Multiplicative interaction models are widely used in social science to test whether the relationship between an outcome and an independent variable changes with a moderating variable. Current empirical practice overlooks two important problems. First, these models assume a linear interaction effect that changes at a constant rate with the moderator. Second, reliably estimating the conditional effects of the independent variable at all values of the moderator requires sufficient common support. Replicating nearly 50 interaction effects from 22 recent publications in five top political science journals, we find that these core assumptions fail in a majority of cases, suggesting that a large portion of findings across all subfields based on interaction models are modeling artifacts or are at best highly model dependent. We propose simple diagnostics to assess the validity of these assumptions and offer flexible estimation strategies that allow for nonlinear interaction effects and safeguard against excessive extrapolation.