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On the identifiability and estimation of generalized linear models with parametric nonignorable missing data mechanism

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  • Cui, Xia
  • Guo, Jianhua
  • Yang, Guangren

Abstract

We address the problem of identifying and estimating generalized linear models when the response variable is nonignorably missing. Three types of monotone missing data mechanism are assumed, including Logit model, Probit model and complementary Log–log model. In this situation, likelihood based on observed data may not be identifiable. In this article, we prove the model parameters are identifiable under very mild conditions and then construct estimators based on a likelihood-based approach. The proposed estimators are shown to be consistent and asymptotically normal. Simulation studies demonstrate that the proposed inference procedure performs well in many settings. We apply the proposed method to a data set from research in Chinese Household Income Project study.

Suggested Citation

  • Cui, Xia & Guo, Jianhua & Yang, Guangren, 2017. "On the identifiability and estimation of generalized linear models with parametric nonignorable missing data mechanism," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 64-80.
    • Handle: RePEc:eee:csdana:v:107:y:2017:i:c:p:64-80
    DOI: 10.1016/j.csda.2016.10.017
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    References listed on IDEAS

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    1. Sheng Wang & Jun Shao & Jae Kwang Kim, "undated". "An Instrumental Variable Approach for Identification and Estimation with Nonignorable Nonresponse," Mathematica Policy Research Reports a9593fac2c9746f486d2162f9, Mathematica Policy Research.
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    3. repec:mpr:mprres:8160 is not listed on IDEAS
    4. Gong Tang, 2003. "Analysis of multivariate missing data with nonignorable nonresponse," Biometrika, Biometrika Trust, vol. 90(4), pages 747-764, December.
    5. Danping Liu & Xiao-Hua Zhou, 2010. "A Model for Adjusting for Nonignorable Verification Bias in Estimation of the ROC Curve and Its Area with Likelihood-Based Approach," Biometrics, The International Biometric Society, vol. 66(4), pages 1119-1128, December.
    6. Jiwei Zhao & Jun Shao, 2015. "Semiparametric Pseudo-Likelihoods in Generalized Linear Models With Nonignorable Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1577-1590, December.
    7. Qin J. & Leung D. & Shao J., 2002. "Estimation With Survey Data Under Nonignorable Nonresponse or Informative Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 193-200, March.
    8. Kim, Jae Kwang & Yu, Cindy Long, 2011. "A Semiparametric Estimation of Mean Functionals With Nonignorable Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 157-165.
    9. Wang Miao & Peng Ding & Zhi Geng, 2016. "Identifiability of Normal and Normal Mixture Models with Nonignorable Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1673-1683, October.
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    Cited by:

    1. Jierui Du & Xia Cui, 2024. "Semiparametric estimation in generalized additive partial linear models with nonignorable nonresponse data," Statistical Papers, Springer, vol. 65(5), pages 3235-3259, July.
    2. Tabrizi, Elham & Samani, Ehsan Bahrami & Ganjali, Mojtaba, 2020. "A note on the identifiability of latent variable models for mixed longitudinal data," Statistics & Probability Letters, Elsevier, vol. 167(C).
    3. Takahiro Hoshino & Keisuke Takahata, 2018. "Identification of heterogeneous treatment effects as a function of potential untreated outcome under the nonignorable assignment condition," Keio-IES Discussion Paper Series 2018-005, Institute for Economics Studies, Keio University.

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