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Scaling a Conditional Proximity Matrix to Symmetry

Published online by Cambridge University Press:  01 January 2025

Joseph Levin  and
Morton Brown
Joseph Levin*
Affiliation:
Tel-Aviv University
Morton Brown
Affiliation:
Tel-Aviv University
*
Requests for reprints should be sent to Dr. Joseph Levin, Department of Psychology, Tel-Aviv University, ISRAEL.
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Abstract

Two least squares procedures for symmetrization of a conditional proximity matrix are derived. The solutions provide multiplicative constants for scaling the rows or columns of the matrix to maximize symmetry. It is suggested that the symmetrization is applicable for the elimination of bias effects like response bias, or constraints on the marginal frequencies imposed by the experimental design, as in confusion matrices.

Keywords

scalingconditional proximity matrixsymmetrization
Type
Notes And Comments
Information
Psychometrika , Volume 44 , Issue 2 , June 1979 , pp. 239 - 243
Copyright
Copyright © 1979 The Psychometric Society

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Footnotes

The application of the scaling procedure to a matrix of conditional probabilities was suggested by one of the referees, whose helpful comments are gratefully acknowledged.

References

Bishop, Y. M., Fienberg, S. E., & Holland, P. Discrete multivariate analysis; theory and practice, 1975, Cambridge, Mass.: M.I.T. Press.Google Scholar
Coombs, C. H. A theory of data, 1964, New York: Wiley.Google Scholar
Foa, U. G. Interpersonal and economic resources. Science, 1971, 171, 345–351.CrossRefGoogle ScholarPubMed
Indow, T., & Uchizono, T. Multidimensional mapping of Munsell colors varying in hue and chroma. Journal of Experimental Psychology, 1960, 59, 321–329.CrossRefGoogle ScholarPubMed
Laumann, E. O., & Guttman, L. The relative associational contiguity of occupations in an urban setting. American Sociological Review, 1966, 31, 169–178.CrossRefGoogle Scholar
Lingoes, J. C. The Guttman-Lingoes nonmetric program series, 1973, Ann Arbor: Mathesis Press.Google Scholar