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.