COMPOSITIONAL DATA ANALYSIS: THE APPLIED GEOCHEMIST AND THE COMPOSITIONAL DATA ANALYST

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1 COMPOSITIONAL DATA ANALYSIS: THE APPLIED GEOCHEMIST AND THE COMPOSITIONAL DATA ANALYST Alecos Demetriades a, Antonella Buccianti b a Institute of Geology and Mineral Exploration, 1 Spirou Louis Street, Entrance C, Olympic Village, Acharnae, Athens, GR-13677, Hellas b Department of Earth Sciences, University of Florence, Via G. La Pira 4, Firenze (I), Italy Extended abstract Geochemical data are a classical example of compositional (closed) data (Aitchison, 1982, 1986, 1997), because they are reported as concentrations in units of weight per cent (wt%) or mg/kg or µg/kg (Reimann et al., 2008; Buccianti and Grunsky, 2014; Filzmoser et al., 2014a, b). If, for example, all naturally occurring chemical elements in a sample are analysed, the analytical results shall sum up to a constant (100 wt% or 1,000,000 mg/kg); this is the key idea that compositional data represent parts of some whole, and they only carry relative information. Hence, no single chemical element is free to vary separately from the rest of the total chemical composition of a geological sample. Although in practice, not all naturally occurring chemical elements in a natural sample are determined, the total element concentrations, nevertheless, still depend on each other. The relevant information for each element in a geochemical data set of a single sample lies, therefore, in the ratios between all elements determined, and not in the measured element concentrations as such. The above statements, because of their simplicity, are apparently understood by most applied geochemists. Mathematically oriented geochemists, such as Chayes (1960) showed that correlations among compositional variables do not necessarily reflect petrologic or geochemical, relationships because these variables must sum to a constant for each specimen (Miesch 1976a, p.a29). The following statements from Miesch (1976a, p.a32) are quite interesting: Extensions of the method of Q-mode analysis that may be applied to compositional data were given by Miesch (1976b, c), and a computer program for the extended method was given by Klovan and Miesch (1976). The extended method requires that the variables in the matrix of data sum to a constant for each sample, but compositional data generally have, or can be adjusted to have, this property. In most situations the variables sum to 100 percent or 10 6 ppm. It should be noted that Miesch (1990) had an option for ratio transformations prior to principal component and factor analysis, and Russian geochemists employed element ratios for mapping primary geochemical patterns (Beus and Grigorian, 1977). Although the compositional nature of geochemical data was definitely known well before Aitchison (1982, 1986), one may ask why has it taken so long for applied geochemists to start using compositional data analysis? In fact, very few applied geochemists used the R-factor program by Miesch (1990). Still many applied geochemists use classical 1

2 statistical parameters, such as the mean and standard deviation, while it is known that geochemical data do not follow the normal distribution, and they should use nonparametric statistics, such as the median and median absolute deviation, with Kürzl (1988) popularising the use of Tukey s (1977) exploratory data analysis in the statistical treatment of geochemical data, and more recently Reimann et al. (2008). Why this resistance to change? Of course, the mathematics behind compositional data analysis are beyond the background knowledge of the average applied geochemist, although routines are available in (i) R, an open source software, which can be freely downloaded from the CRAN server at and (ii) CoDaPack (Comas-Cufi and Thió- Henestrosa, 2011), which again can be freely downloaded from It is believed that this resistance to change is mainly because applied geochemists are satisfied with the conventional statistical procedures, and more recently exploratory data analysis, as both provide information, which is directly linked to concentration units (wt%, mg/kg, µg/kg). Their resistance in using compositional data (CoData) analysis is that the concentration units property is lost. This is probably the most important reason, because geochemical data are used not only by scientists, but also by policy makers for legislative purposes. The second possible reason is that professional applied geochemists are afraid to embark in the adventure of using compositional data analysis techniques, because they are not proficient in these methods, and they normally need the backing of a CoData statistician. The EuroGeoSurveys Geochemistry Expert Group is collaborating with Peter Filzmoser, (Institute for Statistics and Probability Theory, Vienna University of Technology), and for the first time centred logratio (clr)-transformed maps have been plotted for all determined variables of the European Agricultural and Grazing land soil project, known with the acronym GEMAS (Reimann et al., 2012, 2014). The maps of clr-transformed variables are interesting, when compared with the conventional geochemical maps, as interpretable natural patterns emerge. The authors of this presentation have started collaboration during the compilation of the Special Issue of the Journal of Geochemical Exploration on Continental, Regional and Local Scale Geochemical Mapping (Demetriades et al., 2015), where Buccianti (2015) used compositional data analysis techniques on the stream water data of the FOREGS Geochemical Atlas of Europe (Salminen et al., 2005; De Vos, Tarvainen et al., 2006). This collaboration is carrying on with the processing of reconnaissance stream sediment geochemical data from the Lake Kastoria s drainage basin in Hellas, and will continue. Examples of the aforementioned projects, namely GEMAS, FOREGS and Kastoria will be presented. In collaboration with Jennifer Mckinley (Queen s University Belfast, Environmental Change and Resilience) and other partners an EU Commission e-cost proposal European Network for Analysing Regional Geochemistry through Optimised Statistics 2

3 (ENARGOS) was submitted for collaboration of CoData statisticians and applied geochemists. If this project proposal is not approved, then this collaboration will continue on a different basis. There are on-going discussions for a closer collaboration with the IUGS Commission on Global Geochemical Baselines. On this basis, Raimon Tolosana-Delgado (Helmholtz-Zentrum Dresden-Rossendorf, Helmholtz Institute Freiberg for Resource Technology, Department of Modelling and Evaluation) has participated in the recent joint April 2017 meeting of the EuroGeoSurveys Geochemistry Expert Group and IUGS Commission on Global Geochemical Baselines in Vienna. It is concluded that there is a need of closer collaboration between CoData statisticians and applied geochemists, because the former must understand the needs of the latter. References Aitchison, J., The statistical analysis of compositional data (with discussion). Journal of Royal Statistical Society, Series B (Statistical Methodology), 44(2), Aitchison, J., The Statistical Analysis of Compositional Data. Chapman & Hall, London, 416 pp. Aitchison, J., The one-hour course in compositional data analysis or compositional data analysis is simple. In: Pawlowsky-Glahn, V (Editor), Proceedings of IAMG'97 - The third annual conference of the International Association for Mathematical Geology, volume I, II and addendum, International Centre for Numerical Methods in Engineering (CIMNE), Barcelona (E), 1100, Beus, A.A., Grigorian, S.V., Geochemical exploration methods for mineral deposits. Applied Publishing Ltd., Wilmette, Illinois, USA, 287 pp. Buccianti, A., The FOREGS repository: Modelling variability in stream water on a continental scale revising classical diagrams from CoDA (compositional data analysis) perspective. In: Demetriades, A., Birke, M., Albanese, S., Schoeters, I., De Vivo, B. (Guest Editors), Special Issue: Continental, regional and local scale geochemical mapping. Journal of Geochemical Exploration, 154, Buccianti, A., Grunsky, E. (Guest Editors), Compositional. Special Issue, Journal of Geochemical Exploration, 141, 100 pp. Chayes, F., On correlation between variables of constant sum. Journal of Geophysical Research, 65(12), Coma-Cufi, M., Thió-Henestrosa, S., CoDaPack 2.0: a stand-alone, multi-platform compositional software. In: Egozcue, J.J., Tolosana-Delgado, R., Ortego, M.I. (Editors), CoDaWork 11: 4 th International Workshop on Compositional Data Analysis. Sant Feliu de Guíxols. Demetriades, A., Birke, M., Albanese, S., Schoeters, I., De Vivo, B. (Guest Editors), Continental, regional and local scale geochemical mapping. Special Issue, Journal of Geochemical Exploration, 154, 264 pp. 3

4 De Vos, W., Tarvainen, T. (Chief Editors), Salminen, R., Reeder, S., De Vivo. B., Demetriades, A., Pirc, S., Batista, M.J., Marsina, K., Ottesen, R.T., O Connor, P.J., Bidovec, M., Lima, A., Siewers, U., Smith, B., Taylor, H., Shaw, R., Salpeteur, I., Gregorauskiene, V., Halamic, J., Slaninka, I., Lax, K., Gravesen, P., Birke, M., Breward, N., Ander, E.L., Jordan, G., Duris, M., Klein, P., Locutura, J., Bel-lan, A., Pasieczna, A., Lis, J., Mazreku, A., Gilucis, A., Heitzmann, P., Klaver, G., Petersell, V., Geochemical Atlas of Europe. Part 2 Interpretation of geochemical maps, Additional Tables, Figures, Maps and related publications. Geological Survey of Finland, Espoo, Finland, 692 pp. Filzmoser, P., Reimann, C., Birke, M., 2014a. Univariate Data Analysis and Mapping. Chapter 8 In: Reimann, C., Birke, M., Demetriades, A., Filzmoser, P., O Connor, P. (Editors), Chemistry of Europe's agricultural soils Part A. Geologisches Jahrbuch (Reihe B102), Schweizerbarth, Hannover, Filzmoser, P., Reimann, C., 2014b. Multivariate Data Analysis. Chapter 9 In: Reimann, C., Birke, M., Demetriades, A., Filzmoser, P., O Connor, P. (Editors), Chemistry of Europe's agricultural soils Part A. Geologisches Jahrbuch (Reihe B102), Schweizerbarth, Hannover, Klovan, J. E., Miesch, A.T., Extended CABFAC and QMODEL computer programs for Q-mode factor analysis of compositional data. Computers and Geosciences, 1(3), Kürzl, H., Exploratory data analysis: recent advances for the interpretation of geochemical data. Journal of Geochemical Exploration, 30(3), Miesch, A.T., 1976a. Geochemical survey of Missouri: methods of sampling, laboratory analysis and statistical reduction of data. U.S. Geol. Surv., Prof. Paper 954-A, 39 pp. Miesch, A.T., 1976b. Q-mode factor analysis of compositional data. Computers and Geosciences, 1(3), Miesch, A.T., 1976c. Q-mode factor analysis of geochemical and petrologic data matrices with constant row-sums. U.S. Geol. Survey Prof. Paper 574-G, 47 pp. Miesch, A.T., G-RFAC User's Manual. Grand Junction, Colorado, Miesch Programs, 72 pp. Reimann, C., Filzmoser, P., Garret, R.G., Dutter, R., Statistical data analysis explained: Applied environmental statistics with R. John Wiley & Sons, Ltd., Chichester, U.K., 343 pp. Reimann, C., Filzmoser, P., Fabian, K., Hron, K., Birke, M., Demetriades, A., Dinelli, E., Ladenberger, A., GEMAS Project Team, The concept of compositional data analysis in practice Total major element concentrations in agricultural and grazing land soils of Europe. Science of the Total Environment, 426, Reimann, C., Birke, M., Demetriades, A., Filzmoser, P., O'Connor, P. (Editors), Chemistry of Europe's agricultural soils Part A: Methodology and interpretation of 4

5 the GEMAS data set. Geologisches Jahrbuch (Reihe B 102), Schweizerbarth, Hannover, 528 pp. Salminen, R. (Chief Editor), Batista, M.J., Bidovec, M., Demetriades, A., De Vivo, B., De Vos, W., Duris, M., Gilucis, A., Gregorauskiene, V., Halamic, J., Heitzmann, P., Lima, A., Jordan, G., Klaver, G., Klein, P., Lis, J., Locutura, J., Marsina, K., Mazreku, A., O Connor, P.J., Olsson S.Å., Ottesen, R.T., Petersell, V., Plant, J.A., Reeder, S., Salpeteur, I., Sandström, H., Siewers, U., Steenfelt, A., Tarvainen, T., FOREGS Geochemical Atlas of Europe, Part 1: Background Information, Methodology and Maps. Geological Survey of Finland, Espoo, 526 pp. Tukey, J.W., Exploratory data analysis. Addison-Wesly, Reading, MA., 506 pp. 5