Measure of Departure from Collapsed Symmetry for Multi-way Contingency Tables with Ordered Categories

Abstract

For multi-way tables with ordered categories, Tahata et al.\ (2008) considered the collapsed symmetry model, which indicates the symmetry for the tables collapsed the original table by choosing the cut point in the categories. The present paper proposes a measure to represent the degree of departure from collapsed symmetry for multi-way tables. The measure proposed is expressed by using the Cressie-Read power-divergence or the Patil-Taillie diversity index. The measure would be useful for comparing the degrees of departure from collapsed symmetry in several multi-way tables. Examples are given.