摘要：For r× r tables with ordered categories, Tomizawa (1995) considered the collapsed symmetry model. This model indicates the structure of symmetry for the r− 1 ways of collapsing the r× r table into a 2 × 2 table by choosing cut points after the u -th row and after the u -th column for u= 1 ,...,r− 1. This paper proposes a collapsed symmetry ( C ) model for multi-way tables with ordered categories. The proposed model is an extension of the complete symmetry model and a special case of the marginal homogeneity ( M ) model. Also for multi-way tables, this paper proposes the collapsed quasi-symmetry ( CQS ) model which is an extension of the C model, and gives a theorem that the C model holds if and only if both the CQS and M models hold. An example is given.
