Cross-validation of multiway component models

Abstract

Two cross-validation methods are presented for multiway component models. They are used for choosing the numbers of components to use in Tucker3 models describing three-way data. The approach is general and can easily be adapted to other three-way and multiway models. A model is estimated after leaving out a small part of the multiway data array. The predictive residual error sum of squares (PRESS) is calculated for the eliminated part of the data by comparing the model values with the actual data. PRESS of the entire data set can be calculated like this sequentially. The methods are the leave-bar-out cross-validation method, which leaves out data slices in all modes, and the EM cross-validation method, which handles eliminated data as missing values. A method to calculate the statistical significance of the PRESS reduction for an additional component, the so called W-statistic, is provided for Tucker3 models. A strategy is proposed to search along an efficient path, to reduce computation time, since the number of feasible models as a function of the total number of components summed over the modes increases fast. Copyright © 1999 John Wiley & Sons, Ltd.