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

[Han-Lin Lai]

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