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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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/113148/ http://psasir.upm.edu.my/id/eprint/113148/1/113148.pdf |
| _version_ | 1848866141329424384 |
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| author | Saied Ismaeel, Shelan Midi, Habshah M. Taher Omar, Kurdistan |
| author_facet | Saied Ismaeel, Shelan Midi, Habshah M. Taher Omar, Kurdistan |
| author_sort | Saied Ismaeel, Shelan |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T14:15:53Z |
| format | Article |
| id | upm-113148 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:15:53Z |
| publishDate | 2024 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-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 |
| 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 |
| title | 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_short | 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 |
| url | http://psasir.upm.edu.my/id/eprint/113148/ http://psasir.upm.edu.my/id/eprint/113148/ http://psasir.upm.edu.my/id/eprint/113148/ http://psasir.upm.edu.my/id/eprint/113148/1/113148.pdf |