Instrumental variables in factor analysis Authors
First Online: 01 June 1964 Received: 02 April 1963 Revised: 12 October 1963 DOI:
Cite this article as: Madansky, A. Psychometrika (1964) 29: 105. doi:10.1007/BF02289693 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.
Albert, A. A. The minimum rank of a correlation matrix.
Proc. Nat. Acad. Sci.
PubMedCentral PubMed CrossRef
Anderson, T. W. and Rubin, H. Statistical inference in factor analysis. In J. Neyman (Ed.),
Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Vol. V. Berkeley: Univ. Calif. Press, 1956. Pp. 98–121.
Burt, C. Alternative methods of factor analysis and their relations to Pearson's method of “principal axes.”
Brit. J. Psychol. (Statist. Sec.), 1949, 2, 98–121.
Cattell, R. B. Parallel proportional profiles and other principles for determining the choice of factors by rotation.
Cattell, R. B. and Cattell, A. K. S. Factor rotation for proportional profiles: Analytical solution and an example.
Brit. J. statist. Psychol.
Creasy, M. A. Analysis of variance as an alternative to factor analysis.
J. roy. statist. Soc. (Series B), 1957, 19, 318–325.
Geary, R. C. Determination of linear relations between systematic parts of variables with errors of observation the variances of which are unknown.
Gibson, W. A. Proportional profiles and latent structure.
Gibson, W. A. Remarks on Tucker's inter-battery method of factor analysis.
Gibson, W. A. A retraction on inter-battery factor analysis.
Gibson, W. A. An asymmetric approach to multiple-factor analysis.
Brit. J. statist. Psychol.
Harris, C. W. Some Rao-Guttman relationships.
Kaiser, H. F. and Caffrey, J. Alpha factor analysis.
Psychometrika (in press).
Madansky, A. The fitting of straight lines when both variables are subject to error.
J. Amer. statist. Ass.
Neyman, J. Remarks on a paper by E. C. Rhodes.
J. roy. statist. Soc., 1937, 100, 50–57.
Rao, C. R. Estimation and tests of significance in factor analysis.
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.
Sargan, J. D. The estimation of economic relationships using instrumental variables.
Thomson, G. H. A hierarchy without a general factor.
Brit. J. Psychol., 1916, 8, 271–281.
Econometrics. New York: Wiley, 1952.
Tucker, L. R. An inter-battery method of factor analysis.
CrossRef Copyright information
© Psychometric Society 1964