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

Political Analysis, forthcoming

150 Pages Posted: 29 Feb 2016 Last revised: 29 Apr 2018

See all articles by Jens Hainmueller

Jens Hainmueller

Stanford University - Department of Political Science; Stanford Graduate School of Business; Stanford Immigration Policy Lab

Jonathan Mummolo

Princeton University

Yiqing Xu

University of California, San Diego (UCSD) - Department of Political Science

Date Written: April 20, 2018

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 modeling artifacts or are at best highly 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.

Keywords: interaction effects, regression models, conditional hypothesis

JEL Classification: C10, C14

Suggested Citation

Hainmueller, Jens and Mummolo, Jonathan and Xu, Yiqing, How Much Should We Trust Estimates from Multiplicative Interaction Models? Simple Tools to Improve Empirical Practice (April 20, 2018). Political Analysis, forthcoming. Available at SSRN: https://ssrn.com/abstract=2739221 or http://dx.doi.org/10.2139/ssrn.2739221

Jens Hainmueller (Contact Author)

Stanford University - Department of Political Science ( email )

Stanford, CA 94305
United States

HOME PAGE: http://www.stanford.edu/~jhain/

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Stanford Immigration Policy Lab

30 Alta Road
Stanford, CA 94305
United States

Jonathan Mummolo

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

Yiqing Xu

University of California, San Diego (UCSD) - Department of Political Science ( email )

9500 Gilman Drive
Code 0521
La Jolla, CA 92093-0521
United States

HOME PAGE: http://yiqingxu.org

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