Skip to main content
×
×
Home

An Introduction to the Augmented Inverse Propensity Weighted Estimator

  • Adam N. Glynn (a1) and Kevin M. Quinn (a2)
  • Please note a correction has been issued for this article.
Abstract

In this paper, we discuss an estimator for average treatment effects (ATEs) known as the augmented inverse propensity weighted (AIPW) estimator. This estimator has attractive theoretical properties and only requires practitioners to do two things they are already comfortable with: (1) specify a binary regression model for the propensity score, and (2) specify a regression model for the outcome variable. Perhaps the most interesting property of this estimator is its so-called “double robustness.” Put simply, the estimator remains consistent for the ATE if either the propensity score model or the outcome regression is misspecified but the other is properly specified. After explaining the AIPW estimator, we conduct a Monte Carlo experiment that compares the finite sample performance of the AIPW estimator to three common competitors: a regression estimator, an inverse propensity weighted (IPW) estimator, and a propensity score matching estimator. The Monte Carlo results show that the AIPW estimator has comparable or lower mean square error than the competing estimators when the propensity score and outcome models are both properly specified and, when one of the models is misspecified, the AIPW estimator is superior.

Copyright
Corresponding author
e-mail: aglynn@iq.harvard.edu (corresponding author)
Footnotes
Hide All

Authors's note: We thank the editors and three anonymous referees for helpful comments on an earlier draft of this paper. An R package that implements the estimators discussed in this paper is available at http://cran.r-project.org/as a contributed package with the name CausalGAM.

Footnotes
References
Hide All
Angrist, Joshua D., Imbens, Guido W., and Rubin, Donald B. 1996. Identification of causal effects using instrumental variables. Journal of the American Statistical Association 91: 444–55.
Busso, Matias, DiNardo, John, and McCrary, Justin. 2009a. Finite sample properties of semiparametric estimators of average treatment effects. Berkeley: University of California, Working paper.
Busso, Matias, DiNardo, John, and McCrary, Justin. 2009b. New evidence on the finite sample properties of propensity score matching and reweighting estimators. Working paper, University of California Berkeley.
Cochran, William G. 1968. The effectiveness of adjustment by subclassification in removing bias in observational studies. Biometrics 24: 295313.
Diamond, A., and Sekhon, J. S. 2005. Genetic matching for estimating causal effects: A general multivariate matching method for achieving balance in observational studies. http://sekhon.berkeley.edu/papers/GenMatch.
Glynn, Adam, and Quinn, Kevin. 2009. Estimation of causal effects with generalized additive models. Vienna, Austria: R Foundation for Statistical Computing.
Hastie, Trevor. 2009. Generalized additive models. Vienna, Austria: R Foundation for Statistical Computing.
Ho, D. E., Imai, K., King, G., and Stuart, E. A. 2007. Matching as nonparametric preprocessing for reducing model dependence in parametric causal inference. Political Analysis 15: 199.
Imbens, Guido W. 2004. Nonparametric estimation of average treatment effects under exogeneity: A review. The Review of Economics and Statistics 86: 429.
Kang, Joseph D.Y., and Schafer, Joseph L. 2007a. Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data.” Statistical Science 22: 523–39.
Kang, Joseph D.Y., and Schafer, Joseph L. 2007b. Rejoinder: Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 22: 574–80.
King, Gary, and Zeng, Langche. 2006. The dangers of extreme counterfactuals. Political Analysis 14: 131–59.
Lunceford, Jared K., and Davidian, Marie. 2004. Stratification and weighting via the propensity score in estimation of causal treatment effects: A comparative study. Statistics in Medicine 23: 2937–60.
Morgan, Stephen L., and Winship, Christopher. 2007. Counterfactuals and causal inference: Methods and principles for social research. New York: Cambridge University Press.
Pearl, Judea. 1995. Causal diagrams for empirical research. Biometrika 82: 669710.
Pearl, Judea. 2000. Causality: Models, reasoning, and inference. New York: Cambridge University Press.
R Development Core Team. 2007. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
Ridgeway, Greg, and McCaffrey, Daniel F. 2007. Comment: Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 22(4): 540–3.
Robins, J. M. 1986. A new approach to causal inference in mortality studies with a sustained exposure period-application to control of the healthy worker survivor effect. Mathematical Modeling 7: 1393–512.
Robins, James M. 1999. Robust estimation in sequentially ignorable missing data and causal inference models. Proceedings of the American Statistical Association Section on Bayesian Statistical Science 610.
Robins, James M., Rotnitzky, Andrea, and Zhao, Lue Ping. 1994. Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association 89: 846–66.
Robins, James, Sued, Mariela, Lei-Gomez, Quanhong, and Rotnitzky, Andrea. 2007. Comment: performance of double-robust estimators when “inverse probability” weights are highly variable. Statistical Science 22: 544–59.
Robins, J. M., and Wang, N. 2000. Inference for imputation estimators. Biometrika 87(1): 113–24.
Rosenbaum, Paul R., and Rubin, Donald B. 1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70: 4155.
Rubin, D. B. 2006. Matched sampling for causal effects. New York: Cambridge University Press.
Scharfstein, Daniel O., Rotnitzky, Andrea, and Robins, James M. 1999. Rejoinder to adjusting for nonignorable drop-out using semiparametric nonresponse models. Journal of the American Statistical Association 94: 1135–46.
Sekhon, Jasjeet S. 2009. Multivariate and propensity score matching with balance optimization. Vienna, Austria: R Foundation for Statistical Computing.
Tan, Zhiqiang. 2007. Comment: Understanding OR, PS, and DR. Statistical Science 22(4): 560–68.
Tsiatis, Anastasios A. 2006. Semiparametric theory and missing data. New York: Springer.
Tsiatis, Anastasios A., and Davidian, Marie. 2007. Comment: Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data.” Statistical Science 22(4): 569–73.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Political Analysis
  • ISSN: 1047-1987
  • EISSN: 1476-4989
  • URL: /core/journals/political-analysis
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed

A correction has been issued for this article: