The multiple adaptations of multiple imputation

Multiple imputation was first conceived as a tool that statistical agencies could use to handle nonresponse in large-sample public use surveys. In the last two decades, the multiple-imputation framework has been adapted for other statistical contexts. For example, individual researchers use multiple imputation to handle missing data in small samples, statistical agencies disseminate multiply-imputed data sets for purposes of protecting data confidentiality, and survey methodologists and epidemiologists use multiple imputation to correct for measurement errors. In some of these settings, Rubin's original rules for combining the point and variance estimates from the multiply-imputed data sets are not appropriate, because what is known-and thus the conditional expectations and variances used to derive inferential methods-differs from that in the missing-data context. These applications require new combining rules and methods of inference. In fact, more than 10 combining rules exist in the published literature. This article describes some of the main adaptations of the multiple-imputation framework, including missing data in large and small samples, data confidentiality, and measurement error. It reviews the combining rules for each setting and explains why they differ. Finally, it highlights research topics in extending the multiple-imputation framework.