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Two-Level Stochastic Search Variable Selection in GLMs with Missing Predictors

Author

Listed:
  • Mitra Robin

    (Southampton Statistical Sciences Research Institute)

  • Dunson David

    (Duke University)

Abstract

Stochastic search variable selection (SSVS) algorithms provide an appealing and widely used approach for searching for good subsets of predictors while simultaneously estimating posterior model probabilities and model-averaged predictive distributions. This article proposes a two-level generalization of SSVS to account for missing predictors while accommodating uncertainty in the relationships between these predictors. Bayesian approaches for allowing predictors that are missing at random require a model on the joint distribution of the predictors. We show that predictive performance can be improved by allowing uncertainty in the specification of predictor relationships in this model. The methods are illustrated through simulation studies and analysis of an epidemiologic data set.

Suggested Citation

  • Mitra Robin & Dunson David, 2010. "Two-Level Stochastic Search Variable Selection in GLMs with Missing Predictors," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-40, October.
    • Handle: RePEc:bpj:ijbist:v:6:y:2010:i:1:n:33
    DOI: 10.2202/1557-4679.1173
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    References listed on IDEAS

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    1. Cottet, Remy & Kohn, Robert J. & Nott, David J., 2008. "Variable Selection and Model Averaging in Semiparametric Overdispersed Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 661-671, June.
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    3. 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.
    4. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, October.
    5. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
    6. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    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.
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    Cited by:

    1. Joseph Antonelli & Georgia Papadogeorgou & Francesca Dominici, 2022. "Causal inference in high dimensions: A marriage between Bayesian modeling and good frequentist properties," Biometrics, The International Biometric Society, vol. 78(1), pages 100-114, March.
    2. Lee, Min Cherng & Mitra, Robin, 2016. "Multiply imputing missing values in data sets with mixed measurement scales using a sequence of generalised linear models," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 24-38.

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