Abstract

In spatial statistics, homogeneity of a point pattern is formally defined as
constant first-order intensity. This study introduces a new definition of
homogeneity for spatial linear networks, based on two complementary aspects.
One is locational and describes where line segments are concentrated. The other
is directional and describes how those segments are oriented. We extend
intensity-based concepts for homogeneity testing to cover both the number of
line segments per spatial unit and their mean directional orientation.
The network is partitioned into a grid of quadrats. A modified Chi-Square test on
segment counts per unit area assesses the locational component, while a
non-parametric bootstrap test on differences in circular means across quadrats
assesses the directional component. A conclusion drawn from a single fixed grid
may be an artefact of grid placement, so a sensitivity analysis with multiple
grid resolutions and controlled grid jittering is conducted to evaluate spatial
robustness. A simulation study calibrates the size and power of both tests.
The methods are illustrated on road networks.