A homogeneity test for spatial line patterns

Abstract

Spatial linear networks exhibit a variety of patterns. Like spatial point patterns, they can be homogeneous or heterogeneous. Although there exist a wide variety of tests for the homogeneity of point patterns, no statistical tests currently exist to quantify the homogeneity of spatial linear networks. This research provides two statistical methodologies to test for homogeneity in spatial linear networks, using point pattern methods. The first methodology approximates spatial linear networks by point patterns, obtained by taking the midpoint of each line. The second methodology projects each line of a spatial linear network into a space defined by the distance from the origin and orientation of the line, thus representing lines as three dimensional points. In both methodologies, existing tests for homogeneity of point patterns are then applied to the point pattern representations of the linear networks. The methodologies are applied to test for homogeneity of formal and informal road networks in South Africa. This research is in line with UN Sustainable Development Goals 3, 9 and 10.