[R] glmm: random term, overdispersion and comparisons

[Ellen Andresen]

Hello,
I studied the effect of a hurricane in Cozumel on understory birds. I
have bird abundances (i.e. counts) registered always on the SAME six
sites (i.e. blocks). I have data for: before the hurricane, first year
after the hurricane, second year after the hurricane. I each of these
time periods, I also have data for summer season and for winter
season. I do not have a balanced design, in one of the time periods I
only have data for 5 of the six sites, and for another period I only
have data for 3 of the six sites.
I am defining Poisson error distrubution for the response variable.
I am using 'glmer' with two fixed factors, and I am interested in
their interaction:
- factor hurricane (three levels: before, after 1 y, after 2 y)
- factor season (two levels: summer, winter)
I am also specifying a random factor (sites), and I am specifying the
nested structure of the design. However, I don't know if I am
specifying the random part of the model in the correct way; this is
what I am doing:
       abundance ~ hurricane*season + (1|site/hurricane/season)

I have three questions:
1. Is the random part specified correctly?
2. How do I check for overdispersion, and how can I correct for it?
(for each site I only have one observation; sites are my replicates)
3. How do I make the following comparisons: I am interested in testing
for each season separately, after 1 y vs. before the hurricane, and
after 2 years vs. before the hurricane.

Thank you so much!
Ellen Andresen
UNAM-Mexico