Robust propensity score weighting estimation under missing at random

TL;DR

This paper introduces a new robust and doubly robust propensity score weighting estimator for missing at random data, which is efficient, resistant to outliers, and maintains consistency if either the outcome or response model is correct.

Contribution

It develops an innovative estimator using information projection with calibration constraints, extending to outlier-robust estimation, and provides asymptotic properties and empirical validation.

Findings

Estimator is robust against model misspecification and outliers.

Simulation confirms improved robustness and efficiency.

Application demonstrates practical utility in real data analysis.

Abstract

Missing data is frequently encountered in many areas of statistics. Propensity score weighting is a popular method for handling missing data. The propensity score method employs a response propensity model, but correct specification of the statistical model can be challenging in the presence of missing data. Doubly robust estimation is attractive, as the consistency of the estimator is guaranteed when either the outcome regression model or the propensity score model is correctly specified. In this paper, we first employ information projection to develop an efficient and doubly robust estimator under indirect model calibration constraints. The resulting propensity score estimator can be equivalently expressed as a doubly robust regression imputation estimator by imposing the internal bias calibration condition in estimating the regression parameters. In addition, we generalize the information projection to allow for outlier-robust estimation. Some asymptotic properties are presented. The simulation study confirms that the proposed method allows robust inference against not only the violation of various model assumptions, but also outliers. A real-life application is presented using data from the Conservation Effects Assessment Project.