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 (see Supplementary Material S0 for an extended summary in Spanish).

中文翻译：

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超越性能基线：工艺生产研究中成分可变性的 Beta 回归模型


考古文物的化学分析通常用于出处研究，以及评估过去工匠是否以特定性能特征为目标。传统上，这些问题的答案是通过确定成分平均值并研究它们与候选原材料来源的地球化学特征或所研究材料的相应物理或化学性质的相关性来寻求的。无论多么有用，这种方法都只能利用隐藏在考古文物化学成分中的部分潜在信息。我们认为，在考古组合内部和之间观察到的不同程度的成分分散，特别是它们作为行为意义因素（例如物品的大小、功能或恢复位置）的变化，本身就是信息来源。为了同时获得对这两种类型的可变性（平均值和离散度）的概率见解，我们为考古科学引入了可变离散 β 回归模型。在此过程中，我们展示了采用 beta 分布如何为以前的解决方案提供一种显着改进的替代方案，以对场内成分数据进行建模 - 即那些涉及对数转换数据的简单线性回归的解决方案。这些方法通常会导致数值上不可能的预测，而 beta 回归将模型预测限制在成分上限和下限之间，解释了成分数据固有的不一致方差，并明确允许将成分离散度建模为协变量的函数。 最后，我们扩展了该工具集，展示了在框架内使用分层模型规范如何同时考虑本地变化和更广泛共享的材料加工和采购实践，并缓解与采样不确定性有关的问题。我们基于包含 243 个元素分析的数据集，通过对哥伦比亚东部高地 Muisca 黄金采购实践（公元 600-1600 年）的研究来证明所提出的方法。结果使我们能够论证从各种遥远来源进口的新鲜地质黄金的区域内移动。我们认为，这些移动可能是由于人们聚集到同一地点进行庆祝活动而贡献的黄金造成的。对成分数据进行建模的方法很容易适用于考古科学的其他子学科，例如陶瓷和玻璃的成分研究，或在同位素研究中对饮食的可变性进行建模（西班牙语的扩展摘要见补充材料 S0）。