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

Published online by Cambridge University Press:  01 January 2025

Richard G. Montanelli Jr.  and
Lloyd G. Humphreys
Richard G. Montanelli Jr.*
Affiliation:
University of Illinois at Urbana-Champaign
Lloyd G. Humphreys
Affiliation:
University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to Richard G. Montanelli, Jr., 132 Digital Computer Laboratory, University of Illinois at Urbana-Champaign, Department of Computer Science, Urbana, Illinois 61801.
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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.

Keywords

number of factorsfactor analysisparallel analysis
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 3 , September 1976 , pp. 341 - 348
Copyright
Copyright © 1976 The Psychometric Society

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Footnotes

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.

References

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