Comments on “the Measurement of Factorial Indeterminacy”

Guttman’s index of indeterminacy (2 ρ 2 − 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 ρ 2 for predicting the factor from the observed variables is the average correlation ρ AB between independently selected alternative solutions A and B , while var ( ρ AB ) = (1 − ρ 2 ) 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, ρ 2 is the lower bound for E( ρ AB ); however, E( ρ AB ) need not be a modal value in the distribution of ρ AB . Guttman’s index and E( ρ AB ) measure different aspects of the same indeterminacy problem.