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Linear Structural Equations with Latent Variables

Published online by Cambridge University Press:  01 January 2025

P. M. Bentler  and
David G. Weeks
P. M. Bentler*
Affiliation:
University of California, Los Angeles
David G. Weeks
Affiliation:
Washington University
*
Requests for reprints should be sent to P. M. Bentler, Department of Psychology, University of California, Los Angeles, California 90024.
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Abstract

An interdependent multivariate linear relations model based on manifest, measured variables as well as unmeasured and unmeasurable latent variables is developed. The latent variables include primary or residual common factors of any order as well as unique factors. The model has a simpler parametric structure than previous models, but it is designed to accommodate a wider range of applications via its structural equations, mean structure, covariance structure, and constraints on parameters. The parameters of the model may be estimated by gradient and quasi-Newton methods, or a Gauss-Newton algorithm that obtains least-squares, generalized least-squares, or maximum likelihood estimates. Large sample standard errors and goodness of fit tests are provided. The approach is illustrated by a test theory model and a longitudinal study of intelligence.

Keywords

structural equationssimultaneous equationslinear relationscovariance structureslatent variableserrors in variablesfactor analysisstructural models
Type
Original Paper
Information
Psychometrika , Volume 45 , Issue 3 , September 1980 , pp. 289 - 308
Copyright
Copyright © 1980 The Psychometric Society

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Footnotes

This investigation was supported in part by a Research Scientist Development Award (KO2-DA00017) and a research grant (DA01070) from the U. S. Public Health Service.

References

Reference Notes

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