Abstract
In this paper, we consider detecting unidimensional structure that may be involved in a matrix representing asymmetric relationships among a set of objects. For this purpose, we focus on the procedure of asymmmetric MDS based on a model and the two procedures based on matrix decomposition. With a brief review for each procedure, we state conditions or theorems under which such a structure is derived from the data matrix. Using brand switching data, we provide illustrative examples for the arguments.
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References
BOCK, R.D. and JONES, L.V. (1968): The Measurement and Prediction of Judgment and Choice. San Francisco: Holden-Day.
BOVE,G. and CRITCHLEY,F.(1992): Metric multidimensional scaling for asymmetric proximities when the asymmetry is one-dimensional. In R.Steyer, K.F.Wender and K.F.Wida-man (1992), Proceedings of the 7th European Meeting of the Psychometric Society,Gustav Fischer Verlag.
DESARBO,W.S. and DE SOETE,G. (1984): On the use of hierarchical clustering for the analysis of nonsymmetric proximities. The Journal of Consumer Research, 11, 601–610.
ESCOUFIER,Y. and GRORUD,A. (1980): Analyse factorielle des matrices carrees non-symétriques. In Diday, E. (Eds.) Data Analysis and Informatics, 263–276, New York: North Holland.
FERLIGOJ,A. and BATAGELJ,V. (1983): Some types of clustering with relational constraints. Psychometrika, 48, 541–552.
GOWER,J.C. (1977): The analysis of asymmetry and orthogonality. In J.R.Barra et.al.(ed.), Recent Developments in Statistics, 109–123, North-Holland.
OKADA,A. and IMAIZUMI,T. (1987): Nonmetric multidimensional scaling of asymmetric proximities. Behaviormetrika, 21, 81–96.
SAITO,T. (1991): Analysis of asymmetric proximity matrix by a model of distance and additive terms. Behaviormetrika, 29, 45–60.
SAITO,T. (1994): Psychological scaling of the asymmetry observed in comparative judgement. British Jornal of Mathematical and Statistical Psychology, 47, 4162.
SAITO,T.(1997): Line structure derived from decomposition of asymmetric matrix. Journal of the Japanese Society of Computer Statistics, 10–1, 6–16, 1997.
SAITO,T. (1998): Typical patterns inherent in asymmetric data matrices; Valdes Research Paper, Series E, No. 2, 1–18.
WEEKS,D.G. and BENTLER,P.M. (1982): Restricted multidimensional scaling model for nonsymmetric proximities. Psychometrika, 47, 201–208.
Zielman,B. and Heiser,W.J. (1993): Analysis of asymmetry by a slide vector model. Psychometrika, 58, 101-114.
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Saito, T. (2000). Unidimensional Structure Detected by Analysis of an Asymmetric Data Matrix. In: Gaul, W., Opitz, O., Schader, M. (eds) Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58250-9_28
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DOI: https://doi.org/10.1007/978-3-642-58250-9_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67731-4
Online ISBN: 978-3-642-58250-9
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