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Permutation and Bayesian tests for testing random effects in linear mixed-effects models

Rao, Kaidi; Drikvandi, Reza; Saville, Ben

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Authors

Kaidi Rao

Ben Saville



Abstract

In many applications of linear mixed‐effects models to longitudinal and multilevel data especially from medical studies, it is of interest to test for the need of random effects in the model. It is known that classical tests such as the likelihood ratio, Wald, and score tests are not suitable for testing random effects because they suffer from testing on the boundary of the parameter space. Instead, permutation and bootstrap tests as well as Bayesian tests, which do not rely on the asymptotic distributions, avoid issues with the boundary of the parameter space. In this paper, we first develop a permutation test based on the likelihood ratio test statistic, which can be easily used for testing multiple random effects and any subset of them in linear mixed‐effects models. The proposed permutation test would be an extension to two existing permutation tests. We then aim to compare permutation tests and Bayesian tests for random effects to find out which test is more powerful under which situation. Nothing is known about this in the literature, although this is an important practical problem due to the usefulness of both methods in tackling the challenges with testing random effects. For this, we consider a Bayesian test developed using Bayes factors, where we also propose a new alternative computation for this Bayesian test to avoid some computational issue it encounters in testing multiple random effects. Extensive simulations and a real data analysis are used for evaluation of the proposed permutation test and its comparison with the Bayesian test. We find that both tests perform well, albeit the permutation test with the likelihood ratio statistic tends to provide a relatively higher power when testing multiple random effects

Citation

Rao, K., Drikvandi, R., & Saville, B. (2019). Permutation and Bayesian tests for testing random effects in linear mixed-effects models. Statistics in Medicine, 38(25), 5034-5047. https://doi.org/10.1002/sim.8350

Journal Article Type Article
Acceptance Date Jul 28, 2019
Online Publication Date Aug 28, 2019
Publication Date 2019-11
Deposit Date Oct 6, 2020
Publicly Available Date Mar 28, 2024
Journal Statistics in Medicine
Print ISSN 0277-6715
Electronic ISSN 1097-0258
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 38
Issue 25
Pages 5034-5047
DOI https://doi.org/10.1002/sim.8350

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