A Monte Carlo permutation procedure for testing variance components using robust estimation methods

Permutation methods offer an acceptable and convenient tool for inferring zero variance components in linear mixed models using the likelihood ratio test. However, when data exhibit heavy-tailed distribution, heavy-skewed distribution or outliers, maximum likelihood estimation may not be the best choice in constructing useful test statistics. In this article, we propose the use of robust rank-based estimation as an alternative. The finite sample distribution of our test statistic is well approximated using suitable permutations of the cluster indices that are exchangeable when the null hypothesis is true. Empirical results, comparing the new test to existing tests, indicate that all tests maintain acceptable Type I error rates when data exhibit heavy-tailed or heavy-skewed distributions. However, only our new test remains robust against the presence of outlier in the response space. Besides, it is only the latter case where other tests could show a competing power to our test. Otherwise, the new test is superior with an outstanding power under the remaining settings.