Methods for estimating the precision of survey estimates when imputation has been used - ARCHIVED

In almost all large surveys, some form of imputation is used. This paper develops a method for variance estimation when single (as opposed to multiple) imputation is used to create a completed data set. Imputation will never reproduce the true values (except in truly exceptional cases). The total error of the survey estimate is viewed in this paper as the sum of sampling error and imputation error. Consequently, an overall variance is derived as the sum of a sampling variance and an imputation variance. The principal theme is the estimation of these two components, using the data after imputation, that is, the actually observed values and the imputed values. The approach is model assisted in the sense that the model implied by the imputation method and the randomization distribution used for sample selection will together determine the appearance of the variance estimators. The theoretical findings are confirmed by a Monte Carlo simulation.