Imputation with verifiable identification condition for nonignorable missing outcomes

Missing data often results in undesirable bias and loss of efficiency. These results become substantial problems when the response mechanism is nonignorable, such that the response model depends on the unobserved variable. It is often necessary to estimate the joint distribution of the unobserved variables and response indicators to further manage nonignorable nonresponse. However, model misspecification and identification issues prevent robust estimates, despite carefully estimating the target joint distribution. In this study we model the distribution of the observed parts and derived sufficient conditions for model identifiability, assuming a logistic distribution of the response mechanism and a generalized linear model as the main outcome model of interest. More importantly, the derived sufficient conditions are testable with the observed data and do not require any instrumental variables, which have often been assumed to guarantee model identifiability but cannot be practically determined beforehand. To analyse missing data, we propose a new fractional imputation method which incorporates verifiable identifiability using only the observed data. Furthermore, we present the performance of the proposed estimators in numerical studies and apply the proposed method to two sets of real data, namely, Opinion Poll for the 2022 South Korean Presidential Election, and public data collected from the US National Supported Work Evaluation Study.