A rationale and test for the number of factors in factor analysis


It is suggested that if Guttman's latent-root-one lower bound estimate for the rank of a correlation matrix is accepted as a psychometric upper bound, following the proofs and arguments of Kaiser and Dickman, then the rank for a sample matrix should be estimated by subtracting out the component in the latent roots which can be attributed to sampling error, and least-squares “capitalization” on this error, in the calculation of the correlations and the roots. A procedure based on the generation of random variables is given for estimating the component which needs to be subtracted.

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I wish to acknowledge the valuable help given by J. Jaspers and L. G. Humphreys in the development of the ideas presented in this paper.

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Horn, J.L. A rationale and test for the number of factors in factor analysis. Psychometrika 30, 179–185 (1965). https://doi.org/10.1007/BF02289447

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  • Public Policy
  • Correlation Matrix
  • Statistical Theory
  • Latent Root
  • Sampling Error