Compositional techniques to deal with concentrations below the detection limit in geochemistry
DOI:
https://doi.org/10.21701/bolgeomin.122.4.004Keywords:
imputation, log-ratio, percentages, simplex, ternary diagramAbstract
In most geochemical analyses log-ratio techniques are required to analyse compositional data sets. When a chemical element is present at a low concentration it is usually identified as a value below the detection limit and added to the data set either as zero or simply by attaching a less-than label. In any case, the ocurrence of such concentrations prevents us from applying the log-ratio approach. We review here the theoretical bases of the most recent proposals for dealing with these types of observation, give some advice on their practical application and illustrate their performance through some examples using geochemical data.
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References
Aitchison, J. 1986. The statistical analysis of compositional data. London, Chapman and Hall Ltd https://doi.org/10.1007/978-94-009-4109-0
reprinted in 2003 at Caldwell, NJ: Blackburn Press, 416 pp.
Aitchison, J. and Kay, J. 2003. Possible solution of some essential zero problems in compositional data analysis. En: Proceedings of CoDaWork'03, The 1st Compositional Data Analysis Workshop, Thió-Henestrosa, S. and J.A. Martín-Fernández (Eds.), Universitat de Girona, CD-ROM (ISBN 84-8458-111-X, http://ima.udg.es/Activitats/CoDaWork03/), October 15-17, 6 pp.
Bacon-Shone, J. 2008. Discrete and continuous compositions. In: Proceedings of CoDaWork'08, The 3rd Compo-sitional Data Analysis Workshop, Daunis-i-Estadella, J. and J. A. Martín-Fernández (eds.), Universitat de Girona, CD-ROM (ISBN 84-8458-272-4, http://ima.udg.es/Activitats/CoDaWork08/), May 27-30, 11 pp.
Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G. y Barceló-Vidal, C. 2003. Isometric log-ratio transformations for compositional data analysis. Mathematical Geology 35(3), 279-300. https://doi.org/10.1023/A:1023818214614
Little, R. J. A. y Rubin, D. B. 2002. Statistical Analysis with Missing Data (2nd ed.). John Wiley and Sons, New York (USA). 381 pp. https://doi.org/10.1002/9781119013563
Martín-Fernández, J.A., Barceló-Vidal, C. and Pawlowsky-Glahn, V. 2003. Dealing with zeros and missing values in compositional data sets using nonparametric imputation. Mathematical Geology 35(3), 253-278. https://doi.org/10.1023/A:1023866030544
Martín-Fernández, J.A., Palarea-Albaladejo, J. and Olea, R.A. 2011. Dealing with Zeros. In: Pawlowsky, V. and Buccianti, A. (eds) Compositional Data Analysis: Theory and Applications. Chichester (UK), John Wiley & Sons. Chapter 4, 43-58. https://doi.org/10.1002/9781119976462.ch4
Martín-Fernández, J. A. and Thió-Henestrosa, S. 2006. Rounded zeros: some practical aspects for compositional data. In: A. Buccianti, G. Mateu-Figueras and V. Pawlowsky-Glahn (eds.), Compositional data analysis from theory to practice. London: The Geological Society, Special Publications 264, 191-201. https://doi.org/10.1144/GSL.SP.2006.264.01.14
Ó.Kovács, L. and Kovács, G.P. 2001. Petrochemical database of the Cenozoic volcanites in Hungary: structure and statistics. Acta Geologica Hungarica 44 (4), 381-417.
Palarea-Albaladejo, J., Martín-Fernández, J.A. and Gómez-García, J. 2007. A parametric approach for dealing with compositional rounded zeros. Mathematical Geology 39(7), 625-645. https://doi.org/10.1007/s11004-007-9100-1
Palarea-Albaladejo, J. and Martín-Fernández, J. A. 2008. A modified EM alr-algorithm for replacing rounded zeros in compositional data sets. Computer&Geosciences 34(8), 902-917. https://doi.org/10.1016/j.cageo.2007.09.015
Pierotti, M.E.R., Martín-Fernández, J.A. y Seehausen, O. 2009. A mapping individual variation in male mating preference space: multiple choice in a colour polymorphic cichlid fish. Evolution 63 (9), 2372-2388. https://doi.org/10.1111/j.1558-5646.2009.00716.x
Walley, P. 1996. Inferences from multinomial data: learning about a bag of marbles (with discussion). Journal Royal Statistical Society B 58, 3-57. https://doi.org/10.1111/j.2517-6161.1996.tb02065.x
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Funding data
Ministerio de Ciencia e Innovación
Grant numbers MTM2009-13272
Agència de Gestió d'Ajuts Universitaris i de Recerca
Grant numbers 2009SGR424
