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An Analysis of Guttman's Simplex

Published online by Cambridge University Press:  01 January 2025

Philip H. DuBois
Philip H. DuBois*
Affiliation:
Washington University
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Abstract

Applying a Spearman formula for factor loadings to a variant of the diagonal method, the Guttman simplex model is factored algebraically into n/2 additive factors. The finding that communalities can be discovered such that the rank of a simplex becomes n/2 is contradictory to Guttman's contention that the minimal rank is n − 2. Certain matrices of 4 and 5 variables presented by Guttman as simplexes, can, in general, be considered 2-factor matrices, easily analyzed to simple structure without rotation. One example of 6 variables is factored by the method described to a 3-factor structure.

Type
Original Paper
Information
Psychometrika , Volume 25 , Issue 2 , June 1960 , pp. 173 - 182
Copyright
Copyright © 1960 The Psychometric Society

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Footnotes

*

Prepared under Contract 816(02) between the Office of Naval Research and Washington University and presented in part at a meeting of the Southern Society for Philosophy and Psychology, St. Louis, Missouri, March 27, 1959. Permission is granted for reproduction, translation, publication, use, and disposal in whole and in part by or for the United States Government.

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