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Bayesian semiparametric models for nonignorable missing mechanisms in generalized linear models

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  • Z. I. Kalaylioglu
  • O. Ozturk

Abstract

Semiparametric models provide a more flexible form for modeling the relationship between the response and the explanatory variables. On the other hand in the literature of modeling for the missing variables, canonical form of the probability of the variable being missing ( p ) is modeled taking a fully parametric approach. Here we consider a regression spline based semiparametric approach to model the missingness mechanism of nonignorably missing covariates. In this model the relationship between the suitable canonical form of p (e.g. probit p ) and the missing covariate is modeled through several splines. A Bayesian procedure is developed to efficiently estimate the parameters. A computationally advantageous prior construction is proposed for the parameters of the semiparametric part. A WinBUGS code is constructed to apply Gibbs sampling to obtain the posterior distributions. We show through an extensive Monte Carlo simulation experiment that response model coefficent estimators maintain better (when the true missingness mechanism is nonlinear) or equivalent (when the true missingness mechanism is linear) bias and efficiency properties with the use of proposed semiparametric missingness model compared to the conventional model.

Suggested Citation

  • Z. I. Kalaylioglu & O. Ozturk, 2013. "Bayesian semiparametric models for nonignorable missing mechanisms in generalized linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(8), pages 1746-1763, August.
    • Handle: RePEc:taf:japsta:v:40:y:2013:i:8:p:1746-1763
    DOI: 10.1080/02664763.2013.794329
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    References listed on IDEAS

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    1. Lan Huang & Ming-Hui Chen & Joseph G. Ibrahim, 2005. "Bayesian Analysis for Generalized Linear Models with Nonignorably Missing Covariates," Biometrics, The International Biometric Society, vol. 61(3), pages 767-780, September.
    2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, November.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, November.
    4. 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.
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