Abstract
This paper is concerned with methods of three-way two-mode multidimensional scaling which were developed for the joint analysis of a number of promities matrices. The classification of these methods into trilinear and quadrilinear models (Kruskal (1983)) is outlined, and it is shown, that a number of specific properties and interpretations are associated with this classification the methods within each class have in common. Finally, relationships of the methods within and between the two model classes are outlined.
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References
CARROLL, J.D. and CHANG, J.J. (1970): Analysis of individual differences in multidimensional scaling via an N-way generalization of Eckart-Young decomposition. Psychometrika, 35, 283–319.
KROLAK-SCHWERDT, S. (1991): Modelle der dreimodalen Faktorenanalyse: formale Eigenschaften, theoretische Zusammenhänge und ihre Implikationen für das Konzept individueller Differenzen. Psychologische Beiträge, 133, 314–346.
KROLAK-SCHWERDT, S. (in press): A three-way multidimensional scaling approach to the analysis of judgments about persons. Studies in Classification, Data Analysis, and Knowledge Organisation, Vol. 27 Classification: The ubigitous challenge. Springer, Berlin.
KROONENBERG, P.M. (1983): Three-mode principal component analysis. DSWO Press, Leiden.
KROONENBERG, P.M. (1994): The TUCKALS line. A suite of programs for three-way data analysis. Computational statistics and data analysis, 18, 73–96.
KROONENBERG, P.M. and DE LEEUW, J. (1980): Principal component analysis of three-mode data by means of alternating least squares algorithms. Psychometrika, 45, 69–97.
KRUSKAL, J.B. (1976): More factors than subjects, tests and treatments: An indeterminacy theorem for canonical decomposition and individual differences scaling. Psychometrika, 41, 281–293.
KRUSKAL, J.B. (1983): Multilinear methods. In R. Gnanadesikan (Ed.): Proceedings of Symposia in Applied Mathematics (Vol. 28, pp. 75–104). Providence: American Mathematical Society.
ORLIK, P. (1980): Das SUMMAX-Modell der dreimodalen Faktorenanalyse mit interpretierbarer Kernmatrix. Archiv für Psychologic, 133, 189–218.
TORGERSON, W.S. (1958): Theory and methods of scaling. Wiley, New York.
TUCKER, L.R. (1966): Some mathematical notes on three-mode factor analysis. Psychometrika, 31, 279–311.
TUCKER, L.R. (1972): Relations between multidimensional scaling and three-mode factor analysis. Psychometrika, 37, 3–27.
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Krolak-Schwerdt, S. (2005). Three-Way Multidimensional Scaling: Formal Properties and Relationships Between Scaling Methods. In: Baier, D., Decker, R., Schmidt-Thieme, L. (eds) Data Analysis and Decision Support. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28397-8_10
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DOI: https://doi.org/10.1007/3-540-28397-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26007-3
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