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st: RE: RE: RE: Re: Compositional data


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: RE: Re: Compositional data
Date   Wed, 5 Mar 2008 21:24:50 -0000

If three variables say x, y, z add to 1 then x + y + z = 1 defines a
plane in 3-space 
and you can lay such a plane flat, i.e. project it onto 2-space 
without distortion. That, as everyone knows, is the reason you can draw
a triangular plot
(or whatever else it's called). 

What is about that which is not Euclidean? I think Euclid 
would have felt very much at home with that triangle. 

Anyway, all the alternatives I know to that stretch and shrink different
parts of the 
space, and none is more intuitive than the original. But some can be
more convenient. 

For example, to pick an application out of the air, many elections can
be condensed to 
three fractions of the total vote

Very slightly left-wing party
Right-wing party 
A sum of nice people going nowhere much plus greens plus isolationists
plus nasties 

as is roughly true of British politics. But data for such variables tend
to concentrate in a 
rather small part of the triangle. There are alternatives, such as
showing only part of the triangle, 
but they are difficult to program for elegantly. Or rather, I would
rather try the alternatives. 

Nick
n.j.cox@durham.ac.uk 

Verkuilen, Jay

>>For more details on the Aitchison book, which sells under a slightly
different title, see

http://www.blackburnpress.com/stanofcoda.html<<

Whoops. Yes, it's Statistical Analysis of Compositional Data... sitting
right there on the shelf in front of me. 

http://en.wikipedia.org/wiki/John_Aitchison


>>A project of mine for 2008, already started, is to publish Stata
programs for alternatives 
to such plots, all using some kind of transformation, including some
suggested by Aitchison.<<

Interesting. I look forward to seeing these, as reading a triangle plot
is difficult and often misleading, because the metric is so far from
Euclidean. 


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