Hierarchical subspace models for contingency tables

Authors:
Hisayuki Hara;Tomonari Sei;Akimichi Takemura
Affiliations:
Faculty of Economics, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata 950-2042, Japan;Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan;Graduate School of Information Science and Technology, University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo 113-8656, Japan and CREST, JST, Japan
Venue:
Journal of Multivariate Analysis
Year:
2012

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Abstract

For the statistical analysis of multiway contingency tables, we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom than the usual hierarchical model, while preserving the localization property of the inference in the hierarchical model. This approach also enables us to evaluate the localization property of a given log-affine model. We discuss estimation and exact tests of the proposed model and illustrate the advantage of the proposed modeling with some data sets.