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The Fit of MDS and Unfolding Solutions

  • Ingwer Borg
  • Patrick J. F. Groenen
  • Patrick Mair
Chapter
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Abstract

Ways to assess the goodness of an MDS solution are discussed. The Stress measure is defined as an index that aggregates representation errors. Criteria for evaluating Stress are presented. Stress per Point (SPP) is defined as a way to assess the fit of single points.

Keywords

Representation error Stress Disparity Shepard diagram Stress-1 Stress norm SPP 

References

  1. Borg, I., & Groenen, P. J. F. (2005). Modern Multidimensional Scaling (2nd ed.). New York: Springer.zbMATHGoogle Scholar
  2. De Leeuw, J., & Meulman, J. (1986). A special jackknife for multidimensional scaling. Journal of Classification, 3, 97–112.CrossRefGoogle Scholar
  3. Jacoby, W. G., & Armstrong, D. A. (2014). Bootstrap confidence regions for multidimensional scaling solutions. American Journal of Political Science, 58, 264–278.CrossRefGoogle Scholar
  4. Mair, P., Borg, I., & Rusch, T. (2016). Goodness-of-fit assessment in multidimensional scaling and unfolding. Multivariate Behavioral Research, 51, 772–789.Google Scholar
  5. Spence, I., & Graef, J. (1974). The determination of the underlying dimensionality of an empirically obtained matrix of proximities. Multivariate Behavioral Research, 9, 331–341.CrossRefGoogle Scholar
  6. Spence, I., & Ogilvie, J. C. (1973). A table of expected stress values for random rankings in nonmetric multidimensional scaling. Multivariate Behavioral Research, 8, 511–517.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Ingwer Borg
    • 1
  • Patrick J. F. Groenen
    • 2
  • Patrick Mair
    • 3
  1. 1.Westfälische Wilhelms-UniversitätMuensterGermany
  2. 2.Econometric InstituteErasmus University RotterdamRotterdamThe Netherlands
  3. 3.Department of PsychologyHarvard UniversityCambridgeUSA

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