balances {robCompositions}

Balance calculation

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

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

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)