Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-02-11T09:31:37.741Z Has data issue: false hasContentIssue false
  • English
  • Français

Alternative Measures of Fit for the Schönemann-Carroll Matrix Fitting Algorithm

Published online by Cambridge University Press:  01 January 2025

James C. Lingoes  and
Peter H. Schönemann
James C. Lingoes
Affiliation:
The University of Michigan
Peter H. Schönemann
Affiliation:
Purdue University
Get access Rights & Permissions [Opens in a new window]

Abstract

In connection with a least-squares solution for fitting one matrix, A, to another, B, under optimal choice of a rigid motion and a dilation, Schönemann and Carroll suggested two measures of fit: a raw measure, e, and a refined similarity measure, es, which is symmetric. Both measures share the weakness of depending upon the norm of the target matrix, B, e.g., e(A, kB) ≠ e(A, B) for k ≠ 1. Therefore, both measures are useless for answering questions of the type: “Does A fit B better than A fits C?”. In this note two new measures of fit are suggested which do not depend upon the norms of A and B, which are (0, 1)-bounded, and which, therefore, provide meaningful answers for comparative analyses.

Type
Original Paper
Information
Psychometrika , Volume 39 , Issue 4 , December 1974 , pp. 423 - 427
Copyright
Copyright © 1974 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

*

This research in nonmetric techniques is supported in part by a grant from the National Science Foundation (GS-2850) to the University of Michigan.

References

Lingoes, J. C. The Guttman-Lingoes Nonmetric Program Series, 1973, Ann Arbor, Michigan: Mathesis Press.Google Scholar
Schönemann, P. H. and Carroll, R. M. Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika, 1970, 35, 245–255.CrossRefGoogle Scholar