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A remedial measure of multicollinearity in multiple linear regression in the presence of high leverage points

The ordinary least squares (OLS) is the widely used method in multiple linear regression model due to tradition and its optimal properties. Nonetheless, in the presence of multicollinearity, the OLS method is inefficient because the standard errors of its estimates become inflated. Many methods have...

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Main Authors: Saied Ismaeel, Shelan, Midi, Habshah, M. Taher Omar, Kurdistan
Format: Article
Language:English
Published: Penerbit Universiti Kebangsaan Malaysia 2024
Online Access:http://psasir.upm.edu.my/id/eprint/113148/1/113148.pdf
http://psasir.upm.edu.my/id/eprint/113148/
https://www.ukm.my/jsm/pdf_files/SM-PDF-53-4-2024/14.pdf
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spelling my.upm.eprints.1131482024-11-18T01:26:56Z http://psasir.upm.edu.my/id/eprint/113148/ A remedial measure of multicollinearity in multiple linear regression in the presence of high leverage points Saied Ismaeel, Shelan Midi, Habshah M. Taher Omar, Kurdistan The ordinary least squares (OLS) is the widely used method in multiple linear regression model due to tradition and its optimal properties. Nonetheless, in the presence of multicollinearity, the OLS method is inefficient because the standard errors of its estimates become inflated. Many methods have been proposed to remedy this problem that include the Jackknife Ridge Regression (JAK). However, the performance of JAK is poor when multicollinearity and high leverage points (HLPs) which are outlying observations in the X- direction are present in the data. As a solution to this problem, Robust Jackknife Ridge MM (RJMM) and Robust Jackknife Ridge GM2 (RJGM2) estimators are put forward. Nevertheless, they are still not very efficient because they suffer from long computational running time, some elements of biased and do not have bounded influence property. This paper proposes a robust Jackknife ridge regression that integrates a generalized M estimator and fast improvised Gt (GM-FIMGT) estimator, in its establishment. We name this method the robust Jackknife ridge regression based on GM-FIMGT, denoted as RJFIMGT. The numerical results show that the proposed RJFIMGT method was found to be the best method as it has the least values of RMSE and bias compared to other methods in this study. Penerbit Universiti Kebangsaan Malaysia 2024 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/113148/1/113148.pdf Saied Ismaeel, Shelan and Midi, Habshah and M. Taher Omar, Kurdistan (2024) A remedial measure of multicollinearity in multiple linear regression in the presence of high leverage points. Sains Malaysiana, 53 (4). pp. 907-920. ISSN 0126-6039 https://www.ukm.my/jsm/pdf_files/SM-PDF-53-4-2024/14.pdf 10.17576/jsm-2024-5304-14
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description The ordinary least squares (OLS) is the widely used method in multiple linear regression model due to tradition and its optimal properties. Nonetheless, in the presence of multicollinearity, the OLS method is inefficient because the standard errors of its estimates become inflated. Many methods have been proposed to remedy this problem that include the Jackknife Ridge Regression (JAK). However, the performance of JAK is poor when multicollinearity and high leverage points (HLPs) which are outlying observations in the X- direction are present in the data. As a solution to this problem, Robust Jackknife Ridge MM (RJMM) and Robust Jackknife Ridge GM2 (RJGM2) estimators are put forward. Nevertheless, they are still not very efficient because they suffer from long computational running time, some elements of biased and do not have bounded influence property. This paper proposes a robust Jackknife ridge regression that integrates a generalized M estimator and fast improvised Gt (GM-FIMGT) estimator, in its establishment. We name this method the robust Jackknife ridge regression based on GM-FIMGT, denoted as RJFIMGT. The numerical results show that the proposed RJFIMGT method was found to be the best method as it has the least values of RMSE and bias compared to other methods in this study.
format Article
author Saied Ismaeel, Shelan
Midi, Habshah
M. Taher Omar, Kurdistan
spellingShingle Saied Ismaeel, Shelan
Midi, Habshah
M. Taher Omar, Kurdistan
A remedial measure of multicollinearity in multiple linear regression in the presence of high leverage points
author_facet Saied Ismaeel, Shelan
Midi, Habshah
M. Taher Omar, Kurdistan
author_sort Saied Ismaeel, Shelan
title A remedial measure of multicollinearity in multiple linear regression in the presence of high leverage points
title_short A remedial measure of multicollinearity in multiple linear regression in the presence of high leverage points
title_full A remedial measure of multicollinearity in multiple linear regression in the presence of high leverage points
title_fullStr A remedial measure of multicollinearity in multiple linear regression in the presence of high leverage points
title_full_unstemmed A remedial measure of multicollinearity in multiple linear regression in the presence of high leverage points
title_sort remedial measure of multicollinearity in multiple linear regression in the presence of high leverage points
publisher Penerbit Universiti Kebangsaan Malaysia
publishDate 2024
url http://psasir.upm.edu.my/id/eprint/113148/1/113148.pdf
http://psasir.upm.edu.my/id/eprint/113148/
https://www.ukm.my/jsm/pdf_files/SM-PDF-53-4-2024/14.pdf
_version_ 1816132735843958784
score 13.244413

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