Exploration of geological variability and possible processes through the use of compositional data analysis: an example using scottish metamorphosed

Developments in the statistical analysis of compositional data over the last twodecades have made possible a much deeper exploration of the nature of variability,and the possible processes associated with compositional data sets from manydisciplines. In this paper we concentrate on geochemical data sets. First we explainhow hypotheses of compositional variability may be formulated within the naturalsample space, the unit simplex, including useful hypotheses of subcompositionaldiscrimination and specific perturbational change. Then we develop through standardmethodology, such as generalised likelihood ratio tests, statistical tools to allow thesystematic investigation of a complete lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require specialconstruction. We comment on the use of graphical methods in compositional dataanalysis and on the ordination of specimens. The recent development of the conceptof compositional processes is then explained together with the necessary tools for astaying- in-the-simplex approach, namely compositional singular value decompositions. All these statistical techniques are illustrated for a substantial compositional data set, consisting of 209 major-oxide and rare-element compositions of metamorphosed limestones from the Northeast and Central Highlands of Scotland.Finally we point out a number of unresolved problems in the statistical analysis ofcompositional processes

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

The allometry of non-employment. What can compositional data analysis tell us about labour market performance across the UK's regions?

The low levels of unemployment recorded in the UK in recent years are widely cited asevidence of the country’s improved economic performance, and the apparent convergence of unemployment rates across the country’s regions used to suggest that the longstanding divide in living standards between the relatively prosperous ‘south’ and the more depressed ‘north’ has been substantially narrowed. Dissenters from theseconclusions have drawn attention to the greatly increased extent of non-employment(around a quarter of the UK’s working age population are not in employment) and themarked regional dimension in its distribution across the country. Amongst these dissenters it is generally agreed that non-employment is concentrated amongst oldermales previously employed in the now very much smaller ‘heavy’ industries (e.g. coal,steel, shipbuilding).This paper uses the tools of compositiona l data analysis to provide a much richer picture of non-employment and one which challenges the conventional analysis wisdom about UK labour market performance as well as the dissenters view of the nature of theproblem. It is shown that, associated with the striking ‘north/south’ divide in nonemployment rates, there is a statistically significant relationship between the size of the non-employment rate and the composition of non-employment. Specifically, it is shown that the share of unemployment in non-employment is negatively correlated with the overall non-employment rate: in regions where the non-employment rate is high the share of unemployment is relatively low. So the unemployment rate is not a very reliable indicator of regional disparities in labour market performance. Even more importantly from a policy viewpoint, a significant positive relationship is found between the size ofthe non-employment rate and the share of those not employed through reason of sicknessor disability and it seems (contrary to the dissenters) that this connection is just as strong for women as it is for men

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

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

The agreement between ipsative and normative questionnaires using compositional data analysis techniques

The main instrument used in psychological measurement is the self-report questionnaire. One of its majordrawbacks however is its susceptibility to response biases. A known strategy to control these biases hasbeen the use of so-called ipsative items. Ipsative items are items that require the respondent to makebetween-scale comparisons within each item. The selected option determines to which scale the weight ofthe answer is attributed. Consequently in questionnaires only consisting of ipsative items everyrespondent is allotted an equal amount, i.e. the total score, that each can distribute differently over thescales. Therefore this type of response format yields data that can be considered compositional from itsinception.Methodological oriented psychologists have heavily criticized this type of item format, since the resultingdata is also marked by the associated unfavourable statistical properties. Nevertheless, clinicians havekept using these questionnaires to their satisfaction. This investigation therefore aims to evaluate bothpositions and addresses the similarities and differences between the two data collection methods. Theultimate objective is to formulate a guideline when to use which type of item format.The comparison is based on data obtained with both an ipsative and normative version of threepsychological questionnaires, which were administered to 502 first-year students in psychology accordingto a balanced within-subjects design. Previous research only compared the direct ipsative scale scoreswith the derived ipsative scale scores. The use of compositional data analysis techniques also enables oneto compare derived normative score ratios with direct normative score ratios. The addition of the secondcomparison not only offers the advantage of a better-balanced research strategy. In principle it also allowsfor parametric testing in the evaluation

Coordinated effects of sequence variation on DNA binding, chromatin structure, and transcription.

DNA sequence variation has been associated with quantitative changes in molecular phenotypes such as gene expression, but its impact on chromatin states is poorly characterized. To understand the interplay between chromatin and genetic control of gene regulation, we quantified allelic variability in transcription factor binding, histone modifications, and gene expression within humans. We found abundant allelic specificity in chromatin and extensive local, short-range, and long-range allelic coordination among the studied molecular phenotypes. We observed genetic influence on most of these phenotypes, with histone modifications exhibiting strong context-dependent behavior. Our results implicate transcription factors as primary mediators of sequence-specific regulation of gene expression programs, with histone modifications frequently reflecting the primary regulatory event.

A compositional statistical analysis of capital stock

Most of economic literature has presented its analysis under the assumption of homogeneous capital stock.However, capital composition differs across countries. What has been the pattern of capital compositionassociated with World economies? We make an exploratory statistical analysis based on compositional datatransformed by Aitchinson logratio transformations and we use tools for visualizing and measuring statisticalestimators of association among the components. The goal is to detect distinctive patterns in the composition.As initial findings could be cited that:1. Sectorial components behaved in a correlated way, building industries on one side and , in a lessclear view, equipment industries on the other.2. Full sample estimation shows a negative correlation between durable goods component andother buildings component and between transportation and building industries components.3. Countries with zeros in some components are mainly low income countries at the bottom of theincome category and behaved in a extreme way distorting main results observed in the fullsample.4. After removing these extreme cases, conclusions seem not very sensitive to the presence ofanother isolated cases

Magma generation at the easternmost section of the Hellenic arc: Hf, Nd, Pb and Sr isotope geochemistry of Nisyros and Yali volcanoes (Greece)

Geochemical and petrographical studies of lavas and ignimbrites from the Quaternary Nisyros-Yali volcanic system in the easternmost part of the Hellenic arc (Greece) reveal insight into magma generating processes. A compositional gap between 61 and 68 wt.% SiO2 is recognized that coincides with the stratigraphic distinction between pre-caldera and postcaldera volcanic units. Trace element systematics support the subdivision of Nisyros and Yali volcanic units into two distinct suites of rocks. The variation of Nd and Hf present day isotope data and the fact that they are distinct from the isotope compositions of MORB rule out an origin by pure differentiation and require assimilation of a crustal component. Lead isotope ratios of Nisyros and Yali volcanic rocks support mixing of mantle material with a lower crust equivalent. However, Sr-87/Sr-86 ratios of 0.7036-0.7048 are incompatible with a simple binary mixing scenario and give low depleted mantle extraction ages (< 0.1 Ga), in contrast with Pb model ages of 0.3 Ga and Hf and Nd model ages of ca. 0.8 Ga. The budget of fluid-mobile elements Sr and Pb is likely to be dominated by abundant hydrous fluids characterised by mantle-like Sr isotope ratios. Late stage fluids probably were enriched in CO2, needed to explain the high Th concentrations. The occurrence of hydrated minerals (e.g., amphibole) in the first post-caldera unit with the lowermost Sr-87/Sr-86 ratio of 0.7036 +/- 2 can be interpreted as the result of the increased water activity in the source. The presence of two different plagioclase phenocryst generations in the first lava subsequent to the caldera-causing event is indicative for a longer storage time of this magma at a shallower level. A model capable of explaining these observations involves three evolutionary stages. First stage, assimilation of lower crustal material by a primitive magma of mantle origin (as modelled by Nd-Hf isotope systematics). This stage ended by an interruption in replenishment that led to an increase of crystallization and, hence, an increase in viscosity, suppressing eruption. During this time gap, differentiation by fractional crystallization led to enrichment of incompatible species, especially aqueous fluids, to silica depolymerisation and to a decrease in viscosity, finally enabling eruption again in the third stage. (c) 2005 Elsevier B.V. All rights reserved.

Validation of order rank scales based on compositional data analysis: a proposal

Usually, psychometricians apply classical factorial analysis to evaluate construct validity of order rankscales. Nevertheless, these scales have particular characteristics that must be taken into account: totalscores and rank are highly relevant

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

Brachial artery peak velocity variation to predict fluid responsiveness in mechanically ventilated patients

INTRODUCTION Although several parameters have been proposed to predict the hemodynamic response to fluid expansion in critically ill patients, most of them are invasive or require the use of special monitoring devices. The aim of this study is to determine whether noninvasive evaluation of respiratory variation of brachial artery peak velocity flow measured using Doppler ultrasound could predict fluid responsiveness in mechanically ventilated patients. METHODS We conducted a prospective clinical research in a 17-bed multidisciplinary ICU and included 38 mechanically ventilated patients for whom fluid administration was planned due to the presence of acute circulatory failure. Volume expansion (VE) was performed with 500 mL of a synthetic colloid. Patients were classified as responders if stroke volume index (SVi) increased >or= 15% after VE. The respiratory variation in Vpeakbrach (DeltaVpeakbrach) was calculated as the difference between maximum and minimum values of Vpeakbrach over a single respiratory cycle, divided by the mean of the two values and expressed as a percentage. Radial arterial pressure variation (DeltaPPrad) and stroke volume variation measured using the FloTrac/Vigileo system (DeltaSVVigileo), were also calculated. RESULTS VE increased SVi by >or= 15% in 19 patients (responders). At baseline, DeltaVpeakbrach, DeltaPPrad and DeltaSVVigileo were significantly higher in responder than nonresponder patients [14 vs 8%; 18 vs. 5%; 13 vs 8%; P < 0.0001, respectively). A DeltaVpeakbrach value >10% predicted fluid responsiveness with a sensitivity of 74% and a specificity of 95%. A DeltaPPrad value >10% and a DeltaSVVigileo >11% predicted volume responsiveness with a sensitivity of 95% and 79%, and a specificity of 95% and 89%, respectively. CONCLUSIONS Respiratory variations in brachial artery peak velocity could be a feasible tool for the noninvasive assessment of fluid responsiveness in patients with mechanical ventilatory support and acute circulatory failure. TRIAL REGISTRATION ClinicalTrials.gov ID: NCT00890071.

Genetic-morphometric variation in Culex quinquefasciatus from Brazil and La Plata, Argentina

Variation among natural populations of Culex (Culex) quinquefasciatus Say is associated with different vectorial capacities. The species Cx. quinquefasciatus is present in the equatorial, tropical and subtropical zones in the Brazilian territory, with intermediate forms between Cx. quinquefasciatus and Culex pipiens occurring in regions of latitudes around 33°-35°S. Herein, we studied geographically distinct populations of Cx. quinquefasciatus by genetic characterization and analysis of intra-specific wing morphometrics. After morphological analysis, molecular characterization of Cx. quinquefasciatus and intermediate forms was performed by polymerase chain reaction of the polymorphic nuclear region of the second intron of the acetylcholinesterase locus. Additionally, the morphology of adult female wings collected from six locations was analyzed. Wing centroid sizes were significantly different between some geographical pairs. Mean values of R2/R2+3 differed significantly after pairwise comparisons. The overall wing shape represented by morphometric characters could be divided into two main groupings. Our data suggest that Brazilian samples are morphologically and genetically distinct from the Argentinean samples and also indicated a morphological distinction between northern and southern populations of Brazilian Cx. quinquefasciatus. We suggest that wing morphology may be used for preliminary assessment of population structure of Cx. quinquefasciatusin Brazil.