[R] confidence / prediction ellipse

David Winsemius dwinsemius at comcast.net
Mon Jan 28 05:38:50 CET 2013 

On Jan 27, 2013, at 8:16 PM, Giuseppe Amatulli wrote:

> Dear all,
> thanks for your input.
>
> Bert - yes you get the point, i would to like to draw an ellipse  
> contour
> for a population quantile.
> Indeed, as you mention data.ellipse() should draw that. In other  
> words if i
> re-run my model for another prediction (getting a new vector b) i  
> would
> have the 95% probability that my prediction fall inside the ellipse.

install.packages("hdrcde")  # from Rob Hyndman
require(hdrcde) x <- c(rnorm(200,0,1),rnorm(200,4,1))
y <- c(rnorm(200,0,1),rnorm(200,4,1))
par(mfrow=c(1,2))
plot(x,y, pch="+", cex=.5)
hdr.boxplot.2d(x,y)


-- 
David.
>
>
> On 27 January 2013 17:26, Bert Gunter <gunter.berton at gene.com> wrote:
>
>> All:
>>
>> Aha! -- The light dawneth, methinks (maybe...)
>>
>> Giuseppe: I re-read the SAS link you sent and if I have parsed it
>> correctly, what SAS chooses to call an ellipse for "prediction" -- a
>> rather idiosyncratic way to describe it, imo -- I believe the rest of
>> us would call a contour for a population quantile. The key phrase  
>> that
>> indicates this is "It [the elliptical region] also approximates a
>> region containing a specified percentage of the population. "
>>
>> So, if I'm right, I believe you just need to use car's data.ellipse()
>> function.
>>
>> And if I'm wrong, my little corner of the globe remains cloaked in
>> darkness confusion.
>>
>> Cheers,
>> Bert
>>
>> On Sun, Jan 27, 2013 at 12:43 PM, John Fox <jfox at mcmaster.ca> wrote:
>>> Dear Giuseppe and Bert,
>>>
>>> I also didn't follow what's intended, more or less for the same  
>>> reasons
>> as
>>> Bert mentioned, which is why I didn't reply to the initial  
>>> posting. In
>> the
>>> car package, confidenceEllipse() draws confidence ellipses for a  
>>> pair of
>>> coefficients from a statistical model, and dataEllipse() draws
>>> bivariate-normal concentration ellipses for the bivariate  
>>> distribution of
>>> two variables.
>>>
>>> I'm copying to Georges Monette and Michael Friendly, coauthors of  
>>> these
>>> functions, in case they have something to add.
>>>
>>> I hope that this helps, but I doubt that it does.
>>>
>>> John
>>>
>>> -----------------------------------------------
>>> John Fox
>>> Senator McMaster Professor of Social Statistics
>>> Department of Sociology
>>> McMaster University
>>> Hamilton, Ontario, Canada
>>>
>>>
>>>
>>>
>>>> -----Original Message-----
>>>> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org
>> ]
>>>> On Behalf Of Giuseppe Amatulli
>>>> Sent: Sunday, January 27, 2013 11:41 AM
>>>> To: Bert Gunter
>>>> Cc: r-help at r-project.org
>>>> Subject: Re: [R] confidence / prediction ellipse
>>>>
>>>> Hi,
>>>> thanks for your replay.
>>>> My values of a and b are respectively:
>>>> a = observation of an event
>>>> b = prediction of a model.
>>>>
>>>> Therefore i would like to draw the confidence region for  
>>>> predicting a
>>>> new
>>>> observation, and according to this
>>>> http://v8doc.sas.com/sashtml/insight/chap40/sect35.htm the  
>>>> prediction
>>>> ellipse should be more appropriate.
>>>>
>>>> But i'm not able to track back the function
>>>> radius <- sqrt(dfn * qf(level, dfn, dfd))
>>>> in order to change it and draw a prediction ellipses.
>>>>
>>>> Regards
>>>> Giuseppe
>>>>
>>>>
>>>>
>>>>
>>>> On 26 January 2013 17:19, Bert Gunter <gunter.berton at gene.com>  
>>>> wrote:
>>>>
>>>>> Well, I'd guess you have to first define what you mean by  
>>>>> "prediction
>>>>> ellipse," as the confidence ellipses are for the bivariate
>>>>> distribution of 2 parameter estimates -- as I understand it --
>>>>> whereas predictions depend on the covariate values and are for a
>>>>> single response value (unless you have fitted multiple  
>>>>> responses, I
>>>>> suppose).
>>>>>
>>>>> -- Bert
>>>>>
>>>>> On Sat, Jan 26, 2013 at 1:12 PM, Giuseppe Amatulli
>>>>> <giuseppe.amatulli at gmail.com> wrote:
>>>>>> Hi,
>>>>>> I'm using the R library(car) to draw confidence/prediction  
>>>>>> ellipses
>>>> in a
>>>>>> scatterplot.
>>>>>>> From what i understood  the ellipse() function return an ellipse
>>>> based
>>>>>> parameters:  shape, center,  radius .
>>>>>> If i read  dataEllipse() function i can see how these  
>>>>>> parameters are
>>>>>> calculated for a confidence ellipse.
>>>>>>
>>>>>> ibrary(car)
>>>>>>
>>>>>> a=c(12,12,4,5,63,63,23)
>>>>>> b=c(13,15,7,10,73,83,43)
>>>>>>
>>>>>> v <- cov.trob(cbind(a, b))
>>>>>> shape <- v$cov
>>>>>> center <- v$center
>>>>>>
>>>>>> radius <- sqrt(2 * qf(0.95, 2, length(a) - 1))   # radius <-
>>>> sqrt(dfn *
>>>>>> qf(level, dfn, dfd))
>>>>>>
>>>>>> conf.elip = ellipse(center, shape, radius,draw = F)
>>>>>> plot(conf.elip, type='l')
>>>>>> points(a,b)
>>>>>>
>>>>>> My question is how I can calculate shape, center and radius  to
>>>> obtain a
>>>>>> prediction ellipses rather than a confidence ellipse?
>>>>>> Thanks in Advance
>>>>>> Giuseppe
>>>>>>
>>>>>> --
>>>>>> Giuseppe Amatulli
>>>>>> Web: www.spatial-ecology.net
>>>>>>
>>>>>>        [[alternative HTML version deleted]]
>>>>>>
>>>>>> ______________________________________________
>>>>>> R-help at 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.
>>>>>
>>>>>
>>>>>
>>>>> --
>>>>>
>>>>> Bert Gunter
>>>>> Genentech Nonclinical Biostatistics
>>>>>
>>>>> Internal Contact Info:
>>>>> Phone: 467-7374
>>>>> Website:
>>>>>
>>>>> http://pharmadevelopment.roche.com/index/pdb/pdb-functional-
>>>> groups/pdb-biostatistics/pdb-ncb-home.htm
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> Giuseppe Amatulli
>>>> Web: www.spatial-ecology.net
>>>>
>>>>      [[alternative HTML version deleted]]
>>>>
>>>> ______________________________________________
>>>> R-help at 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.
>>>
>>
>>
>>
>> --
>>
>> Bert Gunter
>> Genentech Nonclinical Biostatistics
>>
>> Internal Contact Info:
>> Phone: 467-7374
>> Website:
>>
>> http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm
>>
>
>
>
> -- 
> Giuseppe Amatulli
> Web: www.spatial-ecology.net
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at 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, MD
Alameda, CA, USA

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