Distributional equivalence and subcompositional coherence in the analysis of contingency tables, ratio-scale measurements and compositional data

We consider two fundamental properties in the analysis of two-way tables of positive data: the principle of distributional equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional coherence, which forms the basis of compositional data analysis. For an analysis to be subcompositionally coherent, it suffices to analyse the ratios of the data values. The usual approach to dimension reduction in compositional data analysis is to perform principal component analysis on the logarithms of ratios, but this method does not obey the principle of distributional equivalence. We show that by introducing weights for the rows and columns, the method achieves this desirable property. This weighted log-ratio analysis is theoretically equivalent to spectral mapping , a multivariate method developed almost 30 years ago for displaying ratio-scale data from biological activity spectra. The close relationship between spectral mapping and correspondence analysis is also explained, as well as their connection with association modelling. The weighted log-ratio methodology is applied here to frequency data in linguistics and to chemical compositional data in archaeology.

Factor structure of the SOCRATES questionnaire in hospitalized medical patients.

The Stages of Change Readiness and Treatment Eagerness Scale (SOCRATES), a 19-item instrument developed to assess readiness to change alcohol use among individuals presenting for specialized alcohol treatment, has been used in various populations and settings. Its factor structure and concurrent validity has been described for specialized alcohol treatment settings and primary care. The purpose of this study was to determine the factor structure and concurrent validity of the SOCRATES among medical inpatients with unhealthy alcohol use not seeking help for specialized alcohol treatment. The subjects were 337 medical inpatients with unhealthy alcohol use, identified during their hospital stay. Most of them had alcohol dependence (76%). We performed an Alpha Factor Analysis (AFA) and Principal Component Analysis (PCA) of the 19 SOCRATES items, and forced 3 factors and 2 components, in order to replicate findings from Miller and Tonigan (Miller, W. R., & Tonigan, J. S., (1996). Assessing drinkers' motivations for change: The Stages of Change Readiness and Treatment Eagerness Scale (SOCRATES). Psychology of Addictive Behavior, 10, 81-89.) and Maisto et al. (Maisto, S. A., Conigliaro, J., McNeil, M., Kraemer, K., O'Connor, M., & Kelley, M. E., (1999). Factor structure of the SOCRATES in a sample of primary care patients. Addictive Behavior, 24(6), 879-892.). Our analysis supported the view that the 2 component solution proposed by Maisto et al. (Maisto, S.A., Conigliaro, J., McNeil, M., Kraemer, K., O'Connor, M., & Kelley, M.E., (1999). Factor structure of the SOCRATES in a sample of primary care patients. Addictive Behavior, 24(6), 879-892.) is more appropriate for our data than the 3 factor solution proposed by Miller and Tonigan (Miller, W. R., & Tonigan, J. S., (1996). Assessing drinkers' motivations for change: The Stages of Change Readiness and Treatment Eagerness Scale (SOCRATES). Psychology of Addictive Behavior, 10, 81-89.). The first component measured Perception of Problems and was more strongly correlated with severity of alcohol-related consequences, presence of alcohol dependence, and alcohol consumption levels (average number of drinks per day and total number of binge drinking days over the past 30 days) compared to the second component measuring Taking Action. Our findings support the view that the SOCRATES is comprised of two important readiness constructs in general medical patients identified by screening.

Analysis of matched matrices

We consider the joint visualization of two matrices which have common rowsand columns, for example multivariate data observed at two time pointsor split accord-ing to a dichotomous variable. Methods of interest includeprincipal components analysis for interval-scaled data, or correspondenceanalysis for frequency data or ratio-scaled variables on commensuratescales. A simple result in matrix algebra shows that by setting up thematrices in a particular block format, matrix sum and difference componentscan be visualized. The case when we have more than two matrices is alsodiscussed and the methodology is applied to data from the InternationalSocial Survey Program.

A note on the dual scaling of dominance data and its relationship to correspondence analysis

Dual scaling of a subjects-by-objects table of dominance data (preferences,paired comparisons and successive categories data) has been contrasted with correspondence analysis, as if the two techniques were somehow different. In this note we show that dual scaling of dominance data is equivalent to the correspondence analysis of a table which is doubled with respect to subjects. We also show that the results of both methods can be recovered from a principal components analysis of the undoubled dominance table which is centred with respect to subject means.

Soil spectral library and its use in soil classification

Soil science has sought to develop better techniques for the classification of soils, one of which is the use of remote sensing applications. The use of ground sensors to obtain soil spectral data has enabled the characterization of these data and the advancement of techniques for the quantification of soil attributes. In order to do this, the creation of a soil spectral library is necessary. A spectral library should be representative of the variability of the soils in a region. The objective of this study was to create a spectral library of distinct soils from several agricultural regions of Brazil. Spectral data were collected (using a Fieldspec sensor, 350-2,500 nm) for the horizons of 223 soil profiles from the regions of Matão, Paraguaçu Paulista, Andradina, Ipaussu, Mirandópolis, Piracicaba, São Carlos, Araraquara, Guararapes, Valparaíso (SP); Naviraí, Maracajú, Rio Brilhante, Três Lagoas (MS); Goianésia (GO); and Uberaba and Lagoa da Prata (MG). A Principal Component Analysis (PCA) of the data was then performed and a graphic representation of the spectral curve was created for each profile. The reflectance intensity of the curves was principally influenced by the levels of Fe2O3, clay, organic matter and the presence of opaque minerals. There was no change in the spectral curves in the horizons of the Latossolos, Nitossolos, and Neossolos Quartzarênicos. Argissolos had superficial horizon curves with the greatest intensity of reflection above 2,200 nm. Cambissolos and Neossolos Litólicos had curves with greater reflectance intensity in poorly developed horizons. Gleisols showed a convex curve in the region of 350-400 nm. The PCA was able to separate different data collection areas according to the region of source material. Principal component one (PC1) was correlated with the intensity of reflectance samples and PC2 with the slope between the visible and infrared samples. The use of the Spectral Library as an indicator of possible soil classes proved to be an important tool in profile classification.

Morphostructural characterization of soil conventionally tilled with mechanized and animal traction with and without cover crop

The structural stability and restructuring ability of a soil are related to the methods of crop management and soil preparation. A recommended strategy to reduce the effects of soil preparation is to use crop rotation and cover crops that help conserve and restore the soil structure. The aim of this study was to evaluate and quantify the homogeneous morphological units in soil under conventional mechanized tillage and animal traction, as well as to assess the effect on the soil structure of intercropping with jack bean (Canavalia ensiformis L.). Profiles were analyzed in April of 2006, in five counties in the Southern-Central region of Paraná State (Brazil), on family farms producing maize (Zea mays L.), sometimes intercropped with jack bean. The current structures in the crop profile were analyzed using Geographic Information Systems (GIS) and subsequently principal component analysis (PCA) to generate statistics. Morphostructural soil analysis showed a predominance of compact units in areas of high-intensity cultivation under mechanized traction. The cover crop did not improve the structure of the soil with low porosity and compact units that hamper the root system growth. In areas exposed to animal traction, a predominance of cracked units was observed, where roots grew around the clods and along the gaps between them.

Multivariate analysis and geostatistics of the fertility of a humic rhodic hapludox under coffee cultivation

The spatial variability of soil and plant properties exerts great influence on the yeld of agricultural crops. This study analyzed the spatial variability of the fertility of a Humic Rhodic Hapludox with Arabic coffee, using principal component analysis, cluster analysis and geostatistics in combination. The experiment was carried out in an area under Coffea arabica L., variety Catucai 20/15 - 479. The soil was sampled at a depth 0.20 m, at 50 points of a sampling grid. The following chemical properties were determined: P, K+, Ca2+, Mg2+, Na+, S, Al3+, pH, H + Al, SB, t, T, V, m, OM, Na saturation index (SSI), remaining phosphorus (P-rem), and micronutrients (Zn, Fe, Mn, Cu and B). The data were analyzed with descriptive statistics, followed by principal component and cluster analyses. Geostatistics were used to check and quantify the degree of spatial dependence of properties, represented by principal components. The principal component analysis allowed a dimensional reduction of the problem, providing interpretable components, with little information loss. Despite the characteristic information loss of principal component analysis, the combination of this technique with geostatistical analysis was efficient for the quantification and determination of the structure of spatial dependence of soil fertility. In general, the availability of soil mineral nutrients was low and the levels of acidity and exchangeable Al were high.

Development of a two-step screening ESI-TOF-MS method for rapid determination of significant stress-induced metabolome modifications in plant leaf extracts: the wound response in Arabidopsis thaliana as a case study.

To study the stress-induced effects caused by wounding under a new perspective, a metabolomic strategy based on HPLC-MS has been devised for the model plant Arabidopsis thaliana. To detect induced metabolites and precisely localise these compounds among the numerous constitutive metabolites, HPLC-MS analyses were performed in a two-step strategy. In a first step, rapid direct TOF-MS measurements of the crude leaf extract were performed with a ballistic gradient on a short LC-column. The HPLC-MS data were investigated by multivariate analysis as total mass spectra (TMS). Principal components analysis (PCA) and hierarchical cluster analysis (HCA) on principal coordinates were combined for data treatment. PCA and HCA demonstrated a clear clustering of plant specimens selecting the highest discriminating ions given by the complete data analysis, leading to the specific detection of discrete-induced ions (m/z values). Furthermore, pool constitution with plants of homogeneous behaviour was achieved for confirmatory analysis. In this second step, long high-resolution LC profilings on an UPLC-TOF-MS system were used on pooled samples. This allowed to precisely localise the putative biological marker induced by wounding and by specific extraction of accurate m/z values detected in the screening procedure with the TMS spectra.

Correlation between species composition and soil properties in the pastures of Plana de Vic (Catalonia, Spain)

The correlation between the species composition of pasture communities and soil properties in Plana de Vic has been studied using two multivariate methods, Correspondence Analysis (CA) for the vegetation data and Principal Component Analysis (PCA) for the soil data. To analyse the pastures, we took 144 vegetation relevés (comprising 201 species) that have been classified into 10 phytocoenological communities elsewhere. Most of these communities are almost entirely built up by perennials, ranging from xerophilous, clearly Mediterranean, to mesophilous, related to medium-European pastures, but a few occurring in shallow soils are dominated by therophytes. As for the soil properties, we analysed texture, pH, depth, bulk density, organic matter, C/N ratio and the carbonates content of 25 samples, correspondingto representative relevés of the communities studied.

Tire traces: discrimination and classification of pyrolysis-GC/MS profiles

Tire traces can be observed on several crime scenes as vehicles are often used by criminals. The tread abrasion on the road, while braking or skidding, leads to the production of small rubber particles which can be collected for comparison purposes. This research focused on the statistical comparison of Py-GC/MS profiles of tire traces and tire treads. The optimisation of the analytical method was carried out using experimental designs. The aim was to determine the best pyrolysis parameters regarding the repeatability of the results. Thus, the pyrolysis factor effect could also be calculated. The pyrolysis temperature was found to be five time more important than time. Finally, a pyrolysis at 650 °C during 15 s was selected. Ten tires of different manufacturers and models were used for this study. Several samples were collected on each tire, and several replicates were carried out to study the variability within each tire (intravariability). More than eighty compounds were integrated for each analysis and the variability study showed that more than 75% presented a relative standard deviation (RSD) below 5% for the ten tires, thus supporting a low intravariability. The variability between the ten tires (intervariability) presented higher values and the ten most variant compounds had a RSD value above 13%, supporting their high potential of discrimination between the tires tested. Principal Component Analysis (PCA) was able to fully discriminate the ten tires with the help of the first three principal components. The ten tires were finally used to perform braking tests on a racetrack with a vehicle equipped with an anti-lock braking system. The resulting tire traces were adequately collected using sheets of white gelatine. As for tires, the intravariability for the traces was found to be lower than the intervariability. Clustering methods were carried out and the Ward's method based on the squared Euclidean distance was able to correctly group all of the tire traces replicates in the same cluster than the replicates of their corresponding tire. Blind tests on traces were performed and were correctly assigned to their tire source. These results support the hypothesis that the tested tires, of different manufacturers and models, can be discriminated by a statistical comparison of their chemical profiles. The traces were found to be not differentiable from their source but differentiable from all the other tires present in the subset. The results are promising and will be extended on a larger sample set.

UPLC-TOF-MS for plant metabolomics: a sequential approach for wound marker analysis in Arabidopsis thaliana.

The model plant Arabidopsis thaliana was studied for the search of new metabolites involved in wound signalling. Diverse LC approaches were considered in terms of efficiency and analysis time and a 7-min gradient on a UPLC-TOF-MS system with a short column was chosen for metabolite fingerprinting. This screening step was designed to allow the comparison of a high number of samples over a wide range of time points after stress induction in positive and negative ionisation modes. Thanks to data treatment, clear discrimination was obtained, providing lists of potential stress-induced ions. In a second step, the fingerprinting conditions were transferred to longer column, providing a higher peak capacity able to demonstrate the presence of isomers among the highlighted compounds.

Raman analysis of multilayer automotive paints in forensic science: measurement variability and depth profile?

The aim of this work is to study the influence of several analytical parameters on the variability of Raman spectra of paint samples. In the present study, microtome thin section and direct (no preparation) analysis are considered as sample preparation. In order to evaluate their influence on the measures, an experimental design such as 'fractional full factorial' with seven factors (including the sampling process) is applied, for a total of 32 experiments representing 160 measures. Once the influence of sample preparation highlighted, a depth profile of a paint sample is carried out by changing the focusing plane in order to measure the colored layer under a clearcoat. This is undertaken in order to avoid sample preparation such a microtome sectioning. Finally, chemometric treatments such as principal component analysis are applied to the resulting spectra. The findings of this study indicate the importance of sample preparation, or more specifically, the surface roughness, on the variability of the measurements on a same sample. Moreover, the depth profile experiment highlights the influence of the refractive index of the upper layer (clearcoat) when measuring through a transparent layer.

Detection and chemical profiling of medicine counterfeits by Raman spectroscopy and chemometrics

Raman spectroscopy combined with chemometrics has recently become a widespread technique for the analysis of pharmaceutical solid forms. The application presented in this paper is the investigation of counterfeit medicines. This increasingly serious issue involves networks that are an integral part of industrialized organized crime. Efficient analytical tools are consequently required to fight against it. Quick and reliable authentication means are needed to allow the deployment of measures from the company and the authorities. For this purpose a method in two steps has been implemented here. The first step enables the identification of pharmaceutical tablets and capsules and the detection of their counterfeits. A nonlinear classification method, the Support Vector Machines (SVM), is computed together with a correlation with the database and the detection of Active Pharmaceutical Ingredient (API) peaks in the suspect product. If a counterfeit is detected, the second step allows its chemical profiling among former counterfeits in a forensic intelligence perspective. For this second step a classification based on Principal Component Analysis (PCA) and correlation distance measurements is applied to the Raman spectra of the counterfeits.

Classification and fingerprinting of different berries based on biochemical profiling and antioxidant capacity

The objective of this work was to evaluate the biochemical composition of six berry types belonging to Fragaria, Rubus, Vaccinium and Ribes genus. Fruit samples were collected in triplicate (50 fruit each) from 18 different species or cultivars of the mentioned genera, during three years (2008 to 2010). Content of individual sugars, organic acids, flavonols, and phenolic acids were determined by high performance liquid chromatography (HPLC) analysis, while total phenolics (TPC) and total antioxidant capacity (TAC), by using spectrophotometry. Principal component analysis (PCA) and hierarchical cluster analysis (CA) were performed to evaluate the differences in fruit biochemical profile. The highest contents of bioactive components were found in Ribes nigrum and in Fragaria vesca, Rubus plicatus, and Vaccinium myrtillus. PCA and CA were able to partially discriminate between berries on the basis of their biochemical composition. Individual and total sugars, myricetin, ellagic acid, TPC and TAC showed the highest impact on biochemical composition of the berry fruits. CA separated blackberry, raspberry, and blueberry as isolate groups, while classification of strawberry, black and red currant in a specific group has not occurred. There is a large variability both between and within the different types of berries. Metabolite fingerprinting of the evaluated berries showed unique biochemical profiles and specific combination of bioactive compound contents.

Chemical characteristics of grape juices from different cultivar and rootstock combinations

The objective of this work was to evaluate the influence of different combinations of grape cultivars and rootstocks on chemical characteristics of grape juices. Six treatments were evaluated, consisting of combinations between the Isabel Precoce and BRS Cora grape cultivars and the 'IAC 766', 'IAC 313', and 'IAC 572' rootstocks. Approximately 10 L of juice were obtained per treatment. Analyses of color, total soluble solids content, pH, anthocyanins, total phenolics, total sugars, and quantification and identification of biogenic amines by HPLC were performed. Biogenic amines, such as putrescine, cadaverine, spermidine, and spermine, were found in all evaluated cultivars. By principal component analysis (PCA), treatments can be divided into two groups, according to the cultivar. Juices obtained from 'Isabel Precoce' are characterized by higher levels of total sugar content and soluble solids; however, juices from 'BRS Cora' are positively correlated with phenolic content, anthocyanins, and color and acidity parameters. The differences found by PCA for juices from the Isabel Precoce and BRS Cora cultivars indicate that, regardless of the rootstock used, the most important factor in the chemical characterization of juices is the grape cultivar.