Type I and Type II Error Under RandomâEffects Misspecification in Generalized Linear Mixed Models
2007
Litière, Saskia | Alonso, Ariel | Molenberghs, Geert
Generalized linear mixed models (GLMMs) have become a frequently used tool for the analysis of nonâGaussian longitudinal data. Estimation is based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. Recent research is showing that the results obtained from these models are not always robust against departures from the assumptions on which these models are based. In the present work we have used simulations with a logistic randomâintercept model to study the impact of misspecifying the randomâeffects distribution on the type I and II errors of the tests for the mean structure in GLMMs. We found that the misspecification can either increase or decrease the power of the tests, depending on the shape of the underlying randomâeffects distribution, and it can considerably inflate the type I error rate. Additionally, we have found a theoretical result which states that whenever a subset of fixedâeffects parameters, not included in the randomâeffects structure equals zero, the corresponding maximum likelihood estimator will consistently estimate zero. This implies that under certain conditions a significant effect could be considered as a reliable result, even if the randomâeffects distribution is misspecified.
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