[R] Prediction confidence intervals for a Poisson GLM

[stephenb]

I am following up on an old post. Please, comment:

it appears that 

predict(glm.model,type="response",se.fit=T)

will do all the conversions and give se on the scale of the response. This
only takes into account the error in parameter estimation. what a
"prediction" interval is meant to be usually means it has to capture the
error due to both parameter estimation and sampling variation ie it
encompasses the actual realizations.
for a given parameter there is sampling variation and that is not included
in the output of predict. the discreteness of models makes it quite
difficult to estimate a percentile interval, though. for binary outcomes, I
think it does not make sense. for Poisson and binomial (grouped binary) I
think it is possible to get approximations at least and this is what the
original poster needed I think.

so, let's say we have plow and pup for an observation from predict. if
size=100 for that obs.
predlow=qbinom(.025,100,plow)
predup=qbinom(.975,100,pup)

will give the prediction bounds. this I think partly ignores possible
overdispersion. Please, suggest a better way taking overdispersion into
account (in the qbinom part).

Thanks everybody.
Stephen B.
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