Areal Interpolation and Dasymetric Modeling

Abstract

Frequently in spatial analysis, data are collected using one measurement system while analyses are conducted using a different measurement system. In these two systems, data regarding individual objects often are aggregated into areal units because (1) data concerning personal information are restricted by privacy and confidentiality regulations; (2) aggregated data require less storage and have a computational advantage over data in disaggregated form; and (3) geographers traditionally study data at a regional level (Openshaw and Taylor 1981). Areal interpolation refers to the procedures for transferring attribute data from one partitioning of geographic space (a set of source units) to another (a set of target units) (Goodchild and Lam 1980). Areal interpolation is needed to estimate attribute information for different geographic partitionings at the same scale (an alternative geography problem), for spatial partitionings at a finer resolution (a small area problem), for reconciling boundary changes in spatial units over time (a temporal mismatch problem), or for incomplete coverage (a missing data problem). Geographic information systems (GISs) have increased the need to change measurement systems because a GIS integrates source data from different systems into a common database, and GIS analyses also create new data layers with different spatial units from source layers, such as in an overlay operation. As areal interpolation methods for solving these aforementioned estimation problems developed, several critical components to the solution methodology emerged. First, different statistical methods were adapted for areal interpolation, ranging from simple proportions to more sophisticated procedures such as expectation maximization (EM) algorithms and various forms of regression analysis. Second, many of these methods began to incorporate ancillary data that act as control units on the geographic distribution of the attributes being estimated. In doing so, source data are used to estimate a density surface for control units, such as in dasymetric mapping, followed by this density surface being aggregated by target zones to create final estimates. Consequently, researchers have focused not only on better analytical methods but also on the incorporation of better data that are available for source zones and control zones. The purpose of this special issue is to examine the status of these developments in areal interpolation. The first three articles involve expanding, improving, and redeveloping a popular areal interpolation approach, the EM algorithm. Schroeder and Van Riper (2013) present a geographically weighted expectation-maximization (GWEM) dasymetric interpolation algorithm. Their approach expands existing EM algorithms by introducing the benefits of geographically weighted regression (GWR), which allows the densities of different control units to have a different ratio among all source units. The GWEM algorithm incorporates the best of both EM and GWR, while overcoming the limitations of each individual technique. Schroeder and Van Riper use their GWEM algorithm to interpolate historical 1980 census data backward to 1970 data with land use and land cover data as control units. It achieves better accuracy than that Geographical Analysis (2013) 45, 213–215