Non-Bayesian multiple imputation

Multiple imputation is a method specifically designed for variance estimation in the presence of missing data. Rubin’s combination formula requires that the imputation method is “proper” which essentially means that the imputations are random draws from a posterior distribution in a Bayesian framework. In national statistical institutes (NSI’s) like Statistics Norway, the methods used for imputing for nonresponse are typically non-Bayesian, e.g., some kind of stratified hot-deck. Hence, Rubin’s method of multiple imputation is not valid and cannot be applied in NSI’s. This paper deals with the problem of deriving an alternative combination formula that can be applied for imputation methods typically used in NSI’s and suggests an approach for studying this problem. Alternative combination formulas are derived for certain response mechanisms and hot-deck type imputation methods.