Testing polynomial covariate effects in linear and generalized linear mixed models

TL;DR

This paper reviews various hypothesis testing procedures, including R tests, likelihood ratio tests, score tests, and residual-based tests, for assessing polynomial covariate effects in linear and generalized linear mixed models, highlighting their derivations and performance.

Contribution

It provides a comprehensive review and comparison of multiple testing methods for polynomial covariate effects in mixed models, including new simulation results.

Findings

Likelihood ratio and score tests compared via simulation

Different tests exhibit varying power and size properties

Guidance provided for selecting appropriate tests in practice

Abstract

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.