Variance component testing in generalised linear models with random effects

There is considerable interest in testing for overdispersion, correlation and heterogeneity across groups in biomedical studies. In this paper, we cast the problem in the framework of generalised linear models with random effects. We propose a global score test for the null hypothesis that all the variance components are zero. This test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects. We also propose individual score tests and their approximations for testing the variance components separately. Both tests can be easily implemented using existing statistical software. We illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings, and evaluate their performance through simulation.