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Sparse Estimation and Uncertainty with Application to Subgroup Analysis

Published online by Cambridge University Press:  22 February 2017

Marc Ratkovic  and
Dustin Tingley
Marc Ratkovic*
Affiliation:
Assistant Professor, Department of Politics, Princeton University, Princeton NJ 08544, USA. Email: [email protected], http://www.princeton.edu/∼ratkovic
Dustin Tingley
Affiliation:
Professor of Government, Harvard University, USA. Email: [email protected], http://scholar.harvard.edu/dtingley
*
*Email: [email protected]
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Abstract

We introduce a Bayesian method, LASSOplus, that unifies recent contributions in the sparse modeling literatures, while substantially extending pre-existing estimators in terms of both performance and flexibility. Unlike existing Bayesian variable selection methods, LASSOplus both selects and estimates effects while returning estimated confidence intervals for discovered effects. Furthermore, we show how LASSOplus easily extends to modeling repeated observations and permits a simple Bonferroni correction to control coverage on confidence intervals among discovered effects. We situate LASSOplus in the literature on how to estimate subgroup effects, a topic that often leads to a proliferation of estimation parameters. We also offer a simple preprocessing step that draws on recent theoretical work to estimate higher-order effects that can be interpreted independently of their lower-order terms. A simulation study illustrates the method’s performance relative to several existing variable selection methods. In addition, we apply LASSOplus to an existing study on public support for climate treaties to illustrate the method’s ability to discover substantive and relevant effects. Software implementing the method is publicly available in the R package sparsereg.

Type
Articles
Information
Political Analysis , Volume 25 , Issue 1 , January 2017 , pp. 1 - 40
Copyright
Copyright © The Author(s) 2017. Published by Cambridge University Press on behalf of the Society for Political Methodology. 

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Footnotes

Authors’ note: We are grateful to Neal Beck, Scott de Marchi, In Song Kim, John Londregan, Luke Miratrix, Michael Peress, Jasjeet Sekhon, Yuki Shiraito, Brandon Stewart, and Susan Athey for helpful comments on an earlier draft. Earlier versions presented at the 2015 Summer Methods Meeting, Harvard IQSS Applied Statistics Workshop, Princeton Political Methodology Colloquium, DARPA/ISAT Conference “What If? Machine Learning for Causal Inference,” and EITM 2016. We are also grateful to two anonymous reviewers for detailed feedback on an earlier version. All mistakes are because of the authors. Replication data is available at Ratkovic and Tingley 2016.

Contributing Editor: R. Michael Alvarez

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