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On the structure of PLS in orthogonal designs
Author(s) -
Langsrud Øyvind,
Næs Tormod
Publication year - 1995
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1180090606
Subject(s) - principal component analysis , mathematics , ordinary least squares , rank (graph theory) , partial least squares regression , eigenvalues and eigenvectors , principal component regression , data matrix , interpretation (philosophy) , zero (linguistics) , matrix (chemical analysis) , least squares function approximation , statistics , total least squares , regression analysis , combinatorics , chemistry , computer science , chromatography , physics , clade , biochemistry , linguistics , philosophy , quantum mechanics , estimator , gene , programming language , phylogenetic tree
This paper presents an interpretation of PLS applied to orthogonal explanatory variables. In particular, it is shown that in fractional factorial multiresponse experiments PLS2 gives identical results to ordinary least squares applied to principal components of the response variables. The general relationship is that the reduced‐rank regression algorithm which first projects Y onto the X ‐space and then truncates this matrix by principal component analysis before performing ordinary least squares estimation gives the same predictor as PLS2 and SIMPLS if all the non‐zero eigenvalues of X T X are identical.