JSM 2005 - Toronto

Abstract #302477

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 211
Type: Invited
Date/Time: Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #302477
Title: Variable Selection and Model Averaging in Heteroscedastic and Overdispersed Generalized Linear Models
Author(s): Remy Cottet*+ and Robert Kohn and David Nott
Companies: University of New South Wales and University of New South Wales and University of New South Wales
Address: Kensington, Sydney, 2052, Australia
Keywords: double exponential models ; generalized linear models ; variance estimation ; semi parametric models
Abstract:

In this paper, we describe methods for mean and variance estimation where the responses are modeled using the double exponential family of distributions of Effron (1986). This type of multiplicative mixture of distributions allows us to model heterogeneous Gaussian data, as well as overdispersed and underdispersed count data. It also includes the standard normal, Poisson, and binomial models as special cases. Mean and dispersion parameters are modeled as a sum of additive function of predictors where the additive terms are represented by truncated cubic smoothing splines. Variable selection is developed to test the presence of overdispersion as well as to uncover the shape of the flexible forms. We carry out inference in a Bayesian way, simultaneously estimating both a mean and variance function using shrinkage type of priors. The methodology is applied to simulated and real datasets from animal teratology, health, and environment. All computation is carried out using MCMC simulation.

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