Finding a Flexible Hot-Deck Imputation Method for Multinomial Data

Abstract

Abstract Detailed breakdowns on totals are often collected in surveys, such as a breakdown of total product sales by product type. These multinomial data are often sparsely reported with wide variability in proportions across units. In addition, there are often true zeros that differ across units even within industry; for example, one establishment sells jeans but not shoes, and another sells shoes but not socks. It is quite common to have large fractions of missing data for these detailed items, even when totals are relatively completely observed. Hot-deck imputation, which fills in missing data with observed data values, is an attractive approach. The entire set of proportions can be simultaneously imputed to preserve multinomial distributions, and zero values can be imputed. However, it is not clear what variant of the hot deck is best. We describe a large set of “flavors” of the hot deck and compare them through simulation and by application to data from the 2012 Economic Census. We consider different ways to create the donor pool: choosing one nearest neighbor (NN), choosing from five NNs, or using all units as the donor pool. We also consider different ways to impute from the donor: directly impute the donor’s vector of proportions or randomly draw from a multinomial distribution using this vector of proportions. We consider scenarios where a strong predictor of these multinomial distributions exists as well as when covariate information is weak.