In both data sets, we quantile transformed each single phenotype to a standard normal distribution to guard against model misspecification. Although this strategy does not guarantee that the transformed phenotypes follow a multivariate normal distribution jointly, it often works well in practice when the number of phenotypes is small (see, e.g. 22). For both data sets, we used a standard mvLMM with an intercept term (without any other covariates), and test each SNP in turn. Because the software MTMM relies on the commercial software ASREML to estimate the variance components in the null model, we modified the MTMM source code so that it can read in the estimated variance components from GEMMA.
