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

conditional likelihoods, which then allows for the use of univariate techniques for fitting
multivariate (but conditional) predicted means.
In the application of person pair imputations, none of the variables imputed were part of a
multivariate set, so it was not necessary to set up a hierarchy of variables for the series of
conditional models described above. Instead, each pair variable was imputed one at a time,
where the only multivariate application was the necessity to have a multivariate predicted mean
vector when the response was polytomous. What is provided below is an abbreviated description
of the method in the univariate case only. A description of the multivariate case is described in
the 2006 NSDUH imputation report (Ault et al., 2008).
N.3 Outline and Description of Method
The procedure for implementing PMN in the 2006 survey, where imputed variables were
not part of any multivariate set, entailed four steps, which are listed below.
N.3.1 Step 1: Setup for Model Building and Hot-Deck Assignment
For each model that was fitted, two groups were created: complete data respondents and
incomplete data respondents (item respondents and item nonrespondents, respectively).
Complete data respondents had complete data across the variables of interest, and incomplete
data respondents encompassed the remainder of respondents. Models were constructed using
complete data respondents only.
N.3.2 Step 2: Modeling
The model was built using the complete data respondents only with weights adjusted for
item nonresponse.
N.3.3 Step 3: Computation of Predicted Means and Delta Neighborhoods
Once the model was fitted, the predicted means for item respondents and item
nonrespondents were calculated using the model coefficients. This predicted mean (or predictive
mean vector in the polytomous response case) was the matching variable in a random NNHD.
For each item nonrespondent, a distance was calculated between the predicted mean of
the item nonrespondent and the predicted means of every item respondent. Those item
respondents whose predicted means were "close" (within a predetermined value delta) to the item
nonrespondent were considered as part of the "delta neighborhood" for the item nonrespondent
and were potential donors. If the number of item respondents who qualified as donors was
greater than some number, k, only those item respondents with the smallest k distances were
eligible donors.
The pool of donors was further restricted to satisfy constraints to make imputed values
consistent with the preexisting nonmissing values of the item nonrespondent. An example of this
N-5