Bayesian inference for finite mixtures of generalized linear models with random effects

We present an hierarchical Bayes approach to modeling parameter heterogeneity in generalized linear models. The model assumes that there are relevant subpopulations and that within each subpopulation the individual-level regression coefficients have a multivariate normal distribution. However, class membership is not known a priori, so the heterogeneity in the regression coefficients becomes a finite mixture of normal distributions. This approach combines the flexibility of semiparametric, latent class models that assume common parameters for each sub-population and the parsimony of random effects models that assume normal distributions for the regression parameters. The number of subpopulations is selected to maximize the posterior probability of the model being true. Simulations are presented which document the performance of the methodology for synthetic data with known heterogeneity and number of sub-populations. An application is presented concerning preferences for various aspects of personal computers.