[R] Negative intercept in glm poisson model

[Duncan Murdoch]

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