On collapsing categories in two-way
contingency tables
Maria Kateri and George Iliopoulos
The issue of collapsing categories of a contingency table's classification
variables is well-known and has been dealt 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 (1981) 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.
AMS 2000 subject classifications: 62H17.
Key words and phrases: Contingency tables, collapsing categories,
generalized association models, f-divergence.