Multiple Imputation for a Continuous Variable

Abstract

Multiple imputation (MI) is invented by Rubin in 1970’s. He recommends to create imputations through a Bayesian process. Most software’s are respectively following Bayesian principles. Since MI is not much used in official statistics, on the contrary to single imputation, any Bayesian framework is not there necessarily appropriate. Nevertheless, MI can be considered to be useful for several reasons. Björnstad suggests another approach, non-Bayesian imputation. It thus does not require any Bayesian rules for imputing the missing values several times. This paper first presents an approach to imputation that is not much applied. It strictly follows a two-stage strategy, so that the imputation model is first estimated and then completed by the imputation task. These tasks are called model-donor and real-donor that are clearer than those used traditionally. The approach is concretized with apattern of examples in which the variable being imputed is income. Bayesian and non-Bayesian methods are compared. The main result is that a Bayesian framework is not necessarily superior, at least if the applications are done by software’s such as SAS and SPSS. If a user himself can create imputations using an appropriate non-Bayesian framework, the performance is often better.