scholarly journals Supplemental Material for Adapting Fit Indices for Bayesian Structural Equation Modeling: Comparison to Maximum Likelihood

2015 ◽  
Vol 37 (4) ◽  
pp. 410-420 ◽  
Author(s):  
Andreas Stenling ◽  
Andreas Ivarsson ◽  
Urban Johnson ◽  
Magnus Lindwall

Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.


2019 ◽  
Vol 35 (3) ◽  
pp. 317-325 ◽  
Author(s):  
Dorota Reis

Abstract. Interoception is defined as an iterative process that refers to receiving, accessing, appraising, and responding to body sensations. Recently, following an extensive process of development, Mehling and colleagues (2012) proposed a new instrument, the Multidimensional Assessment of Interoceptive Awareness (MAIA), which captures these different aspects of interoception with eight subscales. The aim of this study was to reexamine the dimensionality of the MAIA by applying maximum likelihood confirmatory factor analysis (ML-CFA), exploratory structural equation modeling (ESEM), and Bayesian structural equation modeling (BSEM). ML-CFA, ESEM, and BSEM were examined in a sample of 320 German adults. ML-CFA showed a poor fit to the data. ESEM yielded a better fit and contained numerous significant cross-loadings, of which one was substantial (≥ .30). The BSEM model with approximate zero informative priors yielded an excellent fit and confirmed the substantial cross-loading found in ESEM. The study demonstrates that ESEM and BSEM are flexible techniques that can be used to improve our understanding of multidimensional constructs. In addition, BSEM can be seen as less exploratory than ESEM and it might also be used to overcome potential limitations of ESEM with regard to more complex models relative to the sample size.


Methodology ◽  
2007 ◽  
Vol 3 (3) ◽  
pp. 100-114 ◽  
Author(s):  
Polina Dimitruk ◽  
Karin Schermelleh-Engel ◽  
Augustin Kelava ◽  
Helfried Moosbrugger

Abstract. Challenges in evaluating nonlinear effects in multiple regression analyses include reliability, validity, multicollinearity, and dichotomization of continuous variables. While reliability and validity issues are solved by employing nonlinear structural equation modeling, multicollinearity remains a problem which may even be aggravated when using latent variable approaches. Further challenges of nonlinear latent analyses comprise the distribution of latent product terms, a problem especially relevant for approaches using maximum likelihood estimation methods based on multivariate normally distributed variables, and unbiased estimates of nonlinear effects under multicollinearity. The only methods that explicitly take the nonnormality of nonlinear latent models into account are latent moderated structural equations (LMS) and quasi-maximum likelihood (QML). In a small simulation study both methods yielded unbiased parameter estimates and correct estimates of standard errors for inferential statistics. The advantages and limitations of nonlinear structural equation modeling are discussed.


2012 ◽  
Vol 23 (3) ◽  
pp. 619-626 ◽  
Author(s):  
Pim Edelaar ◽  
David Serrano ◽  
Martina Carrete ◽  
Julio Blas ◽  
Jaime Potti ◽  
...  

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