An extended asymmetry model for square contingency tables with ordered categories

Abstract

For square contingency tables with ordered categories, McCullagh [6] considered the palindromic symmetry model. The present paper proposes an extended palindromic symmetry model. The model indicates a structure of asymmetry between the cumulative probability that an observation will fall in row category i or below and column category $\mathit{j}\mathrm{(}\mathrm{>}\mathit{i}\mathrm{)}$ or above and the cumulative probability that it falls in column category i or below and row category j or above. The proposed model indicates the generalized marginal homogeneity model in Tahata and Tomizawa [9] as a special case.