clr {compositions} R Documentation

## Centered log ratio transform

### Description

Compute the centered log ratio transform of a (dataset of) composition(s) and its inverse.

### Usage

          clr( x,... )
clrInv( z,..., orig=gsi.orig(z) )


### Arguments

 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.

### Details

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.

### Value

clr gives the centered log ratio transform, clrInv gives closed compositions with the given clr-transform

### Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

### References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data, Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

ilr,alr,apt

### Examples

(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=".")


[Package compositions version 2.0-8 Index]