S. Tomizawa, DIAGONALS-PARAMETER SYMMETRY MODEL FOR CUMULATIVE PROBABILITIES IN SQUARE CONTINGENCY-TABLES WITH ORDERED CATEGORIES, Biometrics, 49(3), 1993, pp. 883-887
For the analysis of square contingency tables with ordered categories,
Goodman (1979, Biometrika 66, 413418) considered the diagonals-parame
ter symmetry (DPS) model, which has a multiplicative form for cell pro
babilities. This paper proposes another DPS model which has a similar
multiplicative form for cumulative probabilities that an observation w
ill fall in row (column) category i or below and column (row) category
j (>i) or above. Special cases of the proposed model include conditio
nal symmetry and symmetry. The relationship with a stochastic ordering
for marginal distributions is also described. Moreover, the relations
hips between the proposed model and the (generalized) palindromic symm
etry models are described. An example is given.