[R] Plotting Bivariate Normal Data

[Kjetil Brinchmann Halvorsen]

John Fox wrote:

>Dear Sarah,
>
>If the data are allegedly bivariate normal, then they are probably two
>vectors, not one. Assuming that this is the case, I know of nothing quite as
>neat as a univariate QQ plot to check visually for bivariate normality
>(perhaps someone else has a suggestion here), but you could superimpose
>  
>
What about using Independent component analysis to find the most 
non-normal linear combination
and make a qq-plot of that?

Something like:

library(fastICA)    # on CRAN
x <- matrix(rchisq(10000, df=2), 1000, 10)
P <- svd(matrix(rnorm(100), 10,10))$u    #  random orthogonal matrix
y <- x %*% P
 y.ica <- fastICA(y, 2)
 qqnorm(y.ica$S[,1])

But I have never seen this suggested in print, although it seems quite
natural. Anybody knows if something like this is considered a reasonable 
test
of multivariate normality?

Kjetil






>bivariate-normal contours on a scatterplot of the data, perhaps along with a
>bivariate density estimate. The car and ellipse packages can do the former,
>while the locfit and sm packages (and possibly others) can do the latter.
>
>I hope this helps,
> John
>
>--------------------------------
>John Fox
>Department of Sociology
>McMaster University
>Hamilton, Ontario
>Canada L8S 4M4
>905-525-9140x23604
>http://socserv.mcmaster.ca/jfox 
>-------------------------------- 
>
>  
>
>>-----Original Message-----
>>From: r-help-bounces at stat.math.ethz.ch 
>>[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of sarah english
>>Sent: Saturday, October 23, 2004 7:34 AM
>>To: r-help at stat.math.ethz.ch
>>Subject: [R] Plotting Bivariate Normal Data
>>
>>
>>Dear list 
>> 
>>I have a vector of values that allegedly have a bivariate 
>>normal distribution. 
>>
>> 
>>
>>I  want to create a plot that shows the values I have 
>>obtained, and the  bivariate normal distribution curve for the data.
>>
>>
>>Is there a  way of doing this in R? 
>>
>>
>> 
>>
>>Many thanks for your help, 
>>
>>Sarah.
>>
>>
>>
>>		
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>
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>  
>


-- 

Kjetil Halvorsen.

Peace is the most effective weapon of mass construction.
               --  Mahdi Elmandjra