Partial least squares models and their formulations, diagnostics and applications to spectroscopy

Mauricio Huerta; VICTOR ELISEO LEIVA SANCHEZ; Carolina Marchant; Marcelo Rodríguez

doi:10.1007/978-3-030-21248-3_35

Partial least squares models and their formulations, diagnostics and applications to spectroscopy

Mauricio Huerta, VICTOR ELISEO LEIVA SANCHEZ, Carolina Marchant, Marcelo Rodríguez

SCHOOL OF INDUSTRIAL ENGINEERING

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Partial least squares (PLS) models are a multivariate technique developed to solve the problem of multicollinearity and/or high dimensionality related to explanatory variables in multiple linear models. PLS models have been extensively applied assuming normality, but this assumption is not always fulfilled. For example, if the response variable has an asymmetric distribution or it is bounded into an interval, normality is violated. In this work, we present a collection of PLS models and their formulations, diagnostics and applications. Formulations are based on different symmetric, asymmetric and bounded distributions, such as normal, beta and Birnbaum-Saunders. Diagnostics are based on residuals and the Cook and Mahalanobis distances. Applications are provided using real-world spectroscopy data.

Original language	English
Title of host publication	Proceedings of the 13th International Conference on Management Science and Engineering Management, 2019 - Volume 1
Editors	Jiuping Xu, Gheorghe Duca, Fang Lee Cooke, Syed Ejaz Ahmed
Publisher	Springer Verlag
Pages	470-495
Number of pages	26
ISBN (Print)	9783030212476
DOIs	https://doi.org/10.1007/978-3-030-21248-3_35
State	Published - 1 Jan 2020
Event	13th International Conference on Management Science and Engineering Management, ICMSEM 2019 - St. Catharines, Canada Duration: 5 Aug 2019 → 8 Aug 2019

Publication series

Name	Advances in Intelligent Systems and Computing
Volume	1001
ISSN (Print)	2194-5357

Conference

Conference	13th International Conference on Management Science and Engineering Management, ICMSEM 2019
Country	Canada
City	St. Catharines
Period	5/08/19 → 8/08/19

Keywords

Cook distance
Linear models
Mahalanobis distance
NIR spectra data
Principal component analysis
Quantile residuals
R software

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Huerta, M., LEIVA SANCHEZ, VICTOR. ELISEO., Marchant, C., & Rodríguez, M. (2020). Partial least squares models and their formulations, diagnostics and applications to spectroscopy. In J. Xu, G. Duca, F. L. Cooke, & S. E. Ahmed (Eds.), Proceedings of the 13th International Conference on Management Science and Engineering Management, 2019 - Volume 1 (pp. 470-495). (Advances in Intelligent Systems and Computing; Vol. 1001). Springer Verlag. https://doi.org/10.1007/978-3-030-21248-3_35

Huerta, Mauricio ; LEIVA SANCHEZ, VICTOR ELISEO ; Marchant, Carolina ; Rodríguez, Marcelo. / Partial least squares models and their formulations, diagnostics and applications to spectroscopy. Proceedings of the 13th International Conference on Management Science and Engineering Management, 2019 - Volume 1. editor / Jiuping Xu ; Gheorghe Duca ; Fang Lee Cooke ; Syed Ejaz Ahmed. Springer Verlag, 2020. pp. 470-495 (Advances in Intelligent Systems and Computing).

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title = "Partial least squares models and their formulations, diagnostics and applications to spectroscopy",

abstract = "Partial least squares (PLS) models are a multivariate technique developed to solve the problem of multicollinearity and/or high dimensionality related to explanatory variables in multiple linear models. PLS models have been extensively applied assuming normality, but this assumption is not always fulfilled. For example, if the response variable has an asymmetric distribution or it is bounded into an interval, normality is violated. In this work, we present a collection of PLS models and their formulations, diagnostics and applications. Formulations are based on different symmetric, asymmetric and bounded distributions, such as normal, beta and Birnbaum-Saunders. Diagnostics are based on residuals and the Cook and Mahalanobis distances. Applications are provided using real-world spectroscopy data.",

keywords = "Cook distance, Linear models, Mahalanobis distance, NIR spectra data, Principal component analysis, Quantile residuals, R software",

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Huerta, M, LEIVA SANCHEZ, VICTORELISEO, Marchant, C & Rodríguez, M 2020, Partial least squares models and their formulations, diagnostics and applications to spectroscopy. in J Xu, G Duca, FL Cooke & SE Ahmed (eds), Proceedings of the 13th International Conference on Management Science and Engineering Management, 2019 - Volume 1. Advances in Intelligent Systems and Computing, vol. 1001, Springer Verlag, pp. 470-495, 13th International Conference on Management Science and Engineering Management, ICMSEM 2019, St. Catharines, Canada, 5/08/19. https://doi.org/10.1007/978-3-030-21248-3_35

Partial least squares models and their formulations, diagnostics and applications to spectroscopy. / Huerta, Mauricio; LEIVA SANCHEZ, VICTOR ELISEO; Marchant, Carolina; Rodríguez, Marcelo.

Proceedings of the 13th International Conference on Management Science and Engineering Management, 2019 - Volume 1. ed. / Jiuping Xu; Gheorghe Duca; Fang Lee Cooke; Syed Ejaz Ahmed. Springer Verlag, 2020. p. 470-495 (Advances in Intelligent Systems and Computing; Vol. 1001).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Huerta, Mauricio

AU - LEIVA SANCHEZ, VICTOR ELISEO

AU - Marchant, Carolina

AU - Rodríguez, Marcelo

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N2 - Partial least squares (PLS) models are a multivariate technique developed to solve the problem of multicollinearity and/or high dimensionality related to explanatory variables in multiple linear models. PLS models have been extensively applied assuming normality, but this assumption is not always fulfilled. For example, if the response variable has an asymmetric distribution or it is bounded into an interval, normality is violated. In this work, we present a collection of PLS models and their formulations, diagnostics and applications. Formulations are based on different symmetric, asymmetric and bounded distributions, such as normal, beta and Birnbaum-Saunders. Diagnostics are based on residuals and the Cook and Mahalanobis distances. Applications are provided using real-world spectroscopy data.

AB - Partial least squares (PLS) models are a multivariate technique developed to solve the problem of multicollinearity and/or high dimensionality related to explanatory variables in multiple linear models. PLS models have been extensively applied assuming normality, but this assumption is not always fulfilled. For example, if the response variable has an asymmetric distribution or it is bounded into an interval, normality is violated. In this work, we present a collection of PLS models and their formulations, diagnostics and applications. Formulations are based on different symmetric, asymmetric and bounded distributions, such as normal, beta and Birnbaum-Saunders. Diagnostics are based on residuals and the Cook and Mahalanobis distances. Applications are provided using real-world spectroscopy data.

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KW - Mahalanobis distance

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Huerta M, LEIVA SANCHEZ VICTORELISEO, Marchant C, Rodríguez M. Partial least squares models and their formulations, diagnostics and applications to spectroscopy. In Xu J, Duca G, Cooke FL, Ahmed SE, editors, Proceedings of the 13th International Conference on Management Science and Engineering Management, 2019 - Volume 1. Springer Verlag. 2020. p. 470-495. (Advances in Intelligent Systems and Computing). https://doi.org/10.1007/978-3-030-21248-3_35

Partial least squares models and their formulations, diagnostics and applications to spectroscopy

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