R help - Mar 2005 - Negative intercept in glm poisson model

Federico Gherardini wrote:
> I'm trying to fit a glm model using family=poisson(link =
"identity"). The
> problem is that the glm function fits a model with a negative intercept, 
> which sounds like a nonsense to me, being the response a Poisson variable. 
Not really.  The negative intercept is on the scale of the linear 
predictor.  The expected response, which is the exponential of the 
linear predictor, is always positive.

Dear list,
I'm trying to fit a glm model using family=poisson(link =
"identity"). The
problem is that the glm function fits a model with a negative intercept, 
which sounds like a nonsense to me, being the response a Poisson variable.
>From a previous discussion on this list I've understood that the glm
function
uses IRLS for the fitting without any constraint so it is possible for it to 
end up in a region of values which are not admissible given the model, and in 
fact sometimes it fails asking for valid starting values. In this case I 
expected it to fail asking to supply starting values, and instead it fits the 
model just nice with this negative intercept. What am I missing?

Thanks,
Cheers
Federico

On Tue, 1 Mar 2005 15:10:35 +0100, Federico Gherardini
<f.gherardini at pigrecodata.net> wrote :
>Dear list,
>I'm trying to fit a glm model using family=poisson(link =
"identity"). The
>problem is that the glm function fits a model with a negative intercept, 
>which sounds like a nonsense to me, being the response a Poisson variable. 
>>From a previous discussion on this list I've understood that the glm
function
>uses IRLS for the fitting without any constraint so it is possible for it to
>end up in a region of values which are not admissible given the model, and
in
>fact sometimes it fails asking for valid starting values. In this case I 
>expected it to fail asking to supply starting values, and instead it fits
the
>model just nice with this negative intercept. What am I missing?
The problem isn't in the software, it's due to using an identity link
with a model that does not allow a negative mean.  Suppose glm()
constrained the intercept to be positive, and you ended up fitting a
positive slope:  then you would still get negative predictions for
sufficiently large negative values of the predictor variables.

Duncan Murdoch