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Application of Optimal Sign-Vectors to Reliability and Cluster Analysis

Published online by Cambridge University Press:  01 January 2025

J. Arthur Woodward  and
P. M. Bentler
J. Arthur Woodward*
Affiliation:
University of California, Los Angeles
P. M. Bentler
Affiliation:
University of California, Los Angeles
*
Requests for reprints should be sent to J. Arthur Woodward, Department of Psychology, University of California, Los Angeles, California 90024.
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Abstract

Expressions involving optimal sign vectors are derived so as to yield two new applications. First, coefficient alpha for the sign-weighted composite is maximized in analogy to Lord's scale-independent solution with differential weights. Second, optimal sign vectors are used to define two groups of objects that are maximally distinct in terms of a function of the squared euclidean distances between groups. An efficient computing algorithm is described along with several examples.

Keywords

optimal weightsreliabilitycluster analysisclassification
Type
Notes And Comments
Information
Psychometrika , Volume 44 , Issue 3 , September 1979 , pp. 337 - 341
Copyright
Copyright © 1979 The Psychometric Society

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Footnotes

This research was supported in part by a research grant (DA 01070) from the U.S. Public Health Service.

References

Reference Note

Demaree, R. G., & Jernigan, L. On determining the direction of scoring in scale construction. Paper presented at the annual meeting of the Southwestern Psychological Association, San Antonio, 1971.Google Scholar

References

Green, B. F. Parameter sensitivity in multivariate methods. Multivariate Behavioral Research, 1977, 12, 263–287.CrossRefGoogle ScholarPubMed
Hestenes, M. R. Optimization theory: The finite dimensional case, 1975, New York: Wiley.Google Scholar
Horst, P. Factor analysis of data matrices, 1965, New York: Holt.Google Scholar
Kendall, M. G. Multivariate analysis, 1975, New York: Hafner.Google Scholar
Lord, F. M. Some relations between Guttman's principal components of scale analysis and other psychometric theory. Psychometrika, 1958, 23, 291–296.CrossRefGoogle Scholar
Rozeboom, W. W. Foundations of the theory of prediction, 1966, Homewood, Ill.: Dorsey.Google Scholar