A multivariate zero-inflated binomial model for the analysis of correlated proportional data

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Correlated proportional data often exhibit excessive zeros, posing challenges for standard statistical models.
• Existing methods may not adequately address the complexities of zero-inflation and correlation simultaneously.

Purpose of the Study:

• To introduce a novel multivariate zero-inflated binomial (MZIB) distribution.
• To develop statistical methods for parameter estimation and hypothesis testing in the MZIB model.
• To apply the proposed methodology to real-world correlated proportional data.

Main Methods:

• Development of the multivariate zero-inflated binomial (MZIB) distribution.
• Application of Fisher scoring and Expectation-Maximization (EM) algorithms for parameter estimation.
• Derivation of score tests and likelihood ratio tests for zero-inflation and probability comparisons.
• Simulation studies to assess algorithm performance and test power.
• Illustration using whitefly data.

Main Results:

• The distributional properties of the MZIB model were investigated.
• EM and Fisher scoring algorithms were successfully adapted for parameter estimation, with and without covariates.
• Score and likelihood ratio tests were derived for key hypotheses.
• Simulation results demonstrated the performance of the estimation algorithms and the power of the derived tests.

Conclusions:

• The proposed MZIB distribution provides a flexible framework for analyzing correlated proportional data with excessive zeros.
• The developed estimation and testing procedures are effective for the MZIB model.
• The methodology offers a valuable tool for researchers dealing with complex count data in various scientific fields.