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A criterion-based model comparison statistic for structural equation models with heterogeneous data

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  • Li, Yun-Xian
  • Kano, Yutaka
  • Pan, Jun-Hao
  • Song, Xin-Yuan

Abstract

Heterogeneous data are common in social, educational, medical and behavioral sciences. Recently, finite mixture structural equation models (SEMs) and two-level SEMs have been respectively proposed to analyze different kinds of heterogeneous data. Due to the complexity of these two kinds of SEMs, model comparison is difficult. For instance, the computational burden in evaluating the Bayes factor is heavy, and the Deviance Information Criterion may not be appropriate for mixture SEMs. In this paper, a Bayesian criterion-based method called the Lv measure, which involves a component related to the variability of the prediction and a component related to the discrepancy between the data and the prediction, is proposed. Moreover, the calibration distribution is introduced for formal comparison of competing models. Two simulation studies, and two applications based on real data sets are presented to illustrate the satisfactory performance of the Lv measure in model comparison.

Suggested Citation

  • Li, Yun-Xian & Kano, Yutaka & Pan, Jun-Hao & Song, Xin-Yuan, 2012. "A criterion-based model comparison statistic for structural equation models with heterogeneous data," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 92-107.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:92-107
    DOI: 10.1016/j.jmva.2012.05.010
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Asim Ansari & Kamel Jedidi, 2000. "Bayesian factor analysis for multilevel binary observations," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 475-496, December.
    4. Conor Dolan & Han Maas, 1998. "Fitting multivariage normal finite mixtures subject to structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 63(3), pages 227-253, September.
    5. Ming-Hui Chen, 2004. "Bayesian criterion based model assessment for categorical data," Biometrika, Biometrika Trust, vol. 91(1), pages 45-63, March.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    7. 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.
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    Cited by:

    1. Li, Yunxian & Tang, Niansheng & Jiang, Xuejun, 2016. "Bayesian approaches for analyzing earthquake catastrophic risk," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 110-119.

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