Conditional compositional biplots: theory and application

The biplot has proved to be a powerful descriptive and analytical tool in many areas of applications of statistics. For compositional data the necessary theoretical adaptation has been provided, with illustrative applications, by Aitchison (1990) and Aitchison and Greenacre (2002). These papers were restricted to the interpretation of simple compositional data sets. In many situations the problem has to be described in some form of conditional modelling. For example, in a clinical trial where interest is in how patients’ steroid metabolite compositions may change as a result of different treatment regimes, interest is in relating the compositions after treatment to the compositions before treatment and the nature of the treatments applied. To study this through a biplot technique requires the development of some form of conditional compositional biplot. This is the purpose of this paper. We choose as a motivating application an analysis of the 1992 US President ial Election, where interest may be in how the three-part composition, the percentage division among the three candidates - Bush, Clinton and Perot - of the presidential vote in each state, depends on the ethnic composition and on the urban-rural composition of the state. The methodology of conditional compositional biplots is first developed and a detailed interpretation of the 1992 US Presidential Election provided. We use a second application involving the conditional variability of tektite mineral compositions with respect to major oxide compositions to demonstrate some hazards of simplistic interpretation of biplots. Finally we conjecture on further possible applications of conditional compositional biplots

A new distribution on the simplex containing the Dirichlet family

The Dirichlet family owes its privileged status within simplex distributions to easyness of interpretation and good mathematical properties. In particular, we recall fundamental properties for the analysis of compositional data such as closure under amalgamation and subcomposition. From a probabilistic point of view, it is characterised (uniquely) by a variety of independence relationships which makes it indisputably the reference model for expressing the non trivial idea of substantial independence for compositions. Indeed, its well known inadequacy as a general model for compositional data stems from such an independence structure together with the poorness of its parametrisation. In this paper a new class of distributions (called Flexible Dirichlet) capable of handling various dependence structures and containing the Dirichlet as a special case is presented. The new model exhibits a considerably richer parametrisation which, for example, allows to model the means and (part of) the variance-covariance matrix separately. Moreover, such a model preserves some good mathematical properties of the Dirichlet, i.e. closure under amalgamation and subcomposition with new parameters simply related to the parent composition parameters. Furthermore, the joint and conditional distributions of subcompositions and relative totals can be expressed as simple mixtures of two Flexible Dirichlet distributions. The basis generating the Flexible Dirichlet, though keeping compositional invariance, shows a dependence structure which allows various forms of partitional dependence to be contemplated by the model (e.g. non-neutrality, subcompositional dependence and subcompositional non-invariance), independence cases being identified by suitable parameter configurations. In particular, within this model substantial independence among subsets of components of the composition naturally occurs when the subsets have a Dirichlet distribution

L'Activité de l'enseignant dans les situations de rencontre avec des oeuvres d'art (littérature, arts visuels): quels gestes professionnels spécifiques? (Co) activité de l'enseignant et de l'élève au moment de "parler de l'oeuvre"

Les travaux ici présentés se définissent explicitement comme des recherches sur des situations de formation d’enseignants non spécialistes aux problématiques des Enseignements Artistiques et Culturels1 [EAC]. Cela ne signifie pas que ces travaux relèvent de ce qui serait une «recherche appliquée»; bien au contraire, nous postulons que ces situations professionnelles renvoient à la recherche «fondamentale» en sciences des arts des questions originales et difficiles. Une des difficultés de la formation d’enseignants polyvalents est justement de leur apporter, dans des délais forcément réduits, des connaissances solides, alors qu’elles portent sur des champs disciplinaires multiples, et sur des noeuds théoriques qui se révèlent complexes

El Copagament: el moment del colze a colze?

La modalitat del copagament és una opció que pren força a mesura que s’estén la sensació que, per salvar l’estat del benestar, caldrà que tots treballem colze a colze. L’aprovació de l’anomenada Llei de dependència és un primer tast d’aquesta fórmula que, per als professionals del dret, planteja dubtes sobre la seva configuració jurídica

Towards closure between measured and modelled UV under clear skies at four diverse sites

The purpose of this work is determine the extent of closure between measurements and models of UV irradiances at diverse sites using state of the art instruments, models, and the best available data as inputs to the models. These include information about aerosol optical depth (unfortunately not extending down as far into the UVB region as desirable because such information is not generally available), ozone column amounts, as well as vertical profiles of temperature. We concentrate on clear-sky irradiances, and report the results in terms of UV Index (UVI)