Dear Thomas: Thanks for your reply. Spencer Graves
Thomas Lumley wrote:
On Thu, 20 May 2004, Spencer Graves wrote:
Cassel, Sarndal and Wretman (1977) Foundations of Inference in
Survey Sampling (Krieger) insisted that for infinite population
inference (what Deming called an 'analytic study'), the sampling
probabilities should be ignored UNLESS they related somehow to something
of interest in the model. In other words, is the sampling informative
or noninformative? If noninformative, the sampling probabilities do not
appear in the likelihood and therefore should not affect inference. As
I recall, Cassel, Sarndal and Wretman said that if stratified random
sampling is used, and if the stratification system is included in the
model, then the sampling is noninformative, and the sampling
probabilities should not affect inference.
This is the point of including the sampling weights as a predictor. These weights carry all the informativeness of the sampling scheme, and so correctly modelling them is sufficient. If the sampling is already non-informative then including them as a predictor is harmless.
However, my point was that you may not want to condition on all the variables that go into the sampling scheme, in which case the simplest solution may be design-based inference.
-thomas
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