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Compression and Conditional Effects: A Product Term Is Essential When Using Logistic Regression to Test for Interaction*

  • Carlisle Rainey

Previous research in political methodology argues that researchers do not need to include a product term in a logistic regression model to test for interaction if they suspect interaction due to compression alone. I disagree with this claim and offer analytical arguments and simulation evidence that when researchers incorrectly theorize interaction due to compression, models without a product term bias the researcher, sometimes heavily, toward finding interaction. However, simulation studies also show that models with a product term fit a broad range of non-interactive relationships surprisingly well, enabling analysts to remove most of the bias toward finding interaction by simply including a product term.

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Carlisle Rainey is Assistant Professor of Political Science in the Texas A&M University, 2010 Allen Building, College Station, TX 77843 ( The author thanks Kenneth Benoit, Bill Berry, Scott Clifford, Justin Esarey, and two anonymous reviewers for helpful comments on earlier versions of this manuscript. The author also thanks John Oneal and Bruce Russet for making their data available, the Center for Computational Research at the University at Buffalo for providing support for the simulations. Code and data necessary to replicate the simulations and empirical analysis is available at and at To view supplementary material for this article, please visit http://10.1017/psrm.2015.59

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Ai, Chunrong, and Norton, Edward C.. 2003. ‘Interaction Terms in Logit and Probit Models’. Economics Letters 80(1):123129.
Berry, Frances Stokes, and Berry, William D.. 1990. ‘State Lottery Adoptions as Policy Innovations: An Event History Analysis’. American Political Science Review 84(2):395415.
Berry, Frances Stokes, and Berry, William D.. 1991. ‘Specifying a Model of State Policy Innovation’. American Political Science Review 85(2):573579.
Berry, William, DeMeritt, Jacqueline H. R., and Esarey, Justin. 2010. ‘Testing for Interaction in Binary Logit and Probit Models: Is a Product Term Essential?’. American Journal of Political Science 54:248266.
Berry, William, DeMeritt, Jacqueline H. R., and Esarey, Justin. 2015. ‘Bias and Overconfidence in Parametric Models of Interactive Processes’. American Journal of Political Science.
Berry, William, Golder, Matt, and Milton, Daniel. 2012. ‘Improving Tests of Theories Positing Interaction’. Journal of Politics 77(3):653671.
Bowen, Harry P. 2012. ‘Testing Moderating Hypotheses in Limited Dependent Variable and Other Nonlinear Models: Secondary Versus Total Interaction’. Journal of Management 38(3):860889.
Brambor, Thomas, Clark, William Roberts, and Golder, Matt. 2006. ‘Understanding Interaction Models: Improving Empirical Analyses’. Political Analysis 14:6382.
Bremer, Stuart A. 1992. ‘Dangerous Dyads: Conditions Affecting the Likelihood of Interstate War, 1816–1965’. Journal of Conflict Resolution 36(2):309341.
Clark, William Roberts, Gilligan, Michael J., and Golder, Matt. 2006. ‘A Simple Multivariate Test for Asymmetric Hypotheses’. Political Analysis 14(3):311331.
Diehl, Paul F. 1991. ‘Geography and War: A Review and Assessment of the Empirical Literature’. International Interactions 17(1):1127.
Frant, Howard. 1991. ‘Specifying a Model of State Policy Innovation’. American Political Science Review 85(2):571573.
Friedrich, Robert. 1982. ‘In Defense of Multiplicative Terms in Multiple Regression Equations’. American Journal of Political Science 26:797833.
Greene, William. 2010. ‘Testing Hypotheses About Interaction Terms in Nonlinear Models’. Economics Letters 107(2):291296.
Hanmer, Michael, and Kalkan, Kerem Ozan. 2013. ‘Behind the Curve: Clarifying the Best Approach to Calculating Predicted Probabilities and Marginal Effects from Limited Dependent Variable Models’. American Journal of Political Science 57(1):263277.
Huang, Chi, and Shields, Todd G.. 2000. ‘Interpretation of Interaction Effects in Logit and Probit Analyses’. American Politics Research 28(1):8095.
Kam, Cindy D., and Franzese, Robert. 2007. Modeling and Interpreting Interactive Hypotheses in Regression Analysis. Ann Arbor: University of Michigan Press.
King, Gary, Tomz, Michael, and Wittenberg, Jason. 2000. ‘Making the Most of Statistical Analyses: Improving Interpretation and Presentation’. American Journal of Political Science 44:341355.
Nagler, Jonathan. 1991. ‘The Effect of Registration Laws and Education on U.S. Voter Turnout’. American Journal of Political Science 85:13931405.
Nagler, Jonathan. 1994. ‘Scobit: An Alternative Estimator to Logit and Probit’. American Journal of Political Science 38(1):230255.
Norton, Edward C., Wang, Hua, and Ai, Chunrong. 2004. ‘Computing Interaction Effects and Standard Errors in Logit and Probit Models’. The Stata Journal 4(2):154167.
Oneal, John R., and Russet, Bruce. 2001. Triangulating Peace: Democracy, Interdependence, and International Organizations. New York: W. W. Norton.
Ray, James Lee. 1998. ‘Does Democracy Cause Peace?’. Annual Review of Political Science 1(1):2746.
Tomz, Michael R., and Weeks, Jessica L. P.. 2013. ‘Public Opinion and the Democratic Peace’. American Political Science Review 107(4):849865.
Train, Kenneth E. 2009. Discrete Choice Models with Simulation. New York: Cambridge University Press.
Tsai, Tsung-han, and Gill, Jeff. 2013. ‘Interaction in General Linear Models: Theoretical Issues and An Application to Personal Vote Earning Attributes’. Social Sciences 2(2):91113.
Wolfinger, Raymond E., and Rosenstone, Steven J.. 1980. Who Votes? New Haven: Yale University Press.
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Political Science Research and Methods
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