An improvised SIMPLS estimator based on MRCD-PCA weighting function and its application to real data
Multicollinearity often occurs when two or more predictor variables are correlated, especially for high dimensional data (HDD) where p>>n . The statistically inspired modification of the partial least squares (SIMPLS) is a very popular technique for solving a partial least squares regression...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Published: |
Multidisciplinary Digital Publishing Institute
2021
|
| _version_ | 1796983153813880832 |
|---|---|
| author | Siti Zahariah Midi, Habshah Mustafa, Mohd Shafie |
| author_facet | Siti Zahariah Midi, Habshah Mustafa, Mohd Shafie |
| author_sort | Siti Zahariah |
| collection | UPM |
| description | Multicollinearity often occurs when two or more predictor variables are correlated, especially for high dimensional data (HDD) where p>>n
. The statistically inspired modification of the partial least squares (SIMPLS) is a very popular technique for solving a partial least squares regression problem due to its efficiency, speed, and ease of understanding. The execution of SIMPLS is based on the empirical covariance matrix of explanatory variables and response variables. Nevertheless, SIMPLS is very easily affected by outliers. In order to rectify this problem, a robust iteratively reweighted SIMPLS (RWSIMPLS) is introduced. Nonetheless, it is still not very efficient as the algorithm of RWSIMPLS is based on a weighting function that does not specify any method of identification of high leverage points (HLPs), i.e., outlying observations in the X-direction. HLPs have the most detrimental effect on the computed values of various estimates, which results in misleading conclusions about the fitted regression model. Hence, their effects need to be reduced by assigning smaller weights to them. As a solution to this problem, we propose an improvised SIMPLS based on a new weight function obtained from the MRCD-PCA diagnostic method of the identification of HLPs for HDD and name this method MRCD-PCA-RWSIMPLS. A new MRCD-PCA-RWSIMPLS diagnostic plot is also established for classifying observations into four data points, i.e., regular observations, vertical outliers, and good and bad leverage points. The numerical examples and Monte Carlo simulations signify that MRCD-PCA-RWSIMPLS offers substantial improvements over SIMPLS and RWSIMPLS. The proposed diagnostic plot is able to classify observations into correct groups. On the contrary, SIMPLS and RWSIMPLS plots fail to correctly classify observations into correct groups and show masking and swamping effects. |
| first_indexed | 2024-03-06T11:02:24Z |
| format | Article |
| id | upm.eprints-95857 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-03-06T11:02:24Z |
| publishDate | 2021 |
| publisher | Multidisciplinary Digital Publishing Institute |
| record_format | dspace |
| spelling | upm.eprints-958572023-03-29T04:01:57Z http://psasir.upm.edu.my/id/eprint/95857/ An improvised SIMPLS estimator based on MRCD-PCA weighting function and its application to real data Siti Zahariah Midi, Habshah Mustafa, Mohd Shafie Multicollinearity often occurs when two or more predictor variables are correlated, especially for high dimensional data (HDD) where p>>n . The statistically inspired modification of the partial least squares (SIMPLS) is a very popular technique for solving a partial least squares regression problem due to its efficiency, speed, and ease of understanding. The execution of SIMPLS is based on the empirical covariance matrix of explanatory variables and response variables. Nevertheless, SIMPLS is very easily affected by outliers. In order to rectify this problem, a robust iteratively reweighted SIMPLS (RWSIMPLS) is introduced. Nonetheless, it is still not very efficient as the algorithm of RWSIMPLS is based on a weighting function that does not specify any method of identification of high leverage points (HLPs), i.e., outlying observations in the X-direction. HLPs have the most detrimental effect on the computed values of various estimates, which results in misleading conclusions about the fitted regression model. Hence, their effects need to be reduced by assigning smaller weights to them. As a solution to this problem, we propose an improvised SIMPLS based on a new weight function obtained from the MRCD-PCA diagnostic method of the identification of HLPs for HDD and name this method MRCD-PCA-RWSIMPLS. A new MRCD-PCA-RWSIMPLS diagnostic plot is also established for classifying observations into four data points, i.e., regular observations, vertical outliers, and good and bad leverage points. The numerical examples and Monte Carlo simulations signify that MRCD-PCA-RWSIMPLS offers substantial improvements over SIMPLS and RWSIMPLS. The proposed diagnostic plot is able to classify observations into correct groups. On the contrary, SIMPLS and RWSIMPLS plots fail to correctly classify observations into correct groups and show masking and swamping effects. Multidisciplinary Digital Publishing Institute 2021 Article PeerReviewed Siti Zahariah and Midi, Habshah and Mustafa, Mohd Shafie (2021) An improvised SIMPLS estimator based on MRCD-PCA weighting function and its application to real data. Symmetry-Basel, 13 (11). art. no. 2211. pp. 1-22. ISSN 2073-8994 https://www.mdpi.com/2073-8994/13/11/2211 10.3390/sym13112211 |
| spellingShingle | Siti Zahariah Midi, Habshah Mustafa, Mohd Shafie An improvised SIMPLS estimator based on MRCD-PCA weighting function and its application to real data |
| title | An improvised SIMPLS estimator based on MRCD-PCA weighting function and its application to real data |
| title_full | An improvised SIMPLS estimator based on MRCD-PCA weighting function and its application to real data |
| title_fullStr | An improvised SIMPLS estimator based on MRCD-PCA weighting function and its application to real data |
| title_full_unstemmed | An improvised SIMPLS estimator based on MRCD-PCA weighting function and its application to real data |
| title_short | An improvised SIMPLS estimator based on MRCD-PCA weighting function and its application to real data |
| title_sort | improvised simpls estimator based on mrcd pca weighting function and its application to real data |
| work_keys_str_mv | AT sitizahariah animprovisedsimplsestimatorbasedonmrcdpcaweightingfunctionanditsapplicationtorealdata AT midihabshah animprovisedsimplsestimatorbasedonmrcdpcaweightingfunctionanditsapplicationtorealdata AT mustafamohdshafie animprovisedsimplsestimatorbasedonmrcdpcaweightingfunctionanditsapplicationtorealdata AT sitizahariah improvisedsimplsestimatorbasedonmrcdpcaweightingfunctionanditsapplicationtorealdata AT midihabshah improvisedsimplsestimatorbasedonmrcdpcaweightingfunctionanditsapplicationtorealdata AT mustafamohdshafie improvisedsimplsestimatorbasedonmrcdpcaweightingfunctionanditsapplicationtorealdata |