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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 , where , , and are, respectively, dependent variable, kth independent variable, and the Gaussian error at location i; ( ) is the x-y coordinate of the ith location; and coefficients 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. . Local terms Global terms where is the lth independent variable with a fixed coefficient . 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. kiikiikixvuy,),(iyikx,iiivu,),(iikvukilillikiikizxvuy,,),(ilz,l

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) (ii) GWR4 is copyrighted by the GWR4 development team. 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, 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.

5 3. Starting the program, Exiting the program, and Tab design < Starting the program > To start the program, double click the GWR4 shortcut icon on the desktop, or select it from the GWR4 program group. < Tab design > Ensure that there are five tabs labelled Step 1 to Step 5. Click a tab label to move to the corresponding tab page. The first tab page when the program starts is “Step 1: Data>”. Tab labels < Exiting the program > Figure 3.1: GWR4 startup screen To exit the program, select “Quit(Q)” on the File menu (alternatively, you can press the Alt and “F” keys simultaneously and then press the “Q” key), or you can click the close button in the top-right corner of the window.

6 Five steps in GWR calibration We regard a session as the overall process by which settings are used to calibrate a GWR model. To build and proceed through your own session, you can generally follow the following five steps (Figure 4.1). Each step is separated into a tabbed page of the software. As described before, to move to a different page, click the corresponding tab label in the upper part of the window. Step1: Data> Start your session by giving it a title then open your data file. Step2: Model> Specify one regression type and the variable settings needed for GWR modelling. Step 3: Kernel> Choose a geographic kernel type and its bandwidth size. Automated optimisation of bandwidth size is also available. Step 4: Output> Specify filenames for the files storing the modelling results. Step 5: Execute> Execute the session to compare necessary calculations and read results. Figure 3.2: Steps in a GWR modelling session with respect to the five tabs

7 4. Step 1: The Data Tab Data preparation < What fields do I have to prepare in my dataset? > To calibrate a GWR model, you must prepare a tabular dataset that contains fields of dependent and independent variables, and x-y coordinates. Every variable should consist of numeric values, except for Areal key, as an identifier of observation. Areal key is treated as a string field in GWR4. < Coordinates > Both projected and latitude/longitude (lat/lon) decimal degrees coordinates can be used as x-y coordinates in GWR4. However, projected coordinates are superior to decimal degrees in terms of computing time. < Possible data formats > GWR4 can open data files in text format delimited by space, comma, or tab; as well as files in dbase IV format (*.dbf). The most popular type is CSV (a text format that uses the comma delimiter). < dbase IV files > Since the shapefile spatial data format—a common GIS file format from ESRI Inc.—uses dbase IV as an attribute database linking with geographic objects, the function to read dbase file provides an easy way to use such a GIS data file in GWR4. However, there is one caveat for this function: In the case of dbase IV, the length of the filename must not exceed 8 characters, due to the restriction on database connection used in this software. Some examples of readable and unreadable filenames are shown below: Readable filenames: tokyom.dbf, tokyodat.dbf Unreadable filenames: dublindata.dbf, irelandmortality.dbf < Field names > In the case of text formats, the first line (row) of the data file must be the list of field names. (A dbase IV file automatically has the field name lists.)

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