Model determination for categorical data with factor level merging

• 成果类型: Article
• 署名作者: Dellaportas, P; Tarantola, C
• 署名单位: University of Pavia; Athens University of Economics & Business
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2005.00501.x
• 发表日期: 2005
• 页码: 269-283
• 关键词: multidimensional contingency-tables; log-linear models; Graphical Models; bayesian model; collapsibility

摘要

We deal with contingency table data that are used to examine the relationships between a set of categorical variables or factors. We assume that such relationships can be adequately described by the cond`itional independence structure that is imposed by an undirected graphical model. If the contingency table is large, a desirable simplified interpretation can be achieved by combining some categories, or levels, of the factors. We introduce conditions under which such an operation does not alter the Markov properties of the graph. Implementation of these conditions leads to Bayesian model uncertainty procedures based on reversible jump Markov chain Monte Carlo methods. The methodology is illustrated on a 2x3x4 and up to a 4x5x5x2x2 contingency table.