A Regression Equation for the Parallel Analysis Criterion in Principal Components Analysis: Mean and 95th Percentile Eigenvalues.

Monte Carlo research increasingly seems to favor the use of parallel analysis as a method for determining the "correct" number of factors in factor analysis or components in principal components analysis. We present a regression equation for predicting parallel analysis values used to decide the number of principal components to retain. This equation is appropriate for predicting criterion mean eigenvalues and was derived from random data sets containing between 5 and 50 variables and between 50 and 500 subjects. This relatively simple equation is more accurate for predicting mean eigenvalues from random data matrices with unities in the diagonals than a previously published equation. Moreover, given that the parallel analysis decision rule may be too dependent on chance, our equation is also used to predict the 95th percentile point in distributions of eigenvalues generated from random data matrices. Multiple correlations for all analyses were at least .95. Regression weights for predicting the first 33 mean and 95th percentile eigenvalues are given in easy-to-use tables.