Compositional data analysis in geo-environmental sciences

J. J. Egozcue; V. Pawlowsky-Glahn

doi:10.21701/bolgeomin.122.4.002

Autores/as

J. J. Egozcue Dep. Matemática Aplicada III, Universidad Politécnica de Cataluña
V. Pawlowsky-Glahn Dep. Informática y Matemática Aplicada, Universidad de Girona

DOI:

https://doi.org/10.21701/bolgeomin.122.4.002

Palabras clave:

biplot, correlación espuria, dendrograma, geometría de Aitchison, símplex

Resumen

Los datos composicionales (concentraciones) son frecuentes en geociencias. No tener en cuenta el carácter composicional puede llevar a conclusiones erróneas. La correlación espuria (K. Pearson, 1897) tiene consecuencias devastadoras. Partiendo de los trabajos de J. Aitchison en los años 80, surge una metodología libre de estos inconvenientes. La geometría del símplex permite representar composiciones en coordenadas ortogonales, pudiendo aplicarse métodos estadísticos usuales. Facilita la computación y el análisis. El uso de (log) cocientes evita la interpretación individual de concentraciones desatendiendo su carácter relativo. Se ilustra con un conjunto de análisis hidro-químicos.

Descargas

Los datos de descargas todavía no están disponibles.

Citas

Aitchison, J. 1982. The statistical analysis of compositional data (with discussion). Journal of the Royal Statistical Society, Series B (Statistical Methodology), 44(2), 139-177. https://doi.org/10.1111/j.2517-6161.1982.tb01195.x

Aitchison, J. 1986. The Statistical Analysis of Compositional Data. Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). (Reprinted in 2003 with additional material by The Blackburn Press). 416 p.

Aitchison, J. 1997. The one-hour course in compositional data analysis or compositional data analysis is simple. In V. Pawlowsky-Glahn (Ed.), Proceedings of IAMG'97 - The third annual conference of the International Association for Mathematical Geology, Volume I, II and addendum, pp. 3-35. International Center for Numerical Methods in Engineering (CIMNE), Barcelona (E), 1100 p.

Aitchison, J., Barceló-Vidal, C., Egozcue, J.J. and Pawlowsky-Glahn, V. 2002. A concise guide for the algebraic-geometric structure of the simplex, the sample space for compositional data analysis. In U. Bayer, H. Burger, and W. Skala (Eds.), Proceedings of IAMG'02 - The eighth annual conference of the International Association for Mathematical Geology, Volume I and II, pp. 387-392. Selbstverlag der Alfred-Wegener-Stiftung, Berlin, 1106 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. https://doi.org/10.1007/s11004-005-7383-7

Aitchison, J. and Greenacre, M. 2002. Biplots for compositional data. Journal of the Royal Statistical Society, Series C (Applied Statistics), 51(4), 375-392. https://doi.org/10.1111/1467-9876.00275

Aitchison, J. and Shen, S.M. 1980. Logistic-normal distributions. Some properties and uses. Biometrika, 67(2), 261-272. https://doi.org/10.1093/biomet/67.2.261

Barceló-Vidal, C., Martín-Fernández, J.A. and Pawlowsky-Glahn, V. 2001. Mathematical foundations of compositional data analysis. In G. Ross (Ed.), Proceedings of IAMG'01 - The sixth annual conference of the International Association for Mathematical Geology, pp. 20 p. CD-ROM.

Billheimer, D., Guttorp, P. and Fagan, W.F. 2001. Statistical interpretation of species composition. Journal of the American Statistical Association, 96(456), 1205-1214. https://doi.org/10.1198/016214501753381850

Chayes, F. 1960. On correlation between variables of constant sum. Journal of Geophysical Research, 65(12), 4185-4193. https://doi.org/10.1029/JZ065i012p04185

Egozcue, J. and Pawlowsky-Glahn, V. 2006a. Exploring compositional data with the coda-dendrogram. In E. Pirard (Ed.), Proceedings of IAMG'06 - The eleventh annual conference of the International Association for Mathematical Geology.

Egozcue, J. and Pawlowsky-Glahn, V. 2006b. Simplicial geometry for compositional data. Special Publications Volume 264. Geological Society, London. https://doi.org/10.1144/GSL.SP.2006.264.01.11

Egozcue, J.J. 2009. Reply to "On the Harker variation diagrams; ..." by J. A. Cortés. Mathematical Geosciences, 41(7), 829-834. https://doi.org/10.1007/s11004-009-9238-0

Egozcue, J.J. and Pawlowsky-Glahn, V. 2005. Groups of parts and their balances in compositional data analysis. Mathematical Geology, 37(7), 795-828. https://doi.org/10.1007/s11004-005-7381-9

Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G. and Barceló-Vidal, C. 2003. Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3), 279-300. https://doi.org/10.1023/A:1023818214614

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

Moeller, P., Weise, S.M., Tesmer, M., Dulsky, P., Pekdeger, A., Bayer, U. and Magri, F. 2008. Salinization of groundwater in the North German Basin: results from conjoint investigation of major, trace element and multi-isotope distribution. Int. J. Earth Sci. 97, 1057-1073. https://doi.org/10.1007/s00531-007-0211-1

Pawlowsky-Glahn, V. and Egozcue, J.J. 2001. Geometric approach to statistical analysis on the simplex. Stochastic Environmental Research and Risk Assessment 15(5), 384-398. https://doi.org/10.1007/s004770100077

Pawlowsky-Glahn, V. and Egozcue, J.J. 2002. BLU estimators and compositional data. Mathematical Geology 34(3), 259-274. https://doi.org/10.1023/A:1014890722372

Pearson, K. 1897. Mathematical contributions to the theory of evolution. on a form of spurious correlation which may arise when indices are used in the measurement of organs. Proceedings of the Royal Society of London, LX, 489-502. https://doi.org/10.1098/rspl.1896.0076

Thió-Henestrosa, S., Egozcue, J.J., Pawlowsky-Glahn, V., Kovàcs, L.O. and Kovàcs, G.P. 2008. Balance-dendrogram. A new routine of CoDaPack. Computers and Geosciences, 34, 1682-1696. https://doi.org/10.1016/j.cageo.2007.06.011