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Bayesian variable selection for mixed effects model with shrinkage prior

Author

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  • Mingan Yang

    (San Diego State University)

  • Min Wang

    (Texas Tech University)

  • Guanghui Dong

    (Sun Yat-sen University)

Abstract

Recently, many shrinkage priors have been proposed and studied in linear models to address massive regression problems. However, shrinkage priors are rarely used in mixed effects models. In this article, we address the problem of joint selection of both fixed effects and random effects with the use of several shrinkage priors in linear mixed models. The idea is to shrink small coefficients to zero while minimally shrink large coefficients due to the heavy tails. The shrinkage priors can be obtained via a scale mixture of normal distributions to facilitate computation. We use a stochastic search Gibbs sampler to implement a fully Bayesian approach for variable selection. The approach is illustrated using simulated data and a real example.

Suggested Citation

  • Mingan Yang & Min Wang & Guanghui Dong, 2020. "Bayesian variable selection for mixed effects model with shrinkage prior," Computational Statistics, Springer, vol. 35(1), pages 227-243, March.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:1:d:10.1007_s00180-019-00895-x
    DOI: 10.1007/s00180-019-00895-x
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    3. Yang, Mingan, 2012. "Bayesian variable selection for logistic mixed model with nonparametric random effects," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2663-2674.
    4. 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.
    5. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    6. Michael J. Daniels, 2002. "Bayesian analysis of covariance matrices and dynamic models for longitudinal data," Biometrika, Biometrika Trust, vol. 89(3), pages 553-566, August.
    7. Bo Cai & David B. Dunson, 2006. "Bayesian Covariance Selection in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 62(2), pages 446-457, June.
    8. Zhen Chen & David B. Dunson, 2003. "Random Effects Selection in Linear Mixed Models," Biometrics, The International Biometric Society, vol. 59(4), pages 762-769, December.
    9. Dan Jackson & Sylwia Bujkiewicz & Martin Law & Richard D. Riley & Ian R. White, 2018. "A matrix†based method of moments for fitting multivariate network meta†analysis models with multiple outcomes and random inconsistency effects," Biometrics, The International Biometric Society, vol. 74(2), pages 548-556, June.
    10. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    11. Satkartar K. Kinney & David B. Dunson, 2007. "Fixed and Random Effects Selection in Linear and Logistic Models," Biometrics, The International Biometric Society, vol. 63(3), pages 690-698, September.
    12. Zhu, Zhongyi & Fung, Wing K., 2004. "Variance component testing in semiparametric mixed models," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 107-118, October.
    13. Geert Verbeke & Geert Molenberghs, 2003. "The Use of Score Tests for Inference on Variance Components," Biometrics, The International Biometric Society, vol. 59(2), pages 254-262, June.
    14. Howard D. Bondell & Arun Krishna & Sujit K. Ghosh, 2010. "Joint Variable Selection for Fixed and Random Effects in Linear Mixed-Effects Models," Biometrics, The International Biometric Society, vol. 66(4), pages 1069-1077, December.
    15. Mingan Yang & David Dunson, 2010. "Bayesian Semiparametric Structural Equation Models with Latent Variables," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 675-693, December.
    16. Mingan Yang, 2018. "Assessment of Noninferiority (and Equivalence) for Simple Crossover Trials Using Bayesian Approach," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 506-519, December.
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    Cited by:

    1. Mingan Yang, 2020. "Bayesian Mixed Effects Model with Variable Selection," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 10(2), pages 27-29, August.

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