  Quantifying the degree of spatial dependence for linguistic variables is a
key task for analyzing dialectal variation. However, existing approaches have
important drawbacks. First, they are based on parametric models of dependence,
which limits their power in cases where the underlying parametric assumptions
are violated. Second, they are not applicable to all types of linguistic data:
some approaches apply only to frequencies, others to boolean indicators of
whether a linguistic variable is present. We present a new method for measuring
geographical language variation, which solves both of these problems. Our
approach builds on Reproducing Kernel Hilbert space (RKHS) representations for
nonparametric statistics, and takes the form of a test statistic that is
computed from pairs of individual geotagged observations without aggregation
into predefined geographical bins. We compare this test with prior work using
synthetic data as well as a diverse set of real datasets: a corpus of Dutch
tweets, a Dutch syntactic atlas, and a dataset of letters to the editor in
North American newspapers. Our proposed test is shown to support robust
inferences across a broad range of scenarios and types of data.
