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} }
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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References
SHOWING 1-8 OF 8 REFERENCES
Some necessary conditions for common-factor analysis
- Mathematics
- 1954
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…
The Application of Electronic Computers to Factor Analysis
- Computer Science
- 1960
A survey of available computer programs for factor analytic computations and a analysis of the problems of the application of computers to factor analysis.
The advanced theory of statistics (Vols. I and II). London~ Eng
- The advanced theory of statistics (Vols. I and II). London~ Eng
- 1958
Advanced statistical methods in biornetric research Original manuscript received 1
- Advanced statistical methods in biornetric research Original manuscript received 1
- 1952