Comparing Different Methods for Implementing Parallel Analysis: A Practical Index of Accuracy

The accuracy of three methods of implementing parallel analysis with mean eigenvalues (regression, interpolation, and computation with three samples of random data) was compared and the index of accuracy was the proportion of agreement on the number of components for extraction suggested by each of these three procedures.

Abstract

Of the various methods and rules-of-thumb for deciding the 4correct" number of components to retain in principal components analysis, parallel analysis is arguably the most useful. Recently, researchers have become interested in developing alternative methods of implementing parallel analysis and of comparing their accuracy. The accuracy of three methods of implementing parallel analysis with mean eigenvalues (regression, interpolation, and computation with three samples of random data) was compared. The index of accuracy was the proportion of agreement on the number of components for extraction suggested by each of these three procedures and those suggested by implementing parallel analysis with 40 runs of random data, in a sample of 28 published correlation matrices. Moreover, the accuracy of two methods of implementing parallel analysis with 95th percentile eigenvalues (regression and interpolation) was compared using the aforementioned index of accuracy. In separate analyses for mean and 95th percentile eigenvalue strategies, no evidence of differential accuracy emerged. Implications for implementing parallel analysis are discussed.