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Estimation and Tests of Significance in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

C. Radhakrishna Rao
C. Radhakrishna Rao*
Affiliation:
University of Illinois
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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.

Type
Original Paper
Information
Psychometrika , Volume 20 , Issue 2 , June 1955 , pp. 93 - 111
Copyright
Copyright © 1955 The Psychometric Society

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