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Summary

This study introduces the zero-inflated Conway-Maxwell Poisson (ZICMP) regression model. The ZICMP model demonstrates comparable or superior performance to existing zero-inflated models, offering a valuable alternative for count data analysis.

Keywords:
Poissongeneralized Poissonover and under-dispersionregressionscore and likelihood ratio testsstructural zeroszero-inflation/deflation

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Count data frequently exhibit excess zeros, violating standard Poisson assumptions.
  • Existing zero-inflated models like ZIP and ZIGP have limitations.
  • The Conway-Maxwell Poisson distribution offers flexibility for over/under-dispersion.

Purpose of the Study:

  • Introduce and develop a novel zero-inflated Conway-Maxwell Poisson (ZICMP) regression model.
  • Propose score and likelihood ratio tests for the ZICMP inflation parameter.
  • Evaluate the ZICMP model's performance against established alternatives.

Main Methods:

  • Development of the ZICMP regression model formulation.
  • Implementation of score and likelihood ratio tests for parameter assessment.
  • Simulation studies to assess test performance under various conditions.
  • Application to a real-world data example for practical illustration.

Main Results:

  • The ZICMP regression model is successfully developed and implemented.
  • Score and likelihood ratio tests provide effective tools for analyzing the inflation parameter.
  • Simulation results validate the performance of the proposed tests.
  • Empirical analysis shows ZICMP offers comparable or better fit than ZIP and ZIGP models.

Conclusions:

  • The ZICMP regression model is a viable and effective alternative for analyzing data with excess zeros.
  • The developed statistical tests are reliable for model diagnostics.
  • The ZICMP model provides enhanced flexibility and potentially improved fit for count data compared to existing methods.