We propose new ways of robustifying goodness-of-fit tests for structural equation modeling under non-normality. These test statistics have limit distributions characterized by eigenvalues whose estimates are highly unstable and biased in known directions. To take this into account, we design model-based trend predictions to approximate the…

Although generalizability theory (GT) designs typically are analyzed using analysis of variance (ANOVA) procedures, they also can be integrated into structural equation models (SEMs). In this tutorial, we review basic concepts for conducting univariate and multivariate GT analyses and demonstrate advantages of doing such analyses within SEM…

Structural equation models offer a valuable tool for delineating the complicated interrelationships among multiple variables, including observed and latent variables. Over the last few decades, structural equation models have successfully analyzed complete and right-censored survival data, exemplified by wide applications in psychological, social,…

This study aims to address a gap in the social and behavioral sciences literature concerning interaction effects between latent factors in multiple-group analysis. By comparing two approaches for estimating latent interactions within multiple-group analysis frameworks using simulation studies and empirical data, we assess their relative merits.…

The latent growth model (LGM) is a popular tool in the social and behavioral sciences to study development processes of continuous and discrete outcome variables. A special case are frequency measurements of behaviors or events, such as doctor visits per month or crimes committed per year. Probability distributions for such outcomes include the…

This article presents a multiple-group latent class-profile analysis (LCPA) by taking a Bayesian approach in which a Markov chain Monte Carlo simulation is employed to achieve more robust estimates for latent growth patterns. This article describes and addresses a label-switching problem that involves the LCPA likelihood function, which has…

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…

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…

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 directly applicable latent variable modeling procedure for classical item analysis is outlined. The method allows one to point and interval estimate item difficulty, item correlations, and item-total correlations for composites consisting of categorical items. The approach is readily employed in empirical research and as a by-product permits…