Latent Roots of Random Data Correlation Matrices with Squared Multiple Correlations on the Diagonal: A Monte Carlo Study

Abstract

In order to make the parallel analysis criterion for determining the number of factors easy to use, regression equations for predicting the logarithms of the latent roots of random correlation matrices, with squared multiple correlations on the diagonal, are presented. The correlation matrices were derived from distributions of normally distributed random numbers. The independent variables are log ( N − 1) and log {[ n ( n − 1)/2] − [( i − 1) n ]}, where N is the number of observations; n , the number of variables; and i , the ordinal position of the eigenvalue. The results were excellent, with multiple correlation coefficients ranging from .9948 to .9992.