Skip to main content
SpringerLink
Log in

Variants of Different MDS Models

  • Chapter
  • First Online:
Applied Multidimensional Scaling

Part of the book series: SpringerBriefs in Statistics ((BRIEFSSTATIST))

  • 3534 Accesses

Abstract

Various form of MDS are discussed: Ordinal MDS, metric MDS, MDS with different distance functions, MDS for more than one proximity value per distance, MDS for asymmetric proximities, individual differences MDS models, and unfolding.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    The distance of a point \(i\) from the origin in Indscal’s subject space represents the goodness of the Indscal solution for person \(i\). Figure 5.5 therefore exhibits that, for example, the data of person 1 are only relatively poorly explained by the Indscal solution, while the opposite is true for persons 10, 7, or 11.

  2. 2.

    This program is included in the NewMDSX package.

  3. 3.

    Note also that if the number of points is small and the dimensionality is high (e.g., if \(n=5\) and \(m=3\)), the model has many free parameters which help to generate a good model fit. For theory construction, such special cases are usually of little interest.

  4. 4.

    Such data express the extent to which \(i\) dominates \(j\) in some sense. For example, dominance could mean “X is better than Y by x units”, “I would vote for A rather than for B”, or “I agree most with X”.

  5. 5.

    Just like folding an umbrella, or like picking up a handkerchief at this point.

References

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

    Google Scholar 

  • Borg, I., & Lingoes, J. C. (1978). What weights should weights have in individual differences scaling? Quality and Quantity, 12, 223–237.

    Google Scholar 

  • Borg, I., & Staufenbiel, T. (2007). Theorien und Methoden der Skalierung (4th ed.). Bern: Huber.

    Google Scholar 

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

    Google Scholar 

  • Carroll, J. D. (1980). Models and methods for multidimensional analysis of preferential choice or other dominance data. In E. D. Lantermann& H. Feger (Eds.), Similarity and choice. Bern: Huber.

    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, 283–320.

    Google Scholar 

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

    Google Scholar 

  • Kruskal, J. B., & Wish, M. (1978). Multidimensional scaling. Beverly Hills, CA: Sage.

    Google Scholar 

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

    Google Scholar 

  • Schönemann, P. H. (1994). Measurement: The reasonable ineffectiveness of mathematics in the social sciences. In I. Borg & P. P. Mohler (Eds.), Trends and perspectives in empirical social research (pp. 149–160). Berlin: De Gruyter.

    Google Scholar 

  • Schönemann, P. H., & Borg, I. (1983). Grundlagen der metrischen mehrdimensionalen Skalierme-thoden. In H. Feger & J. Bredenkamp (Eds.), Enzyklopädie der Psychologie: Messen und Testen (pp. 257–345). Göttingen: Hogrefe.

    Google Scholar 

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

    Google Scholar 

  • Tversky, A. (1977). Features of similarity. Psychological Review, 84, 327–352.

    Google Scholar 

  • Wish, M. (1971). Individual differences in perceptions and preferences among nations. In C. W. King & D. Tigert (Eds.), Attitude research reaches new heights (pp. 312–328). Chicago: American Marketing Association.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Zeppelin University, Friedrichshafen, Germany

    Ingwer Borg

  2. Econometric Institute, Erasmus University Rotterdam, Rotterdam, PA, The Netherlands

    Patrick J.F. Groenen

  3. Institute for Statistics and Mathematics, Vienna University of Economics and Business, Vienna, Austria

    Patrick Mair

Authors
  1. Ingwer Borg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrick J.F. Groenen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Patrick Mair
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ingwer Borg .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 The Author(s)

About this chapter

Cite this chapter

Borg, I., Groenen, P.J., Mair, P. (2013). Variants of Different MDS Models. In: Applied Multidimensional Scaling. SpringerBriefs in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31848-1_5

Download citation

Publish with us

Policies and ethics

Search

Navigation