Research in education and behavioral sciences often involves the use of latent variable models that are related to indicators, as well as related to covariates or outcomes. Such models are subject to interpretational confounding, which occurs when fitting the model with covariates or outcomes alters the results for the measurement model. This has…

Penalized structural equation models (PSEM) is a new powerful estimation technique that can be used to tackle a variety of difficult structural estimation problems that can not be handled with previously developed methods. In this paper we describe the PSEM framework and illustrate the quality of the method with simulation studies.…

Small sample sizes pose a severe threat to convergence and accuracy of between-group level parameter estimates in multilevel structural equation modeling (SEM). However, in certain situations, such as pilot studies or when populations are inherently small, increasing samples sizes is not feasible. As a remedy, we propose a two-stage regularized…

Many education tests and psychological surveys elicit respondent views of similar constructs across scenarios (e.g., story followed by multiple choice questions) by repeating common statements across scales (one-statement-multiple-scale, OSMS). However, a respondent's earlier responses to the common statement can affect later responses to it…

Precisely estimating factor scores is challenging, especially when models are mis-specified. Stemming from network analysis, centrality measures offer an alternative approach to estimating the scores. Using a two-fold simulation design with varying availability of a priori theoretical knowledge, this study implemented hybrid centrality to estimate…

Many applications of structural equation modeling involve ordinal (e.g., Likert) variables. A popular way of dealing with ordinal variables is to estimate the model with polychoric correlations rather than Pearson correlations. Such an estimation also requires the asymptotic covariance matrix of polychoric correlations. It is computationally…

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…

Latent class analysis (LCA) refers to techniques for identifying groups in data based on a parametric model. Examples include mixture models, LCA with ordinal indicators, and latent class growth analysis. Despite its popularity, there is limited guidance with respect to decisions that must be made when conducting and reporting LCA. Moreover, there…

In latent growth curve modeling (LGCM), overall fit indices have garnered increased disputation for model selection, and model fit evaluation based on the mean structure has becoming popularity. The present study developed a versatile fit index, named Weighted Root Mean Squared Errors (WRMSE), based on individual case residuals (ICRs) with the aim…

Model-Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) is a limited information, equation-by-equation, noniterative estimator for latent variable models. Associated with this estimator are equation-specific tests of model misspecification. One issue with equation-specific tests is that they lack specificity, in that they indicate…

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…

The logistic and confined exponential curves are frequently used in studies of growth and learning. These models, which are nonlinear in their parameters, can be estimated using structural equation modeling software. This paper proposes a single combined model, a weighted combination of both models. Mplus, Proc Calis, and lavaan code for the model…

In parallel process latent growth curve mediation models, the mediation pathways from treatment to the intercept or slope of outcome through the intercept or slope of mediator are often of interest. In this study, we developed causal mediation analysis methods for these mediation pathways. Particularly, we provided causal definitions and…

This study examined the false positive (FP) rates and sensitivity of Bayesian fit indices to structural misspecification in Bayesian structural equation modeling. The impact of measurement quality, sample size, model size, the magnitude of misspecified path effect, and the choice or prior on the performance of the fit indices was also…

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,…