Shows that the conventional noncentrality parameter estimator of covariance structure models, currently implemented in popular structural modeling programs, possesses asymptotically potentially large bias, variance, and mean squared error (MSE). Presents a formal expression for its large-sample bias and quantifies large-sample bias and MSE. (SLD)

Investigated the impact of categorization on confirmatory factor analysis parameter estimates, standard errors, and five ad hoc fit indexes through simulation studies. Results replicate some previous studies but also suggest that tests of parameter estimates will be underestimated and the amount of underestimation will increase as saturation…

Discusses two criticisms raised by L. Hayduk and D. Glaser of the most commonly used point estimate of the Root Mean Square Error (RMSEA) and points out misconceptions in their discussion. Although there are apparent flaws in their arguments, the RMSEA is open to question for several other reasons. (SLD)

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)

Monte Carlo methods were used to study the accuracy and utility of estimators of overall error and error due to approximation in structural equation modeling. Effects of sample size, indicator reliabilities, and degree of misspecification were examined. The rescaled noncentrality parameter also was examined. Choosing among competing models is…

A Monte Carlo approach was used to examine bias in the estimation of indirect effects and their associated standard errors. Results illustrate the adverse effects of nonnormality on the accuracy of significance tests in latent variable models estimated using normal theory maximum likelihood statistics. (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)