Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A monte carlo study Authors Richard G. MontanelliJr. Department of Computer Science 132 Digital Computer Laboratory, University of Illinois at Urbana-Champaign Lloyd G. Humphreys Department of Computer Science 132 Digital Computer Laboratory, University of Illinois at Urbana-Champaign Article

Received: 17 April 1975 Revised: 22 December 1975 Accepted: 26 February 1976 DOI :
10.1007/BF02293559

Cite this article as: Montanelli, R.G. & Humphreys, L.G. Psychometrika (1976) 41: 341. doi:10.1007/BF02293559
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 ]}, whereN is the number of observations;n , the number of variables; andi , the ordinal position of the eigenvalue. The results were excellent, with multiple correlation coefficients ranging from .9948 to .9992.

Key words number of factors factor analysis parallel analysis This research was supported by the Office of Naval Research under Contract N00014-67-A-0305-0012, Lloyd G. Humphreys, principal investigator, and by the Department of Computer Science of which Richard G. Montanelli, Jr., is a member.

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© Psychometric Society 1976