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Reducing Model Misspecification and Bias in the Estimation of Interactions

Published online by Cambridge University Press:  23 July 2021

Matthew Blackwell Open the ORCID record for Matthew Blackwell [Opens in a new window]  and
Michael P. Olson
Matthew Blackwell*
Affiliation:
Department of Government, Harvard University, Cambridge, MA, USA. Email: mblackwell@gov.harvard.edu, URL: http://www.mattblackwell.org
Michael P. Olson
Affiliation:
Department of Political Science, Washington University in St. Louis, St. Louis, MO, USA. Email: michael.p.olson@wustl.edu, URL: http://www.michaelpatrickolson.com
*
Corresponding author Matthew Blackwell
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Abstract

Analyzing variation in treatment effects across subsets of the population is an important way for social scientists to evaluate theoretical arguments. A common strategy in assessing such treatment effect heterogeneity is to include a multiplicative interaction term between the treatment and a hypothesized effect modifier in a regression model. Unfortunately, this approach can result in biased inferences due to unmodeled interactions between the effect modifier and other covariates, and including these interactions can lead to unstable estimates due to overfitting. In this paper, we explore the usefulness of machine learning algorithms for stabilizing these estimates and show how many off-the-shelf adaptive methods lead to two forms of bias: direct and indirect regularization bias. To overcome these issues, we use a post-double selection approach that utilizes several lasso estimators to select the interactions to include in the final model. We extend this approach to estimate uncertainty for both interaction and marginal effects. Simulation evidence shows that this approach has better performance than competing methods, even when the number of covariates is large. We show in two empirical examples that the choice of method leads to dramatically different conclusions about effect heterogeneity.

Keywords

interactionsregressionmachine learninglasso
Type
Article
Information
Political Analysis , Volume 30 , Issue 4 , October 2022 , pp. 495 - 514
Copyright
© The Author(s) 2021. Published by Cambridge University Press on behalf of the Society for Political Methodology

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Footnotes

Edited by Jeff Gill

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