Three-Mode Factor Analysis (3MFA) and PARAFAC are methods to describe
three-way data. Both methods employ models with components for the thr
ee modes of a three-way array; the 3MFA model also uses a three-way co
re array for linking all components to each other. The use of the core
array makes the 3MFA model more general than the PARAFAC model (thus
allowing a better fit), but also more complicated. Moreover, in the 3M
FA model the components are not uniquely determined, and it seems hard
to choose among all Possible solutions. A particularly interesting fe
ature of the PARAFAC model is that it does give unique components. The
present paper introduces a class of 3MFA models in between 3MFA and P
ARAFAC that share the good properties of the 3MFA model and the PARAFA
C model: They fit (almost) as well as the 3MFA model, they are relativ
ely simple and they have the same uniqueness properties as the PARAFAC
model.