First Steps

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


The basic ideas of MDS are introduced doing MDS by hand. Then, MDS is done using statistical software. The goodness of the MDS configuration is evaluated by correlating its distances with the data. Unfolding is introduced with a small example.


MDS Iteration Proximities Dimensional interpretation Goodness of fit Unfolding 


  1. De Leeuw, J., & Mair, P. (2009). Multidimensional scaling using majorization: SMACOF in R. Journal of Statistical Software, 31(3), 1–30.
  2. R Development Core Team. (2017). R: A language and environment for statistical computing [Manual]. Vienna, Austria.

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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