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Multiple Group Comparisons of the Fixed and Random Effects From the Generalized Linear Mixed Model

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  • Daniel Kasper
  • Katrin Schulz-Heidorf
  • Knut Schwippert

Abstract

In this article, we extend Liao’s test for across-group comparisons of the fixed effects from the generalized linear model to the fixed and random effects of the generalized linear mixed model (GLMM). Using as our basis the Wald statistic, we developed an asymptotic test statistic for across-group comparisons of these effects. The test can be applied when the fixed and random effects are multivariate normally distributed, and it works well for any link function and conditional distribution of the dependent variable of the GLMM. We also derived the asymptotic properties of this test, and because power information does not exist for either our new test statistic or Liao’s test, we implemented a power study to demonstrate the superiority of these tests over the alternatively proposed F test. Using an example, we show the application of the test and then discuss its possible restrictions with respect to the distribution of the random effects.

Suggested Citation

  • Daniel Kasper & Katrin Schulz-Heidorf & Knut Schwippert, 2024. "Multiple Group Comparisons of the Fixed and Random Effects From the Generalized Linear Mixed Model," Sociological Methods & Research, , vol. 53(1), pages 448-504, February.
    • Handle: RePEc:sae:somere:v:53:y:2024:i:1:p:448-504
    DOI: 10.1177/0049124120986182
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    References listed on IDEAS

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    1. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
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