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

[Spencer Graves]

      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. 

      From this paradigm, using weights inversely proportional to 
sampling probabilities is (primarily?) a tool for finite population 
inference -- what Deming called an 'enumerative study'.  For an 
enumerative study, the purpose is to make inference about a fixed, 
finite population, e.g., how to feed the people in Japan who would 
otherwise starve within the next week or month, which was the situation 
when Deming directed a survey there shortly after World War II.  For an 
analytic study, the purpose is more long term, e.g., how to design a 
national alimentary system to feed the people who will be there 10 or 30 
years from now.  Since most of my work has dealt processed that will 
create the future, rather than dealing with fixed, finite populations, I 
have ignored sampling probabilities in most of my work (though I have 
not worked much recently with sample surveys). 

      Is this still consistent with current thinking?  Is it feasible to 
summarize in a few words what Pferrermann, Korn et al. say about this? 

      Thanks,
      spencer graves

Thomas Lumley wrote:

>On Thu, 20 May 2004, Baskin, Robert wrote:
>
>  
>
>>Han-Lin
>>
>>I don't think I have seen a reply so I will suggest that maybe you could try
>>a different approach than what you are thinking about doing.  I believe the
>>current best practice is to use the weights as a covariate in a regression
>>model - and bytheway - the weights are the inverse of the probabilities of
>>selection - not the probabilities.
>>
>>Fundamentally, there is a difficulty in making sense out of 'random effects'
>>in a finite population setting.
>>    
>>
>
>I would have thought that it matters why you are fitting a mixed model.
>Often people use mixed models when they are just interested in inference
>about the mean and need to model the covariances to get valid standard
>errors. In that situation you could use an ordinary survey regression to
>get a design-based result.
>
>If you are actually interested in variance components then you need some
>other approach, and putting the weights into the model as a covariate will
>presumably give a valid model-based result (since the weights carry all
>the biased sampling information --- like a propensity score).  Presumably
>this is also more efficient.
>
>However, it could well be that you don't want those variables in the
>model. If the sampling depends on a variable Z correlated with Y and X and
>you want to model the distribution of Y given X, not the distribution of Y
>given X and Z, you are still in trouble.
>
>
>	-thomas
>
>
>
>  
>
>>(plagiarized from some unknown source)
>>See: < 9. Pfeffermann, D. , Skinner, C. J. , Holmes, D. J. , Goldstein, H. ,
>>and Rasbash, J.  (1998), ``Weighting for unequal selection probabilities in
>>multilevel models (Disc: p41-56)'', Journal of the Royal Statistical
>>Society, Series B, Methodological, 60 , 23-40 >
>>
>>which refers back to:
>><29. Pfeffermann, D. , and LaVange, L.  (1989), ``Regression models for
>>stratified multi-stage cluster samples'', Analysis of Complex Surveys,
>>237-260 >
>>
>>If you don't like statistical papers, then see section 4.5 of <8. Korn,
>>Edward Lee , and Graubard, Barry I.  (1999), ``Analysis of health surveys'',
>>John Wiley & Sons (New York; Chichester) > They explain the idea of using
>>weights in a model fairly simply.
>>
>>Bob
>>
>>
>>-----Original Message-----
>>From: Han-Lin Lai [mailto:Han-Lin.Lai at noaa.gov]
>>Sent: Wednesday, May 19, 2004 12:47 PM
>>To: r-help at stat.math.ethz.ch
>>Subject: [R] mixed models for analyzing survey data with unequal selection
>>probability
>>
>>Hi,
>>
>>I need the help on this topic because this is out of my statistical
>>trianing as biologist.  Here is my brief description of the problem.
>>
>>I have a survey that VESSELs are selected at random with the probability
>>of p(j).  Then the tows within the jth VESSEL are sampled at random with
>>probability of p(i|j).  I write my model as
>>
>>y = XB + Zb + e
>>where XB is fixed part, Zb is for random effect (VESSEL) and e is
>>within-vessel error.
>>
>>I feel that I should weight the Zb part by p(j) and the e-part by
>>p(i,j)=p(j)*p(i|j). Is this a correct weighting?
>>
>>How can I implement the weightings in nlme (or lme)?  I think that
>>p(i,j) can be specified by nlme(..., weights=p(i,j),...)?  Where is p(j)
>>to be used in nlme?
>>
>>I appreciate anyone can provide examples and literature for this
>>problem.
>>
>>Cheers!
>>Han
>>
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>>    
>>
>
>Thomas Lumley			Assoc. Professor, Biostatistics
>tlumley at u.washington.edu	University of Washington, Seattle
>
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