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Correctness of Kruskal's Algorithms for Monotone Regression with Ties

Published online by Cambridge University Press:  01 January 2025

Jan de Leeuw
Jan de Leeuw*
Affiliation:
University of Leiden
*
Requests for reprints should be sent to Jan de Leeuw, Department of Data Theory, University of Leiden, Wassenaarseweg 80, Leiden, the Netherlands.
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Abstract

Kruskal has proposed two modifications of monotone regression that can be applied if there are ties in nonmetric scaling data. In this note we prove Kruskal's conjecture that his algorithms give the optimal least squares solution of these modified monotone regression problems. We also propose another (third) approach for dealing with ties.

Keywords

monotone regressionoptimal scaling
Type
Notes And Comments
Information
Psychometrika , Volume 42 , Issue 1 , March 1977 , pp. 141 - 144
Copyright
Copyright © 1977 The Psychometric Society

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Footnotes

Comments by Dr. J. B. Kruskal have been most helpful.

References

Reference Note

Van Eeden, C. Testing and estimating ordered parameters of probability distributions. Unpublished doctoral dissertation, University of Amsterdam, 1958.Google Scholar

References

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Hayashi, C. Minimum dimension analysis MDA: One of the methods of multidimensional quantification. Behaviormetrika, 1974, 1, 1–24.CrossRefGoogle Scholar
Kruskal, J. B. Nonmetric multidimensional scaling: A numerical method. Psychometrika, 1964, 29, 115–129.CrossRefGoogle Scholar