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Incorporating interactions in multi‐block sequential and orthogonalised partial least squares regression
Author(s) -
Næs Tormod,
Måge Ingrid,
Segtnan Vegard H.
Publication year - 2011
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.1406
Subject(s) - partial least squares regression , block (permutation group theory) , curse of dimensionality , set (abstract data type) , mathematics , regression , algorithm , linear regression , regression analysis , basis (linear algebra) , computer science , statistics , combinatorics , geometry , programming language
This paper is about how to incorporate interaction effects in multi‐block methodologies. The method proposed is inspired by polynomial regression modelling in the case with only a few independent variables but extends/generalises the idea to situations where the blocks are potentially very large with respect to the number of variables. The method follows a so‐called type I sums of squares strategy where the linear effects (main effects) are incorporated sequentially and before the interactions. The sequential and orthogonalised partial least squares (SO‐PLS) technique is used as a basis for the proposal. The SO‐PLS method is based on sequential estimation of each new block by the PLS regression method after orthogonalisation with respect to blocks already fitted. The new method preserves the invariance already established for SO‐PLS and can be used for blocks with different dimensionality. The method is tested on one real data set with two independent blocks with different complexity and on a simulated data set with a large number of variables in each block. Copyright © 2011 John Wiley & Sons, Ltd.