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

Abstract

Multiplicative interaction models are widely used in social science to examine whether the relationship between an outcome and an independent variable changes with a moderating variable. Current empirical practice tends to overlook two important problems. First, these models assume a linear interaction effect that changes at a constant rate with the moderator. Second, estimates of the conditional effects of the independent variable can be misleading if there is a lack of common support of the moderator. Replicating 46 interaction effects from 22 recent publications in five top political science journals, we find that these core assumptions often fail in practice, suggesting that a large portion of findings across all political science subfields based on interaction models are fragile and model dependent. We propose a checklist of 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. These statistical routines are available in both R and STATA.

Strategic Candidate Entry and Congressional Elections in the Era of Fox News

“…The alternative specifications yield substantively similar results. We also note that we find evidence of common support for these data using the Hainmueller, Mummolo, and Xu () diagnostics.…”

“…Using the diagnostic recommendations proposed by Hainmueller, Mummolo, and Xu (), we find that the results are not reliant on “extrapolation or interpolation of the functional form to an area where there is no or only sparse data” (165).…”

Poverty and the shadow economy: The role of governmental institutions

“…The underlying interaction model assumes that the interaction is linear and there is common support in the data to estimate across the distribution of the moderator (see Hainmueller, Mummolo, & Xu, 2019). To check that these assumptions are valid, we use the binning estimator to test these assumptions in Equations (2) and (4) (for details, see, Hainmueller et al, 2019).…”

When Do Displaced Persons Return? Postwar Migration among Christians in Mount Lebanon

“…The key variable of interest is the interaction term, , and its component parts, and . We follow the advice of Hainmueller, Mummolo, and Xu () and present marginal effects plots. Since we expect mixed communities and mixed communities with histories of violence to have fewer returnees, plots with downward trends are consistent with Hypotheses 1 and 2.…”