[R-sig-eco] Multivariate proportional response data

Devin Johnson Devin.Johnson at noaa.gov
Fri May 1 18:53:28 CEST 2009


Roy,
You have compositional data. Check out any references by John  
Aitchison. He has a book "The Statistical Analysis of Compositional  
Data" and a host of journal articles. The main approach is to use a  
multivariate logit transform
[y1,...y_{k-1}] = [log(x1/x_k),...,log(x_{k-1}/x_k)]
where [x_1,...,x_k] is your "sum-to-one" composition. Then analyze  
[y_1,...,y_{k-1}] using multivatiate linear models.

--Devin


On May 1, 2009, at 3:14 AM, Roy Sanderson wrote:

> Hello All
>
> I have been given a set of proportion data, that consists of three
> variables that sum to 1.0 that are the response, with two explanatory
> variables (one the day of the experiment, 1 to 30, the other a two- 
> level
> treatment factor).
>
> Given that the three response variables are non-independent, what is  
> the
> best approach to analysing them?  I'm reluctant to arcsine them, and
> analyse each one independently and the raw data are not available,  
> only
> the proportions.  Presumably some sort of multinomial technique  
> might be
> appropriate?
>
> Many thanks for any hints.
>
> Roy
>
> -- 
> Roy Sanderson
> School of Biology
> Devonshire Building
> Newcastle University
> Newcastle upon Tyne NE1 7RU
> r.a.sanderson at newcastle.ac.uk
> 0191 246 4835
>
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----------------------------------------------------------
Devin S. Johnson, Ph.D.
Statistician
NOAA National Marine Mammal Laboratory
7600 Sand Point Way NE
Seattle, WA 98115
Phone: (206) 526-6867
Fax: (206) 526-6115
Email: devin.johnson at noaa.gov



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