A New Class of Conway–Maxwell–Poisson Liu-Type Regression Estimators for Effectively Modeling Multicollinear Count Data

One of the most widely used regression models for count data is the Conway–Maxwell–Poisson regression model (CMPRM), which often provides a better fit for over- and underdispersed count data than traditional models, such as Poisson regression and negative binomial regression. Parameter estimation in the CMPRM is typically performed using the maximum likelihood estimation (MLE) method. However, when explanatory variables are highly correlated, a phenomenon known as multicollinearity arises, posing a significant challenge to the analysis. Multicollinearity makes it difficult to identify the individual effects of explanatory variables, leading to inflated variances and larger standard errors of the MLEs. To address the issue of multicollinearity, this paper introduces a new class of Liu-type estimators within the CMPRM. The proposed estimators aim to improve the estimation accuracy and reliability of the CMPRM compared with existing biased estimation methods. The efficiency of the proposed estimator is evaluated through theoretical comparisons and Monte Carlo simulation experiments conducted under various conditions. Furthermore, two real-data applications are presented to demonstrate the practical usefulness of the proposed estimation method. The results from the theoretical analysis, simulation study, and empirical applications indicate that the proposed estimators outperform existing methods in terms of achieving more accurate and reliable estimates.