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The additive constant problem in multidimensional scaling

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Abstract

The problem of choosing the correct additive constant to convert relative interstimulus distances to absolute interstimulus distances in multidimensional scaling is investigated. An artificial numerical example is constructed, and various trial values of the constant are inserted to demonstrate the effect on the multidimensional map of making a variety of incorrect choices. Finally, a general solution to the problem, suggested by Dr. Ledyard R Tucker, is presented; each of the computational steps in this solution is set down for easy reference.

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Author notes

  1. Samuel J. Messick

    Present address: Menninger Foundation, USA

Authors and Affiliations

  1. Educational Testing Service, USA

    Samuel J. Messick

  2. Yale University, USA

    Robert P. Abelson

Authors
  1. Samuel J. Messick
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  2. Robert P. Abelson
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Additional information

This study was supported in part by Office of Naval Research Contract N6onr-270-20 and by National Science Foundation Grant G-642 to Princeton University.

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Messick, S.J., Abelson, R.P. The additive constant problem in multidimensional scaling. Psychometrika 21, 1–15 (1956). https://doi.org/10.1007/BF02289083

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  • DOI: https://doi.org/10.1007/BF02289083

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