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Bivariate zero-inflated regression for count data: a Bayesian approach with application to plant counts.

Anandamayee Majumdar1, Corinna Gries

  • 1Arizona State University, AZ, USA.

The International Journal of Biostatistics
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This study introduces a new Bayesian bivariate zero-inflated Poisson (ZIP) regression model for analyzing count data with excess zeros. The novel approach enhances parameter estimation and offers a flexible framework for medical and biological applications.

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Area of Science:

  • Statistics
  • Biostatistics
  • Statistical Modeling

Background:

  • Bivariate zero-inflated (BZI) regression models are crucial for medical data with excess zeros.
  • Existing BZI models like BZI Poisson (BZIP) and BZI negative binomial (BZINB) have limitations in parameter estimation.
  • Bayesian approaches offer an alternative for modeling complex count data structures.

Purpose of the Study:

  • To extend multivariate zero-inflated Poisson (ZIP) models to a general bivariate regression formulation.
  • To develop a fully Bayesian approach for parameter estimation in bivariate ZIP models.
  • To provide a flexible modeling framework for bivariate count data with excess zeros in medical and biological fields.

Main Methods:

  • Proposed a bivariate ZIP regression model assuming latent independent Poisson random variables.
  • Employed a fully Bayesian approach, integrating existing methods and generalizing sampling-based techniques.
  • Utilized data augmentation for Gibbs sampler implementation, yielding closed-form posterior distributions.

Main Results:

  • Developed a Bayesian bivariate ZIP procedure for parameter estimation and credible intervals.
  • Simulations demonstrated the effectiveness of the Bayesian BZIP procedure.
  • Applied the methodology to bivariate plant count data, comparing results with independent ZIP models.

Conclusions:

  • The proposed Bayesian bivariate ZIP model provides a robust and flexible method for analyzing count data with excess zeros.
  • The data augmentation techniques facilitate easier implementation of the Gibbs sampler.
  • The methodology is applicable to real-world bivariate count data, particularly in medical and biological research.