A distribution-free test of constant mean in linear mixed effects models

We propose a distribution-free procedure, an analogy of the DIP test in non-parametric regression, to test whether the means of responses are constant over time in repeated measures data. Unlike the existing tests, the proposed procedure requires very minimal assumptions to the distributions of both random effects and errors. We study the asymptotic reference distribution of the test statistic analytically and propose a permutation procedure to approximate the finite-sample reference distribution. The size and power of the proposed test are illustrated and compared with competitors through several simulation studies. We find that it performs well for data of small sizes, regardless of model specification. Finally, we apply our test to a data example to compare the effect of fatigue in two different methods used for cardiopulmonary resuscitation.