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A Scale-Invariant Treatment for Recursive Path Models

Published online by Cambridge University Press:  01 January 2025

Roderick P. McDonald ,
Prudence M. Parker  and
Tomoichi Ishizuka
Roderick P. McDonald*
Affiliation:
University of Illinois
Prudence M. Parker
Affiliation:
Macquarie University
Tomoichi Ishizuka
Affiliation:
National Center for University Examinations, Tokyo
*
Requests for reprints should be sent to R. P. McDonald, Department of Psychology, University of Illinois, 603 East Daniel Street, Champaign, IL 61820.
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Abstract

A reparameterization is formulated that yields estimates of scale-invariant parameters in recursive path models with latent variables, and (asymptotically) correct standard errors, without the use of constrained optimization. The method is based on the logical structure of the reticular action model.

Keywords

scale invariancerecursive modelsanalysis of correlation structures
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 3 , September 1993 , pp. 431 - 443
Copyright
Copyright © 1993 The Psychometric Society

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References

Bentler, P. M. (1985). Theory and implementation of EQS: A structural equations program, Los Angeles: BMDP Statistical Software.Google Scholar
Browne, M. W. (1982). Covariance structures. In Hawkins, D. M. (Eds.), Topics in applied multivariate analysis (pp. 72–141). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Browne, M. W., & du Toit, S. H. C. (1987). Automated fitting of non-standard models (Report W5-39), Pretoria, South Africa: Human Sciences Research Council.Google Scholar
de Pijper, W. M., Saris, W. E. (1984). In Jöreskog, K. G., & Wold, H. (Eds.), Systems under indirect observations: Causality-structure-prediction, Amsterdam: North Holland.Google Scholar
Duncan, O. D., Haller, A. O., & Portes, A. (1968). Peer influences on aspirations: A re-interpretation. American Journal of Sociology, 74, 119–137.CrossRefGoogle Scholar
Fraser, C. (1980). Cosan: User's Guide, Australia: University of New England, Centre for Behavioral Studies in Education.Google Scholar
Hanushek, E. A., & Jackson, J. E. (1977). Statistical methods for social scientists, New York: Academic Press.Google Scholar
Harris, C. W. (1962). Some Rao-Guttman relationships. Psychometrika, 27, 247–263.CrossRefGoogle Scholar
Jöreskog, K. G., & Sörbom, D. (1986). LISREL VI: Analysis of linear structural relationships by maximum likelihood, instrumental variables, and least squares methods, Moorsville, IN: Scientific Software.Google Scholar
Kaiser, H. F., & Caffrey, J. (1965). Alpha factor analysis. Psychometrika, 30, 1–14.CrossRefGoogle ScholarPubMed
Krane, W. R., & McDonald, R. P. (1978). Scale invariance and the factor analysis of correlation matrices. British Journal of Mathematical and Statistical Psychology, 31, 218–228.CrossRefGoogle Scholar
Lee, S.-Y. (1980). The penalty function method in constrained estimation of covariance structure models. Psychometrika, 45, 309–324.CrossRefGoogle Scholar
Lee, S.-Y., & Fong, W.-K. (1983). A scale invariant model for three-mode factor analysis. British Journal of Mathematical and Statistical Psychology, 36, 217–223.CrossRefGoogle Scholar
Lee, S.-Y., & Poon, W.-Y. (1985). Further developments on constrained estimation in analysis of covariance structures. The Statistician, 34, 305–316.CrossRefGoogle Scholar
McArdle, J. J., & McDonald, R. P. (1984). Some algebraic properties of the reticular action model for moment structures. British Journal of Mathematical and Statistical Psychology, 37, 234–251.CrossRefGoogle ScholarPubMed
McDonald, R. P. (1978). A simple comprehensive model for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 31, 59–72.CrossRefGoogle Scholar
McDonald, R. P. (1980). A simple comprehensive model for the analysis of covariance structures: Some remarks on applications. British Journal of Mathematical and Statistical Psychology, 33, 161–183.CrossRefGoogle Scholar
Rindskopf, D. (1984). Using phantom and imaginary variables to parameterize constraints in linear structural models. Psychometrika, 49, 37–47.CrossRefGoogle Scholar
Sobel, M. E. (1986). Some new results on indirect effects and their standard errors in covariance structure models. In Tuma, N. B. (Eds.), Sociological methodology 1986 (pp. 159–186). San Francisco: Jossey-Bass.Google Scholar
Stone, C. A., & Sobel, M. E. (1990). The robustness of total indirect effects in covariance structure models estimated by maximum likelihood. Psychometrika, 55, 337–352.CrossRefGoogle Scholar