Comments on “the Measurement of Factorial Indeterminacy”

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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.

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