This article shows that the mean and covariance structure of the predetermined autoregressive latent trajectory (ALT) model are very flexible. As a result, the shape of the modeled growth curve can be quite different from what one might expect at first glance. This is illustrated with several numerical examples that show that, for example, a…

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…

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…

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…

Mediation is usually assessed by a regression-based or structural equation modeling (SEM) approach that we refer to as the classical approach. This approach relies on the assumption that there are no confounders that influence both the mediator, "M", and the outcome, "Y". This assumption holds if individuals are randomly…

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…

State-space modeling techniques have been compared to structural equation modeling (SEM) techniques in various contexts but their unique strengths have often been overshadowed by their similarities to SEM. In this article, we provide a comprehensive discussion of these 2 approaches' similarities and differences through analytic comparisons and…

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…