Model selection with nonignorable nonresponse

Existing methods for handling nonignorable missing data rely on the correct specification of parametric models, which is difficult to check. By utilizing the information carried in an instrument, we propose a novel model selection criterion, called the penalized validation criterion, in the presence of nonignorable nonresponse with unspecified propensity. The proposed method can consistently select the most compact correct parametric model from a group of candidate models if one of the candidate models is correct. The population parameter estimators based on the selected model are consistent and asymptotically normal. Prior to our study, this type of result had been established only for ignorable missing data or nonignorable missing data under the strong assumption that the nonresponse propensity has a correct parametric model. Simulation results show that our proposed method works quite well. A real-data example is presented.