Multiple imputation for nonignorable missing data

Multiple imputation is a popular technique for analyzing incomplete data. Missing at random mechanism is often assumed when multiple imputation is performed, assuming that the response mechanism does not depend on the missing variable. However, the assumption of ignorable nonresponse may lead to largely biased estimates when in fact the missingness is nonignorable. In this paper, we propose a multiple imputation method in the presence of nonignorable nonresponse. In the proposed method, we take the selection model approach and specify the response model and the respondents’ outcome model to capture the joint model of the study variable and the response indicator. The proposed data augmentation algorithm uses the respondents’ outcome model and incorporates a semiparametric estimation of the respondents’ outcome model. The proposed multiple imputation method performs well if the specified response model is correct. Limited simulation studies are presented to check the performance of the proposed multiple imputation method.