Beyond baselines of performance: Beta regression models of compositional variability in craft production studies

Abstract

Chemical analyses of archaeological artefacts are often used for provenance studies and for assessing whether specific performance characteristics were targeted by craftspeople in the past. Traditionally, the answers to these questions were sought by identifying compositional averages and by studying their correlations with either the geochemical signatures of candidate raw material sources or the corresponding physical or chemical properties of the studied materials. However useful, this approach only exploits part of the potential information locked inside the chemical compositions of archaeological artefacts. We argue that different levels of compositional dispersion observed within and across archaeological assemblages, and in particular changes in them as a function of behaviourally meaningful factors (such as the size, function, or recovery location of the objects), are sources of information in themselves. To gain probabilistic insights into both types of variability (averages and dispersions) simultaneously, we introduce variable dispersion beta regression models for the archaeological sciences. In doing so, we show how adopting the beta distribution provides a significantly improved alternative to previous solutions to modelling compositional data within the field — namely, those involving simple linear regression on log-transformed data. These approaches often result in numerically impossible predictions, whilst beta regression restricts the model predictions between the upper and lower compositional bounds, accounts for the inherently inconsistent variances of compositional data, and explicitly permits the modelling of compositional dispersions as a function of covariates. Finally, we expand upon this toolset by showing how using a hierarchical model specification within the framework accounts for both local variation and more widely shared practices of material processing and procurement concurrently, and alleviates issues to do with sampling uncertainty. We demonstrate the proposed approach with a study of Muisca gold procurement practices (AD 600-1600) in the Eastern Highlands of Colombia, based on a dataset of 243 elemental analyses. The results allow us to argue for intra-regional movements of fresh geological gold imported from a variety of distant sources. We suggest these movements could result from contributions of gold by people converging into the same location for festivities. The approaches taken to modelling compositional data are readily applicable to other sub-disciplines of the archaeological sciences, such as compositional studies of ceramics and glass, or modelling the variability of diets in isotopic studies.