Compositional hypotheses of subcompositional stability and specific perturbation change and their testing

In standard multivariate statistical analysis common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositional change is most readily described in terms of the simplicial operation of perturbation and that subcompositions replace the marginal concept of subvectors. To motivate the statistical developments of this paper we present two challenging compositional problems from food production processes.Against this background the relevance of perturbations and subcompositions can beclearly seen. Moreover we can identify a number of hypotheses of interest involvingthe specification of particular perturbations or differences between perturbations and also hypotheses of subcompositional stability. We identify the two problems as being the counterpart of the analysis of paired comparison or split plot experiments and of separate sample comparative experiments in the jargon of standard multivariate analysis. We then develop appropriate estimation and testing procedures for a complete lattice of relevant compositional hypotheses

Compositional Data Analysis with R

R from http://www.r-project.org/ is ‘GNU S’ – a language and environment for statistical computingand graphics. The environment in which many classical and modern statistical techniques havebeen implemented, but many are supplied as packages. There are 8 standard packages and many moreare 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 isa MixeR package for compositional data analysis that provides support foroperations on compositions: perturbation and power multiplication, subcomposition with or withoutresiduals, 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 ofsubsets 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 simpleand 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

New Features of CoDaPack. An Userfriendly Compositional Data Package

The statistical analysis of compositional data is commonly used in geological studies.As is well-known, compositions should be treated using logratios of parts, which aredifficult to use correctly in standard statistical packages. In this paper we describe thenew features of our freeware package, named CoDaPack, which implements most of thebasic statistical methods suitable for compositional data. An example using real data ispresented to illustrate the use of the package

XVI Olimpíada Nacional de Química 2002-2003

Article que es refereix a la XVI Olimpíada Nacional de Química (2002 – 2003), celebrada el 9-12 de maig de 2003, al Seminari Menor de Tarazona (Saragossa). L’ olimpíada consisteix en dues proves: la primera consisteix en la resolució de 4 problemes llargs, i la segona en 45 preguntes de resposta múltiple (tipus test) que contenen qüestions teòriques i problemes curt. En aquest article s’ esmenten els alumnes que han obtingut alguna mena de distinció, els classificats per a la Fase Nacional, els problemes proposats i les característiques de les preguntes del test

XVIII Olimpíada Nacional de Química 2004-2005

Article que es refereix a la XVIII Olimpíada Nacional de Química (2004 – 2005), celebrada el 15-18 d' abril de 2005, al Luarca(Astúries). L’ olimpíada consisteix en dues proves: la primera consisteix en la resolució de 4 problemes llargs, i la segona en 45 preguntes de resposta múltiple (tipus test) que contenen qüestions teòriques i problemes curts. En aquest article s’ esmenten els alumnes que han obtingut algun tipus de distinció, els classificats per a la Fase Nacional, els problemes proposats i les característiques de les preguntes del test

Thermodynamics and log–contrast analysis in fluid geochemistry

There are two principal chemical concepts that are important for studying the naturalenvironment. The first one is thermodynamics, which describes whether a system is atequilibrium or can spontaneously change by chemical reactions. The second main conceptis how fast chemical reactions (kinetics or rate of chemical change) take place wheneverthey start. In this work we examine a natural system in which both thermodynamics andkinetic factors are important in determining the abundance of NH+4 , NO−2 and NO−3 insuperficial waters. Samples were collected in the Arno Basin (Tuscany, Italy), a system inwhich natural and antrophic effects both contribute to highly modify the chemical compositionof water. Thermodynamical modelling based on the reduction-oxidation reactionsinvolving the passage NH+4 -& NO−2 -& NO−3 in equilibrium conditions has allowed todetermine the Eh redox potential values able to characterise the state of each sample and,consequently, of the fluid environment from which it was drawn. Just as pH expressesthe concentration of H+ in solution, redox potential is used to express the tendency of anenvironment to receive or supply electrons. In this context, oxic environments, as thoseof river systems, are said to have a high redox potential because O2 is available as anelectron acceptor.Principles of thermodynamics and chemical kinetics allow to obtain a model that oftendoes not completely describe the reality of natural systems. Chemical reactions may indeedfail to achieve equilibrium because the products escape from the site of the rectionor because reactions involving the trasformation are very slow, so that non-equilibriumconditions exist for long periods. Moreover, reaction rates can be sensitive to poorly understoodcatalytic effects or to surface effects, while variables as concentration (a largenumber of chemical species can coexist and interact concurrently), temperature and pressurecan have large gradients in natural systems. By taking into account this, data of 91water samples have been modelled by using statistical methodologies for compositionaldata. The application of log–contrast analysis has allowed to obtain statistical parametersto be correlated with the calculated Eh values. In this way, natural conditions in whichchemical equilibrium is hypothesised, as well as underlying fast reactions, are comparedwith those described by a stochastic approach

Compositional ideas in the bayesian analysis of categorical data with application to dose finding clinical trials

Compositional random vectors are fundamental tools in the Bayesian analysis of categorical data.Many of the issues that are discussed with reference to the statistical analysis of compositionaldata have a natural counterpart in the construction of a Bayesian statistical model for categoricaldata.This note builds on the idea of cross-fertilization of the two areas recommended by Aitchison (1986)in his seminal book on compositional data. Particular emphasis is put on the problem of whatparameterization to use

Compositional analysis of archaeological glasses

At CoDaWork'03 we presented work on the analysis of archaeological glass composi-tional data. Such data typically consist of geochemical compositions involving 10-12variables and approximates completely compositional data if the main component, sil-ica, is included. We suggested that what has been termed `crude' principal componentanalysis (PCA) of standardized data often identi ed interpretable pattern in the datamore readily than analyses based on log-ratio transformed data (LRA). The funda-mental problem is that, in LRA, minor oxides with high relative variation, that maynot be structure carrying, can dominate an analysis and obscure pattern associatedwith variables present at higher absolute levels. We investigate this further using sub-compositional data relating to archaeological glasses found on Israeli sites. A simplemodel for glass-making is that it is based on a `recipe' consisting of two `ingredients',sand and a source of soda. Our analysis focuses on the sub-composition of componentsassociated with the sand source. A `crude' PCA of standardized data shows two clearcompositional groups that can be interpreted in terms of di erent recipes being used atdi erent periods, reected in absolute di erences in the composition. LRA analysis canbe undertaken either by normalizing the data or de ning a `residual'. In either case,after some `tuning', these groups are recovered. The results from the normalized LRAare di erently interpreted as showing that the source of sand used to make the glassdi ered. These results are complementary. One relates to the recipe used. The otherrelates to the composition (and presumed sources) of one of the ingredients. It seemsto be axiomatic in some expositions of LRA that statistical analysis of compositionaldata should focus on relative variation via the use of ratios. Our analysis suggests thatabsolute di erences can also be informative

Interpretation of wind components as compositional variables

The classical statistical study of the wind speed in the atmospheric surface layer is madegenerally from the analysis of the three habitual components that perform the wind data,that is, the component W-E, the component S-N and the vertical component,considering these components independent.When the goal of the study of these data is the Aeolian energy, so is when wind isstudied from an energetic point of view and the squares of wind components can beconsidered as compositional variables. To do so, each component has to be divided bythe module of the corresponding vector.In this work the theoretical analysis of the components of the wind as compositionaldata is presented and also the conclusions that can be obtained from the point of view ofthe practical applications as well as those that can be derived from the application ofthis technique in different conditions of weather

Potential risk factors for multiple sclerosis in Rio de Janeiro: a case-control study.

PURPOSE. To evaluate potential risk factors for the development of multiple sclerosis in Brazilian patients. METHOD. A case control study was carried out in 81 patients enrolled at the Department of Neurology of the Hospital da Lagoa in Rio de Janeiro, and 81 paired controls. A standardized questionnaire on demographic, social and cultural variables, and medical and family history was used. Statistical analysis was performed using descriptive statistics and conditional logistic regression models with the SPSS for Windows software program. RESULTS. Having standard vaccinations (vaccinations specified by the Brazilian government) (OR=16.2; 95% CI=2.3-115.2), smoking (OR=7.6; 95% CI=2.1-28.2), being single (OR=4.7; 95% CI=1.4-15.6) and eating animal brain (OR=3.4; 95% CI=1.2-9.8) increased the risk of developing MS. CONCLUSIONS. RESULTS of this study may contribute towards better awareness of the epidemiological characteristics of Brazilian patients with multiple sclerosis.

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 casestudy of how precision could be conveyed if the multivariate nature of data has to betaken into account. In the official release of the Swiss earnings structure survey, the totalsalary is broken down into several wage components. We follow Aitchison's approachfor the analysis of compositional data, which is based on logratios of components. Wefirst present diferent multivariate analyses of the compositional data whereby the wagecomponents are broken down by economic activity classes. Then we propose a numberof ways to assess precision

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 differencesbetween them based on their origin and also on commercial criteria. A particularanalysis based on their vertical zonality is also given for samples from Solnechnoedeposit. All the statistical analysis are made on the subcomposition formed by seventrace elements in cassiterite (In, Sc, Be, W, Nb, Ti and V) using the Aitchison’methodology of analysis of compositional data

Differential cognitive impairment for diverse forms of multiple sclerosis.

BACKGROUND Cognitive impairment is a common feature in multiple sclerosis (MS) patients and occurs in 60% of all cases. Unfortunately, neurological examination does not always agree with the neuropsychological evaluation in determining the cognitive profile of the patient. On the other hand, psychophysiological techniques such as event-related potentials (ERPs) can help in evaluating cognitive impairment in different pathologies. Behavioural responses and EEG signals were recorded during the experiment in three experimental groups: 1) a relapsing-remitting group (RRMS), 2) a benign multiple sclerosis group (BMS) and 3) a Control group. The paradigm employed was a spatial attention task with central cues (Posner experiment). The main aim was to observe the differences in the performance (behavioural variables) and in the latency and amplitude of the ERP components among these groups. RESULTS Our data indicate that both MS groups showed poorer task performance (longer reaction times and lower percentage of correct responses), a latency delay for the N1 and P300 component, and a different amplitude for the frontal N1. Moreover, the deficit in the BMS group, indexed by behavioural and pyschophysiological variables, was more pronounced compared to the RRMS group. CONCLUSION The present results suggest a cognitive impairment in the information processing in all of these patients. Comparing both pathological groups, cognitive impairment was more accentuated in the BMS group compared to the RMSS group. This suggests a silent deterioration of cognitive skills for the BMS that is not usually treated with pharmacological or neuropsychological therapy.

Characterization of Mycobacterium tuberculosis Beijing isolates from the Mediterranean area

BACKGROUND. The Beijing lineage of Mycobacterium tuberculosis is causing concern due to its global distribution and its involvement in severe outbreaks. Studies focused on this lineage are mainly restricted to geographical settings where its prevalence is high, whereas those in other areas are scarce. In this study, we analyze Beijing isolates in the Mediterranean area, where this lineage is not prevalent and is mainly associated with immigrant cases. RESULTS. Only 1% (N = 26) of the isolates from two population-based studies in Spain corresponded to Beijing strains, most of which were pan-susceptible and from Peruvian and Ecuadorian patients. Restriction fragment length polymorphism typing with the insertion sequence IS6110 identified three small clusters (2-3 cases). Mycobacterial interspersed repetitive unit-variable number tandem repeat typing (MIRU-15) offered low discriminatory power, requiring the introduction of five additional loci. A selection of the Beijing isolates identified in the Spanish sample, together with a sample of Beijing strains from Italy, to broaden the analysis context in the Mediterranean area, were assayed in an infection model with THP-1 cells. A wide range of intracellular growth rates was observed with only two isolates showing an increased intracellular replication, in both cases associated with contained production of TNF-alpha. No correlation was observed between virulence and the Beijing phylogenetic group, clustered/orphan status, or resistance. The Beijing strain responsible for extensive spread on Gran Canaria Island was also identified in Madrid, but did not lead to secondary cases and did not show high infectivity in the infection model. CONCLUSIONS. The Beijing lineage in our area is a non-homogeneous family, with only certain highly virulent representatives. The specific characterization of Beijing isolates in different settings could help us to accurately identify the virulent representatives before making general assumptions about this lineage.

CODAPACK3D. A new version of Compositional Data Package

The statistical analysis of compositional data should be treated using logratios of parts,which are difficult to use correctly in standard statistical packages. For this reason afreeware package, named CoDaPack was created. This software implements most of thebasic statistical methods suitable for compositional data.In this paper we describe the new version of the package that now is calledCoDaPack3D. It is developed in Visual Basic for applications (associated with Excel©),Visual Basic and Open GL, and it is oriented towards users with a minimum knowledgeof computers with the aim at being simple and easy to use.This new version includes new graphical output in 2D and 3D. These outputs could bezoomed and, in 3D, rotated. Also a customization menu is included and outputs couldbe saved in jpeg format. Also this new version includes an interactive help and alldialog windows have been improved in order to facilitate its use.To use CoDaPack one has to access Excel© and introduce the data in a standardspreadsheet. These should be organized as a matrix where Excel© rows correspond tothe observations and columns to the parts. The user executes macros that returnnumerical or graphical results. There are two kinds of numerical results: new variablesand descriptive statistics, and both appear on the same sheet. Graphical output appearsin independent windows. In the present version there are 8 menus, with a total of 38submenus which, after some dialogue, directly call the corresponding macro. Thedialogues ask the user to input variables and further parameters needed, as well aswhere to put these results. The web site http://ima.udg.es/CoDaPack contains thisfreeware package and only Microsoft Excel© under Microsoft Windows© is required torun the software.Kew words: Compositional data Analysis, Software