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

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  • Essoham Ali
  • Adewale F. Lukman

Abstract

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.

Suggested Citation

  • Essoham Ali & Adewale F. Lukman, 2026. "Ridge-penalized Zero-Inflated Probit Bell model for multicollinearity in count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 53(4), pages 633-658, March.
    • Handle: RePEc:taf:japsta:v:53:y:2026:i:4:p:633-658
    DOI: 10.1080/02664763.2025.2530551
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