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Quantifying the degree of spatial dependence for linguistic variables is akey task for analyzing dialectal variation. However, existing approaches haveimportant drawbacks. First, they are based on parametric models of dependence,which limits their power in cases where the underlying parametric assumptionsare violated. Second, they are not applicable to all types of linguistic data:some approaches apply only to frequencies, others to boolean indicators ofwhether a linguistic variable is present. We present a new method for measuringgeographical language variation, which solves both of these problems. Ourapproach builds on Reproducing Kernel Hilbert space (RKHS) representations fornonparametric statistics, and takes the form of a test statistic that iscomputed from pairs of individual geotagged observations without aggregationinto predefined geographical bins. We compare this test with prior work usingsynthetic data as well as a diverse set of real datasets: a corpus of Dutchtweets, a Dutch syntactic atlas, and a dataset of letters to the editor inNorth American newspapers. Our proposed test is shown to support robustinferences across a broad range of scenarios and types of data.

A Kernel Independence Test for Geographical Language Variation