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Saskia Litière, Ariel Alonso, Geert Molenberghs, Rejoinder to “A Note on Type II Error under Random Effects Misspecification in Generalized Linear Mixed Models”, Biometrics, Volume 67, Issue 2, June 2011, Pages 656–660, https://doi.org/10.1111/j.1541-0420.2010.01474_2.x
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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, Biometrics 00, 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.
