A structural equation modeling method for examining time-invariance of variable specificity in longitudinal studies with multiple measures is outlined, which is developed within a confirmatory factor-analytic framework. The approach represents a likelihood ratio test for the hypothesis of stability in the specificity part of the residual term…

A correlation structure modeling method for comparison of mediated effects is outlined. The procedure permits point and interval estimation of differences in mediator effects, and is useful with models postulating 1 or more predictor, intervening, or response variables that may also be latent constructs. The approach allows scale-free evaluation…

The coding of time in latent curve models has been shown to have important implications in the interpretation of growth parameters. Centering time is often done to improve interpretation but may have consequences for estimated parameters. This article studies the effects of coding and centering time when there is interindividual heterogeneity in…

Ant colony optimization is a recently proposed heuristic procedure inspired by the behavior of real ants. This article applies the procedure to model specification searches in structural equation modeling and reports the results. The results demonstrate the capabilities of ant colony optimization algorithms for conducting automated searches.

The analysis of interaction among latent variables has received much attention. This article introduces a Bayesian approach to analyze a general structural equation model that accommodates the general nonlinear terms of latent variables and covariates. This approach produces a Bayesian estimate that has the same statistical optimal properties as a…

Some authors have suggested that sample size in covariance structure modeling should be considered in the context of how many parameters are to be estimated (e.g., Kline, 2005). Previous research has examined the effect of varying sample size relative to the number of parameters being estimated (N:q). Although some support has been found for this…

In this investigation, we used a classic latent profile analysis (LPA), a person-centered approach, to identify groups of students who had similar profiles for multiple dimensions of academic self-concept (ASC) and related these LPA groups to a diverse set of correlates. Consistent with a priori predictions, we identified 5 LPA groups representing…

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…

A covariance structure modeling perspective on reliability estimation can be used to construct a formal approach to estimation of reliability in multilevel models. This article presents a didactic discussion of the relation between a structural modeling procedure for scale reliability estimation and the notion of reliability of observed means in…

Latent class analysis (LCA) is a statistical method used to identify a set of discrete, mutually exclusive latent classes of individuals based on their responses to a set of observed categorical variables. In multiple-group LCA, both the measurement part and structural part of the model can vary across groups, and measurement invariance across…

Mediators are variables that explain the association between an independent variable and a dependent variable. Structural equation modeling (SEM) is widely used to test models with mediating effects. This article illustrates how to construct confidence intervals (CIs) of the mediating effects for a variety of models in SEM. Specifically, mediating…

This study introduces a novel application of structural equation modeling (SEM) for the analysis of cortisol data that are collected using a pre-post-post design. By way of an extended example, an SEM model is developed that permits an examination of both the overall level of cortisol, as well as changes in cortisol (reactivity and regulation), as…

A number of authors have proposed that determining an adequate sample size in structural equation modeling can be aided by considering the number of parameters to be estimated. While this advice seems plausible, little empirical support appears to exist. A previous study by Jackson (2001), failed to find support for this hypothesis, however, there…

Univariate latent growth modeling (LGM) of composites of multiple items (e.g., item means or sums) has been frequently used to analyze the growth of latent constructs. This study evaluated whether LGM of composites yields unbiased parameter estimates, standard errors, chi-square statistics, and adequate fit indexes. Furthermore, LGM was compared…

Effects of incomplete data on fit indexes remain relatively unexplored. We evaluate a wide set of fit indexes (?[squared], root mean squared error of appproximation, Normed Fit Index [NFI], Tucker-Lewis Index, comparative fit index, gamma-hat, and McDonald's Centrality Index) varying conditions of sample size (100-1,000 in increments of 50),…