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InsightsNow R&D: Adding new dimensions to regression analysis
Senior Mathematician Dave Plaehn and President and CEO Dave Lundahl have written an article describing a new technique for that expands on a current method of relating multiple sets of data within one model. They illustrate the technique by using both consumer and product profiles to model multiple response variables in a unified framework. Their work is an improvement on a similar technique they presented at the 2006 Sensometrics conference in Norway. The article, "Regression with multiple regressor arrays," appeared in Volume 21 of the Journal of Chemometrics (2007).
ABSTRACT:
Extension of standard regression to the case of multiple regressor arrays is given via the Kronecker product. The method is illustrated using ordinary least squares regression (OLS) as well as the latent variable (LV) methods principal component regression (PCR) and partial least squares regression (PLS). Denoting the method applied to PLS as mrPLS, the latter was shown to explain as much or more variance for the first LV relative to the comparable L-partial least squares regression (L-PLS) model. The same relationship holds when mrPLS is compared to PLS or n-way partial least squares (N-PLS) and the response array is 2-way or 3-way, respectively, where the regressor array corresponding to the first mode of the response array is 2-way and the second mode regressor array is an identity matrix. In a comparison with N-PLS using fragrance data, mrPLS proved superior in a validation sense when model selection was used. Though the focus is on 2-way regressor arrays, the method can be applied to n-way regressors via N-PLS. Copyright © 2007 John Wiley & Sons, Ltd.
Electronic copies of the article are available through the publisher's website.