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Extending the DAG Jackknife to Measure the Variance of an Estimated Total When Imputing for Item Nonresponse with a Survey-Weighted Prediction Model

Keywords: Variance Estimation, Item Nonresponse, Imputation, DAG Jackknife, Adjusted Replication Methods, Mean Squared Error Estimation

The National Agricultural Statistics Service (NASS) uses the delete-a-group (DAG) jackknife to estimate variances and mean squared errors in many of its surveys. The DAG jackknife provides nearly unbiased estimates under a host of complex designs and processes. In this paper, we investigate extending the DAG jackknife to account for the additional variance in an estimated total when imputing for nonresponse with a survey-weighted prediction model, using either the predicted value or the predicted value plus a random error term.

We demonstrate the effectiveness of this variance estimation strategy with simulations using data from the 2007 Census of Agriculture assuming a variety of ignorable item-nonresponse mechanisms. We will focus on imputations that are doubly protected from nonresponse Like the DAG jackknife, an alternative multiple imputation approach can also be doubly protected from nonresponse bias. However, unlike the DAG jackknife, the multiple imputation variance estimator implicitly assumes that both the prediction model and quasi-random response model are correct, and it may not work for a domain total even though the prediction model holds in the domain.