robCompositions (version 2.4.1)

balances: 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)

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).

Arguments

x

data frame or matrix, typically compositional data

y

binary partition

Author

Veronika Pintar, Karel Hron, Matthias Templ

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.

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)