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

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

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 istheny = 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 analysismodel (1) can be written asCov(y) = ΛΛT + ψ (2)where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as theloadings matrix Λ are estimated from an estimation of Cov(y).Given observed clr transformed data Y as realizations of the random vectory. Outliers or deviations from the idealized model assumptions of factor analysiscan severely effect the parameter estimation. As a way out, robust estimation ofthe covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), seePison et al. (2003). Well known robust covariance estimators with good statisticalproperties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), relyon 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 thissingularity problem. The data matrix Y is transformed to a matrix Z by usingan orthonormal basis of lower dimension. Using the ilr transformed data, a robustcovariance matrix C(Z) can be estimated. The result can be back-transformed tothe clr space byC(Y ) = V C(Z)V Twhere the matrix V with orthonormal columns comes from the relation betweenthe clr and the ilr transformation. Now the parameters in the model (2) can beestimated (Basilevsky, 1994) and the results have a direct interpretation since thelinks to the original variables are still preserved.The above procedure will be applied to data from geochemistry. Our specialinterest is on comparing the results with those of Reimann et al. (2002) for the Kolaproject data

Relationship among epidemiological parameters of six childhood infections in a non-immunized Brazilian community

Epidemiological parameters, such as age-dependent force of infection and average age at infection () were estimated for rubella, varicella, rotavirus A, respiratory syncytial virus, hepatitis A and parvovirus B19 infections for a non-immunized Brazilian community, using the same sera samples. The for the aforementioned diseases were 8.45 years (yr) [95% CI: (7.23, 9.48) yr], 3.90 yr [95% CI: (3.51, 4.28) yr], 1.03 yr [95% CI: (0.96, 1.09) yr], 1.58 yr [95% CI: (1.39, 1.79) yr], 7.17 yr [95% CI: (6.48, 7.80) yr] and 7.43 yr [95% CI: (5.68, 9.59) yr], respectively. The differences between average ages could be explained by factors such as differences in the effectiveness of the protection conferred to newborns by maternally derived antibodies, competition between virus species and age-dependent host susceptibility. Our seroprevalence data may illustrate a case of the above-mentioned mechanisms working together within the same population.

Spatial Analysis of Cell Composition Data

A version of Matheron’s discrete Gaussian model is applied to cell composition data.The examples are for map patterns of felsic metavolcanics in two different areas. Q-Qplots of the model for cell values representing proportion of 10 km x 10 km cell areaunderlain by this rock type are approximately linear, and the line of best fit can be usedto estimate the parameters of the model. It is also shown that felsic metavolcanics in theAbitibi area of the Canadian Shield can be modeled as a fractal

Meaning of the λ parameter of skew–normal and log–skew normal distributions in fluid geochemistry

The literature related to skew–normal distributions has grown rapidly in recent yearsbut at the moment few applications concern the description of natural phenomena withthis type of probability models, as well as the interpretation of their parameters. Theskew–normal distributions family represents an extension of the normal family to whicha parameter (λ) has been added to regulate the skewness. The development of this theoreticalfield has followed the general tendency in Statistics towards more flexible methodsto represent features of the data, as adequately as possible, and to reduce unrealisticassumptions as the normality that underlies most methods of univariate and multivariateanalysis. In this paper an investigation on the shape of the frequency distribution of thelogratio ln(Cl−/Na+) whose components are related to waters composition for 26 wells,has been performed. Samples have been collected around the active center of Vulcanoisland (Aeolian archipelago, southern Italy) from 1977 up to now at time intervals ofabout six months. Data of the logratio have been tentatively modeled by evaluating theperformance of the skew–normal model for each well. Values of the λ parameter havebeen compared by considering temperature and spatial position of the sampling points.Preliminary results indicate that changes in λ values can be related to the nature ofenvironmental processes affecting the data

Enhancing MPLS QoS routing algorithms by using the network protection degree paradigm

IP based networks still do not have the required degree of reliability required by new multimedia services, achieving such reliability will be crucial in the success or failure of the new Internet generation. Most of existing schemes for QoS routing do not take into consideration parameters concerning the quality of the protection, such as packet loss or restoration time. In this paper, we define a new paradigm to develop new protection strategies for building reliable MPLS networks, based on what we have called the network protection degree (NPD). This NPD consists of an a priori evaluation, the failure sensibility degree (FSD), which provides the failure probability and an a posteriori evaluation, the failure impact degree (FID), to determine the impact on the network in case of failure. Having mathematical formulated these components, we point out the most relevant components. Experimental results demonstrate the benefits of the utilization of the NPD, when used to enhance some current QoS routing algorithms to offer a certain degree of protection

Calibration of a Structured Light-Based Stereo Catadioptric Sensor

Catadioptric sensors are combinations of mirrors and lenses made in order to obtain a wide field of view. In this paper we propose a new sensor that has omnidirectional viewing ability and it also provides depth information about the nearby surrounding. The sensor is based on a conventional camera coupled with a laser emitter and two hyperbolic mirrors. Mathematical formulation and precise specifications of the intrinsic and extrinsic parameters of the sensor are discussed. Our approach overcomes limitations of the existing omni-directional sensors and eventually leads to reduced costs of production

Interobserver variability of ultrasound parameters in portal hypertension

The aim of this study was to assess interobserver agreement of ultrasound parameters for portal hypertension in hepatosplenic mansonic schistosomiasis. Spleen size, diameter of the portal, splenic and superior mesenteric veins and presence of thrombosis and cavernous transformation were determined by three radiologists in blinded and independent fashion in 30 patients. Interobserver agreement was measured by the kappa index and intraclass correlation coefficient. Interobserver agreement was considered substantial (κ = 0.714-0.795) for portal vein thrombosis and perfect (κ = 1) for cavernous transformation. Interobserver agreement measured by the intraclass correlation coefficient was excellent for longitudinal diameter of the spleen (r = 0.828-0.869) and splenic index (r = 0.816-0.905) and varied from fair to almost perfect for diameter of the portal (r = 0.622-0.675), splenic (r = 0.573-0.913) and superior mesenteric (r = 0.525-0.607) veins. According to the results, ultrasound is a highly reproducible method for the main morphological parameters of portal hypertension in schistosomiasis patients.

Interactions between grain size and composition of sediments: two examples

Two contrasting case studies of sediment and detrital mineral composition are investigated in order to outline interactions between chemical composition and grain size. Modern glacial sediments exhibit a strong dependence of the two parameters due to the preferential enrichment of mafic minerals, especially biotite, in the fine-grained fractions. On the other hand, the composition of detrital heavy minerals (here: rutile) appears to be not systematically related to grain-size, but is strongly controlled by location, i.e. the petrology of the source rocks of detrital grains. This supports the use of rutile as a well-suited tracer mineral for provenance studies. The results further suggest that (i) interpretations derived from whole-rock sediment geochemistry should be flanked by grain-size observations, and (ii) a more sound statistical evaluation of these interactions require the development of new tailor-made statistical tools to deal with such so-called two-way compositions

Immunological and parasitological parameters after treatment with dexamethasone in murine Schistosoma mansoni

This work aimed to evaluate the effect of diphenyl dimethyl bicarboxylate (DDB) and dexamethasone alone and in combination with praziquantel on various parasitological, immunological and pathological parameters reflecting disease severity and morbidity in murine schistosomiasis. DDB and dexamethasone had no effect on worm burden but altered tissue egg distribution. This indicates that, under the schedule used, neither drug interfered with the development of adult worms or oviposition, but both can modulate liver pathology. Dexamethasone resulted in a greater reduction in granuloma size than did DDB. Dexamethasone-treated mice also showed lower levels of serum gamma interferon (IFN-γ), interleukin-12 (IL-12) and IL-4, together with higher IL-10 levels, than infected untreated control animals. These data suggest that dexamethasone is a convenient and promising coadjuvant agent that results in decreased morbidity in murine schistosomiasis.

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 afreeware package, named CoDaPack was created. This software implements most of thebasic statistical methods suitable for compositional data.In this paper we describe the new version of the package that now is calledCoDaPack3D. 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 knowledgeof 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 bezoomed and, in 3D, rotated. Also a customization menu is included and outputs couldbe saved in jpeg format. Also this new version includes an interactive help and alldialog windows have been improved in order to facilitate its use.To use CoDaPack one has to access Excel© and introduce the data in a standardspreadsheet. These should be organized as a matrix where Excel© rows correspond tothe observations and columns to the parts. The user executes macros that returnnumerical or graphical results. There are two kinds of numerical results: new variablesand descriptive statistics, and both appear on the same sheet. Graphical output appearsin independent windows. In the present version there are 8 menus, with a total of 38submenus which, after some dialogue, directly call the corresponding macro. Thedialogues ask the user to input variables and further parameters needed, as well aswhere to put these results. The web site http://ima.udg.es/CoDaPack contains thisfreeware package and only Microsoft Excel© under Microsoft Windows© is required torun the software.Kew words: Compositional data Analysis, Software

A unified approach for representing rows and columns in contingency tables

By using suitable parameters, we present a uni¯ed aproach for describing four methods for representing categorical data in a contingency table. These methods include:correspondence analysis (CA), the alternative approach using Hellinger distance (HD),the log-ratio (LR) alternative, which is appropriate for compositional data, and theso-called non-symmetrical correspondence analysis (NSCA). We then make an appropriate comparison among these four methods and some illustrative examples are given.Some approaches based on cumulative frequencies are also linked and studied usingmatrices.Key words: Correspondence analysis, Hellinger distance, Non-symmetrical correspondence analysis, log-ratio analysis, Taguchi inertia

New tools for epidemiology: a space odyssey

Geographical Information Systems (GIS) facilitate access to epidemiological data through visualization and may be consulted for the development of mathematical models and analysis by spatial statistics. Variables such as land-cover, land-use, elevations, surface temperatures, rainfall etc. emanating from earth-observing satellites, complement GIS as this information allows the analysis of disease distribution based on environmental characteristics. The strength of this approach issues from the specific environmental requirements of those causative infectious agents, which depend on intermediate hosts for their transmission. The distribution of these diseases is restricted, both by the environmental requirements of their intermediate hosts/vectors and by the ambient temperature inside these hosts, which effectively govern the speed of maturation of the parasite. This paper discusses the current capabilities with regard to satellite data collection in terms of resolution (spatial, temporal and spectral) of the sensor instruments on board drawing attention to the utility of computer-based models of the Earth for epidemiological research. Virtual globes, available from Google and other commercial firms, are superior to conventional maps as they do not only show geographical and man-made features, but also allow instant import of data-sets of specific interest, e.g. environmental parameters, demographic information etc., from the Internet.

Acute experimental Trypanosoma cruzi infection: establishing a murine model that utilises non-invasive measurements of disease parameters

Trypanosoma cruzi infection has a large public health impact in Latin American countries. Although the transmission rates via blood transfusions and insect vectors have declined sharply in the past 20 years due to policies of the Southern Cone countries, a large number of people are still at risk for infection. Currently, no accepted experimental model or descriptions of the clinical signs that occur during the course of acute murine infection are available. The aim of this work was to use non-invasive methods to evaluate the clinical signs of Balb/c mice infected with the Y strain of T. cruzi. The infected mice displayed evident clinical changes beginning in the third week of infection. The mice were evaluated based on physical characteristics, spontaneous activity, exploratory behaviour and physiological alterations. We hope that the results presented in this report provide parameters that complement the effective monitoring of trypanocidal treatment and other interventions used to treat experimental Chagas disease.

Controls on ostracod valve geochemistry, Part 1: Variations of environmental parameters in ostracod (micro-)habitats

The variations of environmental conditions (T°, pH, δ13CDIC, [DIC], δ18O, Mg/Ca, and Sr/Ca) of ostracod habitats were examined to determine the controls of environmental parameters on the chemical and isotopic composition of ostracod valves. Results of a one-year monitoring of environmental parameters at five sites, with depths of between 2 and 70 m, in Lake Geneva indicate that in littoral to sub-littoral zones (2, 5, and 13 m), the chemical composition of bottom water varies seasonally in concert with changes in temperature and photosynthetic activity. An increase of temperature and photosynthetic activity leads to an increase in δ13C values of DIC and to precipitation of authigenic calcite, which results in a concomitant increase of Mg/Ca and Sr/Ca ratios of water. In deeper sites (33 and 70 m), the composition of bottom water remains constant throughout the year and isotopic values and trace element contents are similar to those of deep water within the lake. The chemical composition of interstitial pore water also does not reflect seasonal variations but is controlled by calcite dissolution, aerobic respiration, anaerobic respiration with reduction of sulphate and/or nitrate, and methanogenesis that may occur in the sediment pores. Relative influence of each of these factors on the pore water geochemistry depends on sediment thickness and texture, oxygen content in bottom as well as pore water. Variations of chemical compositions of the ostracod valves of this study vary according to the specific ecology of the ostracod species analysed, that is its life-cycle and its (micro-)habitat. Littoral species have compositions that are related to the seasonal variations of temperature, δ13C values of DIC, and of Mg/Ca and Sr/Ca ratios of water. In contrast, the compositions of profundal species are largely controlled by variations of pore fluids along sediment depth profiles according to the specific depth preference of the species. The control on the geochemistry of sub-littoral species is a combination of controls for the littoral and profundal species as well as the specific ecology of the species.