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Missing data often results in undesirable bias and loss of efficiency. Theseresults become substantial problems when the response mechanism isnonignorable, such that the response model depends on the unobserved variable.It is often necessary to estimate the joint distribution of the unobservedvariables and response indicators to further manage nonignorable nonresponse.However, model misspecification and identification issues prevent robustestimates, despite carefully estimating the target joint distribution. In thisstudy we model the distribution of the observed parts and derived sufficientconditions for model identifiability, assuming a logistic distribution of theresponse mechanism and a generalized linear model as the main outcome model ofinterest. More importantly, the derived sufficient conditions are testable withthe observed data and do not require any instrumental variables, which haveoften been assumed to guarantee model identifiability but cannot be practicallydetermined beforehand. To analyse missing data, we propose a new fractionalimputation method which incorporates verifiable identifiability using only theobserved data. Furthermore, we present the performance of the proposedestimators in numerical studies and apply the proposed method to two sets ofreal data, namely, Opinion Poll for the 2022 South Korean PresidentialElection, and public data collected from the US National Supported WorkEvaluation Study.

Imputation with verifiable identification condition for nonignorable missing outcomes