Testing polynomial covariate effects in linear and generalized linear mixed models

Details Testing polynomial covariate effects in linear and generalized linear mixed models Testing polynomial covariate effects in linear and generalized linear mixed models

2008-02-08

arxiv.org/abs/0802.1103v2

Statistics Surveys 2008, Vol. 2, 154-169

Statistics

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Published in at http://dx.doi.org/10.1214/08-SS036 the Statistics Surveys (http://www.i-journals.org/ss/) by the Institute of

Scientific paper

10.1214/08-SS036

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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