Chi-square tests based on maximum likelihood (ML) estimation of covariance structures often incorrectly over-reject the null hypothesis: [sigma] = [sigma(theta)] when the sample size is small. Reweighted least squares (RLS) avoids this problem. In some models, the vector of parameter must contain means, variances, and covariances, yet whether RLS…

Measuring change in an educational or psychological construct over time is often achieved by repeatedly administering the same items to the same examinees over time and fitting a second-order latent growth curve model. However, latent growth modeling with full information maximum likelihood (FIML) estimation becomes computationally challenging…

To examine developmental processes, intervention effects, or both, longitudinal studies often aim to include measurement intervals that are equally spaced for all participants. In reality, however, this goal is hardly ever met. Although different approaches have been proposed to deal with this issue, few studies have investigated the potential…

Determining an appropriate sample size for use in latent variable modeling techniques has presented ongoing challenges to researchers. In particular, small sample sizes are known to present concerns over sampling error for the variances and covariances on which model estimation is based, as well as for fit indexes and convergence failures. The…

This simulation study investigated use of the multilevel structural equation model (MLSEM) for handling measurement error in both mediator and outcome variables ("M" and "Y") in an upper level multilevel mediation model. Mediation and outcome variable indicators were generated with measurement error. Parameter and standard…

A conditionally linear mixed effects model is an appropriate framework for investigating nonlinear change in a continuous latent variable that is repeatedly measured over time. The efficacy of the model is that it allows parameters that enter the specified nonlinear time-response function to be stochastic, whereas those parameters that enter in a…

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…

When structural equation modeling (SEM) analyses are conducted, significance tests for all important model relationships (parameters including factor loadings, covariances, etc.) are typically conducted at a specified nominal Type I error rate ([alpha]). Despite the fact that many significance tests are often conducted in SEM, rarely is…

A latent variable modeling approach is outlined that can be used for meta-analysis of reliability coefficients of multicomponent measuring instruments. Important limitations of efforts to combine composite reliability findings across multiple studies are initially pointed out. A reliability synthesis procedure is discussed that is based on…

The purpose of this simulation study was to assess the performance of latent variable models that take into account the complex sampling mechanism that often underlies data used in educational, psychological, and other social science research. Analyses were conducted using the multiple indicator multiple cause (MIMIC) model, which is a flexible…

Latent means methods such as multiple-indicator multiple-cause (MIMIC) and structured means modeling (SMM) allow researchers to determine whether or not a significant difference exists between groups' factor means. Strong invariance is typically recommended when interpreting latent mean differences. The extent of the impact of noninvariant…

Yuan and Hayashi (2010) introduced 2 scatter plots for model and data diagnostics in structural equation modeling (SEM). However, the generation of the plots requires in-depth understanding of their underlying technical details. This article develops and introduces an R package semdiag for easily drawing the 2 plots. With a model specified in EQS…

This simulation study investigated the sensitivity of commonly used cutoff values for global-model-fit indexes, with regard to different degrees of violations of the assumption of uncorrelated errors in confirmatory factor analysis. It is shown that the global-model-fit indexes fell short in identifying weak to strong model misspecifications under…

Response patterns are of importance to survey researchers because of the insight they provide into the thought processes respondents use to answer survey questions. In this article we propose the use of structural equation modeling to examine response patterns and develop a permutation test to quantify the likelihood of observing a specific…

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…