## Fixed and random effects selection in linear and
logistic models

### Satkartar K. Kinney and David B. Dunson

### ISDS and Biostatistics Branch, NIEHS

* August, 2006 *

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

The manuscript is available in
pdf
format.