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

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

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

Compositional data analysis of archaeological glass: problems and possible solutions

Presentation in CODAWORK'03, session 4: Applications to archeometry

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

Genetic investigation of the functions of c-Myc and N-Myc in Hematopoietic stem cells

Résumé : c-Myc, le premier facteur de transcription de la famille Myc a été découvert il y a maintenant trente ans. Il reste à l'heure actuelle parmi les plus puissants proto-oncogènes connus. c-Myc est dérégulé dans plus de 50% des cancers, où il promeut la prolifération, la croissance cellulaire, et la néoangiogenèse. Myc peut aussi influencer de nombreuses autres fonctions de par sa capacité à activer ou à réprimer la transcription de nombreux gènes, et à agir globalement sur le génome à travers des modifications épigénétiques de la chromatine. La famille d'oncogènes Myc comprend, chez les mammifères, trois protéines structurellement proches: c-Myc, N-Myc et L-Myc. Ces protéines ont les mêmes proprietés biochimiques, exercent les mêmes fonctions mais sont le plus souvent exprimées de façon mutuellement exclusive. Myc a été récemment identifié comme un facteur clef dans la maintenance des cellules souches embryonnaires et adultes ainsi que dans la réacquisition des proprietés des cellules souches. Nous avons précédemment démontré que l'élimination de c-Myc provoque une accumulation de cellules souches hématopoïétiques (CSH) suite à un défaut de différenciation lié à la niche. Les CSH sont responsables de la production de tous les éléments cellulaires du sang pour toute la vie de l'individu et sont définies par leur capacité à s'auto-renouveler tout en produisant des précurseurs hématopoïétiques. Afin de mieux comprendre la fonction de Myc dans les CSH, nous avons choisi de combiner l'utilisation de modèles de souris génétiquement modifiées à une caractérisation systématique des schémas d'expression de c-Myc, N-Myc et L-Myc dans tout le système hématopoïétique. Nous avons ainsi découvert que les CSH les plus immatures expriment des quantités équivalentes de transcrits de c-myc et N-myc. Si les CSH déficientes en N-myc seulement ont une capacité d'auto-renouvellement à long-terme réduite, l'invalidation combinée des gènes c-myc et N-myc conduit à une pan-cytopénie suivie d'une mort rapide de l'animal, pour cause d'apoptose de tous les types cellulaires hématopoïétiques. En particulier, les CSH en cours d'auto-renouvelemment, mais pas les CSH quiescentes, accumulent du Granzyme B (GrB), une molécule fortement cytotoxique qui provoque une mort cellulaire rapide. Ces données ont ainsi mis au jour un nouveau mécanisme dont dépend la survie des CSH, à savoir la répression du GrB, une enzyme typiquement utilisée par le système immunitaire inné pour éliminer les tumeurs et les cellules infectées par des virus. Dans le but d'évaluer l'étendue de la redondance entre c-Myc et N-Myc dans les CSH, nous avons d'une part examiné des souris dans lesquelles les séquences codantes de c-myc sont remplacées par celles de N-myc (NCR) et d'autre part nous avons géneré une série allèlique de myc en éliminant de façon combinatoire un ou plusieurs allèles de c-myc et/ou de N-myc. Alors que l'analyse des souris NCR suggère que c-Myc et N-Myc sont qualitativement redondants, la série allélique indique que les efficiences avec lesquelles ces deux protéines influencent des procédés essentiels à la maintenance des CSH sont différentes. En conclusion, nos données génétiques montrent que l'activité générale de MYC, fournie par c-Myc et N-Myc, contrôle plusieurs aspects cruciaux de la fonction des CSH, notamment l'auto-renouvellement, la survie et la différenciation. Abstract : c-Myc, the first Myc transcription factor was discovered 30 years ago and is to date one of the most potent proto-oncogenes described. It is found to be misregulated in over 50% of all cancers, where it drives proliferation, cell growth and neo-angiogenesis. Myc can also influence a variety of other functions, owing to its ability to activate and repress transcription of many target genes and to globally regulate the genome via epigenetic modifications of the chromatin. The Myc family of oncogenes consists of three closely related proteins in mammals: c-Myc, N-Myc and L-Myc. These proteins share the same biochemical properties, exert mostly the same functions, but are most often expressed in mutually exclusive patterns. Myc is now emerging as a key factor in maintenance of embryonic and adult stem cells as well as in reacquisition of stem cell properties, including induced reprogramming. We previously showed that c-Myc deficiency can cause the accumulation of hematopoietic stem cells (HSCs) due to a niche dependent differentiation defect. HSCs are responsible for life-long replenishment of all blood cell types, and are defined by their ability to self-renew while concomitantly giving rise to more commited progenitors. To gain further insight into the function of Myc in HSCs, in this study we combine the use of genetically-modified mouse models with the systematic characterization of c-myc, N-myc and L-myc transcription patterns throughout the hematopoietic system. Interestingly, the most immature HSCs express not only c-myc, but also about equal amounts of N-myc transcripts. Although conditional deletion of N-myc alone in the bone marrow does not affect steady-state hematopoiesis, N-myc null HSCs show impaired long-term self-renewal capacity. Strikingly, combined deficiency of c-Myc and N-Myc results in pan-cytopenia and rapid lethality, due to the apoptosis of most hematopoietic cell types. In particular, self-renewing HSCs, but not quiescent HSCs or progenitor cell types rapidly up-regulate and accumulate the potent cytotoxic molecule GranzymeB (GrB), causing their rapid cell death. These data uncover a novel pathway on which HSC survival depends on, namely repression of GrB, a molecule typically used by the innate immune system to eliminate tumor and virus infected cells. To evaluate the extent of redundancy between c-Myc and N-Myc in HSCs, we examined mice in which c-myc coding sequences are replaced by that of N-myc (NCR) and also generated an allelic series of myc, by combinatorially deleting one or several c-myc and/or N-myc alleles. While the analysis of NCR mice suggests that c-Myc and N-Myc are qualitatively functionally redundant, our allelic series indicates that the efficiencies with which these two proteins affect crucial HSC maintenance processes are likely to be distinct. Collectively, our genetic data show that general "MYC" activity delivered by c-Myc and N-Myc controls crucial aspects of HSC function, including self-renewal, survival and niche dependent differentiation.

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

Large-Area Photo-Mosaics Using Global Alignment and Navigation Data

Seafloor imagery is a rich source of data for the study of biological and geological processes. Among several applications, still images of the ocean floor can be used to build image composites referred to as photo-mosaics. Photo-mosaics provide a wide-area visual representation of the benthos, and enable applications as diverse as geological surveys, mapping and detection of temporal changes in the morphology of biodiversity. We present an approach for creating globally aligned photo-mosaics using 3D position estimates provided by navigation sensors available in deep water surveys. Without image registration, such navigation data does not provide enough accuracy to produce useful composite images. Results from a challenging data set of the Lucky Strike vent field at the Mid Atlantic Ridge are reported

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

Steroid hormone pulsing drives cyclic gene expression.

Transcriptional cycling of activated glucocorticoid receptor (GR) and ultradian glucocorticoid secretion are well established processes. Ultradian hormone release is now shown to result in pulsatile gene transcription through dynamic exchange of GR with the target-gene promoter and GR cycling through the chaperone machinery.

Local WMR navigation with monocular data

This article presents recent WMR (wheeled mobile robot) navigation experiences using local perception knowledge provided by monocular and odometer systems. A local narrow perception horizon is used to plan safety trajectories towards the objective. Therefore, monocular data are proposed as a way to obtain real time local information by building two dimensional occupancy grids through a time integration of the frames. The path planning is accomplished by using attraction potential fields, while the trajectory tracking is performed by using model predictive control techniques. The results are faced to indoor situations by using the lab available platform consisting in a differential driven mobile robot