For each subject, the relationship between the SNP, x, and the multivariate phenotypes, Y, was defined as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\boldsymbol{Y}} = x{\mathbf{\beta}} + {\mathbf{\epsilon}}, $$ \end{document}Y=xβ+ε, where β is the effect of the SNP on the phenotypes and ε is the error term. In this simulation study, we simulated x based on a minor allele frequency of 0.25. We evaluated the performance of competing methods under three different settings of effect sizes: Null hypothesis (no effects)β=(0,0,0,0,0)′. Moderate equal effect sizesβ=(0.3,0.3,0.3,0.3,0.3)′. Varied effect sizesβ=(0.1,0.2,0.3,0.4,0.5)′.
