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

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.

• Identifiability
• Instrumental variable
• Nonignorable missing data
• Pseudo-likelihood
• Variance estimation.

Additional information

Notes on contributors

Jiwei Zhao

Jiwei Zhao is Assistant Professor, Department of Biostatistics, University at Buffalo, SUNY, Buffalo, NY 14214 (E-mail: [email protected]). Jun Shao is Professor, School of Finance and Statistics, East China Normal University, Shanghai, China 200241, and Department of Statistics, University of Wisconsin, Madison, WI 53706 (E-mail: [email protected]). The research was partially supported by the NSF grant DMS-1305474. The authors thank the editor, the associate editor, and three anonymous referees for their insightful comments and useful suggestions.

Jun Shao

Jiwei Zhao is Assistant Professor, Department of Biostatistics, University at Buffalo, SUNY, Buffalo, NY 14214 (E-mail: [email protected]). Jun Shao is Professor, School of Finance and Statistics, East China Normal University, Shanghai, China 200241, and Department of Statistics, University of Wisconsin, Madison, WI 53706 (E-mail: [email protected]). The research was partially supported by the NSF grant DMS-1305474. The authors thank the editor, the associate editor, and three anonymous referees for their insightful comments and useful suggestions.