New Ridge-Type Estimator to Mitigate Multicollinearity in the Poisson Regression Model: Theory and Simulation

This study builds upon the idea of a ridge-type estimator originally designed for linear regression models, adapting it for use in Poisson regression to effectively address multicollinearity in count data. A simulation-based evaluation of various estimators under multicollinearity is presented. The simulation results, shown for cases where p=2 and p=4, highlight the Mean Square Error (MSE) values for each estimator, identifying the best-performing estimators under different scenarios. The findings emphasize the limitations of the existing Poisson Maximum Likelihood Estimator (PMLE), which consistently demonstrates instability and poor performance in the presence of multicollinearity. In contrast, the newly proposed Poisson New Ridge-Type (PNRT) estimators show superior performance. Among the PNRT variants, the estimator using the median biasing parameter consistently achieves the lowest MSE. The simulations also reveal that larger sample sizes reduce MSE values, indicating improved estimator efficiency. Moreover, higher correlation coefficients (ρ = 0.99) lead to increased MSE, whereas moderate correlations (ρ = 0.75) result in more stable and lower error values. Overall, the PNRT variants demonstrate the lowest MSEs, confirming that lower MSE corresponds to better estimator performance, even under severe multicollinearity.