Based on the premise that relationships between variables measured at different locations might not be constant over space. The prevailing asumption 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 issue. If relationships do vary significantly over space, then serious questions are raised about the reliability of traditional, global-level analyses.

Cover -- Contents -- Acknowledgements -- 1 Local Statistics and Local Models for Spatial Data -- 1.1 Introduction -- 1.2 Local Aspatial Statistical Methods -- 1.3 Local versus Global Spatial Statistics -- 1.4 Spatial Non-stationarity -- 1.5 Examples of Local Univariate Methods for Spatial Data Analysis -- 1.5.1 Local Forms of Point Pattern Analysis -- 1.5.2 Local Graphical Analysis -- 1.5.3 Local Filters -- 1.5.4 Local Measures of Spatial Dependency -- 1.6 Examples of Local Multivariate Methods for Spatial Data Analysis -- 1.6.1 The Spatial Expansion Method -- 1.6.2 Spatially Adaptive Filtering -- 1.6.3 Multilevel Modelling -- 1.6.4 Random Coefficient Models -- 1.6.5 Spatial Regression Models -- 1.7 Examples of Local Methods for Spatial Flow Modelling -- 1.8 Summary -- 2 Geographically Weighted Regression: The Basics -- 2.1 Introduction -- 2.2 An Empirical Example -- 2.2.1 The Data -- 2.2.2 A Global Regression Model -- 2.2.3 Global Regression Results -- 2.3 Borough-Specific Calibrations of the Global Model -- 2.4 Moving Window Regression -- 2.5 Geographically Weighted Regression with Fixed Spatial Kernels -- 2.6 Geographically Weighted Regression with Adaptive Spatial Kernels -- 2.7 The Mechanics of GWR in More Detail -- 2.7.1 The Basic Methodology -- 2.7.2 Local Standard Errors -- 2.7.3 Choice of Spatial Weighting Function -- 2.7.4 Calibrating the Spatial Weighting Function -- 2.7.5 Bias-Variance Trade-Off -- 2.8 Testing for Spatial Non-stationarity -- 2.9 Summary -- 3 Extensions to the Basic GWR Model -- 3.1 Introduction -- 3.2 Mixed GWR Models -- 3.3 An Example -- 3.4 Outliers and Robust GWR -- 3.5 Spatially Heteroskedastic Models -- 3.6 Summary -- 4 Statistical Inference and Geographically Weighted Regression -- 4.1 Introduction -- 4.2 What is Meant by Inference' and How Does it Relate to GWR? -- 4.2.1 How Likely is it that Some Fact is True on the Basis of the Data? -- 4.2.2 Within What Interval Does Some Model Coefficient Lie? -- 4.2.3 Which One of a Series of Potential Mathematical Models is Best'? -- 4.3 GWR as a Statistical Model -- 4.3.1 Local Likelihood -- 4.3.2 Using Classical Inference ... Working with p-values -- 4.3.3 Testing Individual Parameter Stationarity -- 4.4 Confidence Intervals -- 4.5 An Alternative Approach Using the AIC -- 4.6 Two Examples -- 4.6.1 Basic Estimates -- 4.6.2 Estimates of Pointwise Standard Errors -- 4.6.3 Working with the AIC -- 4.7 Summary -- 5 GWR and Spatial Autocorrelation -- 5.1 Introduction -- 5.2 The Empirical Setting -- 5.3 Local Measures of Spatial Autocorrelation using GWR -- 5.4 Residuals in Global Regression Models and in GWR -- 5.5 Local Parameter Estimates from Autoregressive and Non-Autoregressive Models -- 5.6 Spatial Regression Models and GWR -- 5.6.1 Overview -- 5.6.2 Conditional Autoregressive (CA) Models -- 5.6.3 Simultaneous Autoregressive (SA) Models -- 5.6.4 GWR, Conditional Autoregressive Models and Simultaneous Autoregressive Models -- 5.7 Summary -- 6 Scale Issues and Geographically Weighted Regression -- 6.1 Introduction -- 6.2 Bandwidth and Scale: The Example of School Performance Analysis -- 6.2.1 Intr.