Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-02-11T09:41:49.597Z Has data issue: false hasContentIssue false
  • English
  • Français

Contributions to Factor Analysis of Dichotomous Variables

Published online by Cambridge University Press:  01 January 2025

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

Abstract

A new method is proposed for the factor analysis of dichotomous variables. Similar to the method of Christoffersson this uses information from the first and second order proportions to fit a multiple factor model. Through a transformation into a new set of sample characteristics, the estimation is considerably simplified. A generalized least-squares estimator is proposed, which asymptotically is as efficient as the corresponding estimator of Christoffersson, but which demands less computing time.

Keywords

multiple factor modelfirst and second order proportionsgeneralized least-squarestetrachoric correlations
Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 4 , December 1978 , pp. 551 - 560
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

This research was supported by the Bank of Sweden Tercentenary Foundation under project “Structural Equation Models in the Social Sciences”, project director Karl G. Jöreskog.

References

Reference Notes

Gruvaeus, G. T. & Jöreskog, K. G. A computer program for minimizing a function of several variables, 1970, Princeton, N. J.: Educational Testing Service.Google Scholar
Muthen, B. & Dahlqvist, B. FADIC. Factor analysis of dichotomous variables. A Fortran IV computer program in preparation, 1978.Google Scholar

References

Bock, R. D. & Lieberman, M. Fitting a response model for n dichotomously scored items. Psychometrika, 1970, 35, 179–197.CrossRefGoogle Scholar
Christoffersson, A. Factor analysis of dichotomized variables. Psychometrika, 1975, 40, 5–32.CrossRefGoogle Scholar
Cramér, H. Mathematical methods of statistics, 1946, Princeton, N. J.: Princeton University Press.Google Scholar
Fletcher, R. & Powell, M. J. D. A rapidly convergent descent method for minimization. The Computer Journal, 1963, 6, 163–168.CrossRefGoogle Scholar
Jöreskog, K. G. Factor analysis by least squares and maximum likelihood methods. In Enslein, K., Ralston, K. A. & Wilf, M.S. (Eds.), Statistical methods for digital computers, 1977, N. Y.: Wiley.Google Scholar
Kirk, D. B. On the numerical approximation of the bivariate normal (tetrachoric) correlation coefficient. Psychometrika, 1973, 38, 259–268.CrossRefGoogle Scholar
Lord, F. & Novick, H. Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-Wesley Publishing Company.Google Scholar
Rotter, J. B. Generalized expectancies for internal versus external control of reinforcement. Psychological Monographs, 1966, 80, (Whole Number 609).CrossRefGoogle ScholarPubMed