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…

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…

GSCA Pro is free, user-friendly software for generalized structured component analysis structural equation modeling (GSCA-SEM), which implements three statistical methods for estimating models with factors only, models with components only, and models with both factors and components. This tutorial aims to provide step-by-step illustrations of how…

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…

Researchers often study dynamic processes of latent variables in everyday life, such as the interplay of positive and negative affect over time. An intuitive approach is to first estimate the measurement model of the latent variables, then compute factor scores, and finally use these factor scores as observed scores in vector autoregressive…

Structural equation modeling (SEM) is being applied to ever more complex data types and questions, often requiring extensions such as regularization or novel fitting functions. To extend SEM, researchers currently need to completely reformulate SEM and its optimization algorithm -- a challenging and time-consuming task. In this paper, we introduce…

A conditionally linear mixed effects model is an appropriate framework for investigating nonlinear change in a continuous latent variable that is repeatedly measured over time. The efficacy of the model is that it allows parameters that enter the specified nonlinear time-response function to be stochastic, whereas those parameters that enter in a…

Yuan and Hayashi (2010) introduced 2 scatter plots for model and data diagnostics in structural equation modeling (SEM). However, the generation of the plots requires in-depth understanding of their underlying technical details. This article develops and introduces an R package semdiag for easily drawing the 2 plots. With a model specified in EQS…

Researchers in the behavioral and social sciences often have expectations that can be expressed in the form of inequality constraints among the parameters of a structural equation model resulting in an informative hypothesis. The questions they would like an answer to are "Is the hypothesis Correct" or "Is the hypothesis…

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…

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…

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…

Multiple-group analysis in covariance-based structural equation modeling (SEM) is an important technique to ensure the invariance of latent construct measurements and the validity of theoretical models across different subpopulations. However, not all SEM software packages provide multiple-group analysis capabilities. The sem package for the R…

Latent class analysis (LCA) is an increasingly popular tool that researchers can use to identify latent groups in the population underlying a sample of responses to categorical observed variables. LCA is most commonly used in an exploratory fashion whereby no parameters are specified a priori. Although this exploratory approach is reasonable when…

We highlight critical conceptual and statistical issues and how to resolve them in conducting Satorra-Bentler (SB) scaled difference chi-square tests. Concerning the original (Satorra & Bentler, 2001) and new (Satorra & Bentler, 2010) scaled difference tests, a fundamental difference exists in how to compute properly a model's scaling correction…