## Decompositions of symmetry model into marginal homogeneity and distance subsymmetry in square contingency tables with ordered categories.(English)Zbl 1141.62329

Summary: For square contingency tables with ordered categories, this paper proposes some distance subsymmetry models. One model indicates that the cumulative probability that an observation will fall in row category $$i$$ or below and column category $$i+k$$ $$(k\geq 2)$$ 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 a 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.

### MSC:

 62H17 Contingency tables