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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. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: RE: RE: Re: Compositional data***From:*"Clive Nicholas" <clivelists@googlemail.com>

**st: RE: RE: RE: RE: Re: Compositional data***From:*"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>

**References**:**st: RE: Re: Compositional data***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**st: RE: RE: Re: Compositional data***From:*"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>

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