Bayesian Methods for Sets of Multi-Way Contingency Tables

• Activity Number: 598
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Theresa Smith*+
• Companies: University of Washington
• Keywords: multi-way tables ; model uncertainty ; Markov chain Monte Carlo

Abstract

Cross-tabulated categorical data are common in many fields including political science, sociology, and public health. The data are often collected from different geographical areas, time points or experimental conditions, which leads to contingency tables associated with each of these groups. The problem of analyzing sets of multi-dimensional contingency tables has not received much attention in the recent literature. Existing approaches incorporate heterogeneity between tables via the parameters of hierarchical models, but the parameterization of these hierarchical models does not vary from table to table. Further, many of these approaches do not generalize well beyond two dimensions. We develop a flexible Bayesian approach that incorporates model uncertainty by identifying clusters of tables that share the same hierarchical model. With this method, we can quantify similarities between subsets of tables and the best-fitting models for each table. We use this approach to investigate the relationship between low birth weight and three risk factors in North Carolina from 2007 to 2009.