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 © 1999 John Wiley & Sons, Ltd.

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