A compositional statistical analysis of capital stock

Most of economic literature has presented its analysis under the assumption of homogeneous capital stock.However, capital composition differs across countries. What has been the pattern of capital compositionassociated with World economies? We make an exploratory statistical analysis based on compositional datatransformed by Aitchinson logratio transformations and we use tools for visualizing and measuring statisticalestimators of association among the components. The goal is to detect distinctive patterns in the composition.As initial findings could be cited that:1. Sectorial components behaved in a correlated way, building industries on one side and , in a lessclear view, equipment industries on the other.2. Full sample estimation shows a negative correlation between durable goods component andother buildings component and between transportation and building industries components.3. Countries with zeros in some components are mainly low income countries at the bottom of theincome category and behaved in a extreme way distorting main results observed in the fullsample.4. After removing these extreme cases, conclusions seem not very sensitive to the presence ofanother isolated cases

Validation of order rank scales based on compositional data analysis: a proposal

Usually, psychometricians apply classical factorial analysis to evaluate construct validity of order rankscales. Nevertheless, these scales have particular characteristics that must be taken into account: totalscores and rank are highly relevant

Assessing the Precision of Compositional Data in a Stratified Double Stage Cluster Sample: Application to the Swiss Earnings Structure Survey

Precision of released figures is not only an important quality feature of official statistics,it is also essential for a good understanding of the data. In this paper we show a casestudy of how precision could be conveyed if the multivariate nature of data has to betaken into account. In the official release of the Swiss earnings structure survey, the totalsalary is broken down into several wage components. We follow Aitchison's approachfor the analysis of compositional data, which is based on logratios of components. Wefirst present diferent multivariate analyses of the compositional data whereby the wagecomponents are broken down by economic activity classes. Then we propose a numberof ways to assess precision

Turner syndrome: evaluation of prenatal diagnosis in 19 European registries.

This study evaluated the prenatal diagnosis of Turner syndrome by ultrasound examination in an unselected population from all over Europe. Data from 19 congenital malformation registries from 11 European countries were analyzed. Turner syndrome was diagnosed in 125 cases (7.2%) in a total of 1,738 chromosome abnormalities. Sixty-seven percent of cases were detected prenatally by ultrasound examination due to the presence of congenital defects. The most frequent anomalies were cystic hygroma (59.5%) and hydrops fetalis (19%). The most frequent karyotype was 45,X (81.6%) followed by different types of mosaicism (16.8%). Significant differences in congenital defects (P = 0.0003) were observed between 45,X karyotypes and 45,X mosaicism cases. Prenatal counseling for 45,X mosaicism should take into account the expectation of a milder phenotype. In 78.6% of cases diagnosed by ultrasound examination due to congenital anomalies, the pregnancy was terminated. Prenatal detection of Turner syndrome by ultrasound examination was high in this unselected population.

Genome-wide analysis of SREBP1 activity around the clock reveals its combined dependency on nutrient and circadian signals.

In mammals, the circadian clock allows them to anticipate and adapt physiology around the 24 hours. Conversely, metabolism and food consumption regulate the internal clock, pointing the existence of an intricate relationship between nutrient state and circadian homeostasis that is far from being understood. The Sterol Regulatory Element Binding Protein 1 (SREBP1) is a key regulator of lipid homeostasis. Hepatic SREBP1 function is influenced by the nutrient-response cycle, but also by the circadian machinery. To systematically understand how the interplay of circadian clock and nutrient-driven rhythm regulates SREBP1 activity, we evaluated the genome-wide binding of SREBP1 to its targets throughout the day in C57BL/6 mice. The recruitment of SREBP1 to the DNA showed a highly circadian behaviour, with a maximum during the fed status. However, the temporal expression of SREBP1 targets was not always synchronized with its binding pattern. In particular, different expression phases were observed for SREBP1 target genes depending on their function, suggesting the involvement of other transcription factors in their regulation. Binding sites for Hepatocyte Nuclear Factor 4 (HNF4) were specifically enriched in the close proximity of SREBP1 peaks of genes, whose expression was shifted by about 8 hours with respect to SREBP1 binding. Thus, the cross-talk between hepatic HNF4 and SREBP1 may underlie the expression timing of this subgroup of SREBP1 targets. Interestingly, the proper temporal expression profile of these genes was dramatically changed in Bmal1-/- mice upon time-restricted feeding, for which a rhythmic, but slightly delayed, binding of SREBP1 was maintained. Collectively, our results show that besides the nutrient-driven regulation of SREBP1 nuclear translocation, a second layer of modulation of SREBP1 transcriptional activity, strongly dependent from the circadian clock, exists. This system allows us to fine tune the expression timing of SREBP1 target genes, thus helping to temporally separate the different physiological processes in which these genes are involved.

Inference of distributional parameters from compositional samples containing nondetects

Low concentrations of elements in geochemical analyses have the peculiarity of beingcompositional data and, for a given level of significance, are likely to be beyond thecapabilities of laboratories to distinguish between minute concentrations and completeabsence, thus preventing laboratories from reporting extremely low concentrations of theanalyte. Instead, what is reported is the detection limit, which is the minimumconcentration that conclusively differentiates between presence and absence of theelement. A spatially distributed exhaustive sample is employed in this study to generateunbiased sub-samples, which are further censored to observe the effect that differentdetection limits and sample sizes have on the inference of population distributionsstarting from geochemical analyses having specimens below detection limit (nondetects).The isometric logratio transformation is used to convert the compositional data in thesimplex to samples in real space, thus allowing the practitioner to properly borrow fromthe large source of statistical techniques valid only in real space. The bootstrap method isused to numerically investigate the reliability of inferring several distributionalparameters employing different forms of imputation for the censored data. The casestudy illustrates that, in general, best results are obtained when imputations are madeusing the distribution best fitting the readings above detection limit and exposes theproblems of other more widely used practices. When the sample is spatially correlated, itis necessary to combine the bootstrap with stochastic simulation

IgG and IgM western blot assay for diagnosis of congenital toxoplasmosis

The aim of this study was to evaluate the utility of western blot (WB) analysis as a diagnostic tool for congenital toxoplasmosis in 215 newborn infants. The children were submitted to clinical examinations to assess macular, neurological and hearing signals. The WB results obtained were compared to the persistence of IgG antibodies at the end of 12 months, which is regarded as the "gold standard" diagnosis of congenital toxoplasmosis. Association between the WB results and the clinical signs presented by the infants was also assessed. Of the 215 children, 177 had a confirmed congenital toxoplasmosis diagnosis and 38 were uninfected. IgG-WB showed a sensitivity of 73.5% and a specificity of 97.4%. IgM-WB showed a sensitivity of 54.8% and a specificity of 94.7%. The IgG-WB and IgM-WB combination increased the sensitivity to 86.5%. The IgM-WB-positive children had a 1.4-fold greater risk of presenting active macular lesions than did those that were IgM-WB-negative. This study showed that the WB assay is a useful tool to confirm a diagnosis of congenital toxoplasmosis and that the IgM-WB-positive results can indicate active macular lesions in newborn infants.

A compositional approach to stable isotope data analysis

Isotopic data are currently becoming an important source of information regardingsources, evolution and mixing processes of water in hydrogeologic systems. However, itis not clear how to treat with statistics the geochemical data and the isotopic datatogether. We propose to introduce the isotopic information as new parts, and applycompositional data analysis with the resulting increased composition. Results areequivalent to downscale the classical isotopic delta variables, because they are alreadyrelative (as needed in the compositional framework) and isotopic variations are almostalways very small. This methodology is illustrated and tested with the study of theLlobregat River Basin (Barcelona, NE Spain), where it is shown that, though verysmall, isotopic variations comp lement geochemical principal components, and help inthe better identification of pollution sources

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

Multivariate ARIMA Compositional Time Series Analysis

A compositional time series is obtained when a compositional data vector is observed atdifferent points in time. Inherently, then, a compositional time series is a multivariatetime series with important constraints on the variables observed at any instance in time.Although this type of data frequently occurs in situations of real practical interest, atrawl through the statistical literature reveals that research in the field is very much in itsinfancy and that many theoretical and empirical issues still remain to be addressed. Anyappropriate statistical methodology for the analysis of compositional time series musttake into account the constraints which are not allowed for by the usual statisticaltechniques available for analysing multivariate time series. One general approach toanalyzing compositional time series consists in the application of an initial transform tobreak the positive and unit sum constraints, followed by the analysis of the transformedtime series using multivariate ARIMA models. In this paper we discuss the use of theadditive log-ratio, centred log-ratio and isometric log-ratio transforms. We also presentresults from an empirical study designed to explore how the selection of the initialtransform affects subsequent multivariate ARIMA modelling as well as the quality ofthe forecasts

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table hasn rows and m columns and all probabilities are non-null. This kind of table can beseen as an element in the simplex of n · m parts. In this context, the marginals areidentified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclideanelements of the Aitchison geometry of the simplex can also be translated into the tableof probabilities: subspaces, orthogonal projections, distances.Two important questions are addressed: a) given a table of probabilities, which isthe nearest independent table to the initial one? b) which is the largest orthogonalprojection of a row onto a column? or, equivalently, which is the information in arow explained by a column, thus explaining the interaction? To answer these questionsthree orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independenttwo-way tables and fully dependent tables representing row-column interaction. Animportant result is that the nearest independent table is the product of the two (rowand column)-wise geometric marginal tables. A corollary is that, in an independenttable, the geometric marginals conform with the traditional (arithmetic) marginals.These decompositions can be compared with standard log-linear models.Key words: balance, compositional data, simplex, Aitchison geometry, composition,orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure,contingency table

Compositional data and Simpson's paradox

Simpson's paradox, also known as amalgamation or aggregation paradox, appears whendealing with proportions. Proportions are by construction parts of a whole, which canbe interpreted as compositions assuming they only carry relative information. TheAitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinearoperation within that structure. Here we propose to use balances, which are specificelements of this structure, to analyse situations where the paradox might appear. Withthe proposed approach we obtain that the centre of the tables analysed is a naturalway to compare them, which avoids by construction the possibility of a paradox.Key words: Aitchison geometry, geometric mean, orthogonal projection

Compositional Time Series: An Application

The composition of the labour force is an important economic factor for a country.Often the changes in proportions of different groups are of interest.I this paper we study a monthly compositional time series from the Swedish LabourForce Survey from 1994 to 2005. Three models are studied: the ILR-transformed series,the ILR-transformation of the compositional differenced series of order 1, and the ILRtransformationof the compositional differenced series of order 12. For each of thethree models a VAR-model is fitted based on the data 1994-2003. We predict the timeseries 15 steps ahead and calculate 95 % prediction regions. The predictions of thethree models are compared with actual values using MAD and MSE and the predictionregions are compared graphically in a ternary time series plot.We conclude that the first, and simplest, model possesses the best predictive power ofthe three models

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Serological diagnosis of paracoccidioidomycosis in HIV-coinfected patients

Paracoccidioidomycosis should be differentiated from other opportunistic diseases in human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) patients who live in Latin America. Laboratory investigation can begin with serological tests, which are rapid and efficient. In the present study, double immunodiffusion (DID), counterimmunoelectrophoresis (CIEP) and an enzyme linked immunosorbent assay (ELISA) tests were assessed for the detection of anti-Paracoccidioides brasiliensis antibodies in 40 patients coinfected with HIV. The results were compared to those obtained for 75 non-HIV-infected patients with endemic paracoccidioidomycosis. Anti-P. brasiliensis antibodies were detected in 65% (DID), 79% (CIEP) and 95% (ELISA) of the patients with HIV/AIDS, significantly lower rates than those detected in cases of endemic paracoccidioidomycosis, which were 89%, 99% and 100%, respectively. The reactive sera of HIV-infected patients also showed lower anti-P. brasiliensis antibody titres than those of non-HIV-infected patients. Despite the lower intensity of the specific humoral response, serological tests are useful for the diagnosis of opportunistic paracoccidioidomycosis in the HIV/AIDS population. We suggest optimization of the laboratory diagnosis by combining the ELISA test with CIEP or DID.