Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-08T11:06:19.123Z Has data issue: false hasContentIssue false
  • English
  • Français

A Generalization of Verhelst's Solution for a Constrained Regression Problem in Alscal and Related MDS-Algorithms

Published online by Cambridge University Press:  01 January 2025

Jos M. F. ten Berge
Jos M. F. ten Berge*
Affiliation:
University of Groningen
*
Reprint requests should be addressed to Jos ten Berge, Subfakulteit Psychologie R.U. Groningen, Grote Markt 31/32, 9712 HV Groningen, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

Verhelst derived a solution for a constrained regression problem which occurs in the interval measurement application of ALSCAL and related MDS-algorithms. In the present paper it is shown that Verhelst's solution is based on an implicit nonsingularity assumption. A general solution, which contains Verhelst's solution as a special case, is derived by a simple completing-the-squares type approach instead of partial differentiation with a Lagrange multiplier. In addition, this approach permits the identification of a small interval which uniquely contains the optimal value of a parameter needed to solve the special case where Verhelst's solution is valid.

Type
Notes And Comments
Information
Psychometrika , Volume 48 , Issue 4 , December 1983 , pp. 631 - 638
Copyright
Copyright © 1983 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

The author is obliged to Dirk Knol and Klaas Nevels for helpful comments.

References

Takane, Y., Young, F. W. & De Leeuw, Nonmetric individual differences multidimensional scaling: An alternating least-squares method with optimal scaling features. Psychometrika, 1977, 42, 7–67.CrossRefGoogle Scholar
Verhelst, N. D. A note on Alscal: The estimation of the additive constant. Psychometrika, 1981, 46, 465–468.CrossRefGoogle Scholar