Theoretic fit and empirical fit: The performance of maximum likelihood versus generalized least squares estimation in structural equation models

In research the goal is often to construct models that reflect the structures and parameters of some unobservable causal mechanism. The degree of isomorphism between such a theoretic model and a "true" model can be labeled "theoretic fit". In the absence of direct evidence that the researcher's theoretic model accurately reflects the true model, indices of "empirical fit" (Chi-Square, etc.) are used as indirect evidence of verisimilitude. The issue addressed here is: Is empirical fit necessarily a good indicator of theoretic fit? This study uses simulation to compare the ability of Maximum Likelihood (ML) and Generalized Least Squares (GLS) estimation to provide theoretic fit in models that are parsimonious representations of a true model. We find that empirical fit using GLS was actually superior to that obtained when parameters in the incomplete model were constrained to the true values of the generating model. However, this apparent goodness of fit of GLS is obtained through greater distortion of the parameter estimates. In short, better empirical fit obtained for GLS, compared with ML, was obtained at the cost of lower theoretic fit.