Diagonals-Parameter Symmetry Model for Cumulative Probabilities in Square Contingency Tables with Ordered Categories

Abstract

For the analysis of square contingency tables with ordered categories, Goodman (1979, Biometrika 66, 413-418) considered the diagonals-parameter symmetry (DPS) model, which has a multiplicative form for cell probabilities. This paper proposes another DPS model which has a similar multiplicative form for cumulative probabilities that an observation will fall in row (column) category i or below and column (row) category j (>i) or above. Special cases of the proposed model include conditional symmetry and symmetry. The relationship with a stochastic ordering for marginal distributions is also described. Moreover, the relationships between the proposed model and the (generalized) palindromnic symmetry models are described. An example is given.