RESEARCH ARTICLE


Normal Distribution Type Symmetry Model for Square Contingency Tables with Ordered Categories



Kouji Tahata, Kouji Yamamoto*, Sadao Tomizawa
Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, 278-8510, Japan.


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© 2009 Tahata et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, 278-8510, Japan. E-mail: yamamoto_kouji@ymail.plala.or.jp


Abstract

For square contingency tables with ordered categories, this paper proposes a model that the cell probabilities have a similar structure of bivariate normal density function with equal marginal variances. The proposed model is special cases of Agresti's linear diagonals-parameter symmetry model and Goodman's diamond model. Examples with real data are given and the simulation studies based on the bivariate normal distribution are also given.

Keywords: Diamond model, Linear diagonals-parameter symmetry, Normal distribution, Ordered category..