Inference in Multiscale Geographically Weighted Regression

Hanchen Yu, Stewart Fotheringham, Ziqi Li, Taylor Oshan, Wei Kang, Levi John Wolf

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
JournalGeographical Analysis
DOIs
StateAccepted/In press - Jan 1 2019

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regression
smoothing
software
matrix
statistics
parameter
global model
test
project

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Earth-Surface Processes

Cite this

Inference in Multiscale Geographically Weighted Regression. / Yu, Hanchen; Fotheringham, Stewart; Li, Ziqi; Oshan, Taylor; Kang, Wei; Wolf, Levi John.

In: Geographical Analysis, 01.01.2019.

Research output: Contribution to journalArticle

Yu, Hanchen ; Fotheringham, Stewart ; Li, Ziqi ; Oshan, Taylor ; Kang, Wei ; Wolf, Levi John. / Inference in Multiscale Geographically Weighted Regression. In: Geographical Analysis. 2019.
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