[R-sig-ME] fitting models with poisson distributed data

[Ken Beath]

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/*
>
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