Analyzing Imputed Survey Data Sets with Model Assisted Estimators

Multiple imputation has been previously applied for mass imputation, that is, the imputation from a subsample with complete information to a larger sample. In such applications, the missing data rates are often substantial, such as 80 percent or more, but valid inferences should, in principle, be within reach when probability sampling is used. Yet, limitations of multiple imputation can become severely amplified in this setting (Fay 1994). This article combines an alternative strategy to multiple imputation, called fractionally weighted imputation, with a model assisted approach to estimation. This combination affords several advantages: 1) more efficient model based estimates when the model is true, 2) consistent estimates of the variances for the model based estimates, 3) resistance of the model assisted estimates to model failure, 4) consistence estimates of the variance of the model assisted estimates, 5) estimates of bias for the model based estimates, and 6) consistent estimates of the variance of the bias estimates. With this array of information, analysts will be in an improved position to analyze imputed data sets effectively.