Analysis of sensitivity with respect to a compositional parameter : A comment on 'Local sensitivity analysis for compositional data with application to soil texture in hydrologic modelling' by L. Loosvelt and co-authors

A comment about the article “Local sensitivity analysis for compositional data with application to soil texture in hydrologic modelling” writen by L. Loosvelt and co-authors. The present comment is centered in three specific points. The first one is related to the fact that the authors avoid the use of ilr-coordinates. The second one refers to some generalization of sensitivity analysis when input parameters are compositional. The third tries to show that the role of the Dirichlet distribution in the sensitivity analysis is irrelevant

Subtypes of adolescents with substance use disorders and psychiatric comorbidity using cluster and discriminant analysis of MMPI-A profiles

The main aim of this study was to replicate and extend previous results on subtypes of adolescents with substance use disorders (SUD), according to their Minnesota Multiphasic Personality Inventory for adolescents (MMPI-A) profiles. Sixty patients with SUD and psychiatric comorbidity (41.7% male, mean age = 15.9 years old) completed the MMPI-A, the Teen Addiction Severity Index (T-ASI), the Child Behaviour Checklist (CBCL), and were interviewed in order to determine DSMIV diagnoses and level of substance use. Mean MMPI-A personality profile showed moderate peaks in Psychopathic Deviate, Depression and Hysteria scales. Hierarchical cluster analysis revealed four profiles (acting-out, 35% of the sample; disorganized-conflictive, 15%; normative-impulsive, 15%; and deceptive-concealed, 35%). External correlates were found between cluster 1, CBCL externalizing symptoms at a clinical level and conduct disorders, and between cluster 2 and mixed CBCL internalized/externalized symptoms at a clinical level. Discriminant analysis showed that Depression, Psychopathic Deviate and Psychasthenia MMPI-A scales correctly classified 90% of the patients into the clusters obtained.

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

In any discipline, where uncertainty and variability are present, it is important to haveprinciples which are accepted as inviolate and which should therefore drive statisticalmodelling, 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 andfrom these a sensible, meaningful methodology has been developed for the statisticalanalysis of compositional data, the application of inappropriate and/or meaninglessmethods persists in many areas of application. This paper identifies at least tencommon fallacies and confusions in compositional data analysis with illustrativeexamples and provides readers with necessary, and hopefully sufficient, arguments topersuade the culprits why and how they should amend their ways

Effects of cobalt-chromium everolimus eluting stents or bare metal stent on fatal and non-fatal cardiovascular events: patient level meta-analysis

Objectives: To examine the safety and effectiveness of cobalt-chromium everolimus eluting stents compared with bare metal stents. Design: Individual patient data meta-analysis of randomised controlled trials. Cox proportional regression models stratified by trial, containing random effects, were used to assess the impact of stent type on outcomes. Hazard ratios with 95% confidence interval for outcomes were reported. Data sources and study selection: Medline, Embase, the Cochrane Central Register of Controlled Trials. Randomised controlled trials that compared cobalt-chromium everolimus eluting stents with bare metal stents were selected. The principal investigators whose trials met the inclusion criteria provided data for individual patients. Primary outcomes: The primary outcome was cardiac mortality. Secondary endpoints were myocardial infarction, definite stent thrombosis, definite or probable stent thrombosis, target vessel revascularisation, and all cause death. Results: The search yielded five randomised controlled trials, comprising 4896 participants. Compared with patients receiving bare metal stents, participants receiving cobalt-chromium everolimus eluting stents had a significant reduction of cardiac mortality (hazard ratio 0.67, 95% confidence interval 0.49 to 0.91; P=0.01), myocardial infarction (0.71, 0.55 to 0.92; P=0.01), definite stent thrombosis (0.41, 0.22 to 0.76; P=0.005), definite or probable stent thrombosis (0.48, 0.31 to 0.73; P<0.001), and target vessel revascularisation (0.29, 0.20 to 0.41; P<0.001) at a median follow-up of 720 days. There was no significant difference in all cause death between groups (0.83, 0.65 to 1.06; P=0.14). Findings remained unchanged at multivariable regression after adjustment for the acuity of clinical syndrome (for instance, acute coronary syndrome v stable coronary artery disease), diabetes mellitus, female sex, use of glycoprotein IIb/IIIa inhibitors, and up to one year v longer duration treatment with dual antiplatelets. Conclusions: This meta-analysis offers evidence that compared with bare metal stents the use of cobalt-chromium everolimus eluting stents improves global cardiovascular outcomes including cardiac survival, myocardial infarction, and overall stent thrombosis.

Effects of cobalt-chromium everolimus eluting stents or bare metal stent on fatal and non-fatal cardiovascular events: patient level meta-analysis

Objectives: To examine the safety and effectiveness of cobalt-chromium everolimus eluting stents compared with bare metal stents. Design: Individual patient data meta-analysis of randomised controlled trials. Cox proportional regression models stratified by trial, containing random effects, were used to assess the impact of stent type on outcomes. Hazard ratios with 95% confidence interval for outcomes were reported. Data sources and study selection: Medline, Embase, the Cochrane Central Register of Controlled Trials. Randomised controlled trials that compared cobalt-chromium everolimus eluting stents with bare metal stents were selected. The principal investigators whose trials met the inclusion criteria provided data for individual patients. Primary outcomes: The primary outcome was cardiac mortality. Secondary endpoints were myocardial infarction, definite stent thrombosis, definite or probable stent thrombosis, target vessel revascularisation, and all cause death. Results: The search yielded five randomised controlled trials, comprising 4896 participants. Compared with patients receiving bare metal stents, participants receiving cobalt-chromium everolimus eluting stents had a significant reduction of cardiac mortality (hazard ratio 0.67, 95% confidence interval 0.49 to 0.91; P=0.01), myocardial infarction (0.71, 0.55 to 0.92; P=0.01), definite stent thrombosis (0.41, 0.22 to 0.76; P=0.005), definite or probable stent thrombosis (0.48, 0.31 to 0.73; P<0.001), and target vessel revascularisation (0.29, 0.20 to 0.41; P<0.001) at a median follow-up of 720 days. There was no significant difference in all cause death between groups (0.83, 0.65 to 1.06; P=0.14). Findings remained unchanged at multivariable regression after adjustment for the acuity of clinical syndrome (for instance, acute coronary syndrome v stable coronary artery disease), diabetes mellitus, female sex, use of glycoprotein IIb/IIIa inhibitors, and up to one year v longer duration treatment with dual antiplatelets. Conclusions: This meta-analysis offers evidence that compared with bare metal stents the use of cobalt-chromium everolimus eluting stents improves global cardiovascular outcomes including cardiac survival, myocardial infarction, and overall stent thrombosis.

L’arbre de régression multivariable et les modèles linéaires généralisés revisités : applications à l’étude de la diversité bêta et à l’estimation de la biomasse d’arbres tropicaux

En écologie, dans le cadre par exemple d’études des services fournis par les écosystèmes, les modélisations descriptive, explicative et prédictive ont toutes trois leur place distincte. Certaines situations bien précises requièrent soit l’un soit l’autre de ces types de modélisation ; le bon choix s’impose afin de pouvoir faire du modèle un usage conforme aux objectifs de l’étude. Dans le cadre de ce travail, nous explorons dans un premier temps le pouvoir explicatif de l’arbre de régression multivariable (ARM). Cette méthode de modélisation est basée sur un algorithme récursif de bipartition et une méthode de rééchantillonage permettant l’élagage du modèle final, qui est un arbre, afin d’obtenir le modèle produisant les meilleures prédictions. Cette analyse asymétrique à deux tableaux permet l’obtention de groupes homogènes d’objets du tableau réponse, les divisions entre les groupes correspondant à des points de coupure des variables du tableau explicatif marquant les changements les plus abrupts de la réponse. Nous démontrons qu’afin de calculer le pouvoir explicatif de l’ARM, on doit définir un coefficient de détermination ajusté dans lequel les degrés de liberté du modèle sont estimés à l’aide d’un algorithme. Cette estimation du coefficient de détermination de la population est pratiquement non biaisée. Puisque l’ARM sous-tend des prémisses de discontinuité alors que l’analyse canonique de redondance (ACR) modélise des gradients linéaires continus, la comparaison de leur pouvoir explicatif respectif permet entre autres de distinguer quel type de patron la réponse suit en fonction des variables explicatives. La comparaison du pouvoir explicatif entre l’ACR et l’ARM a été motivée par l’utilisation extensive de l’ACR afin d’étudier la diversité bêta. Toujours dans une optique explicative, nous définissons une nouvelle procédure appelée l’arbre de régression multivariable en cascade (ARMC) qui permet de construire un modèle tout en imposant un ordre hiérarchique aux hypothèses à l’étude. Cette nouvelle procédure permet d’entreprendre l’étude de l’effet hiérarchisé de deux jeux de variables explicatives, principal et subordonné, puis de calculer leur pouvoir explicatif. L’interprétation du modèle final se fait comme dans une MANOVA hiérarchique. On peut trouver dans les résultats de cette analyse des informations supplémentaires quant aux liens qui existent entre la réponse et les variables explicatives, par exemple des interactions entres les deux jeux explicatifs qui n’étaient pas mises en évidence par l’analyse ARM usuelle. D’autre part, on étudie le pouvoir prédictif des modèles linéaires généralisés en modélisant la biomasse de différentes espèces d’arbre tropicaux en fonction de certaines de leurs mesures allométriques. Plus particulièrement, nous examinons la capacité des structures d’erreur gaussienne et gamma à fournir les prédictions les plus précises. Nous montrons que pour une espèce en particulier, le pouvoir prédictif d’un modèle faisant usage de la structure d’erreur gamma est supérieur. Cette étude s’insère dans un cadre pratique et se veut un exemple pour les gestionnaires voulant estimer précisément la capture du carbone par des plantations d’arbres tropicaux. Nos conclusions pourraient faire partie intégrante d’un programme de réduction des émissions de carbone par les changements d’utilisation des terres.

Lecture Notes on Compositional Data Analysis

These notes have been prepared as support to a short course on compositional data analysis. Their aim is to transmit the basic concepts and skills for simple applications, thus setting the premises for more advanced projects

Compositional data analysis: where we are and where should we be heading?

We take stock of the present position of compositional data analysis, of what has been achieved in the last 20 years, and then make suggestions as to what may be sensible avenues of future research. We take an uncompromisingly applied mathematical view, that the challenge of solving practical problems should motivate our theoretical research; and that any new theory should be thoroughly investigated to see if it may provide answers to previously abandoned practical considerations. Indeed a main theme of this lecture will be to demonstrate this applied mathematical approach by a number of challenging examples

Some last thoughts on compositional data analysis

One of the disadvantages of old age is that there is more past than future: this, however, may be turned into an advantage if the wealth of experience and, hopefully, wisdom gained in the past can be reflected upon and throw some light on possible future trends. To an extent, then, this talk is necessarily personal, certainly nostalgic, but also self critical and inquisitive about our understanding of the discipline of statistics. A number of almost philosophical themes will run through the talk: search for appropriate modelling in relation to the real problem envisaged, emphasis on sensible balances between simplicity and complexity, the relative roles of theory and practice, the nature of communication of inferential ideas to the statistical layman, the inter-related roles of teaching, consultation and research. A list of keywords might be: identification of sample space and its mathematical structure, choices between transform and stay, the role of parametric modelling, the role of a sample space metric, the underused hypothesis lattice, the nature of compositional change, particularly in relation to the modelling of processes. While the main theme will be relevance to compositional data analysis we shall point to substantial implications for general multivariate analysis arising from experience of the development of compositional data analysis…

Comparing correspondence analysis and the log-ratio alternative for representing categorical data

We compare correspondance análisis to the logratio approach based on compositional data. We also compare correspondance análisis and an alternative approach using Hellinger distance, for representing categorical data in a contingency table. We propose a coefficient which globally measures the similarity between these approaches. This coefficient can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions to the difference between the two representations. These three methods of representation can produce quite similar results. One illustrative example is given

Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

An R Library for Compositional Data Analysis in Archaeometry

Compositional data naturally arises from the scientific analysis of the chemical composition of archaeological material such as ceramic and glass artefacts. Data of this type can be explored using a variety of techniques, from standard multivariate methods such as principal components analysis and cluster analysis, to methods based upon the use of log-ratios. The general aim is to identify groups of chemically similar artefacts that could potentially be used to answer questions of provenance. This paper will demonstrate work in progress on the development of a documented library of methods, implemented using the statistical package R, for the analysis of compositional data. R is an open source package that makes available very powerful statistical facilities at no cost. We aim to show how, with the aid of statistical software such as R, traditional exploratory multivariate analysis can easily be used alongside, or in combination with, specialist techniques of compositional data analysis. The library has been developed from a core of basic R functionality, together with purpose-written routines arising from our own research (for example that reported at CoDaWork'03). In addition, we have included other appropriate publicly available techniques and libraries that have been implemented in R by other authors. Available functions range from standard multivariate techniques through to various approaches to log-ratio analysis and zero replacement. We also discuss and demonstrate a small selection of relatively new techniques that have hitherto been little-used in archaeometric applications involving compositional data. The application of the library to the analysis of data arising in archaeometry will be demonstrated; results from different analyses will be compared; and the utility of the various methods discussed

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 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