Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…

Growth mixture modeling (GMM) is a relatively new technique for analyzing longitudinal data. However, when applying GMM, researchers might assume that the higher level (nonrepeated measure) units (e.g., students) are independent from each other even though it might not always be true. This article reports the results of a simulation study…

In research concerning model invariance across populations, researchers have discussed the limitations of the conventional chi-square difference test ([Delta] chi-square test). There have been some research efforts in using goodness-of-fit indexes (i.e., [Delta]goodness-of-fit indexes) for assessing multisample model invariance, and some specific…

Parameter recovery was assessed within mixture confirmatory factor analysis across multiple estimator conditions under different simulated levels of mixture class separation. Mixture class separation was defined in the measurement model (through factor loadings) and the structural model (through factor variances). Maximum likelihood (ML) via the…

Latent difference score models (e.g., McArdle & Hamagami, 2001) are extended to include effects from prior changes to subsequent changes. This extension of latent difference scores allows for testing hypotheses where recent changes, as opposed to recent levels, are a primary predictor of subsequent changes. These models are applied to…

A typical structural equation model is intended to reproduce the means, variances, and correlations or covariances among a set of variables based on parameter estimates of a highly restricted model. It is not widely appreciated that the sample statistics being modeled can be quite sensitive to outliers and influential observations, leading to bias…

Simulation researchers are sometimes faced with the need to use multiple statistical software packages in the process of conducting their research, potentially having to go between software packages manually. This can be a tedious and time-consuming process that generally motivates researchers to use fewer replications in their simulations than…

Among the many methods currently available for estimating latent variable interactions, the unconstrained approach is attractive to applied researchers because of its relatively easy implementation with any structural equation modeling (SEM) software. Using a Monte Carlo simulation study, we extended and evaluated the unconstrained approach to…

To understand one developmental process, it is often helpful to investigate its relations with other developmental processes. Statistical methods that model development in multiple processes simultaneously over time include latent growth curve models with time-varying covariates, multivariate latent growth curve models, and dual trajectory models.…

Meta-analysis is the statistical analysis of a collection of analysis results from individual studies, conducted for the purpose of integrating the findings. Structural equation modeling (SEM), on the other hand, is a multivariate technique for testing hypothetical models with latent and observed variables. This article shows that fixed-effects…

Reliability can be estimated using structural equation modeling (SEM). Two potential problems with this approach are that estimates may be unstable with small sample sizes and biased with misspecified models. A Monte Carlo study was conducted to investigate the quality of SEM estimates of reliability by themselves and relative to coefficient…

Standardized parameter estimates are routinely used to summarize the results of multiple regression models of manifest variables and structural equation models of latent variables, because they facilitate interpretation. Although the typical standardization of interaction terms is not appropriate for multiple regression models, straightforward…

Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this article, the "t" distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian…

Several alternatives are available for specifying the residual structure in latent growth curve modeling. Two specifications involve uncorrelated residuals and represent the most commonly used residual structures. The first, building on repeated measures analysis of variance and common specifications in multilevel models, forces residual variances…

Recent missing data studies have argued in favor of an "inclusive analytic strategy" that incorporates auxiliary variables into the estimation routine, and Graham (2003) outlined methods for incorporating auxiliary variables into structural equation analyses. In practice, the auxiliary variables often have missing values, so it is reasonable to…