The canonical basis in the clr plane used for ilr and ipt transforms.

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Description

Compute the basis of a clr-plane, to use with isometric log-ratio or planar transform of a (dataset of) compositions.

Usage

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          ilrBase( x=NULL , z=NULL , D = NULL, method = "basic" )

          

Arguments

x

optional dataset or vector of compositions

z

optional dataset or vector containing ilr or ipt coordinates

D

number of parts of the simplex

method

method to build the basis, one of "basic", "balanced", "optimal" "PBhclust", "PBmaxvar" or "PBangprox"

Details

Method "basic" computes a triangular Helmert matrix (corresponding to the original ilr transformation defined by Egozcue et al, 2003). In this case, ilrBase is a wrapper catching the answers of gsi.ilrBase and is to be used as the more convenient function.

Method "balanced" returns an ilr matrix associated with a balanced partition, splitting the parts in groups as equal as possible. Transforms ilr and ipt computed with this basis are less affected by any component (as happens with "basic").

The following methods are all data-driven and will fail if x is not given. Some of these methods are extended to non-acomp datasets via the cpt general functionality. Use with care with non-acomp objects!

Method "optimal" is a wrapper to gsi.optimalilrBase, providing the ilr basis with less influence of missing values. It is computed as a hierarchical cluster of variables, with parts previously transformed to 1 (if the value is lost) or 0 (if it is recorded).

Methods "PBhclust", "PBmaxvar" and "PBangprox" are principal balance methods (i.e. balances approximating principal components in different ways). These are all resolved by calls to gsi.PrinBal. Principal balances functionality should be considered beta!

Value

All methods give a matrix containing by columns the basis elements for the canonical basis of the clr-plane used for the ilr and ipt transform. Only one of the arguments x, z or D is needed to determine the dimension of the simplex.

References

Egozcue J.J., V. Pawlowsky-Glahn, G. Mateu-Figueras and C. Barcel'o-Vidal (2003) Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3) 279-300

http://ima.udg.es/Activitats/CoDaWork03

See Also

clr,ilr,ipt

Examples

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ilr(c(1,2,3))
ilrBase(D=2)
ilrBase(c(1,2,3))
ilrBase(z= ilr(c(1,2,3)) )
round(ilrBase(D=7),digits= 3)
ilrBase(D=7,method="basic")
ilrBase(D=7,method="balanced")

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