Incorporating interactions in multi‐block sequential and orthogonalised partial least squares regression

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.     

The potential of Raman spectroscopy for characterisation of the fatty acid unsaturation of salmon

Raman spectroscopy has been evaluated for characterisation of the degree of fatty acid unsaturation (iodine value) of salmon (Salmo salar). The Norwegian Quality Cuts from 50 salmon samples were obtained, and the samples provided an iodine value range of 147.8-170.0 g I₂/100 g fat, reflecting a normal variation of farmed salmon. Raman measurements were performed both on different spots of the intact salmon muscle, on ground salmon samples as well as on oil extracts, and partial least squares regression (PLSR) was utilised for calibration. The oil spectra provided better iodine value predictions than the other data sets, and a correlation coefficient of 0.87 with a root mean square error of cross-validation of 2.5 g I₂/100 g fat was achieved using only one PLSR component. The ground samples provided comparable results, but at least two PLSR components were needed. Higher prediction errors were obtained from Raman spectra of intact salmon muscle, and this may partly be explained by sampling uncertainties in the relation between Raman measurements and reference analysis. All PLSR models obtained were based on chemically sound regression coefficients, and thus information regarding fatty acid unsaturation is readily available from Raman spectra even in systems with high contents of protein and water. The accuracy, the robustness and the low complexity of the PLSR models obtained suggest Raman spectroscopy as a promising method for rapid in-process control of the degree of unsaturation in salmon samples.