| List of tables and displays | p. xiii |
| Preface | p. xviii |
| Acknowledgements | p. xx |
| Introduction to issues in the analysis of spatially referenced data | |
| Introduction | p. 3 |
| Notes | p. 10 |
| Issues in analysing spatial data | p. 12 |
| Spatial data: sources, forms and storage | p. 13 |
| Sources: quality and quantity | p. 13 |
| Forms and attributes | p. 17 |
| Data storage | p. 18 |
| Spatial data analysis | p. 21 |
| The importance of space in the social and environmental sciences | p. 21 |
| Measurement error | p. 21 |
| Continuity effects and spatial heterogeneity | p. 22 |
| Spatial processes | p. 24 |
| Types of analytical problems | p. 26 |
| Problems in spatial data analysis | p. 32 |
| Conceptual models and inference frameworks for spatial data | p. 32 |
| Modelling spatial variation | p. 37 |
| Statistical modelling of spatial data | p. 40 |
| Dependency in spatial data | p. 40 |
| Spatial heterogeneity: regional subdivisions and parameter variation | p. 43 |
| Spatial distribution of data points and boundary effects | p. 44 |
| Assessing model fit | p. 45 |
| Distributions | p. 46 |
| Extreme data values | p. 46 |
| Model sensitivity to the areal system | p. 47 |
| Size-variance relationships in homogeneous aggregates | p. 49 |
| A statistical framework for spatial data analysis | p. 50 |
| Data adaptive modelling | p. 50 |
| Robust and resistant parameter estimation | p. 54 |
| Robust estimation of the centre of a symmetric distribution | p. 55 |
| Robust estimation of regression parameters | p. 56 |
| Notes | p. 61 |
| Parametric models for spatial variation | |
| Statistical models for spatial populations | p. 65 |
| Models for spatial populations: preliminary considerations | p. 66 |
| Spatial stationarity and isotropy | p. 66 |
| Second order (weak) stationarity and isotropy | p. 66 |
| Second order (weak) stationarity and isotropy of differences from the mean | p. 67 |
| Second order (weak) stationarity and isotropy of increments | p. 67 |
| Order relationships in one and two dimensions | p. 69 |
| Population models for continuous random variables | p. 75 |
| Models for the mean of a spatial population | p. 75 |
| Trend surface models | p. 75 |
| Regression model | p. 76 |
| Models for second order or stochastic variation of a spatial population | p. 80 |
| Interaction models for V of a MVN distribution | p. 80 |
| Interaction models for other multivariate distributions | p. 90 |
| Direct specification of V | p. 90 |
| Intrinsic random functions | p. 94 |
| Population models for discrete random variables | p. 99 |
| Boundary models for spatial populations | p. 101 |
| Edge structures, weighting schemes and the dispersion matrix | p. 110 |
| Conclusions: issues in representing spatial variation | p. 113 |
| Notes | p. 115 |
| Simulating spatial models | p. 116 |
| Statistical analysis of spatial populations | p. 118 |
| Model selection | p. 118 |
| Statistical inference with interaction schemes | p. 123 |
| Parameter estimation: maximum likelihood (ML) methods | p. 123 |
| [mu] unknown; V known | p. 123 |
| [mu] known; V unknown | p. 124 |
| [mu] and V unknown | p. 127 |
| Models with non-constant variance | p. 129 |
| Parameter estimation: other methods | p. 130 |
| Ordinary least squares and pseudo-likelihood estimators | p. 130 |
| Coding estimators | p. 131 |
| Moment estimators | p. 133 |
| Parameter estimation: discrete valued interaction models | p. 134 |
| Properties of ML estimators | p. 134 |
| Large sample properties | p. 134 |
| Small sample properties | p. 135 |
| A note on boundary effects | p. 137 |
| Hypothesis testing for interaction schemes | p. 142 |
| Likelihood ratio tests | p. 142 |
| Lagrange multiplier tests | p. 145 |
| Statistical inference with covariance functions and intrinsic random functions | p. 147 |
| Parameter estimation: maximum likelihood methods | p. 150 |
| Parameter estimation: other methods | p. 151 |
| Properties of estimators and hypothesis testing | p. 154 |
| Validation in spatial models | p. 158 |
| The consequences of ignoring spatial correlation in estimating the mean | p. 161 |
| Notes | p. 166 |
| Spatial data collection and preliminary analysis | |
| Sampling spatial populations | p. 171 |
| Introduction | p. 171 |
| Spatial sampling designs | p. 175 |
| Point sampling | p. 175 |
| Quadrat and area sampling | p. 177 |
| Sampling spatial surfaces: estimating the mean | p. 177 |
| Fixed populations with trend or periodicity | p. 178 |
| Populations with second order variation | p. 178 |
| Results for one-dimensional series | p. 180 |
| Results for two-dimensional surfaces | p. 181 |
| Standard errors for confidence intervals and selecting sample size | p. 183 |
| Sampling spatial surfaces: second order variation | p. 186 |
| Kriging | p. 186 |
| Scales of variation | p. 189 |
| Sampling applications | p. 191 |
| Concluding comments | p. 195 |
| Preliminary analysis of spatial data | p. 197 |
| Preliminary data analysis: distributional properties and spatial arrangement | p. 198 |
| Univariate data analysis | p. 198 |
| General distributional properties | p. 200 |
| Spatial outliers | p. 214 |
| Spatial trends | p. 215 |
| Second order non-stationarity | p. 222 |
| Regional subdivisions | p. 223 |
| Multivariate data analysis | p. 223 |
| Data transformations | p. 227 |
| Preliminary data analysis: detecting spatial pattern, testing for spatial autocorrelation | p. 228 |
| Available test statistics | p. 228 |
| Constructing a test | p. 231 |
| Interpretation | p. 234 |
| Choosing a test | p. 237 |
| Describing spatial variation: robust estimation of spatial variation | p. 239 |
| Robust estimators of the semi-variogram | p. 241 |
| Robust estimation of covariances | p. 244 |
| Concluding remarks | p. 244 |
| Notes | p. 245 |
| Modelling spatial data | |
| Analysing univariate data sets | p. 249 |
| Describing spatial variation | p. 250 |
| Non-stationary mean, stationary second order variation: trend surface models with correlated errors | p. 251 |
| Non-stationary mean, stationary increments: semi-variogram models and polynomial generalised covariance functions | p. 282 |
| Discrete data | p. 288 |
| Interpolation and estimating missing values | p. 291 |
| Ad hoc and cartographic techniques | p. 293 |
| Distribution based techniques | p. 296 |
| Sequential approaches (sampling a continuous surface) | p. 297 |
| Simultaneous approaches | p. 304 |
| Extensions | p. 307 |
| Obtaining areal properties | p. 307 |
| Reconciling data sets on different areal frameworks | p. 309 |
| Categorical data | p. 310 |
| Other information for interpolation | p. 310 |
| Notes | p. 311 |
| Analysing multivariate data sets | p. 313 |
| Measures of spatial correlation and spatial association | p. 313 |
| Correlation measures | p. 313 |
| Measures of association | p. 324 |
| Regression modelling | p. 330 |
| Problems due to the assumptions of least squares not being satisfied | p. 334 |
| Problems of model specification and analysis | p. 339 |
| Model discrimination | p. 341 |
| Specifying W | p. 341 |
| Parameter estimation and inference | p. 344 |
| Model evaluation | p. 347 |
| Interpretation problems | p. 348 |
| Problems due to data characteristics | p. 348 |
| Numerical problems | p. 349 |
| Regression applications | |
| Model diagnostics and model revision (a) new explanatory variables | p. 350 |
| Model diagnostics and model revision (b) developing a spatial regression model | p. 354 |
| Regression modelling with census variables: Glasgow health data | p. 365 |
| Identifying spatial interaction and heterogeneity: Sheffield petrol price data | p. 372 |
| Notes | p. 383 |
| Robust estimation of the parameters of interaction schemes | p. 384 |
| Postscript | p. 386 |
| Glossary | p. 389 |
| References | p. 391 |
| Index | p. 406 |
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