, Volume 49, Issue 3, pp 391–402

Upper bounds for Kruskal's stress

  • Jan De Leeuw
  • Ineke Stoop

DOI: 10.1007/BF02306028

Cite this article as:
De Leeuw, J. & Stoop, I. Psychometrika (1984) 49: 391. doi:10.1007/BF02306028


In this paper the relationships between the two formulas for stress proposed by Kruskal in 1964 are studied. It is shown that stress formula one has a system of nontrivial upper bounds. It seems likely that minimization of this loss function will be liable to produce solutions for which this upper bound is small. These are regularly shaped configurations. Even though stress formula two yields less equivocal results, it seems to be expected that minimization of this loss function will tend to produce configurations in which the points are clumped. These results give no clue as to which of the two loss functions is to be preferred.

Key words

nonmetric scaling multidimensional scaling distance geometry 

Copyright information

© The Psychometric Society 1984

Authors and Affiliations

  • Jan De Leeuw
    • 1
  • Ineke Stoop
    • 1
  1. 1.Leiden UniversityThe Netherlands
  2. 2.Department of DatatheoryFSW/RULLeidenThe Netherlands