Thanks to all of you for your suggestions and comments. I really
appreciate it.
Some comments to Dennis' comments:
1) I am not concerned about predicting outside the original range. That
would be nonsense anyway considering the physical phenomenon I am
modeling. I am, however, concerned that the bootstrapping leads to
extremely wide CIs at the extremes of the range when there are few data
points. But I guess there is not much I can do about that as long as I
rely on bootstrapping?
2) I have made a function that does the interpolation to the requested
new x's from the original modeling data to get the residual variance and
the model variance. Then it interpolates the combined SDs back the the
new x values. See below.
3) I understand that. For this project it is not that important that the
final prediction intervals are super accurate. But I need to hit the
ballpark. I am only trying to do something that doesn't crossly
underestimate the prediction error and doesn't make statisticians loose
their lunch a first glance.
I also cannot avoid that my data contains erroneous values and I will
need to build many models unsupervised. But the fit should be good
enough that I plan to eliminate values outside some multiple of the
prediction interval and then re-calculate. And if the model is not good
in any range I will throw it out completely.
Based on the formula of my last message I have made a function that at
least gives less optimistic intervals than what I could get with the
other methods I have tried. The function and example data can be found
here
https://github.com/stanstrup/retpred_shiny/blob/master/retdb_admin/make_predictions_CI_tests.R
in case anymore has any comments, suggestions or expletives to my
implementation.
----------------------
Jan Stanstrup
Postdoc
Metabolomics
Food Quality and Nutrition
Fondazione Edmund Mach
On 08/12/2014 05:40 PM, Bert Gunter wrote:
PI's of what? -- future individual values or mean values?
I assume quantreg provides quantiles for the latter, not the former.
(See ?predict.lm for a terse explanation of the difference). Both are
obtainable from bootstrapping but the details depend on what you are
prepared to assume. Consult references or your local statistician for
help if needed.
-- Bert
Bert Gunter
Genentech Nonclinical Biostatistics
(650) 467-7374
"Data is not information. Information is not knowledge. And knowledge
is certainly not wisdom."
Clifford Stoll
On Tue, Aug 12, 2014 at 8:20 AM, David Winsemius <dwinsem...@comcast.net> wrote:
On Aug 12, 2014, at 12:23 AM, Jan Stanstrup wrote:
Hi,
I am trying to find a way to estimate prediction intervals (PI) for a monotonic
loess curve using bootstrapping.
At the moment my approach is to use the boot function from the boot package to
bootstrap my loess model, which consist of loess + monoproc from the monoproc
package (to force the fit to be monotonic which gives me much improved results
with my particular data). The output from the monoproc package is simply the
fitted y values at each x-value.
I then use boot.ci (again from the boot package) to get confidence intervals. The problem
is that this gives me confidence intervals (CI) for the "fit" (is there a
proper way to specify this?) and not a prediction interval. The interval is thus way too
optimistic to give me an idea of the confidence interval of a predicted value.
For linear models predict.lm can give PI instead of CI by setting interval =
"prediction". Further discussion of that here:
http://stats.stackexchange.com/questions/82603/understanding-the-confidence-band-from-a-polynomial-regression
http://stats.stackexchange.com/questions/44860/how-to-prediction-intervals-for-linear-regression-via-bootstrapping.
However I don't see a way to do that for boot.ci. Does there exist a way to get
PIs after bootstrapping? If some sample code is required I am more than happy
to supply it but I thought the question was general enough to be understandable
without it.
Why not use the quantreg package to estimate the quantiles of interest to you?
That way you would not be depending on Normal theory assumptions which you
apparently don't trust. I've used it with the `cobs` function from the package
of the same name to implement the monotonic constraint. I think there is a
worked example in the quantreg package, but since I bought Koenker's book, I
may be remembering from there.
--
David Winsemius
Alameda, CA, USA
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