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

[Baskin, Robert]

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.

(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