Modeling count data with zero inflation, overdispersion, underdispersion, and multicollinearity using a zero-inflated Conway–Maxwell Poisson Liu-type regression

Count data characterized by overdispersion, underdispersion, and an excess of zero observations present persistent challenges for regression frameworks. The Zero-Inflated Conway–Maxwell Poisson regression model (ZICMPRM) has emerged as a flexible alternative capable of accommodating this full spectrum of dispersion patterns. However, a well-recognized limitation of the maximum likelihood estimator (MLE) is its sensitivity to multicollinearity among covariates, which can substantially inflate variance and compromise inferential reliability. To address this issue, we propose a new Liu-type within the ZICMPRM framework. Theoretical comparison demonstrates that the proposed estimator outperforms the existing estimators in the presence of multicollinearity. The finite-sample performance of the proposed estimator is assessed through an extensive Monte Carlo simulation study, with results consistently demonstrating their superiority over MLE, ridge, and Liu in terms of MSE across varying levels of dispersion and multicollinearity. The practical utility of the estimator is further illustrated through application to real-world count data, where the proposed estimator yields notably more stable and efficient parameter estimates. These findings emphasize the necessity of adopting biased estimation procedures when fitting ZICMPRM to multicollinear data structures.