The Open Mathematics, Statistics and Probability Journal

2009, 1 : 32-37
Published online 2009 April 20. DOI: 10.2174/1876527000901010032
Publisher ID: TOSPJ-1-32

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

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

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.