, Volume 45, Issue 3, pp 289–308

Linear structural equations with latent variables

  • P. M. Bentler
  • David G. Weeks

DOI: 10.1007/BF02293905

Cite this article as:
Bentler, P.M. & Weeks, D.G. Psychometrika (1980) 45: 289. doi:10.1007/BF02293905


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 equationssimultaneous equationslinear relationscovariance structureslatent variableserrors in variablesfactor analysisstructural models

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