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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2024
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| Online Access: | http://journalarticle.ukm.my/23925/ http://journalarticle.ukm.my/23925/1/SE%2014.pdf |
| _version_ | 1848815969744453632 |
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| author | Ismaeel, Shelan Saied Habshah Midi, Omar, Kurdistan M. Taher |
| author_facet | Ismaeel, Shelan Saied Habshah Midi, Omar, Kurdistan M. Taher |
| author_sort | Ismaeel, Shelan Saied |
| building | UKM 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 | 2025-11-15T00:58:26Z |
| format | Article |
| id | oai:generic.eprints.org:23925 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:58:26Z |
| publishDate | 2024 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
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| spelling | oai:generic.eprints.org:239252024-08-06T02:01:32Z http://journalarticle.ukm.my/23925/ A remedial measure of multicollinearity in multiple linear regression in the presence of high leverage points Ismaeel, Shelan Saied Habshah Midi, Omar, Kurdistan M. Taher 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 application/pdf en http://journalarticle.ukm.my/23925/1/SE%2014.pdf Ismaeel, Shelan Saied and Habshah Midi, and Omar, Kurdistan M. Taher (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/english_journals/vol53num4_2024/contentsVol53num4_2024.html |
| spellingShingle | Ismaeel, Shelan Saied Habshah Midi, Omar, Kurdistan M. Taher 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://journalarticle.ukm.my/23925/ http://journalarticle.ukm.my/23925/ http://journalarticle.ukm.my/23925/1/SE%2014.pdf |