Interaction Effects in Nonlinear Models - Testing and Interpreting Core Assumptions of Situational Action Theory

In contrast to the linear regression model, interaction effects―defined as the marginal effect of the moderator variable on the marginal effect of the focal variable on the outcome―are allowed to vary across individuals in nonlinear models. Thus, they do not simply equal the coefficient of the product term variable. Furthermore, even the nonlinear main effects model includes an interaction effect (labeled as structural or model-inherent interaction and/or compression effect) if both covariates contribute significantly to the explanation of the outcome. The presence of the model-inherent interaction is owed to the restricted range of the outcome variable.

However, several scholars have engaged in a discussion whether the model-inherent interaction has a meaningful interpretation. While some scholars argue that substantive interest is only on the interaction that arises from the product term variable and advocate removing the model-induced interaction from the total interaction effect (e.g. Bowen 2012), others adhere to the interpretation of the total effect (e.g. Ai & Norton 2003). So far, the discussion concerning the idea and interpretation of interaction in nonlinear models didn’t result in a common perspective.

To date, there is a lack of a systematically derived justification for one of the options, based on the combination of theoretical and methodological arguments. In order to overcome this shortcoming, we (1) develop a general perspective on the idea and meaning of interaction in nonlinear models, (2) target at developing an application scheme guiding researchers to the appropriate concept of interaction―either including the model-inherent interaction or separating it from the total interaction effect―, and (3) propose statistical tests that allow for an analysis of the interaction effect.

Situational Action Theory, a recently proposed and promising criminological theory (Wikström 2006, Wikström et al. 2012), will serve as theoretical exemplification.