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

3. Brief Description of the Generalized
Exponential Model
In survey practice, design-based weights are typically adjusted in three steps: (1) for
extreme values (ev) via winsorization, (2) for nonresponse (nr) adjustment via weighting class,
and (3) for poststratification (ps) via raking ratio adjustments. If weights are not treated for
extreme values, the resulting estimates, although unbiased, will tend to have low precision. The
bias introduced by winsorization is alleviated to some extent through ps. The nr adjustment is a
correction for bias introduced in estimates based only on responding units, and ps is an
adjustment for coverage (typically undercoverage) bias and variance reduction due to correlation
between the study and control (usually demographic) variables.
There are limitations in the existing methods of weight adjustment for ev, nr, and ps. It
would be desirable to adjust for bias introduced in the ev step (when extreme weights are treated
via winsorization) in that the sample distribution for various demographic characteristics is
preserved. For the nr step, there are general raking type methods, such as the scaled constrained
exponential model developed by Folsom and Witt (1994), where the lower and upper bounds can
be suitably chosen by use of a separate scaling factor. The factor is set as the inverse of the
overall response propensity. It would be desirable to have a model for the nr adjustment factor so
that the desired lower and upper bounds on the factor are part of the model. Note that the lower
bound on the nr adjustment factor should be one, as it is interpreted as the inverse of the
probability of response for a particular unit. For the ps step, on the other hand, the general
calibration methods of Deville and Särndal (1992), such as the logit method, allow for built-in
lower (L) and upper (U) bounds (for ps, typically L < 1 < U). However, it would be desirable to
have nonuniform bounds (L k , U k ) depending on the unit k such that the final adjusted weight, w k ,
could be controlled within certain limits. An important application of this feature would be
weight adjustments in the presence of ev such that the user will have some control on the final
adjustment of the initially identified extreme values.
A modification of the earlier method of the scaled constrained exponential model of
Folsom and Witt (1994), termed as the method of the generalized exponential model (GEM) and
proposed by Folsom and Singh (2000), provides a unified approach to the three weight
adjustments for ev, nr, and ps, and it has the desired features mentioned above. The functional
form of the GEM adjustment factor is provided in Appendix A. It generalizes the logit model of
Deville and Särndal (1992), typically used for ps, such that the bounds (L, U) may depend on k.
Thus, it provides a built-in control on ev during both ps and nr adjustments. In addition, the
bounds are internal to the model and can be set to chosen values (e.g., L k = 1 in the nr step). If
there is a low frequency of ev in the final ps, then a separate ev step may not be necessary.
In fitting GEM to a particular problem, the choice of a large number of predictor
variables along with tight bounds will have an impact on the resulting unequal weighting effect
(UWE) and the proportion of extreme values. In practice, this leads to somewhat subjective
considerations of trade-off between the target set of bounds for a given set of factor effects and
the target UWE and the target proportion of extreme values. It also may be beneficial to look at
the proportion of "outwinsors" (a term coined to signify the extent of residual weights after
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