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Psychometrika

, Volume 39, Issue 4, pp 423–427 | Cite as

Alternative measures of fit for the Schönemann-carroll matrix fitting algorithm

  • James C. Lingoes
  • Peter H. Schönemann
Article

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,e s , 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) fork ≠ 1. Therefore, both measures are useless for answering questions of the type: “DoesA fitB better thanA fitsC?”. In this note two new measures of fit are suggested which do not depend upon the norms ofA andB, which are (0, 1)-bounded, and which, therefore, provide meaningful answers for comparative analyses.

Keywords

Comparative Analysis Public Policy Similarity Measure Statistical Theory Alternative Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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

Copyright information

© Psychometric Society 1974

Authors and Affiliations

  • James C. Lingoes
    • 1
  • Peter H. Schönemann
    • 2
  1. 1.The University of MichiganUSA
  2. 2.Purdue UniversityUSA

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