Crouching TIGER, hidden structure: Exploring the nature of linguistic data using TIGER values

In recent years, techniques such as Bayesian inference of phylogeny have become a standard part of the quantitative linguistic toolkit. While these tools successfully model the tree-like component of a linguistic dataset, real-world datasets generally include a combination of tree-like and nontree-like signals. Alongside developing techniques for modeling nontree-like data, an important requirement for future quantitative work is to build a principled understanding of this structural complexity of linguistic datasets. Some techniques exist for exploring the general structure of a linguistic dataset, such as NeighborNets, δ scores, and Q-residuals; however, these methods are not without limitations or drawbacks. In general, the question of what kinds of historical structure a linguistic dataset can contain and how these might be detected or measured remains critically underexplored from an objective, quantitative perspective. In this article, we propose TIGER values, a metric that estimates the internal consistency of a genetic dataset, as an additional metric for assessing how tree-like a linguistic dataset is. We use TIGER values to explore simulated language data ranging from very tree-like to completely unstructured, and also use them to analyze a cognate-coded basic vocabulary dataset of Uralic languages. As a point of comparison for the TIGER values, we also explore the same data using δ scores, Q-residuals, and NeighborNets. Our results suggest that TIGER values are capable of both ranking tree-like datasets according to their degree of treelikeness, as well as distinguishing datasets with tree-like structure from datasets with a nontree-like structure. Consequently, we argue that TIGER values serve as a useful metric for measuring the historical heterogeneity of datasets. Our results also highlight the complexities in measuring treelikeness from linguistic data, and how the metrics approach this question from different perspectives.