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Longitudinal Factor Analysis

Published online by Cambridge University Press:  01 January 2025

M. C. Corballis
Affiliation:
McGill University
R. E. Traub
Affiliation:
The Ontario Institute for Studies in Education

Abstract

A model is presented for factor analysing scores on a set of psychological tests administered as both pre- and postmeasures in a study of change. The model assumes that the same factors underlie the tests on each occasion, but that factor scores as well as factor loadings may change between occasions. Factors are defined to be orthogonal between as well as within occasions. A two-stage least squares procedure for fitting the model is described, and generally provides a unique rotation solution for the factors on each occasion.

Type
Original Paper
Copyright
Copyright © 1970 The Psychometric Society

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Footnotes

*

We thank M. W. Browne, R. P. McDonald, R. Pruzek, and the Managing Editor for their constructive comments.

References

Browne, M. W. Fitting the factor analysis model. Psychometrika, 1969, 34, 375394.Google Scholar
Corballis, M. C. Practice and the simplex. Psychological Review, 1965, 72, 399406.CrossRefGoogle ScholarPubMed
Eckart, C. and Young, G. The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1, 211218.CrossRefGoogle Scholar
Evans, G. T. Factor analytic treatment of growth data. Multivariate behavioral Research, 1967, 2, 109134.CrossRefGoogle ScholarPubMed
Fleishman, E. A. Factor structure in relation to task difficulty in psychomotor performance. Educational and Psychological Measurement, 1957, 17, 522532.Google Scholar
Fleishman, E. A. Abilities at different stages of practice in rotary pursuit performance. Journal of experimental Psychology, 1960, 60, 162171.CrossRefGoogle ScholarPubMed
Fleishman, E. A. Human abilities and the acquisition of skill. In Bilodeau, E. A. (Eds.), Acquisition of skill. New York: Academic Press. 1966, 147167.Google Scholar
Garrett, H. E. A development theory of intelligence. American Psychologist, 1946, 1, 372378.CrossRefGoogle Scholar
Harman, H. H. and Jones, W. H. Factor analysis by minimizing residuals (minres). Psychometrika, 1966, 31, 351368.CrossRefGoogle ScholarPubMed
Harris, C. W. Canonical factor models for the description of change. In Harris, C. W. (Eds.), Problems in measuring change. Madison, Wis.: Univ. Wis. Press. 1963, 138155.Google Scholar
Harris, C. W. Some recent developments in factor analysis. Educational and Psychological Measurement, 1964, 24, 193206.Google Scholar
Hofstaetter, P. R. The changing composition of intelligence: a study in T-technique. Journal of genetic Psychology, 1954, 85, 159164.CrossRefGoogle ScholarPubMed
Horst, P. Matrix algebra for social scientists, 1963, New York: Holt, Rinehart and Winston.Google Scholar
Hotelling, H. Analysis of a complex of statistical variables into principal components. Journal of educational Psychology, 1933, 24, 417441.Google Scholar
Kaiser, H. F. and Caffrey, J. Alpha factor analysis. Psychometrika, 1965, 30, 114.CrossRefGoogle ScholarPubMed
Lawley, D. N. The estimation of factor loadings by the method of maximum likelihood. Proceedings of the Royal Society of Edinburgh, 1940, 60, 6482.CrossRefGoogle Scholar
Lawley, D. N., Maxwell, A. E.. Factor transformation methods. British Journal of statistical Psychology, 1964, 17, 97103.CrossRefGoogle Scholar
Meyer, W. J. and Bendig, A. W. A longitudinal study of the Primary mental Abilities Test. Journal of educational Psychology, 1961, 52, 5060.CrossRefGoogle Scholar
Thurstone, T. G. Manual for the SRA Primary Mental Abilities, 1958, Chicago, Ill.: Science Research Associates.Google Scholar
Tucker, L. R. Implications of factor analysis of three-way matrices for measurement of change. In Harris, C. W. (Eds.), Problems in measuring change. Madison, Wis.: Univ. Wis. Press. 1963, 122137.Google Scholar