Traditionally, areal interpolation has referred to techniques for transferring attribute values from one partitioning of space to a different partition of space but this is only one of several situations that create the need for estimating unknown data values for areal units. This paper presents a categorization of four areal interpolation problems that includes the``missing'' data problem, the traditional`a lternative geography'' problem, the overlay of a choropelth and an area-class data layer, and the overlay of two choropleth data layers and demonstrates the relationship between the last three problems and general spatial interaction modelling. The``alternative geography'' and overlay of choropleth and area-class data layers mirrors a singly constrained spatial interaction model while the overlay of two choropleth layers is analogous to a doubly constrained interaction model. Iterative proportional fitting techniques with and without ancillary data are developed to solve these three classes of problems.
Data from police accident reports involving pedestrians less than 20 years of age in Hartford, Conn, during 1988 through 1990 were abstracted and entered into a geographic information system. Two high-frequency collision areas were identified and compared. There were 374 child pedestrians involved in collisions (a rate of 28 per 10,000). Two high-occurrence areas accounted for 30% of collisions. Collisions in one of these areas were more likely to involve younger children (8.1 vs 10.2 years of age) and to occur in the late afternoon, and occurred closer to the child's residence, than collisions in the other area. The geographic information system is a useful tool in the study of child pedestrian collisions.
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 30Â30 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.
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