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

• 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. Key-Words: • decomposition; distance subsymmetry model; marginal homogeneity model; ordered category; square contingency table; symmetry model. AMS Subject Classification: • 62H17. 154 S. Tomizawa, N. Miyamoto and M. Ouchi Decompositions of Symmetry Model 155