### Geographically Weighted Regression Using a Non

```Geographically Weighted Regression Using a Non-Euclidean Distance Metric
Binbin Lu
National Centre for Geocomputation, NUI Maynooth, Co.Kildare, Ireland
Introduction
Case study using Network distance
Geographically Weighted Regression (GWR) is a local modelling technique to makes a
Data sources
point-wise calibration around each regression point using a ‘bump of influence’: around
each regression point nearer observations have more influence in estimating the local set
of parameters than observations farther away.
Until now, the Euclidean distance (ED) (straight line distance) has generally been adopted
as the default for GWR applications. However, The degree of connectedness between two
places may not be optimally represented by a straight line. For example, an area might
be divided by a river or buildings and connected internally by bridges or roads; surface
distance would be more reasonable in a mountainous area.
In this work, we are focusing on how to use non-Euclidean distance metrics for calibrating
a GWR model , and evaluate their performance in case studies.
A sample of 2108 properties sold within
London during 2001
Road network data of London provided by
Ordnance survey
Calibrations of GWR models
Geographically Weighted Regression
GWR is proposed as a kind of local technique to estimate regression models with spatially
varying relationships. It makes a point-wise calibration with especially concerning a
‘bump of influence’: around each regression point nearer observations have more
influence in estimating the local set of parameters than observations farther away. a
basic GWR model for each regression point i could be written as:
n
yi  0  ui , vi     k  ui , vi  xik   i
k 1
Calibrated105 GWR models with dependent variable “PURCHASE” and independent variables
from the combinations of the rest 14 factors
The calibration is made in a point-wise mode, and for each location i the regression
coefficients are estimated via the following matrix calculation.

ˆ  ui , vi   X W  ui , vi  X
T

1
X W ui , vi  y
T
Standard GWR calibration
Euclidean distance
(Straight line distance)
Comparison of Akaike Information Criterion (AIC) between calibrations with Euclidean distance
(ED) and results from using network distance (ND)
Non-Euclidean geographical distance metrics
P2  x2 , y2 
...
P1  x1, y1 
Great circle distance
Network distance
Manhattan distance
Cost distance
Acknowledgements
Research presented in this paper was jointly funded by a Strategic Research Cluster grant
(07/SRC/I1168) by Science Foundation Ireland under the National Development Plan. The
authors gratefully acknowledge their support.
Estimation of parameter FLOORSZ fitted
with Euclidean distance
Estimation of parameter FLOORSZ fitted
with Network distance
```