What Happens When Imputation Model and Analysis Procedure Are Uncongenial?
One recurrent criticism of multiple imputation (MI) inference has been that its confidence intervals may not have the nominal coverage rate. This phenomenon is known to be a direct consequence of uncongeniality, that is, the assumptions used by the imputer and the user are incompatible' (Meng, 1994, Statistics Science). In this talk, we show precisely how multiple imputation can be treated as an integration of the knowledge of two parties, namely, the imputer and the user. This new theoretical insight helps to deepen our understanding of previous findings as well as to develop new ones. In particular, it helps to identify circumstances under which the MI confidence intervals are valid in the sense of having at least the declared nominal coverage rate. We also propose extensions that can be used when the original procedure is suspected to undercover.