Polynomial diagonals-parameter symmetry model for square contingency tables with ordered categories

Abstract

Goodman (1979) considered the diagonals-parameter symmetry (DPS) model for square contingency tables with ordered categories. In this paper, two kinds of other expressions of the DPS model are given in which the log odds parameters have polynomial patterns of the distance from the main diagonal (the corner) of the square table, and also various parsimonious polynomial DPS models are given. For two sets of data, these models are systematically applied and the best-fitting model is detected by using Akaike's (1974) information criterion.