In this we 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.

References:

[1] Ali, E., & Lukman, A. F. (2025). Ridge-penalized Zero-Inflated Probit Bell model for multicollinearity in count data. Journal of Applied Statistics, 1–26. https://doi.org/10.1080/02664763.2025.2530551

[2] Essoham Ali & Kim-Hung Pho (06 Aug 2024).A novel model for count data: zero-inflated Probit Bell model with applications.Communications in Statistics - Simulation and Computation.