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Some Relations between Guttman's Principal Components of Scale Analysis and Other Psychometric Theory

Published online by Cambridge University Press:  01 January 2025

Frederic M. Lord
Frederic M. Lord*
Affiliation:
Educational Testing Service
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Abstract

Guttman's principal components for the weighting system are the item scoring weights that maximize the generalized Kuder-Richardson reliability coefficient. The principal component for any item is effectively the same as the factor loading of the item divided by the item standard deviation, the factor loadings being obtained from an ordinary factor analysis of the item intercorrelation matrix.

Type
Original Paper
Information
Psychometrika , Volume 23 , Issue 4 , December 1958 , pp. 291 - 296
Copyright
Copyright © 1958 The Psychometric Society

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References

Cronbach, L. J. Coefficient alpha and the internal structure of tests. Psychometrika, 1951, 16, 297–334.Google Scholar
Dressel, P. L. Some remarks on the Kuder-Richardson reliability coefficient. Psychometrika, 1940, 5, 305–310.CrossRefGoogle Scholar
Edgerton, H. A. and Kolbe, L. E. The method of minimum variation for the combination of criteria. Psychometrika, 1936, 1, 183–187.CrossRefGoogle Scholar
Gulliksen, H. Theory of mental tests, New York: Wiley, 1950.CrossRefGoogle Scholar
Guttman, L. The quantification of a class of attributes: a theory and method of scale construction. In Horst, P. (Ed.), The prediction of personal adjustment. Soc. Sci. Res. Council, Bull. 48, 1941. Pp. 321–345.Google Scholar
Guttman, L. A basis for analyzing test-retest reliability. Psychometrika, 1945, 10, 225–282.CrossRefGoogle ScholarPubMed
Horst, P. Obtaining a composite measure from a number of different measures of the same attribute. Psychometrika, 1936, 1, 53–60.CrossRefGoogle Scholar
Hoyt, C. J. and Stunkard, C. L. Estimation of test reliability for unrestricted item scoring methods. Educ. psychol. Measmt, 1952, 12, 756–758.CrossRefGoogle Scholar
Stouffer, S. A. Measurement and prediction. Studies in social psychology in World War II, Vol. IV, Princeton, N. J.: Princeton Univ. Press, 1950.Google Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar
Tryon, R. C. Reliability and behavior domain validity: reformulation and historical critique. Psychol. Bull., 1957, 54, 229–249.Google ScholarPubMed
Turnbull, H. W. and Aitken, A. C. An introduction to the theory of canonical matrices, Toronto: Blackie, 1950.Google Scholar
Wilks, S. S. Weighting systems for linear functions of correlated variables when there is no dependent variable. Psychometrika, 1938, 3, 23–40.CrossRefGoogle Scholar
Woodbury, M. A. and Lord, F. M. The most reliable composite with a specified true score. Brit. J. statist. Psychol., 1956, 9, 21–28.CrossRefGoogle Scholar

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