[R-sig-eco] Offsets in Poisson or Neg. Bin regression

[Scott Foster]

Hi Ivailo,

Good question.  Difficult to answer, which is probably why you haven't 
had any responses yet (that the list has seen).

If you include an offset term with a log link function then you are 
assuming that the random variable (counts say) depend on the offset with 
a known relationship.  Generally, this is precisely what you want to do 
-- for example standardising counts for the sampling effort taken to 
obtain those counts.

However, in some situations it is conceivable that the sampling effort 
itself affects the count random variable.  An example may be fish in a 
trawl net -- as the net gets full it becomes less and less efficacious.  
In this case you may expect that a single unit of effort change will 
have different effect when there has been lots of previous effort to 
when there hasn't.

If I thought that I was in the latter case, I may fit a model like

log( E( count)) = log( effort) + f(effort) + other stuff.

The function f(effort) can take any form, including beta*log(effort).  
In such a case a test of beta==0 is equivalent to testing if the effect 
of effort is purely scaling or if it is something else/sinister.  
General forms of f(effort) may tell you much more but may also be much 
more confusing.

To choose between the two cases above (offset versus offset+covariate), 
I would base my choice largely on prior knowledge of the system under 
study.  This is especially so if I don't have much data.

I hope that this has helped,

Scott

PS Is it just me or did the original question (damaged embryos with 
offset of number of embryos) sound more like a binomial problem than a 
Poisson/NB one?  Note though that they will start to coincide if the 
number of embryos is large and the probability of damage is small 
(Binomial -> Poisson in the limit).

On 19/06/13 20:53, Ivailo wrote:
> On Tue, Jun 18, 2013 at 11:10 AM, Matias Ledesma <matutetote at hotmail.com> wrote:
>>
>> Philip and Alain,
>>
>> Thank you for your assistence,
>> So, that mean that the  fuction offset its only possible if there is a relationship between the
>> damaged number of embryos and the total number of embryos per amphipod as you explained?
> As I'm facing a similar problem, I'd like to know as well if a
> variable should be passed as an offset to the formula only when it
> influences the outcome in some (linear) way. Does it make sense to
> include the exposure variable in the model as a regular input first,
> and if it's coefficient is around 1 to be taken as an indicator that
> it is better that variable to be included in the model as an offset?
>
> Cheers,
> Ivailo
> --
> UBUNTU: a person is a person through other persons.
>
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-- 
Scott Foster
CSIRO Mathematics, Informatics and Statistics
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