Compositional data analysis of vote shares in the 2001 Australian Federal election

First application of compositional data analysis techniques to Australian election data

Assessing the Precision of Compositional Data in a Stratified Double Stage Cluster Sample: Application to the Swiss Earnings Structure Survey

Precision of released figures is not only an important quality feature of official statistics, it is also essential for a good understanding of the data. In this paper we show a case study of how precision could be conveyed if the multivariate nature of data has to be taken into account. In the official release of the Swiss earnings structure survey, the total salary is broken down into several wage components. We follow Aitchison's approach for the analysis of compositional data, which is based on logratios of components. We first present diferent multivariate analyses of the compositional data whereby the wage components are broken down by economic activity classes. Then we propose a number of ways to assess precision

Group preference structures in AHP–group decision making

This paper presents a procedure that allows us to determine the preference structures (PS) associated to each of the different groups of actors that can be identified in a group decision making problem with a large number of individuals. To that end, it makes use of the Analytic Hierarchy Process (AHP) (Saaty, 1980) as the technique to solve discrete multicriteria decision making problems. This technique permits the resolution of multicriteria, multienvironment and multiactor problems in which subjective aspects and uncertainty have been incorporated into the model, constructing ratio scales corresponding to the priorities relative to the elements being compared, normalised in a distributive manner (wi = 1). On the basis of the individuals’ priorities we identify different clusters for the decision makers and, for each of these, the associated preference structure using, to that end, tools analogous to those of Multidimensional Scaling. The resulting PS will be employed to extract knowledge for the subsequent negotiation processes and, should it be necessary, to determine the relative importance of the alternatives being compared using anyone of the existing procedures

Regression analysis of compositional data when both the dependent variable and independent variable are components

It is well known that regression analyses involving compositional data need special attention because the data are not of full rank. For a regression analysis where both the dependent and independent variable are components we propose a transformation of the components emphasizing their role as dependent and independent variables. A simple linear regression can be performed on the transformed components. The regression line can be depicted in a ternary diagram facilitating the interpretation of the analysis in terms of components. An exemple with time-budgets illustrates the method and the graphical features

Interactions between grain size and composition of sediments: two examples

Two contrasting case studies of sediment and detrital mineral composition are investigated in order to outline interactions between chemical composition and grain size. Modern glacial sediments exhibit a strong dependence of the two parameters due to the preferential enrichment of mafic minerals, especially biotite, in the fine-grained fractions. On the other hand, the composition of detrital heavy minerals (here: rutile) appears to be not systematically related to grain-size, but is strongly controlled by location, i.e. the petrology of the source rocks of detrital grains. This supports the use of rutile as a well-suited tracer mineral for provenance studies. The results further suggest that (i) interpretations derived from whole-rock sediment geochemistry should be flanked by grain-size observations, and (ii) a more sound statistical evaluation of these interactions require the development of new tailor-made statistical tools to deal with such so-called two-way compositions

Comparison studies of tin deposits (Priamurye, Russia) using the Aitchison’s methodology

A study of tin deposits from Priamurye (Russia) is performed to analyze the differences between them based on their origin and also on commercial criteria. A particular analysis based on their vertical zonality is also given for samples from Solnechnoe deposit. All the statistical analysis are made on the subcomposition formed by seven trace elements in cassiterite (In, Sc, Be, W, Nb, Ti and V) using the Aitchison’ methodology of analysis of compositional data

The chemical variability at the surface of Mars: implications for exogenic processes

The chemical composition of sediments and rocks, as well as their distribution at the Martian surface, represent a long term archive of processes, which have formed the planetary surface. A survey of chemical compositions by means of Compositional Data Analysis represents a valuable tool to extract direct evidence for weathering processes and allows to quantify weathering and sedimentation rates. clr-biplot techniques are applied for visualization of chemical relationships across the surface (“chemical maps”). The variability among individual suites of data is further analyzed by means of clr-PCA, in order to extract chemical alteration vectors between fresh rocks and their crusts and for an assessment of different source reservoirs accessible to soil formation. Both techniques are applied to elucidate the influence of remote weathering by combined analysis of several soil forming branches. Vector analysis in the Simplex provides the opportunity to study atmosphere surface interactions, including the role and composition of volcanic gases

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the study of tephrochrology. In this paper, DFA is applied to compositional datasets of two different types of tephras from Mountain Ruapehu in New Zealand and Mountain Rainier in USA. The canonical variables from the analysis are further investigated with a statistical methodology of change-point problems in order to gain a better understanding of the change in compositional pattern over time. Finally, a special case of segmented regression has been proposed to model both the time of change and the change in pattern. This model can be used to estimate the age for the unknown tephras using Bayesian statistical calibration

Statistical Analysis of Eco-Toxicologic Data of Mammals from a Polluted Area

Several eco-toxicological studies have shown that insectivorous mammals, due to their feeding habits, easily accumulate high amounts of pollutants in relation to other mammal species. To assess the bio-accumulation levels of toxic metals and their in°uence on essential metals, we quantified the concentration of 19 elements (Ca, K, Fe, B, P, S, Na, Al, Zn, Ba, Rb, Sr, Cu, Mn, Hg, Cd, Mo, Cr and Pb) in bones of 105 greater white-toothed shrews (Crocidura russula) from a polluted (Ebro Delta) and a control (Medas Islands) area. Since chemical contents of a bio-indicator are mainly compositional data, conventional statistical analyses currently used in eco-toxicology can give misleading results. Therefore, to improve the interpretation of the data obtained, we used statistical techniques for compositional data analysis to define groups of metals and to evaluate the relationships between them, from an inter-population viewpoint. Hypothesis testing on the adequate balance-coordinates allow us to confirm intuition based hypothesis and some previous results. The main statistical goal was to test equal means of balance-coordinates for the two defined populations. After checking normality, one-way ANOVA or Mann-Whitney tests were carried out for the inter-group balances

A compositional approach to stable isotope data analysis

Isotopic data are currently becoming an important source of information regarding sources, evolution and mixing processes of water in hydrogeologic systems. However, it is not clear how to treat with statistics the geochemical data and the isotopic data together. We propose to introduce the isotopic information as new parts, and apply compositional data analysis with the resulting increased composition. Results are equivalent to downscale the classical isotopic delta variables, because they are already relative (as needed in the compositional framework) and isotopic variations are almost always very small. This methodology is illustrated and tested with the study of the Llobregat River Basin (Barcelona, NE Spain), where it is shown that, though very small, isotopic variations comp lement geochemical principal components, and help in the better identification of pollution sources

Los alimentos

Este material se edita dentro de HABITAR, programa did??ctico para el estudio del medio, que ofert?? el Ayuntamiento de Gij??n a la comunidad educativa. El documento en s??, viene precedido por la presentaci??n de los principios educativos y otros principios de procedimiento que guian el programa.En concreto en el tema 'Los alimentos' existen dos partes diferenciadas: por un lado el aspecto del proceso productivo de los alimentos y por otro lado el aspecto de la alimentaci??n humana, de la nutrici??n. La t??cnica de trabajo es la de 'seguir la pista' con objeto de integrar los diferentes aspectos de la producci??n de alimentos facilitando la puesta en relaci??n de este proceso con las caracter??sticas de los alumnos y su importancia en la nutrici??n humana. Se proponen una serie de actividades como juegos (veo-veo, la habitaci??n vac??a, b??squeda del tesoro, el mercado en clase, platos t??picos, etc.) y otras cuyos materiales se ofrecen agrupados en: 1.-Los alimentos que nos dan los alimentos 2.-En la caseria se producen alimentos 3.-El casta??o y el manzano 4.-Del trigo al pan 6.- La compra equilibrada. Finalmente se ofrecen las gu??as para las visitas a una caser??a, el mercado y una panificadora.

La ciudad

Esta unidad trata de buscar un acercamiento afectivo del ni??o a la ciudad, a trav??s de su barrio, iniciando su conocimiento a partir de los elementos b??sicos que lo conforman (edificios, calles, se??ales, r??tulos,etc.). Para desarrollar h??bitos de observaci??n as?? como capacidades b??sicas de orientaci??n y trabajo con croquis, propone una serie de actividades que desarrollan temas como: identificaci??n de edificios y lugares de la ciudad; los servicios p??blicos; observando el barrio; el trabajo; lugares para jugar y divertirse; la vida en la ciudad; el plano de una habitaci??n. Complement??ndose con la gu??a de dos itinerarios: uno por el barrio y otro que consiste en un recorrido panor??mico por la ciudad con el objeto de mostrar la misma desde diferentes puntos de vista.

El r??o

Este estudio a realizar a partir de un itinerario que transcurre por el gijon??s rio Piles, permite a los ni??os conocer 'in situ' de forma general la diversidad de elementos que caracterizan a un ecosistema fluvial y comprobar que estos elementos no se dan aisladamente en la naturaleza sino que existe una relaci??n de interdependencia entre unos y otros. Otro objetivo es el de fomentar en los ni??os el deseo de comprender y valorar el alcance de los problemas ambientales y orientar su conducta hacia una actitud de respeto y consideraci??n hacia el medio ambiente. Se proponen experimentos para verificar las propiedades del agua (temperatura, color), tipo de fondo, medici??n de la contaminaci??n, observaci??n de animales y plantas, etc. Finalmente se describe pormenorizadamente el itinerario por el curso medio y bajo del rio Piles. Este material se edita dentro de 'HABITAR',programa did??ctico para el estudio del medio, que ofert?? el Ayuntamiento de Gij??n a la comunidad educativa. El documento en s??, viene precedido por la presentaci??n de los principios educativos y otros de procedimiento que guian el programa.

El municipio

Este documento se inicia con el estudio del entorno m??s inmediato al ni??o: la calle, el barrio, la localidad, para luego ir ampliando su estudio a otros espacios como el municipio, la comunidad aut??noma, la regi??n, etc. Sigue el siguiente gui??n: esquema conceptual, bloques conceptuales, contenidos, actividades (relaci??n de actividades y gu??a de la visita al Ayuntamiento); se ofrecen ideas y materiales en forma de fichas para profundizar en el tema, del tipo de localizaci??n en un croquis, los servicios de un barrio, encuesta a los habitantes del barrio, localizaci??n en el plano, el concepto de Gij??n y sus parroquias, el censo, estudio de la poblaci??n, los impuestos municipales. El objetivo fundamental es dar a conocer el Ayuntamiento como ??rgano administrativo y gestor de los recursos del municipio. Este material se edita dentro de 'HABITAR', programa did??ctico para el estudio del medio, que ofert?? el Ayuntamiento de Gij??n a la comunidad educativa. El documento en s??, viene precedido por la presentaci??n de los principios educativos y otros de procedimiento que gu??an el programa.

El campo y la ciudad

La propuesta persigue el an??lisis de las diferencias morfol??gicas entre un espacio rural y otro urbano, diferenciando las ??reas en funci??n de su uso y los elementos que los constutuyen. Para ello es esencial el desarrollo de capacidades b??sicas como la observaci??n y otras t??cnicas de tipo instrumental. Aparte de las cuestiones morfol??gicas est??n tambien las de tipo hist??rico y sociol??gico tratando que, de alguna manera, este trabajo sirva de base para trabajar en ciclos superiores, temas como la segregaci??n social y econ??mica, la oposici??n centro-periferia, etc. Para ello se exponen actividades relacionadas con el plano, la localizaci??n en un croquis, la utilizaci??n de fuentes para el estudio del entorno (encuestas, fichas de observaci??n), el estudio de la red viaria, los servicios p??blicos, las tiendas y los mercados, los habitantes. Se completa con la propuesta de 2 itinerarios en la zona rural de Gij??n. Este material se edita dentro de 'HABITAR', programa did??ctico para el estudio del medio, que ofert?? el Ayuntamiento de Gij??n a la comunidad educativa. El documento en s??, viene precedido por la presentaci??n de los principios educativos y otros de procedimiento que gu??an el programa.