Novel robust logistic regression estimators for effectively modeling of multivariate binary data under outliers and multicollinearity: application to heavy metal contamination data in Al-Kharj landfills

Eslam Hussam; Yousef Alharbi; Ahmed M. Gemeay; Samirah Alzubaidi; M. H. Harpy; Ramy Aldallal; M. S. Mohamed; Ali T. Hammad; Eslam Hussam; Yousef Alharbi; Ahmed M. Gemeay; Samirah Alzubaidi; M. H. Harpy; Ramy Aldallal; M. S. Mohamed; Ali T. Hammad

doi:10.3934/math.2026662

AIMS Mathematics

2026, Volume 11, Issue 6: 16095-16128. doi: 10.3934/math.2026662

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Novel robust logistic regression estimators for effectively modeling of multivariate binary data under outliers and multicollinearity: application to heavy metal contamination data in Al-Kharj landfills

1.
Department of Accounting, College of Business Administration in Hawtat Bani Tamim, Prince Sattam bin Abdulaziz University, Saudi Arabia
2.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
4.
Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Mecca, Saudi Arabia
5.
Department of Mathematics, College of Science & Humanity Studies, Prince Sattam Bin Abdulaziz University, Saudi Arabia
6.
Department of Management, College of Business Administration in Hawtat Bani Tamim, Prince Sattam bin Abdulaziz University, Saudi Arabia
7.
Department of Mathematics, College of Science and Humanities in Hawtat Bani Tamim, Prince Sattam bin Abdulaziz University, Saudi Arabia

Received: 07 April 2026 Revised: 08 May 2026 Accepted: 19 May 2026 Published: 05 June 2026
MSC : 62J07, 62J10, 62J12, 62P12

Logistic regression models are widely used for analyzing binary data, with the maximum likelihood estimator (MLE) being the standard method to estimate coefficients. However, the MLE becomes unstable and unreliable in the presence of multicollinearity or outliers. Outliers distort parameter estimates by unduly influencing the likelihood function, leading to bias and poor prediction. Multicollinearity inflates the variance of coefficients, reducing stability and interpretability. While biased estimators exist for multicollinearity and robust estimators for outliers, a unified framework that simultaneously handles both issues is still lacking. To address these issues, we have proposed a class of robust ridge-type estimators that combine robust logistic estimation with shrinkage methods. A comprehensive Monte Carlo simulation study evaluated the proposed estimators under varying levels of outliers and multicollinearity. Results show that our methods consistently outperform the traditional MLE and existing estimators in terms of accuracy and robustness. Finally, we demonstrated practical utility by analyzing heavy metal and metalloid contamination levels in landfill sites in Al-Kharj, Saudi Arabia, with empirical findings confirming that the proposed robust logistic estimators provide reliable and efficient inference when both multicollinearity and outliers are present.
- logistic regression model,
- biased estimator,
- robust estimator,
- multivariate heavy metal contamination data,
- outliers,
- multicollinearity
Citation: Eslam Hussam, Yousef Alharbi, Ahmed M. Gemeay, Samirah Alzubaidi, M. H. Harpy, Ramy Aldallal, M. S. Mohamed, Ali T. Hammad. Novel robust logistic regression estimators for effectively modeling of multivariate binary data under outliers and multicollinearity: application to heavy metal contamination data in Al-Kharj landfills[J]. AIMS Mathematics, 2026, 11(6): 16095-16128. doi: 10.3934/math.2026662

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Abstract

Logistic regression models are widely used for analyzing binary data, with the maximum likelihood estimator (MLE) being the standard method to estimate coefficients. However, the MLE becomes unstable and unreliable in the presence of multicollinearity or outliers. Outliers distort parameter estimates by unduly influencing the likelihood function, leading to bias and poor prediction. Multicollinearity inflates the variance of coefficients, reducing stability and interpretability. While biased estimators exist for multicollinearity and robust estimators for outliers, a unified framework that simultaneously handles both issues is still lacking. To address these issues, we have proposed a class of robust ridge-type estimators that combine robust logistic estimation with shrinkage methods. A comprehensive Monte Carlo simulation study evaluated the proposed estimators under varying levels of outliers and multicollinearity. Results show that our methods consistently outperform the traditional MLE and existing estimators in terms of accuracy and robustness. Finally, we demonstrated practical utility by analyzing heavy metal and metalloid contamination levels in landfill sites in Al-Kharj, Saudi Arabia, with empirical findings confirming that the proposed robust logistic estimators provide reliable and efficient inference when both multicollinearity and outliers are present.

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