Hi Ivailo,
If the effort term is not just present in the model for the purpose of
scaling the outcome random variable, then I think that it should just be
treated as a regression-type problem. All the questions your raised
seem(?) to be standard in that setting too: Is the covariate acting
linearly (on the link scale)? Are any non-linearities (on the link
scale) important enough to warrant using some curvi-linear or
basis-expanded function of the effort variable? And so on...
Yes, the fishing net example *may* be one where the (scaling) effort
variable acts non-linearly. I have not thought about this though. I
typically use effort as a scaling factor only as I have a strong a
priori belief that effort will be multiplicatively related to expected
outcome (log offset with log-link). I am sure that I will need to
revise this belief sometime;-)
Scott
On 27/06/13 16:57, Ivailo wrote:
On Wed, Jun 26, 2013 at 12:42 PM, Scott Foster <scott.fos...@csiro.au> wrote:
Hi again Ivailo,
Yes, the `offset' and the covariate are the same thing. Including them both
simply alters the functional form of the linear predictor in your model.
No, they are not collinear in the typical sense as there is only one
parameter (linear form) between them -- the offset term does not have a
parameter that will be estimated associated with it. For example, with log(
effort) added as a linear covariate the log-link GLM is
log( E(y)) = offset + beta * log( effort) + other_stuff = log( effort) +
beta * log( effort) + other_stuff = beta_1 * log( effort) + other_stuff
where beta_1=1+beta.
If you test that beta==0 (which is not beta_1) then you are testing that the
effect of effect is purely scaling (as per nomenclature before). This is
the same as McCullagh and Nelder's testing to see if beta_1==1. Thanks for
the pointer to McCullagh and Nelder -- I didn't know that they suggested
that.
Thanks a lot for the brilliant explanation, Scott! Now things make
sense to me, and I'm interested what the modeling strategy would be if
beta_1 turns out to be significantly <> 1. Would the option you
mention below be viable alternative in that case?
My depiction of the effect of effort as f( effort) is to allow for the
possibility that the effect of effort may be non-linear on the link scale.
A simple example is when f(effort) is a low-order polynomial. Departures
from effort being a purely scaling term may extend beyond linearity. One
may even want to consider regression splines or even more flexible GAMs.
Having said all this though, it is my practice to be quite conservative with
including effort as anything but a scaling variable (offset). It seems to
me that there needs to be good reason before jumping to strong conclusions
that may have no basis in the phenomenon under study.
I imagine that the fishing-net example you mentioned earlier could be
a case of a non-linear effect of effort -- wouldn't this warrant
modeling the effort as being non-linear on the link scale?
Cheers,
Ivailo
--
UBUNTU: a person is a person through other persons.
--
Scott Foster
CSIRO Mathematics, Informatics and Statistics
GPO Box 1538
Castray Esplanade
Hobart 7001
Tasmania
Australia
Phone: (03) 6232 5178
Fax: (03) 6232 5000
Email: scott.fos...@csiro.au
_______________________________________________
R-sig-ecology mailing list
R-sig-ecology@r-project.org
https://stat.ethz.ch/mailman/listinfo/r-sig-ecology