Questionnaire Dwelling Unit-Level and Person Pair-Level Sampling ...

type of constraint, called a "logical constraint," was given by the pair relationship in the
imputation of multiplicities. Other constraints, called "likeness constraints," were placed on the
pool of donors to make the attributes of the neighborhood as close to that of the recipient as
possible. For example, for the imputation of pair relationships, donors and recipients among pairs
where both respondents were in the 21- to 25-year-old range were restricted to have had the same
or similar marital status whenever possible. A small value of delta also could have been
considered as a likeness constraint. Whenever insufficient donors were available to meet the
likeness constraints, including the preset small value of delta, the constraints were loosened in
priority order according to their perceived importance. As a last resort, if an insufficient number
of donors was available to meet the logical constraints given the loosest set of likeness
constraints allowable, a donor was found using a sequential hot deck, where matching was done
on the predicted mean. (Even though weights would not have been used to determine the donor
in the sequential hot deck, "unweighted" is not an accurate characterization of the imputation
process, because weighting would already have been incorporated in the calculation of the
predicted mean.)
If many variables were imputed in a single multivariate imputation, it was advantageous
to preserve, as much as possible, correlations between variables in the data. However, the more
variables that were included in a multivariate set, the less likely that a neighborhood could have
been used for the imputation within a given delta. Even though there were many advantages to
using multivariate imputation, one disadvantage, in several instances, was not being able to find
a neighborhood within the specified delta.
N.3.4 Step 4: Assignment of Imputed Values Using a Univariate Predictive Mean
Neighborhood
Using a simple random draw from the neighborhood developed in Step 3, a donor was
chosen for each item nonrespondent. If only one response variable was imputed, the assignment
step was a simple replacement of a missing value by the value of the donor.
N.4 Comparison of PMN with Other Available Imputation Methods
The PMN methodology addresses all of the shortcomings of the unweighted sequential
hot-deck method:
• Ability to use covariates to determine donors is far greater than in the hot deck.
As with other model-based techniques, using models allows more covariates to be
incorporated, including demographic characteristics, in a systematic fashion, where
weights can be incorporated without difficulty. However, like a hot deck, covariates
not explicitly modeled can be used to restrict the set of donors using logical
constraints. If there is particular interest in having donors and recipients with similar
values of certain covariates, they can be used to restrict the set of donors using
likeness constraints even if they are already in the model.
• Relative importance of covariates is determined by standard estimating equation
techniques. In other words, there are objective criteria based on methodology, such
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