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Rejoinder to “A Note on Type II Error Under Random Effects Misspecification in Generalized Linear Mixed Models”

Authors

  • Saskia Litière,

    Corresponding author
    1. Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Universiteit Hasselt, Agoralaan 1, B3590 Diepenbeek, Belgium
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  • Ariel Alonso,

    1. Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Universiteit Hasselt, Agoralaan 1, B3590 Diepenbeek, Belgium
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  • Geert Molenberghs

    1. Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Universiteit Hasselt, Agoralaan 1, B3590 Diepenbeek, Belgium
    2. Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Katholieke Universiteit Leuven, Kapucijnenvoer 35, Blok D, bus 7001, B3000 Leuven, Belgium
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email: saskia.litiere@uhasselt.be

Abstract

Summary In this rejoinder, we discuss the impact of misspecifying the random effects distribution on inferences obtained from generalized linear mixed models (GLMMs). Special attention is paid to the power of the tests for the fixed-effect parameters. To study this misspecification, researchers often use simulation designs in which several choices for the true underlying random-effects distribution are considered, while the assumed distribution is kept fixed. Neuhaus, McCulloch, and Boylan (2010, Biometrics00, 000–000) argue that a logically correct approach should consist of varying the assumed, fitted distribution, while holding the true fixed. We argue that both simulation designs can bring valuable insights into the impact of the misspecification. Furthermore, using both designs, we illustrate that the power associated with the tests for the fixed-effect parameters in GLMM may be affected by misspecifying the random-effects distribution.

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