Are we modelling spatially varying processes or non-linear relationships?

Keywords: Generalized Additive Models, Multiscale Geographically Weighted Regression, non-linear regression, spatial regression, spatially varying processes
Session Type: Virtual Paper
Day: Wednesday
Session Start / End Time: 4/7/2021 08:00 AM (Pacific Time (US & Canada)) - 4/7/2021 09:15 AM (Pacific Time (US & Canada))
Room: Virtual 18

Abstract

This research concerns the study of spatially varying parameter estimates commonly obtained in the calibration of local statistical models. The interpretation of the variation observed in such spatially varying parameters is typically explained in terms of spatially varying processes. The GAM framework, however, provides an alternative interpretation of the varying nature of local estimates in terms of nonlinearity. Consequently, there is a problem in determining the provenance of the variation observed in local estimates from local modeling. This paper highlights this issue and provides a simple diagnostic test which should be applied to all studies of local parameter estimates before ascribing such variation to process spatial nonstationarity. The test is demonstrated first through a simulated dataset which provides control over the induced spatial nonstationarity and modeled nonlinearity and is then applied to two real world datasets – one in the real estate research and the other on voting behavior.