Message-ID: <050248A7-9CB7-4080-AEA5-420798CB719A@noaa.gov>
Date: 2009-05-01T16:53:28Z
From: Devin Johnson
Subject: Multivariate proportional response data
In-Reply-To: <1241172882.6476.337.camel@clarinet>
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