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Various definitions of the collapsibility of a hierarchical log linear model for a multidimensional contingency table are considered and shown to be equivalent. Necessary and sufficient conditions for collapsibility are found in terms of the generating class. It is shown that log linear models are appropriate for tables with response and explanatory variables if and only if they are collapsible onto the explanatory variables.
Asmussen et al. (Sat,) studied this question.