21 research outputs found
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 discussedGeologische Vereinigung; Institut d’EstadÃstica de Catalunya; International Association for Mathematical Geology; Patronat de l’Escola Politècnica Superior de la Universitat de Girona; Fundació privada: Girona, Universitat i Futur; Cà tedra LluÃs Santaló d’Aplicacions de la Matemà tica; Consell Social de la Universitat de Girona; Ministerio de Ciencia i TecnologÃa
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 informativeGeologische Vereinigung; Institut d’EstadÃstica de Catalunya; International Association for Mathematical Geology; Patronat de l’Escola Politècnica Superior de la Universitat de Girona; Fundació privada: Girona, Universitat i Futur; Cà tedra LluÃs Santaló d’Aplicacions de la Matemà tica; Consell Social de la Universitat de Girona; Ministerio de Ciencia i TecnologÃa
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 technologiesGeologische Vereinigung; Universitat de Barcelona, Equip de Recerca Arqueomètrica; Institut d’EstadÃstica de Catalunya; International Association for Mathematical Geology; Patronat de l’Escola Politècnica Superior de la Universitat de Girona; Fundació privada: Girona, Universitat i Futur
Compositional data analysis of archaeological glass: problems and possible solutions
Presentation in CODAWORK'03, session 4: Applications to archeometryGeologische Vereinigung; Universitat de Barcelona, Equip de Recerca Arqueomètrica; Institut d’EstadÃstica de Catalunya; International Association for Mathematical Geology; Patronat de l’Escola Politècnica Superior de la Universitat de Girona; Fundació privada: Girona, Universitat i Futur
Recommended from our members
Beyond the histogram - improved approaches to simple data display in archaeology using kernel density estimates
Recommended from our members
Graphical presentation of results from principal components analysis
Recommended from our members
The archaeological use of kernel density estimates
The main aim of this paper is to illustrate by example some of the advantages of kernel density estimates (KDEs) for data presentation in archaeology. At their simplest KDEs can be thought of as an alternative to the histogram which is possibly the most commonly used statistical device in archaeology. The appearance of a histogram, and hence the archaeological inferences drawn from it, depends on both the interval width used and the starting point of the first interval. A KDE overcomes this latter defect and results in a smoother diagram that is more useful for comparative purposes. The problem of choice of interval width remains, but theory exists to guide this choice and this is discussed in the paper. Two-dimensional histograms are difficult to interpret and require large amounts of data, and KDEs offer clear advantages in this case. After a non-technical introduction to KDEs the core of the paper is two sections on univariate and bivariate KDEs. These illustrate potential uses in archaeology and discuss some of the choices that need to be made in implementing the methodology. Some more experimental work with trivariate KDEs is also reported. Papers by the authors that deal with the more technical aspects of the methodology are electronically available
Recommended from our members
MATLAB routines from kernel density estimation and the graphical presentation of archaeological data
Recommended from our members
Grouping ceramic compositional data: an S-Plus implementation
Recommended from our members