Parsimonious Bivariate T-distribution Type Symmetry Models for Square Contingency Tables

Abstract

For square contingency tables with ordered categories, Iki, Ishihara and Tomizawa (2013) considered the t-distribution type symmetry model and Iki, Okada and Tomizawa (2018) extended this model. These models are appropriate for a square contingency table if it is reasonable to assume an underlying bivariate t-distribution having any degrees of freedom. This study proposes three kinds of parsimonious models for these models. Additionally, this paper provides the decompositions of the parsimonious symmetry model using the proposed model. Some simulation studies based on bivariate t-distribution show the performances of the proposed models.