A new mixed-effects regression model for the analysis of zero-modified hierarchical count data

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Traditional Poisson regression models are limited for count data with zero-inflation, overdispersion, or heterogeneity.
• Existing models often address only subsets of these issues, necessitating more comprehensive solutions.

Purpose of the Study:

• To develop a flexible mixed-effects regression model for count data that simultaneously handles zero-modification, overdispersion, and individual heterogeneity.
• To propose a Bayesian framework for parameter inference using the Adaptive Metropolis algorithm.

Main Methods:

• Derivation of a mixed-effects regression model using the hurdle version of the Poisson-Lindley distribution.
• Implementation of a fully Bayesian approach with the Adaptive Metropolis algorithm for approximate posterior inference.
• Assessment of model performance through Monte Carlo simulations and analysis of a real-world dataset.

Main Results:

• The proposed Poisson-Lindley hurdle mixed-effects model effectively accommodates zero-modification, overdispersion, and heterogeneity in count data.
• Bayesian estimators demonstrated good empirical properties in simulation studies.
• The model showed competitiveness against established mixed-effects models for count data.

Conclusions:

• The developed Bayesian hurdle Poisson-Lindley mixed-effects model provides a robust and flexible alternative for analyzing complex count data.
• The approach offers a unified framework for addressing multiple common challenges in count data analysis.
• Sensitivity analysis and diagnostic tools ensure the reliability and interpretability of the model results.