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A New Solution to the Additive Constant Problem in Metric Multidimensional Scaling

Published online by Cambridge University Press:  01 January 2025

Lee G. Cooper
Lee G. Cooper*
Affiliation:
University of California, Los Angeles
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Abstract

A new solution to the additive constant problem in metric multidimensional scaling is developed. This solution determines, for a given dimensionality, the additive constant and the resulting stimulus projections on the dimensions of a Euclidean space which minimize the sum of squares of discrepancies between the formal model for metric multidimensional scaling and the original data. A modification of Fletcher-Powell style functional iteration is used to compute solutions. A scale free index of the goodness of fit is developed to aid in selecting solutions of adequate dimensionality from multiple candidates.

Keywords

Public PolicyOriginal DataEuclidean SpaceFormal ModelStatistical Theory

Information

Type
Original Paper
Information
Psychometrika , Volume 37 , Issue 3 , September 1972, pp. 311 - 322
Copyright
Copyright © 1972 The Psychometric Society

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Footnotes

*

This research is based in part on the author’s Ph.D. dissertation at the University of Illinois at Urbana-Champaign. Computer time was provided by the Campus Computing Network of the University of California, Los Angeles.

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