A General Approach to Confirmatory Maximum Likelihood Factor Analysis
1969/06/01 by Karl G. Jöreskog, K. G. Jöreskog · 2,504 citations
Chemistry · Mathematics · #Applied mathematics #Covariance #Covariance matrix #Generality #Goodness of fit #Likelihood-ratio test #Mathematics #Maximum likelihood #Oblique case #Restricted maximum likelihood #Spectroscopy and Chemometric Analyses #Statistics #Variance (accounting)
paper · doi:10.1007/bf02289343
published in Psychometrika 34(2), 183-202 (Springer Science+Business Media)
openalex publication_date 1969/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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 x 2 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.
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