Modeling interactions in count-data regression: Principles and implementation in Stata

During the past decades, count-data models (in particular, Poisson and negative-binomial-based regression models) have gained relevance in empirical social research. While identifying and interpreting main effects is relatively straightforward for this class of models, the integration of interactions between predictors proves to be complex. As a consequence of the exponential mean function implemented in count-data models (which restricts the possible range of the conditional expected count to nonnegative values), the coefficient of the product term variable (generated by the predictors constituting the interaction) does not—in contrast to the linear model—fully represent the underlying interaction effect. Further, the interaction effect is allowed to vary between individuals and can be divided into two components: a model-inherent interaction effect and a product-term-induced interaction effect. We will derive the total interaction effect for the Poisson and negative binomial models by following a method developed by Norton and Ai (2003) for binary logit and probit models. Further, we will decompose the model-inherent and the product-term-induced interaction effect, discuss their substantive meaning, and provide delta-method standard errors for the respective effects. Finally, we will provide an approach for the estimation and graphical representation of these effects in Stata.