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

[Thomas Lumley]

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