[R-sig-ME] Repeated measures within and across years

[Henrik Singmann]

Hi Kristen,

Although I am no expert in neither count models nor ecology, I will step in with some thoughts as you haven't received any response so far.

One of the advantages of mixed models over the classical approaches is that it allows for replications within a cell of the design. That is, one can usually avoid aggregation (at least if there aren't too many zero cells, I guess).

That being said, in your case the simplest model would be:

count ~ year + (1|site)

A fixed effect for year plus a random effect for site that accounts for differences in overall levels of populations between sites (i.e., a site random intercept). This already accounts for the repeated measure nature of the data.

However, as often said on this list, it is probably a good idea to include random slopes for year as well, to allow the effect of year to also vary site specific:

count ~ year + (year|site)

Next, it might be a good idea to consider within year variations by also modeling the effect of when within a year the data is measured:

count ~ year + jdate + (year + jdate|site)

(I am not so sure if with only three observations per site and year the jdate random slope is estimated precise enough, but one needs to inspect the model afterwards.)

Finally, one could also have the idea that year and jdate interact and come to the largest model (for which the same caveat as above applies):

count ~ year*jdate + (year*jdate|site)

Either of those formulas should be put in a call to glmer(..., family = poisson). However, you will also have to consider the case of over- or underdispersion, but as said above. This is not my field, so I have no idea about it.

Any other model (e.g., including ID) seems inappropriate given my understanding of your data (or I don'T understand what ID is supposed to be).

Hope that helps,
Henrik


Am 24.09.2013 00:24, schrieb Kristen Dybala:
> 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 at ucdavis.edu
> (415) 218-9295 - cell
>
> 	[[alternative HTML version deleted]]
>

-- 
Dipl. Psych. Henrik Singmann
PhD Student
Albert-Ludwigs-Universität Freiburg, Germany
http://www.psychologie.uni-freiburg.de/Members/singmann