Partial Least Squares Models and Their Formulations, Diagnostics and Applications to Spectroscopy

  • Mauricio Huerta
  • Víctor LeivaEmail author
  • Carolina Marchant
  • Marcelo Rodríguez
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1001)


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.


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



The authors thank the editors and reviewers for their comments on this manuscript. This research work was partially supported by FONDECYT 1160868 grant from the Chilean government.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Mauricio Huerta
    • 1
  • Víctor Leiva
    • 1
    Email author
  • Carolina Marchant
    • 2
  • Marcelo Rodríguez
    • 2
  1. 1.School of Industrial EngineeringPontificia Universidad Católica de ValparaísoValparaísoChile
  2. 2.Faculty of Basic SciencesUniversidad Católica del MauleTalcaChile

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