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.     

DETECTING MULTIVARIATE OUTLIERS IN ARTEFACT COMPOSITIONAL DATA*

Multivariate statistical analysis of artefact compositional data, usually undertaken to investigate structure in the data, often incidentally reveals the presence of multivariate outliers. Much statistical methodology dealing with the detection of such outliers is not well suited to archaeometric data that, in the event, consist of two or more groups. The paper provides examples to illustrate the importance of detecting and dealing with outliers, and critically examines a range of different approaches to outlier detection. The examples show that cluster analysis, the technique most widely used for this purpose, can fail to reveal outliers clearly identified by other methods.     

CHEMISTRY VERSUS DATA DISPERSION: IS THERE A BETTER WAY TO ASSESS AND INTERPRET ARCHAEOMETRIC DATA?

Given the common use of chemical concentration data to define ceramic groups that aid in the exploration of ancient technology, trade and provenance, it is important to reflect on how we collectively establish and define both chemical groups and outliers. In this paper, we argue that commonly used data analysis procedures, such as principal component analysis and centred log‐ratio principal component analysis favoured in the examination of ceramic chemical data, although rapid and easy, may overlook existing chemical groups and outliers, especially when the ratio of non‐diagnostic to diagnostic elements is high. To evaluate whether geochemistry is more important than data dispersion in data assessment, we re‐examine chemical concentration data from previously published ceramic, clay and daub samples from the lower Ohio River Valley. We begin by briefly discussing steps we took to ensure that the data set reflects geochemical differences, rather than analytical or data transfer errors. Next, we use bivariate plots, as well as PCA and CLR–PCA, to examine different versions of our altered data, using varying numbers of element combinations. We propose that the careful examination of bivariate plots is critical in establishing the elements that should be included in PCA and other multivariate analyses.     

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.