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| List of tables and displays | |
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| Preface | |
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| Acknowledgements | |
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| Introduction to issues in the analysis of spatially referenced data | |
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| Introduction | |
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| Notes | |
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| Issues in analysing spatial data | |
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| Spatial data: sources, forms and storage | |
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| Sources: quality and quantity | |
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| Forms and attributes | |
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| Data storage | |
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| Spatial data analysis | |
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| The importance of space in the social and environmental sciences | |
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| Measurement error | |
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| Continuity effects and spatial heterogeneity | |
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| Spatial processes | |
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| Types of analytical problems | |
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| Problems in spatial data analysis | |
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| Conceptual models and inference frameworks for spatial data | |
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| Modelling spatial variation | |
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| Statistical modelling of spatial data | |
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| Dependency in spatial data | |
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| Spatial heterogeneity: regional subdivisions and parameter variation | |
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| Spatial distribution of data points and boundary effects | |
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| Assessing model fit | |
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| Distributions | |
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| Extreme data values | |
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| Model sensitivity to the areal system | |
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| Size-variance relationships in homogeneous aggregates | |
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| A statistical framework for spatial data analysis | |
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| Data adaptive modelling | |
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| Robust and resistant parameter estimation | |
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| Robust estimation of the centre of a symmetric distribution | |
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| Robust estimation of regression parameters | |
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| Notes | |
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| Parametric models for spatial variation | |
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| Statistical models for spatial populations | |
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| Models for spatial populations: preliminary considerations | |
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| Spatial stationarity and isotropy | |
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| Second order (weak) stationarity and isotropy | |
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| Second order (weak) stationarity and isotropy of differences from the mean | |
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| Second order (weak) stationarity and isotropy of increments | |
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| Order relationships in one and two dimensions | |
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| Population models for continuous random variables | |
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| Models for the mean of a spatial population | |
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| Trend surface models | |
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| Regression model | |
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| Models for second order or stochastic variation of a spatial population | |
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| Interaction models for V of a MVN distribution | |
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| Interaction models for other multivariate distributions | |
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| Direct specification of V | |
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| Intrinsic random functions | |
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| Population models for discrete random variables | |
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| Boundary models for spatial populations | |
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| Edge structures, weighting schemes and the dispersion matrix | |
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| Conclusions: issues in representing spatial variation | |
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| Notes | |
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| Simulating spatial models | |
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| Statistical analysis of spatial populations | |
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| Model selection | |
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| Statistical inference with interaction schemes | |
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| Parameter estimation: maximum likelihood (ML) methods | |
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| [mu] unknown; V known | |
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| [mu] known; V unknown | |
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| [mu] and V unknown | |
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| Models with non-constant variance | |
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| Parameter estimation: other methods | |
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| Ordinary least squares and pseudo-likelihood estimators | |
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| Coding estimators | |
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| Moment estimators | |
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| Parameter estimation: discrete valued interaction models | |
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| Properties of ML estimators | |
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| Large sample properties | |
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| Small sample properties | |
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| A note on boundary effects | |
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| Hypothesis testing for interaction schemes | |
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| Likelihood ratio tests | |
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| Lagrange multiplier tests | |
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| Statistical inference with covariance functions and intrinsic random functions | |
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| Parameter estimation: maximum likelihood methods | |
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| Parameter estimation: other methods | |
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| Properties of estimators and hypothesis testing | |
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| Validation in spatial models | |
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| The consequences of ignoring spatial correlation in estimating the mean | |
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| Notes | |
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| Spatial data collection and preliminary analysis | |
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| Sampling spatial populations | |
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| Introduction | |
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| Spatial sampling designs | |
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| Point sampling | |
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| Quadrat and area sampling | |
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| Sampling spatial surfaces: estimating the mean | |
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| Fixed populations with trend or periodicity | |
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| Populations with second order variation | |
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| Results for one-dimensional series | |
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| Results for two-dimensional surfaces | |
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| Standard errors for confidence intervals and selecting sample size | |
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| Sampling spatial surfaces: second order variation | |
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| Kriging | |
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| Scales of variation | |
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| Sampling applications | |
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| Concluding comments | |
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| Preliminary analysis of spatial data | |
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| Preliminary data analysis: distributional properties and spatial arrangement | |
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| Univariate data analysis | |
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| General distributional properties | |
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| Spatial outliers | |
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| Spatial trends | |
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| Second order non-stationarity | |
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| Regional subdivisions | |
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| Multivariate data analysis | |
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| Data transformations | |
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| Preliminary data analysis: detecting spatial pattern, testing for spatial autocorrelation | |
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| Available test statistics | |
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| Constructing a test | |
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| Interpretation | |
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| Choosing a test | |
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| Describing spatial variation: robust estimation of spatial variation | |
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| Robust estimators of the semi-variogram | |
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| Robust estimation of covariances | |
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| Concluding remarks | |
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| Notes | |
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| Modelling spatial data | |
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| Analysing univariate data sets | |
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| Describing spatial variation | |
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| Non-stationary mean, stationary second order variation: trend surface models with correlated errors | |
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| Non-stationary mean, stationary increments: semi-variogram models and polynomial generalised covariance functions | |
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| Discrete data | |
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| Interpolation and estimating missing values | |
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| Ad hoc and cartographic techniques | |
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| Distribution based techniques | |
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| Sequential approaches (sampling a continuous surface) | |
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| Simultaneous approaches | |
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| Extensions | |
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| Obtaining areal properties | |
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| Reconciling data sets on different areal frameworks | |
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| Categorical data | |
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| Other information for interpolation | |
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| Notes | |
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| Analysing multivariate data sets | |
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| Measures of spatial correlation and spatial association | |
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| Correlation measures | |
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| Measures of association | |
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| Regression modelling | |
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| Problems due to the assumptions of least squares not being satisfied | |
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| Problems of model specification and analysis | |
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| Model discrimination | |
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| Specifying W | |
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| Parameter estimation and inference | |
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| Model evaluation | |
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| Interpretation problems | |
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| Problems due to data characteristics | |
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| Numerical problems | |
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| Regression applications | |
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| Model diagnostics and model revision (a) new explanatory variables | |
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| Model diagnostics and model revision (b) developing a spatial regression model | |
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| Regression modelling with census variables: Glasgow health data | |
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| Identifying spatial interaction and heterogeneity: Sheffield petrol price data | |
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| Notes | |
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| Robust estimation of the parameters of interaction schemes | |
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| Postscript | |
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| Glossary | |
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| References | |
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| Index | |