Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-07T16:31:30.887Z Has data issue: false hasContentIssue false
  • English
  • Français

Transformation to Achieve a Longitudinally Stationary Factor Pattern Matrix

Published online by Cambridge University Press:  01 January 2025

Stephen L. Bieber  and
William Meredith
Stephen L. Bieber*
Affiliation:
Departments of Statistics and Psychology, University of Wyoming, Laramie
William Meredith
Affiliation:
University of California, Berkeley
*
Requests for reprints should he sent to Stephen L. Bieber, Department of Statistics, University of Wyoming, Laramie, WY 82071.
Get access Rights & Permissions [Opens in a new window]

Abstract

Meredith's method of extracting a factorially invariant solution is adapted to longitudinal settings. An explorational estimation procedure is presented which attempts to identify the longitudinal factor components of an across occasion variance-covariance matrix. This is effected by transforming an initial factor pattern matrix to stationarity. The estimation is performed in two parts, the first employing a stepwise algorithm to ascertain the dimensionality and existence of the longitudinal components and the second being the direct estimation of the existing factor pattern.

Keywords

factor analysis
Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 4 , December 1986 , pp. 535 - 547
Copyright
Copyright © 1986 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.)

References

Bentler, P. M., Lee, S. (1978). Statistical aspects of a three-mode analysis model. Psychometrika, 43, 343–352.CrossRefGoogle Scholar
Bentler, P. M., Weeks, D. G. (1979). Interrelationships among models for the analysis of moment structures. Multivariate Behavioral Research, 14, 169–186.CrossRefGoogle Scholar
Bloxom, B. (1968). A note on invariance in three-mode factor analysis. Psychometrika, 33, 347–350.CrossRefGoogle ScholarPubMed
Cliff, N. (1966). Orthogonal rotation to congruence. Psychometrika, 31, 33–42.CrossRefGoogle Scholar
Cohen, J. (1957). The factorial structure of the WAIS between early adulthood and old age. Journal of Consulting Psychology, 21, 283–290.CrossRefGoogle ScholarPubMed
Jöreskog, K. G. (1970). Factoring the multitest-multioccasion correlation matrix. In Lunneborg, C. E. (Eds.), Current problems and techniques in multivariate psychology (pp. 68–100). Seattle: University of Washington Press.Google Scholar
Jöreskog, K. G., Sörbom, K. (1977). Statistical models and methods for analysis of longitudinal data. In Aigner, D. V., Goldberger, A. S. (Eds.), Latent variables in socioeconomic models (pp. 285–325). Amsterdam: North Holland.Google Scholar
Jöreskog, K. G., Sörbom, D. (1984). LISREL VI users guide, Chicago: International Educational Services.Google Scholar
Kaiser, H. F. (1963). Image analysis. In Harris, C. W. (Eds.), Problems in measuring change (pp. 156–166). Madison: University of Wisconsin Press.Google Scholar
Lawson, C. L., Hanson, R. J. (1974). Solving least squares problems, Englewood Cliffs: Prentice Hall.Google Scholar
Meredith, W. (1964). Rotation to achieve factorial invariance. Psychometrika, 29, 187–206.CrossRefGoogle Scholar
Tucker, L. R. (1951). A method for synthesis of factor analysis studies, Washington, D. C.: Dept. of the Army.CrossRefGoogle Scholar
Tucker, L. R. (1963). Implications of factor analysis of three-way matrices for measurement of change. In Harris, C. W. (Eds.), Problems in measuring change (pp. 122–137). Madison: University of Wisconsin Press.Google Scholar
Winer, B. J. (1971). Statistical principles in experimental design, New York: McGraw-Hill.Google Scholar
Zegers, F. E., ten Berge, J. M. F. (1985). A family of association coefficients. Psychometrika, 50, 17–24.CrossRefGoogle Scholar