Summary: Bayesian Selection of LogLinear Models
James H. Albert
Bowling Green State University
March 15, 1996
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
AMS subject classifications: Primary 62H17, 62F15, 62J12.