Evaluation of New Liu-Ridge Type Rstimators for improved poisson regression: Theory and simulation

Abstract

Poisson regression is a common tool for modelling count data, but its performance deteriorates under multicollinearity among predictors, leading to unstable and inefficient maximum likelihood estimates. This study proposes a Poisson New Liu-Ridge Type Estimator (PNLRTE), a hybrid approach that combines features of the Liu and ridge estimators with multiple shrinkage strategies to improve estimation accuracy. The properties of the new estimator were derived, and its performance was evaluated against existing estimators, including Poisson Maximum Likelihood Estimator (PMLE), Poisson Ridge Estimator (PRE), Poisson Liu Estimator (PLE), Poisson Kibria-Lukman (PK-L), and Poisson Modified Ridge Type (PMRT). Performance was assessed across varying sample sizes, degrees of multicollinearity, number of predictors, and intercept specifications. Results consistently show that the PNLRTE with median shrinkage (PNLRT-ME) outperforms alternatives, achieving the lowest mean squared error (MSE) in most scenarios, particularly under severe multicollinearity and larger samples. Other estimators, such as PLE and PK-L, perform competitively under moderate correlations, while PRE gains efficiency as sample size increases. In contrast, PMLE consistently yields poor results. The findings establish PNLRTE, especially PNLRT-ME, as an efficient alternative for Poisson regression with multicollinearity, providing researchers with a reliable tool for practical applications.