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

Then, for Newton-Raphson iteration v , the value of the p-vector λ is adjusted as
where λ
( 0 )
= 1.
( )
( v) ( v−1) −1
( 1)
( )
ˆ v−
γ =γ + X′
Γ X T − T ,
φ, v−1
x x
The convergence criterion is based on the Euclidean distance
T
−
ˆ
x T x
( v)
. At each
iteration, it is checked to determine whether it is decreasing or not. If not, a half step is used in
the iteration increment.
A.4 Scaled Constrained Exponential Model
In previous surveys, constrained exponential models were used for poststratification, and
scaled constrained exponential models were used for nonresponse adjustments. The term
"constrained exponential model" refers to the logit model of Deville and Särndal (1992), in
which lower and upper bounds do not vary with k (i.e., lk
= l , uk
= u,
and ck
= c = 1, such that
l < 1 < u. Thus, it is a special case of GEM. For the nonresponse adjustment, Folsom and Witt
(1994) modified the constrained exponential models' estimating equations by a scaling factor
(D -1 −1
−1
, the inverse of the overall response propensity), such that 1 < ρ a k < ρ u.
This implies
that choosing l in constrained exponential models as D ensures that the scaled adjustment factor
for nonresponse is at least one.
A-5