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 th e 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 e rror-terms have indeterminate components that are simple linear transf ormations of the indeterminate components of the common factor model; and when they are mixed, a sufficient condition for the error-term ass ociated with a manifest variable to be uniquely determined is that the re is no directed path to it from a latent variable. Moreover, for err or-terms that are indeterminate due to the effects of latent variables it is demonstrated that error-term analysis along the lines of residu al analysis can be employed by the use of suitable estimates of the la tent variables.