Variable Selection and Model Averaging in Semiparametric Overdispersed Generalized Linear Models

TL;DR

This paper introduces a Bayesian variable selection approach for semiparametric overdispersed generalized linear models, allowing flexible modeling of mean and variance with automatic predictor selection.

Contribution

It develops a novel Bayesian framework for variable selection and model averaging in semiparametric overdispersed GLMs, accommodating linear and flexible predictor effects.

Findings

Effective variable selection for mean and variance functions

Flexible modeling of predictors as linear or additive

Demonstrated on real and simulated datasets

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.