Donor Limited Hot Deck Imputation: A Constrained Optimization Problem

Hot deck methods impute missing data by matching records that are complete to those that are missing values. Observations absent within the recipient are then replaced by replicating the values from the matched donor. Some hot deck procedures constrain the frequency with which any donor may be matched to increase the precision of post-imputation parameter-estimates. This constraint, called a donor limit, also mitigates risks of exclusively using one donor for all imputations or using one donor with an extreme value or values "too often." Despite these desirable properties, imputation results of a donor limited hot deck are dependent on the recipients' order of imputation, an undesirable property. For nearest neighbor type hot deck procedures, the implementation of a constraint on donor usage causes the stepwise matching between each recipient and its closest donor to no longer minimize the sum of all donor-recipient distances. Thus, imputation results may further be improved by procedures that minimize the total donor-recipient distance-sum. The discrete optimization problem is formulated and a simulation detailing possible improvements when solving this integer program is presented.