Mapping distributions in non-homogeneous space with distance-based methods[Cartographie des distributions dans un espace non homogène à l'aide de méthodes basées sur la distance]

Distance-based methods (DBMs) are frequently used to analyze spatial structures in economics. Results provided by DBMs are particularly effective for the precise detection of spatial concentration, dispersion or absence of significant patterns at any scale. The utility of plotting the results of DBMs in homogeneous space has already been shown. However, no consideration has been given to mapping results in non-homogeneous space. This paper aims to fill this gap. We provide a technique to map local values when using a relative DBM. We illustrate its advantages at first on a theoretical case and then on a real case drawing on contagious disease data on trees in a Parisian park. Data and R code are given for reproducible research. In both cases, we show that local plotting can enable a more accurate spatial characterization of the underlying patterns. To give an example, our empirical results on infested maple trees support evidence of the existence of a contagion disease because they appear to be located in areas where maples are relatively spatially concentrated.