[R] mixed models for analyzing survey data with unequal selec tion probability

[Thomas Lumley]

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