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
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