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Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations

Author

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  • Yixin Wang
  • Jose R Zubizarreta

Abstract

Summary Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods, which find the weights of minimum dispersion that approximately balance the covariates. We call these weights ‘minimal weights’ and study them under a common optimization framework. Our key observation is that finding weights which achieve approximate covariate balance is equivalent to performing shrinkage estimation of the inverse propensity score. This connection leads to both theoretical and practical developments. From a theoretical standpoint, we characterize the asymptotic properties of minimal weights and show that, under standard smoothness conditions on the propensity score function, minimal weights are consistent estimates of the true inverse probability weights. In addition, we show that the resulting weighting estimator is consistent, asymptotically normal and semiparametrically efficient. From a practical standpoint, we give a finite-sample oracle inequality that bounds the loss incurred by balancing more functions of the covariates than strictly needed. This inequality shows that minimal weights implicitly bound the number of active covariate balance constraints. Finally, we provide a tuning algorithm for choosing the degree of approximate balance in minimal weights. The paper concludes with an empirical study which suggests that approximate balance is preferable to exact balance, especially when there is limited overlap in covariate distributions. Further studies show that the root mean squared error of the weighting estimator can be reduced by as much as a half with approximate balance.

Suggested Citation

  • 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.
  • Handle: RePEc:oup:biomet:v:107:y:2020:i:1:p:93-105.
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    File URL: http://hdl.handle.net/10.1093/biomet/asz050
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    Citations

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    Cited by:

    1. Daouda Bamba, 2023. "Assessing the impact of used vehicle imports ban policy: Evidence from Côte d’Ivoire," CERDI Working papers hal-04391362, HAL.
    2. Shixiao Zhang & Peisong Han & Changbao Wu, 2023. "Calibration Techniques Encompassing Survey Sampling, Missing Data Analysis and Causal Inference," International Statistical Review, International Statistical Institute, vol. 91(2), pages 165-192, August.
    3. Ruoqi Yu, 2021. "Evaluating and improving a matched comparison of antidepressants and bone density," Biometrics, The International Biometric Society, vol. 77(4), pages 1276-1288, December.
    4. David Gilchrist & Thomas Emery & Nuno Garoupa & Rok Spruk, 2023. "Synthetic Control Method: A tool for comparative case studies in economic history," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 409-445, April.
    5. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    6. Rui Chen & Guanhua Chen & Menggang Yu, 2023. "Entropy balancing for causal generalization with target sample summary information," Biometrics, The International Biometric Society, vol. 79(4), pages 3179-3190, December.
    7. Vahe Avagyan & Stijn Vansteelandt, 2021. "Stable inverse probability weighting estimation for longitudinal studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 1046-1067, September.
    8. Sean Yiu & Li Su, 2022. "Joint calibrated estimation of inverse probability of treatment and censoring weights for marginal structural models," Biometrics, The International Biometric Society, vol. 78(1), pages 115-127, March.
    9. Dmitry Arkhangelsky & David Hirshberg, 2023. "Large-Sample Properties of the Synthetic Control Method under Selection on Unobservables," Papers 2311.13575, arXiv.org, revised Dec 2023.
    10. Dasom Lee & Shu Yang & Lin Dong & Xiaofei Wang & Donglin Zeng & Jianwen Cai, 2023. "Improving trial generalizability using observational studies," Biometrics, The International Biometric Society, vol. 79(2), pages 1213-1225, June.
    11. 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.
    12. María de los Angeles Resa & José R. Zubizarreta, 2020. "Direct and stable weight adjustment in non‐experimental studies with multivalued treatments: analysis of the effect of an earthquake on post‐traumatic stress," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1387-1410, October.
    13. David Bruns-Smith & Oliver Dukes & Avi Feller & Elizabeth L. Ogburn, 2023. "Augmented balancing weights as linear regression," Papers 2304.14545, arXiv.org, revised Jun 2024.

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