TY - JOUR
T1 - On a partial least squares regression model for asymmetric data with a chemical application in mining
AU - Huerta, Mauricio
AU - Leiva, Víctor
AU - Liu, Shuangzhe
AU - Rodríguez, Marcelo
AU - Villegas, Danny
N1 - Funding Information:
The authors would like to thank the editors and four reviewers very much for their constructive comments on an earlier version of this manuscript which resulted in this improved version. This research was supported partially by grant “ Fondecyt 1160868 ” from the National Commission for Scientific and Technological Research of the Chilean government .
Publisher Copyright:
© 2019 Elsevier B.V.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/7/15
Y1 - 2019/7/15
N2 - In chemometrical applications, covariates in regression models are often correlated, causing a collinearity problem that can be solved by partial least squares (PLS)regression. In addition, high dimensionality in the space of covariates is also a problem with more parameters than cases, a phenomenon usually found in chemical spectral data that can also be solved by PLS regression. The Birnbaum-Saunders distribution has theoretical justifications for modeling chemical data. In this paper, a new methodology based on PLS regression models is proposed considering a reparameterized Birnbaum-Saunders (RBS)distribution for the response, which is useful for describing asymmetric data frequently found in chemical phenomena. We estimate the RBS-PLS model parameters using the maximum likelihood method. A bootstrap approach is employed to obtain the optimal number of PLS components. Quantile residuals and Cook and Mahalanobis type distances are utilized for detecting possible anomalies in the modeling. We conduct perturbation studies to assess the performance of these diagnostic tools. The proposed methodology is applied to real-world kaolinite data and compared to other competing models. This provides a useful illustration of chemical analysis in the mining industry.
AB - In chemometrical applications, covariates in regression models are often correlated, causing a collinearity problem that can be solved by partial least squares (PLS)regression. In addition, high dimensionality in the space of covariates is also a problem with more parameters than cases, a phenomenon usually found in chemical spectral data that can also be solved by PLS regression. The Birnbaum-Saunders distribution has theoretical justifications for modeling chemical data. In this paper, a new methodology based on PLS regression models is proposed considering a reparameterized Birnbaum-Saunders (RBS)distribution for the response, which is useful for describing asymmetric data frequently found in chemical phenomena. We estimate the RBS-PLS model parameters using the maximum likelihood method. A bootstrap approach is employed to obtain the optimal number of PLS components. Quantile residuals and Cook and Mahalanobis type distances are utilized for detecting possible anomalies in the modeling. We conduct perturbation studies to assess the performance of these diagnostic tools. The proposed methodology is applied to real-world kaolinite data and compared to other competing models. This provides a useful illustration of chemical analysis in the mining industry.
KW - Bootstrapping
KW - Cook and Mahalanobis distances
KW - Diagnostic analysis
KW - GLM
KW - Likelihood method
KW - NIR spectral data
KW - PCA
KW - R software
KW - Statistical residuals
UR - http://www.scopus.com/inward/record.url?scp=85066243590&partnerID=8YFLogxK
UR - http://www.mendeley.com/research/partial-least-squares-regression-model-asymmetric-data-chemical-application-mining
U2 - 10.1016/j.chemolab.2019.04.013
DO - 10.1016/j.chemolab.2019.04.013
M3 - Article
AN - SCOPUS:85066243590
SN - 0169-7439
VL - 190
SP - 55
EP - 68
JO - Chemometrics and Intelligent Laboratory Systems
JF - Chemometrics and Intelligent Laboratory Systems
ER -