A NEW CLASS OF POISSON BIASING RIDGE‑TYPE ESTIMATOR: SIMULATION AND THEORY APPROACH

Abstract

Multicollinearity poses a significant challenge to the accuracy and reliability of Poisson
regression models, leading to inflated variance and biased estimates. This study proposes a novel
estimation approach, leveraging a modified version of the Liu estimator, to mitigate the adverse
effects of multicollinearity in Poisson regression models. A comprehensive simulation study is
conducted to evaluate the performance of the proposed estimator against traditional estimators,
including the Maximum Likelihood Estimator (MLE), Ridge Regression Estimator (RRE), Liu
Regression Estimator (RRE) and Modified Ridge Type Regression Estimator (MRTE). The
results demonstrate the superior performance of the proposed estimator both in theoretical and
simulation approach, particularly in simulation approach scenarios characterized by large sample
sizes, from small to large number of explanatory variables and different levels of
multicollinearity. Also, a biasing parameter k of the median version also accounted for the
smallest mean square error (MSE), under different experimental design used in the study. The
findings of this study contribute to the ongoing discussion on multicollinearity in Poisson
regression models and provide a valuable estimation approach for researchers and practitioners
dealing with multicollinearity count data.