Bayesian Analysis of Marginal Log-Linear Graphical Models for Three Way Contingency Tables

TL;DR

This paper develops a Bayesian framework for analyzing three-way contingency tables using marginal log-linear models, focusing on model selection, estimation, and computational methods, with applications to real datasets.

Contribution

It introduces a comprehensive Bayesian approach for marginal log-linear graphical models, including prior selection, estimation, and model determination for three-way tables.

Findings

Effective Bayesian methodology for model analysis and selection.

Application to real datasets demonstrating practical utility.

Insights into marginal independence structures in contingency tables.

Abstract

This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. We use a marginal log-linear parametrization, under which the model is defined through suitable zero-constraints on the interaction parameters calculated within marginal distributions. We undertake a comprehensive Bayesian analysis of these models, involving suitable choices of prior distributions, estimation, model determination, as well as the allied computational issues. The methodology is illustrated with reference to two real data sets.