Centred Log-Ratio (clr) transformation
Undertakes a centred log-ratio transformation to remove the effects of closure in a data matrix.
clr(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. A centred log-ratio is one procedure for removing closure effects, others are additive log-ratios (alr) and isometric log-ratios (ilr).
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 clr transform is suitable for the study of correlation coefficients and subsequent multivariate data analyses. However, for the calculation of Mahalanobis distances, which require matrix inversion, ilr should be used. Furthermore, in some cases it is preferable to use an ilr transform prior to undertaking a Principal Component or Factor Analysis, however, a clr transform is often sufficient.
The ifclose option can be useful if a petrochemical ternary system is under investigation. A data subset for a ternary system may be closed and transformed for investigation in x-y plots and comparison with the inferences that may be drawn from a classical ternary diagram display. Ternary plots are not included in this release of 'rgr', their use is discouraged as they do not reveal the true inter-component relationships. However, their use as classification tools is acknowledged where a user's data may be compared to data for known rock types and processes, etc. R users interested in ternary and classification diagrams rather than exploratory data analysis should investigate GCDkit (ver 2.3, R 2.7.0 2008/05/11) by Janousek, Farrow, Erban and Smid. See also Janousek et al. (2006).
Robert G. Garrett
Aitchison, J., 1984. The statistical analysis of geochemical compositions. Mathematical Geology, 16(6):531-564.
Aitchison, J., 1986. The Statistical Analysis of Compositional data. Chapman and Hall, London, U.K., 416 p.
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.
Janousek, V., Farrow, C.M. and Erban, V., 2006. Interpretation of whole-rock geochemical data in igneous geochemistry introducing Geochemical Data Toolkit (GCDkit). Journal of Petrology, 47(6):1255-1259.
Reimann, C., Filzmoser, P., Garrett, R. and Dutter, R., 2008. Statistical Data Analysis Explained: Applied Environmental Statistics with R. Wiley, 362 p.
## Make test data available data(sind) sind.mat <- as.matrix(sind[, -c(1:3)]) ## Undertake clr transform, note necessity ## of converting percent Fe to mg/kg sind.mat[, 2] <- sind.mat[, 2] * 10000 temp <- clr(sind.mat) temp ## Clean-up and detach test data rm(sind.mat) rm(temp)
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