Multiscalar analysis and map generalisation of discrete social phenomena: Statistical problems and political consequences

Abstract

Despite the great number of statistical methods which has been developed in the last decades for the generalisation and interpolation of statistical surfaces, many theoretical and methodological problems remain for the application of those methods to the analysis of the spatial distributions of social phenomena. Indeed, maps of social indexes are derived from a spatial aggregation of discrete events or objects and the spatial continuity is not an inherent property of those distributions. A phenomenon like the population density or the rate of population variation can not be defined directly by an objective measure in any location as it is the case for physical phenomena (temperature, altitude). Accordingly, the usual methods of spatial interpolation based on sampling theory and inferential statistics (triangulation, kriging, {\ldots}) can not be applied for the analysis of those distributions of discrete phenomena and other solutions are needed for the estimation of continuous surfaces of the distribution.

The Hypercarte Project, a research network established in 1996, has proposed a general solution to this problem. This solution is based on the concept of multiscalar spatial neighbourhood, with a particular insight to the case of gaussian neighbourhood which presents interesting theoretical and empirical properties for the analysis of the distribution of social and economic distributions. In a first part, the paper presents a detailed description of the mathematical basis of this method on a theoretical example. In a second part, the political consequences of the method are analysed through a classical problem of territorial planning.