Bayesian structural equation modeling: a more flexible representation of substantive theory

This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that bet...

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Bibliographic Details
Published in:Psychological methods Vol. 17; no. 3; p. 313
Main Authors: Muthén, Bengt, Asparouhov, Tihomir
Format: Journal Article
Language:English
Published: United States 01.09.2012
Subjects:
Bayes Theorem
Factor Analysis, Statistical
Humans
Likelihood Functions
Markov Chains
Models, Statistical
Monte Carlo Method
Neuropsychological Tests - statistics & numerical data
Personality Tests - statistics & numerical data
ISSN:1939-1463, 1939-1463
Online Access:Get more information
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Summary:This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to a conventional model such that a nonidentified model is obtained if maximum-likelihood estimation is applied. This approach is useful for measurement aspects of latent variable modeling, such as with confirmatory factor analysis, and the measurement part of structural equation modeling. Two application areas are studied, cross-loadings and residual correlations in confirmatory factor analysis. An example using a full structural equation model is also presented, showing an efficient way to find model misspecification. The approach encompasses 3 elements: model testing using posterior predictive checking, model estimation, and model modification. Monte Carlo simulations and real data are analyzed using Mplus. The real-data analyses use data from Holzinger and Swineford's (1939) classic mental abilities study, Big Five personality factor data from a British survey, and science achievement data from the National Educational Longitudinal Study of 1988.
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ISSN:1939-1463
1939-1463
DOI:10.1037/a0026802