Help on PARAFAC nested

In two-way analysis, many models are nested, which means that an F+1 component model contains the solution to an F-component model plus one additional component.

In for example PCA, it holds that the two first scores of a three-component model are identical to the components of a two-component model. This is of practical importance, since one need only to estimate one additional component to obtain the “next” model.

The multi-way PLS regression model is also nested but for PARAFAC and Tucker no nestedness holds.

Therefore, one has to recalculate the whole model for every number of components.