# balances: Balance calculation In robCompositions: Compositional Data Analysis

## Description

Given a D-dimensional compositional data set and a sequential binary partition, the function bal calculates the balances in order to express the given data in the (D-1)-dimensional real space.

## Usage

 `1` ```balances(x, y) ```

## Arguments

 `x` data frame or matrix, typically compositional data `y` binary partition

## Details

The sequential binary partition constructs an orthonormal basis in the (D-1)-dimensional hyperplane in real space, resulting in orthonormal coordinates with respect to the Aitchison geometry of compositional data.

## Value

 `balances` The balances represent orthonormal coordinates which allow an interpretation in sense of groups of compositional parts. Output is a matrix, the D-1 colums contain balance coordinates of the observations in the rows. `V` A Dx(D-1) contrast matrix associated with the orthonormal basis, corresponding to the sequential binary partition (in clr coefficients).

## Author(s)

Veronika Pintar, Karel Hron, Matthias Templ

## References

(Egozcue, J.J., Pawlowsky-Glahn, V. (2005) Groups of parts and their balances in compositional data analysis. Mathematical Geology, 37 (7), 795???828.)

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```data(expenditures, package = "robCompositions") y1 <- data.frame(c(1,1,1,-1,-1),c(1,-1,-1,0,0), c(0,+1,-1,0,0),c(0,0,0,+1,-1)) y2 <- data.frame(c(1,-1,1,-1,-1),c(1,0,-1,0,0), c(1,-1,1,-1,1),c(0,-1,0,1,0)) y3 <- data.frame(c(1,1,1,1,-1),c(-1,-1,-1,+1,0), c(-1,-1,+1,0,0),c(-1,1,0,0,0)) y4 <- data.frame(c(1,1,1,-1,-1),c(0,0,0,-1,1), c(-1,-1,+1,0,0),c(-1,1,0,0,0)) y5 <- data.frame(c(1,1,1,-1,-1),c(-1,-1,+1,0,0), c(0,0,0,-1,1),c(-1,1,0,0,0)) b1 <- balances(expenditures, y1) b2 <- balances(expenditures, y5) b1\$balances b2\$balances data(machineOperators) sbp <- data.frame(c(1,1,-1,-1),c(-1,+1,0,0), c(0,0,+1,-1)) balances(machineOperators, sbp) ```

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