Several variants of the autoregressive structural equation model were suggested over the past years, including, for example, the random intercept autoregressive panel model, the latent curve model with structured residuals, and the STARTS model. The present work shows how to place these models into a mixed-effects model framework and how to…

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.…

Structural Equation Modeling (SEM) continues to grow in popularity with numerous articles, books, courses, and workshops available to help researchers become proficient with SEM quickly. However, few resources are available to help users gain a deep understanding of the analytic steps involved in SEM, with even fewer providing reproducible syntax…

Multidimensional measuring instruments are often used in behavioral, social, educational, marketing, and biomedical research. For these scales, the paper discusses how to find the optimal score based on their components that is associated with the highest possible reliability. Within the framework of structural equation modeling, an approach to…

We present a method for Bayesian structural equation modeling of sample correlation matrices as correlation structures. The method transforms the sample correlation matrix to an unbounded vector using the matrix logarithm function. Bayesian inference about the unbounded vector is performed assuming a multivariate-normal likelihood, with a mean…

In this article, we pursue two points of discussion. First, a new illustration is presented of the person-oriented tenet according to which it can be hazardous to generalize to the individual results that are based on the analysis of aggregated data. Second, it is illustrated that taking into account serial dependence information can result in not…

Clustered data structures are common in many areas of educational and psychological research (e.g., students clustered in schools, patients clustered by clinician). In the course of conducting research, questions are often administered to obtain scores reflecting latent constructs. Multilevel measurement models (MLMMs) allow for modeling…

Currently, dynamic structural equation modeling (DSEM) and residual DSEM (RDSEM) are commonly used in testing intensive longitudinal data (ILD). Researchers are interested in ILD mediation models, but their analyses are challenging. The present paper mathematically derived, empirically compared, and step-by-step demonstrated three types (i.e.,…

We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite requirement on correlation matrices, from sign indeterminacy of factor loadings, and from order constraints on…

When comparing relations and means of latent variables, it is important to establish measurement invariance (MI). Most methods to assess MI are based on confirmatory factor analysis (CFA). Recently, new methods have been developed based on exploratory factor analysis (EFA); most notably, as extensions of multi-group EFA, researchers introduced…

In the past decade, moderated mediation analysis has been extensively and increasingly employed in social and behavioral sciences. With its widespread use, it is particularly important to ensure the moderated mediation analysis will not bring spurious results. Spurious effects have been studied in both mediation and moderation analysis, but this…

A procedure for evaluating the average R-squared index for a given set of observed variables in an exploratory factor analysis model is discussed. The method can be used as an effective aid in the process of model choice with respect to the number of factors underlying the interrelationships among studied measures. The approach is developed within…

In physical education and exercise science, it is common to examine mean differences between groups or to assess change across time. However, before group differences or change can be confidently examined, measurement invariance can be tested. Measurement invariance tests the equivalence of a construct across groups or across time. If measurement…

The present study describes an R function that implements six corrective procedures developed by Bartlett, Swain, and Yuan in the correction of 21 statistics associated with the omnibus Chi-square test, the residuals, or fit indices in confirmatory factor analysis (CFA) and structural equation modeling (SEM).

Despite the sensitivity of fit indices to various model and data characteristics in structural equation modeling, these fit indices are used in a rigid binary fashion as a mere rule of thumb threshold value in a search for model adequacy. Here, we address the behavior and interpretation of the popular Comparative Fit Index (CFI) by stressing that…