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st: RE: Re: Compositional data


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Re: Compositional data
Date   Wed, 5 Mar 2008 20:41:20 -0000

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

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

A standard graphic for your 3-D response data is variously known as a 

triangle 
triangular
trilinear
triaxial
trinomial
ternary 
three-element 
mixture or 
barycentric

plot, chart, graph or diagram. A Stata implementation is in -triplot-
from SSC. 
Stata graphics freaks might note that it is really a scatter plot in
disguise. 

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. 

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

Verkuilen, Jay

>>I would like to estimate the following model:
i have n firms, each firm has a bundle of 3 products, characterized by
the different resource allocation for each product, measured in % which
sums up to 100%. That is, e.g.  firm 1 has 20% of production devoted to
product 1, 30% to product 2, etc., 100% in total. I would like to
explain the resource allocation choice by a firm.  Thus, the dependent
variable is actually 3 variables, which are continuous variables (% of
resources) and are interdependent.  

Which econometric model should I use and how to handle this in stata?
Thanks very much in advance, Regards, Elena<<

As Maarten noted, you have compositional data. Might I suggest looking
at the book by John Aitchison, Compositional Data Analysis (2003)? Also
Fry, J.M., Fry, T.R.L. and K.R. McLaren, (1996), "The Stochastic
Specification of Demand Share Equations: Restricting Budget Shares to
the Unit Simplex", Journal of Econometrics, 73, 377-385. 

The Dirichlet distribution is convenient but has a very restrictive
covariance structure, because it is fully determined by its marginals. 

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