[R-sig-ME] Using Observations as Random Effect in GLMM?

[John Maindonald]

I've been looking recently at animal count data that I've modeled
as Poisson with an observation level random effect, and have
worried a bit about such issues.

The observation level random effects model and the over-dispersion 
model add variances on different scales -- for the observation level
random effects random effects model the added variance is 
proportional to the square of the Poisson mean, whereas for the
over-dispersion model it is proportional to the mean. (These 
comments assume small additional error; but they do delineate
the broad ballparks in which the two models operate.   The glmer() 
function is making its own very specific assumptions about the 
scale on which to add the additional normal error.

The models are thus pretty much equivalent only if the range of 
expected values is small.  It would be useful to have more flexibility,
at the observation level at least, in the modelling of the extra-Poisson
error.  Among the various packages that handle GLMMs, do any of
them offer such flexibility, maybe allowing e.g. a quasi-Poisson error? 

(Sure, there are issues about how legit quasi-Poisson errors are.  
I expect however someone will sometime work out how to give them 
full theoretical respectability, and they will duly be admitted to the part 
of the statistical pantheon allocated to those models that are thus 
theoretically respectable.)


John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm

On 22/01/2012, at 7:44 AM, Daniel Hocking wrote:

> Hi everyone,
> 
> I am having trouble with overdispersion when trying to model count data using a GLMM. Beyond going to a negative binomial or Poisson-lognormal distribution, I have seen the suggestion (from Ben Bolker I believe) to include observation as a random effect. For example using the lme4 package my code would look something like this:
> 
> glmer(count ~ SoilT + SoilT2 + RH + rain24 + drought +
> rain24*SoilT + drought*rain24 + (1 | plot) + (1 | obs), data = Data,
> family = poisson)
> 
> When I try this I get a fitted vs. residual plot with large residuals at low fitted values funneling down to small residuals as the fitted values get larger. This indicates heterogeneity. I was wondering if that is expected for some reason with observation-level random effects or if this model just doesn't meet the assumptions of GLMM for my data?
> 
> Thanks,
> Dan
> ------------------------------------------------------------------------------------
> Daniel J. Hocking
> 122 James  Hall
> Department of Natural Resources & the Environment
> University of New Hampshire
> Durham, NH 03824
> 
> dhocking at unh.edu
> http://sites.google.com/site/danieljhocking/
> http://quantitativeecology.blogspot.com/
> http://richnessoflife.blogspot.com/
> 
> "Without data, you are just another person with an opinion."
> 
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