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

6.2.4.3 Constraints on Hot-Deck Neighborhoods and Assignment of Imputed
Values
If possible, donor pairs in the hot-deck step of PMN were chosen with predicted means
within delta 17 of the recipient pair's predicted mean(s), where the value(s) of delta varied
depending upon the value of the predicted means. In this case, delta was defined as 5 percent of
the predicted probability if the probability was less than 0.5, and 5 percent of 1 minus the
predicted probability if the probability was greater than 0.5. This allowed a looser delta for
predicted probabilities close to 0.5 and a tighter delta for predicted probabilities close to 0 or 1.
The range of values for delta across various predicted probabilities is shown in Table 6.8. If no
donor pairs were available with predicted means within delta of the recipient pair's predicted
mean, the neighborhood was abandoned, and the donor pair with the closest predicted mean was
chosen.
Table 6.8 Values of Delta for Various Predicted Probabilities
Predicted Probability (p)
Delta
p < 0.5
0.05*p
p > 0.5
0.05*(1-p)
In general, the members of the neighborhoods were restricted to satisfy two types of
constraints: "logical constraints" and "likeness constraints." Constraints that made the imputed
values consistent with preexisting values of other variables were called logical constraints and
were required for the candidate donor pair to be a member of the neighborhood. Likeness
constraints were implemented to make donor pairs and recipient pairs as much alike as possible.
Although logical constraints could not have been loosened, likeness constraints could have been
loosened if they had forced the donor pool to be too sparse. Details of these imputation
procedures are provided in Appendix N.
In addition to the likeness constraint defined by delta, other likeness constraints also were
included in the neighborhoods. These constraints follow:
Older pair member age constraint, 26+-year-old pair members. The 26+ age group,
associated with age group pairs 7 through 10, was split up into three groups: 26 to 34, 35 to 49,
and 50+. This was most useful to delineate child-parent pairs.
Marital status constraints. Each respondent's marital status, as entered in the core section
of the questionnaire, was closely related to the relationship between the pair members. 18 This
marital status variable had four levels among respondents aged 15 or older: married, widowed,
separated or divorced, and never married. Marital status likeness constraints combined the
information from this variable for both pair members, where the levels were collapsed in
17 "Delta" refers to the value that defined the neighborhood of donor pairs that were "close" to the recipient
pair. The difference between the predicted mean of the recipient pair and the predicted means of the donor pairs
must have been less than delta. See Appendix N for more details.
18 Pairs that included a pair member with an imputed marital status were not eligible to be donor pairs. If a
recipient pair had a pair member with an imputed marital status, then donor pairs had any marital status, unless one
of the pair members in the recipient pair had a nonimputed marital status indicating married, widowed, or divorced.
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