[R] Plotting Bivariate Normal Data
jfox at mcmaster.ca
Tue Oct 26 01:23:28 CEST 2004
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
Department of Sociology
Canada L8S 4M4
> -----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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