Summary: Bayesian Selection of Log­Linear Models
James H. Albert
Bowling Green State University
March 15, 1996

Abstract
A general methodology is presented for finding suitable Poisson log­linear models with applications
to multiway contingency tables. Mixtures of multivariate normal distributions are used to model
prior opinion when a subset of the regression vector is believed to be nonzero. This prior distri­
bution is studied for two and three­way contingency tables, in which the regression coefficients are
interpretable in terms of odds­ratios in the table. Efficient and accurate schemes are proposed
for calculating the posterior model probabilities. The methods are illustrated for a large number
of two­way simulated tables and for two three­way tables. These methods appear to be useful in
selecting the best log­linear model and in estimating parameters of interest that reflect uncertainty
in the true model.
Key words and phrases: Bayes factors, Laplace method, Gibbs sampling, Model selection, Odds
ratios.
AMS subject classifications: Primary 62H17, 62F15, 62J12.

1 Introduction

Source: Albert, James H. - Department of Mathematics and Statistics, Bowling Green State University

Collections: Mathematics