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Checking the Random Effects Distribution in Binary Response Mixed Models

Howard Mackey, University of California-Santa Barbara Department of Statistics and Applied Probability

Mixed effects models are often used to analyze binary response data which have been gathered in clusters of groups. An example may be responses that are assumed to follow a logit model within clusters, with coefficients which vary across clusters according to a specified probability distribution G. The posterior distribution of the random effects can be used to assess model fit but does not have an analytic solution for many practical choices of G, requiring numerical integration to obtain moments or quantiles. Here we pose the model in terms of a tolerance random variable. This often results in a simple form for an approximate posterior distribution where moments and quantiles are easily calculated. Finally we propose a check for outliers in the random effects distribution and illustrate it using both real and simulated data.

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