variation | R Documentation |

Estimates the variation matrix with robust methods.

```
variation(x, method = "robustPivot", algorithm = "MCD")
```

`x` |
data frame or matrix with positive entries |

`method` |
method used for estimating covariances. See details. |

`algorithm` |
kind of robust estimator (MCD or MM) |

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`

.

The (robust) variation matrix.

Karel Hron, Matthias Templ

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

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

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

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