On the Interpretation of Exact Results for Structural Equation Estimators

In an unnormalised structural equation only the direction of the coefficient vector is determined. An estimator for the coefficients in the normalised equation defines an estimator for the direction of the coefficient vector in the unnormalised equation, and the density of the former induces a density for the latter. Though complex, the induced densities of the direction estimators are much more revealing about the properties of the estimators than their counterparts for the normalised case. The results help to explain other evidence of the superiority of the limited information maximum likelihood estimator