An Empirical Comparison of Three Indices of Factorial Similarity

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Abstract
The need for an adequate methodological resolution to the factor-matching (invariance) problem—long recognized as critical by theoretically oriented factor analysts—is also being strongly felt by applied behavioral scientists today. As factor analysis has become more generally utilized in the behavioral sciences, the demand for a valid, general index of factorial similarity has grown proportionally. Recent research has resulted in a number of analytic indices which are purported to represent validly the degree of similarity among factors; the present paper concerns an empirical comparison of three such measures as to how well they perform this task. The congruency coefficient, coefficient of invariance, and Cattell's s-index were chosen for comparison. The 3 coefficients were assessed on a number of distinct data sets which reflected dissimilarities arising from different sources. All 3 techniques were observed to possess validity but also to have limiting conditions. Conclusions suggest that the adequacy of the methods cannot be judged in absolute terms but rather must be assessed in terms of the particular requirements of the data.

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