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The MDS Models: Basics

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Abstract

Fundamental concepts of MDS models are discussed. Since MDS includes a family of different models and various terms are used to describe these models as well as their corresponding elements, I explain these models and their associated terms using more understandable language.

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References

  • Borg, I. (1977). Some basic concepts of facet theory. In J. C. Lingoes (Ed.), Progressively complex linear transformations for finding geometric similarities among data structures (pp. 65–102). Mimeo.

    Google Scholar 

  • Borg, I., & Groenen, P. J. F. (2005). Modern multidimensional scaling: Theory and applications (2nd ed.). New York, NY: Springer.

    MATH  Google Scholar 

  • Bozdogan, H. (1987). Model selection and Akaike’s information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52(3), 345–370.

    Article  MathSciNet  Google Scholar 

  • Carroll, J. D. (1972). Individual differences and multidimensional scaling. In R. N. Shepard, A. K. Romney, & S. Nerlove (Eds.), Multidimensional scaling: Theory and applications in the behavioral sciences (Vol. I). New York, NY: Academic Press.

    Google Scholar 

  • 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, 238–319.

    Article  Google Scholar 

  • Carroll, J. D., & Chang, J. J. (1972, March). IDIOSCAL (Individual Differences in Orientation Scaling): A generalization of INDSCAL allowing idosyncratic reference systems as well as analytic approximation to INDSCAL. Paper presented at the The Psychometric Society, Princeton, NJ.

    Google Scholar 

  • Carroll, J. D., & Wish, M. (1973). Models and methods for three-way multidimensional scaling. In R. C. Atkinson, D. H. Krantz, R. D. Luce, & P. Suppes (Eds.), Contemporary developments in mathematical psychology. San Francisco, CA: W. H. Freeman.

    Google Scholar 

  • Coombs, C. H. (1950). Psychological scaling without a unit of measurement. Psychological Review, 57(3), 145–158.

    Article  Google Scholar 

  • Coombs, C. H. (1964). A theory of data. New York, NY: Wiley.

    Google Scholar 

  • Cox, T. F., & Cox, M. A. A. (2001). Multidimensional scaling (2nd ed.). Boca Raton, FL: Chapman & Hall/CRC.

    MATH  Google Scholar 

  • Coxon, A. P. M. (1982). The user’s guide to multidimensional scaling. London: Heinemann Educational Books.

    Google Scholar 

  • Coxon, A. P. M., Brier, A. P., & Hawkins, P. K. (2005). The New MDSX program series, version 5. Edinburgh: London: New MDSX Project.

    Google Scholar 

  • Davison, M. L. (1983). Multidimensional scaling. New York: Wiley.

    MATH  Google Scholar 

  • Guttman, L. (1968). A general non-metric technique for finding the smallest co-ordinate space for a configuration of points. Psychometrika, 33, 469–506.

    Article  Google Scholar 

  • Kruskal, J. B. (1964). Nonmetric scaling: A numerical method. Psychometrika, 29, 28–42.

    MathSciNet  MATH  Google Scholar 

  • Kuhfeld, W., Young, F. W., & Kent, D. P. (1987). New developments in psychometric and market research procedures. SUGI, 12, 1101–1106.

    Google Scholar 

  • Lingoes, J. C. (1977). Progressively complex linear transformations for finding geometric similarities among data structures. Mimeo.

    Google Scholar 

  • Lingoes, J. C., & Borg, I. A. (1978). A direct approach to individual differences scaling using increasingly complex transformations. Psychometrika, 43, 491–519.

    Article  MathSciNet  Google Scholar 

  • MacCallum, R. C. (1977). Effects of conditionality on INOSCALand ALSCALweights. Psychometrika, 42, 297–305.

    Article  Google Scholar 

  • MacKay, D. B. (1989). Probabilistic multidimensional scaling: An anisotropic model for distance judgments. Journal of Mathematical Psychology, 33, 187–205.

    Article  MathSciNet  Google Scholar 

  • MacKay, D. B. (2007). Internal multidimensional unfolding about a single-idea--A probabilistic solution. Journal of Mathematical Psychology, 51(5), 305–318.

    Article  MathSciNet  Google Scholar 

  • MacKay, D. B., Easley, R. F., & Zinnes, J. L. (1995). A single ideal point model for market structure analysis. Journal of Marketing Research, XXXII, 433–443.

    Article  Google Scholar 

  • MacKay, D. B., & Zinnes, J. (2014). PROSCAL professional: A program for probabilistic scaling: www.proscal.com.

  • MacKay, D. B., & Zinnes, J. L. (1986). A probabilistic model for the multidimensional scaling of proximity and preference data. Marketing Science, 5, 325–344.

    Article  Google Scholar 

  • Ramsay, J. O. (1977). Maximum likelihood estimation in multidimensional scaling. Psychometrika, 42, 241–266.

    Article  Google Scholar 

  • Sammon, J. W. (1969). A nonlinear mapping for data structure analysis. IEEE Transportation & Computing, 18, 401–409.

    Article  Google Scholar 

  • SAS Institute. (2010). SAS/STAT(R) 9.22 user’s guide. Cary, NC: SAS Institute Inc..

    Google Scholar 

  • Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2), 461–464.

    Article  MathSciNet  Google Scholar 

  • Shepard, L. (1962). The analysis of proximities: Multidimensional scaling with an unknown distance. I and II. Psychometrika, 27, 323–355.

    Article  MathSciNet  Google Scholar 

  • Inc, S. P. S. S. (2007). SPSS Statistics 17.0: Command syntax reference. Chicago, IL: SPSS Inc..

    Google Scholar 

  • Takane, Y. (1978). A maximum likelihood method for nonmetric multidimensional scaling: I The case in which all empirical pairwise orderings are independent-theory. Japanese Psychological Research, 20, 7–17.

    Article  Google Scholar 

  • Takane, Y., & Carroll, J. D. (1981). Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities. Psychometrika, 46, 389–405.

    Article  MathSciNet  Google Scholar 

  • Thurstone, L. L. (1928). Attitudes can be measured. American Journal of Sociology, 33, 529–554.

    Article  Google Scholar 

  • Torgerson, W. S. (1952). Multidimensinoal scaling: I. Theory and method. Psychometrika, 17(4), 401–419.

    Article  MathSciNet  Google Scholar 

  • Tucker, L. R. (1960). Intra-individual and inter-individual multidimensionality. In H. Gulliksen & S. Messick (Eds.), Psychological scaling: Theory and applications (pp. 155–167). New York: Wiley.

    Google Scholar 

  • Tucker, L. R. (1972). Relations between multidimensional scaling and three-mode factor analysis. Psychometrika, 37, 3–27.

    Article  MathSciNet  Google Scholar 

  • Tversky, A., & Krantz, D. H. (1970). Dimensional representation and the metric structure of similarity data. Journal of Mathematical Psychology, 7, 572–596.

    Article  MathSciNet  Google Scholar 

  • Young, G., & Householder, A. S. (1941). Note on multidimensional psychophysical analysis. Psychometrika, 6, 331–333.

    Article  Google Scholar 

  • Zinnes, J. L., & MacKay, D. B. (1983). Probabilistic multidimensional scaling: Complete and incomplete data. Psychometrika, 48, 24–48.

    Article  Google Scholar 

  • Zinnes, J. L., & MacKay, D. B. (1992). A probabilistic multidimensional scaling approach: Properties and procedures. In F. G. Ashby (Ed.), Multidimensional models of perception and cognition (pp. 35–60). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

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Authors and Affiliations

  1. Department of Education Science and Professional Program, University of Missouri-St. Louis, St. Louis, MO, USA

    Cody S. Ding

  2. Center for Neurodynamics, University of Missouri-St. Louis, St. Louis, MO, USA

    Cody S. Ding

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  1. Cody S. Ding
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Ding, C.S. (2018). The MDS Models: Basics. In: Fundamentals of Applied Multidimensional Scaling for Educational and Psychological Research. Springer, Cham. https://doi.org/10.1007/978-3-319-78172-3_3

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