ON COLLAPSING CATEGORIES IN TWO-WAY CONTINGENCY TABLES

摘要

The issue of collapsing categories of a contingency table's classification variables is well known and has been dealt with in the framework of classical models such as models of independence and association, canonical correlation and logistic regression. The most often used criterion is based on the homogeneity of the corresponding categories which was connected to association and correlation models by Goodman (1981a,b) and Gilula (1986), respectively. In this paper we relate homogeneity to a class of generalized association models, based on the f-divergence. The main issue raised in this paper is that the homogeneity and the structural criteria can not be contradictory. It is proved that collapsing among homogeneous categories does not affect the underlying structure of the table.