Abstract
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.
