Decompositions of Symmetry Model into Marginal Homogeneity and Distance Subsymmetry in Square Contingency Tables with Ordered Categories

Abstract

For square contingency tables with ordered categories, this paper proposes some distance subsymmetry models. The one model indicates that the cumulative probability that an observation will fall in row category i or below and column category i + k (k ≥ 2) or above, is equal to the probability that it falls in column category i or below and row category i+k or above. This paper also gives the decomposition of the symmetry model into the marginal homogeneity model and some distance subsymmetry models. The father-son occupational mobility data in Britain and the women’s unaided vision data in Britain are analyzed.