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

Interactions between grain size and composition of sediments: two examples

Two contrasting case studies of sediment and detrital mineral composition are investigated in order to outline interactions between chemical composition and grain size. Modern glacial sediments exhibit a strong dependence of the two parameters due to the preferential enrichment of mafic minerals, especially biotite, in the fine-grained fractions. On the other hand, the composition of detrital heavy minerals (here: rutile) appears to be not systematically related to grain-size, but is strongly controlled by location, i.e. the petrology of the source rocks of detrital grains. This supports the use of rutile as a well-suited tracer mineral for provenance studies. The results further suggest that (i) interpretations derived from whole-rock sediment geochemistry should be flanked by grain-size observations, and (ii) a more sound statistical evaluation of these interactions require the development of new tailor-made statistical tools to deal with such so-called two-way compositions

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

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

Revisiting the compositional data. Some fundamental questions and new prospects in Archaeometry and Archaeology

In this paper we examine the problem of compositional data from a different starting point. Chemical compositional data, as used in provenance studies on archaeological materials, will be approached from the measurement theory. The results will show, in a very intuitive way that chemical data can only be treated by using the approach developed for compositional data. It will be shown that compositional data analysis is a particular case in projective geometry, when the projective coordinates are in the positive orthant, and they have the properties of logarithmic interval metrics. Moreover, it will be shown that this approach can be extended to a very large number of applications, including shape analysis. This will be exemplified with a case study in architecture of Early Christian churches dated back to the 5th-7th centuries AD