Details

<p>Acknowledgements</p> <p>Contents</p> <p><b>1 Local Statistics and Local Models for Spatial Data 1</b></p> <p>1.1 Introduction 1</p> <p>1.2 Local Aspatial Statistical Methods 3</p> <p>1.3 Local versus Global Spatial Statistics 6</p> <p>1.4 Spatial Non-stationarity 9</p> <p>1.5 Examples of Local Univariate Methods for Spatial Data Analysis 11</p> <p>1.5.1 Local Forms of Point Pattern Analysis 11</p> <p>1.5.2 Local Graphical Analysis 12</p> <p>1.5.3 Local Filters 13</p> <p>1.5.4 Local Measures of Spatial Dependency 14</p> <p>1.6 Examples of Local Multivariate Methods for Spatial Data Analysis 15</p> <p>1.6.1 The Spatial Expansion Method 16</p> <p>1.6.2 Spatially Adaptive Filtering 17</p> <p>1.6.3 Multilevel Modelling 18</p> <p>1.6.4 Random Coef®cient Models 20</p> <p>1.6.5 Spatial Regression Models 21</p> <p>1.7 Examples of Local Methods for Spatial Flow Modelling 24</p> <p>1.8 Summary 25</p> <p><b>2 Geographically Weighted Regression:The Basics 27</b></p> <p>2.1 Introduction 27</p> <p>2.2 An Empirical Example 27</p> <p>2.2.1 The Data 28</p> <p>2.2.2 A Global Regression Model 28</p> <p>2.2.3 Global Regression Results 34</p> <p>2.3 Borough-Speci®c Calibrations of the Global Model 38</p> <p>2.4 Moving Window Regression 42</p> <p>2.5 Geographically Weighted Regression with Fixed Spatial Kernels 44</p> <p>2.6 Geographically Weighted Regression with Adaptive Spatial Kernels 46</p> <p>xi</p> <p>2.7 The Mechanics of GWR in More Detail 52</p> <p>2.7.1 The Basic Methodology 52</p> <p>2.7.2 Local Standard Errors 54</p> <p>2.7.3 Choice of Spatial Weighting Function 56</p> <p>2.7.4 Calibrating the Spatial Weighting Function 59</p> <p>2.7.5 Bias-Variance Trade-Off 62</p> <p>2.8 Testing for Spatial Non-stationarity 63</p> <p>2.9 Summary 64</p> <p><b>3 Extensions to the Basic GWR Model 65</b></p> <p>3.1 Introduction 65</p> <p>3.2 Mixed GWR Models 65</p> <p>3.3 An Example 68</p> <p>3.4 Outliers and Robust GWR 73</p> <p>3.5 Spatially Heteroskedastic Models 80</p> <p>3.6 Summary 82</p> <p><b>4 Statistical Inference and Geographically Weighted Regression 83</b></p> <p>4.1 Introduction 83</p> <p>4.2 What is Meant by `Inference' and How Does it Relate to GWR? 84</p> <p>4.2.1 How Likely is it that Some Fact is True on the Basis of the Data? 85</p> <p>4.2.2 Within What Interval Does Some Model Coef®cient Lie? 85</p> <p>4.2.3 Which One of a Series of Potential Mathematical Models is `Best'? 86</p> <p>4.3 GWR as a Statistical Model 87</p> <p>4.3.1 Local Likelihood 90</p> <p>4.3.2 Using Classical Inference ± Working with p-values 91</p> <p>4.3.3 Testing Individual Parameter Stationarity 92</p> <p>4.4 Con®dence Intervals 94</p> <p>4.5 An Alternative Approach Using the AIC 95</p> <p>4.6 Two Examples 97</p> <p>4.6.1 Basic Estimates 97</p> <p>4.6.2 Estimates of Pointwise Standard Errors 99</p> <p>4.6.3 Working with the AIC 99</p> <p>4.7 Summary 102</p> <p><b>5 GWR and Spatial Autocorrelation 103</b></p> <p>5.1 Introduction 103</p> <p>5.2 The Empirical Setting 104</p> <p>5.3 Local Measures of Spatial Autocorrelation using GWR 104</p> <p>5.4 Residuals in Global Regression Models and in GWR 112</p> <p>5.5 Local Parameter Estimates from Autoregressive and Non-Autoregressive Models 117</p> <p>5.6 Spatial Regression Models and GWR 121</p> <p>5.6.1 Overview 121</p> <p>5.6.2 Conditional Autoregressive (CA) Models 122</p> <p>5.6.3 Simultaneous Autoregressive (SA) Models 122</p> <p>5.6.4 GWR, Conditional Autoregressive Models and Simultaneous Autoregressive Models 123</p> <p>5.7 Summary 124</p> <p><b>6 Scale Issues and Geographically Weighted Regression 127</b></p> <p>6.1 Introduction 127</p> <p>6.2 Bandwidth and Scale: The Example of School Performance Analysis 130</p> <p>6.2.1 Introduction 130</p> <p>6.2.2 The School Performance Data 131</p> <p>6.2.3 Global Regression Results 133</p> <p>6.2.4 Local Regression Results 134</p> <p>6.3 GWR and the MAUP 144</p> <p>6.3.1 Introduction 144</p> <p>6.3.2 An Experiment 147</p> <p>6.4 Summary 153</p> <p><b>7 Geographically Weighted Local Statistics 159</b></p> <p>7.1 Introduction 159</p> <p>7.2 Basic Ideas 161</p> <p>7.3 A Single Continuous Variable 163</p> <p>7.4 Two Continuous Variables 173</p> <p>7.5 A Single Binary Variable 175</p> <p>7.6 A Pair of Binary Variables 177</p> <p>7.7 Towards More Robust Geographically Weighted Statistics 181</p> <p>7.8 Summary 183</p> <p><b>8 Extensions of Geographical Weighting 187</b></p> <p>8.1 Introduction 187</p> <p>8.2 Geographically Weighted Generalised Linear Models 188</p> <p>8.2.1 A Poisson GWGLM 190</p> <p>8.2.2 A Binomial GWGLM 193</p> <p>8.3 Geographically Weighted Principal Components 196</p> <p>8.3.1 Local Multivariate Models 196</p> <p>8.3.2 Calibrating Local Multivariate Models 198</p> <p>8.3.3 Interpreting S and r 199</p> <p>8.3.4 An Example 200</p> <p>8.4 Geographically Weighted Density Estimation 202</p> <p>8.4.1 Kernel Density Estimation 202</p> <p>8.4.2 Geographically Weighted Kernels 203</p> <p>8.4.3 An Example Using House Prices 203</p> <p>8.5 Summary 205</p> <p><b>9 Software for Geographically Weighted Regression 207</b></p> <p>9.1 Introduction 207</p> <p>9.2 Some Terminology 208</p> <p>9.3 The Data File 208</p> <p>9.4 What Do INeed to Specify? 209</p> <p>9.5 Kernels 210</p> <p>9.6 Choosing a Bandwidth 211</p> <p>9.6.1 User-Supplied Bandwidth 211</p> <p>9.6.2 Estimation by Cross-validation 212</p> <p>9.6.3 Estimation by Minimising the AIC 212</p> <p>9.6.4 The Golden Section Search 212</p> <p>9.7 Signi®cance Tests 213</p> <p>9.8 Casewise Diagnostics for GWR 214</p> <p>9.8.1 Standardised Residuals 214</p> <p>9.8.2 Local r-square 215</p> <p>9.8.3 In¯uence Statistics 216</p> <p>9.9 A Worked Example 216</p> <p>9.9.1 Running GWR 2.0 on a PC 216</p> <p>9.9.2 The Outputs 224</p> <p>9.9.3 Running GWR 2.0 under UNIX 230</p> <p>9.10 Visualising the Output 231</p> <p>9.10.1 Viewing the Results in ArcView 233</p> <p>9.10.2 Point Symbols 234</p> <p>9.10.3 Area Symbols 236</p> <p>9.10.4 Contour Plots 237</p> <p>9.10.5 Pseudo-3D Display 238</p> <p>9.11 Summary 239</p> <p><b>10 Epilogue 241</b></p> <p>10.1 Overview 241</p> <p>10.2 Summarising the Book 242</p> <p>10.3 Empirical Applications of GWR 243</p> <p>10.4 Software Development 245</p> <p>10.4.1 Embedding GWR in Larger Packages 246</p> <p>10.4.2 Software Extending the Basic GWR Idea 247</p> <p>10.5 Cautionary Notes 248</p> <p>10.5.1 Multiple Hypothesis Testing 249</p> <p>10.5.2 Locally Varying Intercepts 251</p> <p>10.5.3 Interpretation of Parameter Surfaces 251</p> <p>10.6 Summary 252</p> <p>Bibliography 255</p> <p>Index 267</p> Acknowledgements.<br /> <br /> Local Statistics and Local Models for Spatial Data.<br /> <br /> Geographically Weighted Regression: The Basics.<br /> <br /> Extensions to the Basic GWR Model.<br /> <br /> Statistical Inference and Geographically Weighted Regression.<br /> <br /> GWR and Spatial Autocorrelation.<br /> <br /> Scale Issues and Geographically Weighted Regression.<br /> <br /> Geographically Weighted Local Statistics.<br /> <br /> Extensions of Geographically Weighting.<br /> <br /> Software for Geographically Weighted Regression.<br /> <br /> Epilogue.<br /> <br /> Bibliography.<br /> <br /> Index.

"...this excellent volume..." (Geomatics World, July/August 2003)

A. Stewart Fotheringham, Professor of Quantitative Geography, University of Newcastle. Chris Brunsdon, Senior Lecturer in Spatial Analysis, University of Newcastle. Martin Charlton, Lecturer in Geographical Information Systems, University of Newcastle.

<i>Geographically Weighted Regression: The Analysis of Spatially Varying Relationships</i> is based on the premise that relationships between variables measured at different locations might not be constant over space. The prevailing assumption is that such relationships are constant, an assumption that would appear to be the result of convenience rather than of any serious examination of the issues. If relationships do vary significantly over space, then serious questions are raised about the reliability of traditional, global-level analyses. <p>Geographically Weighted Regression, as part of a broader research area in local modelling, provides a new analytical tool and a different perspective on spatial analysis. Instead of being restricted to simple global analyses in which interesting local variations in relationships are 'averaged away' and unobservable, GWR allows local relationships to be measured and mapped. In many ways the output from GWR is similar to that presented by a microscope: previously unimagined detail suddenly comes into focus. This book challenges many of the global statements of spatial relationships that have been made in the academic literature.</p> <p><i>Geographically Weighted Regression: The Analysis of Spatially Varying Relationships</i> contains a broad discussion of local models in general and of the details of GWR, and provides many empirical examples on issues such as house price determinants, educational attainment levels and school performance statistics. A unique accompanying feature of this book is the author-written software that allows users to undertake sophisticated and complex forms of GWR within a user-friendly, Windows-based, front-end. This software is readily available from the authors and notes on using the software and an example application are documented in the book itself.</p> <p><i>Geographically Weighted Regression: The Analysis of Spatially Varying Relationships</i> is an essential resource for quantitative spatial analysts and GIS researchers and students. It will be of interest to researchers in any discipline in which spatial data are used across the broad spectrum of social sciences, medicine, science and engineering. The underlying message is that locality is important and measuring local relationships is vital to understanding spatial processes.</p> <p>'Stewart Fotheringham and his colleagues have produced a book that will be widely used by geographers and others interested in spatial analysis. Geographically weighted regression is an important method, and the authors have developed and explained it well.' Peter Rogerson, Department of Geography, University at Buffalo, USA</p> <p> 'The realisation that almost any statistic can be made 'local', and that mapping the results almost always leads to greater insight is powering a revolution in spatial analysis. In particular, the localisation of standard regression models, or GWR, has led to important and powerful insights. This book, written by the team that has done most to develop it, makes this approach accessible for the first time under a single cover. It should be required reading for anyone involved with the analysis of spatially referenced data.' David Unwin, School of Geography, Birkbeck College London</p>

GB