[R] Error using glm with poisson family and identity link

[Thomas Lumley]

On Thu, 25 Nov 2004, Peter Dalgaard wrote:

>
> I haven't got all that much experience with it, but obviously, the
> various algorithms for constrained optimization (box- or otherwise) at
> least allow you to find a proper maximum likelihood estimator.
>
>

It's harder than it looks (well, my experience is with the log-binomial 
model, but it should be similar).  The constraints are not box 
constraints, but a more general set of linear constraints, and you either 
have to find the convex hull of the data or use a constraint for every 
data point.

Also, the algorithm in glm.fit, while not perfect, is a little smarter 
than a simple IRLS. It uses step-halving to back away from the edge, and 
when the parameter space is convex it has a reasonable chance of creeping 
along the boundary to the true MLE.

I think better glm fitting is worth pursuing: computational difficulties 
with the log-binomial model have forced many epidemiologists turn to 
estimators other than the MLE (or contrasts other than the relative risk), 
which is a pity.


 	-thomas