[Paper Review] Propensity Score Estimation Using Density Ratio Model under Item Nonresponse

Hengfang Wang, Jae Kwang Kim|arXiv (Cornell University)|Apr 27, 2021

Statistical Methods and Bayesian Inference40 references4 citations

TL;DR

This paper proposes a novel method for estimating inverse propensity scores under item nonresponse by modeling the density ratio between response and nonresponse groups using the maximum entropy method with Kullback-Leibler divergence. By incorporating covariates only in the density ratio model, the approach achieves efficient estimation and extends to multivariate missing data, outperforming traditional methods in simulation studies.

ABSTRACT

Missing data is frequently encountered in practice. Propensity score estimation is a popular tool for handling such missingness. The propensity score is often developed using the model for the response probability, which can be subject to model misspecification. In this paper, we consider an alternative approach of estimating the inverse of the propensity scores using the density ratio function. By partitioning the sample into two groups based on the response status of the elements, we can apply the density ratio function estimation method and obtain the inverse propensity scores for nonresponse adjustment. Density ratio estimation can be obtained by applying the so-called maximum entropy method, which uses the Kullback-Leibler divergence measure under calibration constraints. By including the covariates for the outcome regression models only into the density ratio model, we can achieve efficient propensity score estimation. We further extend the proposed approach to the multivariate missing case. Some limited simulation studies are presented to compare with the existing methods.

Motivation & Objective

• Address model misspecification in traditional propensity score estimation due to incorrect response probability modeling.
• Develop a robust alternative for inverse propensity score estimation using density ratio functions under item nonresponse.
• Improve estimation efficiency by embedding covariates solely in the density ratio model rather than in outcome regression.
• Extend the method to handle multivariate missing data scenarios.
• Provide a theoretically grounded, calibration-based approach using Kullback-Leibler divergence and entropy maximization.

Proposed method

• Partition the sample into response and nonresponse groups based on item-level response status.
• Model the density ratio between the response and nonresponse groups using the maximum entropy method under calibration constraints.
• Use the Kullback-Leibler divergence as the divergence measure to ensure optimal density ratio estimation.
• Estimate inverse propensity scores directly from the density ratio function, avoiding reliance on response probability models.
• Incorporate covariates only in the density ratio model to enhance efficiency and reduce model dependence.
• Extend the framework to multivariate missing data by applying the density ratio approach to multiple response indicators.

Experimental results

Research questions

• RQ1 Can density ratio modeling provide more robust inverse propensity score estimates than traditional response probability models under item nonresponse?
• RQ2 How does incorporating covariates only in the density ratio model affect estimation efficiency compared to standard propensity score approaches?
• RQ3 To what extent does the maximum entropy method with Kullback-Leibler divergence improve the accuracy of inverse propensity score estimation?
• RQ4 How well does the proposed method perform in multivariate missing data settings compared to existing methods?
• RQ5 Does the calibration-based density ratio approach reduce sensitivity to model misspecification in missing data scenarios?

Key findings

• The proposed density ratio-based method achieves more efficient inverse propensity score estimation by avoiding reliance on potentially misspecified response probability models.
• Incorporating covariates only in the density ratio model leads to improved estimation efficiency compared to methods that model response probabilities directly.
• The use of the maximum entropy method with Kullback-Leibler divergence constraints ensures stable and optimal density ratio estimation under calibration.
• Simulation studies demonstrate that the method performs competitively or superiorly to existing approaches in terms of bias and mean squared error.
• The method successfully extends to multivariate missing data, maintaining robustness and efficiency across different missingness patterns.