Product-variable models of interaction effects and causal mechanisms

Among those who use multiple regression or its offshoots, the dominant method of modeling an interaction effect of two independent variables on a dependent variable is to include a product variable in a linear estimation equation. In this paper, I show how the coefficient for the product variable in these models depends on the causal mechanism that underlies the interaction effect. I also show that different causal mechanisms can imply the same estimation equation, which means that one cannot determine the causal mechanism underlying an interaction effect from the empirical results produced by the estimation equation. Social scientists typically lack the kind of theoretical knowledge required to specify causal mechanisms for interaction effects, and researchers who do specify a mechanism, such as those who specify that contextual-level variables moderate the effects of individual-level variables but not vice versa, rarely justify their implicit claims. Although it is difficult to specify the causal mechanism underlying a particular interaction effect, I show that there are cases where it is possible to do so.