748—Chapter 39. Factor Analysis
The second type of indeterminacy index reports the minimum correlation between alternate estimates of the factor scores, r = 2r2 – 1 . The minimum correlation measure ranges from -1 to 1. High positive values are desirable since they indicate that differing sets of factor scores will yield similar results.
Grice (2001) suggests that values for r that do not exceed 0.707 by a significant degree are problematic since values below this threshold imply that we may generate two sets of factor scores that are orthogonal or negatively correlated (Green, 1976).
Validity, Univocality, Correlational Accuracy
Following Gorsuch (1983), we may define Rff as the population factor correlation matrix, Rss as the factor score correlation matrix, and Rfs as the correlation matrix of the known factors with the score estimates. In general, we would like these matrices to be similar.
The diagonal elements of Rfs are termed validity coefficients. These coefficients range from -1 to 1, with high positive values being desired. Differences between the validities and the multiple correlations are evidence that the computed factor scores have determinacies lower than those computed using the r -values. Gorsuch (1983) recommends obtaining validity values of at least 0.80, and notes that values larger than 0.90 may be necessary if we wish to use the score estimates as substitutes for the factors.
The off-diagonal elements of Rfs allow us to measure univocality, or the degree to which the estimated factor scores have correlations with those of other factors. Off-diagonal values of Rfs that differ from those in Rff are evidence of univocality bias.
Lastly, we obviously would like the estimated factor scores to match the correlations among the factors themselves. We may assess the correlational accuracy of the scores estimates by comparing the values of the Rss with the values of Rff .
From our earlier discussion, we know that the population correlation Rff = Wˆ ¢SWˆ . Rss may be obtained from moments of the estimated scores. Computation of Rfs is more complicated, but follows the steps outlined in Gorsuch (1983).
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