Collapsibility of Multidimensional Contingency Tables

Abstract

Summary Multidimensional contingency tables can be summed over factors, without affecting the log-linear parameters describing interactions of other factors, under less restrictive conditions than generally recognized. Examples are given that contradict a theorem of Bishop, Fienberg and Holland (1975). Necessary and sufficient conditions for collapsibility are given, and an example applying the results to categorical data is presented.