Relations between Models for Three-Way Factor Analysis and Multidimensional Scaling

Unconstrained spatial models for analyzing three-way data may be classified by the type of geometric model (distance models, scalar product models), the number of reduced modes (7), the number of spaces and their interrelations (1), to state three of many organizing ways. Number of spaces and their relations refers to a classification of the models into trilinear and quadrilinear cases: a)trilinear models: CANDECOMP and INDSCAL (2) rest on a trilinear model as well as PARAFAC (4) and SUMMAX (9).b)quadrilinear models: Tucker’s Three-Mode Factor Analysis (10), (7) and SUM-MAX in its extended form (9) use a quadrilinear model.