Addressing multicollinearity in general linear model: A novel approach for ridge parameter with performance...

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Multicollinearity in regression modeling leads to imprecise parameter estimates and inflated standard errors.
• This instability hinders accurate assessment of explanatory variable impacts and increases the risk of Type-II errors.

Purpose of the Study:

• To propose novel ridge constants for ridge regression.
• To evaluate the performance of these new ridge choices against existing methods.

Main Methods:

• Introduction of new ridge constant choices within the ridge regression framework.
• Performance evaluation using Monte Carlo simulations with Mean Square Error (MSE) as the metric.
• Validation through two real-life case studies.

Main Results:

• The proposed ridge estimator demonstrates superior performance compared to existing ridge constants across various multicollinearity levels.
• Effectiveness is observed across different sample sizes, numbers of explanatory variables, and error variance structures.
• Simulation findings are supported by consistent results from real-world applications.

Conclusions:

• The novel ridge constants provide a more robust solution for handling multicollinearity in regression analysis.
• These improved methods enhance the reliability of parameter estimation and the overall accuracy of regression models.
• The proposed techniques offer practical benefits for researchers and practitioners dealing with ill-conditioned data.