We address the problem of selecting which variables should be included in the fixed and random components of logistic mixed effects models for correlated data. A fully Bayesian variable selection is implemented using a stochastic search Gibbs sampler to estimate the exact model-averaged posterior distribution. This approach automatically identifies subsets of predictors having non-zero fixed effect coefficients or non-zero random effects variance, while allowing for uncertainty in the model selection process. Default priors are proposed for the variance components and an efficient parameter expansion Gibbs sampler is developed for posterior computation. The approach is illustrated using simulated data and an epidemiologic example.
Keywords: Bayesian model selection; Logistic regression; Mixed effects model; Model averaging; Parameter expansion; Random effects; Variance components test; Variable selection
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