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Bayesian local influence of semiparametric structural equation models

Author

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  • Ouyang, Ming
  • Yan, Xiaodong
  • Chen, Ji
  • Tang, Niansheng
  • Song, Xinyuan

Abstract

The authors develop a Bayesian local influence method for semiparametric structural equation models. The effects of minor perturbations to individual observations, the prior distributions of parameters, and the sampling distribution on the statistical inference are assessed with various perturbation schemes. A Bayesian perturbation manifold is constructed to characterize such perturbation schemes. The first- and second-order influence measures are proposed to quantify the degree of minor perturbations on different aspects of a statistical model via objective functions, such as Bayes factor. Simulation studies are conducted to evaluate the empirical performance of the Bayesian local influence procedure. An application to a study of bone mineral density is presented.

Suggested Citation

  • Ouyang, Ming & Yan, Xiaodong & Chen, Ji & Tang, Niansheng & Song, Xinyuan, 2017. "Bayesian local influence of semiparametric structural equation models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 102-115.
    • Handle: RePEc:eee:csdana:v:111:y:2017:i:c:p:102-115
    DOI: 10.1016/j.csda.2017.01.007
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    References listed on IDEAS

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    1. Hong‐Tu Zhu & Sik‐Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
    2. Sik-Yum Lee & Nian-Sheng Tang, 2004. "Local influence analysis of nonlinear structural equation models," Psychometrika, Springer;The Psychometric Society, vol. 69(4), pages 573-592, December.
    3. Hongtu Zhu & Joseph G. Ibrahim & Niansheng Tang, 2011. "Bayesian influence analysis: a geometric approach," Biometrika, Biometrika Trust, vol. 98(2), pages 307-323.
    4. Tang, Nian-Sheng & Duan, Xing-De, 2014. "Bayesian influence analysis of generalized partial linear mixed models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 86-99.
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    Cited by:

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