R help - Oct 2003 - Confidence ellipse for correlation

Hello,

SAS' point and click interface has the option of produce a scatterplot with
a
superimposed confidence ellipse for the correlation coefficient. Since I 
generally like R so much better, I would like to reproduce this in R. I've 
been playing with the ellipse package. In order to have the points and the 
ellipse on the same graph I've done the following. 
(Load ellipse package...)
> data(Puromycin)
> attach(Puromycin)
> my<-mean(rate)
> mx<-mean(conc)
> sdy<-sd(rate)
> sdx<-sd(conc)
> r<-cor(conc,rate)
> plot(ellipse(r,scale=c(sdx,sdy),centre=c(mx,my)),type='l')
> points(conc,rate)
1) Is my use of 'scale' and 'centre' theoretically correct?
2) Is there a more efficient way to get the 5 parameters? (I guess I could 
write a little function, but has it already been done?)

The non-linear relationship between these variables brings up another point: 
Is there a way to plot a contour (empirical?) containing, say, 95% of the 
values.

Thanks for your time!

Tanya

On Tue, 28 Oct 2003, Tanya Murphy wrote:
> Hello,
> 
> SAS' point and click interface has the option of produce a scatterplot
with a
> superimposed confidence ellipse for the correlation coefficient. Since I 
> generally like R so much better, I would like to reproduce this in R.
I've
> been playing with the ellipse package. In order to have the points and the 
> ellipse on the same graph I've done the following. 
> (Load ellipse package...)
> > data(Puromycin)
> > attach(Puromycin)
> > my<-mean(rate)
> > mx<-mean(conc)
> > sdy<-sd(rate)
> > sdx<-sd(conc)
> > r<-cor(conc,rate)
> > plot(ellipse(r,scale=c(sdx,sdy),centre=c(mx,my)),type='l')
> > points(conc,rate)
> 
> 1) Is my use of 'scale' and 'centre' theoretically correct?
Depends on whose theory you have in mind!  This is not `a confidence
ellipse for the correlation coefficient', as confidence ellipses are for
pairs of parameters, not variables.  It seems to be a plot of a contour of
the fitted bivariate normal.
> 2) Is there a more efficient way to get the 5 parameters? (I guess I could 
> write a little function, but has it already been done?)
You could do things like
mxy <- mean(Puromycin[c("rate", "conc")])
sxy <- sapply(Puromycin[c("rate", "conc")], sd)
> The non-linear relationship between these variables brings up another
point:
> Is there a way to plot a contour (empirical?) containing, say, 95% of the 
> values.
Yes.  You need a 2D density estimate (e.g. kde2d in MASS) then compute the
density values at the points and draw the contour of the density which
includes 95% of the points (at a level computed from the sorted values via
quantile()).

-- 
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 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

Dear Tanya,

I believe that the data.ellipse function in the car package will do what 
you want (but note that the probability contours are for a bivariate-normal 
distribution, and hence won't necessarily enclose approximately the 
specified proportion of the data).

I hope that this helps,
  John

At 01:57 PM 10/28/2003 -0500, you wrote:
>Hello,
>
>SAS' point and click interface has the option of produce a scatterplot
with a
>superimposed confidence ellipse for the correlation coefficient. Since I
>generally like R so much better, I would like to reproduce this in R.
I've
>been playing with the ellipse package. In order to have the points and the
>ellipse on the same graph I've done the following.
>(Load ellipse package...)
> > data(Puromycin)
> > attach(Puromycin)
> > my<-mean(rate)
> > mx<-mean(conc)
> > sdy<-sd(rate)
> > sdx<-sd(conc)
> > r<-cor(conc,rate)
> > plot(ellipse(r,scale=c(sdx,sdy),centre=c(mx,my)),type='l')
> > points(conc,rate)
>
>1) Is my use of 'scale' and 'centre' theoretically correct?
>2) Is there a more efficient way to get the 5 parameters? (I guess I could
>write a little function, but has it already been done?)
>
>The non-linear relationship between these variables brings up another point:
>Is there a way to plot a contour (empirical?) containing, say, 95% of the
>values.
>
>Thanks for your time!
>
>Tanya
-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox