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Semiparametric Pseudo-Likelihoods in Generalized Linear Models With Nonignorable Missing Data

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  • Jiwei Zhao
  • Jun Shao

Abstract

We consider identifiability and estimation in a generalized linear model in which the response variable and some covariates have missing values and the missing data mechanism is nonignorable and unspecified. We adopt a pseudo-likelihood approach that makes use of an instrumental variable to help identifying unknown parameters in the presence of nonignorable missing data. Explicit conditions for the identifiability of parameters are given. Some asymptotic properties of the parameter estimators based on maximizing the pseudo-likelihood are established. Explicit asymptotic covariance matrix and its estimator are also derived in some cases. For the numerical maximization of the pseudo-likelihood, we develop a two-step iteration algorithm that decomposes a nonconcave maximization problem into two problems of maximizing concave functions. Some simulation results and an application to a dataset from cotton factory workers are also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:512:p:1577-1590
    DOI: 10.1080/01621459.2014.983234
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    References listed on IDEAS

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    1. Kott, Phillip S. & Chang, Ted, 2010. "Using Calibration Weighting to Adjust for Nonignorable Unit Nonresponse," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1265-1275.
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    3. 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.
    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.
    5. Gong Tang, 2003. "Analysis of multivariate missing data with nonignorable nonresponse," Biometrika, Biometrika Trust, vol. 90(4), pages 747-764, December.
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