Developed an extension of the general latent variable growth curve modeling framework to four levels of the hierarchy. The extension merged two common analytical approaches: full information maximum likelihood (ML) latent growth modeling and limited information multilevel latent growth modeling using an ML estimator. Results for data from 250…

An Expectation-Maximization (EM) algorithm in a maximum likelihood framework is developed to estimate finite mixtures of multivariate regression and simultaneous equation models with multiple endogenous variables. A dataset with cross-sectional observations for a diverse sample of businesses illustrates the semiparametric approach. (SLD)

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…

Investigated the assumption that determining an adequate sample size in structural equation modeling can be aided by considering the number of parameters to be estimated. Findings from maximum likelihood confirmatory factor analysis support previous research on the effect of sample size, measured variable reliability, and the number of measured…

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)

Used simulation to compare structural equation modeling methods for estimating and testing hypotheses about an interaction between continuous variables. Findings indicate that the two-stage least squares procedure exhibited more bias and lower power than the other methods. The Jaccard-Wan procedure (J. Jaccard and C. Wan, 1995) and maximum…

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)