Extensions of linear diagonal-parameter symmetry and quasi-symmetry models for cumulative probabilities in square contingency tables

For square contingency tables with ordered categories, CAUSSINUS [Annales de la Faculte des Sciences de l'Universite de Toulouse (1965) Vol. 29, pp. 77–182] and AGRESTI [Statistics and Probability Letters (1983) Vol. 1, pp. 313–316] considered the quasi-symmetry and the linear diagonal-parameter symmetry models, respectively, which have multiplicative forms for cell probabilities. This paper proposes two kinds of models that have the similar multiplicative forms for cumulative probabilities that an observation will fall in row (column) category i or below and column (row) category j (>i) or above. The endometrial cancer data are analyzed using these models.