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Parameterizing Inequality Constraints on Unique Variances in Linear Structural Models

Published online by Cambridge University Press:  01 January 2025

David Rindskopf
David Rindskopf*
Affiliation:
City University of New York
*
Requests for reprints should be addressed to David Rindskopf, Educational Psychology, CUNY Graduate Center, 33 West 42nd Street, New York, NY, 10036.
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Abstract

Current computer programs for analyzing linear structural models will apparently handle only two types of constraints: fixed parameters, and equality of parameters. An important constraint not handled is inequality; this is particularly crucial for preventing negative variance estimates. In this paper, a method is described for imposing several kinds of inequality constraints in models, without the necessity for having computer programs which explicitly allow such constraints. The examples discussed include the prevention of Heywood cases, extension to inequalities of parameters to be greater than a specified value, and imposing ordered inequalities.

Keywords

structural modelsinequality constraints
Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 1 , March 1983 , pp. 73 - 83
Copyright
Copyright © 1983 The Psychometric Society

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Footnotes

Work on this project was aided by the City University of New York–Professional Staff Congress Research Award Program Grant Number 13631.

References

Bentler, P. M. Multistructure statistical model applied to factor analysis. Multivariate Behavioral Research, 1976, 11, 3–25.Google ScholarPubMed
Bentler, P. M., & Weeks, D. G. Linear structural equations with latent variables. Psychometrika, 1980, 45, 289–308.Google Scholar
Jöreskog, K. G. Estimation and testing of simplex models. British Journal of Mathematical and Statistical Psychology, 1970, 23, 121–145.CrossRefGoogle Scholar
Jöreskog, K. G. Structural equation models in the social sciences: Specification, estimation and testing. In Krishnaiah, P. R. (Eds.), Applications of statistics, Amsterdam: North-Holland, 1977.Google Scholar
Jöreskog, K. G., & Sörbom, D. Statistical models and methods for analysis of longitudinal data. In Aigner, D. J., Goldberger, A. S. (Eds.), Latent variables in socioeconomic models, Amsterdam: North-Holland, 1977.Google Scholar
Jöreskog, K. G., & Sörbom, D. LISREL IV: Analysis of linear structural relationships by the method of maximum likelihood, Chicago: National Educational Resources, 1978.Google Scholar
Lawley, D. N., & Maxwell, A. E. Factor analysis as a statistical method 2nd Edition, London: Butterworth, 1971.Google Scholar
Lee, S. Y. Estimation of covariance structure models with parameters subject to functional restraints. Psychometrika, 1980, 45, 309–324.CrossRefGoogle Scholar
McDonald, R. P. A simple comprehensive model for the analysis of covariance structures: Some remarks on applications. British Journal of Mathematical and Statistical Psychology, 1980, 33, 161–183.CrossRefGoogle Scholar
Werts, C. E., Linn, R. L., & Jöreskog, K. G. Estimating the parameters of path models involving unmeasured variables. In Blalock, H. M. Jr. (Eds.), Causal models in the social sciences, Chicago: Aldine, 1971.Google Scholar
Wismer, D. A., & Chattergy, R. Introduction to nonlinear optimization: A problem solving approach, New York: North Holland, 1978.Google Scholar