Relative fit indices using the null model as the reference point in computation may differ across estimation methods, as this article illustrates by comparing maximum likelihood, ordinary least squares, and generalized least squares estimation in structural equation modeling. The illustration uses a covariance matrix for six observed variables…

Used simulation to demonstrate how the choice of estimation method affects indexes of fit and parameter bias for different sample sizes when nested models vary in terms of specification error and the data demonstrate different levels of kurtosis. Discusses results for maximum likelihood (ML), generalized least squares (GLS), and weighted least…

Actual kurtotic and skewed data and varied sample sizes and estimation methods demonstrated that normal theory maximum likelihood and generalized least square estimators were fairly consistent and almost identical. Standard errors tended to underestimate the estimator's true variation but the problem was not serious for large samples. (SLD)

Goodness of fit indexes developed by R. P. McDonald (1989) and Satorra-Bentler scale correction methods (A. Satorra and P. M. Bentler, 1988) were studied. The Satorra-Bentler index is shown to have the least error under each distributional misspecification level when the model has correct structural specification. (SLD)

LISREL 8 invokes a ridge option when maximum likelihood or generalized least squares are used to estimate a structural equation model with a nonpositive definite covariance or correlation matrix. Implications of the ridge option for model fit, parameter estimates, and standard errors are explored through two examples. (SLD)