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

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.