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Bayesian Adaptive Lasso for Regression Models with Nonignorable Missing Responses

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  • Yuanying Zhao
  • Xingde Duan

Abstract

The main purpose of this article is to develop a Bayesian adaptive lasso procedure for analyzing linear regression models with nonignorable missing responses, in which the missingness mechanism is specified by a logistic regression model. A sampling procedure combining the Gibbs sampler and Metropolis‐Hastings algorithm is employed to obtain the Bayesian estimates of the regression coefficients, shrinkage coefficients, missingness mechanism models parameters, and their standard errors. We extend the partial posterior predictive p value for goodness‐of‐fit statistic to investigate the plausibility of the posited model. Finally, several simulation studies and the air pollution data example are undertaken to demonstrate the newly developed methodologies.

Suggested Citation

  • Yuanying Zhao & Xingde Duan, 2022. "Bayesian Adaptive Lasso for Regression Models with Nonignorable Missing Responses," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:3168735
    DOI: 10.1155/2022/3168735
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    References listed on IDEAS

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    2. Ibrahim, Joseph G. & Zhu, Hongtu & Tang, Niansheng, 2008. "Model Selection Criteria for Missing-Data Problems Using the EM Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1648-1658.
    3. 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.
    4. Ruixin Guo & Hongtu Zhu & Sy-Miin Chow & Joseph G. Ibrahim, 2012. "Bayesian Lasso for Semiparametric Structural Equation Models," Biometrics, The International Biometric Society, vol. 68(2), pages 567-577, June.
    5. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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