Interpreting the outcomes of two-part models

Interaction effects capture the impact of one explanatory variable x 1 on the marginal effect of another explanatory variable x 2. To explore interaction effects, the so-called interaction terms x 1 x 2 are typically included in estimation specifications. While in linear models the effect of a marginal change in the interaction term is equal to the interaction effect, this equality generally does not hold in nonlinear specifications (Ai and Norton, 2003). This article provides for a general derivation of marginal and interaction effects in both linear and nonlinear models and calculates the formulae of the marginal and interaction effects resulting from the Two-Part Model (2PM), a commonly employed censored regression model. Drawing on a survey of automobile use from Germany, we illustrate several subtleties inherent to the substantive interpretation of interaction effects gleaned from nonlinear models, such as the 2PM.