Research on Matching Methods for Causal Inference in Observational Studies



The estimation of causal effects is a central goal of social science research. In this project, we develop propensity score methods that can help empirical researchers conduct reliable and efficient causal inference in both experimental and observational studies.

First, we generalize the propensity score methods, which are originally developed for binary treatments, to arbitrary treatment types including continuous and multinomial treatments. This is an important generalization because many causal variables of interest in social science research are not binary. We show how our generalization preserves the basic advantages of the propensity score methods; dimension reduction, balance diagnostics, use of simple nonparametric estimation methods such as subclassification.

Second, develop the robust estimation method of propensity scores in a variety of situations. The key idea is to estimate propensity score such that the resulting covariate balance is optimized. Our proposed method, Covariate Balancing Propensity Score (CBPS), is simple and yet significantly outperforms the standard estimatiod method. The simplicity of CBPS also allows us to extend the method to more complicated situations, including the marginal structural models in panel data settings.

  Manuscripts and Publications

Generalization of propensity score:
Imai, Kosuke, and David A. van Dyk. (2004). ``Causal Inference With General Treatment Regimes: Generalizing the Propensity Score.'' Journal of the American Statistical Association, Vol. 99, No. 467 (September), pp. 854-866.
Zhao, Shandong, David A. van Dyk, and Kosuke Imai. ``Propensity-Score Based Methods for Causal Inference in Observational Studies with Fixed Non-Binary Treatments.''
Covariate Balancing Propensity Score (CBPS):
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.
Imai, Kosuke and Marc Ratkovic. (2015). ``Robust Estimation of Inverse Probability Weights for Marginal Structural Models.'' Journal of the American Statistical Association, Vol. 110, No. 511 (September), pp. 1013-1023. (lead article)
Fong, Christian, Chad Hazlett, and Kosuke Imai. ``Covariate Balancing Propensity Score for a Continuous Treatment: Application to the Efficacy of Political Advertisements.''
Fan, Jianqing, Kosuke Imai, Han Liu, Yang Ning, and Xiaolin Yang. ``Improving Covariate Balancing Propensity Score: A Doubly Robust and Efficient Approach.''
Ning, Yang, Sida Peng, and Kosuke Imai. ``High Dimensional Propensity Score Estimation via Covariate Balancing.''
Applications of propensity score:
Imai, Kosuke. (2005). ``Do Get-Out-The-Vote Calls Reduce Turnout? The Importance of Statistical Methods for Field Experiments.'' American Political Science Review, Vol. 99, No. 2 (May), pp. 283-300.

  Statistical Software

Fong ,Christian, Marc Ratkovic, Chad Hazlett, and Kosuke Imai. ``CBPS: R Package for Covariate Balancing Propensity Score.'' available through The Comprehensive R Archive Network. 2016.


National Science Foundation, (2006-2009). ``Collaborative Research: Generalized Propensity Score Methods,'' (Methodology, Measurement and Statistics Program; SES-0550873).

© Kosuke Imai
 Last modified: Tue May 9 22:15:29 EDT 2017