Comparing correspondence analysis and the log-ratio alternative for representing categorical data

We compare correspondance análisis to the logratio approach based on compositional data. We also compare correspondance análisis and an alternative approach using Hellinger distance, for representing categorical data in a contingency table. We propose a coefficient which globally measures the similarity between these approaches. This coefficient can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions to the difference between the two representations. These three methods of representation can produce quite similar results. One illustrative example is given

Comparing correspondence analysis and the log-ratio alternative for representing categorical data

We compare correspondance análisis to the logratio approach based on compositional data. We also compare correspondance análisis and an alternative approach using Hellinger distance, for representing categorical data in a contingency table. We propose a coefficient which globally measures the similarity between these approaches. This coefficient can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions to the difference between the two representations. These three methods of representation can produce quite similar results. One illustrative example is given

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.

The use of forensic polycyclic aromatic hydrocarbon signatures and Compound Ratio Analysis Techniques (CORAT) for the source characterisation of petrogenic/pyrogenic environmental releases.

This study utilised recent developments in forensic aromatic hydrocarbon fingerprint analysis to characterise and identify specific biogenic, pyrogenic and petrogenic contamination. The fingerprinting and data interpretation techniques discussed include the recognition of: The distribution patterns of hydrocarbons (alkylated naphthalene, phenanthrene, dibenzothiophene, fluorene, chrysene and phenol isomers), • Analysis of “source-specific marker” compounds (individual saturated hydrocarbons, including n-alkanes (n-C5 through 0-C40) • Selected benzene, toluene, ethylbenzene and xylene isomers (BTEX), • The recalcitrant isoprenoids; pristane and phytane and • The determination of diagnostic ratios of specific petroleum / non-petroleum constituents, and the application of various statistical and numerical analysis tools. An unknown sample from the Irish Environmental Protection Agency (EPA) for origin characterisation was subjected to analysis by gas chromatography utilising both flame ionisation and mass spectral detection techniques in comparison to known reference materials. The percentage of the individual Polycyclic Aromatic Hydrocarbons (PAIIs) and biomarker concentrations in the unknown sample were normalised to the sum of the analytes and the results were compared with the corresponding results with a range of reference materials. In addition, to the determination of conventional diagnostic PAH and biomarker ratios, a number of “source-specific markers” isomeric PAHs within the same alkylation levels were determined, and their relative abundance ratios were computed in order to definitively identify and differentiate the various sources. Statistical logarithmic star plots were generated from both sets of data to give a pictorial representation of the comparison between the unknown sample and reference products. The study successfully characterised the unknown sample as being contaminated with a “coal tar” and clearly demonstrates the future role of compound ratio analysis (CORAT) in the identification of possible source contaminants.

Carbon isotopic ratio analysis by gas chromatography/combustion/isotope ratio mass spectrometry for the detection of gamma-hydroxybutyric acid (GHB) administration to humans.

Since GHB (gamma-hydroxybutyric acid) is naturally produced in the human body, clinical and forensic toxicologists must be able to discriminate between endogenous levels and a concentration resulting from exposure. To suggest an alternative to the use of interpretative concentration cut-offs, the detection of exogenous GHB in urine specimens was investigated by means of gas chromatography/combustion/isotope ratio mass spectrometry (GC/C/IRMS). GHB was isolated from urinary matrix by successive purification on Oasis MCX and Bond Elute SAX solid-phase extraction (SPE) cartridges prior to high-performance liquid chromatography (HPLC) fractioning using an Atlantis dC18 column eluted with a mixture of formic acid and methanol. Subsequent intramolecular esterification of GHB leading to the formation of gamma-butyrolactone (GBL) was carried out to avoid introduction of additional carbon atoms for carbon isotopic ratio analysis. A precision of 0.3 per thousand was determined using this IRMS method for samples at GHB concentrations of 10 mg/L. The (13)C/(12)C ratios of GHB in samples of subjects exposed to the drug ranged from -32.1 to -42.1 per thousand, whereas the results obtained for samples containing GHB of endogenous origin at concentration levels less than 10 mg/L were in the range -23.5 to -27.0 per thousand. Therefore, these preliminary results show that a possible discrimination between endogenous and exogenous GHB can be made using carbon isotopic ratio analyses.

Source inference of exogenous gamma-hydroxybutyric acid (GHB) administered to humans by means of carbon isotopic ratio analysis: novel perspectives regarding forensic investigation and intelligence issues.

γ-Hydroxybutyric acid (GHB) is an endogenous short-chain fatty acid popular as a recreational drug due to sedative and euphoric effects, but also often implicated in drug-facilitated sexual assaults owing to disinhibition and amnesic properties. Whilst discrimination between endogenous and exogenous GHB as required in intoxication cases may be achieved by the determination of the carbon isotope content, such information has not yet been exploited to answer source inference questions of forensic investigation and intelligence interests. However, potential isotopic fractionation effects occurring through the whole metabolism of GHB may be a major concern in this regard. Thus, urine specimens from six healthy male volunteers who ingested prescription GHB sodium salt, marketed as Xyrem(®), were analysed by means of gas chromatography/combustion/isotope ratio mass spectrometry to assess this particular topic. A very narrow range of δ(13)C values, spreading from -24.810/00 to -25.060/00, was observed, whilst mean δ(13)C value of Xyrem(®) corresponded to -24.990/00. Since urine samples and prescription drug could not be distinguished by means of statistical analysis, carbon isotopic effects and subsequent influence on δ(13)C values through GHB metabolism as a whole could be ruled out. Thus, a link between GHB as a raw matrix and found in a biological fluid may be established, bringing relevant information regarding source inference evaluation. Therefore, this study supports a diversified scope of exploitation for stable isotopes characterized in biological matrices from investigations on intoxication cases to drug intelligence programmes.

Power transformations in correspondence analysis

Power transformations of positive data tables, prior to applying the correspondence analysis algorithm, are shown to open up a family of methods with direct connections to the analysis of log-ratios. Two variations of this idea are illustrated. The first approach is simply to power the original data and perform a correspondence analysis this method is shown to converge to unweighted log-ratio analysis as the power parameter tends to zero. The second approach is to apply the power transformation to thecontingency ratios, that is the values in the table relative to expected values based on the marginals this method converges to weighted log-ratio analysis, or the spectral map. Two applications are described: first, a matrix of population genetic data which is inherently two-dimensional, and second, a larger cross-tabulation with higher dimensionality, from a linguistic analysis of several books.

An R Library for Compositional Data Analysis in Archaeometry

Compositional data naturally arises from the scientific analysis of the chemical composition of archaeological material such as ceramic and glass artefacts. Data of this type can be explored using a variety of techniques, from standard multivariate methods such as principal components analysis and cluster analysis, to methods based upon the use of log-ratios. The general aim is to identify groups of chemically similar artefacts that could potentially be used to answer questions of provenance. This paper will demonstrate work in progress on the development of a documented library of methods, implemented using the statistical package R, for the analysis of compositional data. R is an open source package that makes available very powerful statistical facilities at no cost. We aim to show how, with the aid of statistical software such as R, traditional exploratory multivariate analysis can easily be used alongside, or in combination with, specialist techniques of compositional data analysis. The library has been developed from a core of basic R functionality, together with purpose-written routines arising from our own research (for example that reported at CoDaWork'03). In addition, we have included other appropriate publicly available techniques and libraries that have been implemented in R by other authors. Available functions range from standard multivariate techniques through to various approaches to log-ratio analysis and zero replacement. We also discuss and demonstrate a small selection of relatively new techniques that have hitherto been little-used in archaeometric applications involving compositional data. The application of the library to the analysis of data arising in archaeometry will be demonstrated; results from different analyses will be compared; and the utility of the various methods discussed

Carbon and nitrogen stable isotope ratio analysis of freshwater, brackish and marine fish from Belgian archaeological sites (1st and 2nd millennium AD)

Carbon and nitrogen stable isotope ratios were measured in 157 fish bone collagen samples from 15 different archaeological sites in Belgium which ranged in ages from the 3rd to the 18th c. AD. Due to diagenetic contamination of the burial environment, only 63 specimens produced results with suitable C:N ratios (2.9–3.6). The selected bones encompass a wide spectrum of freshwater, brackish, and marine taxa (N = 18), and this is reflected in the δ13C results (−28.2‰ to −12.9%). The freshwater fish have δ13C values that range from −28.2‰ to −20.2‰, while the marine fish cluster between −15.4‰ and −13.0‰. Eel, a catadromous species (mostly living in freshwater but migrating into the sea to spawn), plots between −24.1‰ and −17.7‰, and the anadromous fish (living in marine environments but migrating into freshwater to spawn) show a mix of freshwater and marine isotopic signatures. The δ15N results also have a large range (7.2‰ to 16.7‰) indicating that these fish were feeding at many different trophic levels in these diverse aquatic environments. The aim of this research is the isotopic characterization of archaeological fish species (ecology, trophic level, migration patterns) and to determine intra-species variation within and between fish populations differing in time and location. Due to the previous lack of archaeological fish isotope data from Northern Europe and Belgium in particular, these results serve as an important ecological backdrop for the future isotopic reconstruction of the diet of human populations dating from the historical period (1st and 2nd millennium AD), where there is zooarchaeological and historical evidence for an increased consumption of marine fish.

RAMSY: Ratio Analysis of Mass Spectrometry to Improve Compound Identification

The complexity of biological samples poses a major challenge for reliable compound identification in mass spectrometry (MS). The presence of interfering compounds that cause additional peaks in the spectrum can make interpretation and assignment difficult. To overcome this issue, new approaches are needed to reduce complexity and simplify spectral interpretation. Recently, focused on unknown metabolite identification, we presented a new approach, RANSY (ratio analysis of nuclear magnetic resonance spectroscopy; Anal. Chem. 2011, 83, 7616-7623), which extracts the signals related to the same metabolite based on peak intensity ratios. On the basis of this concept, we present the ratio analysis of mass spectrometry (RAMSY) method, which facilitates improved compound identification in complex MS spectra. RAMSY works on the principle that, under a given set of experimental conditions, the abundance/intensity ratios between the mass fragments from the same metabolite are relatively constant. Therefore, the quotients of average peak ratios and their standard deviations, generated using a small set of MS spectra from the same ion chromatogram, efficiently allow the statistical recovery of the metabolite peaks and facilitate reliable identification. RAMSY was applied to both gas chromatography/MS and liquid chromatography tandem MS (LC-MS/MS) data to demonstrate its utility. The performance of RAMSY is typically better than the results from correlation methods. RAMSY promises to improve unknown metabolite identification for MS users in metabolomics or other fields.

Applications of Stable Isotope Ratio Analysis for Social Science Research

Stable Isotope Ratio Analysis (SIRA) is the measurement of variation in different isotopes of same elements in a material. This technique is well-established in the natural sciences and has been long part of the methodological arsenal in fields such as geology and biology. More recently this technique has begun to be utilized in the social sciences, moving from initial applications in anthropology to potential uses in geography, public health, forensic science, and others. This presentation will discuss the techniques behind SIRA, examples of current applications in the natural and social sciences, and potential avenues of future research.

Log-ratio of silica to aluminium counts (ln(Si/Al)) from ODP site 108-658

Growing evidence suggests that the low atmospheric CO2 concentration of the ice ages resulted from enhanced storage of CO2 in the ocean interior, largely as a result of changes in the Southern Ocean1. Early in the most recent deglaciation, a reduction in North Atlantic overturning circulation seems to have driven CO2 release from the Southern Ocean**2, 3, 4, 5, but the mechanism connecting the North Atlantic and the Southern Ocean remains unclear. Biogenic opal export in the low-latitude ocean relies on silicate from the underlying thermocline, the concentration of which is affected by the circulation of the ocean interior. Here we report a record of biogenic opal export from a coastal upwelling system off the coast of northwest Africa that shows pronounced opal maxima during each glacial termination over the past 550,000 years. These opal peaks are consistent with a strong deglacial reduction in the formation of silicate-poor glacial North Atlantic intermediate water**2 (GNAIW). The loss of GNAIW allowed mixing with underlying silicate-rich deep water to increase the silicate supply to the surface ocean. An increase in westerly-wind-driven upwelling in the Southern Ocean in response to the North Atlantic change has been proposed to drive the deglacial rise in atmospheric CO2 (refs 3, 4). However, such a circulation change would have accelerated the formation of Antarctic intermediate water and sub-Antarctic mode water, which today have as little silicate as North Atlantic Deep Water and would have thus maintained low silicate concentrations in the Atlantic thermocline. The deglacial opal maxima reported here suggest an alternative mechanism for the deglacial CO2 release**5, 6. Just as the reduction in GNAIW led to upward silicate transport, it should also have allowed the downward mixing of warm, low-density surface water to reach into the deep ocean. The resulting decrease in the density of the deep Atlantic relative to the Southern Ocean surface promoted Antarctic overturning, which released CO2 to the atmosphere.