Parametric Collapsibility and the Lack of Moderating Effects in Contingency Tables with a Dichotomous Response Variable

SUMMARY We consider contingency tables having one variable specified as a response with just two categories. We look at conditions for collapsibility of a symmetric and a directed measure of association, the odds-ratio and the relative risk: situations are discussed under which equal partial associations coincide with the corresponding marginal association. Contrary to the odds-ratio the relative risk is collapsible, if there are independencies in the marginal distribution of the influencing variables. This fact is exploited to derive conditions for the lack of a moderating effect, the latter being a much discussed concept in the social science literature.