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ABSTRACT 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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