Because Muncie's Densities Are Not Manhattan's: Using Geographical Weighting in the Expectation–Maximization Algorithm for Areal Interpolation

Abstract

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), 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 (LULC) ancillary data to population counts from a nationwide sample of 1980 U.S. 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.区域插值可通过变换一组源区感兴趣变量的数据得到目标区域同一变量的分布。采用与感兴趣变量空间分布密切相关的辅助控制区来引导插值是最常用的一种方法，通常涉及采用源区域数据估计每个控制区内感兴趣变量的密度值。本文引入了地理加权最大期望算法（GWEM）来进行密度估计，综合了过去常用的最大期望算法（EM）和地理加权回归（GWR）两种技术特征。EM算法为数据分布约束的集成提供框架，地理加权则允许估计估计控制区密度比例的空间变异。以美国1980年全国普查区域的土地利用/土地覆被数据种群统计为例，对该方法的精度进行了评估。结果显示，GWEM比多种现有方法准确性更高。采用目标密度加权法（TDW）以1970年束密度来进行插值在许多情况下优于GWEM，融合GWEM‐TDW两种方法可大幅改善估计结果。