A Quantile Regression Approach to Areal Interpolation

Abstract

Areal interpolation has been developed to provide attribute estimates whenever data compilation or an analysis requires a change in the measurement support. Over time numerous approaches have been proposed to solve the problem of areal interpolation. Quantile regression is used in this study as the basis of the areal interpolator because it provides estimates conditioned on local parameters rather than global ones. An empirical case study is provided using a data set in northern New England. Land cover data, provided by the National Oceanic Atmospheric Administration, derived from remotely sensed images for 2001 captured by the LANDSAT Thematic Mapper at a resolution of 30 × 30 meters, are used for the ancillary variables for the regression model. The utility of quantile regression as an areal interpolation method is evaluated against simple averages, areal weighting, dasymetric interpolation, and ordinary least squares and spatial regression methods. For the empirical data set used in the study, results show that quantile regression was a better interpolator for the given data set but that binary dasymetric interpolation was a close second. These results were only for one data set and further evaluation is necessary before more general conclusions can be made. Key Words: areal interpolation, dasymetric mapping, linear programming, quantile regression.La interpolación areal ha sido desarrollada para proveer estimativos de atribución cuandoquiera que la compilación de datos o un análisis requiera un cambio en el apoyo de la medición. Con el tiempo se han propuesto numerosos enfoques para resolver el problema de la interpolación areal. La regresión de cuantiles se utiliza en este estudio como la base de la interpolación areal porque esta proporciona estimativos más condicionados en parámetros locales que en los globales. Se presenta un estudio empírico de caso en el que se utilizó un conjunto de datos referidos a la parte norte de Nueva Inglaterra. Se usaron datos de cobertura del suelo suministrados por la Administración Nacional Oceánica Atmosférica -que habían sido derivados en 2001 de imágenes de percepción remota captadas por el Mapeador Temático LANDSAT a una resolución de 30 × 30 en metros -para las variables auxiliares del modelo de regresión. La utilidad de la regresión de cuantiles como método de interpolación areal es evaluada frente a promedios simples, peso porárea, interpolación dasimétrica, mínimos cuadrados ordinarios y métodos de regresión espacial. Para el conjunto de datos empíricos usados en el estudio, los resultados muestran que la regresión de cuantiles fue un mejor interpolador para el conjunto de datos dado, aunque la interpolación binaria dasimétrica estuvo muy cerca en el segundo lugar. Estos resultados se refieren a un solo conjunto de datos, por lo que se hace necesaria una evaluación adicional antes de que se puedan formular conclusiones más generales. Palabras clave: interpolación areal, mapeo dasimétrico, programación linear, regresión de cuantiles.

Incorporating spatial non-stationarity to improve dasymetric mapping of population

“…However, these studies neglect the rather arbitrary nature of administrative boundaries, which are unlikely to delineate areas with homogeneous population distribution characteristics. Therefore, local regression approaches that estimate separate coefficients for each population record have been tested through (i) quantile regression (Cromley, Hanink, & Bentley, 2012) and (ii) geographically weighted regression (Dong et al, 2010;Lin, Cromley, & Zhang, 2011;Lo, 2008). While the application of these techniques showed an improvement upon the global regression approach, it still did not seem to solve the classic problem at the population distribution's extremes though.…”

A local polycategorical approach to areal interpolation

“…They also pointed out that choices of bandwidths and scales of target zones have a significant impact on the performances of GWR-based AI models, while the locations of estimation points did not matter as much as the former two factors. Cromley et al (2012) have also used quantile regression (Koenker & Bassett, 1978) as the basis for estimating the density surface for ancillary classes. By associating every observation (source zone) with a quantile level, density values for each ancillary class within the observation can be estimated.…”

“…Local models, in which the relationship between an attribute variable and ancillary information is estimated using a selected subset of observations from the full set, are now fairly common in AI procedures as they address the heterogeneity problem with respect to any relationship. By close scrutiny of two statistical interpolators that emphasize local variation, a geographically weighted regression (GWR)-based (Lin, Cromley, & Zhang, 2011) and a quantile regression (QR)-based interpolator (Cromley, Hanink, & Bentley, 2012), this study proposes a new local polycategorical AI procedure that integrates the positive aspects of both aforementioned regressions. QR is a regression with varying parameter estimates like GWR, but these regression models differ in two respects: (1) QR minimizes the sum of absolute deviations whereas GWR minimizes the sum of squared deviations, and (2) QR estimates are a function of a position in the statistical distribution (the quantile level) rather than a position in geographic space.…”

Evaluating geo-located Twitter data as a control layer for areal interpolation of population

“…The third category includes intelligent methods that integrate land cover data in the population estimation, ranging from a simple binary dasymetric method (Fisher & Langford, 1996;Flowerdew & Green, 1989;Holt, Lo, & Hodler, 2004) to more sophisticated procedures such as those that are logical extensions of Wright's (1936) original dasymetric mapping (see Eicher & Brewer, 2001;Langford, 2006;Mennis, 2003;Mennis & Hultgren, 2006;Reibel & Agrawal, 2007) and various forms of statistical analysis (Cromley, Hanink, & Bentley, 2012;Langford, Maguire, & Unwin, 1991;Lin, Cromley, & Zhang, 2011;Lo, 2008;Schroeder and Van Riper, 2013;Yuan, Smith, & Limp, 1997). An alternative approach in this category did not use the land cover categories as the correlate but instead integrated an impervious surface fraction derived from Thematic Mapper (TM) imagery into a cokriging method to interpolate population density using the spatial correlation and crosscorrelation between population and this fraction (Wu & Murray, 2005).…”