Exploring Spatial Scale in Geography -- Contents -- Preface -- Acknowledgements -- About the Companion Website -- 1 Introduction -- 1.1 The purpose of the book -- 1.1.1 What this book adds -- 1.1.2 Scales of analysis and alternative definitions -- 1.3 Case studies and examples -- 1.4 Why is spatial scale important? -- 1.5 Structure of the book -- 1.6 Further reading -- References -- 2 Scale in Spatial Data Analysis: Key Concepts -- 2.1 Definitions of spatial scale -- 2.2 Spatial autocorrelation and spatial dependence -- 2.3 Scale dependence -- 2.4 Scale and data models -- 2.5 Spatial scales of inquiry -- 2.6 Scale and spatial data analysis -- 2.7 Scale and neighbourhoods -- 2.8 Scale and space -- 2.9 Scale, spatial data analysis and physical processes -- 2.10 Scale, spatial data analysis and social processes -- 2.11 Summary -- 2.12 Further reading -- References -- 3 The Modifiable Areal Unit Problem -- 3.1 Basic concepts -- 3.2 Scale and zonation effects -- 3.3 The ecological fallacy -- 3.4 The MAUP and univariate statistics -- 3.4.1 Case study: segregation in Northern Ireland -- 3.4.2 Spatial approaches to segregation -- 3.5 Geographical weighting and the MAUP -- 3.6 The MAUP and multivariate statistics -- 3.6.1 Case study: population variables in Northern Ireland -- 3.7 Zone design -- 3.8 Summary -- 3.9 Further reading -- References -- 4 Measuring Spatial Structure -- 4.1 Basic concepts -- 4.2 Measures of spatial autocorrelation -- 4.2.1 Neighbourhood size -- 4.2.2 Spatial autocorrelation and kernel size -- 4.2.3 Spatial autocorrelation and lags -- 4.2.4 Local measures -- 4.2.5 Global and local and spatial scale -- 4.3 Geostatistics and characterising spatial structure -- 4.3.1 The theory of regionalised variables -- 4.4 The variogram -- 4.4.1 Bias in variogram estimation -- 4.5 The covariance function and correlogram.

4.6 Alternative measures of spatial structure -- 4.7 Measuring dependence between variables -- 4.8 Variograms of risk -- 4.9 Variogram clouds and h-scatterplots -- 4.10 Variogram models -- 4.11 Fitting variogram models -- 4.12 Variogram case study -- 4.12 Variogram case study -- 4.13 Anisotropy and variograms -- 4.13.1 Variogram surfaces -- 4.13.2 Geometric and zonal anisotropy -- 4.14 Variograms and non-stationarity -- 4.14.1 Variograms and long-range trends -- 4.14.2 Variogram non-stationarity -- 4.15 Space-time variograms -- 4.16 Software -- 4.17 Other methods -- 4.18 Point pattern analysis -- 4.18.1 Spatial dependence and point patterns -- 4.18.2 Local function -- 4.18.3 Cross function -- 4.19 Summary -- 4.20 Further reading -- References -- 5 Scale and Multivariate Data -- 5.1 Regression frameworks -- 5.2 Spatial scale and regression -- 5.3 Global regression -- 5.4 Spatial regression -- 5.5 Regression and spatial data -- 5.5.1 Generalised least squares -- 5.5.2 Spatial autoregressive models -- 5.5.3 Spatially lagged dependent variable models and spatial error models case study -- 5.6 Local regression and spatial scale -- 5.6.1 Spatial expansion method -- 5.6.2 Geographically weighted regression -- 5.6.3 Scale and GWR -- 5.6.4 GWR case study: fixed bandwidths -- 5.6.5 GWR case study: variable bandwidths -- 5.6.6 Bayesian spatially varying coefficient process models -- 5.7 Multilevel modelling -- 5.7.1 Case study -- 5.8 Spatial structure of multiple variables -- 5.9 Multivariate analysis and spatial scale -- 5.10 Summary -- 5.11 Further reading -- References -- 6 Fractal Analysis -- 6.1 Basic concepts -- 6.2 Measuring fractal dimension -- 6.2.1 Walking-divider method -- 6.2.2 Box-counting method -- 6.2.3 Variogram method -- 6.3 Fractals and spatial structure -- 6.3.1 Case study: fractal of land surfaces -- 6.3.2 Case study: local fractal.

6.3.3 Fractals and topographic form -- 6.4 Other applications of fractal analysis -- 6.4.1 Fractals and remotely sensed imagery -- 6.4.2 Fractals and urban form -- 6.5 How useful is the fractal model in geography? -- 6.6 Summary -- 6.7 Further reading -- References -- 7 Scale and Gridded Data: Fourier and Wavelet Transforms -- 7.1 Basic concepts -- 7.2 Fourier transforms -- 7.2.1 Continuous Fourier transform -- 7.2.2 Discrete Fourier transform -- 7.2.3 Fast Fourier transform -- 7.2.4 FFT case study -- 7.2.5 Spectral analysis and the covariance function -- 7.2.6 Spectral analysis case study -- 7.3 Wavelet transforms -- 7.3.1 Continuous wavelet transforms -- 7.3.2 Discrete wavelet transforms -- 7.3.3 The Haar basis functions -- 7.3.4 Other basis functions -- 7.3.5 Fast wavelet transform -- 7.3.6 Two-dimensional wavelet transforms -- 7.4 Wavelet analysis applications and other issues -- 7.5 Summary -- 7.6 Further reading -- References -- 8 Areal Interpolation -- 8.1 Basic concepts -- 8.2 Areal weighting -- 8.3 Using additional data -- 8.3.1 Types of secondary data sources for mapping populations -- 8.4 Surface modelling -- 8.4.1 Population surface case study -- 8.5 Other approaches to changing support -- 8.6 Summary -- 8.7 Further reading -- References -- 9 Geostatistical Interpolation and Change of Support -- 9.1 Basic concepts -- 9.2 Regularisation -- 9.2.1 Regularisation with an irregular support -- 9.3 Variogram deconvolution -- 9.3.1 Variogram deconvolution for irregular supports -- 9.3.2 Variography and change of support -- 9.4 Kriging -- 9.4.1 Punctual kriging -- 9.4.2 Poisson kriging -- 9.4.3 Factorial kriging -- 9.4.4 Factorial kriging case study -- 9.4.5 Kriging in the presence of a trend -- 9.4.6 Cokriging -- 9.4.7 Kriging with an external drift and other techniques -- 9.4.8 Interpreting the kriging variance -- 9.4.9 Cross-validation.

9.4.10 Conditional simulation -- 9.4.11 Comparison of kriging approaches -- 9.5 Kriging and change of support -- 9.5.1 Block kriging -- 9.5.2 Area-to-point kriging -- 9.5.3 Case study -- 9.6 Assessing uncertainty and optimal sampling design -- 9.6.1 Nested sampling -- 9.6.2 Assessing optimal sampling design -- 9.6.3 Optimal spatial resolution -- 9.6.4 Other approaches to optimal sampling design -- 9.7 Summary -- 9.8 Further reading -- References -- 10 Summary and Conclusions -- 10.1 Overview of key concepts and methods -- 10.2 Problems and future directions -- 10.3 Summary -- References -- Index -- Supplemental Images.