Skip to main content

Historical Review

  • Chapter
  • First Online:
  • 776 Accesses

Abstract

Briefly discuss the key development of MDS models over time. Explain some new or possible applications of MDS analysis. Strengths and limitations are also discussed.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Akaike, H. (1973). Information theory as an extension of the maximum likelihood principle. In B. N. Petrov & F. Csaki (Eds.), Second international symposium on information theory (pp. 267–281). Budapest: Akademiai Kiado.

    Google Scholar 

  • Attneave, F. (1950). Dimensions of similarity. American Journal of Psychology, 63, 516–536.

    Article  Google Scholar 

  • Bloxom, B. (1968). Individual differences in multidimensional scaling models. Research Bulletin, 68–45. Princeton: Educational Testing Service.

    Google Scholar 

  • Busing, F. M. T. A., & de Rooij, M. (2009). Unfolding incomplete data: Guidelines for unfolding row-conditional rank order data with random missings. Journal of Classification, 26, 329–360.

    Article  MathSciNet  Google Scholar 

  • Busing, F. M. T. A., Groenen, P. J. K., & Heiser, W. J. (2005). Avoiding degeneracy in multidimensional unfolding by penalizing on the coefficient of variation. Psychometrika, 70(1), 71–98.

    Article  MathSciNet  Google Scholar 

  • Busing, F. M. T. A., Heiser, W. J., & Cleaver, G. (2010). Restricted unfolding: Preference analysis with optimal transformations of preferences and attributes. Food Quality and Preference, 21(1), 82–92.

    Article  Google Scholar 

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

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

    Google Scholar 

  • Davison, M. L., Gasser, M., & Ding, S. (1996). Identifying major profile patterns in a population: An exploratory study of WAIS and GATB patterns. Psychological Assessment, 8, 26–31.

    Article  Google Scholar 

  • DeSarbo, W. S., Howard, D., & Jedidi, K. (1991). Multiclus: A new method for simultaneously performing multidimensional scaling and cluster analysis. Psychometrika, 56, 121–136.

    Article  Google Scholar 

  • Ding, C. S. (2001). Profile analysis: Multidimensional scaling approach. Practical Assessment, Research, and Evaluation, 7(16).

    Google Scholar 

  • Ding, C. S. (2007). Studying growth heterogeneity with multidimensional scaling profile analysis. International Journal of Behavioral Development, 31(4), 347–356.

    Article  Google Scholar 

  • Ding, C. S., & Davison, M. L. (2010). Multidimensional scaling analysis using Akaike’s information criterion. Educational and Psychological Measurement, 70(2), 199–214.

    Google Scholar 

  • Ding, C. S., Davison, M. L., & Petersen, A. C. (2005). Multidimensional scaling analysis of growth and change. Journal of Educational Measurement, 42, 171–191.

    Article  Google Scholar 

  • Horan, C. B. (1969). Multidimensional scaling: Combining observations when individuals have different perceptual structure. Psychometrika, 34, 139–165.

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • MacKay, D. B., & Zinnes, J. (2005). PROSCAL professional: A program for probabilistic scaling: www.proscal.com.

  • McGee, V. C. (1968). Multidimensional scaling of n sets of similarity measures: A nonmetric scaling. Multivariate Behavioral Research, 3, 233–248.

    Article  Google Scholar 

  • Messick, S. J., & Abelson, R. P. (1956). The additive constant problem in multidimensional scaling. Psychometrika, 21, 1–15.

    Article  Google Scholar 

  • Muthen, B. (2001). Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class/latent growth modeling. In L. M. Collins & A. Sayer (Eds.), New methods for the analysis of change (pp. 291–322). Washington, DC: American Psychological Association.

    Google Scholar 

  • Nagin, D. (1999). Analyzing developmental trajectories: A semi-parametric, group-based approach. Psychological Methods, 4, 139–177.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ramsay, J. O. (1991). MULTISCALE manual (extended version). Montreal: McGill University.

    Google Scholar 

  • Schiffman, S. S., Reynolds, M. L., & Young, F. W. (1981). Introduction to multidimensional scaling: Theory, methods and applications. New York: Academic Press.

    MATH  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 

  • Shepard, R. N., Romney, A. K., & Nerlove, S. B. (Eds.). (1972). Multidimensional scaling: Theory (Vol. 1). New York: Seminar Press.

    Google Scholar 

  • Takane, Y. (1978a). A maximum likelihood method for nonmetric multidimensional scaling: I the case in which all empirical pairwise orderings are independent-evaluation. Japanese Psychological Research, 20, 105–114.

    Article  Google Scholar 

  • Takane, Y. (1978b). 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 

  • Takane, Y., Young, F. W., & De Leeuw, J. (1977). Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features. Psychometrika, 42, 7–67.

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Treat, T. A., McFall, R. M., Viken, R. J., Nosofsky, R. M., MacKay, D. B., & Kruschke, J. K. (2002). Assessing clinically relevant perceptual organization with multidimensional scaling techniques. Psychological Assessment, 14, 239–252.

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Tucker, L. R., & Messick, S. J. (1963). An individual differences model for multidimensional scaling. Psychometrika, 28, 333–367.

    Article  Google Scholar 

  • Vera, J., Macias, R., & Heiser, W. J. (2009). A latent class multidimensional scaling model for two-way one-mode continuous rating dissimilarity data. Psychometrika, 2009, 297–315.

    Article  MathSciNet  Google Scholar 

  • Young, F. W. (1987). Multidimensional scaling: History, theory, and applications. In R. M. Hamer (Ed.), Multidimensional scaling: History, theory, and applications. Hillsdale: Lawrence Erlbaum Associates.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ding, C.S. (2018). Historical Review. In: Fundamentals of Applied Multidimensional Scaling for Educational and Psychological Research. Springer, Cham. https://doi.org/10.1007/978-3-319-78172-3_14

Download citation

Publish with us

Policies and ethics