Using geographically weighted regression to solve the areal interpolation problem

Abstract

Areal interpolation is used to transfer attribute information from the initial set of source units with known values to the target units with unknown values before subsequent spatial analysis can occur. The areal units with unknown attribute information can be either at a finer scale or misaligned with respect to the source data layer. This article presents and describes a geographically weighted regression (GWR) method for solving areal interpolation problems for nested areal units and misaligned areal units. Population data, selected as the attribute information, are interpolated from census tracts to block groups (a finer scale) and pseudo-tracts (misaligned from tracts but at the same approximate scale). Root mean square error, adjusted root mean square error, and mean absolute error are calculated to evaluate the performance of the interpolation methods. The land cover data derived from Landsat Thematic Mapper Satellite Imagery with a 30×30 m spatial resolution are applied to as the ancillary data to describe the underlying distribution of population. To evaluate the utility of GWR as an areal interpolation method, the simple areal weighting method, a dasymetric method, and different ordinary least squares regression methods are used in this article as comparison methods. Results suggest that GWR is a better interpolator for the misaligned data problem than for the finer scale data problem. The latter is a result of issues associated with the scaling step to ensure the pycnophylatic property required in areal interpolation.