, Volume 42, Issue 1, pp 7–67

Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features

  • Yoshio Takane
  • Forrest W. Young
  • Jan de Leeuw

DOI: 10.1007/BF02293745

Cite this article as:
Takane, Y., Young, F.W. & de Leeuw, J. Psychometrika (1977) 42: 7. doi:10.1007/BF02293745


A new procedure is discussed which fits either the weighted or simple Euclidian model to data that may (a) be defined at either the nominal, ordinal, interval or ratio levels of measurement; (b) have missing observations; (c) be symmetric or asymmetric; (d) be conditional or unconditional; (e) be replicated or unreplicated; and (f) be continuous or discrete. Various special cases of the procedure include the most commonly used individual differences multidimensional scaling models, the familiar nonmetric multidimensional scaling model, and several other previously undiscussed variants.

The procedure optimizes the fit of the model directly to the data (not to scalar products determined from the data) by an alternating least squares procedure which is convergent, very quick, and relatively free from local minimum problems.

The procedure is evaluated via both Monte Carlo and empirical data. It is found to be robust in the face of measurement error, capable of recovering the true underlying configuration in the Monte Carlo situation, and capable of obtaining structures equivalent to those obtained by other less general procedures in the empirical situation.

Key words

Euclidian model INDSCAL measurement similarities data analysis similarities data quantification successive block algorithm 

Copyright information

© Psychometric Society 1977

Authors and Affiliations

  • Yoshio Takane
    • 2
  • Forrest W. Young
    • 2
  • Jan de Leeuw
    • 1
  1. 1.University of LeidenThe Netherlands
  2. 2.Psychometric LabUniversity of North CarolinaChapel Hill

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