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From |
"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: RE: RE: RE: Re: Compositional data |

Date |
Wed, 5 Mar 2008 16:35:42 -0500 |

Nick Cox wrote >>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.<< The issue is that the Euclidean distance between points in a triangle plot doesn't say what most people think it says in analogy to an ordinary scatterplot. That's all I meant. >>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. << The fact that compositional data are dependent due to the sum constraint makes them strange. Unordered choice data has the exact same problem. Aitchison provides some ways of dealing with the issue, but only at the expense of having to look at nasty things like log-ratios. As an aside, why did you guys kick out simplex corner observations in the Dirichlet model? These are perfectly valid observations, indeed quite possibly very informative ones since they say "I spent all my budget on X". A boundary point is a pain because the likelihood is undefined there, but the procedure described in one of Tim Fry's articles (Fry, et al, Modelling Zeroes in Microdata, Applied Economics, 2000, 33, 383-392) avoids the problem and preserves subcompositional invariance. Jay * * 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: Re: Compositional data***From:*Maarten buis <maartenbuis@yahoo.co.uk>

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

**Re: st: RE: RE: RE: RE: Re: Compositional data***From:*Maarten buis <maartenbuis@yahoo.co.uk>

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

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