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Semiparametric Bayesian analysis of nonlinear reproductive dispersion mixed models for longitudinal data

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  • Tang, Nian-Sheng
  • Zhao, Yuan-Ying

Abstract

In the development of nonlinear reproductive dispersion mixed models, it is commonly assumed that distribution of random effects is normal. The normality assumption is likely violated in many practical applications. In this paper, we assume that distribution of random effects is specified by a Dirichlet process prior for relaxing this limitation. A semiparametric Bayesian approach combining the stick-breaking prior and the blocked Gibbs sampler as well as the Metropolis–Hastings algorithm is developed for simulating observations from the posterior distributions and producing the joint Bayesian estimates of unknown parameters and random effects. Two goodness-of-fit statistics are presented to assess the plausibility of the posited model, and the procedures for computing the Bayes factor, pseudo-Bayes factor and deviance information criterion for model comparison are given. Also, we propose two Bayesian case deletion influence measures including the ϕ-divergence and Cook’s posterior mean distance. Four simulation studies and a real example are presented to illustrate the newly developed Bayesian methodologies.

Suggested Citation

  • Tang, Nian-Sheng & Zhao, Yuan-Ying, 2013. "Semiparametric Bayesian analysis of nonlinear reproductive dispersion mixed models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 68-83.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:68-83
    DOI: 10.1016/j.jmva.2012.09.005
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    References listed on IDEAS

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    1. Sik-Yum Lee, 2006. "Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 541-564, September.
    2. Hyunsoon Cho & Joseph G. Ibrahim & Debajyoti Sinha & Hongtu Zhu, 2009. "Bayesian Case Influence Diagnostics for Survival Models," Biometrics, The International Biometric Society, vol. 65(1), pages 116-124, March.
    3. Daowen Zhang & Marie Davidian, 2001. "Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, The International Biometric Society, vol. 57(3), pages 795-802, September.
    4. Chen, Xue-Dong & Tang, Nian-Sheng, 2010. "Bayesian analysis of semiparametric reproductive dispersion mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2145-2158, September.
    5. 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.
    6. Wendimagegn Ghidey & Emmanuel Lesaffre & Paul Eilers, 2004. "Smooth Random Effects Distribution in a Linear Mixed Model," Biometrics, The International Biometric Society, vol. 60(4), pages 945-953, December.
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    Cited by:

    1. Lu, Weisheng & Tam, Vivian W.Y., 2013. "Construction waste management policies and their effectiveness in Hong Kong: A longitudinal review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 23(C), pages 214-223.
    2. Zhao Yuanying & Xu Dengke & Duan Xingde & Pang Yicheng, 2014. "Bayesian Subset Selection for Reproductive Dispersion Linear Models," Journal of Systems Science and Information, De Gruyter, vol. 2(1), pages 77-85, February.
    3. Dengke Xu & Zhongzhan Zhang & Liucang Wu, 2014. "Bayesian analysis of joint mean and covariance models for longitudinal data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2504-2514, November.

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