Whittemore's notion of collapsibility in multidimensional contingency tables

We develop simple necessary and sufficient conditions for a hierarchical log linear model to be strictly collapsible in the sense defined by Whittemore (1978). We then show that collapsibility as defined by Asmussen & Edwards (1983) can be viewed as equivalent to collapsibility as defined by Whittemore (1978) and illustrate why Bishop, Fienberg, & Holland's (1975, p.47) conditions for collapsibility are sufficient but not necessary. Finally, we discuss how collapsibility facilitates interpretation of certain hierarchical log linear models and formulation of hypotheses concerning marginal distributions associated with multidimensional contingency tables.