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

Aquatic community patterns across environmental gradients in a Mediterranean floodplain and their application to ecosystem restoration

El presente estudio tiene como objetivo proporcionar una base de conocimiento sólida para la restauración ecológica de ríos, basada en la respuesta de comunidades acuáticas a cambios en la conectividad hídrica, factores medioambientales y presión antrópica. La conectividad hídrica lateral resultó ser el factor principal que estructura hábitats y comunidades acuáticas en el Ebro; mientras que la turbidez, salinidad y concentración de nutrientes fueron factores secundarios. La combinación de estos factores establece un marco ecológico que permite realizar predicciones acerca de los patrones taxonómicos y funcionales con más probabilidades de ocurrir en la llanura del Ebro. La posibilidad de que se creen nuevos humedales de forma natural en el Ebro es muy baja, mientras los que quedan están amenazados por una baja renovación del agua. El objetivo de la restauración ecológica debe por tanto consistir en re-establecer un amplio rango de condiciones hídricas, de acuerdo con el potencial sostenible del ecosistema.

Compositional hypotheses of subcompositional stability and specific perturbation change and their testing

In standard multivariate statistical analysis common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositional change is most readily described in terms of the simplicial operation of perturbation and that subcompositions replace the marginal concept of subvectors. To motivate the statistical developments of this paper we present two challenging compositional problems from food production processes. Against this background the relevance of perturbations and subcompositions can be clearly seen. Moreover we can identify a number of hypotheses of interest involving the specification of particular perturbations or differences between perturbations and also hypotheses of subcompositional stability. We identify the two problems as being the counterpart of the analysis of paired comparison or split plot experiments and of separate sample comparative experiments in the jargon of standard multivariate analysis. We then develop appropriate estimation and testing procedures for a complete lattice of relevant compositional hypotheses

Values and their influence on the life satisfaction of adolescents aged 12 to 16: a study of some correlates

In this research we explore several aspects of quality of life in young people, working with factors such as self-esteem, locus of control, perceived social support, values, and so on. We examine the correlations among factors that influence the values and life satisfaction of adolescents aged 12-16. Furthermore, we analyze the data obtained from the children, on the one hand, and their parents, on the other, we explore the relationships between the factors and we consider the agreements and discrepancies between the responses of parents and their offspring

Attention, memory and verbal learning and their relation to schizotypal traits in unaffected parents of schizophrenic patients

The main objective of this ex post facto study is to compare the differences in cognitive functions and their relation to schizotypal personality traits between a group of unaffected parents of schizophrenic patients and a control group. A total of 52 unaffected biological parents of schizophrenic patients and 52 unaffected parents of unaffected subjects were assessed in measures of attention (Continuous Performance Test- Identical Pairs Version, CPT-IP), memory and verbal learning (California Verbal Learning Test, CVLT) as well as schizotypal personality traits (Oxford-Liverpool Inventory of Feelings and Experiences, O-LIFE). The parents of the patients with schizophrenia differ from the parents of the control group in omission errors on the Continuous Performance Test- Identical Pairs, on a measure of recall and on two contrast measures of the California Verbal Learning Test. The associations between neuropsychological variables and schizotpyal traits are of a low magnitude. There is no defined pattern of the relationship between cognitive measures and schizotypal traits