| Preface |
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xiii | |
| Acknowledgements |
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xv | |
| About the Companion Website |
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xvii | |
| 1 Introduction |
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1 | (8) |
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1.1 The purpose of the book |
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1 | (3) |
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1.1.1 What this book adds |
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3 | (1) |
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1.1.2 Scales of analysis and alternative definitions |
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3 | (1) |
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4 | (1) |
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1.3 Case studies and examples |
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5 | (1) |
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1.4 Why is spatial scale important? |
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5 | (1) |
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1.5 Structure of the book |
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6 | (1) |
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6 | (1) |
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7 | (2) |
| 2 Scale in Spatial Data Analysis: Key Concepts |
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9 | (20) |
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2.1 Definitions of spatial scale |
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9 | (2) |
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2.2 Spatial autocorrelation and spatial dependence |
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11 | (2) |
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13 | (1) |
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2.4 Scale and data models |
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14 | (1) |
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2.5 Spatial scales of inquiry |
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14 | (1) |
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2.6 Scale and spatial data analysis |
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14 | (1) |
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2.7 Scale and neighbourhoods |
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15 | (1) |
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16 | (7) |
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2.9 Scale, spatial data analysis and physical processes |
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23 | (2) |
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2.10 Scale, spatial data analysis and social processes |
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25 | (1) |
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26 | (1) |
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26 | (1) |
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26 | (3) |
| 3 The Modifiable Areal Unit Problem |
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29 | (16) |
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29 | (1) |
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3.2 Scale and zonation effects |
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29 | (3) |
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3.3 The ecological fallacy |
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32 | (2) |
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3.4 The MAUP and univariate statistics |
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34 | (4) |
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3.4.1 Case study: segregation in Northern Ireland |
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35 | (3) |
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3.4.2 Spatial approaches to segregation |
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38 | (1) |
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3.5 Geographical weighting and the MAUP |
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38 | (1) |
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3.6 The MAUP and multivariate statistics |
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39 | (2) |
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3.6.1 Case study: population variables in Northern Ireland |
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40 | (1) |
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41 | (1) |
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42 | (1) |
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42 | (1) |
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42 | (3) |
| 4 Measuring Spatial Structure |
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45 | (58) |
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45 | (1) |
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4.2 Measures of spatial autocorrelation |
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45 | (8) |
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47 | (1) |
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4.2.2 Spatial autocorrelation and kernel. size |
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47 | (3) |
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4.2.3 Spatial autocorrelation and lags |
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50 | (1) |
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50 | (1) |
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4.2.5 Global and local I and spatial scale |
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51 | (2) |
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4.3 Geostatistics and characterising spatial structure |
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53 | (4) |
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4.3.1 The theory of regionalised variables |
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54 | (3) |
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57 | (2) |
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4.4.1 Bias in variogram estimation |
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59 | (1) |
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4.5 The covariance function and correlogram |
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59 | (1) |
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4.6 Alternative measures of spatial structure |
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60 | (3) |
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4.7 Measuring dependence between variables |
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63 | (1) |
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64 | (1) |
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4.9 Variogram clouds and h-scatterplots |
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64 | (1) |
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65 | (3) |
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4.11 Fitting variogram models |
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68 | (2) |
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4.12 Variogram case study |
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70 | (4) |
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4.13 Anisotropy and variograms |
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74 | (3) |
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4.13.1 Variogram surfaces |
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74 | (1) |
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4.13.2 Geometric and zonal anisotropy |
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75 | (2) |
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4.14 Variograms and non-stationarity |
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77 | (5) |
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4.14.1 Variograms and long-range trends |
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77 | (2) |
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4.14.2 Variogram non-stationarity |
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79 | (3) |
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4.15 Space-time variograms |
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82 | (1) |
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83 | (1) |
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83 | (1) |
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4.18 Point pattern analysis |
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84 | (13) |
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4.18.1 Spatial dependence and point patterns |
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85 | (6) |
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91 | (1) |
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92 | (5) |
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97 | (1) |
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97 | (1) |
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97 | (6) |
| 5 Scale and Multivariate Data |
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103 | (32) |
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5.1 Regression frameworks |
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104 | (1) |
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5.2 Spatial scale and regression |
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104 | (1) |
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105 | (1) |
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105 | (1) |
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5.5 Regression and spatial data |
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106 | (5) |
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5.5.1 Generalised least squares |
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106 | (1) |
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5.5.2 Spatial autoregressive models |
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107 | (2) |
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5.5.3 Spatially lagged dependent variable models and spatial error models case study |
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109 | (2) |
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5.6 Local regression and spatial scale |
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111 | (8) |
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5.6.1 Spatial expansion method |
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111 | (1) |
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5.6.2 Geographically weighted regression |
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112 | (3) |
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115 | (1) |
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5.6.4 GWR case study: fixed bandwidths |
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115 | (1) |
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5.6.5 GWR case study: variable bandwidths |
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116 | (2) |
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5.6.6 Bayesian spatially varying coefficient process models |
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118 | (1) |
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119 | (10) |
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125 | (4) |
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5.8 Spatial structure of multiple variables |
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129 | (1) |
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5.9 Multivariate analysis and spatial scale |
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130 | (1) |
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131 | (1) |
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131 | (1) |
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131 | (4) |
| 6 Fractal Analysis |
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135 | (24) |
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135 | (3) |
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6.2 Measuring fractal dimension |
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138 | (4) |
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6.2.1 Walking-divider method |
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139 | (1) |
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6.2.2 Box-counting method |
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140 | (2) |
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142 | (1) |
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6.3 Fractals and spatial structure |
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142 | (10) |
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6.3.1 Case study: fractal D of land surfaces |
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143 | (3) |
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6.3.2 Case study: local fractal D |
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146 | (3) |
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6.3.3 Fractals and topographic form |
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149 | (3) |
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6.4 Other applications of fractal analysis |
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152 | (3) |
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6.4.1 Fractals and remotely sensed imagery |
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152 | (1) |
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6.4.2 Fractals and urban form |
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153 | (2) |
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6.5 How useful is the fractal model in geography? |
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155 | (1) |
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155 | (1) |
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155 | (1) |
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155 | (4) |
| 7 Scale and Gridded Data: Fourier and Wavelet Transforms |
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159 | (24) |
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159 | (1) |
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160 | (8) |
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7.2.1 Continuous Fourier transform |
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160 | (1) |
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7.2.2 Discrete Fourier transform |
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161 | (2) |
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7.2.3 Fast Fourier transform |
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163 | (1) |
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163 | (2) |
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7.2.5 Spectral analysis and the covariance function |
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165 | (2) |
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7.2.6 Spectral analysis case study |
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167 | (1) |
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168 | (12) |
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7.3.1 Continuous wavelet transforms |
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169 | (1) |
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7.3.2 Discrete wavelet transforms |
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170 | (1) |
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7.3.3 The Haar basis functions |
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171 | (1) |
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7.3.4 Other basis functions |
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172 | (1) |
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7.3.5 Fast wavelet transform |
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173 | (1) |
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7.3.6 Two-dimensional wavelet transforms |
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174 | (6) |
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7.4 Wavelet analysis applications and other issues |
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180 | (1) |
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180 | (1) |
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180 | (1) |
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181 | (2) |
| 8 Areal Interpolation |
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183 | (18) |
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183 | (1) |
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184 | (2) |
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8.3 Using additional data |
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186 | (7) |
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8.3.1 Types of secondary data sources for mapping populations |
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192 | (1) |
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193 | (3) |
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8.4.1 Population surface case study |
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195 | (1) |
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8.5 Other approaches to changing support |
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196 | (1) |
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197 | (1) |
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198 | (1) |
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198 | (3) |
| 9 Geostatistical Interpolation and Change of Support |
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201 | (40) |
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201 | (1) |
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201 | (4) |
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9.2.1 Regularisation with an irregular support |
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204 | (1) |
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9.3 Variogram deconvolution |
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205 | (5) |
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9.3.1 Variogram deconvolution for irregular supports |
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206 | (2) |
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9.3.2 Variography and change of support |
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208 | (2) |
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210 | (16) |
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210 | (2) |
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212 | (1) |
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213 | (2) |
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9.4.4 Factorial kriging case study |
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215 | (1) |
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9.4.5 Kriging in the presence of a trend |
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215 | (7) |
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222 | (1) |
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9.4.7 Kriging with an external drift and other techniques |
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222 | (1) |
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9.4.8 Interpreting the kriging variance |
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223 | (1) |
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223 | (1) |
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9.4.10 Conditional simulation |
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224 | (1) |
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9.4.11 Comparison of kriging approaches |
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224 | (2) |
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9.5 Kriging and change of support |
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226 | (5) |
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226 | (1) |
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9.5.2 Area-to-point kriging |
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227 | (2) |
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229 | (2) |
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9.6 Assessing uncertainty and optimal sampling design |
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231 | (5) |
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231 | (1) |
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9.6.2 Assessing optimal sampling design |
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232 | (3) |
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9.6.3 Optimal spatial resolution |
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235 | (1) |
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9.6.4 Other approaches to optimal sampling design |
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236 | (1) |
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236 | (1) |
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236 | (1) |
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236 | (5) |
| 10 Summary and Conclusions |
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241 | (6) |
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10.1 Overview of key concepts and methods |
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241 | (2) |
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10.2 Problems and future directions |
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243 | (2) |
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245 | (1) |
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245 | (2) |
| Index |
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247 | |
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