[R] Confidence intervals

Prof Brian Ripley ripley at stats.ox.ac.uk
Wed Aug 16 20:50:47 CEST 2000

On Wed, 16 Aug 2000, Joseph Brian Adams, PhD wrote:

> I have been wondering about this as well.  In my case, I would like to create
> confidence intervals for the predicted outputs in a logistic model.  How does
> predict.glm(...) calculate the standard errors for the prediction?  I haven't
> been able to find a reference in Hosmer & Lemeshow' text (Applied Logistic
> Regression).

Well, that's not a book on GLMs, is it?  (It's also a good example of how
*not* to do model selection with logistic regression, and we use one of
its examples as a case study for our Master's course.)  As usual for GLMs,
by local linear approximation by a weighted least-squares fit, as you will
see by reading the R code (it calls predict.lm).

> On Thu, 10 Aug 2000, you wrote:
> > 
> > Hi,
> > 
> > I know this is not exactly an R question but may be someone will nice enough
> to give me a pointer. I'm using nnet to fit a non linear univariate function. I
> wonder if there is a way to estimate a confidence interval for the predicted
> output beside using the residuals? The data set I use is relatively small and I
> use only a few (5:10) of these as test set or should I say validation set. >  >

nnet fits are normally too non-linear for the local linear approximation
to be viable.  You could follow the ideas of confint in package MASS,
that is profile the likelihood and interpolate, but that is not so clear
for prediction.  Given that nnet can find multiple local minima, I would
bootstrap the problem if you can.

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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