Marginal Effects in Interaction Models: Determining and Controlling the False Positive Rate

Abstract

When a researcher suspects that the marginal effect of $x$ on $y$ varies with $z$ , a common approach is to plot $\partial y/\partial x$ at different values of $z$ along with a pointwise confidence interval generated using the procedure described in Brambor, Clark, and Golder to assess the magnitude and statistical significance of the relationship. Our article makes three contributions. First, we demonstrate that the Brambor, Clark, and Golder approach produces statistically significant findings when $\partial y/\partial x=0$ at a rate that can be many times larger or smaller than the nominal false positive rate of the test. Second, we introduce the interactionTest software package for R to implement procedures that allow easy control of the false positive rate. Finally, we illustrate our findings by replicating an empirical analysis of the relationship between ethnic heterogeneity and the number of political parties from Comparative Political Studies.