A gradient perspective on modeling interdialectal transitions

Finding the boundaries of linguistic variants and studying transitions between variants are key interests in classical linguistic geography. However, the definition of boundaries in areal linguistics is vague, and a quantitative characterization of transitions at the interface between dialectal variants is missing. We conceptualize these transitions as gradients, aiming to quantitatively account for the transition patterns which are traditionally only implicitly inferred from visualizations. Fitting of logistic functions in different spatial scopes (profiles as well as surfaces) is proposed as an approach to model the transition at the interface between the dominant usage areas of dialectal variants. Logistic functions can accommodate the breadth of boundary concepts, ranging from sharp isoglosses to transitions with different gradualities. The parameters of the fitted logistic models as well as supplementary measures then allow for the quantitative characterization and comparison of transitions across variables. To demonstrate the proposed methodology, we use Swiss German syntactic data on dialectal variables with a single transition zone.