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<p>For count data with overdispersion and excessive zeros, the most commonly used regression model is the zero-inflated negative binomial (ZINB) regression model. The multicollinearity problem has a detrimental impact on the estimation of parameters in the ZINB regression model. Many studies are available for the ZINB regression model to address this issue, but these have primarily focused on the logit link function. As we know, the ZINB regression model uses different link functions. Thus, to mitigate the detrimental consequences of multicollinearity, a novel estimator known as the ZINB ridge estimator (ZINBRE) is used with different ridge parameters and link functions. So, the objective of this study is to compare the performance of different ridge parameters with different link functions for the ZINB regression model. A Monte Carlo simulation study is conducted to demonstrate the superiority of the ZINBRE with different link functions. Based on the results of the simulation study, the ZINBRE outperforms for the probit and logit link functions under various ridge parameters. A real application is also considered for verification of simulation findings.</p>

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Performance of Link Functions and New Ridge Parameter Estimators for the Zero-Inflated Negative Binomial Ridge Regression Model: Simulation and Application

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Faiza Batool,
  • Muhammad Aslam,
  • Muhammad Amin

摘要

For count data with overdispersion and excessive zeros, the most commonly used regression model is the zero-inflated negative binomial (ZINB) regression model. The multicollinearity problem has a detrimental impact on the estimation of parameters in the ZINB regression model. Many studies are available for the ZINB regression model to address this issue, but these have primarily focused on the logit link function. As we know, the ZINB regression model uses different link functions. Thus, to mitigate the detrimental consequences of multicollinearity, a novel estimator known as the ZINB ridge estimator (ZINBRE) is used with different ridge parameters and link functions. So, the objective of this study is to compare the performance of different ridge parameters with different link functions for the ZINB regression model. A Monte Carlo simulation study is conducted to demonstrate the superiority of the ZINBRE with different link functions. Based on the results of the simulation study, the ZINBRE outperforms for the probit and logit link functions under various ridge parameters. A real application is also considered for verification of simulation findings.