[R-sig-ME] GLMMs with unequal group sizes
Grant T. Stokke
gts127 at psu.edu
Thu Jun 11 05:41:52 CEST 2009
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
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