Finite mixture models are well known to have poorly behaved likelihood functions featuring singularities and multiple optima. Growth mixture models may suffer from fewer of these problems, potentially benefiting from the structure imposed on the estimated class means and covariances by the specified growth model. As demonstrated here, however,…

A maximum likelihood approach to correlational outlier identification is introduced and compared to the Mahalanobis D squared and Comrey D statistics through Monte Carlo simulation. Identification performance depends on the nature of correlational outliers and the measure used, but the maximum likelihood approach is the most robust performance…

Asymptotic distributions of the estimators of communalities are derived for the maximum likelihood method in factor analysis. It is shown that equating the asymptotic standard error of the communality estimate to the unique variance estimate is not correct for the unstandardized case. Monte Carlo simulations illustrate the study. (SLD)

Functional and structural relationship alternatives to the standard "F"-test for analysis of covariance (ANCOVA) are discussed for cases when the covariate is measured with error. An approximate statistical test based on the functional relationship approach is preferred on the basis of Monte Carlo simulation results. (SLD)

Type I error rates of the likelihood ratio test for the detection of differential item functioning (DIF) were investigated using Monte Carlo simulations. The graded response model with five ordered categories was used to generate data sets of a 30-item test for samples of 300 and 1,000 simulated examinees. All DIF comparisons were simulated by…

This Monte-Carlo study compared modified Newton (NW), expectation-maximization algorithm (EM), and minimum Cramer-von Mises distance (MD), used to estimate parameters of univariate mixtures of two components. Data sets were fixed at size 160 and manipulated by mean separation, variance ratio, component proportion, and non-normality. Results…

Effects of test length, sample size, and assumed ability distribution were investigated in a multiple replication Monte Carlo study under the 1-parameter (1P) and 2-parameter (2P) logistic graded model with five score levels. Accuracy and variability of item parameter and ability estimates were examined. Monte Carlo methods were used to evaluate…

In an experiment manipulating artificial data in a factorial design, model misspecification and varying levels of error in measurement and in model structure are shown to have significant effects on LISREL parameter estimates in a modified peer influence model. (Author/LMO)