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

conducted for the multiplicities associated with the four sibling-sibling pair domains. The parentchild
domains were hierarchical, however, where the imputations could not have been conducted
independently if consistency was to be maintained. Hence, only two models were fitted to the
child-parent pairs, using just the domains with children 12 to 20 years old. One set of models
was for the number of the parent's children, and the other set was for the number of parents of
the child. Using the predicted means from these models, a single donor pair for each focus was
selected from which the multiplicity counts were determined for 12-to-14, 12-to-17, 15-to-17,
and 12-to-20 child-parent pairs. No imputation was required for the spouse-spouse multiplicity
counts, since a selected respondent in a spouse-spouse pair naturally had only one spouse.
The first step for these six models was to define respondents, nonrespondents, and the
item response mechanism for each model, separately. For a pair to be considered a complete data
responding pair with regard to multiplicities, the multiplicity had to be nonmissing for all of the
variables being imputed. For the parent-child pairs, this meant that the multiplicity had to be
nonmissing for the domains with children 12 to 20 years old. A nonmissing multiplicity for this
domain would automatically guarantee nonmissing multiplicities for the subset parent-child
domains. Response propensity adjustments were then computed for each of the six models in
order to make the respondent pair weights representative of the entire sample of pairs. These
adjustments were calculated using an item response propensity model. This model is a special
case of GEM, which is described in greater detail in Appendix A.
6.3.3.2 Model Building and Determination of Predicted Means
The PMN method is a two-step process. The first step is the modeling step, followed by a
hot-deck step where imputed values replace missing multiplicities. The different attributes of the
six multiplicity models, corresponding to the six pair domains, are described in this subsection.
Response categories. The response categories for the six multiplicity final response
models were simply the multiplicity counts for each domain among the complete data cases.
Covariates in models. The pool of covariates for the response propensity models was the
same pool that was used for the pair relationship response propensity models. By the same token,
this pool also was used for the final response multiplicity models when the household
composition age count variables were missing. 22 When these variables were not missing, the
same pool again was used as with the pair relationship models. Naturally, the final set of
covariates differed from the initial pool. The final set of covariates that were used in the models
is provided in Appendix Q.
Building of models. For the child-focus parent-child domains, the count being modeled
was the number of parents. In most cases, since the pair relationship had already been
established, only two responses were possible within the parent-child pair relationship: one
parent or two parents. There were rare instances where three parents could live in the household,
with some combination of biological, step, foster, or adoptive parents. (Usually three parents
were present when a stepparent lived in the house with the two biological parents.) For the
purposes of modeling, the rare instances with more than two parents in the household were
22 The widowed, divorced, and never married categories for marital status were combined into a single level
for the multiplicity models.
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