A more interpretable regression model for count data with excess of zeros

2025-09-29

AI Summary

Medical count data frequently exhibit excessive zeros, and although conventional zero-inflated models provide adequate fit, they suffer from poor interpretability. This paper proposes a reparameterized zero-inflated Poisson regression model that decouples the zero-inflation mechanism from the count mean, enabling regression coefficients to directly quantify the independent effects of covariates on both the event incidence rate and the zero-inflation probability—thereby substantially enhancing interpretability. Methodologically, the approach integrates maximum likelihood estimation, Monte Carlo simulation for assessing estimator accuracy, and a suite of diagnostic residual tools tailored to zero-inflated settings. Simulation studies confirm unbiased and robust parameter estimation. Applied to multinational child mortality data, the model achieves superior goodness-of-fit compared to standard alternatives and yields clear, substantively meaningful interpretations: it disentangles how socioeconomic factors differentially influence mortality risk versus the underlying zero-truncation mechanism. The framework thus balances statistical rigor with practical interpretability.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

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
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Count data are common in medical research. When these data have more zeros than expected by the most used count distributions, it is common to employ a zero-inflated regression model. However, the interpretability of these models is much lower than the most used count regression models. In this work, we introduce a more interpretable regression model for count data with excess of zeros based on a reparameterization of the zero-inflated Poisson distribution. We discuss inferential and diagnostic tools and perform a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimator. Finally, the usefulness of the proposed regression model is illustrated through an application on children mortality.

Problem

• Developing interpretable regression for zero-inflated count data
• Reparameterizing zero-inflated Poisson distribution for clarity
• Addressing medical count data with excess zeros interpretability

Innovation

• Reparameterizes zero-inflated Poisson distribution for interpretability
• Develops inferential tools and diagnostic methods
• Uses maximum likelihood estimation via Monte Carlo simulation