Where do Moderation Terms Come from in Binary Choice Models?

If the most parsimonious behavioral model between an observed behavior, Y , and some factors, X, can be defined as f(Y|X1,X2), then fx1 will measure the impact in behavior of a change in factor X1. Additionally, if fx1x2 != 0, then the impact in behavior of a change in factor X1 is qualified, or moderated by X2. If this is the case, X2 is said to be a moderating variable and fx1x2 is said to be the moderating effect. When Y is modeled via a logistic regression, the moderation effect will exist regardless of whether the index function of the logit specification includes a moderation term or not. Thus, including a moderation terms in the index function will help the researcher more precisely qualify the moderation effect between X1 and X2. The question that naturally arises is whether the researcher must include the moderation term or not. In this document, we provide the conditions in which moderation terms will naturally arise in a logistic regression and introduce some modeling guidelines. We do so by introducing a general framework that nests models with no moderation terms in three scenarios for the independent variables, commonly found in applied research.