Isometric Log-Ratio (ilr) transformation
Undertakes an isometric log-ratio transformation to remove the effects of closure in a data matrix.
ilr(xx, ifclose = FALSE, ifwarn = TRUE)
xx |
a |
ifclose |
if it is required to close a data set prior to transformation set |
ifwarn |
by default |
Most analytical chemical data for major, minor and trace elements are of a closed form, i.e. for a physical individual 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 matrices are not suitable for univariate EDA inspection as the new synthetic variables bear a complex relationship to the original measurements. For univariate studies use function gx.ilr, and for bivariate studies use gx.symm.coords Other procedures for removing closure effects are additive log-ratios (alr) and centred log-ratios (clr).
x |
a |
Any less than detection limit values represented by negative values, or zeros or other numeric codes representing blanks in the data, must be removed prior to executing this function, see ltdl.fix.df.
Any rows containing NAs in the data matrix are removed prior to undertaking the transformation.
The ilr transform is recommended for the calculation of Mahalanobis distances, a procedure which requires matrix inversion. When a Principal Component or Factor Analysis is required use of the ilr transform may be preferrable, see also the notes in clr. In that instance back transformation from the isometrically transformed variables to the original variables is required. Interested R users should refer to the papers by Filzmoser et al. (see below).
Peter Filzmoser and Karel Hron, with additions by Robert G. Garrett
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.
## Make test data sind available data(sind.mat2open) ## Undertake ilr transform temp <- ilr(sind.mat2open) temp ## Clean-up rm(temp)
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