What do you do in such situations?
Sundar Dorai-Raj and I have extended "glm" concepts to models driven by a sum of k independent Poissons, with the a linear model for log(defectRate[i]) for each source (i = 1:k). To handle convergence problems, etc., I think we need to use informative Bayes, but we're not there yet. In any context where things are done more than once [which covers most human activities], informative Bayes seems sensible.
A related question comes with data representing the differences between Poisson counts, e.g., with d[i] = X[i]-X[i-1] = the number of new defects added between steps i-1 and i in a manufacturing process. Most of the time, d[i] is nonnegative. However, in some cases, it can be negative, either because of metrology errors in X[i] or because of defect removal between steps i-1 and i.
Comments?
Best Wishes,
Spencer GravesPeter Dalgaard wrote:
Spencer Graves <[EMAIL PROTECTED]> writes:
Dear Federico: Why do you use the "identity" link? That can
produce situations with an average of (-2) Poisson defects per unit,
for example. That's physical nonsense.
So is _not_ using the identity link when the model is manifestly additive on the identity scale. E.g. calibrating differential spectrofluorometry with photon counters recording linear combinations of intensities at different wavelengths.
I've bumped into similar situations before (binomial(link=identity), I think it was then) and the glm.fit algorithm could use improvement in dealing with the parameter constraints in these cases. With the standard IRLS algorithm, if the maximum is on the boundary, you basically hit a random point on the boundary and get stuck there with a search direction pointing out of the valid region.
-- Spencer Graves, PhD, Senior Development Engineer O: (408)938-4420; mobile: (408)655-4567
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