Multiple Imputation in a Complex Sample Survey

Multiple imputation for missing survey data is relatively new concept. As defined by one of its leading proponents, "multiple imputation is the technique that replaces each missing or deficient value with two or more acceptable values representing a distribution of possibilities" (Rubin 1987, p.2). Multiply-imputed data reflects the uncertainty contained in the imputation process in a way not possible with singly-imputed data. Incorporating multiple imputation into a survey, both as an imputation method and in subsequent estimation, does present some practical problems. So far, most discussions of multiple imputation have been limited to surveys with some relatively tractable sample design (or have disregarded the sample design (Oh and Scheuren 1980)). However, complex sample surveys are another important set of surveys. In addition to the need for large-scale imputation for many missing items, complex sample surveys are characterized by features such as multistage stratified cluster sampling (possibly listsupplemented), reweighting for unit nonresponse, and possible post-stratification adjustments. Incorporating multiple imputation into such a survey would seem to be a formidable task. This paper describes proposed procedures, and presents results, for incorporating multiple imputation into one complex sample survey, the Energy Information Administration's Commercial Buildings Energy Consumption Survey (CBECS) (Energy Information Administration 1988, 1989). The CBECS, conducted triennially, has a