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Using Phantom and Imaginary Latent Variables to Parameterize Constraints in Linear Structural Models

Published online by Cambridge University Press:  01 January 2025

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

The most widely-used computer programs for structural equation models analysis are the LISREL series of Jöreskog and Sörbom. The only types of constraints which may be made directly are fixing parameters at a constant value and constraining parameters to be equal. Rindskopf (1983) showed how these simple properties could be used to represent models with more complicated constraints, namely inequality constraints on unique variances. In this paper, two new concepts are introduced which enable a much wider variety of constraints to be made. The concepts, “phantom” and “imaginary” latent variables, allow fairly general equality and inequality constraints on factor loadings and structural model coefficients.

Keywords

Computer ProgramEquation ModelPublic PolicyLatent VariableFactor Loading

Information

Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 1 , March 1984 , pp. 37 - 47
Copyright
Copyright © 1984 The Psychometric Society

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Footnotes

During the preparation of this article, it was discovered that another researcher, Jack McArdle, had concurrently and independently discovered some of the techniques reported here. While he has chosen not to publish his research, I wish to acknowledge his work. I would like to thank Art Woodward for telling me about “sort-of simple” structure.

References

Reference Notes

Rindskopf, D. (1982). Parameterizing equality constraints in factor analysis and structural modeling. Unpublished manuscript.Google Scholar

References

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