Three case studies illustrating the properties of ordinary and partial least squares regression in different mixture models

Abstract

Mixture designs and corresponding analysis techniques are of considerable importance in food science and industry. Mixture data are generally challenging to model, since the mixture restrictions leads to both exact and near collinearity. Scheffé found an excellent way to eliminate the exact collinearity, by using a certain reparameterization of the ordinary least squares (OLS) regression model. Near collinearities can be eliminated by, for instance, variable selection. Partial least squares (PLS) regression does not assume linearly independent variables and handles both exact and near collinearity by projecting onto a lower dimensional subspace. Lately also variable selection has been combined with PLS regression in order to get more parsimonious models. In the present study, models found by OLS and PLS regression, both combined with variable selection, are compared with regard to interpretation, response optimisation and prediction, for regular mixtures, mixture–process and crossed mixture data. Examples from sausages and hearth bread production are considered.