Diagonal uniform association symmetry modelsfor cumulative probabilities in square tables

For the analysis of square contingency tables with ordered categories, Tomizawa (1991) considered the diagonal uniform association symmetry (DUS) model, which has a multiplicative form for cell probabilities and has the structure of uniform association in the tables constructed using two diagonals that are equidistant from the main diagonal. This paper proposes another DUS model which has a similar multiplicative form for cumulative probabilities. The model indicates that the odds that an observation will fall in row category i or below and column category i+k or above, instead of in column category i or below and row category i+k or above, increase (decrease) exponentially as the cutpoint i increases for a fixed k. Examples are given.