[R] Plotting Bivariate Normal Data

[John Fox]

Dear Bert,

The data.ellipse() function in the car package optionally uses the
covariance matrix and location vector returned by cov.trob() (from the MASS
package). I believe that any 1D function of the two variables is potentially
problematic. As to why do it -- comparing the bivariate distribution to the
bivariate normal might be an interesting way to think about the shape of the
distribution.

Regards,
 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 Berton Gunter
> Sent: Monday, October 25, 2004 1:31 PM
> To: R-Help
> Subject: Re: [R] Plotting Bivariate Normal Data
> 
>  
> Just a little addendum to Martin's comments below. It is well 
> known that using LS centers and covariances for the 
> M-distances is generally not a good way to do this, as these 
> statistics, themselves, are distorted by the long "tails" (do 
> > 1D distributions have "tails"?)  so that the problems are 
> hidden (see Brian Ripley's comments on the R-Help "robust 
> regression with groups" thread  from last week). Hence, one 
> should use a resistant center (the medioid, say) and a 
> resistant covariance matrix (e.g., from cov.rob()) to compute 
> the M-distances.
> 
> ... But then, this begs the question: Why do normality testing at all?
> (again, see BR's comments). Better to use robust/resistant 
> statistical procedures for estimation from the beginning, 
> though, unfortunately, this shatters the nice simple 
> mathematical framework for inference. 
> 
> -- Bert Gunter
> Genentech Non-Clinical Statistics
> South San Francisco, CA
>  
> "The business of the statistician is to catalyze the 
> scientific learning process."  - George E. P. Box
>  
>  
> 
> > Since one of the more severe and common deviations from 
> normality is 
> > "long tailed"ness (in all it's vaguety), we have been 
> recommending to 
> > QQ-plot mahalanobis distances against chi squared quantiles - even 
> > before looking at the univariate QQ plots.
> > 
> > Exactly for this reason, in R,
> > 	example(mahalanobis)
> > shows a version of how to do this!
> > 
> > Martin Maechler, ETH Zurich
> > 
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