summary.acomp {compositions} R Documentation

## Summarizing a compositional dataset in terms of ratios

### Description

Summaries in terms of compositions are quite different from classical ones. Instead of analysing each variable individually, we must analyse each pair-wise ratio in a log geometry.

### Usage

          ## S3 method for class 'acomp'
summary( object, ... ,robust=getOption("robust"))


### Arguments

 object a data matrix of compositions, not necessarily closed ... not used, only here for generics robust A robustness description. See robustnessInCompositions for details. The parameter can be null for avoiding any estimation.

### Details

It is quite difficult to summarize a composition in a consistent and interpretable way. We tried to provide such a summary here, based on the idea of the variation matrix.

### Value

The result is an object of type "summary.acomp"

 mean the mean.acomp composition mean.ratio a matrix containing the geometric mean of the pairwise ratios variation the variation matrix of the dataset ({variation.acomp}) expsd a matrix containing the one-sigma factor for each ratio, computed as exp(sqrt(variation.acomp(W))). To obtain a two-sigma-factor, one has to take its squared value (power 1.96, actually). invexpsd the inverse of the preceding one, giving the reverse bound. Additionally, it can be "almost" intepreted as a correlation coefficient, with values near one indicating high proportionality between the components. min a matrix containing the minimum of each of the pairwise ratios q1 a matrix containing the 1-Quartile of each of the pairwise ratios median a matrix containing the median of each of the pairwise ratios q1 a matrix containing the 3-Quartile of each of the pairwise ratios max a matrix containing the maximum of each of the pairwise ratios

### Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de, R. Tolosana-Delgado

### References

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

acomp
data(SimulatedAmounts)