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Summary

This study introduces a ridge estimator for the Zero-Inflated Probit Bell (ZIPBell) regression model. This method enhances parameter stability for complex count data, even with correlated predictors.

Keywords:
62J0562J0762J12Count dataZero-Inflated Probit Bell modelmulticollinearitypenalized estimationridge regression

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Count data often exhibit excess zeros (structural zeros) and potential multicollinearity.
  • Existing models like the Zero-Inflated Bell (ZIBell) model address structural zeros.
  • The probit link function is effective for modeling the zero-inflation component.

Purpose of the Study:

  • To develop a ridge estimator for the Zero-Inflated Probit Bell (ZIPBell) regression model.
  • To stabilize parameter estimates in the presence of multicollinearity in ZIPBell models.
  • To provide a robust method for analyzing complex count data with structural zeros and correlated predictors.

Main Methods:

  • Development of a ridge penalized estimator for the ZIPBell model.
  • Adaptation of the Zero-Inflated Bell (ZIBell) model by incorporating a probit link function for the zero-inflation part.
  • Utilizing ridge penalization to reduce variance and mitigate multicollinearity effects.

Main Results:

  • The proposed ridge estimator demonstrates robustness across varying levels of multicollinearity.
  • The method effectively stabilizes parameter estimates without excluding correlated predictors.
  • Numerical studies and an empirical application confirm the approach's reliability for sparse and complex count data.

Conclusions:

  • The ridge estimator for the ZIPBell model offers a valuable tool for analyzing count data with structural zeros and multicollinearity.
  • This methodology enhances the reliability of parameter estimation in challenging statistical scenarios.
  • The approach provides a stable and effective alternative for complex count data analysis.