Robust inference in the multilevel zero-inflated negative binomial model

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.