  Survey data collection often is plagued by unit and item nonresponse. To
reduce reliance on strong assumptions about the missingness mechanisms,
statisticians can use information about population marginal distributions
known, for example, from censuses or administrative databases. One approach
that does so is the Missing Data with Auxiliary Margins, or MD-AM, framework,
which uses multiple imputation for both unit and item nonresponse so that
survey-weighted estimates accord with the known marginal distributions.
However, this framework relies on specifying and estimating a joint
distribution for the survey data and nonresponse indicators, which can be
computationally and practically daunting in data with many variables of mixed
types. We propose two adaptations to the MD-AM framework to simplify the
imputation task. First, rather than specifying a joint model for unit
respondents' data, we use random hot deck imputation while still leveraging the
known marginal distributions. Second, instead of sampling from conditional
distributions implied by the joint model for the missing data due to item
nonresponse, we apply multiple imputation by chained equations for item
nonresponse before imputation for unit nonresponse. Using simulation studies
with nonignorable missingness mechanisms, we demonstrate that the proposed
approach can provide more accurate point and interval estimates than models
that do not leverage the auxiliary information. We illustrate the approach
using data on voter turnout from the U.S. Current Population Survey.
