Multivariate statistical analysis to support the minimum streamflow regionalization

ABSTRACT This study aimed to develop a methodology based on multivariate statistical analysis of principal components and cluster analysis, in order to identify the most representative variables in studies of minimum streamflow regionalization, and to optimize the identification of the hydrologically homogeneous regions for the Doce river basin. Ten variables were used, referring to the river basin climatic and morphometric characteristics. These variables were individualized for each of the 61 gauging stations. Three dependent variables that are indicative of minimum streamflow (Q7,10, Q90 and Q95). And seven independent variables that concern to climatic and morphometric characteristics of the basin (total annual rainfall – Pa; total semiannual rainfall of the dry and of the rainy season – Pss and Psc; watershed drainage area – Ad; length of the main river – Lp; total length of the rivers – Lt; and average watershed slope – SL). The results of the principal component analysis pointed out that the variable SL was the least representative for the study, and so it was discarded. The most representative independent variables were Ad and Psc. The best divisions of hydrologically homogeneous regions for the three studied flow characteristics were obtained using the Mahalanobis similarity matrix and the complete linkage clustering method. The cluster analysis enabled the identification of four hydrologically homogeneous regions in the Doce river basin.

Application of exploratory factor analysis to assess fish consumption in a university community

The objective of this research was to use the technique of Exploratory Factor Analysis (EFA) for the adequacy of a tool for the assessment of fish consumption and the characteristics involved in this process. Data were collected during a campaign to encourage fish consumption in Brazil with the voluntarily participation of members of a university community. An assessment instrument consisting of multiple-choice questions and a five-point Likert scale was designed and used to measure the importance of certain attributes that influence the choice and consumption of fish. This study sample was composed of of 224 individuals, the majority were women (65.6%). With regard to the frequency of fish consumption, 37.67% of the volunteers interviewed said they consume the product two or three times a month, and 29.6% once a week. The Exploratory Factor Analysis (EFA) was used to group the variables; the extraction was made using the principal components and the rotation using the Quartimax method. The results show clusters in two main constructs, quality and consumption with Cronbach Alpha coefficients of 0.75 and 0.69, respectively, indicating good internal consistency.

Factor Analysis of a Large DSGE Model

We study the workings of the factor analysis of high-dimensional data using artificial series generated from a large, multi-sector dynamic stochastic general equilibrium (DSGE) model. The objective is to use the DSGE model as a laboratory that allow us to shed some light on the practical benefits and limitations of using factor analysis techniques on economic data. We explain in what sense the artificial data can be thought of having a factor structure, study the theoretical and finite sample properties of the principal components estimates of the factor space, investigate the substantive reason(s) for the good performance of di¤usion index forecasts, and assess the quality of the factor analysis of highly dissagregated data. In all our exercises, we explain the precise relationship between the factors and the basic macroeconomic shocks postulated by the model.

Analysis of scoliosis trunk deformities using ICA

This paper describes a method for analyzing scoliosis trunk deformities using Independent Component Analysis (ICA). Our hypothesis is that ICA can capture the scoliosis deformities visible on the trunk. Unlike Principal Component Analysis (PCA), ICA gives local shape variation and assumes that the data distribution is not normal. 3D torso images of 56 subjects including 28 patients with adolescent idiopathic scoliosis and 28 healthy subjects are analyzed using ICA. First, we remark that the independent components capture the local scoliosis deformities as the shoulder variation, the scapula asymmetry and the waist deformation. Second, we note that the different scoliosis curve types are characterized by different combinations of specific independent components.

A compositional data analysis package for R providing multiple approaches

”compositions” is a new R-package for the analysis of compositional and positive data. It contains four classes corresponding to the four different types of compositional and positive geometry (including the Aitchison geometry). It provides means for computation, plotting and high-level multivariate statistical analysis in all four geometries. These geometries are treated in an fully analogous way, based on the principle of working in coordinates, and the object-oriented programming paradigm of R. In this way, called functions automatically select the most appropriate type of analysis as a function of the geometry. The graphical capabilities include ternary diagrams and tetrahedrons, various compositional plots (boxplots, barplots, piecharts) and extensive graphical tools for principal components. Afterwards, ortion and proportion lines, straight lines and ellipses in all geometries can be added to plots. The package is accompanied by a hands-on-introduction, documentation for every function, demos of the graphical capabilities and plenty of usage examples. It allows direct and parallel computation in all four vector spaces and provides the beginner with a copy-and-paste style of data analysis, while letting advanced users keep the functionality and customizability they demand of R, as well as all necessary tools to add own analysis routines. A complete example is included in the appendix

Compositional analysis of archaeological glasses

At CoDaWork'03 we presented work on the analysis of archaeological glass composi- tional data. Such data typically consist of geochemical compositions involving 10-12 variables and approximates completely compositional data if the main component, sil- ica, is included. We suggested that what has been termed `crude' principal component analysis (PCA) of standardized data often identi ed interpretable pattern in the data more readily than analyses based on log-ratio transformed data (LRA). The funda- mental problem is that, in LRA, minor oxides with high relative variation, that may not be structure carrying, can dominate an analysis and obscure pattern associated with variables present at higher absolute levels. We investigate this further using sub- compositional data relating to archaeological glasses found on Israeli sites. A simple model for glass-making is that it is based on a `recipe' consisting of two `ingredients', sand and a source of soda. Our analysis focuses on the sub-composition of components associated with the sand source. A `crude' PCA of standardized data shows two clear compositional groups that can be interpreted in terms of di erent recipes being used at di erent periods, re ected in absolute di erences in the composition. LRA analysis can be undertaken either by normalizing the data or de ning a `residual'. In either case, after some `tuning', these groups are recovered. The results from the normalized LRA are di erently interpreted as showing that the source of sand used to make the glass di ered. These results are complementary. One relates to the recipe used. The other relates to the composition (and presumed sources) of one of the ingredients. It seems to be axiomatic in some expositions of LRA that statistical analysis of compositional data should focus on relative variation via the use of ratios. Our analysis suggests that absolute di erences can also be informative

A compositional approach to stable isotope data analysis

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

Application of compositional data analysis to geochemical data of marine sediments

In an earlier investigation (Burger et al., 2000) five sediment cores near the Rodrigues Triple Junction in the Indian Ocean were studied applying classical statistical methods (fuzzy c-means clustering, linear mixing model, principal component analysis) for the extraction of endmembers and evaluating the spatial and temporal variation of geochemical signals. Three main factors of sedimentation were expected by the marine geologists: a volcano-genetic, a hydro-hydrothermal and an ultra-basic factor. The display of fuzzy membership values and/or factor scores versus depth provided consistent results for two factors only; the ultra-basic component could not be identified. The reason for this may be that only traditional statistical methods were applied, i.e. the untransformed components were used and the cosine-theta coefficient as similarity measure. During the last decade considerable progress in compositional data analysis was made and many case studies were published using new tools for exploratory analysis of these data. Therefore it makes sense to check if the application of suitable data transformations, reduction of the D-part simplex to two or three factors and visual interpretation of the factor scores would lead to a revision of earlier results and to answers to open questions . In this paper we follow the lines of a paper of R. Tolosana- Delgado et al. (2005) starting with a problem-oriented interpretation of the biplot scattergram, extracting compositional factors, ilr-transformation of the components and visualization of the factor scores in a spatial context: The compositional factors will be plotted versus depth (time) of the core samples in order to facilitate the identification of the expected sources of the sedimentary process. Kew words: compositional data analysis, biplot, deep sea sediments

Analysis of spectroscopic measurements of leaf water content at terahertz frequencies using linear transforms

We provide a unified framework for a range of linear transforms that can be used for the analysis of terahertz spectroscopic data, with particular emphasis on their application to the measurement of leaf water content. The use of linear transforms for filtering, regression, and classification is discussed. For illustration, a classification problem involving leaves at three stages of drought and a prediction problem involving simulated spectra are presented. Issues resulting from scaling the data set are discussed. Using Lagrange multipliers, we arrive at the transform that yields the maximum separation between the spectra and show that this optimal transform is equivalent to computing the Euclidean distance between the samples. The optimal linear transform is compared with the average for all the spectra as well as with the Karhunen–Loève transform to discriminate a wet leaf from a dry leaf. We show that taking several principal components into account is equivalent to defining new axes in which data are to be analyzed. The procedure shows that the coefficients of the Karhunen–Loève transform are well suited to the process of classification of spectra. This is in line with expectations, as these coefficients are built from the statistical properties of the data set analyzed.

The underlying return generating factors for REIT returns: an application of independent component analysis

Multi-factor approaches to analysis of real estate returns have, since the pioneering work of Chan, Hendershott and Sanders (1990), emphasised a macro-variables approach in preference to the latent factor approach that formed the original basis of the arbitrage pricing theory. With increasing use of high frequency data and trading strategies and with a growing emphasis on the risks of extreme events, the macro-variable procedure has some deficiencies. This paper explores a third way, with the use of an alternative to the standard principal components approach – independent components analysis (ICA). ICA seeks higher moment independence and maximises in relation to a chosen risk parameter. We apply an ICA based on kurtosis maximisation to weekly US REIT data using a kurtosis maximising algorithm. The results show that ICA is successful in capturing the kurtosis characteristics of REIT returns, offering possibilities for the development of risk management strategies that are sensitive to extreme events and tail distributions.

On the variability of the surface environment response to synoptic forcing over complex terrain: a multivariate data analysis approach

Synoptic climatology relates the atmospheric circulation with the surface environment. The aim of this study is to examine the variability of the surface meteorological patterns, which are developing under different synoptic scale categories over a suburban area with complex topography. Multivariate Data Analysis techniques were performed to a data set with surface meteorological elements. Three principal components related to the thermodynamic status of the surface environment and the two components of the wind speed were found. The variability of the surface flows was related with atmospheric circulation categories by applying Correspondence Analysis. Similar surface thermodynamic fields develop under cyclonic categories, which are contrasted with the anti-cyclonic category. A strong, steady wind flow characterized by high shear values develops under the cyclonic Closed Low and the anticyclonic H–L categories, in contrast to the variable weak flow under the anticyclonic Open Anticyclone category.

Multivariate analysis of the energy cycle of the South American rainy season

The South American (SA) rainy season is studied in this paper through the application of a multivariate Empirical Orthogonal Function (EOF) analysis to a SA gridded precipitation analysis and to the components of Lorenz Energy Cycle (LEC) derived from the National Centers for Environmental Prediction (NCEP) reanalysis. The EOF analysis leads to the identification of patterns of the rainy season and the associated mechanisms in terms of their energetics. The first combined EOF represents the northwest-southeast dipole of the precipitation between South and Central America, the South American Monsoon System (SAMS). The second combined EOF represents a synoptic pattern associated with the SACZ (South Atlantic convergence zone) and the third EOF is in spatial quadrature to the second EOF. The phase relationship of the EOFs, as computed from the principal components (PCs), suggests a nonlinear transition from the SACZ to the fully developed SAMS mode by November and between both components describing the SACZ by September-October (the rainy season onset). According to the LEC, the first mode is dominated by the eddy generation term at its maximum, the second by both baroclinic and eddy generation terms and the third by barotropic instability previous to the connection to the second mode by September-October. The predominance of the different LEC components at each phase of the SAMS can be used as an indicator of the onset of the rainy season in terms of physical processes, while the existence of the outstanding spectral peaks in the time dependence of the EOFs at the intraseasonal time scale could be used for monitoring purposes. Copyright (C) 2009 Royal Meteorological Society

Automatic spiral analysis for objective assessment of motor symptoms in Parkinson's disease

Objective: To develop a method for objective quantification of PD motor symptoms related to Off episodes and peak dose dyskinesias, using spiral data gathered by using a touch screen telemetry device. The aim was to objectively characterize predominant motor phenotypes (bradykinesia and dyskinesia), to help in automating the process of visual interpretation of movement anomalies in spirals as rated by movement disorder specialists. Background: A retrospective analysis was conducted on recordings from 65 patients with advanced idiopathic PD from nine different clinics in Sweden, recruited from January 2006 until August 2010. In addition to the patient group, 10 healthy elderly subjects were recruited. Upper limb movement data were collected using a touch screen telemetry device from home environments of the subjects. Measurements with the device were performed four times per day during week-long test periods. On each test occasion, the subjects were asked to trace pre-drawn Archimedean spirals, using the dominant hand. The pre-drawn spiral was shown on the screen of the device. The spiral test was repeated three times per test occasion and they were instructed to complete it within 10 seconds. The device had a sampling rate of 10Hz and measured both position and time-stamps (in milliseconds) of the pen tip. Methods: Four independent raters (FB, DH, AJ and DN) used a web interface that animated the spiral drawings and allowed them to observe different kinematic features during the drawing process and to rate task performance. Initially, a number of kinematic features were assessed including ‘impairment’, ‘speed’, ‘irregularity’ and ‘hesitation’ followed by marking the predominant motor phenotype on a 3-category scale: tremor, bradykinesia and/or choreatic dyskinesia. There were only 2 test occasions for which all the four raters either classified them as tremor or could not identify the motor phenotype. Therefore, the two main motor phenotype categories were bradykinesia and dyskinesia. ‘Impairment’ was rated on a scale from 0 (no impairment) to 10 (extremely severe) whereas ‘speed’, ‘irregularity’ and ‘hesitation’ were rated on a scale from 0 (normal) to 4 (extremely severe). The proposed data-driven method consisted of the following steps. Initially, 28 spatiotemporal features were extracted from the time series signals before being presented to a Multilayer Perceptron (MLP) classifier. The features were based on different kinematic quantities of spirals including radius, angle, speed and velocity with the aim of measuring the severity of involuntary symptoms and discriminate between PD-specific (bradykinesia) and/or treatment-induced symptoms (dyskinesia). A Principal Component Analysis was applied on the features to reduce their dimensions where 4 relevant principal components (PCs) were retained and used as inputs to the MLP classifier. Finally, the MLP classifier mapped these components to the corresponding visually assessed motor phenotype scores for automating the process of scoring the bradykinesia and dyskinesia in PD patients whilst they draw spirals using the touch screen device. For motor phenotype (bradykinesia vs. dyskinesia) classification, the stratified 10-fold cross validation technique was employed. Results: There were good agreements between the four raters when rating the individual kinematic features with intra-class correlation coefficient (ICC) of 0.88 for ‘impairment’, 0.74 for ‘speed’, 0.70 for ‘irregularity’, and moderate agreements when rating ‘hesitation’ with an ICC of 0.49. When assessing the two main motor phenotype categories (bradykinesia or dyskinesia) in animated spirals the agreements between the four raters ranged from fair to moderate. There were good correlations between mean ratings of the four raters on individual kinematic features and computed scores. The MLP classifier classified the motor phenotype that is bradykinesia or dyskinesia with an accuracy of 85% in relation to visual classifications of the four movement disorder specialists. The test-retest reliability of the four PCs across the three spiral test trials was good with Cronbach’s Alpha coefficients of 0.80, 0.82, 0.54 and 0.49, respectively. These results indicate that the computed scores are stable and consistent over time. Significant differences were found between the two groups (patients and healthy elderly subjects) in all the PCs, except for the PC3. Conclusions: The proposed method automatically assessed the severity of unwanted symptoms and could reasonably well discriminate between PD-specific and/or treatment-induced motor symptoms, in relation to visual assessments of movement disorder specialists. The objective assessments could provide a time-effect summary score that could be useful for improving decision-making during symptom evaluation of individualized treatment when the goal is to maximize functional On time for patients while minimizing their Off episodes and troublesome dyskinesias.

Solid phase microextraction as a reliable alternative to conventional extraction techniques to evaluate the pattern of hydrolytically released components in Vitis vinifera L. grapes

In present research, headspace solid-phase microextraction (HS-SPME) followed by gas chromatography–mass spectrometry (GC–qMS), was evaluated as a reliable and improved alternative to the commonly used liquid–liquid extraction (LLE) technique for the establishment of the pattern of hydrolytically released components of 7 Vitis vinifera L. grape varieties, commonly used to produce the world-famous Madeira wine. Since there is no data available on their glycosidic fractions, at a first step, two hydrolyse procedures, acid and enzymatic, were carried out using Boal grapes as matrix. Several parameters susceptible of influencing the hydrolytic process were studied. The best results, expressed as GC peak area, number of identified components and reproducibility, were obtained using ProZym M with b-glucosidase activity at 35 °C for 42 h. For the extraction of hydrolytically released components, HS-SPME technique was evaluated as a reliable and improved alternative to the conventional extraction technique, LLE (ethyl acetate). HS-SPME using DVB/CAR/PDMS as coating fiber displayed an extraction capacity two fold higher than LLE (ethyl acetate). The hydrolyzed fraction was mainly characterized by the occurrence of aliphatic and aromatic alcohols, followed by acids, esters, carbonyl compounds, terpenoids, and volatile phenols. Concerning to terpenoids its contribution to the total hydrolyzed fraction is highest for Malvasia Cândida (23%) and Malvasia Roxa (13%), and their presence according previous studies, even at low concentration, is important from a sensorial point of view (can impart floral notes to the wines), due to their low odor threshold (μg/L). According to the obtained data by principal component analysis (PCA), the sensorial properties of Madeira wines produced by Malvasia Cândida and Malvasia Roxa could be improved by hydrolysis procedure, since their hydrolyzed fraction is mainly characterized by terpenoids (e.g. linalool, geraniol) which are responsible for floral notes. Bual and Sercial grapes are characterized by aromatic alcohols (e.g. benzyl alcohol, 2-phenylethyl alcohol), so an improvement in sensorial characteristics (citrus, sweet and floral odors) of the corresponding wines, as result of hydrolytic process, is expected.

Multivariate analysis of fresh-cut carambola slices stored under different temperatures

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)