Multi-block regression based on combinations of orthogonalisation, PLS-regression and canonical correlation analysis

Tormod Næs; Oliver Tomic; Nils Kristian Afseth; Vegard Segtnan; Ingrid Måge

doi:10.1016/j.chemolab.2013.03.006

Multi-block regression based on combinations of orthogonalisation, PLS-regression and canonical correlation analysis

Tormod Næs, Oliver Tomic, Nils Kristian Afseth, Vegard Segtnan, Ingrid Måge

Food Analytics and Biotechnology

41 Citations (Scopus)

Abstract

This paper reviews the basic ideas underlying two new multi-block techniques, the SO-PLS and the PO-PLS regression methods. A discussion is given about how the two methods are related to each other and to standard regression and analysis of variance (ANOVA). In particular the relation between SO-PLS and Type I ANOVA is underlined. It is shown how the sums of squares can be split according to blocks introduced and also how two-way ANOVA applied to cross-validated residuals, can be utilised for testing significance of the blocks. Different ways of interpreting the results for both methods are considered and illustrated by examples. Relations to other proposed methods and ideas are discussed.

Original language	English
Journal	Chemometrics and Intelligent Laboratory Systems
Volume	124
Pages (from-to)	32-42
Number of pages	11
ISSN	0169-7439
DOIs	https://doi.org/10.1016/j.chemolab.2013.03.006
Publication status	Published - 5 May 2013

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10.1016/j.chemolab.2013.03.006

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title = "Multi-block regression based on combinations of orthogonalisation, PLS-regression and canonical correlation analysis",

abstract = "This paper reviews the basic ideas underlying two new multi-block techniques, the SO-PLS and the PO-PLS regression methods. A discussion is given about how the two methods are related to each other and to standard regression and analysis of variance (ANOVA). In particular the relation between SO-PLS and Type I ANOVA is underlined. It is shown how the sums of squares can be split according to blocks introduced and also how two-way ANOVA applied to cross-validated residuals, can be utilised for testing significance of the blocks. Different ways of interpreting the results for both methods are considered and illustrated by examples. Relations to other proposed methods and ideas are discussed.",

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AU - Næs, Tormod

AU - Tomic, Oliver

AU - Afseth, Nils Kristian

AU - Segtnan, Vegard

AU - Måge, Ingrid

PY - 2013/5/5

Y1 - 2013/5/5

N2 - This paper reviews the basic ideas underlying two new multi-block techniques, the SO-PLS and the PO-PLS regression methods. A discussion is given about how the two methods are related to each other and to standard regression and analysis of variance (ANOVA). In particular the relation between SO-PLS and Type I ANOVA is underlined. It is shown how the sums of squares can be split according to blocks introduced and also how two-way ANOVA applied to cross-validated residuals, can be utilised for testing significance of the blocks. Different ways of interpreting the results for both methods are considered and illustrated by examples. Relations to other proposed methods and ideas are discussed.

AB - This paper reviews the basic ideas underlying two new multi-block techniques, the SO-PLS and the PO-PLS regression methods. A discussion is given about how the two methods are related to each other and to standard regression and analysis of variance (ANOVA). In particular the relation between SO-PLS and Type I ANOVA is underlined. It is shown how the sums of squares can be split according to blocks introduced and also how two-way ANOVA applied to cross-validated residuals, can be utilised for testing significance of the blocks. Different ways of interpreting the results for both methods are considered and illustrated by examples. Relations to other proposed methods and ideas are discussed.

U2 - 10.1016/j.chemolab.2013.03.006

DO - 10.1016/j.chemolab.2013.03.006

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JO - Chemometrics and Intelligent Laboratory Systems

JF - Chemometrics and Intelligent Laboratory Systems

ER -

Multi-block regression based on combinations of orthogonalisation, PLS-regression and canonical correlation analysis

Abstract

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