Generalized p value tests for variance components in a class of linear mixed models

The problems of testing hypotheses on variance components in linear mixed effects models have been addressed by various workers, although existing methodology is still restricted to a narrow range of models. To overcome this difficulty we develop new general p value tests in general settings. The p values are motivated by a useful matrix inequality. It is shown that the proposed test is invariant under the group of location-scale transformations. Numerical results show that the test can control the Type I errors satisfactorily, and it also exhibits good power properties. Most importantly, the new methods are simple and easy to apply.