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

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 two decades have made possible a much deeper exploration of the nature of variability, and the possible processes associated with compositional data sets from many disciplines. In this paper we concentrate on geochemical data sets. First we explain how hypotheses of compositional variability may be formulated within the natural sample space, the unit simplex, including useful hypotheses of subcompositional discrimination and specific perturbational change. Then we develop through standard methodology, such as generalised likelihood ratio tests, statistical tools to allow the systematic investigation of a complete lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require special construction. We comment on the use of graphical methods in compositional data analysis and on the ordination of specimens. The recent development of the concept of compositional processes is then explained together with the necessary tools for a staying- 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 of compositional processes

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 compositional data have a natural counterpart in the construction of a Bayesian statistical model for categorical data. 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 what parameterization 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 10-12 variables and approximates completely compositional data if the main component, sil- ica, is included. We suggested that what has been termed `crude' principal component analysis (PCA) of standardized data often identi ed interpretable pattern in the data more 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 may not be structure carrying, can dominate an analysis and obscure pattern associated with variables present at higher absolute levels. We investigate this further using sub- compositional data relating to archaeological glasses found on Israeli sites. A simple model 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 components associated with the sand source. A `crude' PCA of standardized data shows two clear compositional groups that can be interpreted in terms of di erent recipes being used at di erent periods, re ected in absolute di erences in the composition. LRA analysis can be 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 LRA are di erently interpreted as showing that the source of sand used to make the glass di ered. These results are complementary. One relates to the recipe used. The other relates to the composition (and presumed sources) of one of the ingredients. It seems to be axiomatic in some expositions of LRA that statistical analysis of compositional data should focus on relative variation via the use of ratios. Our analysis suggests that absolute di erences can also be informative

The single principle of compositional data analysis, continuing fallacies, confusions and misunderstandings and some suggested remedies

In any discipline, where uncertainty and variability are present, it is important to have principles which are accepted as inviolate and which should therefore drive statistical modelling, statistical analysis of data and any inferences from such an analysis. Despite the fact that two such principles have existed over the last two decades and from these a sensible, meaningful methodology has been developed for the statistical analysis of compositional data, the application of inappropriate and/or meaningless methods persists in many areas of application. This paper identifies at least ten common fallacies and confusions in compositional data analysis with illustrative examples and provides readers with necessary, and hopefully sufficient, arguments to persuade the culprits why and how they should amend their ways

Analysis and Simulation of Transverse Random Fracture of Long Fibre Reinforced Composites

La present tesi proposa una metodología per a la simulació probabilística de la fallada de la matriu en materials compòsits reforçats amb fibres de carboni, basant-se en l'anàlisi de la distribució aleatòria de les fibres. En els primers capítols es revisa l'estat de l'art sobre modelització matemàtica de materials aleatoris, càlcul de propietats efectives i criteris de fallada transversal en materials compòsits. El primer pas en la metodologia proposada és la definició de la determinació del tamany mínim d'un Element de Volum Representatiu Estadístic (SRVE) . Aquesta determinació es du a terme analitzant el volum de fibra, les propietats elàstiques efectives, la condició de Hill, els estadístics de les components de tensió i defromació, la funció de densitat de probabilitat i les funcions estadístiques de distància entre fibres de models d'elements de la microestructura, de diferent tamany. Un cop s'ha determinat aquest tamany mínim, es comparen un model periòdic i un model aleatori, per constatar la magnitud de les diferències que s'hi observen. Es defineix, també, una metodologia per a l'anàlisi estadístic de la distribució de la fibra en el compòsit, a partir d'imatges digitals de la secció transversal. Aquest anàlisi s'aplica a quatre materials diferents. Finalment, es proposa un mètode computacional de dues escales per a simular la fallada transversal de làmines unidireccionals, que permet obtenir funcions de densitat de probabilitat per a les variables mecàniques. Es descriuen algunes aplicacions i possibilitats d'aquest mètode i es comparen els resultats obtinguts de la simulació amb valors experimentals.

A general-method for tracking analysis and its application to meteorological data

Recent interest in the validation of general circulation models (GCMs) has been devoted to objective methods. A small number of authors have used the direct synoptic identification of phenomena together with a statistical analysis to perform the objective comparison between various datasets. This paper describes a general method for performing the synoptic identification of phenomena that can be used for an objective analysis of atmospheric, or oceanographic, datasets obtained from numerical models and remote sensing. Methods usually associated with image processing have been used to segment the scene and to identify suitable feature points to represent the phenomena of interest. This is performed for each time level. A technique from dynamic scene analysis is then used to link the feature points to form trajectories. The method is fully automatic and should be applicable to a wide range of geophysical fields. An example will be shown of results obtained from this method using data obtained from a run of the Universities Global Atmospheric Modelling Project GCM.

Can knowledge of the state of the stratosphere be used to improve statistical forecasts of the troposphere?

Recent analysis of the Arctic Oscillation (AO) in the stratosphere and troposphere has suggested that predictability of the state of the tropospheric AO may be obtained from the state of the stratospheric AO. However, much of this research has been of a purely qualitative nature. We present a more thorough statistical analysis of a long AO amplitude dataset which seeks to establish the magnitude of such a link. A relationship between the AO in the lower stratosphere and on the 1000 hPa surface on a 10-45 day time-scale is revealed. The relationship accounts for 5% of the variance of the 1000 hPa time series at its peak value and is significant at the 5% level. Over a similar time-scale the 1000 hPa time series accounts for 1% of itself and is not significant at the 5% level. Further investigation of the relationship reveals that it is only present during the winter season and in particular during February and March. It is also demonstrated that using stratospheric AO amplitude data as a predictor in a simple statistical model results in a gain of skill of 5% over a troposphere-only statistical model. This gain in skill is not repeated if an unrelated time series is included as a predictor in the model. Copyright © 2003 Royal Meteorological Society

CAMCR: Computer assisted mixture model analysis for capture-recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

Sequentially testing for a gene-drug interaction in a genomewide analysis

Assaying a large number of genetic markers from patients in clinical trials is now possible in order to tailor drugs with respect to efficacy. The statistical methodology for analysing such massive data sets is challenging. The most popular type of statistical analysis is to use a univariate test for each genetic marker, once all the data from a clinical study have been collected. This paper presents a sequential method for conducting an omnibus test for detecting gene-drug interactions across the genome, thus allowing informed decisions at the earliest opportunity and overcoming the multiple testing problems from conducting many univariate tests. We first propose an omnibus test for a fixed sample size. This test is based on combining F-statistics that test for an interaction between treatment and the individual single nucleotide polymorphism (SNP). As SNPs tend to be correlated, we use permutations to calculate a global p-value. We extend our omnibus test to the sequential case. In order to control the type I error rate, we propose a sequential method that uses permutations to obtain the stopping boundaries. The results of a simulation study show that the sequential permutation method is more powerful than alternative sequential methods that control the type I error rate, such as the inverse-normal method. The proposed method is flexible as we do not need to assume a mode of inheritance and can also adjust for confounding factors. An application to real clinical data illustrates that the method is computationally feasible for a large number of SNPs. Copyright (c) 2007 John Wiley & Sons, Ltd.

CAMCR: Computer-Assisted Mixture model analysis for Capture–Recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

A structural analysis of M protein in coronavirus assembly and morphology

The M protein of coronavirus plays a central role in virus assembly, turning cellular membranes into workshops where virus and host factors come together to make new virus particles. We investigated how M structure and organization is related to virus shape and size using cryo-electron microscopy, tomography and statistical analysis. We present evidence that suggests M can adopt two conformations and that membrane curvature is regulated by one M conformer. Elongated M protein is associated with rigidity, clusters of spikes and a relatively narrow range of membrane curvature. In contrast, compact M protein is associated with flexibility and low spike density. Analysis of several types of virus-like particles and virions revealed that S protein, N protein and genomic RNA each help to regulate virion size and variation, presumably through interactions with M. These findings provide insight into how M protein functions to promote virus assembly.

The use of trajectory cluster analysis to interpret trace gas measurements at Mace Head, Ireland

A first step in interpreting the wide variation in trace gas concentrations measured over time at a given site is to classify the data according to the prevailing weather conditions. In order to classify measurements made during two intensive field campaigns at Mace Head, on the west coast of Ireland, an objective method of assigning data to different weather types has been developed. Air-mass back trajectories calculated using winds from ECMWF analyses, arriving at the site in 1995–1997, were allocated to clusters based on a statistical analysis of the latitude, longitude and pressure of the trajectory at 12 h intervals over 5 days. The robustness of the analysis was assessed by using an ensemble of back trajectories calculated for four points around Mace Head. Separate analyses were made for each of the 3 years, and for four 3-month periods. The use of these clusters in classifying ground-based ozone measurements at Mace Head is described, including the need to exclude data which have been influenced by local perturbations to the regional flow pattern, for example, by sea breezes. Even with a limited data set, based on 2 months of intensive field measurements in 1996 and 1997, there are statistically significant differences in ozone concentrations in air from the different clusters. The limitations of this type of analysis for classification and interpretation of ground-based chemistry measurements are discussed.

Integrated cytokine and metabolic analysis of pathological responses to parasite exposure in rodents

Parasitic infections cause a myriad of responses in their mammalian hosts, on immune as well as on metabolic level. A multiplex panel of cytokines and metabolites derived from four parasite-rodent models, namely, Plasmodium berghei-mouse, Trypanosoma brucei brucei-mouse, Schistosoma mansoni-mouse, and Fasciola hepatica-rat were statistically coanalyzed. 1H NMR spectroscopy and multivariate statistical analysis were used to characterize the urine and plasma metabolite profiles in infected and noninfected animals. Each parasite generated a unique metabolic signature in the host. Plasma cytokine concentrations were obtained using the ‘Meso Scale Discovery’ multi cytokine assay platform. Multivariate data integration methods were subsequently used to elucidate the component of the metabolic signature which is associated with inflammation and to determine specific metabolic correlates with parasite-induced changes in plasma cytokine levels. For example, the relative levels of acetyl glycoproteins extracted from the plasma metabolite profile in the P. berghei-infected mice were statistically correlated with IFN-γ, whereas the same cytokine was anticorrelated with glucose levels. Both the metabolic and the cytokine data showed a similar spatial distribution in principal component analysis scores plots constructed for the combined murine data, with samples from all infected animals clustering according to the parasite species and whereby the protozoan infections (P. berghei and T. b. brucei) grouped separately from the helminth infection (S. mansoni). For S. mansoni, the main infection-responsive cytokines were IL-4 and IL-5, which covaried with lactate, choline, and D-3-hydroxybutyrate. This study demonstrates that the inherently differential immune response to single and multicellular parasites not only manifests in the cytokine expression, but also consequently imprints on the metabolic signature, and calls for in-depth analysis to further explore direct links between immune features and biochemical pathways.

On the statistical modeling of persistence in total ozone anomalies

Geophysical time series sometimes exhibit serial correlations that are stronger than can be captured by the commonly used first‐order autoregressive model. In this study we demonstrate that a power law statistical model serves as a useful upper bound for the persistence of total ozone anomalies on monthly to interannual timescales. Such a model is usually characterized by the Hurst exponent. We show that the estimation of the Hurst exponent in time series of total ozone is sensitive to various choices made in the statistical analysis, especially whether and how the deterministic (including periodic) signals are filtered from the time series, and the frequency range over which the estimation is made. In particular, care must be taken to ensure that the estimate of the Hurst exponent accurately represents the low‐frequency limit of the spectrum, which is the part that is relevant to long‐term correlations and the uncertainty of estimated trends. Otherwise, spurious results can be obtained. Based on this analysis, and using an updated equivalent effective stratospheric chlorine (EESC) function, we predict that an increase in total ozone attributable to EESC should be detectable at the 95% confidence level by 2015 at the latest in southern midlatitudes, and by 2020–2025 at the latest over 30°–45°N, with the time to detection increasing rapidly with latitude north of this range.