Abstract
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:
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a)
trilinear models: CANDECOMP and INDSCAL (2) rest on a trilinear model as well as PARAFAC (4) and SUMMAX (9).
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b)
quadrilinear models: Tucker’s Three-Mode Factor Analysis (10), (7) and SUM-MAX in its extended form (9) use a quadrilinear model.
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References
Carroll, J.D. & Arabie, P. (1980). Multidimensional scaling. Annual Review of Psychology,31,607–649.
Carroll, J.D. & Chang, J.J. (1970). Analysis of individual differences in multidimensional scaling via an n-way generalization of’Eckart-Young ‘decomposition Psychometrika,35,283–319.
Carroll, J.D. & Wish, M. (1974). Models and methods for three-way multidimensional scaling. In: Krantz, D.H., Atkinson, R.C., Luce, R.D. & Suppes, P. (Eds.). Contemporary developments in mathematical psychology, Vol. 2,57–105.
Harshman, R.A. (1970). Foundations of the PARAFAC proe-dure: models and conditions for an’explanatory’ multi-modal factor analysis. UCLA Working Papers in Phonetics,16,1–84.
Helm, C.E. (1964). Multidimensional ratio scaling analysis of perceived color relations. Journal of the Optical Society of America,54,256–262.
Krolak-Schwerdt, S. (1989). Modelle der dreimodalen Faktorenanalyse, Ph.D thesis, in preparation, Universität des Saarlandes, F.R.G
Kroonenberg, P.M. (1983). Three-mode principal component analysis. Leiden: DSWO Press.
Kruskal, J.B. (1976). More factors than subjects, tests and treatments: an indeterminacy theorem for canonical ecomposition and individual differences scaling. Psychometrika,41,281–293.
Orlik, P. (1980). Das Summax-Modell der dreimodalen Faktorenanalyse mit interpretierbarer Kernmatrix. Archiv für Psycho-logie,133,189–218.
Tucker, L.R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika,31,279–311.
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© 1989 Springer-Verlag Berlin · Heidelberg
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Krolak-Schwerdt, S., Kohler, A. (1989). Relations between Models for Three-Way Factor Analysis and Multidimensional Scaling. In: Optiz, O. (eds) Conceptual and Numerical Analysis of Data. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75040-3_9
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DOI: https://doi.org/10.1007/978-3-642-75040-3_9
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