Citation
Imai, Kosuke and Marc Ratkovic. (2014). “Covariate Balancing Propensity Score.” Journal of the Royal Statistical Society, Series B (Statistical Methodology), Vol. 76, No. 1 (January), pp. 243-246.
Abstract
The propensity score plays a central role in a variety of causal inference settings. In particular, matching and weighting methods based on the estimated propensity score have become increasingly common in observational studies. Despite their popularity and theoretical appeal, the main practical difficulty of these methods is that the propensity score must be estimated. Researchers have found that slight misspecification of the propensity score model can result in substantial bias of estimated treatment effects. In this paper, we introduce covariate balancing propensity score (CBPS) methodology, which models treatment assignment while optimizing the covariate balance. This is done by exploiting the dual characteristics of the propensity score as a covariate balancing score and the conditional probability of treatment assignment. The estimation of the CBPS is done within the generalized method of moments or empirical likelihood framework. We find that the CBPS dramatically improves the poor empirical performance of propensity score matching and weighting methods reported in the literature. We also show that the CBPS can be extended to a number of other important settings, including the estimation of the generalized propensity score for non-binary treatments and the generalization of experimental estimates to a target population. Open-source software is available for implementing the proposed methods.
Extensions, Improvements, and Generalizations
- “Optimal Covariate Balancing Conditions in Propensity Score Estimation ,” develops more theory and improvements.
- “Covariate Balancing Propensity Score for General Treatment Regimes,” generalizes the CBPS to the multi-valued and continuous treatments.
- “Robust Estimation of Inverse Probability Weights for Marginal Structural Models,” generalizes the CBPS to the longitudinal data settings.
- “High Dimensional Propensity Score Estimation via Covariate Balancing,” extends the CBPS to high-dimensional settings.
Software
- Fong, Christian, Marc Ratkovic, and Kosuke Imai. “CBPS: R Package for Covariate Balancing Propensity Score.” available through The Comprehensive R Archive Network. 2014.
- For an independent examination of CBPS’s performance, see Richard Wyss et al. (2014). “The Role of Prediction Modeling in Propensity Score Estimation: An Evaluation of Logistic Regression, bCART, and the Covariate-Balancing Propensity Score” American Journal of Epidemiology, and Markus Frolich et al. (2015). “The Finite Sample Performance of Semi- and Nonparametric Estimators for Treatment Effects and Policy Evaluation” IZA Discussion Paper No. 8756.
- See this World Bank blog post that discusses this paper.