fitting models with poisson distributed data

On 25/10/2008, at 9:37 AM, Page E. Van Meter wrote:

Hi,
Now that I have the code figured out, I hoping for some help on 
defining my model. I might be guilty of trying to fit an overly 
complex model to my data, although my model seems very simple in 
comparison to what has been discussed here. I'm hoping for feedback 
on my model design. Thanks in advance!

I have some pretty ugly longitudinal data measuring hormones and 
behaviors from individual hyenas over many years (355 samples from 39 
individuals). We collect hormone samples based on opportunity and 
have several samples from each individual (3-9 samples per hyena). My 
ultimate goal is to see if my hormone data explains any of the 
variation we see in the behavior data (aggression, I'll call it 
aggs). My dependent measurement is a behavior rate, count of aggs 
over time just prior to hormone sample collection. It is very zero 
heavy (lots of individuals did not aggress prior to hormone sample 
donation) and resistant to transformation to normality, but seems to 
be a pretty poisson distribution. My predictors are hormones and 
reproductive state (pregnant or lactating, which effect both 
aggression and hormones).

From the output the estimated scale (I don't see this in the version 
of lmer I'm using?)  is 7.7 so data is definitely not Poisson. 
Assuming Poisson will give incorrect p values.

Seeing the quasi Poisson doesn't seem to work properly I'm not certain 
what is a good choice. I haven't tried it but maybe quasi Poisson 
works in one of the GEE packages.

It may be Ok to limit the analysis to no aggression/aggression 
allowing fitting as binomial data.

Ken

m2<-lmer(aggs~reprostate+hrm1+hrm2+(1|id), family=poisson, aggs)

Generalized linear mixed model fit using Laplace
Formula: aggs ~ reprostate + hrm1 + hrm2 + (1 | id)
 Data: aggs
Family: poisson(log link)
 AIC   BIC logLik deviance
12369 12387  -6179    12359
Random effects:
Groups Name        Variance Std.Dev.
id     (Intercept) 4.9353   2.2216 number of obs: 307, groups: id, 39

Estimated scale (compare to  1 )  7.682887

Fixed effects:
          Estimate Std. Error z value Pr(>|z|)   (Intercept) 
-3.07625    0.39575  -7.773 7.65e-15 ***
reprostate 2.32056    0.07724  30.044  < 2e-16 ***
hrm1        0.12575    0.04020   3.128  0.00176 **
hrm2       -0.80434    0.04770 -16.862  < 2e-16 ***
---

Correlation of Fixed Effects:
       (Intr) statct ecent
statecat -0.381             ecent    -0.085  0.271      acent     
0.136 -0.339 -0.079

-- 
************************************
Page E. Van Meter
Michigan State University
Department of Zoology
vanmete7 at msu.edu
**http://msu.edu/~vanmete7/*