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

TL;DR

This paper introduces a new goodness-of-fit test for logistic propensity score models in nonignorable missing data scenarios, using residuals and bootstrap methods to ensure accuracy and consistency.

Contribution

It develops a novel testing procedure that accounts for partial observability and provides theoretical guarantees for its asymptotic properties.

Findings

The test maintains correct size under the null hypothesis.

It is consistent and has high power under model misspecification.

Simulation and real data show good finite-sample performance.

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.