  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.
