Robust Negative Binomial Regression via the Kibria–Lukman Strategy: Methodology and Application

Adewale F. Lukman (), Olayan Albalawi, Mohammad Arashi, Jeza Allohibi, Abdulmajeed Atiah Alharbi and Rasha A. Farghali
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Adewale F. Lukman: Department of Mathematics and Statistics, University of North Dakota, Grand Forks, ND 58202, USA
Olayan Albalawi: Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia
Mohammad Arashi: Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 9177948974, Razavi Khorasan, Iran
Jeza Allohibi: Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawara 42353, Saudi Arabia
Abdulmajeed Atiah Alharbi: Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawara 42353, Saudi Arabia
Rasha A. Farghali: Department of Mathematics, Insurance and Applied Statistics, Helwan University, Cairo 11795, Egypt

Mathematics, 2024, vol. 12, issue 18, 1-16

Abstract: Count regression models, particularly negative binomial regression (NBR), are widely used in various fields, including biometrics, ecology, and insurance. Over-dispersion is likely when dealing with count data, and NBR has gained attention as an effective tool to address this challenge. However, multicollinearity among covariates and the presence of outliers can lead to inflated confidence intervals and inaccurate predictions in the model. This study proposes a comprehensive approach integrating robust and regularization techniques to handle the simultaneous impact of multicollinearity and outliers in the negative binomial regression model (NBRM). We investigate the estimators’ performance through extensive simulation studies and provide analytical comparisons. The simulation results and the theoretical comparisons demonstrate the superiority of the proposed robust hybrid KL estimator (M-NBKLE) with predictive accuracy and stability when multicollinearity and outliers exist. We illustrate the application of our methodology by analyzing a forestry dataset. Our findings complement and reinforce the simulation and theoretical results.

Keywords: negative binomial; multicollinearity; outliers; regularization; robust hybrid KL estimator; over-dispersion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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