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Modelling Spatial and Spatial-Temporal Data: A Bayesian Approach

Modelling Spatial and Spatial-Temporal Data: A Bayesian Approach

Wydawnictwo Apple Academic Press Inc.
Data wydania 07/02/2020
Liczba stron 608
Forma publikacji książka w twardej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
ISBN 9781482237429
Kategorie Metodyka psychologiczna, Statystyka ekonomiczna, Prawdopodobieństwo i statystyka
661.00 PLN (z VAT)
$165.94 / €146.24 / £121.78 /
Produkt na zamówienie
Dostawa 14 dni
Do schowka

Opis książki

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 small-area 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. 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 the 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.

Modelling Spatial and Spatial-Temporal Data: A Bayesian Approach

Spis treści


Section I. Fundamentals for modelling spatial and spatial-temporal data

1. Challenges and opportunities analysing spatial and spatial-temporal data


Four main challenges when analysing spatial and spatial-temporal data



Data sparsity


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


2. Concepts for modelling spatial and spatial-temporal data: an introduction to "spatial thinking"


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


Appendix: Geographic Information Systems

3. The nature of spatial and spatial-temporal attribute data


Data collection processes in the social sciences

Natural 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


4. Specifying spatial relationships on the map: the weights matrix


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



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


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


Section II Modelling spatial data

6. Exploratory analysis of spatial data


Techniques for the exploratory analysis of univariate spatial data


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 for spatial heterogeneity in the spatial dependence structure: detecting local spatial clusters

The Local Moran's I

The multiple testing problem when using local Moran's I

Kulldorff's spatial scan statistic

Exploring relationships between variables:

Scatterplots and the bivariate Moran scatterplot

Quantifying bivariate association

The Clifford-Richardson test of bivariate correlation in the presence of spatial autocorrelation

Testing for association "at a distance" and the global bivariate Moran's I

Checking for spatial heterogeneity in the outcome-covariate relationship: Geographically weighted regression (GWR)

Overdispersion and zero-inflation in spatial count data

Testing for overdispersion

Testing for zero-inflation

Concluding remarks


Appendix: An R function to perform the zero-inflation test by van den Broek (1995)

7. Bayesian models for spatial data I: Non-hierarchical and exchangeable hierarchical models


Estimating small area income: a motivating example and different modelling strategies

Modelling the 109 parameters non-hierarchically

Modelling the 109 parameters hierarchically

Modelling the Newcastle income data using non-hierarchical models

An identical parameter model based on Strategy 1

An independent parameters model based on Strategy 2

An exchangeable hierarchical model based on Strategy 3

The logic of information borrowing and shrinkage

Explaining the nature of global smoothing due to exchangeability

The variance partition coefficient (VPC)

Applying an exchangeable hierarchical model to the Newcastle income data

Concluding remarks


Appendix: Obtaining the simulated household income data

8. Bayesian models for spatial data II: hierarchical models with spatial dependence


The intrinsic conditional autoregressive (ICAR) model

The ICAR model using a spatial weights matrix with binary entries

The WinBUGS implementation of the ICAR model

Applying the ICAR model using spatial contiguity to the Newcastle income data


A summary of the properties of the ICAR model using a binary spatial weights matrix

The ICAR model with a general weights matrix

Expressing the ICAR model as a joint distribution and the implied restriction on W

The sum-to-zero constraint

Applying the ICAR model using general weights to the Newcastle income data


The proper CAR (pCAR) model

Prior choice for ?


Applying the pCAR model to the Newcastle income data


Locally adaptive models

Choosing an optimal W matrix from all possible specifications

Modelling the elements of the W matrix

Applying some of the locally adaptive spatial models to a subset of the Newcastle income data

The Besag, York and Mollie (BYM) model

Two remarks on applying the BYM model in practice

Applying the BYM model to the Newcastle income data

Comparing the fits of different Bayesian spatial models

DIC comparison

Model comparison based on the quality of the MSOA-level average income estimates

Concluding remarks


9. Bayesian hierarchical models for spatial data: applications


Application 1: Modelling the distribution of high intensity crime areas in a city


Data and exploratory analysis

Methods discussed in Haining and Law (2007) to combine the PHIA and EHIA maps

A joint analysis of the PHIA and EHIA data using the MVCAR model


Another specification of the MVCAR model and a limitation of the MVCAR approach

Conclusion and discussion

Application 2: Modelling the association between air pollution and stroke mortality

Background and data


Interpreting the statistical results

Conclusion and discussion

Application 3: Modelling the village-level incidence of malaria in a small region of India


Data and exploratory analysis

Model I: A Poisson regression model with random effects

Model II: A two-component Poisson mixture model

Model III: A two-component Poisson mixture model with zero-inflation


Conclusion and model extensions

Application 4: Modelling the small area count of cases of rape in Stockholm, Sweden

Background and data


"whole map" analysis using Poisson regression

"localised" analysis using Bayesian profile regression


"Whole map" associations for the risk factors

"Local" associations for the risk factors



10. Spatial econometric models


Spatial econometric models

Three forms of spatial spillover

The spatial lag model (SLM)

Formulating the model

An example of the SLM

The reduced form of the SLM and the constraint on?

Specification of the spatial weights matrix

Issues with model fitting and interpreting coefficients

The spatially lagged covariates model (SLX)

Formulating the model

An example of the SLX model

The spatial error model (SEM)

The spatial Durbin model (SDM)

Formulating the model

Relating the SDM model to the other three spatial econometric models

Prior specifications

An example: modelling cigarette sales in 46 US states

Data description, exploratory analysis and model specifications


Interpreting covariate effects

Definitions of the direct, indirect and total effects of a covariate

Measuring direct and indirect effects without the SAR structure on the outcome variables

For the LM and SEM models

For the SLX model

Measuring direct and indirect effects when the outcome variables are modelled by the SAR structure

Understanding direct and indirect effects in the presence of spatial feedback

Calculating the direct and indirect effects in the presence of spatial feedback

Some properties of direct and indirect effects

A property (limitation) of the average direct and average indirect effects under the SLM model


The estimated effects from the cigarette sales data

Model fitting in WinBUGS

Derivation of the likelihood function

Simplifications to the likelihood function

The zeros-trick in WinBUGS

Calculating the covariate effects in WinBUGS

Concluding remarks

Other spatial econometric models and two problems of identifiability

Comparing the hierarchical modelling approach and the spatial econometric modelling approach: a summary


11. Spatial Econometric Modelling: applications

Application 1: Modelling the voting outcomes at the local authority district level in England from the 2016 EU referendum



Exploratory data analysis

Modelling using spatial econometric models


Conclusion and discussion

Application 2: Modelling price competition between petrol retail outlets in a large city



Exploratory data analysis

Spatial econometric modelling and results

A spatial hierarchical model with t4 likelihood

Conclusion and discussion

Final remarks on spatial econometric modelling of spatial data


Appendix: Petrol price data

Section III Modelling spatial-temporal data

12. Modelling spatial-temporal data: an introduction


Modelling annual counts of burglary cases at the small area level: a motivating example and frameworks for modelling spatial-temporal data

Modelling small area temporal data

Issues to consider when modelling temporal patterns in the small area setting

Issues relating to temporal dependence

Issues relating to temporal heterogeneity and spatial heterogeneity in modelling small area temporal patterns

Issues relating to flexibility of a temporal model

Modelling small area temporal patterns: setting the scene

A linear time trend model

Model formulations

Modelling trends in the Peterborough burglary data

Results from fitting the linear trend model without temporal noise

Results from fitting the linear trend model with temporal no

Random walk models

Model formulations

The RW(1) model: its formulation via the full conditionals and its properties

WinBUGS implementation of the RW(1) model

Example: modelling burglary trends using the Peterborough data

The random walk model of order 2

Interrupted time series (ITS) models

Quasi-experimental designs and the purpose of ITS modelling

Model formulations

WinBUGS implementation


Concluding remarks


Appendix Three different forms for specifying the impact function, f

13. Exploratory analysis of spatial-temporal data


Patterns of spatial-temporal data

Visualizing spatial-temporal datayou

Tests of space-time interaction

The Knox test

An instructive example of the Knox test and different methods to derive a p-value

Applying the Knox test to the malaria data

Kulldorff's space-time scan statistic

Application: the simulated small area COPD mortality data

Assessing space-time interaction in the form of varying local time trend patterns

Exploratory analysis of the local trends in the Peterborough burglary data

Exploratory analysis of the local time trends in the England COPD mortality data

Concluding remarks


14. Bayesian hierarchical models for spatial-temporal data I: space-time separable models


Estimating small area burglary rates over time: setting the scene

The space-time separable modelling framework

Model formulations

Do we combine the space and time components additively or multiplicatively?

Analysing the Peterborough burglary data using a space-time separable model


Concluding remarks


15. Bayesian hierarchical models for spatial-temporal data II: space-time inseparable models


From space-time separability to space-time inseparability: the big picture

Type I space-time interaction

Example: a space-time model with Type I space-time interaction

WinBUGS implementation

Type II space-time interaction

Example: two space-time models with Type II space-time interaction

WinBUGS implementation

Type III space-time interaction

Example: a space-time model with Type III space-time interaction

WinBUGS implementation

Results from analysing the Peterborough burglary data: Part I

Type IV space-time interaction

Strategy 1: extending Type II to Type IV

Strategy 2: extending Type III to Type IV

Examples of strategy 2

Strategy 3: Clayton's rule

Structure matrices and Gaussian Markov random fields

Taking the Kronecker product

Exploring the induced space-time dependence structure via the full conditionals

Summary on Type IV space-time interaction

Concluding remarks


16. Modelling spatial-temporal data: applications


Application 1: evaluating a targeted crime reduction intervention

Background and data

Constructing different control groups

Evaluation using ITS

WinBUGS implementation


Some remarks

Application 2: assessing the stability of risk in space and time

Studying the temporal dynamics of crime hotspots and coldspots: background, data and the modelling idea

Model formulations

Classification of areas

Model implementation and area classification

Interpreting the statistical results

Application 3: detecting unusual local time patterns in small area data

Small area disease surveillance: background and modelling idea

Model formulation

Detecting unusual areas with a control of the false discovery rate

Fitting BaySTDetect in WinBUGS

A simulated dataset to illustrate the use of BaySTDetect

Results from the simulated dataset

General results from Li et al. (2012) and an extension of BaySTDetect

Application 4: Investigating the presence of spatial-temporal spillover effects on village-level malaria risk in Kalaburagi, Karnataka, India

Background and study objective




Concluding remarks


Section IV Directions in spatial and spatial-temporal data analysis

17. Modelling spatial and spatial-temporal data: Future agendas?

Topic 1: Modelling multiple related outcomes over space and time

Topic 2: Joint modelling of georeferenced longitudinal and time-to-event data

Topic 3: Multiscale modelling

Topic 4: Using survey data for small area estimation

Topic 5: Combining data at both aggregate and individual levels to improve ecological inference

Topic 6: Geostatistical modelling

Spatial dependence

Mapping to reduce visual bias

Modelling scale effects

Topic 7: Modelling count data in spatial econometrics

Topic 8: Computation

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