GOODNESS OF FIT TESTS FOR GENERALIZED LINEAR MIXED MODELS
Slud, Eric V
Pfeiffer, Ruth M
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Generalized Linear mixed models (GLMMs) are widely used for regression analysis of data, continuous or discrete, that are assumed to be clustered or correlated. Assessing model fit is important for valid inference. We therefore propose a class of chi-squared goodness-of-fit tests for GLMMs. Our test statistic is a quadratic form in the differences between observed values and the values expected under the estimated model in cells defined by a partition of the covariate space. We show that this test statistic has an asymptotic chi-squared distribution. We study the power of the test through simulations for two special cases of GLMMs, linear mixed models (LMMs) and logistic mixed models. For LMMs, we further derive the analytical power of the test under contiguous local alternatives and compare it with simulated empirical power. Three examples are used to illustrate the proposed test.