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


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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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

Chunrong Ai , and Edward C. Norton . 2003. ‘Interaction Terms in Logit and Probit Models’. Economics Letters 80(1):123129.

William Berry , Jacqueline H. R. DeMeritt , and Justin Esarey . 2010. ‘Testing for Interaction in Binary Logit and Probit Models: Is a Product Term Essential?’. American Journal of Political Science 54:248266.

Harry P Bowen . 2012. ‘Testing Moderating Hypotheses in Limited Dependent Variable and Other Nonlinear Models: Secondary Versus Total Interaction’. Journal of Management 38(3):860889.

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Chi Huang , and Todd G. Shields . 2000. ‘Interpretation of Interaction Effects in Logit and Probit Analyses’. American Politics Research 28(1):8095.

Gary King , Michael Tomz , and Jason Wittenberg . 2000. ‘Making the Most of Statistical Analyses: Improving Interpretation and Presentation’. American Journal of Political Science 44:341355.

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Tsung-han Tsai , and Jeff Gill . 2013. ‘Interaction in General Linear Models: Theoretical Issues and An Application to Personal Vote Earning Attributes’. Social Sciences 2(2):91113.

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Political Science Research and Methods
  • ISSN: 2049-8470
  • EISSN: 2049-8489
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