GWR4.09 User Manual
GWR4
Windows Application for Geographically
Weighted Regression Modelling
Tomoki Nakaya
Update 24 March 2016
Update 12 March 2014
Updated 20 Nov 2012
Updated 7 May 2012
3 June 2009
GWR 4 Development Team
Tomoki Nakaya (Department of Geography, Ritsumeikan University),
Martin Charlton, Chris Brunsdon, Paul Lewis (National Centre of
Geocomputation, National University of Ireland),
Jing Yao (School of Social and Political Sciences, University of Glasgow),
A Stewart Fotheringham (School of Geographical Sciences &
Urban Planning, Arizona State University)
1
Contents
1. Introduction ................................................................................................ 2
What is GWR4? .................................................................................................. 2
New features compared to GWR3.x ................................................................... 3
Notes for use of GWR4 ....................................................................................... 4
2. Installation / Uninstallation ....................................................................... 4
3. Starting the program, Exiting the program, and Tab design ...................... 5
Five steps in GWR calibration ........................................................................... 6
4. Step 1: The Data Tab .................................................................................. 7
Data preparation ................................................................................................ 7
Operations in the data tab page ........................................................................ 9
5. Step 2: The Model Tab .............................................................................. 10
Basic operations: using an example of Gaussian GWR .................................. 11
Semiparametric GWR ...................................................................................... 13
Extensions of GWR: GWGLM .......................................................................... 15
Geographically weighted Poisson regression (GWPR) ................................ 15
Geographically weighted logistic regression (GWLR) ................................. 16
Modelling Options ............................................................................................ 18
Standardisation ............................................................................................ 18
Geographical variability test ........................................................................ 18
LtoG / GtoL variable selection. ..................................................................... 21
6. Step 3: The Kernel Tab ............................................................................. 22
Possible fixed and adaptive kernel functions for geographical weighting ...... 23
Bandwidth selection routines .......................................................................... 24
Selection criteria .............................................................................................. 26
7. Step 4: The Output Tab ............................................................................ 27
Session Control File ......................................................................................... 27
Common output files ........................................................................................ 28
The “Prediction at non-regression points” option ............................................ 28
8. Step 5: The Execute Tab ........................................................................... 29
The Execute button .......................................................................................... 29
Fields in a listwise output ............................................................................... 31
Handling a session and batch mode (optional) ................................................ 32
Example output ................................................................................................ 33
9. References ................................................................................................ 39
2
1. Introduction
What is GWR4?
GWR4 is a new release of a Microsoft Windows-based application software for
calibrating geographically weighted regression (GWR) models, which can be used
to explore geographically varying relationships between dependent/response
variables and independent/explanatory variables. A GWR model can be considered
a type of regression model with geographically varying parameters. A conventional
GWR is described by the equation
k
iikiiki
xvuy
,
),(
,
where
i
y
,
ik
x
,
, and
i
are, respectively, dependent variable, kth independent
variable, and the Gaussian error at location i; (
ii
vu ,
) is the x-y coordinate of the ith
location; and coefficients
),(
iik
vu
are varying conditionals on the location. Such
modelling is likely to attain higher performance than traditional regression models,
and reading the coefficients can lead to a new interpretation of the phenomena
under study. An important extension of GWR is its semiparametric formation by
mixing globally fixed and geographically varying coefficients.
k
i
l
illikiiki
zxvuy
,,
),(
.
where
il
z
,
is the lth independent variable with a fixed coefficient
l
. Such a model
may reduce the model complexities and enhance its predictable performance. Using
the framework of geographically weighted generalised linear modelling (GWGLM),
logistic and Poisson regression models with geographically varying coefficients are
also popular for binary or count data modelling. GWR4 enables the fitting of such
GWR and GWGLM models with their semiparametric formations, associated
statistical tests, and model selections by user-defined data and model settings.
Local terms
Global terms
3
Main features
(1) Semiparametric GWR
As noted above, a most remarkable feature of this release is the function to fit
semiparametric GWR models, which allow you to mix globally fixed terms and
locally varying terms of explanatory variables simultaneously. The function
can be applied to popular types of generalized linear modelling including
Gaussian, Poisson, and logistic regressions. Using the semiparametric
modelling scheme, a new statistical test of geographical variability on
geographically varying coefficients is enabled. It is also possible to use variable
selection routines by which variables are automatically selected as either fixed
or varying terms by recursive model comparisons.
(2) Interface
A tabbed interface has been introduced to enable modelling sessions to
intuitively proceed in a step-by-step manner. Datasets and geographically
listwise results can be viewed in separate spreadsheet-like windows. Several
popular file types can be used as input data files (space, comma, tab separated
text, and dbase IV formats). In addition, Areal key field can be integrated into
the output of GWR modelling, enabling you to join your output CSV file to a
GIS attribute table via the key field for mapping the result in a GIS
environment. GWR4 can be also used by a batch mode without the Windows
interface.
(3) Requirements
GWR4 runs on Windows Vista, Windows 7, 8 and 10 environments with
the .NET Framework 4. The maximum size of data is dependent on your local
machine environment. GWR4 dynamically allocates memory for large matrices
(n by n, where n is the number of regression points) even for conventional GWR
models. Thus using a PC having relatively large memory size (equal to or larger
than 4GB) for running GWR4 is recommended. If the PC has multi-core
processors, GWR4 automatically uses multi-threading routines to speed-up the
computation.
4
Notes for use of GWR4
(i) GWR4 is copyrighted by the GWR4 development team.
(ii) GWR4 can be freely distributed and used for academic and non-profit
purposes. The developers of GWR4 are not responsible for any
difficulties that users of the software may encounter.
(iii) When any results using GWR4 are published, the author(s) should
clearly state that GWR4 was used. Recommended citations for the
theoretical backgrounds of GWR4 modelling may be found in the
References in this manual.
2. Installation / Uninstallation
< How to install GWR4 >
Download the GWR4 installer, GWR4_setup.exe,
and then double-click the icon.
< .NET Framework and Visual C++ 2012/2015 Redistributable Package>
GWR4 works only in Microsoft Windows environments that have the .NET
Framework 4 and Microsoft Visual C++ Redistributable Package installed. If
your PC does not have them installed, a message will pop up suggesting that
you download the .Net Framework 4 Client Profile and the redistributable
package from a Microsoft website, and automatically start setting up them if
your PC is connected to the Internet. If your PC is off-line, obtain the stand
alone installers of the .Net Framework Client Profile and the redistributable
package which are available from from the Microsoft website download centre.
< When the installer starts … >
Follow the instructions to select the GWR4 installation folder and users. If the
installation is successful, a shortcut to the program will appear on your desktop
and in the GWR4 program group. You may access the program by clicking this
shortcut.
< To uninstall >
To uninstall GWR4 from your local environment, you may use “uninstall
GWR4” menu in the GWR4 program group. Alternatively, you can use the
“Uninstall Programs” utility in the Control Panel group in Windows
environments.
GWR4_setup.exe
