An Empirical Kaiser Criterion
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.