, Volume 45, Issue 3, pp 289–308 | Cite as

Linear structural equations with latent variables

  • P. M. Bentler
  • David G. Weeks


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.

Key Words

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


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Copyright information

© The Psychometric Society 1980

Authors and Affiliations

  • P. M. Bentler
    • 2
  • David G. Weeks
    • 1
  1. 1.Washington UniversityUSA
  2. 2.Department of PsychologyUniversity of CaliforniaLos Angeles

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