On Aug 14, 2014, at 7:17 AM, Jan Stanstrup wrote:
> Thank you very much for this snippet!
>
> I used it on my data and indeed it does give intervals which appear quite
> realistic (script and data here
> https://github.com/stanstrup/retpred_shiny/blob/master/retdb_admin/make_predictions_CI_tests.R).
> I also tried getting the intervals with predict.cobs but the methods
> available there gave very narrow bands.
> The only problem I can see is that the fit tend to be a bit on the smooth
> side. See for example the upper interval limits at x = 2 to 3 and x =1.2. If
> then I set lambda to something low like 0.05 the band narrows to nearly
> nothing when there are few points. For example at x = 2.5. Is there some
> other parameter I would be adjusting?
>
Try specifying the number and location of the knots (using my example data):
> Rbs.9 <- cobs(age,analyte,constraint="increase",tau=0.9, nknots=6,
> knots=seq(60,85,by=5))
> plot(age,analyte, ylim=c(0,2000))
> lines(predict(Rbs.9), col = 2, lwd = 1.5)
--
David.
>
>
> ----------------------
> Jan Stanstrup
> Postdoc
>
> Metabolomics
> Food Quality and Nutrition
> Fondazione Edmund Mach
>
>
>
> On 08/14/2014 02:02 AM, David Winsemius wrote:
>>
>> On Aug 12, 2014, at 8:40 AM, 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).
>>
>> I probably should have questioned the poster about what was meant by a
>> "prediction interval for a monotonic loess curve". I was suggesting quantile
>> regression for estimation of a chosen quantile, say the 90th percentile. I
>> was thinking it could produce the analogue of a 90th percentile value (with
>> no reference to a mean value or use of presumed distribution within
>> adjacent windows of say 100-150 points. I had experience using the cobs
>> function (in the package of the same name) as Koenker illustrates:
>>
>> age <- runif(1000,min=60,max=85)
>>
>> analyte <- rlnorm(1000,4*(age/60),age/60)
>> plot(age,analyte)
>>
>> library(cobs)
>> library(quantreg)
>> Rbs.9 <- cobs(age,analyte, constraint="increase",tau=0.9)
>> Rbs.median <- cobs(age,analyte,constraint="increase",tau=0.5)
>>
>> png("cobs.png"); plot(age,analyte, ylim=c(0,2000))
>> lines(predict(Rbs.9), col = "red", lwd = 1.5)
>> lines(predict(Rbs.median), col = "blue", lwd = 1.5)
>> dev.off()
>> <Mail Attachment.png>
>>
>> -- David
>>
>>
>>> 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
>>>>
>>>> ______________________________________________
>>>> 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.
>>
>> David Winsemius
>> Alameda, CA, USA
>>
>
> <boot2ci_PI.png><cobs.png>
David Winsemius
Alameda, CA, USA
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