Compositional data analysis with R

Examples of compositional data. The simplex, a suitable sample space for compositional data and Aitchison's geometry. R, a free language and environment for statistical computing and graphics

Compositional Data Analysis with R

R from http://www.r-project.org/ is ‘GNU S’ – a language and environment for statistical computing and graphics. The environment in which many classical and modern statistical techniques have been implemented, but many are supplied as packages. There are 8 standard packages and many more are available through the cran family of Internet sites http://cran.r-project.org . We started to develop a library of functions in R to support the analysis of mixtures and our goal is a MixeR package for compositional data analysis that provides support for operations on compositions: perturbation and power multiplication, subcomposition with or without residuals, centering of the data, computing Aitchison’s, Euclidean, Bhattacharyya distances, compositional Kullback-Leibler divergence etc. graphical presentation of compositions in ternary diagrams and tetrahedrons with additional features: barycenter, geometric mean of the data set, the percentiles lines, marking and coloring of subsets of the data set, theirs geometric means, notation of individual data in the set . . . dealing with zeros and missing values in compositional data sets with R procedures for simple and multiplicative replacement strategy, the time series analysis of compositional data. We’ll present the current status of MixeR development and illustrate its use on selected data sets

Implantación de un SIG basado en software libre para el estudio de recursos hídricos y procesos hidrológicos

En este trabajo se describe la solución ideada para la implantación de un Sistema de Información Geográfica que debe dar servicio al Instituto Universitario del Agua y del Medio Ambiente de la Universidad de Murcia y al Instituto Euromediterráneo del Agua. Dada la naturaleza de ambas instituciones, se trata de una herramienta orientada fundamentalmente al estudio de recursos hídricos y procesos hidrológicos. El proceso se inició con una identificación de las necesidades de los usuarios (con perfiles y requerimiento diferentes) y el posterior desarrollo del diseño conceptual que pudiera asegurar la satisfacción de estas necesidades. Debido a que los requerimientos de los usuarios así lo demandaban, se ha tenido en cuenta tanto a usuarios que trabajan en entorno linux como a otros que lo hacen en entorno windows. Se ha optado por un sistema basado en software libre utilizando GRASS para el manejo de información raster y modelización; postgis (sobre postgreSQL) y GRASS para la gestión de información vectorial; y QGIS, gvSIG y Kosmo como interfaces gráficas de usuario. Otros programas utilizados para propósitos específicos han sido R, Mapserver o GMT

An R Library for Compositional Data Analysis in Archaeometry

Compositional data naturally arises from the scientific analysis of the chemical composition of archaeological material such as ceramic and glass artefacts. Data of this type can be explored using a variety of techniques, from standard multivariate methods such as principal components analysis and cluster analysis, to methods based upon the use of log-ratios. The general aim is to identify groups of chemically similar artefacts that could potentially be used to answer questions of provenance. This paper will demonstrate work in progress on the development of a documented library of methods, implemented using the statistical package R, for the analysis of compositional data. R is an open source package that makes available very powerful statistical facilities at no cost. We aim to show how, with the aid of statistical software such as R, traditional exploratory multivariate analysis can easily be used alongside, or in combination with, specialist techniques of compositional data analysis. The library has been developed from a core of basic R functionality, together with purpose-written routines arising from our own research (for example that reported at CoDaWork'03). In addition, we have included other appropriate publicly available techniques and libraries that have been implemented in R by other authors. Available functions range from standard multivariate techniques through to various approaches to log-ratio analysis and zero replacement. We also discuss and demonstrate a small selection of relatively new techniques that have hitherto been little-used in archaeometric applications involving compositional data. The application of the library to the analysis of data arising in archaeometry will be demonstrated; results from different analyses will be compared; and the utility of the various methods discussed

A compositional data analysis package for R providing multiple approaches

”compositions” is a new R-package for the analysis of compositional and positive data. It contains four classes corresponding to the four different types of compositional and positive geometry (including the Aitchison geometry). It provides means for computation, plotting and high-level multivariate statistical analysis in all four geometries. These geometries are treated in an fully analogous way, based on the principle of working in coordinates, and the object-oriented programming paradigm of R. In this way, called functions automatically select the most appropriate type of analysis as a function of the geometry. The graphical capabilities include ternary diagrams and tetrahedrons, various compositional plots (boxplots, barplots, piecharts) and extensive graphical tools for principal components. Afterwards, ortion and proportion lines, straight lines and ellipses in all geometries can be added to plots. The package is accompanied by a hands-on-introduction, documentation for every function, demos of the graphical capabilities and plenty of usage examples. It allows direct and parallel computation in all four vector spaces and provides the beginner with a copy-and-paste style of data analysis, while letting advanced users keep the functionality and customizability they demand of R, as well as all necessary tools to add own analysis routines. A complete example is included in the appendix

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition