Just as growth mixture models are useful with single-phase longitudinal data, multiphase growth mixture models can be used with multiple-phase longitudinal data. One of the practically important issues in single- and multiphase growth mixture models is the sample size requirements for accurate estimation. In a Monte Carlo simulation study, the…

This article shows how interfactor correlation is affected by error correlations. Theoretical and practical justifications for error correlations are given, and a new equivalence class of models is presented to explain the relationship between interfactor correlation and error correlations. The class allows simple, parsimonious modeling of error…

A latent variable analysis procedure for evaluation of reliability coefficients for 2-level models is outlined. The method provides point and interval estimates of group means' reliability, overall reliability of means, and conditional reliability. In addition, the approach can be used to test simple hypotheses about these parameters. The…

Recently there has been a renewed interest in formative measurement and its role in properly specified models. Formative measurement models are difficult to identify, and hence to estimate and test. Existing solutions to the identification problem are shown to not adequately represent the formative constructs of interest. We propose a new two-step…

Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…

In this article, a 2-way multigroup common factor model (MG-CFM) is presented. The MG-CFM can be used to estimate interaction effects between 2 grouping variables on 1 or more hypothesized latent variables. For testing the significance of such interactions, a likelihood ratio test is presented. In a simulation study, the robustness of the…

Recently a new mean scaled and skewness adjusted test statistic was developed for evaluating structural equation models in small samples and with potentially nonnormal data, but this statistic has received only limited evaluation. The performance of this statistic is compared to normal theory maximum likelihood and 2 well-known robust test…

Missing data are common in studies that rely on multiple informant data to evaluate relationships among variables for distinguishable individuals clustered within groups. Estimation of structural equation models using raw data allows for incomplete data, and so all groups can be retained for analysis even if only 1 member of a group contributes…

This article has 3 objectives that build on each other. First, we demonstrate how to obtain maximum likelihood estimates for dynamic factor models (the direct autoregressive factor score model) with arbitrary "T" and "N" by means of structural equation modeling (SEM) and compare the approach to existing methods. Second, we go beyond standard time…

The size of a model has been shown to critically affect the goodness of approximation of the model fit statistic "T" to the asymptotic chi-square distribution in finite samples. It is not clear, however, whether this "model size effect" is a function of the number of manifest variables, the number of free parameters, or both. It is demonstrated by…

Although prediction of class membership from observed variables in latent class analysis is well understood, predicting an observed distal outcome from latent class membership is more complicated. A flexible model-based approach is proposed to empirically derive and summarize the class-dependent density functions of distal outcomes with…

Mixed-dyadic data, collected from distinguishable (nonexchangeable) or indistinguishable (exchangeable) dyads, require statistical analysis techniques that model the variation within dyads and between dyads appropriately. The purpose of this article is to provide a tutorial for performing structural equation modeling analyses of cross-sectional…

This article proposes a model-based procedure, intended for personality measures, for exploiting the auxiliary information provided by the certainty with which individuals answer every item (response certainty). This information is used to (a) obtain more accurate estimates of individual trait levels, and (b) provide a more detailed assessment of…

The discrimination between alternative models and the detection of latent classes in the context of latent variable mixture modeling depends on sample size, class separation, and other aspects that are related to power. Prior to a mixture analysis it is useful to investigate model performance in a simulation study that reflects the research…

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…