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Bayesian model selection for generalized linear models using non-local priors

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  • Shi, Guiling
  • Lim, Chae Young
  • Maiti, Tapabrata

Abstract

Variable selection is currently an important research topic under both frequentist and Bayesian framework. While most developments in Bayesian model selection literature are based on a local prior on regression parameters, a nonlocal prior for model selection can be also used. In this article, we extend nonlocal prior approach to logistic regression and to generalized linear models. Laplace approximation is used in implementation to avoid integration in the likelihood. A convergence rate is derived under some regularity conditions. The selection based on a nonlocal prior eliminates unnecessary variables and recommends a simple model. The method is validated by simulation study and illustrated by a real data example.

Suggested Citation

  • Shi, Guiling & Lim, Chae Young & Maiti, Tapabrata, 2019. "Bayesian model selection for generalized linear models using non-local priors," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 285-296.
    • Handle: RePEc:eee:csdana:v:133:y:2019:i:c:p:285-296
    DOI: 10.1016/j.csda.2018.10.007
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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. Valen E. Johnson & David Rossell, 2012. "Bayesian Model Selection in High-Dimensional Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 649-660, June.
    3. Faming Liang & Qifan Song & Kai Yu, 2013. "Bayesian Subset Modeling for High-Dimensional Generalized Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 589-606, June.
    4. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    5. M.‐H. Chen & J. G. Ibrahim & C. Yiannoutsos, 1999. "Prior elicitation, variable selection and Bayesian computation for logistic regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 223-242.
    6. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    7. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    8. Naijun Sha & Marina Vannucci & Mahlet G. Tadesse & Philip J. Brown & Ilaria Dragoni & Nick Davies & Tracy C. Roberts & Andrea Contestabile & Mike Salmon & Chris Buckley & Francesco Falciani, 2004. "Bayesian Variable Selection in Multinomial Probit Models to Identify Molecular Signatures of Disease Stage," Biometrics, The International Biometric Society, vol. 60(3), pages 812-819, September.
    9. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    10. Valen E. Johnson & David Rossell, 2010. "On the use of non‐local prior densities in Bayesian hypothesis tests," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 143-170, March.
    11. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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