On new ridge estimators of the Conway-maxwell Poisson model in the case of highly correlated predictor variables: Application to plywood quality data

Abstract

This paper introduces a new method to handle multicollinearity in regression analysis, specifically for the Conway-Maxwell Poisson (COMP) model, which is used for count data. Multicollinearity, where predictor variables are highly correlated, often causes unstable results in such models. Our approach improves ridge parameter estimation, balancing accuracy and interpretability. Through simulations, we tested the method using mean squared error (MSE) as a main measure of the efficiency of estimation. The results show that our method performs better than traditional approaches, especially when multicollinearity is high or data is over- or underdispersed. It works particularly well with small-to-moderate datasets and complex data structures. This result was confirmed by our real-world application to plywood quality data.