Scoring Methods for Ordinal Multidimensional Forced-Choice Items

In most psychological tests and questionnaires, a test score is obtained by taking the sum of the item scores. In virtually all cases where the test or questionnaire contains multidimensional forced-choice items, this traditional scoring method is also applied. We argue that the summation of scores obtained with multidimensional forced-choice items produces uninterpretable test scores. Therefore, we propose three alternative scoring methods: a weak and a strict rank preserving scoring method, which both allow an ordinal interpretation of test scores; and a ratio preserving scoring method, which allows a proportional interpretation of test scores. Each proposed scoring method yields an index for each respondent indicating the degree to which the response pattern is inconsistent. Analysis of real data showed that with respect to rank preservation, the weak and strict rank preserving method resulted in lower inconsistency indices than the traditional scoring method; with respect to ratio preservation, the ratio preserving scoring method resulted in lower inconsistency indices than the traditional scoring method

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

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)

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing one or more parameters in their definition. Methods that can be linked in this way are correspondence analysis, unweighted or weighted logratio analysis (the latter also known as "spectral mapping"), nonsymmetric correspondence analysis, principal component analysis (with and without logarithmic transformation of the data) and multidimensional scaling. In this presentation I will show how several of these methods, which are frequently used in compositional data analysis, may be linked through parametrizations such as power transformations, linear transformations and convex linear combinations. Since the methods of interest here all lead to visual maps of data, a "movie" can be made where where the linking parameter is allowed to vary in small steps: the results are recalculated "frame by frame" and one can see the smooth change from one method to another. Several of these "movies" will be shown, giving a deeper insight into the similarities and differences between these methods

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

Revisiting the compositional data. Some fundamental questions and new prospects in Archaeometry and Archaeology

In this paper we examine the problem of compositional data from a different starting point. Chemical compositional data, as used in provenance studies on archaeological materials, will be approached from the measurement theory. The results will show, in a very intuitive way that chemical data can only be treated by using the approach developed for compositional data. It will be shown that compositional data analysis is a particular case in projective geometry, when the projective coordinates are in the positive orthant, and they have the properties of logarithmic interval metrics. Moreover, it will be shown that this approach can be extended to a very large number of applications, including shape analysis. This will be exemplified with a case study in architecture of Early Christian churches dated back to the 5th-7th centuries AD

Modelling of Mercury’s surface composition and remote detection from the orbit with the BepiColombo Mercury Planetary Orbiter

It can be assumed that the composition of Mercury’s thin gas envelope (exosphere) is related to the composition of the planets crustal materials. If this relationship is true, then inferences regarding the bulk chemistry of the planet might be made from a thorough exospheric study. The most vexing of all unsolved problems is the uncertainty in the source of each component. Historically, it has been believed that H and He come primarily from the solar wind, while Na and K originate from volatilized materials partitioned between Mercury’s crust and meteoritic impactors. The processes that eject atoms and molecules into the exosphere of Mercury are generally considered to be thermal vaporization, photonstimulated desorption (PSD), impact vaporization, and ion sputtering. Each of these processes has its own temporal and spatial dependence. The exosphere is strongly influenced by Mercury’s highly elliptical orbit and rapid orbital speed. As a consequence the surface undergoes large fluctuations in temperature and experiences differences of insolation with longitude. We will discuss these processes but focus more on the expected surface composition and solar wind particle sputtering which releases material like Ca and other elements from the surface minerals and discuss the relevance of composition modelling

Vertebrates Limb Geometry in the Simplex space

A novel metric comparison of the appendicular skeleton (fore and hind limb) of different vertebrates using the Compositional Data Analysis (CDA) methodological approach it’s presented. 355 specimens belonging in various taxa of Dinosauria (Sauropodomorpha, Theropoda, Ornithischia and Aves) and Mammalia (Prothotheria, Metatheria and Eutheria) were analyzed with CDA. A special focus has been put on Sauropodomorpha dinosaurs and the Aitchinson distance has been used as a measure of disparity in limb elements proportions to infer some aspects of functional morphology

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr) transformation to obtain the random vector y of dimension D. The factor model is then y = Λf + e (1) with the factors f of dimension k < D, the error term e, and the loadings matrix Λ. Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysis model (1) can be written as Cov(y) = ΛΛT + ψ (2) where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as the loadings matrix Λ are estimated from an estimation of Cov(y). Given observed clr transformed data Y as realizations of the random vector y. Outliers or deviations from the idealized model assumptions of factor analysis can severely effect the parameter estimation. As a way out, robust estimation of the covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), see Pison et al. (2003). Well known robust covariance estimators with good statistical properties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), rely on a full-rank data matrix Y which is not the case for clr transformed data (see, e.g., Aitchison, 1986). The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves this singularity problem. The data matrix Y is transformed to a matrix Z by using an orthonormal basis of lower dimension. Using the ilr transformed data, a robust covariance matrix C(Z) can be estimated. The result can be back-transformed to the clr space by C(Y ) = V C(Z)V T where the matrix V with orthonormal columns comes from the relation between the clr and the ilr transformation. Now the parameters in the model (2) can be estimated (Basilevsky, 1994) and the results have a direct interpretation since the links to the original variables are still preserved. The above procedure will be applied to data from geochemistry. Our special interest is on comparing the results with those of Reimann et al. (2002) for the Kola project data

Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model and the design region. The talk will consider the design of experiments for regression models in which there is a single response with the explanatory variables lying in a simplex. One example is experiments on various compositions of glass such as those considered by Martin, Bursnall, and Stillman (2001). Because of the highly symmetric nature of the simplex, the class of models that are of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather different from those of standard regression analysis. The optimum designs are also rather different, inheriting a high degree of symmetry from the models. In the talk I will hope to discuss a variety of modes for such experiments. Then I will discuss constrained mixture experiments, when not all the simplex is available for experimentation. Other important aspects include mixture experiments with extra non-mixture factors and the blocking of mixture experiments. Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007). If time and my research allows, I would hope to finish with a few comments on design when the responses, rather than the explanatory variables, lie in a simplex. References Atkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum Experimental Designs, with SAS. Oxford: Oxford University Press. Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results on optimal and efficient designs for constrained mixture experiments. In A. C. Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000, pp. 225–239. Dordrecht: Kluwer. Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal Statistical Society, Ser. B 20, 344–360. 1

Portal web per la localitzacó de restaurants

Desenvolupament,anàlisi, disseny i implementació d’un portal web, tipus cercador, per la recerca i localització d’establiments tipus restaurant, bars, bufets, etc,. Per altra banda es pretén oferir un sistema de gestió d’informació on les empreses del sector gastronòmic puguin mostrar la seva informació i la seva oferta

Es adequada la avaluación del aprendizaje continuado mediante pruebas parciales y un examen final?

Se ha llevado a cabo un estudio para determinar la utilidad de basar la evaluación de los estudiantes mediante la utilización de pruebas parciales y un examen final. Los resultados obtenidos muestran que la simple aplicación de pruebas parciales sin ningún proceso de feedback no son adecuados ya que no mejoran los contenidos y competencias adquiridos por los estudiantes. Se obtienen los mismos resultados en los exámenes finales tanto cuando se han realizado pruebas parciales sin revisión como cuando únicamente se evalúa con el método tradicional de una examen final. El único resultado apreciable en el caso de aplicar pruebas parciales es una mejora sustancial en el porcentaje de aprobados de las asignaturas. Además, este incremento de los aprobados es superior cuanto mayor sea el peso que tienen las pruebas parciales sobre la calificación definitiva. Cuando se llevan a cabo procesos de feedback para corregir las deficiencias observadas en los conocimientos y competencias adquiridos por los alumnos se obtiene una mejora significativa en los niveles de compresión obtenidos por los estudiantes. Por lo tanto, es imprescindible diseñar sistemas de evaluación continuada en los que exista algún proceso de feedback adecuado sobre los estudiantes si se quiere mejorar su proceso de aprendizaje. Este hecho también requiere una revisión y remodelación de los contenidos de las asignaturas ya que es imprescindible preveer un número de horas sustancial para los procesos de revisión

Tutorización de prácticas clínicas en estudiantes de enfermería en grupos de supervisión de prácticas

Se trata de un estudio cuasi-experimental, en el que a un grupo de estudiantes de 2º de enfermería además de una tutoría personalizada durante las prácticas se les ofrece la posibilidad de realizar una tutoría grupal a modo de grupos de supervisión de prácticas. Se realizaron dos grupos de supervisión de prácticas de 10 personas cada uno (n:20) y sirvió como control el resto de la clase (n:32). Durante las 7 semanas de prácticas clínicas se reunieron los dos grupos una vez a la semana durante 80 minutos junto a un conductor y una observadora. Los alumnos traían casos reales de su práctica en las que se habían sentido mal y/o con dificultades. Los casos eran aceptados y tratados con respeto, y se pensaba en torno a los mismos entre todos, aportando pensamientos y sentimientos que les suscitaban. En todos los alumnos se midió al principio de las prácticas y al final de las mismas lo que les preocupan algunos aspectos de la práctica clínica, síntomas de burnout y sintomatología psiquiátrica. Los alumnos que participaron en los grupos intervención lo hicieron por participar en una asignatura optativa, por lo que la asignación no fue aleatoria. Ese posible sesgo puede explicar las diferentes puntuaciones basales entre ambos grupos: los sujetos pertenecientes al grupo intervención desde el principio estaban más preocupados con diferentes aspectos de las prácticas y presentaban más síntomas. Tras las prácticas se observó una disminución de la preocupación sobre diferentes aspectos de las prácticas en el grupo intervención y en grupo control, así como una disminución de la sintomatología, más importante en el grupo intervención. En cuanto a los síntomas de burnout, se observa un aumento del agotamiento emocional en el grupo intervención y una disminución en el grupo control, y un aumento de la realización personal en ambos grupos, más importante en el grupo intervención. Durante la experiencia cada alumno debía enviar tras cada encuentro por correo electrónico un breve resumen de lo que había aprendido (a modo de diario reflexivo), y al final de la misma se les pasó una encuesta de factores curativos de la psicoterapia de grupo. Los alumnos que habían realizado la experiencia apuntaban que habían aprendido de su experiencia y de la de los demás, y que la presentación de casos y su discusión, les permitía anticipar situaciones que no les habían ocurrido aún. Señalaban que a todos les sucedían cosas similares y al mismo tiempo toman conciencia de la diferencia de escenarios en los que se pueden encontrar (distintos hospitales, servicios, compañeros...). Los factores curativos de la psicoterapia de grupo estuvieron muy presentes en la experiencia de los estudiantes

Passeig per l'invisible: itinerari químic per Girona

La finalitat d'aquesta proposta és facilitar l'aprenentatge de la química a través de l'exposició d'exemples diaris, en una activitat que desenvolupa a més les competències actitudinals. S'ha observat que alguns estudiants de la Facultat de Ciències tenen dificultats per seguir assignatures de química a causa de la seva nul·la o dèbil formació en química a secundària. A més, molts d'ells consideren la química com una ciència complicada, inútil o perillosa. L’activitat presentada és un itinerari químic: un passeig per a una ciutat amb tradició química que mostra exemples quotidians de la presència de la química arreu. S'hi afegeixen experiments i demostracions, a més d'exercicis adaptables al nivell dels estudiants. Tots els professors volem tenir estudiants motivats en les nostres classes perquè sabem que això és bàsic per al seu aprenentatge. L'itinerari ha demostrat la seva validesa especialment en aquest aspecte. A més, permet treballar determinats conceptes del contingut curricular de química. Tot i que els beneficis a llarg termini de la realització de l'itinerari no s'han avaluat encara, els estudiants estan molt satisfets amb el desenvolupament de l'itinerari. Consideren que la informació donada ha millorat la imatge que tenien de química. D'alguna manera, descobreixen quelcom que fins aleshores els havia estat invisible

Public and student awareness science: recreational science as a catalyst

When discussing the traditional and new missions of higher education (1996 Report to UNESCO of the International Commission on Education for the 21st Century) Jacques Delors stated that "Excessive attraction to social sciences has broken equilibrium of available graduates for workforce, thus causing doubts of graduates and employers on the quality of knowledge provided by higher education". Likewise, when discussing the progress of science and technology, the 1998 UNESCO World Conference on Higher Education concluded that "Another challenge concerts the latest advancements of Science, the sine qua non of sustainable development"; and that “with Information Technology, the unavoidable invasion of virtual reality has increased the distance between industrial and developing countries". Recreational Science has a long tradition all over the Educational World; it aims to show the basic aspects of Science, aims to entertain, and aims to induce thinking. Until a few years ago, this field of knowledge consisted of a few books, a few kits and other classical (yet innovative) ways to popularize the knowledge of Nature and the laws governing it. In Spain, the interest for recreational science has increased in the last years. First, new recreational books are being published and found in bookstores. Second the number of Science-related museums and exhibits is increasing. And third, new television shows are produced and new short science-based, superficial sketches are found in variety programs. However, actual programs in Spanish television dealing seriously with Science are scarce. Recreational Science, especially that related to physical phenomena like light or motion, is generally found at Science Museums because special equipment is required. On the contrary, Science related mathematics, quizzes and puzzles use to gather into books, e.g. the extensive collections by Martin Gardner. However, lately Science podcasts have entered the field of science communication. Not only traditional science journals and television channels are providing audio and video podcasts, but new websites deal exclusively with science podcasts, in particular on Recreational Science. In this communication we discuss the above mentioned trends and show our experience in the last two years in participating at Science Fairs and university-sponsored events to attract students to science and technology careers. We show a combination of real examples (e.g., mathemagic), imagination, use of information technology, and use of social networks. We present as well an experience on designing a computational, interactive tool to promote chemistry among high school, prospective students using computers ("Dancing with Bionanomolecules"). Like the concepts related to Web 2.0, it has been already proposed that a new framework for communication of science is emerging, i.e., Science Communication 2.0, where people and institutions develop new innovative ways to explain science topics to diverse publics – and where Recreational Science is likely to play a leading role