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On Bayesian estimation and model comparison of an integrated structural equation model

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  • Lee, Sik-Yum
  • Song, Xin-Yuan

Abstract

In this paper, we introduce a Bayesian approach to the estimation and model comparison of an integrated two-level nonlinear structural equation model with mixed continuous, dichotomous, and ordered categorical data that may be missing at random. This general model can accommodate nonlinearities of latent variables and the effects of fixed covariates on measurement and structural equations in within-groups and between-groups models. A sampling-based algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is proposed for posterior simulation. A procedure that utilizes path sampling is implemented to compute the Bayes factor for model comparison under the framework of the proposed integrated model. Empirical performances of Bayesian methodologies are illustrated via analysis of a real example.

Suggested Citation

  • Lee, Sik-Yum & Song, Xin-Yuan, 2008. "On Bayesian estimation and model comparison of an integrated structural equation model," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4814-4827, June.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:10:p:4814-4827
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    References listed on IDEAS

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    1. Sik-Yum Lee & Jian-Qing Shi, 2001. "Maximum Likelihood Estimation of Two-Level Latent Variable Models with Mixed Continuous and Polytomous Data," Biometrics, The International Biometric Society, vol. 57(3), pages 787-794, September.
    2. Xin-Yuan Song & Sik-Yum Lee, 2002. "Analysis of structural equation model with ignorable missing continuous and polytomous data," Psychometrika, Springer;The Psychometric Society, vol. 67(2), pages 261-288, June.
    3. Asim Ansari & Kamel Jedidi & Laurette Dube, 2002. "Heterogeneous factor analysis models: A bayesian approach," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 49-77, March.
    4. Sik-Yum Lee & Xin-Yuan Song, 2003. "Model comparison of nonlinear structural equation models with fixed covariates," Psychometrika, Springer;The Psychometric Society, vol. 68(1), pages 27-47, March.
    5. D. B. Dunson, 2000. "Bayesian latent variable models for clustered mixed outcomes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 355-366.
    6. J.‐Q. Shi & S.‐Y. Lee, 2000. "Latent variable models with mixed continuous and polytomous data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 77-87.
    7. Asim Ansari & Kamel Jedidi, 2000. "Bayesian factor analysis for multilevel binary observations," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 475-496, December.
    8. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    9. Sik-Yum Lee & Hong-Tu Zhu, 2002. "Maximum likelihood estimation of nonlinear structural equation models," Psychometrika, Springer;The Psychometric Society, vol. 67(2), pages 189-210, June.
    10. Sik-Yum Lee & Xin-Yuan Song, 2004. "Maximum Likelihood Analysis of a General Latent Variable Model with Hierarchically Mixed Data," Biometrics, The International Biometric Society, vol. 60(3), pages 624-636, September.
    11. Lee, Sik-Yum & Song, Xin-Yuan, 2003. "Maximum likelihood estimation and model comparison of nonlinear structural equation models with continuous and polytomous variables," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 125-142, October.
    12. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    13. Richard Scheines & Herbert Hoijtink & Anne Boomsma, 1999. "Bayesian estimation and testing of structural equation models," Psychometrika, Springer;The Psychometric Society, vol. 64(1), pages 37-52, March.
    14. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2004. "Generalized multilevel structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 167-190, June.
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    Cited by:

    1. Nebojsa S. Davcik, 2013. "The Use And Misuse Of Structural Equation Modeling In Management Research," Working Papers Series 2 13-07, ISCTE-IUL, Business Research Unit (BRU-IUL).

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