomic SEM against existing methods— Multi-trait Analysis of GWAS (MTAG)36, Model Averaging Genome-wide Association Meta-analysis (MA-GWAMA), and N-weighted Multivariate GWAMA (N-GWAMA)37—in the Supplementary Note. In addition, we examined the performance of multivariate GWAS in Genomic SEM when specified as an unstructured model that computes an omnibus index of association across all 11 disorders. Unstructured model results were obtained by comparing a maximally complex model in which the SNP is allowed to have direct regression relations with each of the 11 disorders against a null model in which the SNP is associated with none of the disorders. This is in contrast to the multivariate GWAS specified as a factor model discussed initially that estimates SNP effects on the factors, as this defines a structure of the relationship between the SNP and the 11 disorders. Briefly, we find the unstructured model is particularly well suited when the aim is to identify an exhaustive set of SNPs relevant to psychiatric risk, but does little to elucidate the specific patterning of associations. In contrast, the factor model allows us to systematically probe the genetic underpinnings of convergence and divergence across clusters of psychiatric disorders.
