LOG‐RATIO COMPOSITIONAL DATA ANALYSIS IN ARCHAEOMETRY*

Compositional data arise commonly in archaeometry, in the study of artefact compositions where the variables measured either sum to 100%, or can be viewed as a subset of such a set of variables. There has been debate in Archaeometry about the appropriate way to analyse such data statistically, which amounts to argument about how the data should be transformed prior to statistical analysis. This paper reviews aspects of the debate and illustrates, using both simulated and real data, that what has been proposed as the ‘correct’ theoretical approach—log‐ratio analysis—does not always work well. The reasons for this are discussed.     

STATISTICAL ANALYSIS OF CHEMICAL COMPOSITIONAL DATA AND THE COMPARISON OF ANALYSES

Recent statistical work on approaches to analysing compositional data - where variables sum to a constant for each row of a data matrix - may encounter difficulties when applied to data of the kind typically arising in scientific archaeology. The reason is that results obtained may be unsatisfactory from a substantive viewpoint for identifiable technical reasons. This paper explores and illustrates some possible resolutions of the problem. A feature of the approach used is to analyse subsets of the variables on separate scales. A synthesis of the results obtained from separate analyses is essential and the use of multiple correspondence analysis for this purpose is illustrated.     

MODIFIED MAHALANOBIS FILTERS FOR GROUPING POTTERY BY CHEMICAL COMPOSITION*

A statistical procedure for grouping pottery in provenance studies by chemical data is presented, which now is routinely in use in our laboratory. It is based on the Mahalanobis filter method and X² -statistics, and can be used for both establishing groups and assigning single sherds to already known groups, thus replacing principal components analysis or cluster analysis and avoiding their problems in grouping pottery. The new method is able to consider correlations, uncertainties of measurement and constant shifts of the data in case of dilution. In particular, considering dilution effects results in both a better assignment to and separation of reference groups and is also equivalent to the compositional data approach, if log-transformed data are used. Other distortions of data (e.g., mixing of clays) can also be considered.     

MULTIVARIATE MIXTURE OF NORMALS WITH UNKNOWN NUMBER OF COMPONENTS: AN APPLICATION TO CLUSTER NEOLITHIC CERAMICS FROM AEGEAN AND ASIA MINOR USING PORTABLE XRF*

Multivariate techniques and especially cluster analysis have been commonly used in archaeometry. Exploratory and model‐based techniques of clustering have been applied to geochemical (continuous) data of archaeological artefacts for provenance studies. Model‐based clustering techniques such as classification maximum likelihood and mixture maximum likelihood have been used to a lesser extent in this context and, although they seem to be suitable for such data, they either present practical difficulties—such as high dimensionality of the data—or their performance gives no evidence that they are superior to standard methods. In this paper standard statistical methods (hierarchical clustering, principal components analysis) and the recently developed model‐based multivariate mixture of normals with an unknown number of components, are applied and compared. The data set provides chemical compositions of 188 ceramic samples derived from the Aegean islands and surrounding areas.     

MULTIVARIATE ANALYSIS OF COMPOSITIONAL DATA: APPLIED COMPARISONS FAVOUR STANDARD PRINCIPAL COMPONENTS ANALYSIS OVER AITCHISON'S LOGLINEAR CONTRAST METHOD

There has been debate about whether standard principal components analysis is appropriate for the multivariate analysis of compositional data (e.g. oxide composition of glass), Loglinear transformation has been recommended by Aitchison as a prerequisite. This paper argues that previous comparisons of methodological merits have tended to circularity of argument by making assumptions about the form of a good multivariate result. To break the circularity of argument the authors have introduced randomized variables into five data sets. A good result must recognize these randomized variables as noise and place them near the centroid of the principal components scattergram of variable loadings. Standard principal components analysis is found to perform better than loglinear transformation in its ability to recognize the randomized variables. It is concluded that loglinear transformation tends to introduce spurious structure into a table of compositional data. This paper is followed by a comment by M. J. Baxter.     

RQ-MODE PRINCIPAL COMPONENTS ANALYSIS OF CERAMIC COMPOSITIONAL DATA*

RQ-mode principal components analysis (PCA) is a means for calculating variable and object loadings on the same axes, so that elements can be displayed along with data points on a single diagram. The biplots resulting from RQ-mode PCA preserve both Euclidean relations among the objects and variance-covariance structure. When used with data on the chemical composition of archaeological pottery, such biplots facilitate recognizing compositional subgroups and determining the chemical basis of group separation. RQ-mode PCA is illustrated in this paper with neutron activation data on Mesoamerican Plumbate pottery.     

COMPARING GLASS COMPOSITIONAL ANALYSES*

In a recently published study of Romano‐British colourless glass compositions, using inductively coupled plasma spectroscopy, 28 glasses from Colchester sampled in a previous study were resampled. This was done deliberately, with a view to examining the repeatability of results from sampling on different occasions. We report on our results here, developing in the process some simple statistical methodology that could be applied in similar situations. The potential for combining analyses undertaken at different times is discussed and illustrated.     

MATCHING PAST AND PRESENT CERAMIC PRODUCTION IN THE BANDA AREA (GHANA): IMPROVING THE ANALYTICAL PERFORMANCE OF NEUTRON ACTIVATION ANALYSIS IN ARCHAEOLOGY USING MULTIVARIATE ANALYSIS TECHNIQUES*

The transfer of advances in chemometrics into archaeometric research opens up a wide range of new application possibilities in this rapidly developing field. Neutron activation analysis (NAA) of ceramic samples from the Banda Traditional Area (west‐central Ghana) combined with chemometrics allowed us to establish a link between current and ancient systems of ceramics production in the historic settlements of Kuulo Kataa and Makala Kataa. Principal component analysis (PCA) and the soft independent modelling of class analogy (SIMCA) method were applied to the Das Dores Cruz data set in order to unequivocally determine the geographical origin of the diverse archaeological samples. After global autoscaling pretreatment, PCA analysis showed a clear difference between samples from different locations. The classification models obtained by SIMCA showed a classification ability of 100% and a prediction ability of 97.7%, with a mean sensitivity of 84% and a specificity of 100% for the three categories. The application of SIMCA showed that some NAA variables (elements) were more important than others in terms of geographical classification. With the class models that we obtained, we were able to determine the origin of the ancient remains. SIMCA has proved to be a powerful technique for the class modelling of archaeological data.     

THE CHRONOLOGY OF GROUPS OF DIES FOR LARGE ISSUES OF ANCIENT COINS USING MAHALANOBIS DISTANCES*

Discriminant analyses of distances and angles obtained from 25 coins struck by P. Crepusius in 82 BC permitted the correct chronology for five groups of closely-related dies to be obtained by the method of Carter and Frurip. Twenty distances and 15 angles were measured on 10 x projections of the coins which represented five groups of dies separated in time from each other. The use of all or many variables gave poorer results than the use of five to ten variables having a high ‘figure of merit’, defined as the maximum range of mean values for a given variable in the five groups of dies divided by the mean standard deviation of the variable in the five groups. It is recommended that chronologies of ancient coins be determined from Mahalanobis distances by using only variables of relatively high figure of merit.     

CHEMICAL ANALYSES OF GLASS BEADS FOUND IN TWO SARMATIAN BURIALS*

The chemical compositions of 14 glass beads from two Early Sarmatian-period burials were determined. Al, Ca, Fe, Mg, K, Na, and Si were measured by electron probe microbeam analysis, while the Co, Cu, Ga, Mn, Ni, Pb, Rb, Sr, Th, Ti, Y, Zn, and Zr contents were measured using energy dispersive X-ray fluorescence. All the beads can be classed as low-magnesia soda-lime-silica glasses. The blue glass beads examined in this study were coloured with Co and Cu containing minerals. Cluster analysis and principal components analysis suggest that two distinct glass recipes were used to manufacture these beads.     

Model‐based Cluster Analysis of Artefact Compositional Data

Cluster analysis is the most widely used multivariate technique in archaeometry, with the majority of applications being exploratory in nature. Model‐based methods of clustering have their advocates, but have seen little application to archaeometric data. The paper investigates two such methods. They have potential advantages over exploratory techniques, if successful. Mixture maximum‐likelihood worked well using low‐dimensional lead isotope data, but had problems coping with higher‐dimensional ceramic compositional data. For our most challenging example, classification maximum‐likelihood performed comparably with more standard methods, but we find no evidence to suggest that it should supplant these.     

THE EFFICIENT COMPUTATION OF UNBIASED MAHALANOBIS DISTANCES AND THEIR INTERPRETATION IN ARCHAEOMETRY*

This paper argues for cross-validation to reduce bias in estimating Mahalanobis distances of individuals to groups, a particular problem with small sample sizes. Formulae for the efficient computation of cross-validated distances, which avoid excessive matrix inversion, are given. The use of Mahalanobis distances as measures of consistency, or as indications of outlying values, is described. The little-known technique of gamma plotting is outlined and discussed as an aid to interpreting distances in these terms. Both cross-validation and gamma plotting are illustrated in an example on marble composition.     

THE DISCOVERY OF ANOMALOUSLY HIGH SILVER ABUNDANCES IN POTTERY FROM EARLY ROMAN EXCAVATION CONTEXTS IN JERUSALEM*

This is the first study on the differential distribution and concentrations of silver in ceramics recovered from archaeological excavations. The chemical compositions of 1174 pottery vessels from 38 Roman‐period sites in Israel have been determined. Unusually high and variable abundances of silver were discovered in pottery samples of all vessel types and chemical compositions from four distinct archaeological contexts dating to late first century bce to 70 ce Jerusalem. The large majority of the Jerusalem vessels could be distinguished by their silver abundances from all analysed pottery pieces recovered at rural sites outside Jerusalem, even when the pottery types and chemical compositions, except for silver, of pottery found within and outside Jerusalem were indistinguishable. The evidence is suggestive of a human origin for the high and variable silver abundances, and dispersion of the silver by aqueous transport. The differential silver concentrations found in excavated pottery from Jerusalem and other urban and rural sites suggest that attention to the distribution of silver in pottery from excavated contexts may be helpful for evaluating the nature and function of archaeological remains and patterns of urban contamination.     

DETERMINING POTTERY PROVENANCE: APPLICATION OF A NEW HIGH-PRECISION X-RAY FLUORESCENCE METHOD AND COMPARISON WITH INSTRUMENTAL NEUTRON ACTIVATION ANALYSIS*

A recently developed high-precision X-ray fluorescence (XRF) method, applied for the first time to the study of archaeological pottery, determines the abundances of 13 trace and four major elements from one X-ray spectrum acquired over a 1000 second counting interval. For replicate archaeological samples, the short-term and long-term measurement precisions were close to 1% for the ten elements measured with highest precision. These are comparable to the best results achieved on replicates of clay and pottery standards, and obsidian, using instrumental neutron activation analysis (INAA). High-precision XRF analysis, however, does not require a nuclear facility, and is markedly preferable to INAA in terms of the ease of both sample preparation and analytical procedure. Consequently, element abundance data can usually be provided by a single analyst within a few hours after the start of sample preparation. The accuracy of the method, determined by comparison with data of other workers on eight standard reference materials, averaged 2.4% for the ten best-agreeing elements. The effectiveness of the method for determining pottery provenance is demonstrated for a difficult problem, in which high-precision XRF analysis successfully distinguished the products of two nearby pottery manufacturers in Roman Galilee (Shikhin and Nahif) that had not been clearly differentiated by INAA. The greater effectiveness of high-precision XRF than INAA in this provenance study is a result of the different array of elements measured, and the higher precision obtained for certain elements, by XRF. These results suggest that high precision XRF has potential broad applicability for pottery provenance studies.     

MULTIVARIATE ANALYSIS OF THE ENERGY DISPERSIVE X-RAY FLUORESCENCE RESULTS FROM BLUE AND WHITE CHINESE PORCELAINS*

The energy dispersive X-ray fluorescence technique was employed to study non-destructively the surface of 66 samples of Chinese porcelain, of different periods and origins, and determine the contents of 13 chemical elements, namely, Ti, Mn, Fe, Co, Ni, Cu, Zn, Ga, Pb, Rb, Sr, Y and Zr. Principal components analysis was performed on these 13 variables, and scatter plots, incorporating the first, second and third principal components, used to study the clustering behaviour of the data. Based on these results, discriminant analysis was then performed on the data, and discriminant functions established for attributing the period and origin of the porcelains.     

COMPOSITIONAL VARIABILITY IN COLOURLESS ROMAN VESSEL GLASS

A statistical re-analysis is undertaken of 118 inductively coupled plasma spectrometry analyses of Romano-British glass specimens found in excavations at Colchester. There are four vessel types present, some of which are associated with chronologically distinct periods. Previous research has suggested little difference in the mean composition of different types. The present paper shows that there are interesting differences in the variation of compositions within types, with some showing much greater compositional stability then others. Some possible models to explain this phenomenon are discussed.     

A STUDY OF CHINESE PORCELAIN RAW MATERIALS FOR DING,XING, GONGXIAN AND DEHUA WARES*

The raw material used largely determines the type and quality of porcelain produced. Twenty-three raw materials used for making Ding, Xing, Gongxian and Dehua porcelain bodies were studied using principal component analysis. Results show that for Dehua wares, only one raw material was used. For Ding wares, although there were many possible raw materials, the use of one alone is unlikely. Lingshan clay was the main raw material but it has to be mixed with other raw materials: Pinjiawa clay, quartz, feldspar and dolomite. The Xing pieces can be divided into three groups and Gongxian wares into two groups, which are discussed in detail.     

CHARACTERIZATION AND PROVENANCE OF LATE ANTIQUE WINDOW GLASS FROM THE PETRA CHURCH IN JORDAN*

Fifth‐ to seventh‐century window glass fragments from the Petra Church in Jordan were analysed by EPMA and spectrophotometry to characterize their optical properties and chemical composition. The objective of this study was to determine the provenance of the raw glass and the secondary production procedures of the window‐panes. Judging from the material evidence, both the crown window‐panes and possibly the rectangular samples were produced through glass‐blowing techniques. The chemical data show that the assemblage forms a homogeneous group of soda–lime–silica glass of the Levantine I type. The green glass, however, has higher silica and lower soda contents than the aqua‐blue fragments. The composition of one sample suggested the recycling of Roman glass. Our results confirm the trade of glass between the Levantine coast and Petra during Late Antiquity. No colouring agents other than iron were detected. Spectrophotometry confirmed the presence of iron and showed that the window fragments absorbed light relatively equally across the visible part of the spectrum. The windows thus seem to have provided an almost colourless illumination for the sacred interior.     

PROVENANCE STUDIES OF KOREAN CELADONS OF THE KORYǑ PERIOD BY NEUTRON ACTIVATION ANALYSIS*

Neutron activation analyses of the body fabric of celadons from the main production sites of the Koryǒ period have shown differences in composition between kilns. Comparison of over 50 celadon objects in the collections of the British Museum with this data base from the production sites has permitted the assignment of over 40 of the pieces to their kiln of origin The majority show the trace element pattern of the Sadangri kilns, a smaller proportion are assigned to Yuchǒnri, while others are assigned to the kilns at Chinsanri (underglaze iron) and Kyǒngsǒ-dong (unglazed). A representative group of Chinese Yue wares arc clearly different from Koryǒ celadons in trace element composition.     

PHYSICOCHEMICAL COMPOSITIONAL ANALYSIS OF CERAMICS: A CASE STUDY IN KENTING,TAIWAN*

The composition of ceramics does not just reflect the component of some specific, unprocessed, geological, raw material source, but also certain forms of human behaviour involved in its manufacture. The purpose of this research project is to apply the acid‐extraction chemical method, complemented by a thin‐section petrographic study, to the compositional analyses of certain local ceramic collections (mainly from several sites in the southern Taiwan area). The results present the raw materials that the ceramic manufacturers of the two cultural traditions (O‐laun‐pi Phase II and Phase III–IV), which overlapped temporally, used. These materials came from the same sources, but the ceramics were manufactured in different ways. Particularly, the people of O‐laun‐pi Phase III–IV also procured certain materials from either local sources or from somewhere in eastern Taiwan to make their pots. The results also indicate that there might have been a variation in terms of their manufacture among sites of the same cultural tradition.