A Measure for Linguistic Coherence in Spatial Language Variation (2023)

Abstract: Based on historical dialect data we introduce a local measure of linguistic coherence in spatial language variation aiming at the identification of regions which are particularly sensitive to language variation and change. Besides, we use a measure of global coherence for the automated detection of linguistic items (e.g., sounds or morphemes) with higher or lesser language variation. The paper describes both the data and the method and provides analyses examples.

## introduction dialectometric work typically focuses on the cooccurrence of the distribution of variants in different sites (see @xcite . from these cooccurrences, reasonably coherent regions of linguistic similarity can be identified. these regions then provide, for example, clues to the aggregated structuring of higher-level linguistic areas (e.g., within a nation). alternatively, they show to what extent individual sites of a given corpus are integrated into the region under discussion in terms of their similarity or distance to other sites (e.g., @xcite . such analyses, which at the same time constitute the classical field of dialectometry, thus benefit from the aggregation of all linguistic phenomena of a given corpus. however, if the interest is not in the overall structuring of a region, but in the distribution 1 the study builds on r programming (r core team 2021), using the packages spatstat @xcite and rvision @xcite ) mainly. in order to perform our coherence measure more efficiently it has been implemented patterns of individual variants, non-aggregating procedures must be applied. for a single phenomenon, spots of variation may be identified in most cases by visual inspection (see ormeling 2010 for a critical account). however, in order to capture this variation quantitatively, more recent studies have considered a number of solutions, for example based on resampling techniques (e.g., @xcite , kernel density estimation (e.g., @xcite ) or the concept of entropy (e.g., @xcite . this paper presents a diagnostic measure for the detection of coherence or heterogeneity in spatial language variation aimed at identifying those regions that are particularly prone to variation or particularly sensitive to language change. we perform an approach based on nearest neighbor comparison and exemplify the used measure. 1 in the remainder, we provide information on the data and introduce both a local and a global measure of linguistic coherence and diversity. in what follows we present example analyses based on historical dialect data from southwestern germany and discuss the introduced procedure. ## data the study makes use of a data set collected by the german linguist friedrich maurer during the year 1941 in the upper german dialect region within the boundaries of the national territory at the time. the survey was based on a questionnaire with 113 into a r-package (lingugeo). the current version of the lingugeo package can be found at: https://github.com/schoenberga/lin gugeo ## discussion the coh measure, as well as the div measure respectively, reveals spots of local variation, which indicate horizontal (i.e. geographical) or vertical (i.e. social, pragmatic) heterogeneity. @xcite points out, these spots of increased language variation might be possible starting points of language change. in this regard, @xcite considers the model in figure 10 . starting from a situation where variant a is the only available realization of a particular linguistic variable, at a certain time variant b becomes an alternative. this is the situation illustrated by figure 10 for both scenarios (above and below). however, the coh measure goes beyond local variation by modeling the closest relative area of influence of that alternative. figure 10 : possible stages in the formation of language variation and/or language change on the example of two variants a and b; above: scenario 1 (language change); below: scenario 2 (temporary language variation). obviously, analysis using coh (like figure 7 ) does not specify how long the variative phase will persist. furthermore, it could be that variant b disappears again (figure 10 below), and it could just as well be that variant b prevails (figure 10 above) while a disappears. consequently, coh does not allow for a clear prediction of the process of language change, but it does illustrate that, if language change does occur, it is likely to occur at the spots with high div (= 1-coh). against this background, the relevance of the coh measure is to indicate spots of particular linguistic dynamics. identifying these spots enables both prediction and explanation of ongoing and/or completed language change. on the other hand, with cohg* → 1 it can also be shown directly whether a language region has proto-typical variants, which can then be easily identified in the data distribution. furthermore, applying the coherence measure to a collection of multiple linguistic phenomena, as shown in figure 11 , leads to a new perspective on the structuring of linguistic space. instead of highlighting the clusters of linguistic similarity, rather the zones of particular linguistic dynamics are identified. from looking at the coherence values, even without mapping, a first impression is given whether the lemmas in question show a strong spatial clustering or not. this is useful for huge datasets with lots of linguistic variables. at the same time, it becomes evident that the measure is sensitive for outliers (i.e., isolated sites), which are evident by individual points. among the existing dialectometric literature, our coherence measure is comparable to the technique introduced by @xcite using kernel density estimation (kde). our measure explicitly considers geographical neighborhood, but, in contrast to the kde approach, it is more focused on local variation. instead of calculating an adequate bandwith, we choose a certain number of neighbors in order to test for the integration of an individual site into the linguistic area. in this respect, the underlying concept is that linguistic space develops in small-scale communication zones, not in large-scale continua. from a technical perspective, a difference to the kde approach is that we do not rely on the definition of individual variant-occurrence maps as an intermediate step of analysis, but process the variation given in the data set directly. notwithstanding this, there are other studies that work with the notion of coherence or focus on transitional spaces. @xcite , for example, introduce a local measure of incoherence, which, however, focuses on linguistic rather than geographic distances. our measure thus provides an alternative view of the relationship between spatial and linguistic proximity based on individual maps and not on aggregated data. @xcite , nonetheless, illustrates the importance of skewness as a global statistical measure of the linguistic integration of individual sites into the linguistic area and the assessment of transitional zones. similar to @xcite , the basis of linguistic measurement is in goebl's approach not the individual map, but a set of aggregated data. unlike goebl (2010), we focus exclusively on concrete geographic neighbors of an individual site with both the local and global measures, which makes our approach, in the case of the local measure, independent from the overall statistical distribution, which is in dialectometric studies typically shaped by linguistic distance or similarity. ## conclusion this paper introduces a nearest neighbor approach as a diagnostic tool in order to find regions which are more sensitive to language variation and change than others. for this purpose, a local measure of coherence is used (coh). in addition, a global coherence measure (cohg) as well as a corrected global measure (cohg*) was used to quantitatively assess the spatial coherence of more comprehensive data distributions (e.g., on maps) and to automatically identify linguistic items with higher/lesser language variation. two case studies illustrate the application of the method and the informative quality of the measures.