Multivariate proportional response data
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