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Maximum Likelihood Solution to Factor Analysis when Some Factors are Completely Specified

Published online by Cambridge University Press:  01 January 2025

Friedrich Gebhardt
Friedrich Gebhardt*
Affiliation:
C-E-I-R Gmbh, Frankfurt, Germany
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Abstract

In the factor-analytic model, let some of the factors be known (i.e., the factor loadings are given in advance; they may e.g. be obtained from some previous analyses). However, their covariance matrix may, or may not, be known. The remaining factors (if any) are assumed to be uncorrelated among themselves and to the first set. For this model, the maximum likelihood equations are obtained and an iterative method for the solution is proposed.

Keywords

CovarianceCovariance MatrixPublic PolicyFactor LoadingIterative Method
Type
Original Paper
Information
Psychometrika , Volume 36 , Issue 2 , June 1971 , pp. 155 - 163
Copyright
Copyright © 1971 The Psychometric Society

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Footnotes

*

The work was done while the author was at Deutsches Rechenzentrum, Darmstadt, Germany.

References

CRC Standard Mathematical Tables, 16th edition. Cleveland: Chemical Rubber Publishing Co., 1959.Google Scholar
Fletcher, R., & Powell, M. J. D. A rapidly convergent descent method for minimization. Computer Journal, 1963, 2, 163–168.CrossRefGoogle Scholar
Gebhardt, F. Statistische Programme des DRZ. Teil A: Allgemeines. Programm-Information PI-32, 1969, Darmstadt: Deutsches Rechenzentrum.Google Scholar
Gebhardt, F. Statistische Programme des DRZ. Teil B: Einzelbeschreibungen. Programm-Information PI-33, 1969, Darmstadt: Deutsches Rechenzentrum.Google Scholar
Handbook of Tables for Mathematics, 3rd edition. Cleveland: Chemical Rubber Publishing Co., 1967. (in particular: R. E. Bargmann, Matrices and determinants, pp. 144–166).Google Scholar
Jöreskog, K. G. Some contributions to maximum likelihood factor analysis. Psychometrika, 1967, 32, 443–482.CrossRefGoogle Scholar
Jöreskog, K. G.A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 1969, 34, 183–202.CrossRefGoogle Scholar
Jöreskog, K. G., & Lawley, D. N. New methods in maximum likelihood factor analysis. British Journal of Mathematical and Statistical Psychology, 1968, 21, 85–96.CrossRefGoogle Scholar