Linear structural equations with latent variables
 P. M. Bentler,
 David G. Weeks
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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 quasiNewton methods, or a GaussNewton algorithm that obtains leastsquares, generalized leastsquares, 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.
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 Title
 Linear structural equations with latent variables
 Journal

Psychometrika
Volume 45, Issue 3 , pp 289308
 Cover Date
 19800901
 DOI
 10.1007/BF02293905
 Print ISSN
 00333123
 Online ISSN
 18600980
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 structural equations
 simultaneous equations
 linear relations
 covariance structures
 latent variables
 errors in variables
 factor analysis
 structural models
 Industry Sectors
 Authors

 P. M. Bentler ^{(1)}
 David G. Weeks ^{(2)}
 Author Affiliations

 1. Department of Psychology, University of California, 90024, Los Angeles, California
 2. Washington University, USA