**From:** Thomas Lumley (*tlumley@u.washington.edu*)

**Date:** Fri 21 May 2004 - 01:14:34 EST

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Message-id: <Pine.A41.4.58.0405200805530.98828@homer35.u.washington.edu>

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
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*> model - and bytheway - the weights are the inverse of the probabilities of
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*> selection - not the probabilities.
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*>
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*> Fundamentally, there is a difficulty in making sense out of 'random effects'
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*> 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. ,
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*> and Rasbash, J. (1998), ``Weighting for unequal selection probabilities in
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*> multilevel models (Disc: p41-56)'', Journal of the Royal Statistical
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*> Society, Series B, Methodological, 60 , 23-40 >
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*>
*

*> which refers back to:
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*> <29. Pfeffermann, D. , and LaVange, L. (1989), ``Regression models for
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*> stratified multi-stage cluster samples'', Analysis of Complex Surveys,
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*> 237-260 >
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*>
*

*> If you don't like statistical papers, then see section 4.5 of <8. Korn,
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*> Edward Lee , and Graubard, Barry I. (1999), ``Analysis of health surveys'',
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*> John Wiley & Sons (New York; Chichester) > They explain the idea of using
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*> weights in a model fairly simply.
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*>
*

*> Bob
*

*>
*

*>
*

*> -----Original Message-----
*

*> From: Han-Lin Lai [mailto:Han-Lin.Lai@noaa.gov]
*

*> Sent: Wednesday, May 19, 2004 12:47 PM
*

*> To: r-help@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.
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*>
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*> I have a survey that VESSELs are selected at random with the probability
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*> of p(j). Then the tows within the jth VESSEL are sampled at random with
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*> probability of p(i|j). I write my model as
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*>
*

*> y = XB + Zb + e
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*> where XB is fixed part, Zb is for random effect (VESSEL) and e is
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*> within-vessel error.
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*>
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*> I feel that I should weight the Zb part by p(j) and the e-part by
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*> p(i,j)=p(j)*p(i|j). Is this a correct weighting?
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*>
*

*> How can I implement the weightings in nlme (or lme)? I think that
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*> p(i,j) can be specified by nlme(..., weights=p(i,j),...)? Where is p(j)
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*> to be used in nlme?
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*>
*

*> I appreciate anyone can provide examples and literature for this
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*> problem.
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*>
*

*> Cheers!
*

*> Han
*

*>
*

*> ______________________________________________
*

*> R-help@stat.math.ethz.ch mailing list
*

*> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
*

*> PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
*

*>
*

Thomas Lumley Assoc. Professor, Biostatistics

tlumley@u.washington.edu University of Washington, Seattle

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**Next message:**Jonathan Wang: "[R] 'start' argument for fitdistr()"**Previous message:**Baskin, Robert: "RE: [R] mixed models for analyzing survey data with unequal selec tion probability"**In reply to:**Baskin, Robert: "RE: [R] mixed models for analyzing survey data with unequal selec tion probability"**Next in thread:**Spencer Graves: "Re: [R] mixed models for analyzing survey data with unequal selec tion probability"**Reply:**Spencer Graves: "Re: [R] mixed models for analyzing survey data with unequal selec tion probability"

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