Bivariate t-distribution type symmetry model for square contingency tables with ordered categories

Abstract

For the analysis of square contingency tables with the same row and column ordinal classifications, this article proposes a new model, which may be appropriate for a square ordinal table if it is reasonable to assume an underlying bivariate t-distribution with equal marginal variances having any degrees of freedom. The proposed model indicates that the difference between the symmetric two probabilities raised to the power is proportional to the distance from the main diagonal of the table. The model is an extension of the symmetry model. An example is given. The simulation studies based on bivariate t-distribution are given.