CoDa-dendrogram: A new exploratory too

The use of orthonormal coordinates in the simplex and, particularly, balance coordinates, has suggested the use of a dendrogram for the exploratory analysis of compositional data. The dendrogram is based on a sequential binary partition of a compositional vector into groups of parts. At each step of a partition, one group of parts isdivided into two new groups, and a balancing axis in the simplex between both groupsis defined. The set of balancing axes constitutes an orthonormal basis, and the projections of the sample on them are orthogonal coordinates. They can be represented in adendrogram-like graph showing: (a) the way of grouping parts of the compositional vector; (b) the explanatory role of each subcomposition generated in the partition process;(c) the decomposition of the total variance into balance components associated witheach binary partition; (d) a box-plot of each balance. This representation is useful tohelp the interpretation of balance coordinates; to identify which are the most explanatory coordinates; and to describe the whole sample in a single diagram independentlyof the number of parts of the sample

A tale of two logits, compositional data analysis and zero observations

The application of compositional data analysis through log ratio trans-formations corresponds to a multinomial logit model for the shares themselves.This model is characterized by the property of Independence of Irrelevant Alter-natives (IIA). IIA states that the odds ratio in this case the ratio of shares is invariant to the addition or deletion of outcomes to the problem. It is exactlythis invariance of the ratio that underlies the commonly used zero replacementprocedure in compositional data analysis. In this paper we investigate using thenested logit model that does not embody IIA and an associated zero replacementprocedure and compare its performance with that of the more usual approach ofusing the multinomial logit model. Our comparisons exploit a data set that com-bines voting data by electoral division with corresponding census data for eachdivision for the 2001 Federal election in Australia

Modelling structural zeros in compositional data

This analysis was stimulated by the real data analysis problem of householdexpenditure data. The full dataset contains expenditure data for a sample of 1224 households. The expenditure is broken down at 2 hierarchical levels: 9 major levels (e.g. housing, food, utilities etc.) and 92 minor levels. There are also 5 factors and 5 covariates at the household level. Not surprisingly, there are a small number of zeros at the major level, but many zeros at the minor level. The question is how best to model the zeros. Clearly, models that tryto add a small amount to the zero terms are not appropriate in general as at least some of the zeros are clearly structural, e.g. alcohol/tobacco for households that are teetotal. The key question then is how to build suitable conditional models. For example, is the sub-composition of spendingexcluding alcohol/tobacco similar for teetotal and non-teetotal households?In other words, we are looking for sub-compositional independence. Also, what determines whether a household is teetotal? Can we assume that it is independent of the composition? In general, whether teetotal will clearly depend on the household level variables, so we need to be able to model this dependence. The other tricky question is that with zeros on more than onecomponent, we need to be able to model dependence and independence of zeros on the different components. Lastly, while some zeros are structural, others may not be, for example, for expenditure on durables, it may be chance as to whether a particular household spends money on durableswithin the sample period. This would clearly be distinguishable if we had longitudinal data, but may still be distinguishable by looking at the distribution, on the assumption that random zeros will usually be for situations where any non-zero expenditure is not small.While this analysis is based on around economic data, the ideas carry over tomany other situations, including geological data, where minerals may be missing for structural reasons (similar to alcohol), or missing because they occur only in random regions which may be missed in a sample (similar to the durables)

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 two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

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

Excavacions arqueològiques al poblat ibèric de Sant Julià de Ramis

L'ampliació del cementiri municipal de Sant Julià de Ramis va comportar la realització de diverses obres a la muntanya de Sant Julià on es van localitzar diversos indicis que permetien deduir la presència de restes del poblat ibèric de Sant Julià en l'àrea afectada per les obres. Aquests indicis consistien en la presència de diversos blocs de calcària i algun de sorrenca que pressuposaven l'existència d'un gran mur i d'un estrat d'uns 40 cm. de centenars de fragments de ceràmica superposats uns als altres que semblaven pertànyer a un abocador

Hisendats, de classe dominant classe dirigent

Estudi dels hisendats a les comarques gironins durant el s. XIX. Es tractava de famílies que durant centúries havien anat acumulant propietats agrícoles, i així es van consolidar com una minoria de grans propietaris rurals que podien viure de les seves rendes

Records d'un final d'estiu a Olot: Rusiñol al "país del paisatge"

Estudi de Santiago Rusiñol en els seus orígens com a pintor,i descripció de la seva estada a Olot a l'estiu i principis de tardor de 1988, en què va pintar una trentena d'olis, què el mateix any va exposar a la Sala Parés com a part de la seva primera exposició individual. És llavors quan ell decideix dedicar-se a la pintura. El pintor es referia a Olot com el "país del paisatge"

El Creixement urbá a la zona volcànica de la Garrotxa

Descripció del creixement urbà dels municipis que s’inclouen dins la zona del Parc Natural de la Zona Volcànica de la Garrotxa i de com aquest influeix en el parc. Esment del Campus europeu de medi ambient que es celebrà a Olot al 1991

La Ciutat, el paisatge i la nació: Una lectura de l'obra de Pere Coromines

Estudi de l’obra de Pere Coromines i del seu pensament polític a través d’aquesta. Se centra en el tractament que fa l’escriptor de temes com ara la nació, la ciutat (Barcelona), la naturalesa, el paisatge, l’Empordà, la Mediterrània. En paraules de l’autor, “en l'obra de Coromines es detecta una tensió entre la temptació de remuntar-se a un paisatge primigeni, natural, no contaminat, i la reivindicació del paper de la Ciutat en la conformació de la Catalunya nacional”

La Percepció republicana del carlisme: Una aproximació a propòsit de Valentí Almirall i Pere Coromines

Repàs de la relació entre el republicanisme i el carlisme a través de la mirada de Valentí Almirall i de Pere Coromines

An R Library for Compositional Data Analysis in Archaeometry

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

Vers un nou model psicopedagògic d'intervenció educativa

L'objectiu d'aquest article és el plantejament d'un Model d'intewenció Psicopedagògica en el Procés Educatiu que doni resposta a les necessitats educatives, en els cicles d'Educació Infantil i Primària, i amb capacitat d'adaptació als canvis, ara que la nova reforma del sistema educatiu comença a emmarcar la realitat educativa.La seva implantació és en realitat un fet palpable: durant el curs 92/93 s'inicia la sevaaplicació als alumnes del 2n Cicle de l'Ensenyament Infantil i als del lr de l'Ensenyament Primari

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 andpositive 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 workingin coordinates, and the object-oriented programming paradigm of R. In this way,called functions automatically select the most appropriate type of analysis as a functionof the geometry. The graphical capabilities include ternary diagrams and tetrahedrons,various compositional plots (boxplots, barplots, piecharts) and extensive graphical toolsfor principal components. Afterwards, ortion and proportion lines, straight lines andellipses in all geometries can be added to plots. The package is accompanied by ahands-on-introduction, documentation for every function, demos of the graphical capabilitiesand plenty of usage examples. It allows direct and parallel computation inall four vector spaces and provides the beginner with a copy-and-paste style of dataanalysis, while letting advanced users keep the functionality and customizability theydemand of R, as well as all necessary tools to add own analysis routines. A completeexample is included in the appendix

Compositional data analysis in archaeometry

We shall call an n × p data matrix fully-compositional if the rows sum to a constant, and sub-compositional if the variables are a subset of a fully-compositional data set1. Such data occur widely in archaeometry, where it is common to determine the chemical composition of ceramic, glass, metal or other artefacts using techniques such as neutron activation analysis (NAA), inductively coupled plasma spectroscopy (ICPS), X-ray fluorescence analysis (XRF) etc. Interest often centres on whether there are distinct chemical groups within the data and whether, for example, these can be associated with different origins or manufacturing technologies