Testing factorial invariance has recently gained more attention in different social science disciplines. Nevertheless, when examining factorial invariance, it is generally assumed that the observations are independent of each other, which might not be always true. In this study, we examined the impact of testing factorial invariance in multilevel…

Regression mixture models, which have only recently begun to be used in applied research, are a new approach for finding differential effects. This approach comes at the cost of the assumption that error terms are normally distributed within classes. This study uses Monte Carlo simulations to explore the effects of relatively minor violations of…

The purpose of this study was to examine the impact of misspecifying a growth mixture model (GMM) by assuming that Level-1 residual variances are constant across classes, when they do, in fact, vary in each subpopulation. Misspecification produced bias in the within-class growth trajectories and variance components, and estimates were…

Structural equation modeling provides the framework for investigating experimental effects on the basis of variances and covariances in repeated measurements. A special type of confirmatory factor analysis as part of this framework enables the appropriate representation of the experimental effect and the separation of experimental and…

Normal theory maximum likelihood (ML) is by far the most popular estimation and testing method used in structural equation modeling (SEM), and it is the default in most SEM programs. Even though this approach assumes multivariate normality of the data, its use can be justified on the grounds that it is fairly robust to the violations of the…

Recent advances in testing mediation have found that certain resampling methods and tests based on the mathematical distribution of 2 normal random variables substantially outperform the traditional "z" test. However, these studies have primarily focused only on models with a single mediator and 2 component paths. To address this limitation, a…

Although SAS PROC CALIS is not designed to perform multigroup comparisons, it is believed that SAS can be "tricked" into doing so for groups of equal size. At present, there are no comprehensive examples of the steps involved in performing a multigroup comparison in SAS. The purpose of this article is to illustrate these steps. We demonstrate…

Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics. Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem by deriving the direct Quartimin rotation. Jennrich was also the first to develop standard errors for rotated solutions, although these have still not made…

The goals of this article are twofold: (a) briefly highlight the merits of residual centering for representing interaction and powered terms in standard regression contexts (e.g., Lance, 1988), and (b) extend the residual centering procedure to represent latent variable interactions. The proposed method for representing latent variable…