Ridge-penalized Zero-Inflated Probit Bell model for multicollinearity in count data

This article develops a ridge estimator for the Zero-Inflated Probit Bell (ZIPBell) regression model. The ZIPBell model adapts the Zero-Inflated Bell (ZIBell) model originally proposed by Lemonte et al. (2019) by employing a probit link function for the zero-inflation component. Our contribution lies in incorporating ridge penalization into this framework, providing a methodology that stabilizes parameter estimates by reducing variance and mitigating multicollinearity effects without excluding correlated predictors. A numerical study and an empirical application illustrate the robustness of this approach across varying levels of multicollinearity and data sparsity, offering a reliable tool for analyzing complex count data with structural zeros and correlated predictors.