Hostname: page-component-89b8bd64d-shngb Total loading time: 0 Render date: 2026-05-12T02:42:28.868Z Has data issue: false hasContentIssue false
  • English
  • Français

Instrumental Variables in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Albert Madansky
Albert Madansky*
Affiliation:
Rand Corporation
Get access Rights & Permissions [Opens in a new window]

Abstract

The factor analysis model is rewritten as a system of linear structural relations with errors in variables. The method of instrumental variables is applied to this revised form of the model to obtain estimates of the factor loading matrix. The relation between this method and interbattery analysis, proportional profile analysis, and canonical factor analysis is pointed out. In addition, an estimation procedure based on replicated sampling different from proportional profile analysis is given.

Information

Type
Original Paper
Information
Psychometrika , Volume 29 , Issue 2 , June 1964 , pp. 105 - 113
Copyright
Copyright © 1964 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.)

Article purchase

Temporarily unavailable

References

Albert, A. A. The minimum rank of a correlation matrix. Proc. Nat. Acad. Sci., 1944, 30, 144–146.CrossRefGoogle ScholarPubMed
Anderson, T. W. and Rubin, H. Statistical inference in factor analysis. In Neyman, J. (Eds.), Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Vol. V. Berkeley: Univ. Calif. Press, 1956, 98–121.Google Scholar
Burt, C. Alternative methods of factor analysis and their relations to Pearson's method of “principal axes.”. Brit. J. Psychol., 1949, 2, 98–121.Google Scholar
Cattell, R. B. Parallel proportional profiles and other principles for determining the choice of factors by rotation. Psychometrika, 1944, 9, 267–283.CrossRefGoogle Scholar
Cattell, R. B. and Cattell, A. K. S. Factor rotation for proportional profiles: Analytical solution and an example. Brit. J. statist. Psychol., 1955, 8, 83–92.CrossRefGoogle Scholar
Creasy, M. A. Analysis of variance as an alternative to factor analysis. J. roy. statist. Soc. (Series B), 1957, 19, 318–325.CrossRefGoogle Scholar
Geary, R. C. Determination of linear relations between systematic parts of variables with errors of observation the variances of which are unknown. Econometrica, 1949, 17, 30–59.CrossRefGoogle Scholar
Gibson, W. A. Proportional profiles and latent structure. Psychometrika, 1959, 21, 135–144.CrossRefGoogle Scholar
Gibson, W. A. Remarks on Tucker's inter-battery method of factor analysis. Psychometrika, 1960, 25, 19–25.CrossRefGoogle Scholar
Gibson, W. A. A retraction on inter-battery factor analysis. Psychometrika, 1961, 26, 451–452.CrossRefGoogle Scholar
Gibson, W. A. An asymmetric approach to multiple-factor analysis. Brit. J. statist. Psychol., 1961, 14, 97–107.CrossRefGoogle Scholar
Harris, C. W. Some Rao-Guttman relationships. Psychometrika, 1962, 27, 247–264.CrossRefGoogle Scholar
Kaiser, H. F. and Caffrey, J. Alpha factor analysis. Psychometrika (in press).Google Scholar
Madansky, A. The fitting of straight lines when both variables are subject to error. J. Amer. statist. Ass., 1959, 54, 173–205.10.1080/01621459.1959.10501505CrossRefGoogle Scholar
Neyman, J. Remarks on a paper by E. C. Rhodes. J. roy. statist. Soc., 1937, 100, 50–57.Google Scholar
Rao, C. R. Estimation and tests of significance in factor analysis. Psychometrika, 1955, 20, 93–111.CrossRefGoogle Scholar
Rhodes, E. C. On lines and planes of closest fit. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science (Series 7), 1927, 3, 357–364.CrossRefGoogle Scholar
Sargan, J. D. The estimation of economic relationships using instrumental variables. Econometrica, 1958, 26, 393–415.CrossRefGoogle Scholar
Thomson, G. H. A hierarchy without a general factor. Brit. J. Psychol., 1916, 8, 271–281.Google Scholar
Tintner, G. Econometrics, New York: Wiley, 1952.Google Scholar
Tucker, L. R. An inter-battery method of factor analysis. Psychometrika, 1958, 23, 111–136.CrossRefGoogle Scholar