Offsets in Poisson or Neg. Bin regression

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).

Offsets in Poisson or Neg. Bin regression

Thread (7 messages)