Kibria–Lukman estimator for the zero inflated negative binomial regression model: theory, simulation and applications

Abstract

The zero inflated negative binomial model is an appropriate choice to model count response variables with excessive zeros and over-dispersion simultaneously. This article addresses the parameter estimation for the zero-inflated negative binomial model when there are many predictors and the problems of multicollinearity are present. Since, under multicollinearity, the widely used maximum likelihood estimator becomes unstable, this article proposes an alternative estimator, called Kibria–Lukman estimator for the zero inflated negative binomial model and provided some new biasing parameters. Then compared the performance of Kibria–Lukman estimator with some of the traditional biased estimators, that is, ridge and Liu estimators. The superiority of the proposed estimator is systematically scrutinized both theoretically and numerically. For numerical assessment, we conduct a Monte Carlo simulation study under different controlled factors. A numerical example is also applied to appraise the performance of proposed estimator. Based on the simulation and example results, we observed that the performance of the proposed estimator under different biasing parameters was better than that of the maximum likelihood estimator and other involved biased estimation methods when there exists a high but imperfect multicollinearity.

Keywords:

• Biased estimator
• Kibria–Lukman estimator
• Liu estimator
• Multicollinearity
• Ridge estimator
• Zero inflated negative binomial model

Acknowledgements

Authors are grateful to the Editor, the Associate Editor and the anonymous referees for their valuable comments and suggestions, which certainly help to improve quality and presentation of the article.

Disclosure statement

No potential conflict of interest was reported by the author(s).