Ridge Estimation for Simultaneous Poisson Regression System: A Simulation Study

Abstract

This study presents a combined ridge parameter estimation with bootstrap method to handle collinearity in Poisson regression and Seemingly Unrelated Poisson Regressions (SURP) for count data modeling, widely applied in many fields when modeling the effect of a response variable that takes non-negative integer values. Multicollinearity causes issues like inflated standard errors, wider confidence intervals, and type II error increasing, leads to incorrect statistical decision making. This research offers a framework for handling the. The approach enhances coefficient stability and reducing mean squared error (MSE) compared to traditional method for both single-equation Poisson regression and SURP systems with two bivariate Poisson-distributed dependent variables. Simulation study evaluates performance across sample sizes n = 25,50,100,150, and 200, and demonstrates equal correlations ρ = 0.75,0.85,0.95, and 0.99 between explanatory variables X₁​ and X₂​ in both equations in the system and also between response variables Y₁​ and Y₂​. Using R Statistical programming language, Simulation study demonstrates that the new ridge-bootstrap estimator yields lower standard errors than traditional maximum likelihood (ML) estimator across collinear Poisson Regression systems.

DOI : https://doi.org/10.52783/pst.1859