Hostname: page-component-89b8bd64d-sd5qd Total loading time: 0 Render date: 2026-05-11T16:30:13.597Z Has data issue: false hasContentIssue false
  • English
  • Français

Understanding Interaction Models: Improving Empirical Analyses

Published online by Cambridge University Press:  04 January 2017

Thomas Brambor ,
William Roberts Clark  and
Matt Golder
Thomas Brambor
Affiliation:
New York University, Department of Politics, 726 Broadway, 7th Floor, New York, NY 10003. e-mail: thomas.brambor@nyu.edu
William Roberts Clark
Affiliation:
University of Michigan, Center for Political Studies, ISR 4202 Box 1248, 426 Thompson Street, Ann Arbor, MI 48106–1248. e-mail: wrclark@umich.edu
Matt Golder*
Affiliation:
Florida State University, Department of Political Science, 531 Bellamy Building, Tallahassee, FL 32306-2230
*
e-mail: matt.golder@nyu.edu (corresponding author)
Get access Rights & Permissions [Opens in a new window]

Abstract

Multiplicative interaction models are common in the quantitative political science literature. This is so for good reason. Institutional arguments frequently imply that the relationship between political inputs and outcomes varies depending on the institutional context. Models of strategic interaction typically produce conditional hypotheses as well. Although conditional hypotheses are ubiquitous in political science and multiplicative interaction models have been found to capture their intuition quite well, a survey of the top three political science journals from 1998 to 2002 suggests that the execution of these models is often flawed and inferential errors are common. We believe that considerable progress in our understanding of the political world can occur if scholars follow the simple checklist of dos and don'ts for using multiplicative interaction models presented in this article. Only 10% of the articles in our survey followed the checklist.

Information

Type
Research Article
Information
Political Analysis , Volume 14 , Issue 1 , Winter 2006 , pp. 63 - 82
Copyright
Copyright © The Author 2005. Published by Oxford University Press on behalf of the Society for Political Methodology 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

Authors' note: Our thanks go to Nathaniel Beck, Fred Boehmke, Michael Gilligan, Sona Nadenichek Golder, Jonathan Nagler, and two anonymous reviewers for their extremely useful comments on this paper. We also thank the research assistants at Political Analysis—Jeronimo Cortina, Tse-hsin Chen, and Seung Jin Jang—for kindly double-checking the results from our literature survey. Finally, we are grateful to those authors who have provided us with their data. To accompany this paper, we have constructed a Web page at http://homepages.nyu.edu/~mrg217/interaction.html that is devoted to multiplicative interaction models. On this page, you will find (i) the data and computer code necessary to replicate the analyses conducted here, (ii) information relating to marginal effects and standard errors in interaction models, (iii) STATA code for producing figures illustrating marginal effects and confidence intervals for a variety of continuous and limited dependent variable models, and (iv) detailed results from our literature survey. STATA 8 was the statistical package used in this study.

References

Ai, Chunrong, and Norton, Edward. 2003. “Interaction Terms in Logit and Probit Models.” Economics Letters 80: 123–129.CrossRefGoogle Scholar
Aiken, Leona, and West, Stephen. 1991. Multiple Regression: Testing and Interpreting Interactions. London: Sage.Google Scholar
Allison, Paul D. 1977. “Testing for Interaction in Multiple Regression.” American Journal of Sociology 83: 144–153.CrossRefGoogle Scholar
Bernhardt, Irwin, and Jung, Bong S. 1979. “The Interpretation of Least Squares Regression with Interaction or Polynomial Terms.” Review of Economics and Statistics 61: 481–483.CrossRefGoogle Scholar
Berry, Frances Stokes, and Berry, William. 1991. “Specifying a Model of State Policy Innovation.” American Political Science Review 85: 573–579.Google Scholar
Boix, Carles. 1999. “Setting the Rules of the Game: The Choice of Electoral Systems in Advanced Democracies.” American Political Science Review 93: 609–624.CrossRefGoogle Scholar
Brambor, Thomas, Clark, William, and Golder, Matt. 2005. “Are African Party Systems Different?” Unpublished manuscript, New York University.Google Scholar
Braumoeller, Bear. 2004. “Hypothesis Testing and Multiplicative Interaction Terms.” International Organization 58: 807–820.CrossRefGoogle Scholar
Busemeyer, Jerome, and Jones, Lawrence. 1983. “Analysis of Multiplicative Combination Rules When the Causal Variables Are Measured with Error.” Psychological Bulletin 93: 549–562.CrossRefGoogle Scholar
Clark, William Roberts. 2003. Capitalism, Not Globalism: Capital Mobility, Central Bank Independence and the Political Control of the Economy. Ann Arbor: University of Michigan Press.CrossRefGoogle Scholar
Clark, William Roberts, and Reichert, Usha Nair. 1998. “International and Domestic Constraints on Political Business Cycles in OECD Economies.” International Organization 52: 87–120.CrossRefGoogle Scholar
Cleary, Paul, and Kessler, Ronald. 1982. “The Estimation and Interpretation of Modifier Effects.” Journal of Health and Social Behavior 23: 159–169.CrossRefGoogle ScholarPubMed
Cox, D. R. 1984. “Interaction.” International Statistical Review 52: 1–31.CrossRefGoogle Scholar
Duverger, Maurice. 1954. Political Parties. New York: Wiley.Google Scholar
Frant, Howard. 1991. “Specifying a Model of State Policy Innovation.” American Political Science Review 85: 571–573.Google Scholar
Franzese, Robert. 2003a. “Multiple Hands on the Wheel: Empirically Modeling Partial Delegation and Shared Policy Control in the Open and Institutionalized Economy.” Political Analysis 11: 445–474.CrossRefGoogle Scholar
Franzese, Robert. 2003b. “Quantitative Empirical Methods and Context Conditionality.” APSA-CP: Newsletter of the Organized Section on Comparative Politics of the American Political Science Association 14: 20–24.Google Scholar
Friedrich, Robert. 1982. “In Defense of Multiplicative Terms in Multiple Regression Equations.” American Journal of Political Science 26: 797–833.CrossRefGoogle Scholar
Gill, Jeff. 2001. “Interpreting Interactions and Interaction Hierarchies in Generalized Linear Models: Issues and Applications.” Presented at the Annual Meeting of the American Political Science Association, San Francisco.Google Scholar
Golder, Matt. 2003. “Electoral Institutions, Unemployment, and Extreme Right Parties: A Correction.” British Journal of Political Science 33: 525–5346.CrossRefGoogle Scholar
Golder, Matt. Forthcoming. “Presidential Coattails and Legislative Fragmentation.” American Journal of Political Science.Google Scholar
Golder, Sona Nadenichek. 2005. “Pre-electoral Coalitions in Comparative Perspective: A Test of Existing Hypotheses.” Electoral Studies.CrossRefGoogle Scholar
Greene, William. 2003. Econometric Analysis. New Jersey: Prentice Hall.Google Scholar
Griepentrog, Gray, Ryan, Michael J., and Smith, Douglas L. 1982. “Linear Transformations of Polynomial Regression Models.” American Statistician 36: 171–174.Google Scholar
Gujarati, Damodar. 2003. Basic Econometrics. New York: McGraw Hill.Google Scholar
Jaccard, James, and Wan, Choi. 1995. “Measurement Error in the Analysis of Interaction Effects between Continuous Predictors Using Multiple Regression: Multiple Indicator and Structural Equation Approaches.” Pyschological Bulletin 117: 348–357.CrossRefGoogle Scholar
Jaccard, James, Wan, Choi, and Turrisi, Robert. 1990. “The Detection and Interpretation of Interaction Effects between Continuous Variables in Multiple Regression.” Multivariate Behavioral Research 25: 467–478.CrossRefGoogle ScholarPubMed
Kam, Cindy, and Franzese, Robert. 2003. “Modeling and Interpreting Interactive Hypotheses in Regression Analysis: A Brief Refresher and Some Practical Advice.” Unpublished manuscript, University of Michigan.Google Scholar
Mozaffar, Shaheen, Scarritt, James R., and Galaich, Glen. 2003. “Electoral Institutions, Ethnopolitical Cleavages and Party Systems in Africa's Emerging Democracies.” American Political Science Review 97: 379–390.CrossRefGoogle Scholar
Nagler, Jonathan. 1991. “The Effect of Registration Laws and Education on U.S. Voter Turnout.” American Political Science Review 85: 1393–1405.CrossRefGoogle Scholar
Nagler, Jonathan. 1994. “Scobit: An Alternative to Logit and Probit.” American Journal of Political Science 38: 230–255.CrossRefGoogle Scholar
Norton, Edward, Wang, Hua, and Ai, Chunrong. 2004. “Computing Interaction Effects and Standard Errors in Logit and Probit Models.” STATA Journal 4: 103–116.Google Scholar
Rosnow, Ralph, and Rosenthal, Robert. 1989. “Definition and Interpretation of Interaction Effects.” Psychological Bulletin 105: 143–146.CrossRefGoogle Scholar
Rosnow, Ralph, and Rosenthal, Robert. 1991. “If You're Looking at the Cell Means, You're Not Looking at Only the Interaction (Unless All Main Effects Are Zero).” Psychological Bulletin 110: 574–576.CrossRefGoogle Scholar
Samuels, David. 2000. “The Gubernatorial Coattails Effect: Federalism and Congressional Elections in Brazil.” Journal of Politics 62: 240–253.CrossRefGoogle Scholar
Smith, Mark. 2000. “The Contingent Effects of Ballot Initiatives and Candidate Races on Turnout.” American Journal of Political Science 45: 700–706.CrossRefGoogle Scholar
Wright, Gerald. 1976. “Linear Models for Evaluating Conditional Relationships.” American Journal of Political Science 2: 349–373.CrossRefGoogle Scholar