, Volume 41, Issue 3, pp 341–348

Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A monte carlo study

  • Richard G. MontanelliJr.
  • Lloyd G. Humphreys

DOI: 10.1007/BF02293559

Cite this article as:
Montanelli, R.G. & Humphreys, L.G. Psychometrika (1976) 41: 341. doi:10.1007/BF02293559


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 

Copyright information

© Psychometric Society 1976

Authors and Affiliations

  • Richard G. MontanelliJr.
    • 1
  • Lloyd G. Humphreys
    • 1
  1. 1.Department of Computer Science132 Digital Computer Laboratory, University of Illinois at Urbana-ChampaignUrbana

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