Regularized Calibrated Estimation of Propensity Scores with Model Misspecification and High-Dimensional Data

• Activity Number: 639 - Causal Inference Meets Statistical Learning with Complex Data
• Type: Invited
• Date/Time: Thursday, August 2, 2018 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Zhiqiang Tan*
• Companies: Rutgers University
• Keywords: Propensity score; Causal inference; Calibrated estimation; Lasso; Inverse probability weighting; Regularized M-estimation

Abstract

Inverse probability weighting methods using propensity scores are widely used for estimating treatment effects from observational studies. However, such methods can perform poorly even when a propensity score model appears adequate as examined by conventional techniques. In addition, there is increasing difficulty when dealing with a large number of covariates. To address these issues, we study calibrated estimation as an alternative to maximum likelihood estimation for fitting logistic propensity score models. We show that, with possible model misspecification, minimizing the expected calibration loss involves reducing a measure of relative errors. We propose a regularized calibrated estimator by minimizing the calibration loss with a Lasso penalty. We develop a novel Fisher scoring descent algorithm and provide a high-dimensional analysis, leveraging the control of relative errors for calibrated estimation. We present a simulation study and an empirical application to demonstrate the advantages of the proposed methods compared with maximum likelihood and regularization.