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

@article{Horn1965ARA,
  title={A rationale and test for the number of factors in factor analysis},
  author={John Louis Horn},
  journal={Psychometrika},
  year={1965},
  volume={30},
  pages={179-185}
}
  • J. Horn
  • Published 1 June 1965
  • Mathematics
  • Psychometrika
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… 
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LetR be any correlation matrix of ordern, with unity as each main diagonal element. Common-factor analysis, in the Spearman-Thurstone sense, seeks a diagonal matrixU2 such thatG = R − U2 is Gramian
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TLDR
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