Bayesian approaches to the problem of sparse tables in log-linear modeling

This paper presents Bayesian approaches to parameter estimation in the log-linear analysis of sparse frequency tables. The proposed methods overcome the non-estimability problems that may occur when applying maximum likelihood estimation. A crucial point when using Bayesian methods is the specification of the prior distributions for the model parameters. We discuss the various possible priors and assess their influence on the parameter estimates by two empirical examples in which maximum likelihood estimation gives problems. For the practical implementation of the Bayesian estimation methods, we used a Metropolis algorithm.