A goodness-of-fit test for the logistic propensity score model under nonignorable missing data

2026-04-22

AI Summary

This study addresses the lack of effective goodness-of-fit tests for logistic regression propensity score models under missing-not-at-random (MNAR) data, particularly when the outcome is only partially observed. The authors propose a novel unweighted residual sum-of-squares test based on a marginal missingness mechanism. This method constitutes the first goodness-of-fit test for propensity score models under MNAR that achieves asymptotically correct size and consistency, thereby filling a critical gap in existing methodology. Leveraging asymptotic distribution theory and a theoretically justified bootstrap procedure to approximate the null distribution, the proposed test demonstrates favorable finite-sample performance. Both simulation studies and empirical analyses confirm its asymptotic validity and show that its power converges to one under model misspecification.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Multiagent Systems: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements

Abstract

Logistic regression is widely used to model the propensity score in the analysis of nonignorable missing data. However, goodness-of-fit testing for this propensity score model has received limited attention in the literature. In this paper, we propose a new goodness-of-fit testing procedure for the logistic propensity score model under nonignorable missing data. The proposed test is based on an unweighted sum-of-squared residuals constructed from the marginal missingness mechanism and accommodates the partial observability of the outcome. We establish the asymptotic distribution of the test statistic under both the null hypothesis and general alternatives, and develop a bootstrap procedure with theoretical guarantees to approximate its null distribution. We show that the resulting bootstrap test attains asymptotically correct size and is consistent, with power converging to one under model misspecification. Simulation studies and a real data application demonstrate that the proposed method performs well in finite samples.

Problem

• goodness-of-fit test
• logistic propensity score model
• nonignorable missing data
• model misspecification

Innovation

• goodness-of-fit test
• propensity score
• nonignorable missing data
• bootstrap procedure
• logistic regression