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Semiparametric Bayesian analysis of transformation linear mixed models

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  • Tang, Niansheng
  • Wu, Ying
  • Chen, Dan

Abstract

In classical linear mixed models (LMMs), it is commonly assumed that the random effects and within-individual errors independently follow a Gaussian distribution. However, in some applications, this assumption may be inappropriate. To this end, this paper proposes a novel LMM by assuming that the random effects follow an unknown distribution, and the within-individual errors associated with the transformed responses are Gaussian. A semiparametric Bayesian approach is developed to make Bayesian inference on the novel LMM by using the truncated centered Dirichlet Process prior to approximate the unknown distribution of the random effects and using Bayesian P-splines to approximate the transformation function, and combining the Gibbs sampler and the Metropolis–Hastings algorithm. A Bayesian local influence analysis method is developed to assess the effect of minor perturbations. Simulation studies and an example are used to illustrate the proposed methodologies.

Suggested Citation

  • Tang, Niansheng & Wu, Ying & Chen, Dan, 2018. "Semiparametric Bayesian analysis of transformation linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 225-240.
    • Handle: RePEc:eee:jmvana:v:166:y:2018:i:c:p:225-240
    DOI: 10.1016/j.jmva.2018.03.007
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    References listed on IDEAS

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    1. Fabio, Lizandra C. & Paula, Gilberto A. & Castro, Mário de, 2012. "A Poisson mixed model with nonnormal random effect distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1499-1510.
    2. Yang, Mingan & Dunson, David B. & Baird, Donna, 2010. "Semiparametric Bayes hierarchical models with mean and variance constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2172-2186, September.
    3. 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.
    4. Hongtu Zhu & Joseph G. Ibrahim & Niansheng Tang, 2011. "Bayesian influence analysis: a geometric approach," Biometrika, Biometrika Trust, vol. 98(2), pages 307-323.
    5. Hongtu Zhu & Joseph G. Ibrahim & Yueh-Yun Chi & Niansheng Tang, 2012. "Bayesian Influence Measures for Joint Models for Longitudinal and Survival Data," Biometrics, The International Biometric Society, vol. 68(3), pages 954-964, September.
    6. J. D. Opsomer & G. Claeskens & M. G. Ranalli & G. Kauermann & F. J. Breidt, 2008. "Non‐parametric small area estimation using penalized spline regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 265-286, February.
    7. Peng Wang & Guei-feng Tsai & Annie Qu, 2012. "Conditional Inference Functions for Mixed-Effects Models With Unspecified Random-Effects Distribution," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 725-736, June.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    9. W.‐Y. Poon & Y. S. Poon, 1999. "Conformal normal curvature and assessment of local influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 51-61.
    10. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    11. Elizabeth R. Brown & Joseph G. Ibrahim, 2003. "A Bayesian Semiparametric Joint Hierarchical Model for Longitudinal and Survival Data," Biometrics, The International Biometric Society, vol. 59(2), pages 221-228, June.
    12. Gurka, Matthew J., 2006. "Selecting the Best Linear Mixed Model Under REML," The American Statistician, American Statistical Association, vol. 60, pages 19-26, February.
    13. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
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