Counting the Unseen: Estimation of Susceptibility Proportions in Zero-Inflated Models Using a Conditional Likelihood Approach

Abstract

Zero-inflated count data models are widely used in various fields such as ecology, epidemiology, and transportation, where count data with a large proportion of zeros is prevalent. Despite their widespread use, their theoretical properties have not been extensively studied. This study aims to investigate the impact of ignoring heterogeneity in event count intensity and susceptibility probability on zero-inflated count data analysis within the zero-inflated Poisson framework. To address this issue, we propose a novel conditional likelihood approach that uses positive count data only to estimate event count intensity parameters and develop a consistent estimator for estimating the average susceptibility probability. Our approach is compared with the maximum likelihood approach, and we demonstrate our findings through a comprehensive simulation study and real data analysis. The results can also be extended to zero-inflated binomial and geometric models with similar conclusions. These findings contribute to the understanding of the theoretical properties of zero-inflated count data models and provide a practical approach to handling heterogeneity in such models.

KEYWORDS:

• Conditional likelihood
• Intensity heterogeneity
• Susceptibility probability
• Zero-inflated Poisson distribution

Supplementary Materials

Lemma 1–3, proofs for Propositions 1–2, Web Tables 1–6 and Web Figure 1.

Disclosure Statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Acknowledgments

The authors are grateful to the editor, associate editor, and a reviewer for providing helpful comments that have greatly improved the manuscript. We also thank Prof. James T. Peterson and Prof. Shen-Ming Lee for providing datasets used in Section 5, and Dr. Gurutzeta Guillera-Arroita for providing comments to an earlier version of this manuscript.

Additional information

Funding

This work was supported by the National Science and Technology Council of Taiwan.