Multiway multiblock component and covariates regression models

In this paper the general theory of multiway multiblock component and covar iates regression models is explained. Unlike in existing methods such as mu ltiblock PLS and multiblock PCA, in the new proposed method a different num ber of components can be selected for each block. Furthermore, the method c an be generalized to incorporate multiway blocks to which any multiway mode l can be applied. The method is a direct extension of principal covariates regression and therefore works in a simultaneous fashion in which a clearly defined objective criterion is minimized. It can be tuned to fulfil the re quirements of the user. Algorithms to calculate the components will be pres ented. The method will be illustrated with two three-block examples and com pared to existing approaches. The first example is with two-way data and th e second example is with a three-way array. It will be shown that predictio ns are as good as with the existing methods, but because for most blocks fe wer components are required, diagnostic properties of the method are improv ed. Copyright (C) 2000 John Wiley & Sons, Ltd.