Comparisons of Three Approaches for Discrete Conditional Models

Abstract

I compare three approaches to computing a discrete joint density from full conditional densities. Gibbs sampler is naturally the first choice because it is based on the full conditionals. The hybrid method uses the iterative proportional fitting algorithm and is based on the mixed parameterization of a contingency table. We give justifications why the hybrid method has better accuracy. The third method, which is based on the interactions of Ip and Wang (2008b), is an analytical method capable of producing the exact solution, and in addition it is also the most efficient. The illustrating example is two-dimensional, which provides detailed accuracy comparisons for the marginal distributions, the odds ratios, and the expected values. Generalizations to more than two variables are also discussed. In practice, Gibbs sampler has distinct advantages: it is conceptually easy to understand and there are many software tools available. When either the Gibbs sampler has a hard time mixing well or an accuracy of more than two digits is required, the hybrid method and the interaction-based method should be considered as good alternatives.