Variable Selection and Model Averaging in Semiparametric Overdispersed Generalized Linear Models

Abstract

We express the mean and variance terms in a double-exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model and whether they enter linearly or flexibly. When the variance term is null, we obtain a generalized additive model, which becomes a generalized linear model if the predictors enter the mean linearly. The model is estimated using Markov chain Monte Carlo simulation, and the methodology is illustrated using real and simulated data sets.