Modelling Spatial and Spatial-Temporal Data: A Bayesian Approach is aimed at statisticians and quantitative social, economic and public health students and researchers who work with spatial and spatial-temporal data. It assumes a grounding in statistical theory up to the standard linear regression model. The book compares both hierarchical and spatial econometric modelling, providing both a reference and a teaching text with exercises in each chapter. The book provides a fully Bayesian, self-contained, treatment of the underlying statistical theory, with chapters dedicated to substantive applications. The book includes WinBUGS code and R code and all datasets are available online.
Part I covers fundamental issues arising when modelling spatial and spatial-temporal data. Part II focuses on modelling cross-sectional spatial data and begins by describing exploratory methods that help guide the modelling process. There are then two theoretical chapters on Bayesian models and a chapter of applications. Two chapters follow on spatial econometric modelling, one describing different models, the other substantive applications. Part III discusses modelling spatial-temporal data, first introducing models for time series data. Exploratory methods for detecting different types of space-time interaction are presented followed by two chapters on the theory of space-time separable (without space-time interaction) and inseparable (with space-time interaction) models. An applications chapter includes: the evaluation of a policy intervention; analysing the temporal dynamics of crime hotspots; chronic disease surveillance; and testing for evidence of spatial spillovers in the spread of an infectious disease. A final chapter suggests some future directions and challenges.
Autorentext
Robert Haining is Emeritus Professor in Human Geography, University of Cambridge, England. He is the author of Spatial Data Analysis in the Social and Environmental Sciences (1990) and Spatial Data Analysis: Theory and Practice (2003). He is a Fellow of the RGS-IBG and of the Academy of Social Sciences.
Guangquan Li is Senior Lecturer in Statistics in Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle, England. His research includes the development and application of Bayesian methods in the social and health sciences. He is a Fellow of the Royal Statistical Society.
Inhalt
Preface
Section I. Fundamentals for modelling spatial and spatial-temporal data
1. Challenges and opportunities analysing spatial and spatial-temporal data
Introduction
Four main challenges when analysing spatial and spatial-temporal data
Dependency
Heterogeneity
Data sparsity
Uncertainty
Data uncertainty
Model (or process) uncertainty
Parameter uncertainty
Opportunities arising from modelling spatial and spatial-temporal data
Improving statistical precision
Explaining variation in space and time
Example 1: Modelling exposure-outcome relationships
Example 2: Testing a conceptual model at the small area level
Example 3: Testing for spatial spillover (local competition) effects
Example 4: Assessing the effects of an intervention
Investigating space-time dynamics
Spatial and spatial-temporal models: bridging between challenges and opportunities
Statistical thinking in analysing spatial and spatial-temporal data: the big picture
Bayesian thinking in a statistical analysis
Bayesian hierarchical models
Thinking hierarchically
The data model
The process model
The parameter model
Incorporating spatial and spatial-temporal dependence structures in a Bayesian hierarchical model using random effects
Information sharing in a Bayesian hierarchical model through random effects
Bayesian spatial econometrics
Concluding remarks
The datasets used in the book
Exercises
2. Concepts for modelling spatial and spatial-temporal data: an introduction to "spatial thinking"
Introduction
Mapping data and why it matters
Thinking spatially
Explaining spatial variation
Spatial interpolation and small area estimation
Thinking spatially and temporally
Explaining space-time variation
Estimating parameters for spatial-temporal units
Concluding remarks
Exercises
Appendix: Geographic Information Systems
3. The nature of spatial and spatial-temporal attribute data
Introduction
Data collection processes in the social sciences
Natural experiments
Quasi-experiments
Non-experimental observational studies
Spatial and spatial-temporal data: properties
From geographical reality to the spatial database
Fundamental properties of spatial and spatial-temporal data
Spatial and temporal dependence.
Spatial and temporal heterogeneity
Properties induced by representational choices
Properties induced by measurement processes
Concluding remarks
Exercises
4. Specifying spatial relationships on the map: the weights matrix
Introduction
Specifying weights based on contiguity
Specifying weights based on geographical distance
Specifying weights based on the graph structure associated with a set of points
Specifying weights based on attribute values
Specifying weights based on evidence about interactions
Row standardisation
Higher order weights matrices
Choice of W and statistical implications
Implications for small area estimation
Implications for spatial econometric modelling
Implications for estimating the effects of observable covariates on the outcome
Estimating the W matrix
Concluding remarks
Exercises
Appendices
Appendix: Building a geodatabase in R
Appendix: Constructing the W matrix and accessing data stored in a shapefile
5. Introduction to the Bayesian approach to regression modelling with spatial and spatial-temporal data
Introduction
Introducing Bayesian analysis
Prior, likelihood and posterior: what do these terms refer to?
Example: modelling high-intensity crime areas
Bayesian computation
Summarizing the posterior distribution
Integration and Monte Carlo integration
Markov chain Monte Carlo with Gibbs sampling
Introduction to WinBUGS
Practical considerations when fitting models in WinBUGS
Setting the initial values
Checking convergence
Checking efficiency
Bayesian regression models
Example I: modelling household-level income
Example II: modelling annual burglary rates in small areas
Bayesian model comparison and model evaluation
Prior specifications
When we have little prior information
Towards more informative priors for spatial and spatial-temporal data
Concluding remarks
Exercises
Section II Modelling spatial data
6. Exploratory analysis of spatial data
Introduction
Techniques for the exploratory analysis of univariate spatial data
Mapping
Checking for spatial trend
Checking for spatial heterogeneity in the mean
Count data
A Monte Carlo test
Continuous-valued data
Checking for global spatial dependence (spatial autocorrelation)
The Moran scatterplot
The global Moran's I statistic
Other test statistics for assessing global spatial autocorrelation
The join-count test for categorical data
The global Moran's I applied to regression residuals
Checking …