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Compositional data analysis: Where are we and where should we be heading? See ThioHenestrosa and MartınFernandez
, 2003
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Distributional equivalence and subcompositional coherence in the analysis of contingency tables, ratio scale measurements and compositional data. Economics Working Paper 908, Universitat Pompeu Fabra. Accepted for publication
 in Journal of Classification. URL http://www.econ.upf.edu/en/research/onepaper.php?id=908 Greenacre, M.J. (2007). Power transformations in correspondence analysis. Economics Working Paper 1044, Universitat Pompeu Fabra. Accepted for publication in Computa
, 1976
"... Summary. We consider two fundamental properties in the analysis of twoway tables of positive data: the principle of distributional equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional coherence, which forms the basis of compos ..."
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Summary. We consider two fundamental properties in the analysis of twoway tables of positive data: the principle of distributional equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional coherence, which forms the basis of compositional data analysis. For an analysis to be subcompositionally coherent, it suffices to analyse the ratios of the data values. The usual approach to dimension reduction in compositional data analysis is to perform principal component analysis on the logarithms of ratios, but this method does not obey the principle of distributional equivalence. We show that by introducing weights for the rows and columns, the method achieves this desirable property. This weighted logratio analysis is theoretically equivalent to "spectral mapping", a multivariate method developed almost 30 years ago for displaying ratioscale data from biological activity spectra. The close relationship between spectral mapping and correspondence analysis is also explained, as well as their connection with association modelling. The weighted logratio methodology is applied here to frequency data in linguistics and to chemical compositional data in archaeology.
Compositional data and their analysis: An introduction
 Geological Society, London, Special Publications
, 2006
"... Abstract: Compositional data are those which contain only relative information. They are parts of some whole. In most cases they are recorded as closed data, i.e. data summing to a constant, such as 100 % wholerock geochemical data being classic examples. Compositional data have important and part ..."
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Abstract: Compositional data are those which contain only relative information. They are parts of some whole. In most cases they are recorded as closed data, i.e. data summing to a constant, such as 100 % wholerock geochemical data being classic examples. Compositional data have important and particular properties hat preclude the application f standard statistical techniques on such data in raw form. Standard techniques are designed to be used with data that are free to range fromoo to +oo. Compositional data are always positive and range only from 0 to 100, or any other constant, when given in closed form. If one component increases, others must, perforce, decrease, whether or not there is a genetic link between these components. This means that the results of standard statistical analysis of the relationships between raw components orparts in a compositional dataset are clouded by spurious effects. Although such analyses may give apparently interpretable r sults, they are, at best, approximations and need to be treated with considerable circumspection. The methods outlined in this volume are based on the premise that it is the relative variation of components which s of interest, rather than absolute variation. Logratios of components provide the natural means of studying compositional data. In this contribution the basic terms and operations are introduced using simple numerical examples to illustrate their com
1SOME COMMENTS ON COMPOSITIONAL DATA ANALYSIS IN ARCHAEOMETRY, IN PARTICULAR THE FALLACIES IN TANGRI AND WRIGHT’S DISMISSAL OF LOGRATIO ANALYSIS
"... This comment exposes the fallacies in the Tangri and Wright (1993) dismissal of the methodology of logratio analysis of compositional data as dangerous surgery. It suggests that compositional data analysts should pay enough attention to the basic nature of compositional data and some elementary prin ..."
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This comment exposes the fallacies in the Tangri and Wright (1993) dismissal of the methodology of logratio analysis of compositional data as dangerous surgery. It suggests that compositional data analysts should pay enough attention to the basic nature of compositional data and some elementary principles underlying coherent study in order to avoid meaningless inferences.
Contribution biplots
 Journal of Computational and Graphical Statistics
"... Abstract: In order to interpret the biplot it is necessary to know which points – usually variables – are the ones that are important contributors to the solution, and this information is available separately as part of the biplot’s numerical results. We propose a new scaling of the display, called ..."
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Abstract: In order to interpret the biplot it is necessary to know which points – usually variables – are the ones that are important contributors to the solution, and this information is available separately as part of the biplot’s numerical results. We propose a new scaling of the display, called the contribution biplot, which incorporates this diagnostic directly into the graphical display, showing visually the important contributors and thus facilitating the biplot interpretation and often simplifying the graphical representation considerably. The contribution biplot can be applied to a wide variety of analyses such as correspondence analysis, principal component analysis, logratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singularvalue decomposition. In the contribution biplot one set of points, usually the rows of the data matrix, optimally represent the spatial positions of the cases or sample units, according to some distance measure that usually incorporates some form of standardization unless all data are comparable in scale. The other set of points, usually the columns, is represented by vectors that are related to their contributions to the lowdimensional solution. A fringe benefit is that usually only one common scale for row and column points is needed on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot legible. Furthermore, this version of the biplot also solves the problem in correspondence analysis of lowfrequency categories that are located on the periphery of the map, giving the false impression that they are important, when they are in fact contributing minimally to the solution.
Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps
"... Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of twoway tables of nonnegative data. Thanks to the ..."
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Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of twoway tables of nonnegative data. Thanks to the weighting, the method also achieves the property of distributional equivalence.
Benthic foraminiferal morphogroups on the Argentine continental shelf
 Journal of Foraminiferal Research
, 2011
"... The aim of this study is to evaluate the relative influence of abiotic factors on the association and spatial distribution of recent benthic foraminiferal morphogroups in the Argentine continental shelf at,40uS environments as a first step towards establishing their paleoecological significance. For ..."
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The aim of this study is to evaluate the relative influence of abiotic factors on the association and spatial distribution of recent benthic foraminiferal morphogroups in the Argentine continental shelf at,40uS environments as a first step towards establishing their paleoecological significance. Foraminifera are classified into five morphogroups: tapered, elongateflattened, milioline, planoconvex, and roundedplanispiral. Compositional data analysis techniques were used to define morphogroup assemblages, and Classification and Regression Tree Analysis was used to identify environmental variables. The distribution of the morphogroup assemblages were recognized was driven by complex interactions between environmental factors. The most important factor is temperature, although salinity, substrate grain size, and hydrodynamic energy also correlate with the distribution of morphogroups. The morphogroups analysis shows potential for determining present and past environments where the autoecology of the species is unknown or where there is doubt regarding their taxonomic classification.
Exploring compositional data with the robust compositional biplot
 Advances in latent variables
, 2014
"... Abstract Loadings and scores of principal component analysis are popularly displayed together in a planar graph, called biplot, with an intuitive interpretation. In case of compositional data, multivariate observations that carry only relative information (represented usually in proportions or per ..."
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Abstract Loadings and scores of principal component analysis are popularly displayed together in a planar graph, called biplot, with an intuitive interpretation. In case of compositional data, multivariate observations that carry only relative information (represented usually in proportions or percentages), principal component analysis cannot be used for the original compositions. They first need to be transformed using the centered logratio (clr) transformation. If outlying observations occur in compositional data, even the clr (compositional) biplot can lead to useless conclusions. A robust alternative can be computed by using the isometric logratio (ilr) transformation, and by robustly estimating location and covariance. The robust compositional biplot has a big potential in many applications (geology, analytical chemistry, social sciences). Key words: compositional data, principal component analysis, compositional biplot, robust statistics 1
Mineral balance plasticity of cloudberry (rubus chamaemorus) in quebeclabrador
 Am. J. Plant Sci
, 2013
"... Copyright © 2013 Léon Etienne Parent et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The “ionome”, or plant elemental signatu ..."
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Copyright © 2013 Léon Etienne Parent et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The “ionome”, or plant elemental signature, is the elemental composition of an organisms, that may vary with genotypic traits and phenotypic plasticity. Cloudberry (Rubus chamaemorus L.) is a circumboreal wild berry naturally growing in oligotrophic oceanic bogs of Quebec and Labrador. Our objective was to relate cloudberry stand productivity to the ionomes of female ramets and explore the cause of nutrient imbalance in lowperforming stands. We analyzed 13 elements in female ramets collected in 86 natural sites where crop productivity varied widely. We computed orthogonally arranged balances reflecting plant stoichiometric rules and soil biogeochemistry. Balances were expressed as isometric log ratios (ilr) between ad hoc subcompositions. Balances were synthesized into a Mahalanobis distance optimized based on receiving operating characteristics (ROC). The critical Mahalanobis distance was found to be 5.29 for cutoff berry yield of 3.8 g·m−2 with test performance of 0.88, as measured by the area under the ROC curve. Although past research on cloudberry focused mainly on the N/P ratio, this exploratory mineral balance analysis indicated that imbalance in the [P,N  S,C] and [Al  Nutrients] partitions appeared to be the factors limiting the most cloudberry productivity in the bogs. Some highly productive stands showed relatively high C fixation and K use efficiency. Due to the com
TYING UP THE LOOSE ENDS IN SIMPLE, MULTIPLE AND JOINT CORRESPONDENCE ANALYSIS
"... Summary. This paper considers several aspects of simple, multiple and joint correspondence analysis that have been misleading, controversial or lacking proper solutions or clarifications. In each case these “loose ends” have been tied up with specific proposals or explanations. ..."
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Summary. This paper considers several aspects of simple, multiple and joint correspondence analysis that have been misleading, controversial or lacking proper solutions or clarifications. In each case these “loose ends” have been tied up with specific proposals or explanations.