Statistical processing of compositional data. The case of ceramic samples from the archaeological site of Xalasco, Tlaxcala, Mexico

This paper focuses on the implementation of a methodology for identifying chemical groups, the search for data patterns and the determination of outliers in a collection of ceramic samples after compositional analysis. In order to obtain the chemical composition, pottery samples from the archaeological site of Xalasco were analyzed by means of a portable XRF technique. The discrimination of groups was based on the methodology proposed by Aitchison in 1986 for the analysis of compositional data. First, we applied a stepwise method for the selection of variables with the use of biplots. The detection of outliers was managed by using the method known as FAST-MCD. In a second stage, the detected groups and their components were analyzed in a supervised manner using the PLS-DA method. Once the groups were validated, we obtained the balances and the CoDa-dendrogram with the isometric transformation to appreciate the differences in their chemical composition. The results showed a high degree of accuracy in the discrimination between groups, which can be interpreted as different manufacturing processes. The chemical differences among the samples can be understood in terms of the cultural influences reflected in the preparation of the ceramics pastes through time, the availability of raw materials and the organization of pottery production.