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Scaling a Simplex

Published online by Cambridge University Press:  01 January 2025

Henry F. Kaiser
Henry F. Kaiser*
Affiliation:
University of Illinois
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Abstract

A least-squares solution for scaling the variables of a Guttman simplex is developed. The procedure yields a ratio scale, two varieties of interval scale, and orders the variables. A measure of the goodness of fit of the scale to the data is suggested. An example of the application of the method is given. The problem of non-positive correlations is discussed.

Information

Type
Original Paper
Information
Psychometrika , Volume 27 , Issue 2 , June 1962 , pp. 155 - 162
Copyright
Copyright © 1962 The Psychometric Society

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Footnotes

*

I am indebted to Professor Lloyd Humphreys for suggesting this problem. Mr. Joseph Levin independently has arrived at the results of the first section of the paper. The final version of this paper was prepared while the author was a U. S. Public Health Service Fellow at the Center for Advanced Study in the Behavioral Sciences.

References

Gulliksen, H. A least squares solution for paired comparisons with incomplete data. Psychometrika, 1956, 21, 125–134.CrossRefGoogle Scholar
Guttman, L. A new approach to factor analysis: the radex. In Lazarsfeld, P. F. (Eds.), Mathematical thinking in the social sciences, Glencoe, Ill.: Free Press, 1954.Google Scholar
Kaiser, H. F. Contributions to the method of paired comparisons. Unpublished manuscript, 1960..Google Scholar
Mosteller, F. Remarks on the method of paired comparisons. I. The least squares solution assuming equal standard deviations and equal correlations. Psychometrika, 1951, 16, 3–11.CrossRefGoogle Scholar
Stevens, S. S. Mathematics, measurement, and psychophysics. In Stevens, S. S. (Eds.), Handbook of experimental psychology, New York: Wiley, 1951.Google Scholar
Thurstone, L. L. Primary mental abilities, Chicago: Univ. Chicago Press, 1938.Google Scholar