An empirical Kaiser criterion.

Abstract

In exploratory factor analysis (EFA), most popular methods for dimensionality assessment such as the screeplot, the Kaiser criterion, or-the current gold standard-parallel analysis, are based on eigenvalues of the correlation matrix. To further understanding and development of factor retention methods, results on population and sample eigenvalue distributions are introduced based on random matrix theory and Monte Carlo simulations. These results are used to develop a new factor retention method, the Empirical Kaiser Criterion. The performance of the Empirical Kaiser Criterion and parallel analysis is examined in typical research settings, with multiple scales that are desired to be relatively short, but still reliable. Theoretical and simulation results illustrate that the new Empirical Kaiser Criterion performs as well as parallel analysis in typical research settings with uncorrelated scales, but much better when scales are both correlated and short. We conclude that the Empirical Kaiser Criterion is a powerful and promising factor retention method, because it is based on distribution theory of eigenvalues, shows good performance, is easily visualized and computed, and is useful for power analysis and sample size planning for EFA. (PsycINFO Database Record

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“…The model used an oblique rotation to allow for the related nature of the constructs under investigation. Analysis of the empirical Kaiser criterion (Braeken & van Assen, 2016) supported the extraction of 10 factors. These factors explained 67.15% of the total variance.…”

“…The selection of an oblique rotation was appropriate due to the theoretical moderate to high level of correlation among the constructs. Due to the small sample size and expected correlation between the factors, the empirical Kaiser criterion was utilized to determine the number of factors to extract (Braeken & van Assen, 2016), rather than the practice of retaining all factors with an Eigenvalue greater than 1 or visual analysis of a scree plot. Due to the use of the oblique rotation, the structure matrix from the output was used for interpretive work, as the values in the structure matrix represent the full relationship of the indicator with the factor, including that portion of the variance that is related through a correlated factor (Henson & Roberts, 2006).…”