Multiway covariates regression models

An abundance of methods exist to regress a y variable on a set of x variabl es collected in a matrix X. In the chemical sciences a growing number of pr oblems translate into arrays of measurements X and Y, where X and Y are thr ee-way arrays or multiway arrays. In this paper a general model is describe d for regressing such a multiway Y on a multiway X, while taking into accou nt three-way structures in X and Y. A global least squares optimization pro blem is formulated to estimate the parameters of the model. The model is de scribed and illustrated with a real industrial example from batch process o peration. An algorithm is given in an appendix. Copyright (C) 1999 John Wil ey & Sons, Ltd.