Partitioning polytomous variables in multiway contigency analysis

Abstract Examples involving analysis of survey data in the form of three-way contingency tables, some variables in which are polytomous, are presented to demonstrate the possibility of specifying models in terms of the particular categories of the polytomy that enter into relationships with the other variables. Solution of this problem is logically a prior step to the collapsing of polytomous variables if, indeed, that step can be justified at all. The methods used are those associated with incomplete multiway contingency tables. Such tables arise in the present connection when the polytomous variable is represented as a set of dichotomous formal variables.