The Determinacy of Variables in Structural Equation Models

The indeterminacy of variables in a structural equation model - a path model with latent variables - is considered. It is shown that when the variables in the structural ]model are all manifest, the error-terms - disturbances - are uniquely determined given the parameters and the data; when the variables in the structural model are all latent, the error-terms have indeterminate components that are simple linear transformations of the indeterminate I components of the common factor model; and when they are mixed, a sufficient condition for the error-term associated with a manifest variable to be uniquely determined is that there is no directed path to it from a latent variable. Moreover, for error-terms that are indeterminate due to the effects of latent variables it is demonstrated that error-term analysis along the lines of residual analysis can be employed by the use of suitable estimates of the latent variables.