GLMMs with unequal group sizes

Hello,

as a simple quick check, have you tried fitting your model without  
area 3/9 or without both of them and compared the estimates? You  
could then also look at how well your fixed effects estimates  
predict the values in the left-out areas.

HTH

Cheers,

Luca


----- Original Message -----
From: Grant T. Stokke <gts127 at psu.edu>
To: r-sig-mixed-models at r-project.org
Sent: Wed, 10 Jun 2009 23:41:52 -0400 (EDT)
Subject: [R-sig-ME] GLMMs with unequal group sizes

Hello All,

I would like to use GLMMs with a binary response variable (logit  
link) to
model the effects of three environmental covariates on whether  
resource
units were used or unused by a wildlife species.  I have 15  
different study
areas, and very different numbers of used and unused units in each.   
I'm
interested in using fixed effects parameters estimates to predict the
relative probabilities that resource units will be used across the  
entire
population of study areas.  Numbers of used and unused units in each  
area
look something like this:

Area    Unused    Used
01        281        2
02        4415      1
03        343        30
04        256        1
05        2052      4
06        4050      1
07        238        2
08        743        3
09        2476      18
10        2524      1
11        805        1
12        754        4
13        272        1
14        52          1
15        124        1

I've been using study area as a grouping factor for a random  
intercept and
random slope effects:

fullmodel<-glmer(Used~1+x1+x2+x3+(1+x1+x2+x3|Area), family=binomial,
data=mydata)

Using 'glmer', I've been able to fit models to my data without  
convergence
issues, model fit is pretty good, and the results seem to make  
sense.  My
questions are:  Given that the number of used units in each area are  
very
unbalanced, to what degree can I generalize across the entire  
population of
study areas?  Will my estimates for the fixed effects parameters be so
reliant on areas 3 and 9 that I'm really just limited to inferences  
on these
two areas?  Is there a way to quantify the relative weight of each  
study
area in the estimation of the fixed effects parameters (i.e. the  
degree to
which I can generalize across the entire population of study areas)?

I've read of borrow strength, which will certainly play a big role  
with this
dataset, but I haven't found any examples of datasets that are as  
unbalanced
as mine.

I realize that my questions relate to mixed models in general and  
less to
their implementation in R, so I hope I'm not out-of-line in posting  
these
questions here.  I'd guess there are probably answers to these  
questions in
the literature, so I'd truly appreciate any advice on where I should  
look
for more info.

Thanks in advance,

-Grant