A Note on Bootstrap Tests for Variance Components in Generalized Linear Mixed Models

In many applications of generalized linear mixed models to clustered correlated or longitudinal data, often we are interested in testing whether a random effects variance component is zero. The usual asymptotic mixture of chi-square distributions of the score statistic for testing constrained variance components does not necessarily hold. In this paper, we propose and explore a parametric bootstrap test that appears to be valid based on its estimated level of significance under the null hypothesis. Results from a simulation study indicate that the bootstrap test has a level much closer to the nominal one while the asymptotic test is conservative, and is more powerful than the usual asymptotic score test based on a mixture of chi-squares. The proposed bootstrap test is illustrated using three sets of real-life data obtained from clinical trials.