variation {compositions}

Variation matrices of amounts and compositions

Description

Compute the variation matrix in the various approaches of compositional and amount data analysis. Pay attention that this is not computing the variance or covariance matrix!

Usage

    variation(x,...)
          ## S3 method for class 'acomp'
variation(x, ...,robust=getOption("robust"))
          ## S3 method for class 'rcomp'
variation(x, ...,robust=getOption("robust"))
          ## S3 method for class 'aplus'
variation(x, ...,robust=getOption("robust"))
          ## S3 method for class 'rplus'
variation(x, ...,robust=getOption("robust"))
          ## S3 method for class 'rmult'
variation(x, ...,robust=getOption("robust"))
          is.variation(M, tol=1e-10)
          

Arguments

x

a dataset, eventually of amounts or compositions

...

currently unused

robust

A description of a robust estimator. FALSE for the classical estimators. See robustnessInCompositions for further details.

M

a matrix, to check if it is a valid variation

tol

tolerance for the check

Details

The variation matrix was defined in the acomp context of analysis of compositions as the matrix of variances of all possible log-ratios among components (Aitchison, 1986). The generalization to rcomp objects is simply to reproduce the variance of all possible differences between components. The amount (aplus, rplus) and rmult objects should not be treated with variation matrices, because this was intended to skip the existence of a closure (which does not exist in the case of amounts).

Value

The variation matrix of x.

For is.variation, a boolean saying if the matrix satisfies the conditions to be a variation matrix.

Author(s)

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

See Also

cdt, clrvar2ilr, clo, mean.acomp, acomp, rcomp, aplus, rplus

Examples

data(SimulatedAmounts)
meanCol(sa.lognormals)
variation(acomp(sa.lognormals))
variation(rcomp(sa.lognormals))
variation(aplus(sa.lognormals))
variation(rplus(sa.lognormals))
variation(rmult(sa.lognormals))