Multiway covariates regression models

An abundance of methods exist to regress a y variable on a set of x variables collected in a matrix X. In the chemical sciences a growing number of problems translate into arrays of measurements X and Y, where X and Y are three-way arrays or multiway arrays. In this paper a general model is described for regressing such a multiway Y on a multiway X, while taking into account three-way structures in X and Y. A global least squares optimization problem is formulated to estimate the parameters of the model. The model is described and illustrated with a real industrial example from batch process operation. An algorithm is given in an appendix. Copyright (C) 1999 John Wiley & Sons, Ltd.