Shifted factor analysis—Part III: N‐way generalization and application

Abstract The ‘quasi‐ALS’ algorithm for shifted factor estimation is generalized to three‐way and n ‐way models. We consider the case in which mode A is the only shifted sequential mode, mode B determines shifts, and modes above B simply reweight the factors. The algorithm is studied using error‐free and fallible synthetic data. In addition, a four‐way chromatographic data set previously analyzed by Bro et al. ( J. Chemometrics 1999; 13: 295–309) is reanalyzed and (two or) three out of four factors are recovered. The reason for the incomplete success may be factor shape changes combined with the lack of distinct shift patterns for two of the factors. The shifted factor model is compared with Parafac2 from both theoretical and practical points of view. Copyright © 2003 John Wiley & Sons, Ltd.