R: Variation matrices of amounts and compositions

variation {compositions} | R Documentation

## 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))

[Package compositions version 2.0-4 Index]