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Optimally balanced Gaussian process propensity scores for estimating treatment effects

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  • Brian G. Vegetabile
  • Daniel L. Gillen
  • Hal S. Stern

Abstract

Propensity scores are commonly employed in observational study settings where the goal is to estimate average treatment effects. The paper introduces a flexible propensity score modelling approach, where the probability of treatment is modelled through a Gaussian process framework. To evaluate the effectiveness of the estimated propensity score, a metric of covariate imbalance is developed that quantifies the discrepancy between the distributions of covariates in the treated and control groups. It is demonstrated that this metric is ultimately a function of the hyperparameters of the covariance matrix of the Gaussian process and therefore it is possible to select the hyperparameters to optimize the metric and to minimize overall covariate imbalance. The effectiveness of the Gaussian process method is compared in a simulation against other methods of estimating the propensity score and the method is applied to data from a study of Dehejia and Wahba in 1999 to demonstrate benchmark performance within a relevant policy application.

Suggested Citation

  • Brian G. Vegetabile & Daniel L. Gillen & Hal S. Stern, 2020. "Optimally balanced Gaussian process propensity scores for estimating treatment effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 355-377, January.
    • Handle: RePEc:bla:jorssa:v:183:y:2020:i:1:p:355-377
    DOI: 10.1111/rssa.12502
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    References listed on IDEAS

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    1. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-620, September.
    2. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    3. Kosuke Imai & Marc Ratkovic, 2014. "Covariate balancing propensity score," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 243-263, January.
    4. Rosenbaum, Paul R., 2010. "Design Sensitivity and Efficiency in Observational Studies," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 692-702.
    5. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    6. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, January.
    7. Fan Li & Kari Lock Morgan & Alan M. Zaslavsky, 2018. "Balancing Covariates via Propensity Score Weighting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 390-400, January.
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    Cited by:

    1. Kecheng Li & Tugba Akkaya-Hocagil & Richard J. Cook & Louise M. Ryan & R. Colin Carter & Khue-Dung Dang & Joseph L. Jacobson & Sandra W. Jacobson, 2024. "Use of Generalized Propensity Scores for Assessing Effects of Multiple Exposures," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 16(2), pages 347-376, July.

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