R help - Oct 2015 - glmm: random term, overdispersion and comparisons

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

Dear Ellen,

You're using the Poisson distribution. There is no error (noise) term in a
glmm with Poisson distribution.

1) The random part seems to be quite complicated given the sample size.
(1|site) is probably sufficient. Note that your design is not nested but
crossed.
2) Overdispersion is likely in bird abundance. You could use a negative
binomial distribution instead of a Poisson distribution. Then the
overdispersion is modeled. Use the glmer.nb() function.
3) Have a look at the glht() function in the multcomp package. That allows
you to test specific contrasts of your model parameters.

Note that the r-sig-mixedmodels list is more appropriate for follow-up
questions.

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2015-10-01 16:59 GMT+02:00 Ellen Andresen <eandresens at gmail.com>:
> 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
>
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