R: Pivot coordinates and their inverse

pivotCoord {robCompositions} | R Documentation

## Pivot coordinates and their inverse

### Description

Isometric log-ratio transformations and it's inverse transformation with a special choice of balances.

### Usage

    pivotCoord(x, pivotvar = 1, fast = FALSE, method = "pivot",
      base = exp(1), norm = "orthonormal")

    isomLR(x, fast = FALSE, base = exp(1), norm = "sqrt((D-i)/(D-i+1))")

    isomLRinv(x)

    pivotCoordInv(x, norm = "orthonormal")

    isomLRp(x, fast = FALSE, base = exp(1), norm = "sqrt((D-i)/(D-i+1))")

    isomLRinvp(x)

### Arguments

`x` | object of class data.frame or matrix. Positive values only.
`pivotvar` | pivotal variable. If any other number than 1, the data are resorted in that sense that the pivotvar is shifted to the first part.
`fast` | if TRUE, it is approx. 10 times faster but numerical problems in case of high-dimensional data numerical instabilities may occur. Only available for method “pivot”.
`method` | pivot takes the method described in the description. Method "symm" uses symmetric balances (parameters pivotvar and norm have then no effect)
`base` | a positive or complex number: the base with respect to which logarithms are computed. Defaults to `exp(1)`.
`norm` | if FALSE then the normalizing constant is not used, if TRUE `sqrt((D-i)/(D-i+1))` is used (default). The user can also specify a self-defined constant.

### Details

This transformation moves D-part compositional data from the simplex into a (D-1)-dimensional real space isometrically. From our choice of (pivot) balances, all the relative information of one part is seperated from the remaining parts.

### Value

The data represented in pivot coordinates

### Author(s)

Matthias Templ, Karel Hron, Peter Filzmoser

### References

Egozcue J.J., V. Pawlowsky-Glahn, G. Mateu-Figueras and C. Barcel'o-Vidal (2003) Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3) 279-300. \

Hron, K. and Templ, M. and Filzmoser, P. (2010) Imputation of missing values for compositional data using classical and robust methods

Kynclova, P., Hron, K., Filzmoser, P. Correlation between compositional parts based on symmetric balances. Submitted to Mathematical Geosciences. Computational Statistics and Data Analysis, vol 54 (12), pages 3095-3107.

### Examples

    require(MASS)
    Sigma <- matrix(c(5.05,4.95,4.95,5.05), ncol=2, byrow=TRUE)
    z <- pivotCoordInv(mvrnorm(100, mu=c(0,2), Sigma=Sigma))

    data(expenditures)
    ## first variable as pivot variable
    pivotCoord(expenditures)
    ## third variable as pivot variable
    pivotCoord(expenditures, 3)

    x <- exp(mvrnorm(2000, mu=rep(1,10), diag(10)))
    system.time(pivotCoord(x))
    system.time(pivotCoord(x, fast=TRUE))

    ## without normalizing constant
    pivotCoord(expenditures, norm = "orthogonal") # or:
    pivotCoord(expenditures, norm = "1")
    ## other normalization
    pivotCoord(expenditures, norm = "-sqrt((D-i)/(D-i+1))")

    # symmetric balances (results in 2-dim symmetric balances)
    pivotCoord(expenditures, method = "symm")

[Package robCompositions version 2.0.6 Index]