1# RECORD 1ce1eaf3983315cb017b5669a5fa56ba93a3f60d2# TITLE: Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data3# YEAR: 2014.0 VENUE: International Journal of Geographical Information Science DOI: 10.1080/13658816.2013.8657394# AUTHORS: Binbin Lu; M. Charlton; P. Harris; A. Fotheringham5# PAGES: 22 CANDIDATE TABLE PAGES (1-based): []6# ABSTRACT: nan789===== PAGE 1 (score 3, numeric-paren 0, table-words 0, var-words 3) =====1011Geographically weighted regression with a non-Euclidean distance12metric: a case study using hedonic house price data13Binbin Lua*, Martin Charltona, Paul Harrisa and A. Stewart Fotheringhamb14aNational Centre for Geocomputation, National University of Ireland Maynooth, Maynooth, Co.15Kildare, Ireland; bSchool of Geography and Geosciences, University of St. Andrews, St. Andrews,16Scotland, UK17(Received 30 July 2012; final version received 8 November 2013)18Geographically weighted regression (GWR) is an important local technique for explor-19ing spatial heterogeneity in data relationships. In fitting with Tobler’s first law of20geography, each local regression of GWR is estimated with data whose influence21decays with distance, distances that are commonly defined as straight line or22Euclidean. However, the complexity of our real world ensures that the scope of23possible distance metrics is far larger than the traditional Euclidean choice. Thus in24this article, the GWR model is investigated by applying it with alternative, non-25Euclidean distance (non-ED) metrics. Here we use as a case study, a London house26price data set coupled with hedonic independent variables, where GWR models are27calibrated with Euclidean distance (ED), road network distance and travel time metrics.28The results indicate that GWR calibrated with a non-Euclidean metric can not only29improve model fit, but also provide additional and useful insights into the nature of30varying relationships within the house price data set.31Keywords: local regression; non-stationarity; road network distance; travel time; real32estate331.34Introduction35Waldo Tobler’s celebrated dictum, to which he referred as the first law of geography, has36been widely adopted as a basic principle in Geographic Information Science (Goodchild371992). It is at the core of many spatial techniques, such as those found in spatial38interpolation and spatial interaction paradigms (Goodchild 2004, Miller 2004, Sui392004). In most cases, Tobler’s first law (Tobler 1970, p. 236) relates to the data, but it40can similarly relate to a statistic or model. Here, local or non-stationary models are used in41the exploration of some form of spatial heterogeneity. For example, local indicators of42spatial association (Getis and Ord 1992, Anselin 1995) are used to investigate hetero-43geneity in spatial autocorrelation. For this study, our focus lies with the geographically44weighted regression (GWR) model – a technique that investigates heterogeneity in data45relationships across space (Brunsdon et al. 1996). In particular, we empirically assess the46value of applying a non-Euclidean distance (non-ED) metric to GWR, with respect to its47calibration and performance (in terms of model fit and the interpretation of its results).48For analysing or visualising geographical phenomena, non-ED metrics suit situations49when the spatial interaction or spatial behaviour of the process does not follow straight50lines or the standard properties of a metric space (Miller 2000). For instance, non-ED51*Corresponding author. Email: binbin.lu.2009@nuim.ie52International Journal of Geographical Information Science, 201453http://dx.doi.org/10.1080/13658816.2013.86573954© 2014 Taylor & Francis55