Some nonlinear developmental phenomena can be represented by using a simple piecewise procedure in which 2 linear growth models are joined at a single knot. The major problem of using this piecewise approach is that researchers have to optimally locate the knot (or turning point) where the change in the growth rate occurs. A relatively simple way…

Valuable methods have been developed for incorporating ordinal variables into structural equation models using a latent response variable formulation. However, some model parameters, such as the means and variances of latent factors, can be quite difficult to interpret because the latent response variables have an arbitrary metric. This limitation…

The aim of this study was to compare the small sample (N = 1, 3, 5, 10, 15) performance of a Bayesian multivariate vector autoregressive (BVAR-SEM) time series model relative to frequentist power and parameter estimation bias. A multivariate autoregressive model was developed based on correlated autoregressive time series vectors of varying…

This article proposes a comprehensive approach based on structural equation modeling for assessing the amount of trait-level change derived from faking-motivating situations. The model is intended for a mixed 2-wave 2-group design, and assesses change at both the group and the individual level. Theoretically the model adopts an integrative…

Structural equation modeling (SEM) is widely used as a statistical framework to test complex models in behavioral and social sciences. When the number of publications increases, there is a need to systematically synthesize them. Methodology of synthesizing findings in the context of SEM is known as meta-analytic SEM (MASEM). Although correlation…

The REQS package is an interface between the R environment of statistical computing and the EQS software for structural equation modeling. The package consists of 3 main functions that read EQS script files and import the results into R, call EQS script files from R, and run EQS script files from R and import the results after EQS computations.…

Structural equation mixture models (SEMMs) are latent class models that permit the estimation of a structural equation model within each class. Fitting SEMMs is illustrated using data from 1 wave of the Notre Dame Longitudinal Study of Aging. Based on the model used in the illustration, SEMM parameter estimation and correct class assignment are…

One common application of structural equation modeling (SEM) involves expressing and empirically investigating causal explanations. Nonetheless, several aspects of causal explanation that have an impact on behavioral science methodology remain poorly understood. It remains unclear whether applications of SEM should attempt to provide complete…

Growth mixture modeling (GMM) has become a more popular statistical method for modeling population heterogeneity in longitudinal data, but the performance characteristics of GMM enumeration indexes in correctly identifying heterogeneous growth trajectories are largely unknown. Few empirical studies have addressed this issue. This study considered…

In many intervention and evaluation studies, outcome variables are assessed using a multimethod approach comparing multiple groups over time. In this article, we show how evaluation data obtained from a complex multitrait-multimethod-multioccasion-multigroup design can be analyzed with structural equation models. In particular, we show how the…

Identification of structural equation models remains a challenge to many researchers. Although empirical tests of identification are readily available in structural equation modeling software, these examine local identification and rely on sample estimates of parameters. Rules of identification are available, but do not include all models…

In structural equation modeling software, either limited-information (bivariate proportions) or full-information item parameter estimation routines could be used for the 2-parameter item response theory (IRT) model. Limited-information methods assume the continuous variable underlying an item response is normally distributed. For skewed and…

Applied researchers often include mediation effects in applications of advanced methods such as latent variable models and linear growth curve models. Guidance on how to estimate statistical power to detect mediation for these models has not yet been addressed in the literature. We describe a general framework for power analyses for complex…

This article presents several longitudinal mediation models in the framework of latent growth curve modeling and provides a detailed account of how such models can be constructed. Logical and statistical challenges that might arise when such analyses are conducted are also discussed. Specifically, we discuss how the initial status (intercept) and…

Structural equation models are commonly used to estimate relationships between latent variables. Almost universally, the fitted models specify that these relationships are linear in form. This assumption is rarely checked empirically, largely for lack of appropriate diagnostic techniques. This article presents and evaluates two procedures that can…