mixtures as outcome variables

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