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On Various Causes of Improper Solutions in Maximum Likelihood Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Otto P. van Driel
Otto P. van Driel*
Affiliation:
Philips Research Laboratories
*
Requests for reprints should be sent to Otto P. van Driel, Philips Research Laboratories, Eindhoven, The Netherlands.
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Abstract

In the applications of maximum likelihood factor analysis the occurrence of boundary minima instead of proper minima is no exception at all. In the past the causes of such improper solutions could not be detected. This was impossible because the matrices containing the parameters of the factor analysis model were kept positive definite. By dropping these constraints, it becomes possible to distinguish between the different causes of improper solutions. In this paper some of the most important causes are discussed and illustrated by means of artificial and empirical data.

Keywords

multivariate analysisHeywood casesindefinitenessinterpretabilityMALIFA programsamplingfluctuations

Information

Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 2 , June 1978 , pp. 225 - 243
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

The author is indebted to H. J. Prins for stimulating and encouraging discussions.

References

Reference Notes

van Driel, O. P. Description of the MALIFA (maximim likelihood factor analysis) program, 1975, Eindhoven: Philips Research Laboratories.Google Scholar
Mattsson, A., Olsson, U. & Rosén, M. The maximum likelihood method in factor analysis with special consideration to the problem of improper solutions, 1966, Sweden: University of Uppsala, Institute of Statistics.Google Scholar
Veltkamp, G. W. Private communication, 1972.Google Scholar

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