How Much Should We Trust Estimates from Multiplicative Interaction Models? Simple Tools to Improve Empirical Practice

Regressions with multiplicative interaction terms are widely used in the social sciences to test whether the relationship between an outcome and an independent variable changes depending on a moderator. Despite much advice on how to use interaction models, two important problems are currently overlooked in empirical practice. First, multiplicative interaction models are based on the crucial assumption that the interaction effect is linear, which fails unless the effect of the independent variable changes at a constant rate with the moderator. Second, reliably estimating the marginal effect of the independent variable at a given value of the moderator requires sufficient common support. Replicating nearly 50 interaction effects recently published in five top political science journals, we find that these core assumptions fail in a majority of cases, suggesting that a large portion of published findings based on multiplicative interaction models are artifacts of misspecification or are at best highly model dependent. We propose straightforward diagnostic tests to assess the validity of these assumptions and offer simple flexible modeling strategies for estimating potentially nonlinear interaction effects. ∗Associate Professor, Department of Political Science, Stanford University, [email protected]. †PhD Candidate, Department of Political Science, Stanford University, [email protected]. ‡PhD Candidate, Department of Political Science, MIT, [email protected]. We thank all authors who generously provided their replication data. 1