# variation: Robust and classical variation matrix In robCompositions: Compositional Data Analysis

## Description

Estimates the variation matrix with robust methods.

## Usage

 `1` ```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

 ```1 2 3 4 5``` ```data(expenditures) variation(expenditures) # default is method "robustPivot" variation(expenditures, method = "Pivot") variation(expenditures, method = "robustPairwise") variation(expenditures, method = "Pairwise") # same results as Pivot ```

robCompositions documentation built on Jan. 13, 2021, 10:07 p.m.