A Quantile Regression Approach to Areal Interpolation

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 x 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.