Because Muncie's Densities Are Not Manhattan's: Using Geographical Weighting in the EM Algorithm for Areal Interpolation.

Areal interpolation transforms data for a variable of interest from a set of source zones to estimate the same variable's distribution over a set of target zones. One common practice has been to guide interpolation by using ancillary control zones that are related to the variable of interest's spatial distribution. This guidance typically involves using source zone data to estimate the density of the variable of interest within each control zone. This article introduces a novel approach to density estimation, the geographically weighted expectation-maximization (GWEM) algorithm, which combines features of two previously used techniques, the expectation-maximization (EM) algorithm and geographically weighted regression. The EM algorithm provides a framework for incorporating proper constraints on data distributions, and using geographical weighting allows estimated control-zone density ratios to vary spatially. We assess the accuracy of GWEM by applying it with land-use/land-cover ancillary data to population counts from a nationwide sample of 1980 United States census tract pairs. We find that GWEM generally is more accurate in this setting than several previously studied methods. Because target-density weighting (TDW)-using 1970 tract densities to guide interpolation-outperforms GWEM in many cases, we also consider two GWEM-TDW hybrid approaches, and find them to improve estimates substantially.