Improved estimation in negative binomial regression.

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Negative binomial regression is standard for overdispersed count data.
• Maximum likelihood estimation (MLE) for dispersion parameters can be biased in small to moderate samples, impacting mean parameter inference.

Purpose of the Study:

• To propose novel inference methods for negative binomial regression using adjusted score functions.
• To reduce bias in dispersion parameter estimation, thereby improving overall model inference.

Main Methods:

• Score function adjustments targeting mean or median bias reduction.
• Generalization of existing bias-corrected estimating equations for generalized linear models.
• Utilizing an extension of iterative weighted least squares for solving equations.

Main Results:

• Simulation studies demonstrate superior performance of the proposed methods over standard MLE.
• The new methods address numerical issues often encountered with MLE.
• Median bias reduction generally outperformed mean bias reduction and explicit bias correction.

Conclusions:

• Adjusted score function methods provide improved and more reliable inference for negative binomial regression.
• Median bias reduction is recommended for practical applications due to its robust performance.
• The methods are effective in real-world data analysis, as shown by case studies.