Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-08T13:49:11.332Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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 Unpublished doctoral dissertation, University of Amsterdam, 1958.Google Scholar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

Barlow, R. E., Bartholomew, D. J., Bremner, J. M., & Brunk, H. D. Statistical inference under order restrictions, 1972, New York: Wiley.Google Scholar
Bradley, R. A., Katti, S. K., & Coons, I. J. Optimal scaling for ordered categories. Psychometrika, 1962, 27, 355–374.CrossRefGoogle Scholar
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