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Bayesian structural equation modeling method for hierarchical model validation

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  • Jiang, Xiaomo
  • Mahadevan, Sankaran

Abstract

A building block approach to model validation may proceed through various levels, such as material to component to subsystem to system, comparing model predictions with experimental observations at each level. Usually, experimental data becomes scarce as one proceeds from lower to higher levels. This paper presents a structural equation modeling approach to make use of the lower-level data for higher-level model validation under uncertainty, integrating several components: lower-level data, higher-level data, computational model, and latent variables. The method proposed in this paper uses latent variables to model two sets of relationships, namely, the computational model to system-level data, and lower-level data to system-level data. A Bayesian network with Markov chain Monte Carlo simulation is applied to represent the two relationships and to estimate the influencing factors between them. Bayesian hypothesis testing is employed to quantify the confidence in the predictive model at the system level, and the role of lower-level data in the model validation assessment at the system level. The proposed methodology is implemented for hierarchical assessment of three validation problems, using discrete observations and time-series data.

Suggested Citation

  • Jiang, Xiaomo & Mahadevan, Sankaran, 2009. "Bayesian structural equation modeling method for hierarchical model validation," Reliability Engineering and System Safety, Elsevier, vol. 94(4), pages 796-809.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:4:p:796-809
    DOI: 10.1016/j.ress.2008.08.008
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    References listed on IDEAS

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    1. Goldberger, Arthur S, 1972. "Structural Equation Methods in the Social Sciences," Econometrica, Econometric Society, vol. 40(6), pages 979-1001, November.
    2. Asim Ansari & Kamel Jedidi & Sharan Jagpal, 2000. "A Hierarchical Bayesian Methodology for Treating Heterogeneity in Structural Equation Models," Marketing Science, INFORMS, vol. 19(4), pages 328-347, August.
    3. James Martin & Roderick McDonald, 1975. "Bayesian estimation in unrestricted factor analysis: A treatment for heywood cases," Psychometrika, Springer;The Psychometric Society, vol. 40(4), pages 505-517, December.
    4. Rebba, Ramesh & Mahadevan, Sankaran, 2008. "Computational methods for model reliability assessment," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1197-1207.
    5. Sik-Yum Lee, 1981. "A bayesian approach to confirmatory factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 46(2), pages 153-160, June.
    6. Xiaomo Jiang & Sankaran Mahadevan, 2008. "Bayesian validation assessment of multivariate computational models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(1), pages 49-65.
    7. Gerhard Arminger & Bengt Muthén, 1998. "A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the metropolis-hastings algorithm," Psychometrika, Springer;The Psychometric Society, vol. 63(3), pages 271-300, September.
    8. Jiang, Xiaomo & Mahadevan, Sankaran, 2007. "Bayesian risk-based decision method for model validation under uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 707-718.
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    Cited by:

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