Zero-Inflated Logistic Regression Models with Shared Design: Identifiability, Existence of Estimates, and a Relabeling Rule

2026-04-22

AI Summary

This study addresses the issues of parameter non-identifiability and non-existence of estimators in zero-inflated logistic regression models with a shared design matrix. The authors establish sufficient conditions for parameter identifiability, prove the existence and uniqueness of the maximum of the expected log-likelihood on an appropriate quotient space, and propose a concise and effective parameter relabeling rule. By integrating Pólya–Gamma Gibbs sampling with replica exchange Monte Carlo, the method accurately captures the bimodality of the posterior distribution. Simulation studies and analysis of self-reported diabetes data demonstrate that ignoring the zero-inflation mechanism can lead to sign reversal of regression coefficients, whereas the proposed approach effectively mitigates this bias, exhibiting robust performance both theoretically and empirically.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The zero-inflated logistic regression model accommodates binary responses with excess zeros, which often arise from a latent mixture of susceptible and insusceptible subpopulations or asymmetric misclassification of the response. The model has two components: regression for the binary response and a latent binary indicator for the zero-inflation state. In applied settings, it is common to use the same design matrix for both components if there is no prior knowledge. However, this shared-design specification lacks guaranteed identifiability of the regression parameters, as established in prior works. This paper investigates the theoretical properties of the zero-inflated logistic regression model under the shared-design setting and computational methods for applications. First, to motivate the use of the zero-inflated model, we prove that ignoring the zero-inflation mechanism can lead to a sign flip in the pseudo-true coefficient value relative to the true value. We then establish sufficient conditions for the existence of the maximum likelihood estimate. As a main result, we establish that the model under the shared-design setting is identifiable up to exchange symmetry of the parameters for two components and that the expected log-likelihood has a unique maximizer on the resulting quotient space. The posterior bimodality is examined using a Pólya-Gamma Gibbs sampler with replica exchange. Finally, we propose a simple relabeling rule to select a single ordered parameter pair, and evaluate its performance through simulation studies and an application to self-reported diabetes data.

Problem

• zero-inflated logistic regression
• shared design
• identifiability
• parameter estimation
• binary response

Innovation

• zero-inflated logistic regression
• shared design
• identifiability
• exchange symmetry
• relabeling rule