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Residual Balancing: A Method of Constructing Weights for Marginal Structural Models

Published online by Cambridge University Press:  04 March 2020

Xiang Zhou Open the ORCID record for Xiang Zhou [Opens in a new window]  and
Geoffrey T. Wodtke
Xiang Zhou*
Affiliation:
Department of Sociology, Harvard University, 1737 Cambridge Street, Cambridge, MA02138, USA. Email: xiang_zhou@fas.harvard.edu
Geoffrey T. Wodtke
Affiliation:
Department of Sociology, University of Chicago, 1126 E. 59th St. Chicago, IL60637, USA. Email: wodtke@uchicago.edu
*
*Email: xiang_zhou@fas.harvard.edu
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Abstract

When making causal inferences, post-treatment confounders complicate analyses of time-varying treatment effects. Conditioning on these variables naively to estimate marginal effects may inappropriately block causal pathways and may induce spurious associations between treatment and the outcome, leading to bias. To avoid such bias, researchers often use marginal structural models (MSMs) with inverse probability weighting (IPW). However, IPW requires models for the conditional distributions of treatment and is highly sensitive to their misspecification. Moreover, IPW is relatively inefficient, susceptible to finite-sample bias, and difficult to use with continuous treatments. We introduce an alternative method of constructing weights for MSMs, which we call “residual balancing”. In contrast to IPW, it requires modeling the conditional means of the post-treatment confounders rather than the conditional distributions of treatment, and it is therefore easier to use with continuous treatments. Numeric simulations suggest that residual balancing is both more efficient and more robust to model misspecification than IPW and its variants in a variety of scenarios. We illustrate the method by estimating (a) the cumulative effect of negative advertising on election outcomes and (b) the controlled direct effect of shared democracy on public support for war. Open-source software is available for implementing the proposed method.

Keywords

causal inferencebalancingpanel data
Type
Articles
Information
Political Analysis , Volume 28 , Issue 4 , October 2020 , pp. 487 - 506
Copyright
Copyright © The Author(s) 2020. Published by Cambridge University Press on behalf of the Society for Political Methodology.

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Footnotes

Contributing Editor: Jeff Gill

References

Acharya, A., Blackwell, M., and Sen, M.. 2016. “Explaining Causal Findings without Bias: Detecting and Assessing Direct Effects.” American Political Science Review 110(3):512–529.10.1017/S0003055416000216CrossRefGoogle Scholar
Athey, S., Imbens, G. W., and Wager, S.. 2018. “Approximate Residual Balancing: Debiased Inference of Average Treatment Effects in High Dimensions.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 80(4):597–623.10.1111/rssb.12268CrossRefGoogle Scholar
Blackwell, M. 2013. “A Framework for Dynamic Causal Inference in Political Science.” American Journal of Political Science 57(2):504–520.10.1111/j.1540-5907.2012.00626.xCrossRefGoogle Scholar
Cole, S. R., and Hernán, M. A.. 2008. “Constructing Inverse Probability Weights for Marginal Structural Models.” American Journal of Epidemiology 168(6):656–664.CrossRefGoogle ScholarPubMed
Fong, C., Hazlett, C., and Imai, K. et al. . 2018. “Covariate Balancing Propensity Score for a Continuous Treatment: Application to the Efficacy of Political Advertisements.” The Annals of Applied Statistics 12(1):156–177.10.1214/17-AOAS1101CrossRefGoogle Scholar
Hainmueller, J. 2012. “Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies.” Political Analysis 20(1):25–46.10.1093/pan/mpr025CrossRefGoogle Scholar
Imai, K., and Kim, I. S.. 2019. “When Should We Use Unit Fixed Effects Regression Models for Causal Inference with Longitudinal Data?” American Journal of Political Science 63(2):467–490.CrossRefGoogle Scholar
Imai, K., and Ratkovic, M.. 2014. “Covariate Balancing Propensity Score.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 76(1):243–263.CrossRefGoogle Scholar
Imai, K., and Ratkovic, M.. 2015. “Robust Estimation of Inverse Probability Weights for Marginal Structural Models.” Journal of the American Statistical Association 110(511):1013–1023.10.1080/01621459.2014.956872CrossRefGoogle Scholar
Kang, J. D. Y., and Schafer, J. L.. 2007. “Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data.” Statistical Science 22(4):523–539.10.1214/07-STS227CrossRefGoogle Scholar
Ladam, C., Harden, J. J., and Windett, J. H.. 2018. “Prominent Role Models: High-Profile Female Politicians and the Emergence of Women as Candidates for Public Office.” American Journal of Political Science 62(2):369–381.CrossRefGoogle Scholar
Lau, R. R., Sigelman, L., and Rovner, I. B.. 2007. “The Effects of Negative Political Campaigns: A Meta-Analytic Reassessment.” Journal of Politics 69(4):1176–1209.CrossRefGoogle Scholar
Naimi, A. I., Moodie, E. E. M., Auger, N., and Kaufman, J. S.. 2014. “Constructing Inverse Probability Weights for Continuous Exposures: A Comparison of Methods.” Epidemiology 25(2):292–299.CrossRefGoogle ScholarPubMed
Newey, W. K. 1994. “The Asymptotic Variance of Semiparametric Estimators.” Econometrica: Journal of the Econometric Society 62(6):1349–1382.CrossRefGoogle Scholar
Pearl, J. 2001. “Direct and Indirect Effects.” In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence , 411–420. San Francisco, CA: Morgan Kaufmann Publishers Inc.Google Scholar
Pearl, J. 2009. Causality . 2nd Edition. New York: Cambridge University Press.10.1017/CBO9780511803161CrossRefGoogle Scholar
Robins, J. M. 1986. “A New Approach to Causal Inference in Mortality Studies with a Sustained Exposure Period-Application to Control of the Healthy Worker Survivor Effect.” Mathematical Modelling 7(9–12):1393–1512.10.1016/0270-0255(86)90088-6CrossRefGoogle Scholar
Robins, J. M. 2000. “Marginal Structural Models versus Structural Nested Models as Tools for Causal Inference.” In Statistical Models in Epidemiology, the Environment, and Clinical Trials , edited by Halloran, E. M. and Berry, D., 95–133. New York: Springer.10.1007/978-1-4612-1284-3_2CrossRefGoogle Scholar
Robins, J. M. 2003. “Semantics of Causal DAG models and the Identification of Direct and Indirect effects.” Highly Structured Stochastic Systems 27:70–81.Google Scholar
Robins, J. M., Hernan, M. A., and Brumback, B.. 2000. “Marginal Structural Models and Causal Inference in Epidemiology.” Epidemiology 11(5):550–560.10.1097/00001648-200009000-00011CrossRefGoogle ScholarPubMed
Simmons, B. A., and Creamer, C. D.. 2019. “Do Self-Reporting Regimes Matter? Evidence From the Convention Against Torture.” International Studies Quarterly 63(4):1051–1064.Google Scholar
Tomz, M. R., and Weeks, J. L.. 2013. “Public Opinion and the Democratic Peace.” American Political Science Review 107:849–865.CrossRefGoogle Scholar
VanderWeele, T. 2015. Explanation in Causal Inference: Methods for Mediation and Interaction . New York: Oxford University Press.Google Scholar
Vansteelandt, S. 2009. “Estimating Direct Effects in Cohort and Case–Control Studies.” Epidemiology 20(6):851–860.CrossRefGoogle ScholarPubMed
Wang, Y., and Zubizarreta, J. R.. Forthcoming. “Minimal Approximately Balancing Weights: Asymptotic Properties and Practical Considerations.” Biometrica , DOI: 10.1093/biomet/asz050.Google Scholar
Wang, Y., Petersen, M. L., Bangsberg, D., and van der Laan, M. J.. 2006. “Diagnosing Bias in the Inverse Probability of Treatment Weighted Estimator Resulting from Violation of Experimental Treatment Assignment”. University of California, Berkeley Division of Biostatistics Working Paper Series. Paper 211. https://core.ac.uk/download/pdf/61320389.pdf.Google Scholar
Wodtke, G. T., Harding, D. J., and Elwert, F.. 2011. “Neighborhood Effects in Temporal Perspective: The impact of Long-term Exposure to Concentrated Disadvantage on High School Graduation.” American Sociological Review 76(5):713–736.CrossRefGoogle Scholar
Zhao, Q. 2019. “Covariate Balancing Propensity Score by Tailored Loss Functions.” The Annals of Statistics 47(2):965–993.CrossRefGoogle Scholar
Zhao, Q., and Percival, D.. 2017. “Entropy Balancing is Doubly Robust.” Journal of Causal Inference 5(1): 20160010.Google Scholar
Zhou, X., and Wodtke, G. T.. 2019. “A Regression-with-Residuals Method for Estimating Controlled Direct Effects.” Political Analysis 27(3):360–369.CrossRefGoogle Scholar
Zhou, X., and Wodtke, G. T.. 2020. “Replication Data for: Residual Balancing: A Method of Constructing Weights for Marginal Structural Models.” https://doi.org/10.7910/DVN/VZFXYW, Harvard Dataverse, V1.CrossRefGoogle Scholar
Zhukov, Y. M. 2017. “External Resources and Indiscriminate Violence: Evidence from German-Occupied Belarus.” World Politics 69(1):54–97.10.1017/S0043887116000137CrossRefGoogle Scholar
Zubizarreta, J. R. 2015. “Stable Weights that Balance Covariates for Estimation with Incomplete Outcome Data.” Journal of the American Statistical Association 110(511):910–922.CrossRefGoogle Scholar
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