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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi>&l...

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Autores principales:	Siti Zahariah, Habshah Midi, Mohd Shafie Mustafa
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	high dimensional data high leverage point minimum regularized covariance determinant partial least squares regression principal component analysis SIMPLS Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/9c469f28d9f54a4da0799efc21d4ac98
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spelling	oai:doaj.org-article:9c469f28d9f54a4da0799efc21d4ac982021-11-25T19:07:37ZAn Improvised SIMPLS Estimator Based on MRCD-PCA Weighting Function and Its Application to Real Data10.3390/sym131122112073-8994https://doaj.org/article/9c469f28d9f54a4da0799efc21d4ac982021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2211https://doaj.org/toc/2073-8994Multicollinearity often occurs when two or more predictor variables are correlated, especially for high dimensional data (HDD) where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>></mo><mo>></mo><mi>n</mi></mrow></semantics></math></inline-formula>. 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 <i>X</i>-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.Siti ZahariahHabshah MidiMohd Shafie MustafaMDPI AGarticlehigh dimensional datahigh leverage pointminimum regularized covariance determinantpartial least squares regressionprincipal component analysisSIMPLSMathematicsQA1-939ENSymmetry, Vol 13, Iss 2211, p 2211 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	high dimensional data high leverage point minimum regularized covariance determinant partial least squares regression principal component analysis SIMPLS Mathematics QA1-939
spellingShingle	high dimensional data high leverage point minimum regularized covariance determinant partial least squares regression principal component analysis SIMPLS Mathematics QA1-939 Siti Zahariah Habshah Midi Mohd Shafie Mustafa An Improvised SIMPLS Estimator Based on MRCD-PCA Weighting Function and Its Application to Real Data
description	Multicollinearity often occurs when two or more predictor variables are correlated, especially for high dimensional data (HDD) where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>></mo><mo>></mo><mi>n</mi></mrow></semantics></math></inline-formula>. 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 <i>X</i>-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.
format	article
author	Siti Zahariah Habshah Midi Mohd Shafie Mustafa
author_facet	Siti Zahariah Habshah Midi Mohd Shafie Mustafa
author_sort	Siti Zahariah
title	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_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_sort	improvised simpls estimator based on mrcd-pca weighting function and its application to real data
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/9c469f28d9f54a4da0799efc21d4ac98
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An Improvised SIMPLS Estimator Based on MRCD-PCA Weighting Function and Its Application to Real Data

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