Improved testing inference in mixed linear models

TL;DR

This paper develops improved likelihood ratio tests with small sample corrections for fixed effects in mixed linear models, enhancing inference accuracy especially with limited data.

Contribution

It introduces Bartlett corrections for likelihood ratio tests in mixed linear models, accommodating vector parameters and nonlinear covariance structures, extending previous work.

Findings

Proposed tests outperform standard likelihood ratio tests in small samples.

Numerical simulations demonstrate superior finite sample behavior.

Application illustrates practical benefits of the new methods.

Abstract

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Oftentimes, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test and also to a test obtained from a modified profile likelihood function. Our results generalize those in Zucker et al. (Journal of the Royal Statistical Society B, 2000, 62, 827-838) by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report numerical evidence which shows that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed.