On The Relations Among Four Methods of Multidimensional Scaling (original) (raw)
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References
- 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.
Article Google Scholar - Gleason, T.C. (1967). A general model for nonmetric multidimensional scaling. Michigan Mathematical Psychology Program, MMPP 67-3, Ann Arbor, Michigan.
Google Scholar - Gower, J.C. (1966). Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53, 325–338.
Article MathSciNet Google Scholar - Guttman, L. (1946). An approach to quantifying paired comparisons and rank order. Annals of Mathematical Statistics, 17, 144–163.
Article MathSciNet Google Scholar - Guttman, L. (1968). A general nonmetric technique for finding the smallest coordinate space for a configuration of points. Psychometrika, 33, 469–506.
Article Google Scholar - Hayashi, C. (1952). On the prediction of phenomena from qualitative data and the quantification of qualitative data from the mathematico-statistical point of view. Annals of the Institute of Statistical Mathematics, 3, 69–98.
Article Google Scholar - Hayashi, C. (1973). _e_ij gata suryoka to Torgerson-Gower no hoho o megutte (On _e_ij-type quantification method and Torgerson-Gower method). Nihon Tokeigakkaishi (Journal of the Japanese Statistical Society), 3, 41–53.
Google Scholar - Kruskal, J.B. (1964a). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1–29.
Article MathSciNet Google Scholar - Kruskal, J.B. (1964b). Nonmetric multidimensional scaling: a numerical method. Psychometrika, 29, 115–129.
Article MathSciNet Google Scholar - Kruskal, J.B., Young, F.W. & Seery, J. (1973). How to use KYST; Unpublished user’s manual, Bell Laboratories, Murray Hill, N.J.
Google Scholar - de Leeuw, J. (1974). Finding a positive semidefinite matrix of prescribed rank r in a nonlinear differentiable manifold; Technical Report, Bell Laboratories, Murray Hill, N.J.
Google Scholar - de Leeuw, J. (1975). An alternating least squares approach to squared distance scaling; Unpublished manuscript, The University of Leiden, Leiden.
Google Scholar - de Leeuw, J. (1976). Applications of convex analysis to multidimensional scaling; Proceedings of thd European Meeting of Statistics, Grenoble.
Google Scholar - Lingoes, J.C. & Roskam, E.E. (1973). A mathematical and empirical analysis of two multidimensional scaling algorithms. Psychometrika Monograph Supplement 19.
Google Scholar - Okamoto, M. & Toda, J. (1973). Suryokariron 4-rui to shuzahyo bunsekiho (Fourth quantification method and principal coordinate analysis). Nikon Tokeigakkaishi (Journal of the Japanese Statistical Society), 3, 41–53.
Google Scholar - Saito, T., Ogawa, S. & Nojima, E. (1972). Deta kaseki (1): suryoka ni kansuru sogo hokoku (Data analysis I: a summary review article on quantification theory). Soken Kiyo, 2, 23–114.
Google Scholar - Stevens, S.S. (1951). Mathematics, measurement and psychophysics; In S.S. Stevens (ed.). Handbook of experimental psychology. New York: Wiley.
Google Scholar - Takane, Y., Young, F.W. & de Leeuw, J. (1977). Nonmetric individual differences multidimensional scaling: an alternating least squares method with optimal scaling features. Psychometirka, 42, 7–67.
Article Google Scholar - Takeuchi, K. & Yanai, H. (1972). Tahenyyo kaiseki no kiso (Foundations of multivariate analysis); Tokyo: Toyo Keizai Shinpo.
Google Scholar - Togerson, W.S. (1952). Multidimensional scaling: I. Theory and method. Psychometrika, 17, 401–419.
Article MathSciNet Google Scholar - Young, F.W. (1968). TORSCA-9: a FORTRAN IV program for nonmetric multidimensional scaling. Behavioral Science, 13, 343–344.
Article Google Scholar - Young, F.W., de Leeuw, J. & Takane, Y. (1976). Quantifying qualitative data; Psychometric Laboratory Report #49, The University of North Carolina, Chapel Hill, N.C.
Google Scholar - Young, G. & Householder, A.S. (1938). Discussion of a set of points in terms of their mutual distances. Psychometrika, 3, 19–22.
Article Google Scholar