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

A Log-linear model of grain size influence on the geochemistry of sediments

Sediment composition is mainly controlled by the nature of the source rock(s), and chemical (weathering) and physical processes (mechanical crushing, abrasion, hydrodynamic sorting) during alteration and transport. Although the factors controlling these processes are conceptually well understood, detailed quantification of compositional changes induced by a single process are rare, as are examples where the effects of several processes can be distinguished. The present study was designed to characterize the role of mechanical crushing and sorting in the absence of chemical weathering. Twenty sediment samples were taken from Alpine glaciers that erode almost pure granitoid lithologies. For each sample, 11 grain-size fractions from granules to clay (ø grades &-1 to &9) were separated, and each fraction was analysed for its chemical composition.The presence of clear steps in the box-plots of all parts (in adequate ilr and clr scales) against ø is assumed to be explained by typical crystal size ranges for the relevant mineral phases. These scatter plots and the biplot suggest a splitting of the full grain size range into three groups: coarser than ø=4 (comparatively rich in SiO2, Na2O, K2O, Al2O3, and dominated by “felsic” minerals like quartz and feldspar), finer than ø=8 (comparatively rich in TiO2, MnO, MgO, Fe2O3, mostly related to “mafic” sheet silicates like biotite and chlorite), and intermediate grains sizes (4≤ø &8; comparatively rich in P2O5 and CaO, related to apatite, some feldspar).To further test the absence of chemical weathering, the observed compositions were regressed against three explanatory variables: a trend on grain size in ø scale, a step function for ø≥4, and another for ø≥8. The original hypothesis was that the trend could be identified with weathering effects, whereas each step function would highlight those minerals with biggest characteristic size at its lower end. Results suggest that this assumption is reasonable for the step function, but that besides weathering some other factors (different mechanical behavior of minerals) have also an important contribution to the trend.Key words: sediment, geochemistry, grain size, regression, step function

Compliance with guidelines-recommended processes in pneumonia: impact of health status and initial signs

Initial care has been associated with improved survival of community-acquired pneumonia (CAP). We aimed to investigate patient comorbidities and health status measured by the Charlson index and clinical signs at diagnosis associated with adherence to recommended processes of care in CAP. We studied 3844 patients hospitalized with CAP. The evaluated recommendations were antibiotic adherence to Spanish guidelines, first antibiotic dose <6 hours and oxygen assessment. Antibiotic adherence was 72.6%, first dose <6 h was 73.4% and oxygen assessment was 90.2%. Antibiotic adherence was negatively associated with a high Charlson score (Odds ratio [OR], 0.91), confusion (OR, 0.66) and tachycardia ≥100 bpm (OR, 0.77). Delayed first dose was significantly lower in those with tachycardia (OR, 0.75). Initial oxygen assessment was negatively associated with fever (OR, 0.61), whereas tachypnea ≥30 (OR, 1.58), tachycardia (OR, 1.39), age >65 (OR, 1.51) and COPD (OR, 1.80) were protective factors. The combination of antibiotic adherence and timing <6 hours was negatively associated with confusion (OR, 0.69) and a high Charlson score (OR, 0.92) adjusting for severity and hospital effect, whereas age was not an independent factor. Deficient health status and confusion, rather than age, are associated with lower compliance with antibiotic therapy recommendations and timing, thus identifying a subpopulation more prone to receiving lower quality care.

Gut microbiota in children with type 1 diabetes differs from that in healthy children: a case-control study.

BACKGROUND A recent study using a rat model found significant differences at the time of diabetes onset in the bacterial communities responsible for type 1 diabetes modulation. We hypothesized that type 1 diabetes in humans could also be linked to a specific gut microbiota. Our aim was to quantify and evaluate the difference in the composition of gut microbiota between children with type 1 diabetes and healthy children and to determine the possible relationship of the gut microbiota of children with type 1 diabetes with the glycemic level. METHODS A case-control study was carried out with 16 children with type 1 diabetes and 16 healthy children. The fecal bacteria composition was investigated by polymerase chain reaction-denaturing gradient gel electrophoresis and real-time quantitative polymerase chain reaction. RESULTS The mean similarity index was 47.39% for the healthy children and 37.56% for the children with diabetes, whereas the intergroup similarity index was 26.69%. In the children with diabetes, the bacterial number of Actinobacteria and Firmicutes, and the Firmicutes to Bacteroidetes ratio were all significantly decreased, with the quantity of Bacteroidetes significantly increased with respect to healthy children. At the genus level, we found a significant increase in the number of Clostridium, Bacteroides and Veillonella and a significant decrease in the number of Lactobacillus, Bifidobacterium, Blautia coccoides/Eubacterium rectale group and Prevotella in the children with diabetes. We also found that the number of Bifidobacterium and Lactobacillus, and the Firmicutes to Bacteroidetes ratio correlated negatively and significantly with the plasma glucose level while the quantity of Clostridium correlated positively and significantly with the plasma glucose level in the diabetes group. CONCLUSIONS This is the first study showing that type 1 diabetes is associated with compositional changes in gut microbiota. The significant differences in the number of Bifidobacterium, Lactobacillus and Clostridium and in the Firmicutes to Bacteroidetes ratio observed between the two groups could be related to the glycemic level in the group with diabetes. Moreover, the quantity of bacteria essential to maintain gut integrity was significantly lower in the children with diabetes than the healthy children. These findings could be useful for developing strategies to control the development of type 1 diabetes by modifying the gut microbiota.

Intelligent PCA contribution analysis for quality estimation in batch processes. Application in a sequencing batch reactor for wastewater treatment

En aquest treball, es proposa un nou mètode per estimar en temps real la qualitat del producte final en processos per lot. Aquest mètode permet reduir el temps necessari per obtenir els resultats de qualitat de les anàlisi de laboratori. S'utiliza un model de anàlisi de componentes principals (PCA) construït amb dades històriques en condicions normals de funcionament per discernir si un lot finalizat és normal o no. Es calcula una signatura de falla pels lots anormals i es passa a través d'un model de classificació per la seva estimació. L'estudi proposa un mètode per utilitzar la informació de les gràfiques de contribució basat en les signatures de falla, on els indicadors representen el comportament de les variables al llarg del procés en les diferentes etapes. Un conjunt de dades compost per la signatura de falla dels lots anormals històrics es construeix per cercar els patrons i entrenar els models de classifcació per estimar els resultas dels lots futurs. La metodologia proposada s'ha aplicat a un reactor seqüencial per lots (SBR). Diversos algoritmes de classificació es proven per demostrar les possibilitats de la metodologia proposada.

Theory of mind and cognitive processes in aging and Alzheimer type dementia: a systematic review.

OBJECTIVES: Theory of mind (ToM) performance in aging and dementia of the Alzheimer type (DAT) has been a growing interest of researchers and recently, theoretical trends in ToM development have led to a focus on determining the cognitive skills involved in ToM performance. The aim of the present review is to answer three main questions: How is ToM assessed in aging and DAT? How does ToM performance evolve in aging and DAT? Do cognitive processes influence ToM performance in aging and DAT? METHOD: A systematic review was conducted to provide a targeted overview of recent studies relating ToM performance with cognitive processes in aging and DAT. RESULTS: RESULTS suggest a decrease in ToM performance, more pronounced in complex ToM tasks. Moreover, the review points up the strong involvement of executive functions, especially inhibition, and reasoning skills in ToM task achievement. CONCLUSION: Current data suggest that the structure of ToM tasks itself could lead to poor performance, especially in populations with reduced cognitive abilities.

Polymorphism at a sex-linked transcription cofactor in European tree frogs (Hyla arborea): Sex-antagonistic selection or neutral processes?

Nascent sex chromosomes offer a unique opportunity to investigate the evolutionary fate of genesrecently trapped in non-recombining segments. A housekeeping gene (MED15) was recently shown to lie on the nascent sex-chromosomes of the European tree frog (Hyla arborea), with different alleles fixed on the X and the Y chromosomes. Here we document a polymorphism (glutamine deletion) in the X copy of the gene, and use population surveys and experimental crosses to test whether this polymorphism is neutral or maintained by sex-antagonistic selection. Tadpoles from parents of known genotypes revealed significant discrepancies from Mendelian inheritance, suggesting possible sex-antagonistic effects under laboratory conditions. Quantitatively, however, these effects did not meet the conditions for polymorphism maintenance. Furthermore, field estimates of female genotypic frequencies did not differ from Hardy-Weinberg equilibrium and allelic frequencies on the X chromosome did not differ between sexes. In conclusion, although sex antagonistic effects cannot be excluded given the laboratory conditions, the X-linked polymorphism under study appears neutral in the wild. Alternatively, sex-antagonistic selection might still account for the fixation of a male specific allele on the Y chromosome.

Deficits in executive and memory processes in delusional disorder: a case-control study

OBJECTIVE Delusional disorder has been traditionally considered a psychotic syndrome that does not evolve to cognitive deterioration. However, to date, very little empirical research has been done to explore cognitive executive components and memory processes in Delusional Disorder patients. This study will investigate whether patients with delusional disorder are intact in both executive function components (such as flexibility, impulsivity and updating components) and memory processes (such as immediate, short term and long term recall, learning and recognition). METHODS A large sample of patients with delusional disorder (n = 86) and a group of healthy controls (n = 343) were compared with regard to their performance in a broad battery of neuropsychological tests including Trail Making Test, Wisconsin Card Sorting Test, Colour-Word Stroop Test, and Complutense Verbal Learning Test (TAVEC). RESULTS When compared to controls, cases of delusional disorder showed a significantly poorer performance in most cognitive tests. Thus, we demonstrate deficits in flexibility, impulsivity and updating components of executive functions as well as in memory processes. These findings held significant after taking into account sex, age, educational level and premorbid IQ. CONCLUSIONS Our results do not support the traditional notion of patients with delusional disorder being cognitively intact.

Consensus paper: the role of the cerebellum in perceptual processes.

Various lines of evidence accumulated over the past 30 years indicate that the cerebellum, long recognized as essential for motor control, also has considerable influence on perceptual processes. In this paper, we bring together experts from psychology and neuroscience, with the aim of providing a succinct but comprehensive overview of key findings related to the involvement of the cerebellum in sensory perception. The contributions cover such topics as anatomical and functional connectivity, evolutionary and comparative perspectives, visual and auditory processing, biological motion perception, nociception, self-motion, timing, predictive processing, and perceptual sequencing. While no single explanation has yet emerged concerning the role of the cerebellum in perceptual processes, this consensus paper summarizes the impressive empirical evidence on this problem and highlights diversities as well as commonalities between existing hypotheses. In addition to work with healthy individuals and patients with cerebellar disorders, it is also apparent that several neurological conditions in which perceptual disturbances occur, including autism and schizophrenia, are associated with cerebellar pathology. A better understanding of the involvement of the cerebellum in perceptual processes will thus likely be important for identifying and treating perceptual deficits that may at present go unnoticed and untreated. This paper provides a useful framework for further debate and empirical investigations into the influence of the cerebellum on sensory perception.

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completelyabsent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and byMartín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involvedparts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method isintroduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that thetheoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approachhas reasonable properties from a compositional point of view. In particular, it is “natural” in the sense thatit recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in thesame paper a substitution method for missing values on compositional data sets is introduced

CoDaPack. An Excel and Visual Basic based software of compositional data analysis. Current version and discussion form upcoming versions

In the eighties, John Aitchison (1986) developed a new methodological approach for the statistical analysis of compositional data. This new methodology was implemented in Basic routines grouped under the name CODA and later NEWCODA inMatlab (Aitchison, 1997). After that, several other authors have published extensions to this methodology: Marín-Fernández and others (2000), Barceló-Vidal and others (2001), Pawlowsky-Glahn and Egozcue (2001, 2002) and Egozcue and others (2003). (...)