Hostname: page-component-5f745c7db-rgzdr Total loading time: 0 Render date: 2025-01-06T07:47:29.670Z Has data issue: true hasContentIssue false
  • English
  • Français

Factor Analysis by Instrumental Variables Methods

Published online by Cambridge University Press:  01 January 2025

Gösta Hägglund
Gösta Hägglund*
Affiliation:
University of Uppsala
*
Requests for reprints should be sent to Gösta Hägglund, University of Uppsala, Department of Statistics, P. O. Box 513, S-751 20 Uppsata, Sweden.
Get access Rights & Permissions [Opens in a new window]

Abstract

Three alternative estimation procedures for factor analysis based on the instrumental variables method are presented. These procedures are justified by the method of least squares. Formulas for asymptotic standard errors of factor loadings are derived. The procedures are empirically compared to the method of maximum likelihood. The conclusion, based on the data used in this study, is that two of the procedures seem to work well.

Keywords

factor analysisinstrumental variablesleast squaresreference variables
Type
Original Paper
Information
Psychometrika , Volume 47 , Issue 2 , June 1982 , pp. 209 - 222
Copyright
Copyright © 1982 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

Research reported in this article has been supported by the Swedish Research Council in Humanistic and Social Sciences under project Research in Psychometrics, Karl G. Jöreskog project director.

The author wishes to thank Professors Karl G. Jöreskog, Anders Christoffersson and Ejnar Lyttkens, University of Uppsala, for their contributions to this research.

References

Reference Notes

Hägglund, G. Factor analysis by instrumental variables methods: A comparison of three estimation procedures. Research Report 80-2. University of Uppsala, Department of Statistics, 1980.Google Scholar
Hägglund, G. Factor analysis by instrumental variables methods: Least squares justification and standard errors. Research Report 81-1. University of Uppsala, Department of Statistics, 1981.Google Scholar

References

Browne, M. W. Generalized least squares estimators in the analysis of covariance structures. South African Statistical Journal, 1974, 8, 1–24.Google Scholar
Brundy, J. M. & Jorgenson, D. W. Efficient estimation of simultaneous equations by instrumental variables. The Review of Economics and Statistics, 1971, 53, 207–224.CrossRefGoogle Scholar
Goldberger, A. S. Econometric theory, 1964, New York: Wiley.Google Scholar
Harman, H. H. Modern factor analysis, 2nd ed., Chicago: University of Chicago, 1967.Google Scholar
Jöreskog, K. G. A general method for estimating a linear structural equation system. In Goldberger, A. S. and Duncan, O. D. (Eds.), Structural equation models in the social sciences, 1973, New York: Seminar Press.Google Scholar
Jöreskog, K. G. Factor analysis by least squares and maximum likelihood methods. In Enslein, K., Ralston, A. & Wilf, H. S. (Eds.), Statistical methods for digital computers, 1977, New York: Wiley.Google Scholar
Jöreskog, K. G. Basic ideas of factor and component analysis. In Jöreskog, K. G. & Sörbom, D. (Eds.), Advances in factor analysis and structural equation models, 1979, Cambridge, Mass.: ABT Books.Google Scholar
Jöreskog, K. G. & Sörbom, D. LISREL V—Analysis of linear structural relationships by maximum likelihood and least squares methods, 1982, Chicago: National Educational Resources.Google Scholar
Lawley, D. N. & Maxwell, A. E. Factor analysis as a statistical method, 2nd ed., London: Butterworths, 1971.Google Scholar
Lyttkens, E. Instrumental variables estimation of interdependent systems. In Jöreskog, K. G. and Wold, H. (Eds.), Systems under indirect observation: Causality, structure and prediction. Amsterdam: North-Holland Publishing Co.. 1982, 225–261.Google Scholar
Madansky, A. Instrumental Variables in Factor Analysis. Psychometrika, 1964, 29, 105–113.CrossRefGoogle Scholar
Rao, C. R. Least squares theory using an estimated dispersion matrix and its application to measurement of signals. Berkeley, California: University of California Press. 1967, 355–372.Google Scholar
Reiersøl, O. Confluence analysis by means of lag moments and other methods of confluence analysis. Econometrica, 1941, 9, 1–23.CrossRefGoogle Scholar
Sargan, J. D. The estimation of economic relationships using instrumental variables. Econometrica, 1958, 26, 393–415.CrossRefGoogle Scholar
Silvey, S. D. Statistical inference, 1970, Hammondsworth, Middlesex: Penguin Books.Google Scholar
Theil, H. Principles of econometrics, 1971, New York: Wiley.Google Scholar
Wilks, S. S. Mathematical statistics, 1962, New York: Wiley.Google Scholar