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

[Spencer Graves]

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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