Coordinate-Free Multiplicative Models for Contingency Tables

• Activity Number: 686
• Type: Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Anna Klimova*+ and Tamas Rudas and Adrian Dobra
• Companies: University of Washington and Eotvos Lorand University, Budapest and University of Washington
• Keywords: Contingency tables ; coordinate-free approach ; MCMC ; Algebraic inference

Abstract

We begin with a brief review of the coordinate-free approach to categorical data analysis. Coordinate-free partition models are defined in the most general case and are illustrated with a few examples. Within this novel framework, the exponential family properties hold and a version of the IPF algorithm may be used to determine maximum likelihood estimates. Two parameterizations for partition models are introduced during the presentation. It is shown that the evolving generalized odds ratios are variation independent from the sufficient statistics of the model. The algebraic approach is naturally applied for testing partition models. The validity of the proposed methods is demonstrated on a real world data set. We conclude with a discussion of future work on partition models and their perspectives.