Notes and Commentary: Regression Equations for the Latent Roots of Random Data Correlation Matrices with Unities on the Diagonal

Abstract

In order to make parallel analysis more accessible to researchers employing principal component techniques, regression equations are presented for the logarithms of the latent roots of random data correlation matrices with unities on the diagonal. These regression equations have as independent variables logarithms of: the single variable degrees of freedom; Bartlett-Lawley degrees of freedom; the next lowest ordered eigenvalue. The multiple correlation coefficients are at least 0.96 in all cases.