Hi all,
I'm hoping someone can help me wrap my head around an appropriate model
structure for this situation, with repeated measures within a site during
each year, which are then also repeated over many years. We have 14 sites,
each surveyed ~3 times per year, repeated each year for ~13 years (with
random missing data). The response variable is the number of individuals of
one species observed per survey per site per year.

The data look like this:
ID  site year  jdate  count
1    A   1999 150    5
2    A   1999 172    0
3    A   1999 185    3
4    A   2000 143    2
5    A   2000 162    1

[To really get into the nitty gritty, each survey actually consists of 3-5
point counts, but for now at least these have been pooled. Also, we have
done distance sampling analysis to be able to correct for detection
probabilities with an offset.]

We're primarily interested in the long-term trend in abundance across
sites, though eventually we would also like to compare trends between
sites, which received different habitat restoration treatments.

For starters, my questions are:
1) Am I correct in believing I should use mixed modeling (and a random
effect of site) because these data are repeated measures of each site over
time?

2) If so, do I also need to include an individual survey ID effect nested
within site, because there are repeated measures per site per year? (How
would I do this? Will that even work with only 3 surveys per site per
year?) Or does a random effect of site encompass both the repeated measures
across and within years?

3) Does it make sense to consider including a crossed effect of year (as a
factor) in addition to (or instead of) a random slope of year within site?
What about year nested within site?

Any insights would be greatly appreciated.
Thanks,
Kristen


----------------------------------------------------------
Kristen Dybala, Post-doctoral Researcher
Museum of Wildlife and Fish Biology
University of California, Davis
kedybala@ucdavis.edu
(415) 218-9295 - cell

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