A Monte Carlo permutation procedure for testing variance components in generalized linear regression models

Testing zero variance components is of utmost importance in various applications empowered by the use of mixed-effects models. Focusing on generalized linear models, this article proposes a permutation test using an analogue of the ANOVA test statistic that merely requires fitting the null model with independent observations. Monte Carlo simulations reveal that the new test has correct Type-I error rate and that its power compares favorably to an existing bootstrap score test. A real data application illustrates the advantageous capability of the proposed test in detecting the need for random effects.