Mixing compositions and other scales

Theory of compositional data analysis is often focused on the composition only. However in practical applications we often treat a composition together with covariables with some other scale. This contribution systematically gathers and develop statistical tools for this situation. For instance, for the graphical display of the dependence of a composition with a categorical variable, a colored set of ternary diagrams might be a good idea for a first look at the data, but it will fast hide important aspects if the composition has many parts, or it takes extreme values. On the other hand colored scatterplots of ilr components could not be very instructive for the analyst, if the conventional, black-box ilr is used. Thinking on terms of the Euclidean structure of the simplex, we suggest to set up appropriate projections, which on one side show the compositional geometry and on the other side are still comprehensible by a non-expert analyst, readable for all locations and scales of the data. This is e.g. done by defining special balance displays with carefully- selected axes. Following this idea, we need to systematically ask how to display, explore, describe, and test the relation to complementary or explanatory data of categorical, real, ratio or again compositional scales. This contribution shows that it is sufficient to use some basic concepts and very few advanced tools from multivariate statistics (principal covariances, multivariate linear models, trellis or parallel plots, etc.) to build appropriate procedures for all these combinations of scales. This has some fundamental implications in their software implementation, and how might they be taught to analysts not already experts in multivariate analysis

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

Experimental study of textual development in Spanish students of English as a foreign language in segundo de bachillerato : features of written register in compositions of argumentative genre.

Esta investigación pretende, por un lado, describir y explicar los rasgos orales de las redacciones de los estudiantes españoles de inglés como lengua extranjera; y, por otro, intentar mejorar el estilo escrito de los textos de estos estudiantes a través de una intervención pedagógica.. Se diseña y aplica un tratamiento pedagógico a un grupo de estudiantes de segundo de bachillerato de Madrid. La instrucción se centra en hacerles conscientes de los recursos lingüísticos disponibles en inglés para la redacción de un texto. Se comparan las composiciones escritas por los estudiantes antes del tratamiento experimental con sus producciones posteriores, así como con un grupo de control del mismo instituto que no recibe ninguna instrucción. Se cotejan los textos en inglés con redacciones escritas en español por los estudiantes del grupo experimental. Asimismo, los textos escritos en inglés después del tratamiento experimental se comparan con redacciones de un grupo de estudiantes nativos de secundaria. Se analizan dos variables, para las que el estudio aporta sendos instrumentos de medida, la calidad y el grado de estilo escrito de los textos. La comparación de los textos escritos en español y en inglés de los estudiantes españoles del grupo experimental revela que las redacciones en la lengua materna son superiores en relación a su calidad pero no al grado de estilo escrito. Varios resultados estadísticos apuntan que el tratamiento recibido por el grupo experimental contribuye al desarrollo del grado de estilo escrito de los textos en inglés pero no mejora la calidad global de los mismos. Los resultados revelan que el grupo experimental es similar a los nativos en el grado de estilo escrito, aunque éste último supera a los estudiantes del inglés como lengua extranjera en la 'calidad' de los textos. Este estudio concluye que la impronta oral de las redacciones de los estudiantes de inglés como lengua extranjera puede deberse a la combinación de varios factores, la competencia discursiva en la lengua materna, la competencia lingüística/discursiva en la lengua objeto de aprendizaje, el conocimiento socio-cultural y lingüístico de adecuación contextual y el tipo de pedagogía en inglés como lengua extranjera.

The Use of the Common European Framework of Reference for Languages to Evaluate Compositions in the English Exam Section of the University Admission Examination. 'El uso del Marco Com??n Europeo de Referencia para las Lenguas para evaluar las redacciones en la secci??n de ingl??s de la Prueba de Acceso a la Universidad'

Monogr??fico con el t??tulo: 'Nuevas perspectivas en la secci??n de idiomas de la Prueba de Acceso a la Universidad'. Resumen basado en el de la publicaci??n

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)

Geostatistics for constrained variables: positive data, compositions and probabilities. Applications to environmental hazard monitoring

Aquesta tesi estudia com estimar la distribució de les variables regionalitzades l'espai mostral i l'escala de les quals admeten una estructura d'espai Euclidià. Apliquem el principi del treball en coordenades: triem una base ortonormal, fem estadística sobre les coordenades de les dades, i apliquem els output a la base per tal de recuperar un resultat en el mateix espai original. Aplicant-ho a les variables regionalitzades, obtenim una aproximació única consistent, que generalitza les conegudes propietats de les tècniques de kriging a diversos espais mostrals: dades reals, positives o composicionals (vectors de components positives amb suma constant) són tractades com casos particulars. D'aquesta manera, es generalitza la geostadística lineal, i s'ofereix solucions a coneguts problemes de la no-lineal, tot adaptant la mesura i els criteris de representativitat (i.e., mitjanes) a les dades tractades. L'estimador per a dades positives coincideix amb una mitjana geomètrica ponderada, equivalent a l'estimació de la mediana, sense cap dels problemes del clàssic kriging lognormal. El cas composicional ofereix solucions equivalents, però a més permet estimar vectors de probabilitat multinomial. Amb una aproximació bayesiana preliminar, el kriging de composicions esdevé també una alternativa consistent al kriging indicador. Aquesta tècnica s'empra per estimar funcions de probabilitat de variables qualsevol, malgrat que sovint ofereix estimacions negatives, cosa que s'evita amb l'alternativa proposada. La utilitat d'aquest conjunt de tècniques es comprova estudiant la contaminació per amoníac a una estació de control automàtic de la qualitat de l'aigua de la conca de la Tordera, i es conclou que només fent servir les tècniques proposades hom pot detectar en quins instants l'amoni es transforma en amoníac en una concentració superior a la legalment permesa.

Pyrohydrolysis-IRMS determination of silicate chlorine stable isotope compositions. Application to oceanic crust and meteorite samples

This contribution describes the optimization of chlorine extraction from silicate samples by pyrohydrolysis prior to the precise determination of Cl stable-isotope compositions (637 Cl) by gas source, dual inlet Isotope Ratio Mass Spectrometry (IRMS) on CH(3)Clg. The complete method was checked on three international reference materials for Cl-content and two laboratory glass standards. Whole procedure blanks are lower than 0. 5 mu mol, corresponding to less than 10 wt.% of most of the sample chloride analysed. In the absence of international chlorine isotope rock, we report here Cl extracted compared to accepted Cl contents and reproducibilities on Cl and delta Cl-37 measurements for the standard rocks. After extraction, the Cl contents of the three international references compared within error with the accepted values (mean yield = 94 +/-10%) with reproducibilities better than 12% (10). The laboratory glass standards - andesite SO100DS92 and phonolite S9(2) - were used specifically to test the effect of chloride amount on the measurements. They gave Cl extraction yields of 100 +/-6% (1 sigma-; n = 15) and 105 +/- 8% (1 sigma-; n = 7), respectively, with delta Cl-37 values of -0.51 0.14%o and -0.39 0.17%o (1g). In summary, for silicate samples with Cl contents between 39 and 9042 ppm, the Pyrohydrolysis/HPLC method leads to overall CI extraction yields of 100 8%, reproducibilities on Cl contents of 7% and on delta Cl-37 measurements of 0.12%o (all 1 sigma). The method was further applied to ten silicate rocks of various mineralogy and chemistry (meteorite, fresh MORB glasses, altered basalts and setpentinized peridotites) chosen for their large range of Cl contents (70-2156 ppm) and their geological significance. delta Cl-37 values range between -2.33 and -0.50%o. These strictly negative values contrast with the large range and mainly positive values previously reported for comparable silicate samples and shown here to be affected by analytical problems. Thus we propose a preliminary, revised terrestrial CI cycle, mainly dominated by negative and zero delta Cl-37 values. (C) 2007 Elsevier B.V. All rights reserved.

Aqueous geochemistry and oxygen isotope compositions of acid mine drainage from the Río Tinto, SW Spain, highlight inconsistencies in current models

The Rio Tinto river in SW Spain is a classic example of acid mine drainage and the focus of an increasing amount of research including environmental geochemistry, extremophile microbiology and Mars-analogue studies. Its 5000-year mining legacy has resulted in a wide range of point inputs including spoil heaps and tunnels draining underground workings. The variety of inputs and importance of the river as a research site make it an ideal location for investigating sulphide oxidation mechanisms at the field scale. Mass balance calculations showed that pyrite oxidation accounts for over 93% of the dissolved sulphate derived from sulphide oxidation in the Rio Tinto point inputs. Oxygen isotopes in water and sulphate were analysed from a variety of drainage sources and displayed delta O-18((SO4-H2O)) values from 3.9 to 13.6 parts per thousand, indicating that different oxidation pathways occurred at different sites within the catchment. The most commonly used approach to interpreting field oxygen isotope data applies water and oxygen fractionation factors derived from laboratory experiments. We demonstrate that this approach cannot explain high delta O-18((SO4-H2O)) values in a manner that is consistent with recent models of pyrite and sulphoxyanion oxidation. In the Rio Tinto, high delta O-18((SO4-H2O)) values (11.2-13.6 parts per thousand) occur in concentrated (Fe = 172-829 mM), low pH (0.88-1.4), ferrous iron (68-91% of total Fe) waters and are most simply explained by a mechanism involving a dissolved sulphite intermediate, sulphite-water oxygen equilibrium exchange and finally sulphite oxidation to sulphate with O-2. In contrast, drainage from large waste blocks of acid volcanic tuff with pyritiferous veins also had low pH (1.7). but had a low delta O-18((SO4-H2O)) value of 4.0 parts per thousand and high concentrations of ferric iron (Fe(III) = 185 mM, total Fe = 186 mM), suggesting a pathway where ferric iron is the primary oxidant, water is the primary source of oxygen in the sulphate and where sulphate is released directly from the pyrite surface. However, problems remain with the sulphite-water oxygen exchange model and recommendations are therefore made for future experiments to refine our understanding of oxygen isotopes in pyrite oxidation. (C) 2009 Elsevier B.V. All rights reserved.

Comparison of the volatile compositions and flavour properties of cantaloupe, Galia and honeydew muskmelons

Aroma compounds were extracted from three cultivars of muskmelon (Cucumis melo L.) by solid-phase microextraction and analysed by gas chromatography-mass-spectrometry. Sulfur-containing esters and compounds containing a straight six-carbon chain were present at high concentrations in cantaloupe melons. Compounds containing a straight nine-carbon chain were at high concentrations in honeydew melons. Methyl esters were present at the highest levels in Galia melons. The sensory properties of the three melons were also compared. Cantaloupe melons were associated with sweet, floral and fruity aromas and a persistent aftertaste. Galia melons possessed the strongest cucumber-like flavours, while cucumber aroma and sweet flavour scored highly in honeydew melons. (c) 2005 Elsevier Ltd. All rights reserved.

A comparison of the aroma volatiles and fatty acid compositions of grilled beef muscle from Aberdeen Angus and Holstein-Friesian steers fed diets based on silage or concentrates

This paper compares the volatile compound and fatty acid compositions of grilled beef from Aberdeen Angus and Holstein-Friesian steers slaughtered at 14 months, each breed fed from 6 months on either cereal-based concentrates or grass silage. Linoleic acid levels were higher in the muscle of concentrates-fed animals, which in the cooked meat resulted in increased levels of several compounds formed from linoleic acid decomposition. Levels of alpha-linolenic acid, and hence some volatile compounds derived from this fatty acid, were higher in the meat from the silage-fed steers. 1-Octen-3-ol, hexanal, 2-pentylfuran, trimethylamine, cis- and trans-2-octene and 4,5-dimethyl-2-pentyl-3-oxazoline were over 3 times higher in the steaks from the concentrates-fed steers, while grass-derived 1-phytene was present at much higher levels in the beef from the silage-fed steers. Only slight effects of breed were observed. (C) 2004 Elsevier Ltd. All rights reserved.

Markers of intestinally-derived lipoproteins: application to studies of altered diet and meal fatty acid compositions

BACKGROUND AND AIM: The atherogenic potential of dietary derived lipids, chylomicrons (CM) and their remnants (CMr) is now becoming more widely recognised. To investigate factors effecting levels of CM and CMr and their importance in coronary heart disease risk it is essential to use a specific method of quantification. Two studies were carried out to investigate: (i) effects of increased daily intake of long chain n-3 polyunsaturated fatty acid (LC n-3 PUFA), and (ii) effects of increasing meal monounsaturated fatty acid (MUFA) content on the postprandial response of intestinally-derived lipoproteins. The contribution of the intestinally-derived lipoproteins to total lipaemia was assessed by triacylglycerol-rich lipoprotein (TRL) apolipoprotein B-48 (apo B-48) and retinyl ester (RE) concentrations. METHODS AND RESULTS: In a randomised controlled crossover trial (placebo vs LC n-3 PUFA) a mean daily intake of 1.4 g/day of LC n-3 PUFA failed to reduce fasting and postprandial triacylglycerol (TAG) response in 9 healthy male volunteers. Although the pattern and nature of the apo B-48 response was consistent with the TAG response following the two diets, the postprandial RE response differed on the LC n-3 PUFA diet with a lower early RE response and a delayed and more marked increase in RE in the late postprandial period compared with the control diet, but the differences did not reach levels of statistical significance. In the meal study there was no effect of MUFA/SFA content on the total lipaemic response to the meals nor on the contribution of intestinally derived lipoproteins evaluated as TAG, apo B-48 and RE responses in the TRL fraction. In both studies, the RE and apo B-48 measurements provided broadly similar information with respect to lack of effects of dietary or meal fatty acid composition and the presence of single or multiple peak responses. However the apo B-48 and RE measurements differed with respect to the timing of their peak response times, with a delayed RE peak, relalive to apo B-48, of approximately 2-3 hours for the LC n-3 PUFA diet (p = 0.002) study and 1-1.5 hours for the meal MUFA/SFA study. CONCLUSIONS: It was concluded that there are limitations of using RE as a specific CM marker, apo B-48 quantitation was found to be a more appropriate method for CM and CMr quantitation. However it was still considered of value to measure RE as it provided additional information regarding the incorporation of other constituents into the CM particle.

Fatty acid compositions of inositol and choline phospholipids of breast tumours and normal breast tissue

The fatty acid compositions of the -choline and -inositol phospholipids of breast tumours of women undergoing surgery for treatment of breast disease (malignant n = 12; benign n = 10) and normal breast tissue of women undergoing breast reduction surgery (n = 6) were determined. The fatty acid compositions of erythrocyte phospholipids were also determined in the same subjects and in an additional number of normal healthy volunteers (n = 16). Levels of oleic acid were lower in both phospholipid fractions of erythrocytes of women with breast disease and in the phosphatidylcholine fraction of breast tumours compared with normal breast tissue. Significantly higher levels of linoleic acid were found in erythrocytes of tumour-bearing subjects and a similar trend was evident in the phosphatidylcholine fraction of tumour compared with normal breast tissues. Conversely, lower levels of two of the products of linoleic acid chain elongation and desaturation, dihomogamma-linolenic and arachidonic acids, were found in the erythrocyte phospholipids of tumour-bearing subjects and in the choline phospholipids of breast tumour tissues. These data suggest that in women with breast disease, there may be inhibition of 6-desaturase, and enhanced activity of 9-desaturase, enzymes which play an important role in determining membrane phospholipid fatty acid composition. This pattern of altered fatty acid composition characteristic of erythrocyte phospholipids of tumour-bearing subjects and phosphatidylcholine of breast tumour tissue was less evident in the case of the breast tumour phosphatidylinositol in which differences other than those described were seen.

Different risk measures: different portfolio compositions?

Traditionally, the measure of risk used in portfolio optimisation models is the variance. However, alternative measures of risk have many theoretical and practical advantages and it is peculiar therefore that they are not used more frequently. This may be because of the difficulty in deciding which measure of risk is best and any attempt to compare different risk measures may be a futile exercise until a common risk measure can be identified. To overcome this, another approach is considered, comparing the portfolio holdings produced by different risk measures, rather than the risk return trade-off. In this way we can see whether the risk measures used produce asset allocations that are essentially the same or very different. The results indicate that the portfolio compositions produced by different risk measures vary quite markedly from measure to measure. These findings have a practical consequence for the investor or fund manager because they suggest that the choice of model depends very much on the individual’s attitude to risk rather than any theoretical and/or practical advantages of one model over another.