A Comprehensive Workflow for Compositional Data Analysis in Archaeometry, with Code in R

Abstract

Compositional data, which have relative rather than absolute meaning, are common in quantitative archaeological research. Such multivariate data are usually expressed as proportions, summing to 1, or equivalently as percentages. We present a comprehensive and defensible workflow for processing compositional data in archaeometry, using both the original compositional values and their transformation to logratios. The most useful logratio transformations are illustrated and how they affect the interpretation of the final results in the context of both unsupervised and supervised learning. The workflow is illustrated on compositional data from bronze ritual vessels to provide compositional fingerprints for the Shang and Zhou periods of the Chinese Bronze Age. Predictions, with caveats, of the fabrication age of the vessels are made from the compositional data -- in effect, compositional rather than typological seriation of the bronzes. In the Supplementary Material, we further explore the effect of zeros in the dataset and compare logaratio analyses with the chiPower approach, where we replace any value in the original data determined as being below the detection limit of the instruments for the element, with zeros. The data and R code for reproducing all the analyses are provided both in the Supplementary Material and online.