rgr (version 1.1.0)

ilr: Isometric Log-Ratio (ilr) transformation

Description

Undertakes an isometric log-ratio transformation to remove the effects of closure in a data matrix.

Usage

ilr(xx, ifclose = FALSE, ifwarn = TRUE)

Arguments

xx

a n by p matrix to be isometrically log-ratio transformed. It is essential that a single unit of measurement is used. Thus it may be required to convert, for example, determinations in percent to ppm (mg/kg) so that all measurements are in ppm prior to

ifclose

if it is required to close a data set prior to transformation set ifclose = TRUE.

ifwarn

by default ifwarn = TRUE which generates a reminder/warning that when carrying out a centred log-ratio transformation all the data must be in the same measurement units. The message can be suppressed by setting ifwarn = FALSE.

Value

• x
  a n by (p-1) matrix of isometric log-ratio values. The names of the new (p-1) synthetic variables, iso1 through to isop, are entered as column names in the matrix.

Details

Most analytical chemical data for major, minor and trace elements are of a closed form, i.e. for a sample they sum to a constant, whether it be percent, ppm (mg/kg), or some other units. It does not matter that only some components contributing to the constant sum are present in the matrix, the data are closed. As a result, as some elements increase in concentration others must decrease, this leads to correlation measures and graphical presentations that do not reflect the true underlying relationships. However, isometrically transformed data are not suitable for univariate EDA inspection as the new synthetic variables bear a complex relationship to the original measurements. Other procedures for removing closure effects are arithmetic log-ratios (alr) and centred log-ratios (clr).

References

Aitchison, J. and Egozcue, J.J., 2005. Compositional data analysis; where are we and where should we be heading. Mathematical Geology, 37(7):829-850. Buccianti, A., Mateu-Figueras, G, and Pawlowsky-Glahn, V. (eds.), 2006. Compositional data analysis in the geosciences: from theory to practice. The Geological Society Publishing House, Bath, U.K. Special Publication 264, 224 p. Filzmoser, P. and Hron, K., 2008. Outlier detection for compositional data using robust methods. Mathematical Geosciences, 40(3):234-248. Filzmoser, P., Hron, K. and Reimann, C., 2009. Principal component analysis for compositional data with outliers. Environmetrics, 20(6):621-633. Filzmoser, P., Hron, K., Reimann, C. and Garrett, R.G., 2009. Robust factor analysis for compositional data. Computers & Geosciences, 35(9):1854-1861.

See Also

alr, clr, ltdl.fix.df, remove.na

Examples

## Make test data sind available
data(sind)
sind.mat <- as.matrix(sind[, -c(1:3)])

## Undertake ilr transform, note necessity
## of converting percent Fe to mg/kg
sind.mat[, 2] <- sind.mat[, 2] * 10000
temp <- ilr(sind.mat)
temp

## Clean-up and detach test data
rm(sind.mat)
rm(temp)