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Estimation and Tests of Significance in Factor Analysis
Abstract
A distinction is drawn between the method of principal components developed by Hotelling and the common factor analysis discussed in psychological literature both from the point of view of stochastic models involved and problems of statistical inference. The appropriate statistical techniques are briefly reviewed in the first case and detailed in the second. A new method of analysis called the canonical factor analysis, explaining the correlations between rather than the variances of the measurements, is developed. This analysis furnishes one out of a number of possible solutions to the maximum likelihood equations of Lawley. It admits an iterative procedure for estimating the factor loadings and also for constructing the likelihood criterion useful in testing a specified hypothesis on the number of factors and in determining a lower confidence limit to the number of factors.
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Citations
Cited by
Maximum Likelihood from Incomplete Data Via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444
“The suggested method for factor analysis can be related to that published by Rao (1955).”
MethodThe Scree Test For The Number Of Factors
Cattell, R. B. (1966) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr0102_10 · Cited by 13,554
A Reliability Coefficient for Maximum Likelihood Factor Analysis
Tucker, L. R., & Lewis, C. (1973) · Psychometrika · doi:10.1007/bf02291170 · Cited by 7,330
Akaike, H. (1987) · Psychometrika · doi:10.1007/bf02294359 · Cited by 5,264
Akaike, H. (1987) · Springer Series in Statistics · doi:10.1007/978-1-4612-1694-0_29 · Cited by 4,027
Metadata
- Authors
- Rao, C. R.
- Venue
- Psychometrika
- Publisher
- Cambridge University Press (CUP)
- Published
- 1955-06
- Volume
- 20
- Issue
- 2
- Pages
- 93-111
- ISSN
- 0033-3123 (ISSN-L)
- 1860-0980
- OpenAlex
- W2095917182
- Cited by
- 306
- References
- 0
- FWCI
- 13.14
- Type
- journal article
- Language
- en
- Open access
- closed
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