Abstract
The purpose of the present study is to introduce a model and the associated nonmetric algorithm of multidimensional scaling for analyzing one-mode two-way (object × object) asymmetric proximities. In the model each object is represented as a point in a multidimensional Euclidean space, and a point, called the dominance point, is also embedded in the same multidimensional Euclidean space. The dominance point governs the asymmetry in the proximity relationships among objects, and represents the whole one-mode two-way asymmetric proximities dealt with in the analysis. An application to car switching data is presented.
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References
BORG, I. and GROENEN, P.J.F. (2005): Modern Multidimensional Scaling. Springer, New York.
CARROLL, J.D. and ARABIE, P. (1980): Multidimensional Scaling. In: M.R. Rosenzweig and L.W. Porter (Eds.): Annual Review of Psychology, 31. Annual Reviews, Palo Alto, 607–649.
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.
COOMBS, C.H. (1964): A Theory of Data. John Wiley, New York.
CHINO, N., GROROUD, A. and YOSHINO, R. (1996): Complex Analysis of Two-Mode Three-Way Asymmetric Relational Data. Proceedings of the Fifth Conference of the International Federation of Classification Societies. 83–86.
DeSARBO W.S., JOHNSON, M.D., MANRAI, A.K., MANRAI, L.A. and EDWARD, E.A. (1992): TSCALE: A New Multidimensional Scaling Procedure Based on Tversky’s Contrast Model. Psychometrika, 57, 43–69.
HARSHMAN, R.A., GREEN, P.E., WIND, Y. and LUNDY, M.E. (1982): A Model for the Analysis of Asymmetric Data in Marketing Research. Marketing Science, 1, 205–242.
KRUSKAL, J.B. (1964): Nonmetric Multidimensional Scaling: A Numerical Method. Psychometrika, 29, 115–129.
OKADA, A. (1988): Asymmetric Multidimensional Scaling of Car Switching Data. In: W. Gaul and M. Schader (Eds.): Data, Expert Knowledge and Decisions. Springer, Heidelberg, 279–290.
OKADA, A. and IMAIZUMI, T. (1987): Nonmetric Multidimensional Scaling of Asymmetric Proximities. Behaviormetrika, 21, 81–96.
OKADA, A. and IMAIZUMI, T. (1997): Asymmetric Multidimensional Scaling of Two-mode Three-way Proximities. Journal of Classification, 14, 95–224.
OKADA, A. and IMAIZUMI, T. (2003a): Joint Space Model for Multidimensional Scaling of Asymmetric Proximities. Abstracts of the 27th Annual Conference of the German Classification Society. 134.
OKADA, A. and IMAIZUMI, T. (2003b): Asymmetric Multidimensional Scaling Based on Joint Space Model. Proceedings of the 13th International Meeting and the 68th Annual American Meeting of the Psychometric Society.
OKADA, A. and IMAIZUMI, T. (2004): A Joint Space Model of Asymmetric Multidimensional Scaling. Proceedings of the International Meeting and the 69th Annual American Meeting of the Psychometric Society.
OKADA, A. and IMAIZUMI, T. (2005): Joint Space Model for Multidimensional Scaling of Two-Mode Three-Way Asymmetric Proximities. In: D. Baier and K.-D. Wernecke (Eds.): Innovation in Classification, Data Science, and Information Systems. Springer, Berlin Heidelberg, 371–378.
ZIELMAN, B. (1991): Three-Way Scaling of Asymmetric Proximities. Research Report RR91-01. Department of Data Theory, University of Leiden.
ZIELMAN, B. and HEISER, W.J. (1993): Analysis of Asymmetry by a Slide-Vector. Psychometrika, 58,101–114.
ZIELMAN, B. and HEISER, W.J. (1996): Models for Asymmetric Proximities. British Journal of Mathematical and Statistical Psychology, 49, 127–146.
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Okada, A., Imaizumi, T. (2007). Multidimensional Scaling of Asymmetric Proximities with a Dominance Point. In: Decker, R., Lenz, H.J. (eds) Advances in Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70981-7_35
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DOI: https://doi.org/10.1007/978-3-540-70981-7_35
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