Structural Equation Modeling

Random-Intercept Cross-Lagged Panel Models allow for the decomposition of measurements into between- and within-person components and have hence become popular for testing developmental hypotheses. Here, we describe how developmental researchers can implement, test and interpret interaction effects in such models using an empirical example from developmental psychopathology research. We illustrate the analysis of Within × Within and Between × Within interactions utilising data from the United Kingdom-based Millennium Cohort Study within a Bayesian Structural Equation Modelling framework...

A general method is introduced in which variables that are products of other variables in the context of a structural equation model (SEM) can be decomposed into the sources of variance due to the multiplicands. The result is a new category of SEM which we call a Products of Variables Model (PoV). Some useful and practical features of PoV models include estimation of interactions between latent variables, latent variable moderators, manifest moderators with missing values, and manifest or latent squared terms...

The effect of an independent variable on random slopes in growth modeling with latent variables is conventionally used to examine predictors of change over the course of a study. This tutorial demonstrates that the same effect of a covariate on growth can be obtained by using final status centering for parameterization and regressing the random intercepts (or the intercept factor scores) on both the independent variable and a baseline covariate--the framework used to study change with classical regression analysis...

Integrative data analysis (IDA) is an analytic tool that allows researchers to combine raw data across multiple, independent studies, providing improved measurement of latent constructs as compared to single study analysis or meta-analyses. This is often achieved through implementation of moderated nonlinear factor analysis (MNLFA), an advanced modeling approach that allows for covariate moderation of item and factor parameters. The current paper provides an overview of this modeling technique, highlighting distinct advantages most apt for IDA...

This study develops a new limited information estimator for random intercept Multilevel Structural Equation Models (MSEM). It is based on the Model Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) estimator, which has been shown to be an excellent alternative or supplement to maximum likelihood (ML) in SEMs (Bollen, 1996). We also develop a multilevel overidentification test statistic that applies to equations at the within or between levels. Our Monte Carlo simulation analysis suggests that MIIV-2SLS is more robust than ML to misspecification at within or between levels, performs well given fewer that 100 clusters, and shows that our multilevel overidentification test for equations performs well at both levels of the model...

The two-wave mediation model is the most suitable model for examining mediation effects in a randomized intervention and includes measures taken at pretest and posttest. When using self-report measures, the meaning of responses may change for the treatment group over the course of the intervention and result in noninvariance across groups at posttest, a phenomenon referred to as response shift . We investigate how the mediated effect would be impacted by noninvariance when using sum scores (i.e., assuming invariance)...

Mechanisms of behavior change are the processes through which interventions are hypothesized to cause changes in outcomes. Latent growth curve mediation models (LGCMM) are recommended for investigating the mechanisms of behavior change because LGCMM models establish temporal precedence of change from the mediator to the outcome variable. The Correlated Augmented Mediation Sensitivity Analyses (CAMSA) App implements sensitivity analysis for LGCMM models to evaluate if a mediating path (mechanism) is robust to potential confounding variables...

The influx of intensive longitudinal data creates a pressing need for complex modeling tools that help enrich our understanding of how individuals change over time. Multilevel vector autoregressive (mlVAR) models allow for simultaneous evaluations of reciprocal linkages between dynamic processes and individual differences, and have gained increased recognition in recent years. High-dimensional and other complex variations of mlVAR models, though often computationally intractable in the frequentist framework, can be readily handled using Markov chain Monte Carlo techniques in a Bayesian framework...

No abstract text is available yet for this article.

The present article provides a didactic presentation and extension of selected features of Pearl's DAG-based approach to causal inference for researchers familiar with structural equation modeling. We illustrate key concepts using a cross-lagged panel design. We distinguish between (a) forecasts of the value of an outcome variable after an intervention and (b) predictions of future values of an outcome variable. We consider the mean level and variance of the outcome variable as well as the probability that the outcome will fall within an acceptable range...

Technological advances have increased the prevalence of intensive longitudinal data as well as statistical techniques appropriate for these data, such as dynamic structural equation modeling (DSEM). Intensive longitudinal designs often investigate constructs related to affect or mood and do so with multiple item scales. However, applications of intensive longitudinal methods often rely on simple sums or averages of the administered items rather than considering a proper measurement model. This paper demonstrates how to incorporate measurement models into DSEM to (1) provide more rigorous measurement of constructs used in intensive longitudinal studies and (2) assess whether scales are invariant across time and across people, which is not possible when item responses are summed or averaged...

The difference between groups in their random slopes is frequently examined in latent growth modeling to evaluate treatment efficacy. However, when end centering is used for model parameterization with a randomized design, the difference in the random intercepts is the model-estimated mean difference between the groups at the end of the study, which has the same expected value as the product of the coefficient for the slope difference and study duration. A Monte Carlo study found that (a) the statistical power to detect the treatment effect was greater when determined from the intercept instead of the slope difference, and (b) the standard error of the model-estimated mean difference was smaller when obtained from the intercept difference...

An important recent development in mediation analysis is the use of causal mediation analysis. Causal mediation analysis decomposes the total exposure effect into causal direct and indirect effects in the presence of exposure-mediator interaction. However, in practice, traditional mediation analysis is still most widely used. The aim of this paper is to demonstrate the similarities and differences between the causal and traditional estimators for mediation models with a continuous mediator, a binary outcome, and exposure-mediator interaction...

We investigated the performance of two single indicator methods: latent moderated structural equation (LMS) and reliability-adjusted product indicator (RAPI) methods, on testing interaction effects with congeneric measures, which vary in factor loadings and error variances under a common factor. Additionally, in the simulation study, we compared the performance of four reliability estimates (Cronbach's alpha, omega composite, Coefficient H , and greatest lower bound [GLB]) to adjust for the exogenous composites' measurement errors...

No abstract text is available yet for this article.

Integrative data analysis (IDA) involves obtaining multiple datasets, scaling the data to a common metric, and jointly analyzing the data. The first step in IDA is to scale the multisample item-level data to a common metric, which is often done with multiple group item response models (MGM). With invariance constraints tested and imposed, the estimated latent variable scores from the MGM serve as an observed variable in subsequent analyses. This approach was used with empirical multiple group data and different latent variable estimates were obtained for individuals with the same response pattern from different studies...

Mediation analysis is a methodology used to understand how and why an independent variable ( X ) transmits its effect to an outcome ( Y ) through a mediator ( M ). New causal mediation methods based on the potential outcomes framework and counterfactual framework are a seminal advancement for mediation analysis, because they focus on the causal basis of mediation analysis. There are several programs available to estimate causal mediation effects, but these programs differ substantially in data set up, estimation, output, and software platform...

Determining whether measures are equally valid for all individuals is a core component of psychometric analysis. Traditionally, the evaluation of measurement invariance (MI) involves comparing independent groups defined by a single categorical covariate (e.g., men and women) to determine if there are any items that display differential item functioning (DIF). More recently, Moderated Nonlinear Factor Analysis (MNLFA) has been advanced as an approach for evaluating MI/DIF simultaneously over multiple background variables, categorical and continuous...

Many developmental and life course researchers are interested in modeling dynamic developmental processes. Latent change score (LCS) modeling is a potentially powerful modeling technique that can be used to assess complex life course processes, as well as the direction of longitudinal bivariate associations. Advances in modeling software, like Mplus, as well as widening adoption of software by researchers has made LCS modeling simpler. Thus, in the present paper, we provide 1) a theoretical overview of LCS analysis, 2) information on the interpretation of these models, 3) a practical guid7e for estimating these models in Mplus (including example syntax), 4) illustrative examples of LCS analysis, and 5) potential caveats for researchers...

Second order linear differential equations can be used as models for regulation since under a range of parameter values they can account for return to equilibrium as well as potential oscillations in regulated variables. One method that can estimate parameters of these equations from intensive time series data is the method of Latent Differential Equations (LDE). However, the LDE method can exhibit bias in its parameters if the dimension of the time delay embedding and thus the width of the convolution kernel is not chosen wisely...