Mitigating Multicollinearity in Regression: A Study on Improved Ridge Estimators

Nadeem Akhtar (), Muteb Faraj Alharthi and Muhammad Shakir Khan
Additional contact information
Nadeem Akhtar: Higher Education Department, Peshawar 26281, Khyber Pakhtunkhwa, Pakistan
Muteb Faraj Alharthi: Department of Mathematics and Statistics, College of Science, Taif University, Taif 21944, Saudi Arabia
Muhammad Shakir Khan: Directorate General Livestock & Dairy Development Department (Research Wing) Peshawar, Peshawar 24551, Khyber Pakhtunkhwa, Pakistan

Mathematics, 2024, vol. 12, issue 19, 1-17

Abstract: Multicollinearity, a critical issue in regression analysis that can severely compromise the stability and accuracy of parameter estimates, arises when two or more variables exhibit correlation with each other. This paper solves this problem by introducing six new, improved two-parameter ridge estimators (ITPRE): NATPR1, NATPR2, NATPR3, NATPR4, NATPR5, and NATPR6. These ITPRE are designed to remove multicollinearity and improve the accuracy of estimates. A comprehensive Monte Carlo simulation analysis using the mean squared error (MSE) criterion demonstrates that all proposed estimators effectively mitigate the effects of multicollinearity. Among these, the NATPR2 estimator consistently achieves the lowest estimated MSE, outperforming existing ridge estimators in the literature. Application of these estimators to a real-world dataset further validates their effectiveness in addressing multicollinearity, underscoring their robustness and practical relevance in improving the reliability of regression models.

Keywords: multicollinearity; regression analysis; ridge parameters; two-parameter ridge estimators; error variance; estimation performance; Monte Carlo simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/19/3027/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/19/3027/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:19:p:3027-:d:1487784

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().