R: Robust and classical variation matrix

variation {robCompositions} | R Documentation

## Robust and classical variation matrix

### Description

Estimates the variation matrix with robust methods.

### Usage

    variation(x, method = "robustPivot")

### Arguments

`x` | data frame or matrix with positive entries
`method` | method used for estimating covariances. See details.

### Details

The variation matrix is estimated for a given compositional data set. Instead of using the classical standard deviations the miniminm covariance estimator is used (`covMcd`) is used when parameter robust is set to TRUE.

For method `robustPivot` forumala 5.8. of the book (see second reference) is used. Here robust (mcd-based) covariance estimation is done on pivot coordinates. Method `robustPairwise` uses a mcd covariance estimation on pairwise log-ratios. Methods `Pivot` (see second reference) and `Pairwise` (see first reference) are the non-robust counterparts. Naturally, `Pivot` and `Pairwise` gives the same results, but the computational time is much less for method `Pairwise`.

### Value

The (robust) variation matrix.

### Author(s)

Karel Hron, Matthias Templ

### References

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

#' Filzmoser, P., Hron, K., Templ, M. (2018) Applied Compositional Data Analysis. Springer, Cham.

### Examples

    data(expenditures)
    variation(expenditures) # default is method "robustPivot"
    variation(expenditures, method = "Pivot")
    variation(expenditures, method = "robustPairwise")
    variation(expenditures, method = "Pairwise") # same results as Pivot

[Package robCompositions version 2.3.1 Index]