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Best Practices for Estimating, Interpreting, and Presenting Nonlinear Interaction Effects

By on February 6, 2019 in Articles

Trenton D. Mize

Sociological Science, February 6, 2019
10.15195/v6.a4

Abstract
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Many effects of interest to sociologists are nonlinear. Additionally, many effects of interest are interaction effects—that is, the effect of one independent variable is contingent on the level of another independent variable. The proper way to estimate, interpret, and present these two types of effects individually are well known. However, many analyses that combine these two—that is, tests of interaction when the effects of interest are nonlinear—are not properly interpreted or tested. The consequences of approaching nonlinear interaction effects the way one would approach a linear interaction effect are severe and can often result in incorrect conclusions. I cover both nonlinear effects in the context of linear regression, and—most thoroughly—nonlinear effects in models for categorical outcomes (focusing on binary logit/probit). My goal in this article is to synthesize an evolving methodological literature and to provide straightforward advice and techniques to estimate,interpret, and present nonlinear interaction effects.
Creative Commons LicenseThis work is licensed under a Creative Commons Attribution 4.0 International License.

Trenton D. Mize: Department of Sociology and Advanced Methodologies, Purdue University
E-mail: tmize@purdue.edu

Acknowledgements: I thank J. Scott Long, Bianca Manago, Long Doan, and Josh Doyle for their helpful comments on previous drafts and Dave Armstrong and Shawn Bauldry for the many insightful conversations that influenced the content of the article.

Supplemental Material

  • Citation: Mize, Trenton D. 2019. “Best Practices for Estimating, Interpreting, and Presenting Non-linear Interaction Effects.” Sociological Science 6: 81-117.
  • Received: December 18, 2018
  • Accepted: December 27, 2018
  • Editors: Jesper Sørensen, Olav Sorenson
  • DOI: 10.15195/v6.a4


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The Missing Main Effect of Welfare State Regimes: A Comment

By on February 17, 2016 in Articles

David L. Weakliem

Sociological Science, February 17, 2016
DOI 10.15195/v3.a6

Abstract

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This article discusses Nate Breznau’s critique of Brooks and Manza’s “Social Policy Responsiveness in Developed Democracies.” Brooks and Manza found that public opinion influenced welfare state spending, but Breznau argued that this conclusion was an artifact of their model, which included an interaction between opinion and welfare state type but omitted the main effect of welfare state type. Breznau is correct in saying that interactions should not be used without including the main effect, except in rare circumstances which do not apply in this case. However, the classification of welfare state type is made partly on the basis of the dependent variable, welfare spending, so it should not be used as an independent variable. There is, however, a case for including a variable for the type of legal system (common law or civil law), which is correlated with welfare state type. The estimates from a regression including both main and interaction effects support Brooks’s and Manza’s original conclusions about the effect of public opinion. The paper concludes by discussing the strength of the evidence provided by the data.

Creative Commons LicenseThis work is licensed under a Creative Commons Attribution 4.0 International License.

David L. Weakliem: Department of Sociology, University of Connecticut  Email: david.weakliem@uconn.edu

  • Citation: David L. Weakliem. 2016. “The Missing Main Effect of Welfare State Regimes: A Comment”. Sociological Science 3: 109-115
  • Received: November 10, 2015
  • Accepted: December 2, 2015.
  • Editors: Jesper Sørensen, Stephen Morgan
  • DOI: 10.15195/v3.a6

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The Missing Main Effect of Welfare State Regimes: A Replication of ‘Social Policy Responsiveness in Developed Democracies’ by Brooks and Manza

By on August 17, 2015 in Articles

Nate Breznau

Sociological Science, August 17, 2015
DOI 10.15195/v2.a20

Abstract

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This article reports the results of a replication of Brooks and Manza’s “Social Policy Responsiveness in Developed Democracies” published in 2006 in the American Sociological Review. The article finds that Brooks and Manza utilized an interaction term but excluded the main effect of one of the interacted variables. This model specification has specific implications: statistically, that the omitted main effect variable has no correlation with the residual error term from their regression; theoretically speaking, this means that all unobserved historical, cultural, and other characteristics that distinguish liberal democratic welfare regimes from others can be accounted for with a handful of quantitative measures. Using replicated data, this article finds that the Brooks and Manza models fail these assumptions. A sensitivity analysis using more than 800 regressions with different configurations of variables confirms this. In 99.5 percent of the cases, addition of the main effect removes Brooks and Manza’s empirical findings completely. A theoretical discussion illuminates why these findings are not surprising. This article provides a reminder that models and theories are coterminous, each implied by the other.
Nate Breznau: Bremen International Graduate School of Social Sciences, University of Bremen, Germany. Email: breznau.nate@gmail.com

Acknowledgements: This research took place during my doctoral studies at the Bremen International Graduate School of Social Sciences at the University of Bremen. I thank Olaf Groh-Samberg, Steffen Mau, Jonathan Kelley, Judith Offerhaus, Nadine Schöneck- Voß, M.D.R. Evans, Philip Lersch, Olli Kangas, and Timm Fulge for their helpful comments.

Supplemental Material

GitHub replication materials: https://github.com/nbreznau/Replication-Brooks-Manza

  • Citation: Breznau, Nate. 2015. “The Missing Main Effect of Welfare State Regimes: A Replication of ’Social Policy Responsiveness in Developed Democracies’ by Brooks and Manza.” Sociological Science 2: 420-441.
  • Received: March 20, 2015.
  • Accepted: March 24, 2015.
  • Editors: Jesper Sørensen, Olav Sorenson
  • DOI: 10.15195/v2.a20

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