Overview: Structural Equation Modeling with Latent Variables

You can use the CALIS or TCALIS procedure for analysis of covariance structures, fitting systems of linear structural equations, and path analysis. These terms are more or less interchangeable, but they emphasize different aspects of the analysis. The analysis of covariance structures refers to the formulation of a model for the variances and covariances among a set of variables and the fitting of the model to an observed covariance matrix. In linear structural equations, the model is formulated as a system of equations relating several random variables with assumptions about the variances and covariances of the random variables. In path analysis, the model is formulated as a path diagram, in which arrows connecting variables represent variances, covariances, and regression (or path) coefficients. Path models and linear structural equation models can be converted to models of the covariance matrix and can, therefore, be fitted by the methods of covariance structure analysis. All of these methods support the use of hypothetical latent variables and measurement errors in the models.

Loehlin (1987) provides an excellent introduction to latent variable models by using path diagrams and structural equations. A more advanced treatment of structural equation models with latent variables is given by Bollen (1989). Fuller (1987) provides a highly technical statistical treatment of measurement-error models.