Structural Equation Models

2009 ◽  
Author(s):  
Kenneth A. Bollen ◽  
Sophia Rabe‐Hesketh ◽  
Anders Skrondal
Keyword(s):  
Factor Analysis ◽  
Graphical Models ◽  
Latent Variable ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Model Fit ◽  
Model Specification ◽  
Estimation Model ◽  
Recent Developments ◽  
Multilevel Structural Equation

This article explains the use of factor analysis types of models to develop measures of latent concepts which were then combined with causal models of the underlying latent concepts. In particular, it offers an overview of the classic structural equation models (SEMs) when the latent and observed variables are continuous. Then it looks at more recent developments that include categorical, count, and other noncontinuous variables as well as multilevel structural equation models. The model specification, assumptions, and notation are covered. This is followed by addressing implied moments, identification, estimation, model fit, and respecification. The penetration of SEMs has been high in disciplines such as sociology, psychology, educational testing, and marketing, but lower in economics and political science despite the large potential number of applications. Today, SEMs have begun to enter the statistical literature and to re-enter biostatistics, though often under the name ‘latent variable models’ or ‘graphical models’.

Forced Zero Cross-Loading Misspecifications in Measurement Component of Structural Equation Models

Methodology ◽  
2014 ◽  
Vol 10 (4) ◽  
pp. 138-152 ◽  
Author(s):  
Hsien-Yuan Hsu ◽  
Susan Troncoso Skidmore ◽  
Yan Li ◽  
Bruce Thompson
Keyword(s):  
Structural Equation ◽  
Structural Model ◽  
Structural Equation Models ◽  
Equation Model ◽  
Model Fit ◽  
Model Specification ◽  
Simulation Design ◽  
Measurement Models ◽  
Fit Statistics ◽  
Path Coefficients

The purpose of the present paper was to evaluate the effect of constraining near-zero parameter cross-loadings to zero in the measurement component of a structural equation model. A Monte Carlo 3 × 5 × 2 simulation design was conducted (i.e., sample sizes of 200, 600, and 1,000; parameter cross-loadings of 0.07, 0.10, 0.13, 0.16, and 0.19 misspecified to be zero; and parameter path coefficients in the structural model of either 0.50 or 0.70). Results indicated that factor pattern coefficients and factor covariances were overestimated in measurement models when near-zero parameter cross-loadings constrained to zero were higher than 0.13 in the population. Moreover, the path coefficients between factors were misestimated when the near-zero parameter cross-loadings constrained to zero were noteworthy. Our results add to the literature detailing the importance of testing individual model specification decisions, and not simply evaluating omnibus model fit statistics.

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 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.

scholarly journals One Factor SEM and Multilevel SEM Model for Patient Satisfaction Data

2021 ◽  
pp. 39-49
Author(s):  
Rehan Ahmad Khan Sherwani ◽  
Sajjad Ali Gill ◽  
Shaukat Ali Raza ◽  
Shumaila Abbas ◽  
Muhammad Farooq ◽  
...  
Keyword(s):  
Patient Satisfaction ◽  
Structural Equation Model ◽  
Latent Variable ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Factor Model ◽  
Equation Model ◽  
Structured Populations ◽  
Multilevel Structural Equation ◽  
Multilevel Structural Equation Model

Structural equation models are very common in medical, social, management and behavioral sciences where researchers established some causal relations between observed variables and latent variable. In structured populations the assumption of independence of observations is often violated and had been ignored by the researchers. As a result with the correlated structure of the error terms, biased estimates of the parameters have been produced that leads towards incorrect statistical inference. Multilevel structural equation model under one factor model has been proposed, estimated and compared with the traditional structural equation model on patient satisfaction data. Multilevel structural equation model produced better estimates than the structural equation models.

Probability-Based and Measurement-Related Hypotheses With Full Restriction for Investigations by Means of Confirmatory Factor Analysis

Methodology ◽  
2011 ◽  
Vol 7 (4) ◽  
pp. 157-164
Author(s):  
Karl Schweizer
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Cognitive Processing ◽  
Latent Variables ◽  
Repeated Measures ◽  
Latent Variable ◽  
Model Fit ◽  
Repeated Measures Data ◽  
Confirmatory Factor ◽  
And Performance

Probability-based and measurement-related hypotheses for confirmatory factor analysis of repeated-measures data are investigated. Such hypotheses comprise precise assumptions concerning the relationships among the true components associated with the levels of the design or the items of the measure. Measurement-related hypotheses concentrate on the assumed processes, as, for example, transformation and memory processes, and represent treatment-dependent differences in processing. In contrast, probability-based hypotheses provide the opportunity to consider probabilities as outcome predictions that summarize the effects of various influences. The prediction of performance guided by inexact cues serves as an example. In the empirical part of this paper probability-based and measurement-related hypotheses are applied to working-memory data. Latent variables according to both hypotheses contribute to a good model fit. The best model fit is achieved for the model including latent variables that represented serial cognitive processing and performance according to inexact cues in combination with a latent variable for subsidiary processes.

A Cautionary Note on Incremental Fit Indices Reported by LISREL

Methodology ◽  
2005 ◽  
Vol 1 (2) ◽  
pp. 81-85 ◽  
Author(s):  
Stefan C. Schmukle ◽  
Jochen Hardt
Keyword(s):  
Factor Analysis ◽  
Maximum Likelihood ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Null Model ◽  
Likelihood Estimation ◽  
Parameter Estimates ◽  
Fit Indices ◽  
Cautionary Note ◽  
Confirmatory Factor

Abstract. Incremental fit indices (IFIs) are regularly used when assessing the fit of structural equation models. IFIs are based on the comparison of the fit of a target model with that of a null model. For maximum-likelihood estimation, IFIs are usually computed by using the χ2 statistics of the maximum-likelihood fitting function (ML-χ2). However, LISREL recently changed the computation of IFIs. Since version 8.52, IFIs reported by LISREL are based on the χ2 statistics of the reweighted least squares fitting function (RLS-χ2). Although both functions lead to the same maximum-likelihood parameter estimates, the two χ2 statistics reach different values. Because these differences are especially large for null models, IFIs are affected in particular. Consequently, RLS-χ2 based IFIs in combination with conventional cut-off values explored for ML-χ2 based IFIs may lead to a wrong acceptance of models. We demonstrate this point by a confirmatory factor analysis in a sample of 2449 subjects.

A Comparison of Reliability Estimation Based on Confirmatory Factor Analysis and Exploratory Structural Equation Models

2021 ◽  
pp. 001316442110089
Author(s):  
Yuanshu Fu ◽  
Zhonglin Wen ◽  
Yang Wang
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Structural Equation ◽  
Reliability Estimation ◽  
Model Fit ◽  
Equation Modeling ◽  
Factor Loadings ◽  
Reliability Estimates ◽  
Confirmatory Factor ◽  
Composite Reliability

Composite reliability, or coefficient omega, can be estimated using structural equation modeling. Composite reliability is usually estimated under the basic independent clusters model of confirmatory factor analysis (ICM-CFA). However, due to the existence of cross-loadings, the model fit of the exploratory structural equation model (ESEM) is often found to be substantially better than that of ICM-CFA. The present study first illustrated the method used to estimate composite reliability under ESEM and then compared the difference between ESEM and ICM-CFA in terms of composite reliability estimation under various indicators per factor, target factor loadings, cross-loadings, and sample sizes. The results showed no apparent difference in using ESEM or ICM-CFA for estimating composite reliability, and the rotation type did not affect the composite reliability estimates generated by ESEM. An empirical example was given as further proof of the results of the simulation studies. Based on the present study, we suggest that if the model fit of ESEM (regardless of the utilized rotation criteria) is acceptable but that of ICM-CFA is not, the composite reliability estimates based on the above two models should be similar. If the target factor loadings are relatively small, researchers should increase the number of indicators per factor or increase the sample size.

scholarly journals Examining the ParticipACTION brand using the brand equity pyramid

2018 ◽  
Vol 8 (4) ◽  
pp. 378-396 ◽  
Author(s):  
Alexander Lithopoulos ◽  
Peter A. Dacin ◽  
Tanya R. Berry ◽  
Guy Faulkner ◽  
Norm O’Reilly ◽  
...  
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Exploratory Factor Analysis ◽  
Brand Equity ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Equation Modeling ◽  
Content Type ◽  
Activity Promotion ◽  
Confirmatory Factor

Purpose The brand equity pyramid is a theory that explains how people develop loyalty and an attachment to a brand. The purpose of this study is to test whether the predictions made by the theory hold when applied to the brand of ParticipACTION, a Canadian non-profit organization that promotes active living. A secondary objective was to test whether this theory predicted intentions to be more physically active. Design/methodology/approach A research agency conducted a cross-sectional, online brand health survey on behalf of ParticipACTION. Exploratory factor analysis and confirmatory factor analysis established the factor structure. Structural equation modeling was used to test the hypothesized model. Findings A nationally representative sample of Canadian adults (N = 1,191) completed the survey. Exploratory factor analysis and confirmatory factor analysis supported a hypothesized five-factor brand equity framework (i.e. brand identity, brand meaning, brand responses, brand resonance and intentions). A series of structural equation models also provided support for the hypothesized relationships between the variables. Practical implications Though preliminary, the results provide a guide for understanding the branding process in the activity-promotion context. The constructs identified as being influential in this process can be targeted by activity-promotion organizations to improve brand strength. A strong organizational brand could augment activity-promotion interventions. A strong brand may also help the organization better compete against other brands promoting messages that are antithetical to their own. Originality/value This is the first study to test the brand equity pyramid using an activity-promotion brand. Results demonstrate that the brand equity pyramid may be useful in this context.

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