Thread Subject: glmfit 'offset' parameter

Hi

I don't get the purpose/usage of the 'offset' parameter in
the glmfit function doc. I browsed through the references
(Dobson and McCullagh), but didn't find a similar parameter.
Does anyone know its meaning?

Thanks

> I don't get the purpose/usage of the 'offset' parameter in
> the glmfit function doc.

Joe, in regular regression suppose you want to fit a model like this:

   y = a + x1 + b*x2 + error

In other words, you know the coefficient of x1 (we can assume it is 1 here).
It's easy enough to fit this by least squares by re-writing

   y - x1 = a + b*x + error

For generalized linear models, the response isn't a simple sum of a linear
function of the predictors with additive errors, so it's not possible to
re-write in the same way.

Here's a semi-realistic example where this would be useful. Suppose the
number of defects on a surface should be proportional to the surface area,
or the number of events in an interval of time should be proportional to the
length of time. The count of defects or events might reasonably be modeled
by a Poisson distribution. If we subtracted or divided off the area or
time, we'd get something that might not even be integer valued. Instead, if
we model the expected value as

    E[y] = area * exp(a + b*x)

we can take logs to get

   log(E[y]) = log(area) + a + b*x

The offset parameter allows us to handle the term that doesn't have a
coefficient to be estimated.

-- Tom

Joe Ercolino wrote:
> Hi
>
> I don't get the purpose/usage of the 'offset' parameter in
> the glmfit function doc. I browsed through the references
> (Dobson and McCullagh), but didn't find a similar parameter.
> Does anyone know its meaning?


McCullagh&Nelder's book has an example of this in the Poisson chapter,
in the ship damage example: length of service.

Thanks, both replies have been very helpful.

My problem at hand deals with the dose-response of a
population of animals to a toxic agent using the
binomial-probit model. Now I realize that I could use the
average weight of each dose-group of animals to normalize
the dose or use it as an offset. What would be the
difference in these approaches?

Thanks in advance.

Joe Ercolino wrote:
> Thanks, both replies have been very helpful.
>
> My problem at hand deals with the dose-response of a
> population of animals to a toxic agent using the
> binomial-probit model. Now I realize that I could use the
> average weight of each dose-group of animals to normalize
> the dose or use it as an offset. What would be the
> difference in these approaches?

I can't tell you what your model should be. But think of the offset as being a predictor variable for which the coefficient in the linear predictor is held fixed at 1. With a log link (as in a Poisson regression), it's easy to see the effect: it's a multiplicative constant on the predicted mean. M&N's example is to use log(exposure), I think, and the link then exponentiates that back to exposure. With a probit model, the effect is a little less obvious to me.