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VI.—The Estimation of Factor Loadings by the Method of Maximum Likelihood

Published online by Cambridge University Press:  15 September 2014

D. N. Lawley
Affiliation:
Moray House, University of Edinburgh
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Extract

1. When a battery of intelligence tests is administered to a set of persons it is a common practice among psychologists to “explain” the scores obtained in terms of a number of “factors.” Thus if we suppose that there are altogether t tests and that xi, denotes the score of any one person in the ith test, then it is assumed that

where f, g, …, h represent the person's measures in one or more general or group factors, and Si, is the person's specific ability in the ith test. It is further assumed that for a given and supposed infinite population of persons all the factors, specific and otherwise, are distributed normally and independently and that they are standardised, i.e. that their standard deviations are unity.

Type
Proceedings
Copyright
Copyright © Royal Society of Edinburgh 1940

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References

References to Literature

Aitken, A. C., 1937. “The Evaluation of the Latent Roots and Vectors of a Matrix,” Proc. Roy. Soc. Edin., vol. lvii, pp. 269304.Google Scholar
Fisher, R. A., 1921. “On the Mathematical Foundations of Theoretical Statistics,” Phil. Trans., A, vol. ccxxii, pp. 309368.Google Scholar
Fisher, R. A., 1924. “The Conditions under which X 2 Measures the Discrepancy between Observation and Hypothesis,” Journ. Roy. Statist. Soc., vol. lxxxvii, pp. 442449.Google Scholar
Fisher, R. A., 1925. “Theory of Statistical Estimation,Proc. Camb. Phil. Soc., vol. xxii, pp. 700725.CrossRefGoogle Scholar
Thomson, G. H., 1934. “Hotelling's Method modified to give Spearman's g,” Journ. Educ. Psychol., vol. xxv, pp. 366374.CrossRefGoogle Scholar
Thomson, G. H., 1939. The Factorial Analysis of Human Ability, Univ. London Press, pp. 166167.Google Scholar
Wishart, J., 1928. “The Generalised Product Moment Distribution in Samples from a Normal Multivariate Population,” Biometrika, A, vol. xx, pp. 3252.CrossRefGoogle Scholar
Wishart, J., and Bartlett, M. S., 1933. “The Generalised Product Moment Distribution in a Normal System,” Proc. Camb. Phil. Soc., vol. xxix, pp. 260270.Google Scholar