Inference in Multiscale Geographically Weighted Regression

Hanchen Yu · Alexander Stewart Fotheringham · Ziqi Li · Taylor M. Oshan · Wei Kang · Levi John Wolf

414 citations0/0 files storedGeographical Analysis

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Spatial and Panel Data Analysis Geography Education and Pedagogy demographic modeling and climate adaptation

Abstract

A recent paper expands the well‐known geographically weighted regression (GWR) framework significantly by allowing the bandwidth or smoothing factor in GWR to be derived separately for each covariate in the model—a framework referred to as multiscale GWR (MGWR). However, one limitation of the MGWR framework is that, until now, no inference about the local parameter estimates was possible. Formally, the so‐called “hat matrix,” which projects the observed response vector into the predicted response vector, was available in GWR but not in MGWR. This paper addresses this limitation by reframing GWR as a Generalized Additive Model, extending this framework to MGWR and then deriving standard errors for the local parameters in MGWR. In addition, we also demonstrate how the effective number of parameters can be obtained for the overall fit of an MGWR model and for each of the covariates within the model. This statistic is essential for comparing model fit between MGWR, GWR, and traditional global models, as well as for adjusting multiple hypothesis tests. We demonstrate these advances to the MGWR framework with both a simulated data set and a real‐world data set and provide a link to new software for MGWR (MGWR1.0) which includes the novel inferential framework for MGWR described here.

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References

2002Geographically Weighted Regression: The Analysis of Spatially Varying Relationships 2017Multiscale Geographically Weighted Regression (MGWR)1998Geographically Weighted Regression: A Natural Evolution of the Expansion Method for Spatial Data Analysis 2003Spatial Modeling With Spatially Varying Coefficient Processes 1972Generating Models by the Expansion Method: Applications to Geographical Research*1996The geography of parameter space: an investigation of spatial non-stationarity

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