compositions (version 1.30-1)

summary.acomp: 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, \dots ,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.

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

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.

References

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

See Also

acomp

Examples

data(SimulatedAmounts)
summary(acomp(sa.lognormals))