Analysis of Pleistocene paleodrainage evolution in the Po Basin (Italy) by multivariate statistical techniques

In order to obtain a high-resolution Pleistocene stratigraphy, eleven continuouslycored boreholes, 100 to 220m deep were drilled in the northern part of the PoPlain by Regione Lombardia in the last five years. Quantitative provenanceanalysis (QPA, Weltje and von Eynatten, 2004) of Pleistocene sands was carriedout by using multivariate statistical analysis (principal component analysis, PCA,and similarity analysis) on an integrated data set, including high-resolution bulkpetrography and heavy-mineral analyses on Pleistocene sands and of 250 majorand minor modern rivers draining the southern flank of the Alps from West toEast (Garzanti et al, 2004; 2006). Prior to the onset of major Alpine glaciations,metamorphic and quartzofeldspathic detritus from the Western and Central Alpswas carried from the axial belt to the Po basin longitudinally parallel to theSouthAlpine belt by a trunk river (Vezzoli and Garzanti, 2008). This scenariorapidly changed during the marine isotope stage 22 (0.87 Ma), with the onset ofthe first major Pleistocene glaciation in the Alps (Muttoni et al, 2003). PCA andsimilarity analysis from core samples show that the longitudinal trunk river at thistime was shifted southward by the rapid southward and westward progradation oftransverse alluvial river systems fed from the Central and Southern Alps.Sediments were transported southward by braided river systems as well as glacialsediments transported by Alpine valley glaciers invaded the alluvial plain.Kew words: Detrital modes; Modern sands; Provenance; Principal ComponentsAnalysis; Similarity, Canberra Distance; palaeodrainage

The association between obesity and back pain in nine countries: a cross-sectional study

BACKGROUND: The association between obesity and back pain has mainly been studied in high-income settings with inconclusive results, and data from older populations and developing countries are scarce. The aim of this study was to assess this association in nine countries in Asia, Africa, Europe, and Latin America among older adults using nationally-representative data. METHODS: Data on 42116 individuals ≥50 years who participated in the Collaborative Research on Ageing in Europe (COURAGE) study conducted in Finland, Poland, and Spain in 2011-2012, and the World Health Organization's Study on Global Ageing and Adult Health (SAGE) conducted in China, Ghana, India, Mexico, Russia, and South Africa in 2007-2010 were analysed. Information on measured height and weight available in the two datasets was used to calculate Body Mass Index (BMI). Self-reported back pain occurring in the past 30 days was the outcome. Multivariable logistic regression analysis was used to assess the association between BMI and back pain. RESULTS: The prevalence of back pain ranged from 21.5% (China) to 57.5% (Poland). In the multivariable analysis, compared to BMI 18.5-24.9 kg/m(2), significantly higher odds for back pain were observed for BMI ≥35 kg/m(2) in Finland (OR 3.33), Russia (OR 2.20), Poland (OR 2.03), Spain (OR 1.56), and South Africa (OR 1.48); BMI 30.0-34.0 kg/m(2) in Russia (OR 2.76), South Africa (OR 1.51), and Poland (OR 1.47); and BMI 25.0-29.9 kg/m(2) in Russia (OR 1.51) and Poland (OR 1.40). No significant associations were found in the other countries. CONCLUSIONS: The strength of the association between obesity and back pain may vary by country. Future studies are needed to determine the factors contributing to differences in the associations observed.

Compositional data analysis: where we are and where should we be heading?

We take stock of the present position of compositional data analysis, of what has beenachieved in the last 20 years, and then make suggestions as to what may be sensibleavenues of future research. We take an uncompromisingly applied mathematical view,that the challenge of solving practical problems should motivate our theoreticalresearch; and that any new theory should be thoroughly investigated to see if it mayprovide answers to previously abandoned practical considerations. Indeed a main themeof this lecture will be to demonstrate this applied mathematical approach by a number ofchallenging examples

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

Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

An R Library for Compositional Data Analysis in Archaeometry

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

Compositional data analysis in archaeometry

We shall call an n × p data matrix fully-compositional if the rows sum to a constant, and sub-compositional if the variables are a subset of a fully-compositional data set1. Such data occur widely in archaeometry, where it is common to determine the chemical composition of ceramic, glass, metal or other artefacts using techniques such as neutron activation analysis (NAA), inductively coupled plasma spectroscopy (ICPS), X-ray fluorescence analysis (XRF) etc. Interest often centres on whether there are distinct chemical groups within the data and whether, for example, these can be associated with different origins or manufacturing technologies

Compositional data analysis of archaeological glass: problems and possible solutions

Presentation in CODAWORK'03, session 4: Applications to archeometry

Exploration of geological variability and possible processes through the use of compositional data analysis: an example using scottish metamorphosed

Developments in the statistical analysis of compositional data over the last twodecades have made possible a much deeper exploration of the nature of variability,and the possible processes associated with compositional data sets from manydisciplines. In this paper we concentrate on geochemical data sets. First we explainhow hypotheses of compositional variability may be formulated within the naturalsample space, the unit simplex, including useful hypotheses of subcompositionaldiscrimination and specific perturbational change. Then we develop through standardmethodology, such as generalised likelihood ratio tests, statistical tools to allow thesystematic investigation of a complete lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require specialconstruction. We comment on the use of graphical methods in compositional dataanalysis and on the ordination of specimens. The recent development of the conceptof compositional processes is then explained together with the necessary tools for astaying- in-the-simplex approach, namely compositional singular value decompositions. All these statistical techniques are illustrated for a substantial compositional data set, consisting of 209 major-oxide and rare-element compositions of metamorphosed limestones from the Northeast and Central Highlands of Scotland.Finally we point out a number of unresolved problems in the statistical analysis ofcompositional processes

New insights on river water chemistry by using non-centred simplicial principal component analysis: a case study

The use of perturbation and power transformation operations permits the investigation of linear processes in the simplex as in a vectorial space. When the investigated geochemical processes can be constrained by the use of well-known starting point, the eigenvectors of the covariance matrix of a non-centred principalcomponent analysis allow to model compositional changes compared with a reference point.The results obtained for the chemistry of water collected in River Arno (central-northern Italy) have open new perspectives for considering relative changes of the analysed variables and to hypothesise the relative effect of different acting physical-chemical processes, thus posing the basis for a quantitative modelling

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

Diagnosing Patients Combining Principal Components Analysis and Case Based Reasoning

This paper addresses the application of a PCA analysis on categorical data prior to diagnose a patients data set using a Case-Based Reasoning (CBR) system. The particularity is that the standard PCA techniques are designed to deal with numerical attributes, but our medical data set contains many categorical data and alternative methods as RS-PCA are required. Thus, we propose to hybridize RS-PCA (Regular Simplex PCA) and a simple CBR. Results show how the hybrid system produces similar results when diagnosing a medical data set, that the ones obtained when using the original attributes. These results are quite promising since they allow to diagnose with less computation effort and memory storage

Monitoring procedures in environmental geochemistry and compositional data analysis theory

First discussion on compositional data analysis is attributable to Karl Pearson, in 1897. However, notwithstanding the recent developments on algebraic structure of the simplex, more than twenty years after Aitchison’s idea of log-transformations of closed data, scientific literature is again full of statistical treatments of this type of data by using traditional methodologies. This is particularly true in environmental geochemistry where besides the problem of the closure, the spatial structure (dependence) of the data have to be considered. In this work we propose the use of log-contrast values, obtained by asimplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able togenerate the values and to govern their variability. The changes, if compared, for example, with the mean values of the random variables assumed as models, or other reference parameters, allow definingmonitors to be used to assess the extent of possible environmental contamination. Case study on running and ground waters from Chiavenna Valley (Northern Italy) by using Na+, K+, Ca2+, Mg2+, HCO3-, SO4 2- and Cl- concentrations will be illustrated

Elemental analysis of New Zealand Nephrite Jade (pounamu) for forensic purposes

Pounamu (NZ jade), or nephrite, is a protected mineral in its natural form following thetransfer of ownership back to Ngai Tahu under the Ngai Tahu (Pounamu Vesting) Act 1997.Any theft of nephrite is prosecutable under the Crimes Act 1961. Scientific evidence isessential in cases where origin is disputed. A robust method for discrimination of thismaterial through the use of elemental analysis and compositional data analysis is required.Initial studies have characterised the variability within a given nephrite source. This hasincluded investigation of both in situ outcrops and alluvial material. Methods for thediscrimination of two geographically close nephrite sources are being developed.Key Words: forensic, jade, nephrite, laser ablation, inductively coupled plasma massspectrometry, multivariate analysis, elemental analysis, compositional data analysis

Some last thoughts on compositional data analysis

One of the disadvantages of old age is that there is more past than future: this,however, may be turned into an advantage if the wealth of experience and, hopefully,wisdom gained in the past can be reflected upon and throw some light on possiblefuture trends. To an extent, then, this talk is necessarily personal, certainly nostalgic,but also self critical and inquisitive about our understanding of the discipline ofstatistics. A number of almost philosophical themes will run through the talk: searchfor appropriate modelling in relation to the real problem envisaged, emphasis onsensible balances between simplicity and complexity, the relative roles of theory andpractice, the nature of communication of inferential ideas to the statistical layman, theinter-related roles of teaching, consultation and research. A list of keywords might be:identification of sample space and its mathematical structure, choices betweentransform and stay, the role of parametric modelling, the role of a sample spacemetric, the underused hypothesis lattice, the nature of compositional change,particularly in relation to the modelling of processes. While the main theme will berelevance to compositional data analysis we shall point to substantial implications forgeneral multivariate analysis arising from experience of the development ofcompositional data analysis…