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Robust inference in the multilevel zero-inflated negative binomial model.

Eghbal Zandkarimi1, Abbas Moghimbeigi2, Hossein Mahjub3

  • 1Department of Biostatistics, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Iran.

Journal of Applied Statistics
|June 16, 2022
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Summary
This summary is machine-generated.

This study introduces a robust method for analyzing complex count data, offering more stable and accurate estimates than traditional approaches, especially when dealing with outliers.

Keywords:
Expectation-maximization (EM) algorithmdecayed- missing and filled teeth (DMFT)mean square error (MSE)multilevel zero-inflated negative binomial (MZINB)robust expectation-solution (RES)

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Multilevel zero-inflated negative binomial (MZINB) models are popular for correlated count data with excess zeros and over-dispersion.
  • Traditional EM algorithm-based parameter estimation can be unstable with outliers or poorly separated mixture components.

Purpose of the Study:

  • To extend the robust expectation-solution (RES) approach for robust parameter estimation in MZINB models.
  • To enhance the stability and accuracy of regression parameter estimation in the presence of data challenges.

Main Methods:

  • The RES approach applies robust estimating equations in the S-step of the EM algorithm.
  • Robustness is achieved by down-weighting leverage points in the logistic component and bounding deviations in the negative binomial component.

Main Results:

  • Simulation studies demonstrate that the RES algorithm yields consistent estimates with reduced bias compared to the EM algorithm under data contamination.
  • The proposed method shows improved performance in the presence of outliers and separation issues.

Conclusions:

  • The RES algorithm provides a more robust alternative for parameter estimation in MZINB models.
  • This method is applicable to real-world data, such as DMFT index and fertility rate data.