A frequent criticism of exploratory factor analysis (EFA) is that it does not allow correlated residuals to be modelled, while they can be routinely specified in the confirmatory (CFA) model. In this article, we propose an EFA approach in which both the common factor solution and the residual matrix are unrestricted (i.e., the correlated residuals…

The primary objective of this investigation is the formulation of random intercept latent profile transition analysis (RI-LPTA). Our simulation investigation suggests that the election between LPTA and RI-LPTA for examination has negligible impact on the estimation of transition probability parameters when the population parameters are generated…

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…

When comparing latent variables among groups, it is important to first establish the equivalence or invariance of the measurement model across groups. Confirmatory factor analysis (CFA) is a commonly used methodological approach to examine measurement equivalence/invariance (ME/I). Within the CFA framework, the chi-square goodness-of-fit test and…

Little, Bovaird and Widaman (2006) proposed an unconstrained approach with residual centering for estimating latent interaction effects as an alternative to the mean-centered approach proposed by Marsh, Wen, and Hau (2004, 2006). Little et al. also differed from Marsh et al. in the number of indicators used to infer the latent interaction factor…

This article examines 4 approaches for explaining shared method variance, each applied to a longitudinal trait-state-occasion (TSO) model. Many approaches have been developed to account for shared method variance in multitrait-multimethod (MTMM) data. Some of these MTMM approaches (correlated method, orthogonal method, correlated method minus one,…

A major issue in the utilization of covariance structure analysis is model fit evaluation. Recent years have witnessed increasing interest in various test statistics and so-called fit indexes, most of which are actually based on or closely related to F[subscript 0], a measure of model fit in the population. This study aims to provide a systematic…

Multigroup confirmatory factor analysis (MCFA) is a popular method for the examination of measurement invariance and specifically, factor invariance. Recent research has begun to focus on using MCFA to detect invariance for test items. MCFA requires certain parameters (e.g., factor loadings) to be constrained for model identification, which are…

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…

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…

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…

Meta-analytic structural equation modeling (MA-SEM) is increasingly being used to assess model-fit for variables' interrelations synthesized across studies. MA-SEM researchers have analyzed synthesized correlation matrices using structural equation modeling (SEM) estimation that is designed for covariance matrices. This can produce incorrect…

The purpose of this study was to evaluate the robustness of estimated growth curve models when there is stationary autocorrelation among manifest variable errors. The results suggest that when, in practice, growth curve models are fitted to longitudinal data, alternative rival hypotheses to consider would include growth models that also specify…

A linear latent growth curve mixture model is presented which includes switching between growth curves. Switching is accommodated by means of a Markov transition model. The model is formulated with switching as a highly constrained multivariate mixture model and is fitted using the freely available Mx program. The model is illustrated by analyzing…