Decomposition for polynomial cumulative symmetry model in square contingency tables with ordered categories

摘要

For square contingency tables with ordered categories, Goodman (1979) considered the diagonals-parameter symmetry model for the cell probabilities. Tomi-zawa (1993) proposed the cumulative diagonals-parameter symmetry (D) model which has a similar form for cumulative probabilities that an observation will fall in row (column) category i or below and column (row) category j (> i) or above. First, this paper gives another expression of the D model in which the log odds (for the symmetric cumulative probabilities) have polynomial patterns of the distance j — i between the diagonal containing the cutpoint [i and j (> i)] and the main diagonal of the table. Secondly, this paper introduces the cumulative polynomial diagonals-parameter symmetry (C) model which is the parsimonious D model, and the cumulative polynomial diagonal marginal symmetry (M) model. Thirdly, this paper gives the decomposition of the C model into the D and M models.