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Testing for Interaction in Binary Logit and Probit Models: Is a Product Term Essential?

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  • An earlier version of this article was presented at the 2007 annual meeting of the Midwest Political Science Association. We are grateful to Matt Golder and Michael Peress for their helpful comments. Replication data for analyses presented are available at http://garnet.acns.fsu.edu/~wberry/.

William D. Berry is Marian D. Irish Professor and Syde P. Deeb Eminent Scholar in Political Science, Florida State University, Tallahassee, FL 32306–2230 (wberry@fsu.edu). Jacqueline H. R. DeMeritt is Assistant Professor of Political Science, University of North Texas, Denton, TX 76203–5017 (jdemeritt@unt.edu). Justin Esarey is Assistant Professor of Political Science, Emory University, Atlanta, GA 30322 (jesarey@emory.edu).

Abstract

Political scientists presenting binary dependent variable (BDV) models often hypothesize that variables interact to influence the probability of an event, Pr(Y). The current typical approach to testing such hypotheses is (1) estimate a logit or probit model with a product term, (2) test the hypothesis by determining whether the coefficient for this term is statistically significant, and (3) characterize the nature of any interaction detected by describing how the estimated effect of one variable on Pr(Y) varies with the value of another. This approach makes a statistically significant product term necessary to support the interaction hypothesis. We show that a statistically significant product term is neither necessary nor sufficient for variables to interact meaningfully in influencing Pr(Y). Indeed, even when a logit or probit model contains no product term, the effect of one variable on Pr(Y) may be strongly related to the value of another. We present a strategy for testing for interaction in a BDV model, including guidance on when to include a product term.

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