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A General Approach to Nonlinear Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Roderick P. McDonald*
Affiliation:
University of New England, N.S.W., Australia

Abstract

The method presented attempts to allow for nonlinear, possibly nonmonotonic relations between manifest and latent variates. An attempt is made to provide a workable criterion for choosing between alternative models on the basis of observable data as well as for constructing the appropriate function. An idealized numerical example is given.

Type
Original Paper
Copyright
Copyright © 1962 The Psychometric Society

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Footnotes

*

The author is indebted to Mr. E. J. Burr of the Department of Mathematics, University of New England, and to Dr. J. A. Keats of the University of Queensland, for their advice and criticism.

References

Eysenck, H. J. The nature of anxiety and the factorial method. Psychol. Rep., 1958, 4, 453454.CrossRefGoogle Scholar
Gibson, W. A. Three multivariate models: factor analysis, latent structure analysis, and latent profile analysis. Psychometrika, 1959, 24, 229252.CrossRefGoogle Scholar
Gibson, W. A. Nonlinear factors in two dimensions. Psychometrika, 1960, 25, 381392.CrossRefGoogle Scholar
Guttman, L. The principal components of scale analysis. In Stouffer, S. A. et al (Eds.), Measurement and prediction. Princeton: Princeton Univ. Press, 1950, 312361.Google Scholar
Holzinger, K. J. and Harman, H. H. Factor analysis, Chicago: Univ. Chicago Press, 1941.Google Scholar
Kendall, M. G. The advanced theory of statistics. Vol. 2, London: Griffin, 1946.Google Scholar
Kendall, M. G. and Stuart, A. The advanced theory of statistics. Vol. 1, London: Griffin, 1958.Google Scholar
Lazarsfeld, P. F. The logical and mathematical foundation of latent structure analysis. In Stouffer, S. A. et al (Eds.), Measurement and prediction. Princeton: Princeton Univ. Press, 1950, 362412.Google Scholar
Lazarsfeld, P. F. A conceptual introduction to latent structure analysis. In Lazarsfeld, P. F. (Eds.), Mathematical thinking in the social sciences. Glencoe, Ill.: Free Press, 1954, 349387.Google Scholar
Lazarsfeld, P. F. Latent structure analysis and test theory. In Gulliksen, H. and Messick, S. (Eds.), Psychological scaling: theory and applications. New York: Wiley, 1960, 8396.Google Scholar
Suchman, E. A. The intensity component in attitude and opinion research. In Stouffer, S. A. et al (Eds.), Measurement and prediction. Princeton: Princeton Univ. Press, 1950, 213276.Google Scholar
Szegö, G. Orthogonal polynomials. Amer. Math. Soc. Colloquium Publications, Vol. 23, 1959.Google Scholar
Thomson, G. H. The factorial analysis of human ability (4th ed.), New York: Houghton Mifflin, 1950.Google Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar
Torgerson, W. S. Theory and methods of scaling, New York: Wiley, 1959.Google Scholar