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Comments on “the Measurement of Factorial Indeterminacy”

Published online by Cambridge University Press:  01 January 2025

Stanley A. Mulaik
Stanley A. Mulaik*
Affiliation:
Georgia Institute of Technology
*
Requests for reprints should be sent to Dr. Stanley A. Mulaik, School of Psychology, Georgia Institute of Technology, Atlanta, Georgia 30332.
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Abstract

Guttman’s index of indeterminacy (2ρ2 − 1) measures the potential amount of uncertainty in picking the right alternative interpretation for a factor. When alternative solutions for a factor are equally likely to be correct, then the squared multiple correlation ρ2 for predicting the factor from the observed variables is the average correlation ρAB between independently selected alternative solutions A and B, while var (ρAB) = (1 − ρ2)2/s, where s is the dimensionality of the space in which unpredicted components of alternative solutions are to be found. When alternative solutions for the factor are not equally likely to be chosen, ρ2 is the lower bound for E(ρAB); however, E(ρAB) need not be a modal value in the distribution of ρAB. Guttman’s index and E(ρAB) measure different aspects of the same indeterminacy problem.

Keywords

factor analysisfactor scoresinterpretation of factorsidentifiability
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 2 , June 1976 , pp. 249 - 262
Copyright
Copyright © 1976 The Psychometric Society

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