R help - Aug 2014 - Prediction intervals (i.e. not CI of the fit) for monotonic loess curve using bootstrapping

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.


Any hints are highly appreciated.


----------------------
Jan Stanstrup
Postdoc

Metabolomics
Food Quality and Nutrition
Fondazione Edmund Mach

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