Influence Diagnostic Methods in the Poisson Regression Model with the Liu Estimator

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Poisson regression is widely used for count data analysis.
• Multicollinearity and influential observations can negatively impact model estimation and inferences.
• Existing methods struggle to simultaneously address both issues in Poisson regression.

Purpose of the Study:

• To propose novel diagnostic methods for detecting influential observations in Poisson regression.
• To address the challenges posed by simultaneous multicollinearity and influential observations.
• To enhance the reliability and quality of regression estimates in count data models.

Main Methods:

• Development of diagnostic methods based on the Sherman-Morrison Woodbury (SMW) theorem.
• Utilizing approximate deletion formulas for the Poisson regression model with the Liu estimator.
• Assessment through Monte Carlo simulations and real-world data analysis.

Main Results:

• The proposed diagnostic methods demonstrate superiority in detecting unusual observations.
• Effective identification of influential observations in the presence of multicollinearity.
• Improved model fitting and reliability compared to traditional methods.

Conclusions:

• The new diagnostic methods offer a robust solution for handling multicollinearity and influential observations in Poisson regression.
• These methods enhance the accuracy and trustworthiness of count data analysis.
• The findings are valuable for researchers across various fields employing Poisson regression models.