A Tutorial in Bayesian Mediation Analysis With Latent Variables

Methodology ◽  
2019 ◽  
Vol 15 (4) ◽  
pp. 137-146 ◽  
Author(s):  
Milica Miočević
Keyword(s):  
Mediation Analysis ◽  
Latent Variables ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Estimation Method ◽  
Model Specification ◽  
Equation Modeling ◽  
Ml Estimation ◽  
Definition Of ◽  
Bayesian Mediation

Abstract. Maximum Likelihood (ML) estimation is a common estimation method in Structural Equation Modeling (SEM), and parameters in such analyses are interpreted using frequentist terms and definition of probability. It is also possible, and sometimes more advantageous ( Lee & Song, 2004 ; Rindskopf, 2012 ), to fit structural equation models in the Bayesian framework ( Kaplan & Depaoli, 2012 ; Levy & Choi, 2013 ; Scheines, Hoijtink, & Boomsma, 1999 ). Bayesian mediation analysis has been described for manifest variable models ( Enders, Fairchild, & MacKinnon, 2013 ; Yuan & MacKinnon, 2009 ). This tutorial outlines considerations in the analysis and interpretation of results for the single mediator model with latent variables. The reader is guided through model specification, estimation, and the interpretations of results obtained using two kinds of diffuse priors and one set of informative priors. Recommendations are made for applied researchers and annotated syntax is provided in R2OpenBUGS and Mplus. The target audience for this article are researchers wanting to learn how to fit the single mediator model as a Bayesian SEM.

scholarly journals 10. Using Instrumental Variable Tests to Evaluate Model Specification in Latent Variable Structural Equation Models

2009 ◽  
Vol 39 (1) ◽  
pp. 327-355 ◽  
Author(s):  
James B. Kirby ◽  
Kenneth A. Bollen
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Model Specification ◽  
Equation Modeling ◽  
Monte Carlo Experiment ◽  
Full Information ◽  
Limited Information ◽  
Finite Sample

Structural equation modeling (SEM) with latent variables is a powerful tool for social and behavioral scientists, combining many of the strengths of psychometrics and econometrics into a single framework. The most common estimator for SEM is the full-information maximum likelihood (ML) estimator, but there is continuing interest in limited information estimators because of their distributional robustness and their greater resistance to structural specification errors. However, the literature discussing model fit for limited information estimators for latent variable models is sparse compared with that for full-information estimators. We address this shortcoming by providing several specification tests basedon the 2SLS estimator for latent variable structural equation models developed by Bollen (1996). We explain how these tests can be used not only to identify a misspecified model but to help diagnose the source of misspecification within a model. We present and discuss results from a Monte Carlo experiment designed to evaluate the finite sample properties of these tests. Our findings suggest that the 2SLS tests successfully identify most misspecified models, even those with modest misspecification, and that they provide researchers with information that can help diagnose the source of misspecification.

scholarly journals A two-stage estimation procedure for non-linear structural equation models

Biostatistics ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 676-691
Author(s):  
Klaus Kähler Holst ◽  
Esben Budtz-Jørgensen
Keyword(s):  
Linear Model ◽  
Latent Variables ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Outcome Variable ◽  
Two Stage ◽  
Ml Estimation ◽  
Linear Effect ◽  
Non Linear ◽  
Stage Estimation

Summary Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in non-linear models may be complex and require numerical integration. Furthermore, ML inference is sensitive to distributional assumptions. In this article, we introduce a simple two-stage estimation technique for estimation of non-linear associations between latent variables. Here both steps are based on fitting linear SEMs: first a linear model is fitted to data on the latent predictor and terms describing the non-linear effect are predicted by their conditional means. In the second step, the predictions are included in a linear model for the latent outcome variable. We show that this procedure is consistent and identifies its asymptotic distribution. We also illustrate how this framework easily allows the association between latent variables to be modeled using restricted cubic splines, and we develop a modified estimator which is robust to non-normality of the latent predictor. In a simulation study, we compare the proposed method to MLE and alternative two-stage estimation techniques.

scholarly journals On the Interpretation of Parameters in Multivariate Multilevel Models Across Different Combinations of Model Specification and Estimation

2019 ◽  
Vol 2 (3) ◽  
pp. 288-311 ◽  
Author(s):  
Lesa Hoffman
Keyword(s):  
Latent Variables ◽  
Structural Equation ◽  
Multilevel Models ◽  
Structural Equation Models ◽  
Simulated Data ◽  
Recent Change ◽  
Model Specification ◽  
Predictor Variables ◽  
Random Slopes ◽  
Multivariate Multilevel Models

The increasing availability of software with which to estimate multivariate multilevel models (also called multilevel structural equation models) makes it easier than ever before to leverage these powerful techniques to answer research questions at multiple levels of analysis simultaneously. However, interpretation can be tricky given that different choices for centering model predictors can lead to different versions of what appear to be the same parameters; this is especially the case when the predictors are latent variables created through model-estimated variance components. A further complication is a recent change to Mplus (Version 8.1), a popular software program for estimating multivariate multilevel models, in which the selection of Bayesian estimation instead of maximum likelihood results in different lower-level predictors when random slopes are requested. This article provides a detailed explication of how the parameters of multilevel models differ as a function of the analyst’s decisions regarding centering and the form of lower-level predictors (i.e., observed or latent), the method of estimation, and the variant of program syntax used. After explaining how different methods of centering lower-level observed predictor variables result in different higher-level effects within univariate multilevel models, this article uses simulated data to demonstrate how these same concepts apply in specifying multivariate multilevel models with latent lower-level predictor variables. Complete data, input, and output files for all of the example models have been made available online to further aid readers in accurately translating these central tenets of multivariate multilevel modeling into practice.

scholarly journals Power analysis for parameter estimation in structural equation modeling: A discussion and tutorial

2020 ◽  
Author(s):  
Yilin Andre Wang ◽  
Mijke Rhemtulla
Keyword(s):  
Structural Equation Modeling ◽  
Sample Size ◽  
Latent Variables ◽  
Power Analysis ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Regression Coefficient ◽  
Equation Modeling ◽  
Shiny App ◽  
Target Effect

Despite the widespread and rising popularity of structural equation modeling (SEM) in psychology, there is still much confusion surrounding how to choose an appropriate sample size for SEM. Currently available guidance primarily consists of sample size rules of thumb that are not backed up by research, and power analyses for detecting model misfit. Missing from most current practices is power analysis to detect a target effect (e.g., a regression coefficient between latent variables). In this paper we (a) distinguish power to detect model misspecification from power to detect a target effect, (b) report the results of a simulation study on power to detect a target regression coefficient in a 3-predictor latent regression model, and (c) introduce a Shiny app, pwrSEM, for user-friendly power analysis for detecting target effects in structural equation models.

scholarly journals Counterpoint

2021 ◽  
Vol 52 (SI) ◽  
pp. 114-130
Author(s):  
Xi Yu ◽  
Sam Zaza ◽  
Florian Schuberth ◽  
Jörg Henseler
Keyword(s):  
Latent Variables ◽  
Structural Equation ◽  
Model Identification ◽  
Theoretical Concept ◽  
Model Specification ◽  
Equation Modeling ◽  
Model Assessment ◽  
Theoretical Concepts ◽  
Is Research ◽  
Shed Light

Studying and modeling theoretical concepts is a cornerstone activity in information systems (IS) research. Researchers have been familiar with one type of theoretical concept, namely behavioral concepts, which are assumed to exist in nature and measured by a set of observable variables. In this paper, we present a second type of theoretical concept, namely forged concepts, which are designed and assumed to emerge within their environment. While behavioral concepts are classically operationalized as latent variables, forged concepts are better specified as emergent variables. Additionally, we propose composite-based structural equation modeling (SEM) as a subtype of SEM that is eminently suitable to analyze models containing emergent variables. We shed light on the composite-based SEM steps: model specification, model identification, model estimation, and model assessment. Then, we present an illustrative example from the domain of IS research to demonstrate these four steps and show how modeling with emergent variables proceeds.

Using Structural Equation Modeling With Forensic Samples

2007 ◽  
Vol 34 (12) ◽  
pp. 1560-1587 ◽  
Author(s):  
Jeffrey C. Meehan ◽  
Gregory L. Stuart
Keyword(s):  
Structural Equation Modeling ◽  
Latent Variables ◽  
Structural Equation ◽  
Behavioral Science ◽  
Estimation Method ◽  
Equation Modeling ◽  
Fit Indices ◽  
Forensic Research ◽  
Confirmatory Factor ◽  
Requirements Identification

Because of its many advantages, structural equation modeling (SEM) has been used with increasing frequency in behavioral science, and it is a set of techniques that can be useful in analyzing forensic research data. Issues in SEM, including theory, estimation method, sample size and data requirements, identification, and fit indices are discussed. Using a sample of data from men arrested for domestic violence perpetration and court referred to treatment, examples of path analysis, confirmatory factor analysis, and full structural models with latent variables are presented.

scholarly journals Using Structural Equation Modeling to Study Traits and States in Intensive Longitudinal Data

2020 ◽  
Author(s):  
Sebastian Castro-Alvarez ◽  
Jorge Tendeiro ◽  
Rob Meijer ◽  
Laura Francina Bringmann
Keyword(s):  
Longitudinal Data ◽  
Latent Variables ◽  
Structural Equation ◽  
Multilevel Models ◽  
Structural Equation Models ◽  
Longitudinal Research ◽  
Equation Modeling ◽  
Intensive Longitudinal Data ◽  
The Common ◽  
The Stability

Traditionally, researchers have used time series and multilevel models to analyze intensive longitudinal data. However, these models do not directly address traits and states which conceptualize the stability and variability implicit in longitudinal research, and they do not explicitly take into account measurement error. An alternative to overcome these drawbacks is to consider structural equation models (state-trait SEMs) for longitudinal data that represent traits and states as latent variables. Most of these models are encompassed in the Latent State-Trait (LST) theory. These state-trait SEMs can be problematic when the number of measurement occasions increases. As they require the data to be in wide format, these models quickly become overparameterized and lead to non-convergence issues. For these reasons, multilevel versions of state-trait SEMs have been proposed, which require the data in long format. To study how suitable state-trait SEMs are for intensive longitudinal data, we carried out a simulation study. We compared the traditional single level to the multilevel version of three state-trait SEMs. The selected models were the multistate-singletrait (MSST) model, the common and unique trait-state (CUTS) model, and the trait-state-occasion (TSO) model. Furthermore, we also included an empirical application. Our results indicated that the TSO model performed best in both the simulated and the empirical data. To conclude, we highlight the usefulness of state-trait SEMs to study the psychometric properties of the questionnaires used in intensive longitudinal data. Yet, these models still have multiple limitations, some of which might be overcome by extending them to more general frameworks.

scholarly journals Bayesian multilevel structural equation modeling: An investigation into robust prior distributions.

2020 ◽  
Author(s):  
Sara van Erp ◽  
William Browne
Keyword(s):  
Random Effects ◽  
Latent Variables ◽  
Latent Variable ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Equation Modeling ◽  
Prior Distributions ◽  
Inverse Gamma ◽  
Variance Parameters ◽  
Multilevel Structural Equation

Bayesian estimation of multilevel structural equation models (MLSEMs) offers advantages in terms of sample size requirements and computational feasibility, but does require careful specification of the prior distribution especially for the random effects variance parameters. The traditional “non-informative” conjugate choice of an inverse- Gamma prior with small hyperparameters has been shown time and again to be problematic. In this paper, we investigate alternative, more robust prior distributions. In contrast to multilevel models without latent variables, MLSEMs have multiple random effects variance parameters, both for the multilevel structure and for the latent variable structure. It is therefore even more important to construct reasonable priors for these parameters. We find that, although the robust priors outperform the traditional inverse-Gamma prior, their hyperparameters do require careful consideration.

Sign in / Sign up

Export Citation Format

Share Document