How do you measure distance in spatial models? An example using open-space valuation

Spatial distance is a critical component of theories across the social, natural, and information sciences, but too often the methods and metrics used to describe spatial distance are implicit or underspecified. How distance is measured may influence model results in unanticipated ways. We examined the differences among distances calculated in three ways: Euclidean distances, vector-based road-network distances, and raster-based cost-weighted distances. We applied these different measures to the case of the economic value of open space, which is frequently derived using hedonic pricing (HP) models. In HP models, distance to open space is used to quantify access for residential properties. Under the assumption that vector-based road distances better match actual travel distance between homes and open spaces, we compared these distances with Euclidean and raster-based cost-weighted distances, finding that the distance values themselves differed significantly. Open-space values estimated using these distances in hedonic models differed greatly and values for Euclidean and cost-weighted distances to open space were much lower than those for road-network distances. We also highlight computational issues that can lead to counterintuitive effects in distance calculations. We recommend the use of road-network distances in valuing open space using HP models and caution against the use of Euclidean and cost-weighted distances unless there are compelling theoretical reasons to do so.