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A framework for covariate balance using Bregman distances

Author

Listed:
  • Kevin P. Josey
  • Elizabeth Juarez‐Colunga
  • Fan Yang
  • Debashis Ghosh

Abstract

A common goal in observational research is to estimate marginal causal effects in the presence of confounding variables. One solution to this problem is to use the covariate distribution to weight the outcomes such that the data appear randomized. The propensity score is a natural quantity that arises in this setting. Propensity score weights have desirable asymptotic properties, but they often fail to adequately balance covariate data in finite samples. Empirical covariate balancing methods pose as an appealing alternative by exactly balancing the sample moments of the covariate distribution. With this objective in mind, we propose a framework for estimating balancing weights by solving a constrained convex program, where the criterion function to be optimized is a Bregman distance. We then show that the different distances in this class render identical weights to those of other covariate balancing methods. A series of numerical studies are presented to demonstrate these similarities.

Suggested Citation

  • Kevin P. Josey & Elizabeth Juarez‐Colunga & Fan Yang & Debashis Ghosh, 2021. "A framework for covariate balance using Bregman distances," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 790-816, September.
    • Handle: RePEc:bla:scjsta:v:48:y:2021:i:3:p:790-816
    DOI: 10.1111/sjos.12457
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    References listed on IDEAS

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    1. Hainmueller, Jens, 2012. "Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies," Political Analysis, Cambridge University Press, vol. 20(1), pages 25-46, January.
    2. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2006. "Moving the Goalposts: Addressing Limited Overlap in the Estimation of Average Treatment Effects by Changing the Estimand," NBER Technical Working Papers 0330, National Bureau of Economic Research, Inc.
    3. 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.
    4. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    5. José R. Zubizarreta, 2015. "Stable Weights that Balance Covariates for Estimation With Incomplete Outcome Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 910-922, September.
    6. Paul Tseng & Dimitri P. Bertsekas, 1987. "Relaxation Methods for Linear Programs," Mathematics of Operations Research, INFORMS, vol. 12(4), pages 569-596, November.
    7. Yixin Wang & Jose R Zubizarreta, 2020. "Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations," Biometrika, Biometrika Trust, vol. 107(1), pages 93-105.
    8. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    9. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
    10. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    11. Ho, Daniel E. & Imai, Kosuke & King, Gary & Stuart, Elizabeth A., 2007. "Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference," Political Analysis, Cambridge University Press, vol. 15(3), pages 199-236, July.
    12. 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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