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

P
hij ( )
⎡P
P ⎤⎡ 1 1 ⎤
hi () h( j)
= ⎢ ⎥⎢ + ⎥
⎣ K ⎦⎣⎢
1−Phi
()
1−Ph( j)
⎥⎦
(2.1)
by setting K at
Phi
()
K = 2 + ∑ ,
(2.2)
1−
P
hi ()
where i = i th person in the household (whose selection probability depends on his or her
age category: 0, 1, 2, 3, 4, or 5) and
j = j th person in the household (whose selection probability depends on his or her
age category: 0, 1, 2, 3, 4, or 5),
where age category 0 corresponds to dummy persons, 1 to persons aged 12 to 17, 2 to persons
aged 18 to 25, 3 to persons aged 26 to 34, 4 to persons aged 35 to 49, and 5 to persons aged 50 or
older.
The sum of the pairwise selection probabilities taken over all unique pairs will be guaranteed to
be exactly 1.
∑∑ Phij
( )
= 1
(2.3)
i j>
i
It also guarantees that the sum of the pairwise selection probabilities for an individual is equal to
the individual's selection probability
for all values of i.
∑ Phij
( )
= Phi
( )
(2.4)
j≠i
As noted earlier, the above scheme will always select a pair, but it allows all combinations of
eligible persons and dummy persons so that zero, one, or two eligible persons are selected.
Case II: DUs with S < 2
If the sum S of person-level selection probabilities was less than 2, the earlier method
used in previous surveys consisted of dividing 2 - S equally among the 3 dummy persons added
to the household, and then used Brewer's method, as in Case I. However, if the household had
two or more persons, we would have preferred more chances for a pair to be selected. To achieve
this goal, the individual selection probabilities, P h(i) , were scaled upward by the factor F s such
that their sum came close to but did not exceed 2 and such that each person selection probability
did not exceed the maximum allowed probability of 0.99. Thus, denoting the revised person
selection probabilities by P′ h(i) , the factor F s is given by
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