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Testing polynomial covariate effects in linear and generalized linear mixed models

Author(s): Mingyan Huang | Daowen Zhang

Journal: Statistics Surveys
ISSN 1935-7516

Volume: 2;
Start page: 154;
Date: 2008;
Original page

Keywords: Likelihood ratio test | Restricted maximum likelihood (REML) | Score test

An important feature of linear mixed models and generalized linear mixed models is that the conditional mean of the response given the random effects, after transformed by a link function, is linearly related to the fixed covariate effects and random effects. Therefore, it is of practical importance to test the adequacy of this assumption, particularly the assumption of linear covariate effects. In this paper, we review procedures that can be used for testing polynomial covariate effects in these popular models. Specifically, four types of hypothesis testing approaches are reviewed, i.e. R tests, likelihood ratio tests, score tests and residual-based tests. Derivation and performance of each testing procedure will be discussed, including a small simulation study for comparing the likelihood ratio tests with the score tests.
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