clr | R Documentation |
Compute the centered log ratio transform of a (dataset of) composition(s) and its inverse.
clr( x,... )
clrInv( z,..., orig=gsi.orig(z) )
x |
a composition or a data matrix of compositions, not necessarily closed |
z |
the clr-transform of a composition or a data matrix of clr-transforms of compositions, not necessarily centered (i.e. summing up to zero) |
... |
for generic use only |
orig |
a compositional object which should be mimicked by the inverse transformation. It is especially used to reconstruct the names of the parts. |
The clr-transform maps a composition in the D-part Aitchison-simplex
isometrically to a D-dimensonal euclidian vector subspace: consequently, the
transformation is not injective. Thus resulting covariance matrices
are always singular.
The data can then
be analysed in this transformation by all classical multivariate
analysis tools not relying on a full rank of the covariance. See
ilr
and alr
for alternatives. The
interpretation of the results is relatively easy since the relation between each original
part and a transformed variable is preserved.
The centered logratio transform is given by
clr(x) := \left(\ln x_i - \frac1D \sum_{j=1}^D \ln x_j\right)_i
The image of the clr
is a vector with entries
summing to 0. This hyperplane is also called the clr-plane.
clr
gives the centered log ratio transform,
clrInv
gives closed compositions with the given clr-transform
K.Gerald v.d. Boogaart http://www.stat.boogaart.de
Aitchison, J. (1986) The Statistical Analysis of Compositional Data, Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.
ilr
,alr
,apt
(tmp <- clr(c(1,2,3)))
clrInv(tmp)
clrInv(tmp) - clo(c(1,2,3)) # 0
data(Hydrochem)
cdata <- Hydrochem[,6:19]
pairs(clr(cdata),pch=".")
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.