IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v94y2009i4p796-809.html
   My bibliography  Save this article

Bayesian structural equation modeling method for hierarchical model validation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832008002172
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2008.08.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Rebba, Ramesh & Mahadevan, Sankaran, 2008. "Computational methods for model reliability assessment," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1197-1207.
    6. Sik-Yum Lee, 1981. "A bayesian approach to confirmatory factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 46(2), pages 153-160, June.
    7. 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.
    8. Goldberger, Arthur S, 1972. "Structural Equation Methods in the Social Sciences," Econometrica, Econometric Society, vol. 40(6), pages 979-1001, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Juliana Guedes Almeida & Deanne N. Den Hartog & Annebel H. B. Hoogh & Vithor Rosa Franco & Juliana Barreiros Porto, 2022. "Harmful Leader Behaviors: Toward an Increased Understanding of How Different Forms of Unethical Leader Behavior Can Harm Subordinates," Journal of Business Ethics, Springer, vol. 180(1), pages 215-244, September.
    2. Jiang, Xiaomo & Yuan, Yong & Liu, Xian, 2013. "Bayesian inference method for stochastic damage accumulation modeling," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 126-138.
    3. Kwag, Shinyoung & Gupta, Abhinav & Dinh, Nam, 2018. "Probabilistic risk assessment based model validation method using Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 380-393.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. David Kaplan & Chansoon Lee, 2018. "Optimizing Prediction Using Bayesian Model Averaging: Examples Using Large-Scale Educational Assessments," Evaluation Review, , vol. 42(4), pages 423-457, August.
    2. Maura Mezzetti, 2012. "Bayesian factor analysis for spatially correlated data: application to cancer incidence data in Scotland," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(1), pages 49-74, March.
    3. Ao, Dan & Hu, Zhen & Mahadevan, Sankaran, 2017. "Design of validation experiments for life prediction models," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 22-33.
    4. 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.
    5. Hong-Tu Zhu & Sik-Yum Lee, 2001. "A Bayesian analysis of finite mixtures in the LISREL model," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 133-152, March.
    6. Sankararaman, Shankar & Mahadevan, Sankaran, 2011. "Model validation under epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1232-1241.
    7. Piotr Tarka, 2018. "An overview of structural equation modeling: its beginnings, historical development, usefulness and controversies in the social sciences," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(1), pages 313-354, January.
    8. Kwag, Shinyoung & Gupta, Abhinav & Dinh, Nam, 2018. "Probabilistic risk assessment based model validation method using Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 380-393.
    9. Elena A. Erosheva & S. McKay Curtis, 2017. "Dealing with Reflection Invariance in Bayesian Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 295-307, June.
    10. Asim Ansari & Kamel Jedidi, 2000. "Bayesian factor analysis for multilevel binary observations," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 475-496, December.
    11. Terry Elrod & Gerald Häubl & Steven Tipps, 2012. "Parsimonious Structural Equation Models for Repeated Measures Data, with Application to the Study of Consumer Preferences," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 358-387, April.
    12. Ling, You & Mahadevan, Sankaran, 2013. "Quantitative model validation techniques: New insights," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 217-231.
    13. Sankararaman, Shankar & Mahadevan, Sankaran, 2015. "Integration of model verification, validation, and calibration for uncertainty quantification in engineering systems," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 194-209.
    14. Teferra, Kirubel & Shields, Michael D. & Hapij, Adam & Daddazio, Raymond P., 2014. "Mapping model validation metrics to subject matter expert scores for model adequacy assessment," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 9-19.
    15. Vanslette, Kevin & Tohme, Tony & Youcef-Toumi, Kamal, 2020. "A general model validation and testing tool," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    16. Mao, Lu, 2022. "Identification of the outcome distribution and sensitivity analysis under weak confounder–instrument interaction," Statistics & Probability Letters, Elsevier, vol. 189(C).
    17. Francesco Agostinelli & Matthew Wiswall, 2016. "Identification of Dynamic Latent Factor Models: The Implications of Re-Normalization in a Model of Child Development," NBER Working Papers 22441, National Bureau of Economic Research, Inc.
    18. Magnusson, Leandro M. & Tarverdi, Yashar, 2020. "Measuring governance: Why do errors matter?," World Development, Elsevier, vol. 136(C).
    19. George Halkos & Kyriaki Tsilika, 2015. "Programming Identification Criteria in Simultaneous Equation Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 157-170, June.
    20. Zhuanglin Ma & Mingjie Luo & Steven I-Jy Chien & Dawei Hu & Xue Zhao, 2020. "Analyzing drivers’ perceived service quality of variable message signs (VMS)," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-19, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:94:y:2009:i:4:p:796-809. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.