On 19/06/2008, at 9:32 AM, Prof Brian Ripley wrote:
On Thu, 19 Jun 2008, Rolf Turner wrote:
On 19/06/2008, at 8:08 AM, Bryan Hanson wrote:
Hi all. I hope I have my terminology right here...
For a simple lm, one can add “pointwise confidence bounds” to a
fitted line
using something like
predict(results.lm, newdata = something, interval = "confidence")
(I'm following DAAG page 154-155 for this)
I would like to do the same thing for a glm of the logistic
regression type,
for instance, the example in MASS pg 190-192 (available in the
help page for
predict.glm).
However, predict.glm does not have the same kind of features as
"plain old"
predict, i.e. One cannot specify interval = "confidence"
I guess that one reason for that is that prediction intervals
rarely if ever make sense with generalized linear models. So only
one kind of interval is in effect possible.
From what I've read, "pointwise confidence bounds" are computed
from the
SE's for each point. However, I don't see quite where to extract
this
information with a glm
So, is there an existing function that does what I am describing
for a glm,
or can someone point me in the right direction to start writing
my own?
Use predict(<whatever>,type="response",se.fit=TRUE). You get a
list with
three components, the first two of which are the fitted values and
their
standard errors. (The third is the ``scale'' factor, usually/
often equal to 1.)
I would suggest rather computing confidence intervals on linear
predictor scale
and transforming those to response scale. That way you will not
get e.g. negative
values for probabilities in a logistic regression.
I think that for once Brian, you are being too kind! :-) My advice
was even dumber than
you indicate.
E.g. in a logistic model, with (say) eta = beta_0 + beta_1*x one may
find, on the
linear predictor scale, A and B (say) such that P(A <= eta <= B) = 0.95.
Then P(expit(A) <= expit(eta) <= expit(B)) = 0.95, which is exactly
what is wanted.
Doing what I suggested gives C and D (say) such that P(C <= E(expit
(eta-hat)) <= D) = 0.95
(where ``E'' means expected value).
But of course, although E(eta-hat) = eta, it is *NOT* true that E
(expit(eta-hat)) = expit(eta).
So what I proposed does NOT give the confidence interval that is
desired.
Duhhhhh. Apologies (to Bryan Hanson) for being misleading.
cheers,
Rolf
[It probably doesn't make a *lot* of practical difference ``usually''
--- and the standard
errors are approximations anyway ... but one might as well get it
right. Sigh.]
######################################################################
Attention:
This e-mail message is privileged and confidential. If you are not the
intended recipient please delete the message and notify the sender.
Any views or opinions presented are solely those of the author.
This e-mail has been scanned and cleared by MailMarshal
www.marshalsoftware.com
######################################################################
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
