Error using glm with poisson family and identity link

On Thu, 25 Nov 2004, Spencer Graves wrote:

 I generally avoid constrained optimizers for three reasons: 
 1.  My experience with them has included many cases where the
 optimizer would stop with an error when testing parameter
 values that violate the constraints.  If I transform the
 parameter space to remove the constraints, that never happens. 
 The constrained optimizers in R 2.0.1 may not exhibit 
 this behavior, but I have not checked.

They do not, and OTOH if the MLE really does lie on the boundary
(and here it may well, with one data point fitted with mean zero)
transformation will often not find a good solution.

Constrained optimization is a hard problem, good methods are very 
complex and good code to implement them is usually expensive.

I've had success with awkward constrained optimisation using the
Nelder-Mead procedure -- simply make the region beyond the constraint
hot enough for the simplex to recoil on touching it.

I once tested it in what I thought might be a tough case by
planting "trees" all over a shallow quadratic bowl. More
precisely, many circular regions which were not to be entered.
The objective was to locate the minimum of the bowl.

The function was defined so as to take a high value inside
each circular region.

The simplex took a long time to locate the minimum, spending
a lot of the time feeling its way slowly round the "trunks"
of the "trees", and some of the time trotting downhill over
open space, but it did get there. Nelder-Mead is pretty robust.

Best wishes to all,
Ted.


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Date: 26-Nov-04                                       Time: 09:39:08
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