# RECORD 1ce1eaf3983315cb017b5669a5fa56ba93a3f60d
# TITLE: Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data
# YEAR: 2014.0  VENUE: International Journal of Geographical Information Science  DOI: 10.1080/13658816.2013.865739
# AUTHORS: Binbin Lu; M. Charlton; P. Harris; A. Fotheringham
# PAGES: 22  CANDIDATE TABLE PAGES (1-based): []
# ABSTRACT: nan


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Geographically weighted regression with a non-Euclidean distance
metric: a case study using hedonic house price data
Binbin Lua*, Martin Charltona, Paul Harrisa and A. Stewart Fotheringhamb
aNational Centre for Geocomputation, National University of Ireland Maynooth, Maynooth, Co.
Kildare, Ireland; bSchool of Geography and Geosciences, University of St. Andrews, St. Andrews,
Scotland, UK
(Received 30 July 2012; final version received 8 November 2013)
Geographically weighted regression (GWR) is an important local technique for explor-
ing 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, non-
Euclidean 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.
Keywords: local regression; non-stationarity; road network distance; travel time; real
estate
1.
Introduction
Waldo Tobler’s celebrated dictum, to which he referred as the first law of geography, has
been widely adopted as a basic principle in Geographic Information Science (Goodchild
1992). It is at the core of many spatial techniques, such as those found in spatial
interpolation and spatial interaction paradigms (Goodchild 2004, Miller 2004, Sui
2004). In most cases, Tobler’s first law (Tobler 1970, p. 236) relates to the data, but it
can similarly relate to a statistic or model. Here, local or non-stationary models are used in
the exploration of some form of spatial heterogeneity. For example, local indicators of
spatial association (Getis and Ord 1992, Anselin 1995) are used to investigate hetero-
geneity in spatial autocorrelation. For this study, our focus lies with the geographically
weighted regression (GWR) model – a technique that investigates heterogeneity in data
relationships across space (Brunsdon et al. 1996). In particular, we empirically assess the
value of applying a non-Euclidean distance (non-ED) metric to GWR, with respect to its
calibration and performance (in terms of model fit and the interpretation of its results).
For analysing or visualising geographical phenomena, non-ED metrics suit situations
when the spatial interaction or spatial behaviour of the process does not follow straight
lines or the standard properties of a metric space (Miller 2000). For instance, non-ED
*Corresponding author. Email: binbin.lu.2009@nuim.ie
International Journal of Geographical Information Science, 2014
http://dx.doi.org/10.1080/13658816.2013.865739
© 2014 Taylor & Francis