New ridge parameter estimators for the quasi-Poisson ridge regression model

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Quasi-Poisson regression is suitable for over-dispersed count data.
• Quasi-likelihood estimation can yield suboptimal results with multicollinearity.
• Biased estimation methods are used to handle multicollinearity.

Purpose of the Study:

• To explore the ridge estimator for quasi-Poisson regression to mitigate multicollinearity.
• To propose and evaluate new ridge parameter estimators for this model.

Main Methods:

• Derivation of theoretical properties for the ridge estimator.
• Comparison with quasi-likelihood estimator using matrix and scalar mean squared error.
• Numerical evaluation via Monte Carlo simulation and a real-life application.

Main Results:

• The ridge estimator demonstrates superior performance compared to the quasi-likelihood estimator.
• The proposed ridge parameter estimators further enhance performance in the presence of multicollinearity.
• Both simulation and real-life application results confirm the superiority of the ridge approach.

Conclusions:

• The ridge estimator is a valuable tool for quasi-Poisson regression when multicollinearity is present.
• The proposed ridge parameter selection methods offer improved estimation accuracy.
• This study provides strong evidence for the practical utility of ridge regression in count data analysis.