For the error term, we considered two cases. In the first case, the error term was simulated from a multivariate normal distribution with the mean 0 and the variance-covariance Σ, which is a compound symmetry matrix with the value of 1 on the diagonal and the value of ϱ=0,0.25,0.5, or 0.75 on the off-diagonal. In the second case, the error term was simulated from a mixture of two multivariate normal distributions: 90 % from the same multivariate normal distribution in the first case and 10 % from the multivariate normal distribution with the mean 0 and the variance-covariance matrix 5Σ. The purpose of the second case was to simulate long tailed distributions of phenotypic traits which are common in real data. We generated simulated data of 100 subjects under each configuration. In addition, each configuration was repeated 10,000 times. The nominal type I error rate was set at 0.05 and the power was calculated as the proportion of p-values less than 0.05.
