Incorporating interactions in multi-block sequential and orthogonalised partial least squares regression
Article first published online: 27 SEP 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Journal of Chemometrics
Volume 25, Issue 11, pages 601–609, November 2011
How to Cite
Næs, T., Måge, I. and Segtnan, V. H. (2011), Incorporating interactions in multi-block sequential and orthogonalised partial least squares regression. J. Chemometrics, 25: 601–609. doi: 10.1002/cem.1406
- Issue published online: 24 NOV 2011
- Article first published online: 27 SEP 2011
- Manuscript Accepted: 14 JUL 2011
- Manuscript Revised: 6 MAY 2011
- Manuscript Received: 21 DEC 2010
- Agricultural Food Research Foundation of Norway
- PLS regression;
- dummy variables;
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.