When a data set can be considered compositional?

Traditionally, compositional data has been identified with closed data, and the simplex has been considered as the natural sample space of this kind of data. In our opinion, the emphasis on the constrained nature of compositional data has contributed to mask its real nature. More crucial than the constraining property of compositional data is the scale-invariant property of this kind of data. Indeed, when we are considering only few parts of a full composition we are not working with constrained data but our data are still compositional. We believe that it is necessary to give a more precise definition of composition. This is the aim of this oral contribution

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

When zero doesn't mean it and other geomathematical mischief

There is almost not a case in exploration geology, where the studied data doesn’t includes below detection limits and/or zero values, and since most of the geological data responds to lognormal distributions, these “zero data” represent a mathematical challenge for the interpretation. We need to start by recognizing that there are zero values in geology. For example the amount of quartz in a foyaite (nepheline syenite) is zero, since quartz cannot co-exists with nepheline. Another common essential zero is a North azimuth, however we can always change that zero for the value of 360°. These are known as “Essential zeros”, but what can we do with “Rounded zeros” that are the result of below the detection limit of the equipment? Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimes we need to differentiate between a sodic and a potassic alteration. Pre-classification into groups requires a good knowledge of the distribution of the data and the geochemical characteristics of the groups which is not always available. Considering the zero values equal to the limit of detection of the used equipment will generate spurious distributions, especially in ternary diagrams. Same situation will occur if we replace the zero values by a small amount using non-parametric or parametric techniques (imputation). The method that we are proposing takes into consideration the well known relationships between some elements. For example, in copper porphyry deposits, there is always a good direct correlation between the copper values and the molybdenum ones, but while copper will always be above the limit of detection, many of the molybdenum values will be “rounded zeros”. So, we will take the lower quartile of the real molybdenum values and establish a regression equation with copper, and then we will estimate the “rounded” zero values of molybdenum by their corresponding copper values. The method could be applied to any type of data, provided we establish first their correlation dependency. One of the main advantages of this method is that we do not obtain a fixed value for the “rounded zeros”, but one that depends on the value of the other variable. Key words: compositional data analysis, treatment of zeros, essential zeros, rounded zeros, correlation dependency

Comparing methods for dimensionality reduction when data are density functions

Functional Data Analysis (FDA) deals with samples where a whole function is observed for each individual. A particular case of FDA is when the observed functions are density functions, that are also an example of infinite dimensional compositional data. In this work we compare several methods for dimensionality reduction for this particular type of data: functional principal components analysis (PCA) with or without a previous data transformation and multidimensional scaling (MDS) for diferent inter-densities distances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (households income distributions)

Anàlisi dels preus al sector hoteler de la Costa Brava Sud

L'objectiu d'aquesta tesi és analitzar els preus hotelers, que inclouen tant el preu que cobra l'hoteler com el que paga el turista. Més en concret, aquesta tesi pretén entendre i explicar la política de preus del sector hoteler, utilitzant per aquest fi els conceptes, instruments i models de l'anàlisi econòmica. L'explotació exhaustiva dels catàlegs dels operadors turístics representa la principal aposta metodològica d'aquest treball. També s'han creat diferents bases de dades de preus hotelers, s'han explotat les dades i preus de guies hoteleres, i s'han fet enquestes als hotelers per conèixer el preu que paga un turista particular. Les aportacions més importants fan referència als preus del sector hoteler, que és el nucli principal del treball, i es podrien resumir de la manera següent: -Determinar com es determinen els preus en el sector hoteler -Conèixer el grau de competència entre operadors turístics -Disposar d'una evolució temporal i estacional dels preus dels hotels. En aquest sentit, la metodologia i les dades emprades podrien ser un punt de partida per elaborar una sèrie temporal de preus i d'aquesta manera corregir la mancança actual d'un índex de preus hoteler -Identificar els serveis i les característiques dels hotels que no tenen un preu explícit, però que resulten rellevants a l'hora de negociar uns preus superiors -Examinar les estratègies de preus d'alguns operadors turístics estrangers -I, en general, millorar el coneixement sobre els preus hotelers

Contribución metodológica en técnicas de diseñar para fabricación

En el proceso de diseño se toman decisiones que pueden afectar a la fabricabilidad del producto. Cuando el diseñador es experto, considera las limitaciones, las propiedades y el coste de fabricación en la fase de materialización o de detalle. El problema surge cuando el diseñador no es experto o cuando no hay suficiente información y conocimiento de fabricación disponible. Tomando como referencia la teoría de Diseño Axiomático y las técnicas de DFM, se propone una metodología para identificar, definir y formalizar la información de fabricación que debería estar disponible en el diseño para diseñar para fabricar (DFM). También se propone un prototipo de modelo de información para desarrollar una futura herramienta informática que facilitaría la aplicación de esta metodología y que permitiría guiar al diseñador durante el diseño. La metodología ha sido aplicada a una biela de un motor de combustión interna alternativo (MCIA), y a los procesos que se están usando actualmente para fabricarla: forja en matriz cerrada y forja de polvo de metal.