For each simulation scenario (see below) 1,000 datasets were simulated. Empirical significance thresholds for all methods were derived based on permutation of the traits generated in these simulation datasets, resulting in the null distribution of the test statistic. We generated 10 permuted datasets per simulation dataset, resulting in a total of 10,000 permuted replicates per scenario. These replicates were analyzed with the multivariate methods, resulting in a p-value or log10 BF for each replicate per method per scenario. Significance thresholds were set in such a way that 5% of the 10,000 replicates per method yielded a significant result (5% false-positive rate). This was done by sorting the 10,000 association measures in ascending (p-values) or descending order (Bayes Factors) and defining the empirical significance threshold as the mean of the 500th and 501st association measure.
