Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data

Abstract

Geographically weighted regression (GWR) is an important local technique for exploring spatial heterogeneity in data relationships. In fitting with Tobler's first law of geography, each local regression of GWR is estimated with data whose influence decays with distance, distances that are commonly defined as straight line or Euclidean. However, the complexity of our real world ensures that the scope of possible distance metrics is far larger than the traditional Euclidean choice. Thus in this article, the GWR model is investigated by applying it with alternative, nonEuclidean distance (non-ED) metrics. Here we use as a case study, a London house price data set coupled with hedonic independent variables, where GWR models are calibrated with Euclidean distance (ED), road network distance and travel time metrics. The results indicate that GWR calibrated with a non-Euclidean metric can not only improve model fit, but also provide additional and useful insights into the nature of varying relationships within the house price data set.

The Minkowski approach for choosing the distance metric in geographically weighted regression

“…The distance between the datapoint j and the regression point i is d ij that is traditionally an ED metric with planar coordinates. Lu et al (2011Lu et al ( , 2014a extend GWR to use two common non-ED metrics (network and TT), where for this study, we extend further, with the use of Minkowski distance metrics. The kernel bandwidth b (also shown in Figure 2) is the key controlling parameter for any weighting scheme specified and strongly influences all GWR outputs.…”

“…The first use of non-Euclidean distance (non-ED) metrics in GWR modelling can be found in Lu et al (2011Lu et al ( , 2014a) using a house price data set for London, UK. Here, the use of network distance (ND) and travel time (TT) metrics provided greater insight into data relationships than that found with the usual ED metric.…”

A Hybrid Method for Interpolating Missing Data in Heterogeneous Spatio-Temporal Datasets

“…However, spatial heterogeneity (first-order or second-order non-stationarity) and temporal dimension are not considered by these spatial regression models. Although geographically weighted regression (GWR) and spatio-temporal geographically weighted regression (STGWR) are able to construct a regression function for each location [17][18][19], the regression function between missing data and explanatory variables cannot be constructed. Therefore, GWR and STGWR are unsuitable for estimating missing data.…”

Representation of Temperature Variability in Fars Province Using Spatial Statistics

“…‫زمانی‬ , Lu et al, 2014, Razmi et al, 2017 ‫ازاین‬ .) ‫همبستگی‬ ‫ساختار‬ ‫نحوی‬ ‫به‬ ‫است‬ ‫لازم‬ ‫رو‬ ‫داده‬ ‫آن‬ ‫تحلیل‬ ‫در‬ ‫ها‬ ( ‫گردد‬ ‫لحاظ‬ ‫ها‬ Kendall, 1998: 221 Ageena et al, 2013, Nemec et al, 2013, Kim,Singh, 2014, Sun et al, 2015 ) .…”