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Bias Reduction in Logistic Regression with Missing Responses When the Missing Data Mechanism is Nonignorable

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  • Arnab Kumar Maity
  • Vivek Pradhan
  • Ujjwal Das

Abstract

In logistic regression with nonignorable missing responses, Ibrahim and Lipsitz proposed a method for estimating regression parameters. It is known that the regression estimates obtained by using this method are biased when the sample size is small. Also, another complexity arises when the iterative estimation process encounters separation in estimating regression coefficients. In this article, we propose a method to improve the estimation of regression coefficients. In our likelihood-based method, we penalize the likelihood by multiplying it by a noninformative Jeffreys prior as a penalty term. The proposed method reduces bias and is able to handle the issue of separation. Simulation results show substantial bias reduction for the proposed method as compared to the existing method. Analyses using real world data also support the simulation findings. An R package called brlrmr is developed implementing the proposed method and the Ibrahim and Lipsitz method.

Suggested Citation

  • Arnab Kumar Maity & Vivek Pradhan & Ujjwal Das, 2019. "Bias Reduction in Logistic Regression with Missing Responses When the Missing Data Mechanism is Nonignorable," The American Statistician, Taylor & Francis Journals, vol. 73(4), pages 340-349, October.
    • Handle: RePEc:taf:amstat:v:73:y:2019:i:4:p:340-349
    DOI: 10.1080/00031305.2017.1407359
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    Cited by:

    1. Chunhua Chen & Jianwei Ren & Lijun Tang & Haohua Liu, 2020. "Additive integer-valued data envelopment analysis with missing data: A multi-criteria evaluation approach," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-20, June.
    2. Majid Mojirsheibani, 2022. "On the maximal deviation of kernel regression estimators with NMAR response variables," Statistical Papers, Springer, vol. 63(5), pages 1677-1705, October.
    3. Mojirsheibani, Majid, 2021. "On classification with nonignorable missing data," Journal of Multivariate Analysis, Elsevier, vol. 184(C).

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