Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2025-01-06T02:30:19.639Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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

References

Anderson, T. W. & Rubin, H. Statistical inference in factor analysis. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1956, 5, 111–150.Google Scholar
Bechtoldt, H. P. An empirical study of the factor analysis stability hypothesis. Psychometrika, 1961, 26, 405–432.CrossRefGoogle Scholar
Derflinger, G. Neue Iterationsverfahren in der Faktorenanalyse. Biometrische Zeitschrift, 1968, 10, 58–75.CrossRefGoogle Scholar
Derflinger, G. Efficient methods for obtaining the minres and maximum-likelihood solutions in factor analysis. Metrika, 1969, 14, 214–231.CrossRefGoogle Scholar
Driel, O. P. van, Prins, H. J. & Veltkamp, G. W. Estimating the parameters of the factor analysis model without the usual constraints of positive definiteness. Proceedings of the Symposium on Computational Statistics (COMPSTAT), Vienna, 1974, 255–265.Google Scholar
Harman, H. H. Modern factor analysis, 1971, Chicago: Univ. of Chicago Press.Google Scholar
Heywood, H. B. On finite sequences of real numbers. Proceedings of the Royal Society, London, 1931, 134, 486–501.Google Scholar
Jennrich, R. I. Simplified formulae for standard errors in maximum likelihood factor analysis. British Journal of Mathematical and Statistical Psychology, 1974, 27, 122–131.CrossRefGoogle Scholar
Jennrich, R. I. & Ronbinson, S. M. A Newton-Raphson algorithm for maximum likelihood factor analysis. Psychometrika, 1969, 34, 111–123.CrossRefGoogle Scholar
Jöreskog, K. G. Some contributions to maximum likelihood factor analysis. Psychometrika, 1967, 32, 443–482.CrossRefGoogle Scholar
Jöreskog, K. G. & Goldberger, A. S. Factor analysis by generalized least squares. Psychometrika, 1972, 37, 243–260.CrossRefGoogle Scholar
Lawley, D. N. & Maxwell, A. E. Factor analysis as a statistical method, 1971, London: Butterworths.Google Scholar
Marcus, M. & Minc, H. A survey of matrix theory and matrix inequalities, 1964, Boston: Prindle, Weber and Schmidt.Google Scholar
Thurstone, L. L. & Thurstone, T. G. Factorial studies of intelligence. Psychometric Monographs, 1941, 2.Google Scholar
Tumura, Y., Fukutomi, K. and Asoo, Y. On the unique convergence of iterative procedures in factor analysis. TRU Mathematics, 1968, 4, 52–59.Google Scholar