A New Regression Model for the Analysis of Overdispersed and Zero-Modified Count Data

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Traditional count data analysis often relies on the ordinary Poisson distribution, which has limitations in handling data with overdispersion or excess zeros.
• Real-world count data frequently exhibit complex structures like zero inflation/deflation and overdispersion, necessitating more flexible modeling approaches.

Purpose of the Study:

• To develop and evaluate a novel fixed-effects regression model for count data that simultaneously accommodates overdispersion and zero modification.
• To introduce a Bayesian framework for parameter inference in the proposed hurdle Poisson-Sujatha model.

Main Methods:

• Derivation of a fixed-effects regression model based on the hurdle version of the Poisson-Sujatha distribution.
• Application of a fully Bayesian approach using the g-prior method for posterior inference.
• Assessment of model performance through Monte Carlo simulation studies and analysis of a real-world dataset.

Main Results:

• The proposed hurdle Poisson-Sujatha model effectively handles overdispersion and zero modification in count data.
• Bayesian estimators demonstrated favorable empirical properties in simulation studies.
• The model showed competitive performance compared to established count data models when applied to a real dataset.

Conclusions:

• The hurdle Poisson-Sujatha regression model provides a robust and flexible alternative for analyzing complex count data structures.
• The Bayesian approach facilitates reliable parameter estimation and model validation.
• The proposed methodology offers valuable insights for researchers dealing with overdispersed and zero-inflated count data.