The SURVEYIMPUTE Procedure

The SURVEYIMPUTE procedure imputes missing values of an item in a data set by replacing them with observed values from the same item. The principles by which the imputation is performed are particularly useful for survey data. PROC SURVEYIMPUTE also computes replicate weights (such as jackknife weights) that account for the imputation and that can be used for replication-based variance estimation for complex surveys. The procedure implements a fractional hot-deck imputation technique (Kim and Fuller 2004; Fuller 2009; Kim and Shao 2014) in addition to some traditional hot-deck imputation techniques (Andridge and Little 2010).

Nonresponse is a common problem in almost all surveys of human populations. Estimators that are based on survey data that include nonresponse can suffer from nonresponse bias if the nonrespondents are different from the respondents. Estimators that use complete cases (only the observed units) might also be less precise. Imputation techniques are important tools for reducing nonresponse bias and producing efficient estimators.

The main objectives of any imputation technique are to eliminate the nonresponse bias and to provide an imputed data set that results in consistent analyses conducted with the imputed data. In addition, a variance estimator must be available that accounts for both the sampling variance and the imputation variance. Imputation techniques use implicit or explicit models. Some model-based imputation techniques include multiple imputation, mean imputation, and regression imputation. For more information about multiple imputation in SAS/STAT, see Chapter 75: The MI Procedure, and Chapter 76: The MIANALYZE Procedure.

Imputation techniques that do not use explicit models include hot-deck imputation, cold-deck imputation, and fractional imputation. PROC SURVEYIMPUTE implements imputation techniques that do not use explicit models. It also produces replicate weights that can be used with any survey analysis procedure in SAS/STAT to estimate both the sampling variability and the imputation variability.

Hot-deck imputation is the most commonly used imputation technique for survey data. A donor is selected for a recipient unit, and the observed values of the donor are imputed for the missing items of the recipient. Although the imputation method is straightforward, the variance estimator that accounts for imputation variance might not be simple and is often ignored in practice. PROC SURVEYIMPUTE does not create imputation-adjusted replicate weights for hot-deck imputation.

Fractional hot-deck imputation (Kalton and Kish 1984; Fay 1996; Kim and Fuller 2004; Fuller and Kim 2005), also known as fractional imputation (FI), is a variation of hot-deck imputation in which one missing item for a recipient is imputed from multiple donors. Each donor donates a fraction of the original weight of the recipient such that the sum of the fractional weights from all the donors is equal to the original weight of the recipient. For fully efficient fractional imputation (FEFI), all observed values in an imputation cell are used as donors for a recipient unit in that cell (Kim and Fuller 2004).

The SURVEYIMPUTE procedure implements single and multiple hot-deck imputation and FEFI. Available donor selection techniques include simple random selection with or without replacement, probability proportional to weights selection (Rao and Shao 1992), and approximate Bayesian bootstrap selection (Rubin and Schenker 1986).

The remaining sections of this chapter are organized as follows: