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A General Approach to Confirmatory Maximum Likelihood Factor Analysis

Published online by Cambridge University Press:  01 January 2025

K. G. Jöreskog
K. G. Jöreskog*
Affiliation:
Educational Testing Service
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Abstract

We describe a general procedure by which any number of parameters of the factor analytic model can be held fixed at any values and the remaining free parameters estimated by the maximum likelihood method. The generality of the approach makes it possible to deal with all kinds of solutions: orthogonal, oblique and various mixtures of these. By choosing the fixed parameters appropriately, factors can be defined to have desired properties and make subsequent rotation unnecessary. The goodness of fit of the maximum likelihood solution under the hypothesis represented by the fixed parameters is tested by a large sample x2 test based on the likelihood ratio technique. A by-product of the procedure is an estimate of the variance-covariance matrix of the estimated parameters. From this, approximate confidence intervals for the parameters can be obtained. Several examples illustrating the usefulness of the procedure are given.

Type
Original Paper
Information
Psychometrika , Volume 34 , Issue 2 , June 1969 , pp. 183 - 202
Copyright
Copyright © 1969 The Psychometric Society

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Footnotes

*

This work was supported by a grant (NSF-GB 1985) from the National Science Foundation to Educational Testing Service.

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