[R-sig-ME] lme4 with Poisson

[John Maindonald]

Surely, if one uses the lme4 formulation to model observation 
level random effects, this is modelling what is commonly called 
over dispersion.  If the observation level component of variance 
is greater than zero, then any over dispersion is to some extent
accounted for.

There is an issue of whether this is appropriately modelling
overdispersion -- the scale parameter may change with changes
in the fitted value.  Checking for this is a matter of some subtlety.

Now back to Lynne's specific question:

I do not see how one can use a (1/df)*deviance formula to check 
whether the over-dispersion has been accounted for.  I presume
this is the residual df from the fitted model.  For reasons that were
explained on this list quite a long time back, the df are for this
purpose inappropriate.  NB that this is a multi-level model.  Within 
the model formulation that you are using, it is the observation level 
component of variance that tells you about the extent of overdispersion.

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 01/09/2012, at 4:03 AM, Douglas Bates <bates at stat.wisc.edu> wrote:

> On Thu, Aug 30, 2012 at 5:25 PM, Lynne Clay <lynne.clay at xtra.co.nz> wrote:
>> Dear Prof Bates,
>> I'm a doctoral candidate in NZ trying to analyse survey data with random
>> effects with my outcome being a count.  I discovered your lme4 package and
>> have been using this with success, however, I need to check for
>> overdispersion and it is at this point I am having problems.  The formula I
>> have used before has been (1/df)*deviance and if I use this my model is
>> highly overdispersed.  I read on one of the discussion boards that adding an
>> extra random effect (1|id#) addresses the overdispersion problem which I
>> have included but overdispersion continues.
>> 
>> Can overdispersion be calculated in this manner?
> 
> I'm sorry but I know nothing about overdispersion.  To me it is
> completely artificial because there is no probability distribution on
> which to base a statistical model with these properties.
> 
>> Do you have any suggestions of how to deal with this?
> 
> Sorry but I don't.  I have taken the liberty of sending a copy of this
> reply to the R-SIG-Mixed-Models mailing list in the hope that readers
> of that list can help you.
>> 
>> 
>> Lynne
>> 
>> 
>> Lynne Clay
>> PhD Candidate
>> School of Physiotherapy
>> University of Otago
>> PO Box 56
>> Dunedin 9054
>> New Zealand
> 
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