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

1 |

`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 `NA`

s 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.

`clr`

, `ilr`

, `ltdl.fix.df`

, `remove.na`

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