In order to evaluate the relationship between estimates from MTAG and those from a Genomic SEM formulation of the MTAG model, we specified a bivariate system of heritable phenotypes, A and u. Phenotype A was constructed using the GCTA package3, and specified to be 60% heritable, and affected by a random selection 30,000 HapMap3 SNPs. Phenotype u was constructed separately using the GCTA package, and also specified to be 60% heritable, and affected by a different random selection of 30,000 HapMap3 SNPs. Both A and u were standardized (M=0, SD=1). Phenotype B was constructed from phenotypes A and u according to the equation B = .7A + .7u. This procedure resulted in 60% heritabilities for both traits A and B, with a genetic correlation of .7 between them. Sample sizes for phenotypes A and B were 25,000 each, with 10,000 participants contributing data for both phenotypes A and B (i.e. 40% sample overlap), such that the analytic dataset was composed of 40,000 unique individuals in total. Both MTAG11 and a Genomic SEM model specified to satisfy the same moment conditions
