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 are difficult to use correctly in standard statistical packages. In this paper we describe the new features of our freeware package, named CoDaPack, which implements most of the basic statistical methods suitable for compositional data. An example using real data is presented to illustrate the use of the package

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

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 major drawbacks however is its susceptibility to response biases. A known strategy to control these biases has been the use of so-called ipsative items. Ipsative items are items that require the respondent to make between-scale comparisons within each item. The selected option determines to which scale the weight of the answer is attributed. Consequently in questionnaires only consisting of ipsative items every respondent is allotted an equal amount, i.e. the total score, that each can distribute differently over the scales. Therefore this type of response format yields data that can be considered compositional from its inception. Methodological oriented psychologists have heavily criticized this type of item format, since the resulting data is also marked by the associated unfavourable statistical properties. Nevertheless, clinicians have kept using these questionnaires to their satisfaction. This investigation therefore aims to evaluate both positions and addresses the similarities and differences between the two data collection methods. The ultimate 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 three psychological questionnaires, which were administered to 502 first-year students in psychology according to a balanced within-subjects design. Previous research only compared the direct ipsative scale scores with the derived ipsative scale scores. The use of compositional data analysis techniques also enables one to compare derived normative score ratios with direct normative score ratios. The addition of the second comparison not only offers the advantage of a better-balanced research strategy. In principle it also allows for parametric testing in the evaluation

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 composition associated with World economies? We make an exploratory statistical analysis based on compositional data transformed by Aitchinson logratio transformations and we use tools for visualizing and measuring statistical estimators 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 less clear view, equipment industries on the other. 2. Full sample estimation shows a negative correlation between durable goods component and other 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 the income category and behaved in a extreme way distorting main results observed in the full sample. 4. After removing these extreme cases, conclusions seem not very sensitive to the presence of another isolated cases

Regression analysis of compositional data when both the dependent variable and independent variable are components

It is well known that regression analyses involving compositional data need special attention because the data are not of full rank. For a regression analysis where both the dependent and independent variable are components we propose a transformation of the components emphasizing their role as dependent and independent variables. A simple linear regression can be performed on the transformed components. The regression line can be depicted in a ternary diagram facilitating the interpretation of the analysis in terms of components. An exemple with time-budgets illustrates the method and the graphical features

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

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 a freeware package, named CoDaPack was created. This software implements most of the basic statistical methods suitable for compositional data. In this paper we describe the new version of the package that now is called CoDaPack3D. 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 knowledge of 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 be zoomed and, in 3D, rotated. Also a customization menu is included and outputs could be saved in jpeg format. Also this new version includes an interactive help and all dialog windows have been improved in order to facilitate its use. To use CoDaPack one has to access Excel�� and introduce the data in a standard spreadsheet. These should be organized as a matrix where Excel�� rows correspond to the observations and columns to the parts. The user executes macros that return numerical or graphical results. There are two kinds of numerical results: new variables and descriptive statistics, and both appear on the same sheet. Graphical output appears in independent windows. In the present version there are 8 menus, with a total of 38 submenus which, after some dialogue, directly call the corresponding macro. The dialogues ask the user to input variables and further parameters needed, as well as where to put these results. The web site http://ima.udg.es/CoDaPack contains this freeware package and only Microsoft Excel�� under Microsoft Windows�� is required to run the software. Kew words: Compositional data Analysis, Software

Statistical evidences of cyclic changes in volcanic gas chemistry composition by inverse modelling

The identification of compositional changes in fumarolic gases of active and quiescent volcanoes is one of the most important targets in monitoring programs. From a general point of view, many systematic (often cyclic) and random processes control the chemistry of gas discharges, making difficult to produce a convincing mathematical-statistical modelling. Changes in the chemical composition of volcanic gases sampled at Vulcano Island (Aeolian Arc, Sicily, Italy) from eight different fumaroles located in the northern sector of the summit crater (La Fossa) have been analysed by considering their dependence from time in the period 2000-2007. Each intermediate chemical composition has been considered as potentially derived from the contribution of the two temporal extremes represented by the 2000 and 2007 samples, respectively, by using inverse modelling methodologies for compositional data. Data pertaining to fumaroles F5 and F27, located on the rim and in the inner part of La Fossa crater, respectively, have been used to achieve the proposed aim. The statistical approach has allowed us to highlight the presence of random and not random fluctuations, features useful to understand how the volcanic system works, opening new perspectives in sampling strategies and in the evaluation of the natural risk related to a quiescent volcano

Compositions in life science data

The aim of this talk is to convince the reader that there are a lot of interesting statistical problems in presentday life science data analysis which seem ultimately connected with compositional statistics. Key words: SAGE, cDNA microarrays, (1D-)NMR, virus quasispecies

Analysis of Pleistocene paleodrainage evolution in the Po Basin (Italy) by multivariate statistical techniques

In order to obtain a high-resolution Pleistocene stratigraphy, eleven continuously cored boreholes, 100 to 220m deep were drilled in the northern part of the Po Plain by Regione Lombardia in the last five years. Quantitative provenance analysis (QPA, Weltje and von Eynatten, 2004) of Pleistocene sands was carried out by using multivariate statistical analysis (principal component analysis, PCA, and similarity analysis) on an integrated data set, including high-resolution bulk petrography and heavy-mineral analyses on Pleistocene sands and of 250 major and minor modern rivers draining the southern flank of the Alps from West to East (Garzanti et al, 2004; 2006). Prior to the onset of major Alpine glaciations, metamorphic and quartzofeldspathic detritus from the Western and Central Alps was carried from the axial belt to the Po basin longitudinally parallel to the SouthAlpine belt by a trunk river (Vezzoli and Garzanti, 2008). This scenario rapidly changed during the marine isotope stage 22 (0.87 Ma), with the onset of the first major Pleistocene glaciation in the Alps (Muttoni et al, 2003). PCA and similarity analysis from core samples show that the longitudinal trunk river at this time was shifted southward by the rapid southward and westward progradation of transverse alluvial river systems fed from the Central and Southern Alps. Sediments were transported southward by braided river systems as well as glacial sediments transported by Alpine valley glaciers invaded the alluvial plain. Kew words: Detrital modes; Modern sands; Provenance; Principal Components Analysis; Similarity, Canberra Distance; palaeodrainage

Clustering compositional data trajectories

Our essay aims at studying suitable statistical methods for the clustering of compositional data in situations where observations are constituted by trajectories of compositional data, that is, by sequences of composition measurements along a domain. Observed trajectories are known as ���functional data��� and several methods have been proposed for their analysis. In particular, methods for clustering functional data, known as Functional Cluster Analysis (FCA), have been applied by practitioners and scientists in many fields. To our knowledge, FCA techniques have not been extended to cope with the problem of clustering compositional data trajectories. In order to extend FCA techniques to the analysis of compositional data, FCA clustering techniques have to be adapted by using a suitable compositional algebra. The present work centres on the following question: given a sample of compositional data trajectories, how can we formulate a segmentation procedure giving homogeneous classes? To address this problem we follow the steps described below. First of all we adapt the well-known spline smoothing techniques in order to cope with the smoothing of compositional data trajectories. In fact, an observed curve can be thought of as the sum of a smooth part plus some noise due to measurement errors. Spline smoothing techniques are used to isolate the smooth part of the trajectory: clustering algorithms are then applied to these smooth curves. The second step consists in building suitable metrics for measuring the dissimilarity between trajectories: we propose a metric that accounts for difference in both shape and level, and a metric accounting for differences in shape only. A simulation study is performed in order to evaluate the proposed methodologies, using both hierarchical and partitional clustering algorithm. The quality of the obtained results is assessed by means of several indices

CAC controlled services sharing a link with connectionless data services in an ATM network: a performance evaluation study

In the B-ISDN there is a provision for four classes of services, all of them supported by a single transport network (the ATM network). Three of these services, the connected oriented (CO) ones, permit connection access control (CAC) but the fourth, the connectionless oriented (CLO) one, does not. Therefore, when CLO service and CO services have to share the same ATM link, a conflict may arise. This is because a bandwidth allocation to obtain maximum statistical gain can damage the contracted ATM quality of service (QOS); and vice versa, in order to guarantee the contracted QOS, the statistical gain have to be sacrificed. The paper presents a performance evaluation study of the influence of the CLO service on a CO service (a circuit emulation service or a variable bit-rate service) when sharing the same link

Measurement Quality in Indicators of Compositions: a Compositional Multitrait-Multimethod Approach

Compositional data, also called multiplicative ipsative data, are common in survey research instruments in areas such as time use, budget expenditure and social networks. Compositional data are usually expressed as proportions of a total, whose sum can only be 1. Owing to their constrained nature, statistical analysis in general, and estimation of measurement quality with a confirmatory factor analysis model for multitrait-multimethod (MTMM) designs in particular are challenging tasks. Compositional data are highly non-normal, as they range within the 0-1 interval. One component can only increase if some other(s) decrease, which results in spurious negative correlations among components which cannot be accounted for by the MTMM model parameters. In this article we show how researchers can use the correlated uniqueness model for MTMM designs in order to evaluate measurement quality of compositional indicators. We suggest using the additive log ratio transformation of the data, discuss several approaches to deal with zero components and explain how the interpretation of MTMM designs di ers from the application to standard unconstrained data. We show an illustration of the method on data of social network composition expressed in percentages of partner, family, friends and other members in which we conclude that the faceto-face collection mode is generally superior to the telephone mode, although primacy e ects are higher in the face-to-face mode. Compositions of strong ties (such as partner) are measured with higher quality than those of weaker ties (such as other network members)

La presi��n laboral tendenciosa (Mobbing)

El trabajo de investigaci��n surge en el a��o 2001, ante la necesidad de hacer frente a una nueva realidad jur��dica, el mobbing. Para ello fue decisivo el estudio de lo publicado (b��sicamente de ramas ajenas al Derecho) pero sobre todo las entrevistas con las v��ctimas de mobbing y sus asociaciones; este extremo, unido a la ausencia de un tratamiento internacional, oblig�� a un camino autodidacta para definir mobbing jur��dicamente. La Tesis define mobbing como la presi��n laboral tendente a la autoeliminaci��n de un trabajador mediante su denigraci��n (presi��n laboral tendenciosa), y con ello por primera vez se tiene una definici��n de mobbing en l��nea y media, con plena validez jur��dica, que es susceptible de ser memorizada y por lo tanto divulgada, para corregir el problema. El denominado "concepto uniformado de mobbing" recalca la denigraci��n como mecanismo frente a los tratos degradantes y recalca la autoeliminaci��n como finalidad de un comportamiento doloso. El trabajo aporta f��rmulas para deslindar casos de mobbing de otras figuras pr��ximas, y en este sentido debe citarse "la regla del 9" para saber si hay mobbing; en sede de estad��sticas se critican metodol��gicamente muchas de ellas presentadas hasta el momento y se aporta alguna en sede de Tribunales; pero sobre todo se advierte de los riesgos jur��dicos de una previsible regulaci��n espec��fica antimobbing, mediante el examen de las distintas definiciones que se han esgrimido hasta el momento. La segunda parte de la Tesis profundiza sobre el grado de sensibilizaci��n de nuestro ordenamiento jur��dico y Tribunales, a cuyo fin se ha trabajado con m��s de un centernar y medio de sentencias dictadas sobre la materia, y por supuesto la totalidad de las recogidas en las bases de datos de las editoriales. El an��lisis sirve para apreciar la bondad de la sistem��tica aqu�� defendida, poniendo en evidencia errores, y contradicciones. La Tesis advierte que la presi��n laboral tendenciosa m��s all�� de vulnerar el derecho constitucional al trabajo, o los derechos fundamentales a la integridad moral y el honor, es una transgresi��n a todo un "esp��ritu constitucional", y en este sentido se analiza con detalle tanto la posibilidad de recurrir en amparo, como el derecho a la indemnidad para quien se enfrenta a esta situaci��n. Advirtiendo de las ventajas de efectuar esta reacci��n mediante la modalidad procesal de tutela de los derechos fundamentales, se analiza la recurrida acci��n del art.50 ET, donde se realizan aportaciones sugerentes como el plazo prescripci��n o la "doctrina de los antecedentes", y se otorgan respuestas a las preguntas sobre obligaci��n de seguir trabajando y ejecuci��n provisional. En sede de acciones de Seguridad Social, la Tesis distingue entre la incapacidad temporal y permanente (depresiones) y la muerte y supervivencia, aport��ndose sobre la primera la t��cnica denominada "interpretaci��n en tres niveles" y descartando la posibilidad de considerar accidente de trabajo el suicidio tras un mobbing por imperativo legal, pero aportando un suced��neo bastante razonable como es el accidente no laboral. Junto a ello se razona por la viabilidad del recargo del art.123 LGSS. Civilmente, la Tesis se posiciona de "lege ferenda" por reconducir este tipo de acciones resarcitorias del da��o ps��quico y moral al orden civil, por una mayor explicaci��n sobre el origen del quantum, pero sobre todo considera inadmisible la STS 11-3-04, y ello por una pluralidad de argumentos, pero sobre todo por cuanto viene a autorizar "de facto" este tipo de conductas. La posibilidad de accionar administrativamente frente a este riesgo psicosocial se analiza en un doble terreno, la empresa y la Administraci��n. Si bien el cauce sobre el primero tiene algunos meandros que se desbelan, la situaci��n es radicalmente frustrante en la Administraci��n -donde se encuentra el mayor caldo de cultivo del mobbing- , y ello por el RD 707/2002, pero todav��a en mayor medida por el Criterio T��cnico 34/2003 mediante el cual la interpretaci��n del Director General de la Inspecci��n de Trabajo y Seguridad Social ha venido t��citamente a derogar parcialmente la Ley de Prevenci��n de Riesgos Laborales para la Administraci��n. En materia penal, la Tesis se decanta "a priori" por dos tipos penales, los delitos contra los derechos de los trabajadores, y el delito de trato degradante; sin embargo, en la pr��ctica s��lo este segundo es el camino que puede alcanzar buen puerto. Finalmente se realiza un estudio detallado de la Ley 62/2003, ley que se divulg�� como reguladora del acoso moral, y que despu��s se defiende como un avance frente al mobbing. La Tesis advierte que no es cierto ni lo uno, ni lo otro, habiendo creado un "espejismo legal" que puede perjudicar a las v��ctimas de mobbing, adem��s de no servir su estructura para una futura regulaci��n expl��cita antimobbing.