To study the false positive rate and the power to detect GVs using TATES, we simulated genotype-phenotype data for 2000 subjects and 20 phenotypes (standard normally distributed unless stated otherwise) according to various scenarios that are illustrated in Figure 1a–1f. Specifically, the phenotypic correlation structure was due to one underlying common factor (or dimension, Figure 1a, 1e), multiple underlying common factors (Figure 1b–1d), or to a network model, in which correlations between phenotypes are due to direct, mutual relations between the components (Figure 1f). Within these phenotypic correlational settings, the GV affects multiple phenotypes via the common factor (Figure 1a,b,c), or affects a single component directly (Figure 1d–1f). For each scenario, we simulated GVs (MAF of .50) with effect sizes ranging from 0 to 1% explained variance. The false positive rate was also studied given MAF = .05 and N = 12000. Simulations are described in detail in the Materials and Methods section.