[R] mixtures as outcome variables

[James Reilly]

A collection of functions for compositional data analysis were posted on 
the S-news mailing list about a year ago.

Basic Compositional Data Analysis functions for S+/R
http://www.biostat.wustl.edu/archives/html/s-news/2003-12/msg00139.html

James

> Date: Thu, 24 Mar 2005 20:28:51 -0400 
> From: Kjetil Brinchmann Halvorsen <kjetil at acelerate.com> 
> Subject: Re: [R] mixtures as outcome variables 
> Cc: r-help at stat.math.ethz.ch, "Jason W. Martinez" <jmartinez5 at verizon.net> 
> 
> Kjetil Brinchmann Halvorsen wrote:
> 
>>> Jason W. Martinez wrote:
>>>
>>
>>>>> Dear R-users,
>>>>>
>>>>> I have an outcome variable and I'm unsure about how to treat it. Any
>>>>> advice?
>>>>>
>>
>>> If you only concentrate on the relative proportions, this are called 
>>> compositional data. I f your data are in
>>> mydata (n x 4), you obtain compositions by
>>> sweep(mydata, 1, apply(mydata, 1, sum), "/")
>>>
>>> There are not (AFAIK) specific functions/packages for R for 
>>> compositional data AFAIK, but you
>>> can try googling. Aitchison  has a monography (Chapman & Hall) and a 
>>> paper in JRSS B.
>>>
>>> One way to start might be lm's or anova on the symmetric logratio 
>>> transform of the
>>> compositons. The R function lm can take a multivariate response, but 
>>> some extra programming will be needed
>>> for interpretation. With simulated data:
>>>
>>
>>>> > slr
>>
>>> function(y) { # y should sum to 1
>>>          v <- log(y)
>>>          return( v - mean(v) ) }
>>
>>>> > testdata <- matrix( rgamma(120, 2,3), 30, 4)
>>>> > str(testdata)
>>
>>> num [1:30, 1:4] 0.200 0.414 0.311 2.145 0.233 ...
>>
>>>> > comp <- sweep(testdata, 1, apply(testdata,1,sum), "/")
>>
>>> # To get the symmetric logratio transform:
>>> comp <- t(apply(comp, 1, slr))
>>> # Observe:
>>> apply(cov(comp), 1, sum)
>>> [1] -5.551115e-17  2.775558e-17  5.551115e-17 -2.775558e-17
>>
>>>> > lm( comp ~ 1)
>>
>>>
>>> Call:
>>> lm(formula = comp ~ 1)
>>>
>>> Coefficients:
>>>             [,1]      [,2]      [,3]      [,4]   (Intercept)   
>>> 0.17606   0.06165  -0.03783  -0.19988
> 
> 
> Followup:
> 
>  > mmod <- manova(comp ~ x)
>  > summary(mmod)
> Error in summary.manova(mmod) : residuals have rank 3 < 4
>  >
> 
> So the manova() function cannot be used. I guess MANOVA for 
> compositional data should be
> a straight extension, but it must be programmed , standard manova cannot 
> be used.
> 
> Kjetil
> 
> -- Kjetil Halvorsen. Peace is the most effective weapon of mass construction. -- Mahdi Elmandjra