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

Kaidi Rao1, Reza Drikvandi2, Benjamin Saville3,4

  • 1Statistics Section, Department of Mathematics, Imperial College London, London, UK.

Statistics in Medicine
|August 29, 2019
PubMed
Summary
This summary is machine-generated.

A new permutation test for random effects in linear mixed-effects models is proposed. This test, along with Bayesian tests, was compared, with the permutation test showing higher power for multiple random effects.

Keywords:
Bayesian testlinear mixed-effects modelslongitudinal datapermutation testrandom effectsvariance components

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Linear mixed-effects models are crucial for analyzing longitudinal and multilevel data, particularly in medical research.
  • Classical statistical tests (likelihood ratio, Wald, score) are unsuitable for testing random effects due to boundary issues.
  • Permutation, bootstrap, and Bayesian tests offer alternatives by avoiding reliance on asymptotic distributions.

Purpose of the Study:

  • To develop a permutation test for random effects in linear mixed-effects models, extending existing methods.
  • To compare the power of permutation tests and Bayesian tests for random effects.
  • To address the practical challenge of selecting the most powerful test for random effects in various scenarios.

Main Methods:

  • Development of a permutation test utilizing the likelihood ratio test statistic for multiple random effects.
  • Implementation and comparison of the proposed permutation test with a Bayes factor-based Bayesian test.
  • Proposed an alternative computation for the Bayesian test to overcome computational challenges with multiple random effects.
  • Evaluation through extensive simulations and a real-world data analysis.

Main Results:

  • Both permutation and Bayesian tests demonstrate good performance in evaluating random effects.
  • The proposed permutation test with the likelihood ratio statistic exhibited relatively higher power when testing multiple random effects.
  • The study provides empirical evidence on the comparative power of different testing approaches.

Conclusions:

  • The developed permutation test is a valuable extension for testing random effects in linear mixed-effects models.
  • The permutation test, particularly with the likelihood ratio statistic, is recommended for its superior power in multiple random effects scenarios.
  • The findings offer practical guidance for researchers in selecting appropriate statistical tests for random effects analysis.