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LS-PLS Regression: Combining Design and Spectral Data as Predictors

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Kjetil Aune

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kjetil.aune@nofima.no

PLS '07 -- 5th International Symposium on PLS and Related Methods; Ås, Norway, 2007-09-05–2007-09-07

Mevik, Bjørn-Helge; Jørgensen, Kjetil; Måge, Ingrid; Næs, Tormod

In many situations in the industry and in research one performs designed experiments to find the relationship between a set of predictor variables and one or more responses. Often there are other factors that influence the results in addition to the factors that are included in the design. To obtain information about such factors, one can measure them using spectroscopic methods. One is then faced with the challenge of analyzing data that is a combination of a design matrix and one or more spectroscopic matrices with hundreds of highly collinear variables. One answer to this challenge is LS-PLS, a regression method that is a combination of partial least squares regression (PLSR) and ordinary least squares regression (OLSR). The principal idea underlying LS-PLS is first to regress the responses on the design matrix with OLSR, then use PLSR to regress `the rest’ of the responses onto the spectroscopic data. The spectroscopic blocks can be added serially or in parallel, and can be orthogonalised against the preceding matrices. In the end, the results are combined into a single OLS regression. LS-PLS has several advantages: It gives loadings that are easier to interpret It is independent of scaling of the different data matrices It is simple to understand and implement It is easily extended to more complex data situations It gives information about how much each matrix contributes when added to the model In this presentation we describe and illustrate LS-PLS, and compare it with the approach of using a single PLSR on the combined data matrices.

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