[R-sig-ME] single argument anova for GLMMs not yet implemented

[Andrew J Tyre]

I also like the explanation of quasi-likelihood vs. glmm, but I can say 
from an ecological perspective I frequently encounter situations in which 
I have included all the random effects of blocks, plots, times etc, and 
still have massive amounts of overdispersion. A student in my Ecological 
Statistics class examined repeated counts of grasshoppers in plots that 
have or have not received nitrogen addition. A poisson family glmm gives a 
nice account of the effects of total veg biomass, date, and nitrogen 
addition, but the residual deviance  is  > 1700 for a sample size of about 
400. I would love to be able to fit a negative binomial model in that 
case; I typically resort to using WinBUGS and MCMC to do this, but that is 
beyond what I can get my students to do in a one semester course. 

I have encountered situations in which even using a negative binomial 
model (for counts) or beta-binomial type model ( for proportion of success 
data) are insufficient to explain the variability in ecological 
situations. In these cases I usually have reason to believe that there is 
a discrete mixture going on - ie the observations are coming from two or 
more distinct populations which have not been distinguished by anything 
the observer can record, or thought to record (immune status for parasite 
hosts, for example). I have tried quasi- family models in those cases, but 
always felt a little uncomfortable drawing much in the way of inference. I 
understand likelihood! 

Anyway, I appreciate the tool. It is very nice and continues to get 
better! Thanks,

Drew Tyre

School of Natural Resources
University of Nebraska-Lincoln
416 Hardin Hall, East Campus
3310 Holdrege Street
Lincoln, NE 68583-0974

phone: +1 402 472 4054 
fax: +1 402 472 2946
email: atyre2 at unl.edu
http://snr.unl.edu/tyre



"Douglas Bates" <bates at stat.wisc.edu> 
Sent by: r-sig-mixed-models-bounces at r-project.org
12/11/2008 03:00 PM

To
"Andrew Robinson" <A.Robinson at ms.unimelb.edu.au>
cc
R Mixed Models <r-sig-mixed-models at r-project.org>, Murray Jorgensen 
<maj at stats.waikato.ac.nz>
Subject
Re: [R-sig-ME] single argument anova for GLMMs not yet implemented






On Thu, Dec 11, 2008 at 2:52 PM, Andrew Robinson
<A.Robinson at ms.unimelb.edu.au> wrote:
> Echoing Murray's points here - nicely put, Murray - it seems to me
> that the quasi-likelihood and the GLMM are different approaches to the
> same problem.

I agree and I also appreciate Murray's elegant explanation.

> Can anyone provide a substantial example where random effects and
> quasilikelihood have both been necessary?

I'm kind of waiting for Ben Bolker to let us know how things look from
his perspective.  I seem to remember that Ben and others in ecological
fields were concerned about overdispersion, even after incorporating
random effects.


>
> Best wishes,
>
> Andrew
>
>
> On Fri, Dec 12, 2008 at 09:11:39AM +1300, Murray Jorgensen wrote:
>> The following is how I think about this at the moment:
>>
>> The quasi-likelihood approach is an attempt at a model-free approach to
>> the problem of overdispersion in non-Gaussian regression situations
>> where standard distributional assumptions fail to provide the observed
>> mean-variance relationship.
>>
>> The glmm approach, on the other hand, does not abandon models and
>> likelihood but seeks to account for the observed mean-variance
>> relationship by adding unobserved latent variables (random effects) to
>> the model.
>>
>> Seeking to combine the two approaches by using both quasilikelihood
>> *and* random effects would seem to be asking for trouble as being able
>> to use two tools on one problem would give a lot of flexibility to the
>> parameter estimation; probably leading to a very flat quasilikelihood
>> surface and ill-determined optima.
>>
>> But all of the above is only thoughts without the benefit of either
>> serious attempts at fitting real data or doing serious theory so I will
>> defer to anyone who has done either!
>>
>> Philosophically, at least, there seems to be clash between the two
>> approaches and I doubt that attempts to combine them will be 
successful.
>>
>> Murray Jorgensen
>>
>>
>
> --
> Andrew Robinson
> Department of Mathematics and Statistics            Tel: +61-3-8344-6410
> University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
> http://www.ms.unimelb.edu.au/~andrewpr
> http://blogs.mbs.edu/fishing-in-the-bay/
>

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