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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.
Alice S. Whittemore (Sat,) studied this question.