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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. As examples, individual researchers use multiple imputation to handle missing data in small samples; statistical agencies disseminate multiply-imputed datasets 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 (1987) original rules for combining the point and variance estimates from the multiply-imputed datasets are not appropriate, because what is known---and therefore in the conditional expectations and variances used to derive inferential methods---differs from the missing data context. These applications require new combining rules and methods of inference. In this talk, I describe some of the new adaptations of the multiple imputation framework, with particular attention to multiple imputation for protecting data confidentiality. I present the combining rules for each setting and explain why they differ.