A latent variable modeling method is outlined, which accomplishes estimation of criterion validity and reliability for a multicomponent measuring instrument with hierarchical structure. The approach provides point and interval estimates for the scale criterion validity and reliability coefficients, and can also be used for testing composite or…

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…

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…

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…

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…

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…

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…

An interval estimation procedure for proportion of explained observed variance in latent curve analysis is discussed, which can be used as an aid in the process of choosing between linear and nonlinear models. The method allows obtaining confidence intervals for the R[squared] indexes associated with repeatedly followed measures in longitudinal…

Multilevel modeling (MLM) is a popular way of assessing mediation effects with clustered data. Two important limitations of this approach have been identified in prior research and a theoretical rationale has been provided for why multilevel structural equation modeling (MSEM) should be preferred. However, to date, no empirical evidence of MSEM's…

Compared to parametric models, nonparametric and semiparametric approaches to modeling nonlinearity between latent variables have the advantage of recovering global relationships of unknown functional form. Bauer (2005) proposed an indirect application of finite mixtures of structural equation models where latent components are estimated in the…

The latent growth curve modeling (LGCM) approach has been increasingly utilized to investigate longitudinal mediation. However, little is known about the accuracy of the estimates and statistical power when mediation is evaluated in the LGCM framework. A simulation study was conducted to address these issues under various conditions including…

This Monte Carlo simulation study investigated methods of forming product indicators for the unconstrained approach for latent variable interaction estimation when the exogenous factors are measured by large and unequal numbers of indicators. Product indicators were created based on multiplying parcels of the larger scale by indicators of the…

In recent years the use of the latent curve model (LCM) among researchers in social sciences has increased noticeably, probably thanks to contemporary software developments and the availability of specialized literature. Extensions of the LCM, like the the latent change score model (LCSM), have also increased in popularity. At the same time, the R…

A method for interval estimation of scale reliability with discrete data is outlined. The approach is applicable with multi-item instruments consisting of binary measures, and is developed within the latent variable modeling methodology. The procedure is useful for evaluation of consistency of single measures and of sum scores from item sets…

Interval estimation of intraclass correlation coefficients in hierarchical designs is discussed within a latent variable modeling framework. A method accomplishing this aim is outlined, which is applicable in two-level studies where participants (or generally lower-order units) are clustered within higher-order units. The procedure can also be…