Modelling spatial and spatial-temporal data: a Bayesian approach
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| Format: | Book |
| Language: | English |
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Boca Raton ; London ; New York
CRC Press
[2021]
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| Edition: | First issued in paperback 2021 |
| Series: | Chapman and Hall/CRC, Statistics in the social and behavioral sciences
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | References S. 577-596, Index S. 597-608 |
| Physical Description: | xxvi, 608 Seiten Illustrationen, Diagramme, Karten |
| ISBN: | 9781032175003 |
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| adam_text | Contents Preface...........................................................................................................................................................χίχ Acknowledgements.........................................................................................................xxv Part I Fundamentals for Modelling Spatial and Spatial-Temporal Data 1 Challenges and Opportunities Analysing Spatial and Spatial-Temporal Data...... 3 1.1 Introduction........................................................................................................ 3 1.2 Four Main Challenges When Analysing Spatial and Spatial-Temporal Data.........................................................................................4 1.2.1 Dependency............................................................................................ 4 1.2.2 Heterogeneity.........................................................................................8 1.2.3 Data Sparsity.......................................................................................... 10 1.2.4 Uncertainty............................................................................................12 1.2.4.1 Data Uncertainty .................................................................... 12 1.2.4.2 Model (or Process) Uncertainty.............................................. 13 1.2.4.3 Parameter Uncertainty ........................................................... 13 1.3 Opportunities Arising from Modelling Spatial and Spatial-Temporal Data..........14 1.3.1 Improving Statistical
Precision............................................................. 14 1.3.2 Explaining Variation in Space and Time.............................................. 18 1.3.2.1 Example 1: Modelling Exposure-Outcome Relationships......... 18 1.3.2.2 Example 2: Testing a Conceptual Model at the Small Area Level.....................................................................20 1.3.2.3 Example 3: Testing for Spatial Spillover (Local Competition) Effects .............................................................. 22 1.3.2.4 Example 4: Assessing the Effects of an Intervention.............. 24 1.3.3 Investigating Space-Time Dynamics.................................................... 27 1.4 Spatial and Spatial-Temporal Models: Bridging between Challenges and Opportunities ............................................................................................27 1.4.1 Statistical Thinking in Analysing Spatial and Spatial-Temporal Data: The Big Picture............................................................................. 27 1.4.2 Bayesian Thinking in a Statistical Analysis.......................................... 30 1.4.3 Bayesian Hierarchical Models............................................................... 33 1.4.3.1 Thinking Hierarchically..........................................................33 1.4.3.2 Incorporating Spatial and Spatial-Temporal Dependence Structures in a Bayesian Hierarchical Model Using Random Effects....................................................................... 36 1.4.3.3 Information Sharing in a Bayesian Hierarchical Model
through Random Effects......................................................... 37 1.4.4 Bayesian Spatial Econometrics...............................................................39 1.5 Concluding Remarks......................................................................................... 40 1.6 The Datasets Used in the Book.......................................................................... 41 1.7 Exercises............................................................................................................45 vii
viii Contents 2 Concepts for Modelling Spatial and Spatial-Temporal Data: An Introduction to Spatial Thinking ...............................................................................................47 2.1 Introduction.........................................................................................................47 2.2 Mapping Data and Why It Matters................................................................... 48 2.3 Thinking Spatially............................................................................................ 52 2.3.1 Explaining Spatial Variation................................................................. 52 2.3.2 Spatial Interpolation and Small Area Estimation................................. 54 2.4 Thinking Spatially and Temporally.................................................................. 56 2.4.1 Explaining Space-Time Variation.......................................................... 56 2.4.2 Estimating Parameters for Spatial-Temporal Units...............................59 2.5 Concluding Remarks.........................................................................................59 2.6 Exercises............................................................................................................ 60 Appendix: Geographic Information Systems ............................................................61 3 The Nature of Spatial and Spatial-Temporal Attribute Data..................................63 3.1
Introduction...................................................................................................... 63 3.2 Data Collection Processes in the Social Sciences............................................... 63 3.2.1 Natural Experiments............................................................................. 64 3.2.2 Quasi-Experiments................................................................................67 3.2.3 Non-Experimental Observational Studies............................................ 68 3.3 Spatial and Spatial-Temporal Data: Properties.................................................. 71 3.3.1 From Geographical Reality to the Spatial Database............................. 71 3.3.2 Fundamental Properties of Spatial and Spatial-Temporal Data.............74 3.3.2.1 Spatial and Temporal Dependence.......................................... 74 3.3.2.2 Spatial and Temporal Heterogeneity....................................... 75 3.3.3 Properties Induced by Representational Choices..................................76 3.3.4 Properties Induced by Measurement Processes.................................... 83 3.4 Concluding Remarks.........................................................................................84 3.5 Exercises............................................................................................................84 4 Specifying Spatial Relationships on the Map: The Weights Matrix......................87 4.1 Introduction...................................................................................................... 87 4.2
Specifying Weights Based on Contiguity.......................................................... 88 4.3 Specifying Weights Based on Geographical Distance.......................................90 4.4 Specifying Weights Based on the Graph Structure Associated with a Set of Points.............................................................................................................90 4.5 Specifying Weights Based on Attribute Values.................................................92 4.6 Specifying Weights Based on Evidence about Interactions...............................92 4.7 Row Standardisation......................................................................................... 93 4.8 Higher Order Weights Matrices.........................................................................95 4.9 Choice of W and Statistical Implications........................................................... 97 4.9.1 Implications for Small Area Estimation................................................ 97 4.9.2 Implications for Spatial Econometric Modelling.................................102 4.9.3 Implications for Estimating the Effects of Observable Covariates on the Outcome...................................................................................104 4.10 Estimating the W Matrix................................................................................. 105 4.11 Concluding Remarks....................................................................................... 106 4.12
Exercises...........................................................................................................106 4.13 Appendices...................................................................................................... 107 їх Contents Appendix 4.13.1 Building a Geodatabase in R............................................... 107 Appendix 4.13.2 Constructing the W Matrix and Accessing Data Stored in a Shapefile............................................................................ 110 5 Introduction to the Bayesian Approach to Regression Modelling with Spatial and Spatial-Temporal Data..................................................................................... 115 5.1 Introduction..................................................................................................... 115 5.2 Introducing Bayesian Analysis........................................................................ 116 5.2.1 Prior, Likelihood and Posterior: What Do These Terms Refer To?..... 116 5.2.2 Example: Modelling High-Intensity Crime Areas..............................120 5.3 Bayesian Computation.....................................................................................121 5.3.1 Summarising the Posterior Distribution............................................. 121 5.3.2 Integration and Monte Carlo Integration............................................ 123 5.3.3 Markov Chain Monte Carlo with Gibbs Sampling.............................127 5.3.4 Introduction to WinBUGS................................................................... 129 5.3.5 Practical
Considerations when Fitting Models in WinBUGS..............133 5.3.5.1 Setting the Initial Values....................................................... 133 5.3.5.2 Checking Convergence.......................................................... 134 5.3.5.3 Checking Efficiency...............................................................136 5.4 Bayesian Regression Models........................................................................... 137 5.4.1 Example I: Modelling Household-Level Income..................................138 5.4.2 Example II: Modelling Annual Burglary Rates in Small Areas.......... 143 5.5 Bayesian Model Comparison and Model Evaluation...................................... 147 5.6 Prior Specifications ......................................................................................... 148 5.6.1 When We Have Little Prior Information............................................. 148 5.6.2 Towards More Informative Priors for Modelling Spatial and Spatial-Temporal Data......................................................................... 150 5.7 Concluding Remarks....................................................................................... 151 5.8 Exercises.......................................................................................................... 153 Part II Modelling Spatial Data 6 Exploratory Analysis of Spatial Data.....................................................................159 6.1 Introduction.....................................................................................................159 6.2
Techniques for the Exploratory Analysisof Univariate Spatial Data................160 6.2.1 Mapping...............................................................................................161 6.2.2 Checking for Spatial Trend.................................................................. 165 6.2.3 Checking for Spatial Heterogeneity in the Mean.................................168 6.2.3.1 Count Data............................................................................. 168 6.2.3.2 A Monte Carlo Test.................................................................169 6.2.3.3 Continuous-Valued Data....................................................... 170 6.2.4 Checking for Global Spatial Dependence (Spatial Autocorrelation).... 172 6.2.4.1 The Moran Scatterplot........................................................... 173 6.2.4.2 The Global Moran s I Statistic................................................ 174 6.2.4.3 Other Tests for Assessing Global Spatial Autocorrelation.... 177 6.2.4Ճ The Global Moran s I Applied to Regression Residuals......... 178 6.2.4.5 The Join-Count Test for Categorical Data............................... 179
x Contents Checking for Spatial Heterogeneity in the Spatial Dependence Structure: Detecting Local Spatial Clusters.......................................... 181 6.2.5.1 The Local Moran s 1...................................................................182 6.2.5.2 The Multiple Testing Problem When Using Local Moran s /....185 6.2.5.3 Kulldorff s Spatial Scan Statistic............................................. 186 6.3 Exploring Relationships between Variables......................................................191 6.3.1 Scatterplots and the Bivariate Moran Scatterplot...................................191 6.3.2 Quantifying Bivariate Association.......................................................... 193 6.3.2.1 The Clifford-Richardson Test of Bivariate Correlation in the Presence of Spatial Autocorrelation...................................193 6.3.2.2 Testing for Association At a Distance and the Global Bivariate Moran s 1..................................................................... 195 6.3.3 Checking for Spatial Heterogeneity in the Outcome-Covariate Relationship: Geographically Weighted Regression (GWR)................ 195 6.4 Overdispersion and Zero-Inflation in Spatial Count Data................................203 6.4.1 Testing for Overdispersion...................................................................... 204 6.4.2 Testing for Zero-Inflation........................................................................ 206 6.5 Concluding Remarks............................................................................................ 207 6.6
Exercises................................................................................................................ 209 Appendix. An R Function to Perform the Zero-Inflation Test by van Den Broek (1995)............................................................................................ 210 8.2.1.1 8.2.1.2 6.2.5 7 Bayesian Models for Spatial Data I: Non-Hierarchical and Exchangeable Hierarchical Models.....................................................................................................213 7.1 Introduction..........................................................................................................213 7.2 Estimating Small Area Income: A Motivating Example and Different Modelling Strategies..............................................................................................214 7.2.1 Modelling the 109 Parameters Non-Hierarchically...............................216 7.2.2 Modelling the 109 Parameters Hierarchically....................................... 217 7.3 Modelling the Newcastle Income Data Using Non-Hierarchical Models.......218 7.3.1 An Identical Parameter Model Based on Strategy 1.............................. 218 7.3.2 An Independent Parameters Model Based on Strategy 2..................... 220 7.4 An Exchangeable Hierarchical Model Based on Strategy 3...............................223 7.4.1 The Logic of Information Borrowing and Shrinkage............................224 7.4.2 Explaining the Nature of Global Smoothing Due to
Exchangeability........................................................................................ 225 7.4.3 The Variance Partition Coefficient (VPC)............................................... 226 7.4.4 Applying an Exchangeable Hierarchical Model to the Newcastle Income Data.............................................................................................. 228 7.5 Concluding Remarks............................................................................................ 230 7.6 Exercises................................................................................................................ 230 7.7 Appendix: Obtaining the Simulated Household Income Data......................... 231 8 Bayesian Models for Spatial Data II: Hierarchical Models with Spatial Dependence................................................................................................................... 233 8.1 Introduction........................................................................................................... 233 8.2 The Intrinsic Conditional Autoregressive (ICAR) Model................................. 234 8.2.1 The ICAR Model Using a Spatial Weights Matrix with Binary Entries...................................................................................234 8.3 8.4 8.5 8.6 8.7 8.8 The WinBUGS Implementation of the ICAR Model............. 236 Applying the ICAR Model Using Spatial Contiguity to the Newcastle Income Data......................................................238 8.2.1.3
Results........................................................................................ 240 8.2.1.4 A Summary of the Properties of the ICAR Model Using a Binary Spatial Weights Matrix............................................. 244 8.2.2 The ICAR Model with a General Weights Matrix.................................245 8.2.2.1 Expressing the ICAR Model as a Joint Distribution and the Implied Restriction on W..................................................245 8.2.2.2 The Sum-to-Zero Constraint.....................................................246 8.2.2.3 Applying the ICAR Model Using General Weights to the Newcastle Income Data............................................................ 247 8.2.2.4 Results........................................................................................ 248 The Proper CAR (pCAR) Model..........................................................................249 8.3.1 Prior Choice for p..................................................................................... 251 8.3.2 ICAR or pCAR?........................................................................................ 251 8.3.3 Applying the pCAR Model to the Newcastle Income Data..................253 8.3.4 Results.......................................................................................................253 Locally Adaptive Models..................................................................................... 256 8.4.1 Choosing an Optimal W Matrix from All Possible Specifications......258 8.4.2 Modelling the Elements in the W
Matrix...............................................258 8.4.3 Applying Some of the Locally Adaptive Spatial Models to a Subset of the Newcastle Income Data................................................................. 262 The Besag, York and Mollié (BYM) Model......................................................... 266 8.5.1 Two Remarks on Applying the BYM Model in Practice.......................268 8.5.2 Applying the BYM Model to the Newcastle Income Data.................... 269 Comparing the Fits of Different Bayesian Spatial Models.................................274 8.6.1 DIC Comparison.......................................................................................274 8.6.2 Model Comparison Based on the Quality of the MSOA-Level Average Income Estimates....................................................................... 276 Concluding Remarks............................................................................................ 277 Exercises................................................................................................................ 279 9 Bayesian Hierarchical Models for Spatial Data: Applications............................... 281 9.1 Introduction............................................................................................................281 9.2 Application 1: Modelling the Distribution of High Intensity Crime Areas in a City................................................................................................................. 282 9.2.1
Background............................................................................................... 282 9.2.2 Data and Exploratory Analysis............................................................... 283 9.2.3 Methods Discussed in Haining and Law (2007) to Combine the PHIA and EHIA Maps.............................................................................285 9.2.4 A Joint Analysis of the PHIA and EHIA Data Using the MVCAR Model........................................................................................................ 286 9.2.5 Results.......................................................................................................290 9.2.6 Another Specification of the MVCAR Model and a Limitation of the MVCAR Approach.............................................................................293 9.2.7 Conclusion and Discussion..................................................................... 293 9.3 Application 2: Modelling the Association Between Air Pollution and Stroke Mortality....................................................................................................296
xii 9.4 9.5 9.6 Contents Contents 9.3.1 Background and Data .............................................................................296 9.3.2 Modelling..................................................................................................300 9.3.3 Interpreting the Statistical Results.........................................................302 9.3.4 Conclusion and Discussion..................................................................... 305 Application 3: Modelling the Village-Level Incidence of Malaria in a Small Region of India........................................................................................... 308 9.4.1 Background............................................................................................... 308 9.4.2 Data and Exploratory Analysis............................................................... 308 9.4.3 Model I: A Poisson Regression Model with Random Effects............... 310 9.4.4 Model II: A Two-Component Poisson Mixture Model.......................... 311 9.4.5 Model III: A Two-Component Poisson Mixture Model with Zero-Inflation........................................................................................... 313 9.4.6 Results....................................................................................................... 314 9.4.7 Conclusion and Model Extensions..........................................................318 Application 4: Modelling the Small Area Count of Cases of Rape in Stockholm,
Sweden............................................................................................... 321 9.5.1 Background and Data..............................................................................321 9.5.2 Modelling..................................................................................................322 9.5.2.1 A Whole-Map Analysis Using Poisson Regression............ 322 9.5.2.2 A Localised Analysis Using Bayesian Profile Regression...................................................................... 323 9.5.3 Results.......................................................................................................326 9.5.3.1 Whole Map Associations for theRisk Factors...................... 326 9.5.3.2 Local Associationsfor the Risk Factors.................................326 9.5.4 Conclusions.............................................................................................. 329 Exercises ............................................................................................................... 330 10.3 10 Spatial Econometric Models......................................................................................... 333 10.1 Introduction.......................................................................................................... 333 10.2 Spatial Econometric Models................................................................................ 334 10.2.1 Three Forms of Spatial Spillover............................................................ 334 10.2.2 The Spatial Lag Model
(SLM).................................................................. 335 10.2.2.1 Formulating the Model............................................................. 335 10.2.2.2 An Example of the SLM........................................................... 336 10.2.2.3 The Reduced Form of the SLM and the Constraint on б.......337 10.2.2.4 Specification of the Spatial Weights Matrix.............................338 10.2.2.5 Issues with Model Fitting and Interpreting Coefficients......339 10.2.3 The Spatially-Lagged Covariates Model (SLX)...................................... 339 10.2.3.1 Formulating the Model............................................................. 339 10.2.3.2 An Example of the SLX Model.................................................340 10.2.4 The Spatial Error Model (SEM)............................................................... 340 10.2.5 The Spatial Durbin Model (SDM)........................................................... 341 10.2.5.1 Formulating the Model............................................................. 341 10.2.5.2 Relating the SDM Model to the Other Three Spatial Econometric Models................................................................. 342 10.2.6 Prior Specifications.................................................................................. 342 10.2.7 An Example: Modelling Cigarette Sales in 46 US States.......................343 10.2.7.1 Data Description, Exploratory Analysis and Model Specifications.............................................................................343 10.2.7.2
Results........................................................................................ 345 xiii Interpreting Covariate Effects.............................................................................346 10.3.1 Definitions of the Direct, Indirect and Total Effects of a Covariate...... 346 10.3.2 Measuring Direct and Indirect Effects without the SAR Structure on the Outcome Variables........................................................................347 10.3.2.1 For the LM and SEM Models...................................................347 10.3.2.2 For the SLX Model.....................................................................347 10.3.3 Measuring Direct and Indirect Effects When the Outcome Variables are Modelled by the SAR Structure...................................... 350 10.3.3.1 Understanding Direct and Indirect Effects in the Presence of Spatial Feedback....................................................350 10.3.3.2 Calculating the Direct and Indirect Effects in the Presence of Spatial Feedback....................................................351 10.3.3.3 Some Properties of Direct and Indirect Effects..................... 351 10.3.3.4 A Property (Limitation) of the Average Direct and Average Indirect Effects Under the SLM Model.....................354 10.3.3.5 Summary................................................................................... 354 10.3.4 The Estimated Effects from the Cigarette Sales Data........................... 355 10.4 Model Fitting in
WinBUGS.................................................................................. 356 10.4.1 Derivation of the Likelihood Function...................................................357 10.4.2 Simplifications to the Likelihood Computation.................................... 361 10.4.3 The Zeros-Trick in WinBUGS.................................................................. 361 10.4.4 Calculating the Covariate Effects in WinBUGS.................................... 362 10.5 Concluding Remarks............................................................................................365 10.5.1 Other Spatial Econometric Models and the Two Problems of Identifiability............................................................................................ 365 10.5.2 Comparing the Hierarchical Modelling Approach and the Spatial Econometric Approach: A Summary......................................................367 10.6 Exercises................................................................................................................ 370 11 Spatial Econometric Modelling: Applications......................................................... 373 11.1 Application 1: Modelling the Voting Outcomes at the Local Authority District Level in England from the 2016 EU Referendum................................. 373 11.1.1 Introduction..............................................................................................373 11.1.2 Data............................................................................................................374 11.1.3 Exploratory
Data Analysis....................................................................... 375 11.1.4 Modelling Using Spatial Econometric Models...................................... 375 11.1.5 Results.......................................................................................................378 11.1.6 Conclusion and Discussion..................................................................... 381 11.2 Application 2: Modelling Price Competition Between Petrol Retail Outlets in a Large City......................................................................................... 382 11.2.1 Introduction..............................................................................................382 11.2.2 Data........................................................................................................... 383 11.2.3 Exploratory Data Analysis.......................................................................383 11.2.4 Spatial Econometric Modelling and Results.......................................... 384 11.2.5 A Spatial Hierarchical Model with /4 Likelihood................................. 385 11.2.6 Conclusion and Discussion.....................................................................388 11.3 Final Remarks on Spatial Econometric Modelling of Spatial Data...................388 11.4 Exercises................................................................................................................ 389 Appendix: Petrol Retail Price Data................................................................................390
Contents XIV Part III Modelling Spatial-Temporal Data 12 Modelling Spatial-Temporal Data: An Introduction................................................. 395 12.1 Introduction...........................................................................................................395 12.2 Modelling Annual Counts of Burglary Cases at the Small Area Level: A Motivating Example and Frameworks for Modelling Spatial-Temporal Data.......................................................................................... 398 12.3 Modelling Small Area Temporal Data................................................................ 401 12.3.1 Issues to Consider When Modelling Temporal Patterns in the Small Area Setting....................................................................................403 12.3.1.1 Issues Relating to Temporal Dependence............................... 403 12.3.1.2 Issues Relating to Temporal Heterogeneity and Spatial Heterogeneity in Modelling Small Area Temporal Patterns...... 404 12.3.1.3 Issues Relating to Flexibility of a Temporal Model............... 404 12.3.2 Modelling Small Area Temporal Patterns: Setting the Scene.............. 406 12.3.3 A Linear Time Trend Model.................................................................... 407 12.3.3.1 Model Formulations.................................................................. 407 12.3.3.2 Modelling Trends in the PeterboroughBurglary Data............411 12.3.4 Random Walk Models.............................................................................. 416 12.3.4.1 Model
Formulations.................................................................. 417 12.3.4.2 The RW1 Model: Its Formulation Via the Full Conditionals and Its Properties............................................... 418 12.3.4.3 WinBUGS Implementation of the RW1Model......................... 421 12.3.4.4 Example: Modelling Burglary Trends Using the Peterborough Data.................................................................... 421 12.3.4.5 The Random Walk Model of Order 2...................................... 424 12.3.5 Interrupted Time Series (ITS) Models.....................................................426 12.3.5.1 Quasi-Experimental Designs and the Purpose of ITS Modelling.................................................................................. 426 12.3.5.2 Model Formulations.................................................................. 428 12.3.5.3 WinBUGS Implementation........................................................429 12.3.5.4 Results........................................................................................ 432 12.4 Concluding Remarks............................................................................................ 434 12.5 Exercises................................................................................................................ 435 Appendix: Three Different Forms for Specifying the Impact Function/................... 436 13 Exploratory Analysis of Spatial-Temporal Data.........................................................439 13.1
Introduction...........................................................................................................439 13.2 Patterns of Spatial-Temporal Data.......................................................................440 13.3 Visualising Spatial-Temporal Data...................................................................... 443 13.4 Tests of Space-Time Interaction............................................................................448 13.4.1 The Knox Test........................................................................................... 449 13.4.1.1 An Instructive Example of the Knox Test and Different Methods to Derive a p-Value....................................................451 13.4.1.2 Applying the Knox Test to the MalariaData...........................453 13.4.2 Kulldorff s Space-Time Scan Statistic......................................................454 13.4.2.1 Application: The Simulated Small Area COPD Mortality Data............................................................................456 13.4.3 Assessing Space-Time Interaction in the Form of Varying Local Time Trend Patterns.................................................................................459 Contents XV 13.4.3.1 Exploratory Analysis of the Local Trends in the Peterborough Burglary Data.................................................... 460 13.4.3.2 Exploratory Analysis of the Local Time Trends in the England COPD Mortality Data................................................460 13.5 Concluding
Remarks............................................................................................463 13.6 Exercises................................................................................................................ 464 14 Bayesian Hierarchical Models for Spatial-Temporal Data I: Space-Time Separable Models.........................................................................465 14.1 Introduction.......................................................................................................... 465 14.2 Estimating Small Area Burglary Rates Over Time: Setting the Scene............. 465 14.3 The Space-Time Separable Modelling Framework.............................................467 14.3.1 Model Formulations................................................................................ 467 14.3.2 Do We Combine the Space and Time Components Additively or Multiplicatively?....................................................................................... 469 14.3.3 Analysing the Peterborough Burglary Data Using a Space-Time Separable Model....................................................................................... 470 14.3.4 Results.......................................................................................................474 14.4 Concluding Remarks............................................................................................ 478 14.5 Exercises................................................................................................................ 479 15 Bayesian Hierarchical Models for Spatial-Temporal Data
II: Space-Time Inseparable Models........................................................................................................481 15.1 Introduction...........................................................................................................481 15.2 From Space-Time Separability to Space-Time Inseparability: The Big Picture..... 481 15.3 Type I Space-Time Interaction............................................................................. 484 15.3.1 Example: A Space-Time Model with Type I Space-Time Interaction.... 484 15.3.2 WinBUGS Implementation......................................................................486 15.4 Type II Space-Time Interaction............................................................................ 486 15.4.1 Example: Two Space-Time Models with Type II Space-Time Interaction.................................................................................................489 15.4.2 WinBUGS Implementation......................................................................490 15.5 Type III Space-Time Interaction...........................................................................490 15.5.1 Example: A Space-Time Model with Type III Space-Time Interaction.............................................................................491 15.5.2 WinBUGS Implementation.....................................................................492 15.6 Results from Analysing the Peterborough Burglary Data................................ 493 15.7 Type IV Space-Time
Interaction...........................................................................498 15.7.1 Strategy 1: Extending Type II to Type IV................................................499 15.7.2 Strategy 2: Extending Type III to Type IV..............................................501 15.7.2.1 Examples of Strategy 2............................................................. 502 15.7.3 Strategy 3: Clayton s Rule........................................................................504 15.7.3.1 Structure Matrices and Gaussian Markov Random Fields...........................................................................505 15.7.3.2 Taking the Kronecker Product.................................................506 15.7.3.3 Exploring the Induced Space-Time Dependence Structure via the Full Conditionals.......................................................... 508 15.7.4 Summary on Type IV Space-Time Interaction....................................... 512 15.8 Concluding Remarks............................................................................................ 513 15.9 Exercises................................................................................................................ 515
Contents XVI 16 Applications in Modelling Spatial-Temporal Data.................................................. 517 16.1 Introduction..........................................................................................................517 16.2 Application 1: Evaluating a Targeted Crime Reduction Intervention.............. 518 16.2.1 Background and Data.............................................................................. 518 16.2.2 Constructing Different Control Groups.................................................520 16.2.3 Evaluation Using ITS................................................................................521 16.2.4 WinBUGS Implementation...................................................................... 523 16.2.5 Results................................................................ 523 16.2.6 Some Remarks.......................................................................................... 526 16.3 Application 2: Assessing the Stability of Risk in Space and Time....................527 16.3.1 Studying the Temporal Dynamics of Crime Hotspots and Coldspots: Background, Data and the Modelling Idea.........................527 16.3.2 Model Formulations................................................................................ 530 16.3.3 Classification of Areas..............................................................................531 16.3.4 Model Implementation and Area Classification................................... 532 16.3.5 Interpreting the Statistical Results.........................................................
535 16.4 Application 3: Detecting Unusual Local Time Patterns in Small Area Data.....539 16.4.1 Small Area Disease Surveillance: Background and Modelling Idea...... 539 16.4.2 Model Formulation.................................................................................. 540 16.4.3 Detecting Unusual Areas with a Control of the False Discovery Rate.......................................................................................... 543 16.4.4 Fitting BaySTDetect in WinBUGS.......................................................... 543 16.4.5 A Simulated Dataset to Illustrate the Use of BaySTDetect...................546 16.4.6 Results from the Simulated Dataset....................................................... 546 16.4.7 General Results from Li et al. (2012) and an Extension of BaySTDetect.............................................................................................. 548 16.5 Application 4: Investigating the Presence of Spatial-Temporal Spillover Effects on Village-Level Malaria Risk in Kalaburagi, Karnataka, India....................................................................................................550 16.5.1 Background and Study Objective........................................................... 550 16.5.2 Data............................................................................................................551 16.5.3 Modelling..................................................................................................552 16.5.4
Results.......................................................................................................553 16.5.5 Concluding Remarks................................................................................556 16.6 Conclusions............................................................................................................558 16.7 Exercises................................................................................................................ 560 Part IV Addendum 17 Modelling Spatial and Spatial-Temporal Data: Future Agendas?.......................... 565 17.1 Topic 1: Modelling Multiple Related Outcomes Over Space and Time............ 565 17.2 Topic 2: Joint Modelling of Georeferenced Longitudinal and Time-to-Event Data............................................................................................... 567 17.3 Topic 3: Multiscale Modelling..............................................................................567 17.4 Topic 4: Using Survey Data for Small Area Estimation..................................... 568 17.5 Topic 5: Combining Data at Both Aggregate and Individual Levels to Improve Ecological Inference...............................................................................571 Contents XVII 17.6 Topic 6: Geostatistical Modelling.........................................................................572 17.6.1 Spatial Dependence................................................................................. 573 17.6.2 Mapping to Reduce Visual Bias..............................................................
574 17.6.3 Modelling Scale Effects............................................................................574 17.7 Topic 7: Modelling Count Data in Spatial Econometrics................................... 575 17.8 Topic 8: Computation............................................................................................ 575 References.................................................................................................................................. 577 Index.......................................................................................................................................597
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Contents Preface.χίχ Acknowledgements.xxv Part I Fundamentals for Modelling Spatial and Spatial-Temporal Data 1 Challenges and Opportunities Analysing Spatial and Spatial-Temporal Data. 3 1.1 Introduction. 3 1.2 Four Main Challenges When Analysing Spatial and Spatial-Temporal Data.4 1.2.1 Dependency. 4 1.2.2 Heterogeneity.8 1.2.3 Data Sparsity. 10 1.2.4 Uncertainty.12 1.2.4.1 Data Uncertainty . 12 1.2.4.2 Model (or Process) Uncertainty. 13 1.2.4.3 Parameter Uncertainty . 13 1.3 Opportunities Arising from Modelling Spatial and Spatial-Temporal Data.14 1.3.1 Improving Statistical
Precision. 14 1.3.2 Explaining Variation in Space and Time. 18 1.3.2.1 Example 1: Modelling Exposure-Outcome Relationships. 18 1.3.2.2 Example 2: Testing a Conceptual Model at the Small Area Level.20 1.3.2.3 Example 3: Testing for Spatial Spillover (Local Competition) Effects . 22 1.3.2.4 Example 4: Assessing the Effects of an Intervention. 24 1.3.3 Investigating Space-Time Dynamics. 27 1.4 Spatial and Spatial-Temporal Models: Bridging between Challenges and Opportunities .27 1.4.1 Statistical Thinking in Analysing Spatial and Spatial-Temporal Data: The Big Picture. 27 1.4.2 Bayesian Thinking in a Statistical Analysis. 30 1.4.3 Bayesian Hierarchical Models. 33 1.4.3.1 Thinking Hierarchically.33 1.4.3.2 Incorporating Spatial and Spatial-Temporal Dependence Structures in a Bayesian Hierarchical Model Using Random Effects. 36 1.4.3.3 Information Sharing in a Bayesian Hierarchical Model
through Random Effects. 37 1.4.4 Bayesian Spatial Econometrics.39 1.5 Concluding Remarks. 40 1.6 The Datasets Used in the Book. 41 1.7 Exercises.45 vii
viii Contents 2 Concepts for Modelling Spatial and Spatial-Temporal Data: An Introduction to "Spatial Thinking".47 2.1 Introduction.47 2.2 Mapping Data and Why It Matters. 48 2.3 Thinking Spatially. 52 2.3.1 Explaining Spatial Variation. 52 2.3.2 Spatial Interpolation and Small Area Estimation. 54 2.4 Thinking Spatially and Temporally. 56 2.4.1 Explaining Space-Time Variation. 56 2.4.2 Estimating Parameters for Spatial-Temporal Units.59 2.5 Concluding Remarks.59 2.6 Exercises. 60 Appendix: Geographic Information Systems .61 3 The Nature of Spatial and Spatial-Temporal Attribute Data.63 3.1
Introduction. 63 3.2 Data Collection Processes in the Social Sciences. 63 3.2.1 Natural Experiments. 64 3.2.2 Quasi-Experiments.67 3.2.3 Non-Experimental Observational Studies. 68 3.3 Spatial and Spatial-Temporal Data: Properties. 71 3.3.1 From Geographical Reality to the Spatial Database. 71 3.3.2 Fundamental Properties of Spatial and Spatial-Temporal Data.74 3.3.2.1 Spatial and Temporal Dependence. 74 3.3.2.2 Spatial and Temporal Heterogeneity. 75 3.3.3 Properties Induced by Representational Choices.76 3.3.4 Properties Induced by Measurement Processes. 83 3.4 Concluding Remarks.84 3.5 Exercises.84 4 Specifying Spatial Relationships on the Map: The Weights Matrix.87 4.1 Introduction. 87 4.2
Specifying Weights Based on Contiguity. 88 4.3 Specifying Weights Based on Geographical Distance.90 4.4 Specifying Weights Based on the Graph Structure Associated with a Set of Points.90 4.5 Specifying Weights Based on Attribute Values.92 4.6 Specifying Weights Based on Evidence about Interactions.92 4.7 Row Standardisation. 93 4.8 Higher Order Weights Matrices.95 4.9 Choice of W and Statistical Implications. 97 4.9.1 Implications for Small Area Estimation. 97 4.9.2 Implications for Spatial Econometric Modelling.102 4.9.3 Implications for Estimating the Effects of Observable Covariates on the Outcome.104 4.10 Estimating the W Matrix. 105 4.11 Concluding Remarks. 106 4.12
Exercises.106 4.13 Appendices. 107 їх Contents Appendix 4.13.1 Building a Geodatabase in R. 107 Appendix 4.13.2 Constructing the W Matrix and Accessing Data Stored in a Shapefile. 110 5 Introduction to the Bayesian Approach to Regression Modelling with Spatial and Spatial-Temporal Data. 115 5.1 Introduction. 115 5.2 Introducing Bayesian Analysis. 116 5.2.1 Prior, Likelihood and Posterior: What Do These Terms Refer To?. 116 5.2.2 Example: Modelling High-Intensity Crime Areas.120 5.3 Bayesian Computation.121 5.3.1 Summarising the Posterior Distribution. 121 5.3.2 Integration and Monte Carlo Integration. 123 5.3.3 Markov Chain Monte Carlo with Gibbs Sampling.127 5.3.4 Introduction to WinBUGS. 129 5.3.5 Practical
Considerations when Fitting Models in WinBUGS.133 5.3.5.1 Setting the Initial Values. 133 5.3.5.2 Checking Convergence. 134 5.3.5.3 Checking Efficiency.136 5.4 Bayesian Regression Models. 137 5.4.1 Example I: Modelling Household-Level Income.138 5.4.2 Example II: Modelling Annual Burglary Rates in Small Areas. 143 5.5 Bayesian Model Comparison and Model Evaluation. 147 5.6 Prior Specifications . 148 5.6.1 When We Have Little Prior Information. 148 5.6.2 Towards More Informative Priors for Modelling Spatial and Spatial-Temporal Data. 150 5.7 Concluding Remarks. 151 5.8 Exercises. 153 Part II Modelling Spatial Data 6 Exploratory Analysis of Spatial Data.159 6.1 Introduction.159 6.2
Techniques for the Exploratory Analysisof Univariate Spatial Data.160 6.2.1 Mapping.161 6.2.2 Checking for Spatial Trend. 165 6.2.3 Checking for Spatial Heterogeneity in the Mean.168 6.2.3.1 Count Data. 168 6.2.3.2 A Monte Carlo Test.169 6.2.3.3 Continuous-Valued Data. 170 6.2.4 Checking for Global Spatial Dependence (Spatial Autocorrelation). 172 6.2.4.1 The Moran Scatterplot. 173 6.2.4.2 The Global Moran's I Statistic. 174 6.2.4.3 Other Tests for Assessing Global Spatial Autocorrelation. 177 6.2.4Ճ The Global Moran's I Applied to Regression Residuals. 178 6.2.4.5 The Join-Count Test for Categorical Data. 179
x Contents Checking for Spatial Heterogeneity in the Spatial Dependence Structure: Detecting Local Spatial Clusters. 181 6.2.5.1 The Local Moran's 1.182 6.2.5.2 The Multiple Testing Problem When Using Local Moran's /.185 6.2.5.3 Kulldorff's Spatial Scan Statistic. 186 6.3 Exploring Relationships between Variables.191 6.3.1 Scatterplots and the Bivariate Moran Scatterplot.191 6.3.2 Quantifying Bivariate Association. 193 6.3.2.1 The Clifford-Richardson Test of Bivariate Correlation in the Presence of Spatial Autocorrelation.193 6.3.2.2 Testing for Association "At a Distance" and the Global Bivariate Moran's 1. 195 6.3.3 Checking for Spatial Heterogeneity in the Outcome-Covariate Relationship: Geographically Weighted Regression (GWR). 195 6.4 Overdispersion and Zero-Inflation in Spatial Count Data.203 6.4.1 Testing for Overdispersion. 204 6.4.2 Testing for Zero-Inflation. 206 6.5 Concluding Remarks. 207 6.6
Exercises. 209 Appendix. An R Function to Perform the Zero-Inflation Test by van Den Broek (1995). 210 8.2.1.1 8.2.1.2 6.2.5 7 Bayesian Models for Spatial Data I: Non-Hierarchical and Exchangeable Hierarchical Models.213 7.1 Introduction.213 7.2 Estimating Small Area Income: A Motivating Example and Different Modelling Strategies.214 7.2.1 Modelling the 109 Parameters Non-Hierarchically.216 7.2.2 Modelling the 109 Parameters Hierarchically. 217 7.3 Modelling the Newcastle Income Data Using Non-Hierarchical Models.218 7.3.1 An Identical Parameter Model Based on Strategy 1. 218 7.3.2 An Independent Parameters Model Based on Strategy 2. 220 7.4 An Exchangeable Hierarchical Model Based on Strategy 3.223 7.4.1 The Logic of Information Borrowing and Shrinkage.224 7.4.2 Explaining the Nature of Global Smoothing Due to
Exchangeability. 225 7.4.3 The Variance Partition Coefficient (VPC). 226 7.4.4 Applying an Exchangeable Hierarchical Model to the Newcastle Income Data. 228 7.5 Concluding Remarks. 230 7.6 Exercises. 230 7.7 Appendix: Obtaining the Simulated Household Income Data. 231 8 Bayesian Models for Spatial Data II: Hierarchical Models with Spatial Dependence. 233 8.1 Introduction. 233 8.2 The Intrinsic Conditional Autoregressive (ICAR) Model. 234 8.2.1 The ICAR Model Using a Spatial Weights Matrix with Binary Entries.234 8.3 8.4 8.5 8.6 8.7 8.8 The WinBUGS Implementation of the ICAR Model. 236 Applying the ICAR Model Using Spatial Contiguity to the Newcastle Income Data.238 8.2.1.3
Results. 240 8.2.1.4 A Summary of the Properties of the ICAR Model Using a Binary Spatial Weights Matrix. 244 8.2.2 The ICAR Model with a General Weights Matrix.245 8.2.2.1 Expressing the ICAR Model as a Joint Distribution and the Implied Restriction on W.245 8.2.2.2 The Sum-to-Zero Constraint.246 8.2.2.3 Applying the ICAR Model Using General Weights to the Newcastle Income Data. 247 8.2.2.4 Results. 248 The Proper CAR (pCAR) Model.249 8.3.1 Prior Choice for p. 251 8.3.2 ICAR or pCAR?. 251 8.3.3 Applying the pCAR Model to the Newcastle Income Data.253 8.3.4 Results.253 Locally Adaptive Models. 256 8.4.1 Choosing an Optimal W Matrix from All Possible Specifications.258 8.4.2 Modelling the Elements in the W
Matrix.258 8.4.3 Applying Some of the Locally Adaptive Spatial Models to a Subset of the Newcastle Income Data. 262 The Besag, York and Mollié (BYM) Model. 266 8.5.1 Two Remarks on Applying the BYM Model in Practice.268 8.5.2 Applying the BYM Model to the Newcastle Income Data. 269 Comparing the Fits of Different Bayesian Spatial Models.274 8.6.1 DIC Comparison.274 8.6.2 Model Comparison Based on the Quality of the MSOA-Level Average Income Estimates. 276 Concluding Remarks. 277 Exercises. 279 9 Bayesian Hierarchical Models for Spatial Data: Applications. 281 9.1 Introduction.281 9.2 Application 1: Modelling the Distribution of High Intensity Crime Areas in a City. 282 9.2.1
Background. 282 9.2.2 Data and Exploratory Analysis. 283 9.2.3 Methods Discussed in Haining and Law (2007) to Combine the PHIA and EHIA Maps.285 9.2.4 A Joint Analysis of the PHIA and EHIA Data Using the MVCAR Model. 286 9.2.5 Results.290 9.2.6 Another Specification of the MVCAR Model and a Limitation of the MVCAR Approach.293 9.2.7 Conclusion and Discussion. 293 9.3 Application 2: Modelling the Association Between Air Pollution and Stroke Mortality.296
xii 9.4 9.5 9.6 Contents Contents 9.3.1 Background and Data .296 9.3.2 Modelling.300 9.3.3 Interpreting the Statistical Results.302 9.3.4 Conclusion and Discussion. 305 Application 3: Modelling the Village-Level Incidence of Malaria in a Small Region of India. 308 9.4.1 Background. 308 9.4.2 Data and Exploratory Analysis. 308 9.4.3 Model I: A Poisson Regression Model with Random Effects. 310 9.4.4 Model II: A Two-Component Poisson Mixture Model. 311 9.4.5 Model III: A Two-Component Poisson Mixture Model with Zero-Inflation. 313 9.4.6 Results. 314 9.4.7 Conclusion and Model Extensions.318 Application 4: Modelling the Small Area Count of Cases of Rape in Stockholm,
Sweden. 321 9.5.1 Background and Data.321 9.5.2 Modelling.322 9.5.2.1 A "Whole-Map" Analysis Using Poisson Regression. 322 9.5.2.2 A "Localised" Analysis Using Bayesian Profile Regression. 323 9.5.3 Results.326 9.5.3.1 "Whole Map"Associations for theRisk Factors. 326 9.5.3.2 "Local"Associationsfor the Risk Factors.326 9.5.4 Conclusions. 329 Exercises . 330 10.3 10 Spatial Econometric Models. 333 10.1 Introduction. 333 10.2 Spatial Econometric Models. 334 10.2.1 Three Forms of Spatial Spillover. 334 10.2.2 The Spatial Lag Model
(SLM). 335 10.2.2.1 Formulating the Model. 335 10.2.2.2 An Example of the SLM. 336 10.2.2.3 The Reduced Form of the SLM and the Constraint on б.337 10.2.2.4 Specification of the Spatial Weights Matrix.338 10.2.2.5 Issues with Model Fitting and Interpreting Coefficients.339 10.2.3 The Spatially-Lagged Covariates Model (SLX). 339 10.2.3.1 Formulating the Model. 339 10.2.3.2 An Example of the SLX Model.340 10.2.4 The Spatial Error Model (SEM). 340 10.2.5 The Spatial Durbin Model (SDM). 341 10.2.5.1 Formulating the Model. 341 10.2.5.2 Relating the SDM Model to the Other Three Spatial Econometric Models. 342 10.2.6 Prior Specifications. 342 10.2.7 An Example: Modelling Cigarette Sales in 46 US States.343 10.2.7.1 Data Description, Exploratory Analysis and Model Specifications.343 10.2.7.2
Results. 345 xiii Interpreting Covariate Effects.346 10.3.1 Definitions of the Direct, Indirect and Total Effects of a Covariate. 346 10.3.2 Measuring Direct and Indirect Effects without the SAR Structure on the Outcome Variables.347 10.3.2.1 For the LM and SEM Models.347 10.3.2.2 For the SLX Model.347 10.3.3 Measuring Direct and Indirect Effects When the Outcome Variables are Modelled by the SAR Structure. 350 10.3.3.1 Understanding Direct and Indirect Effects in the Presence of Spatial Feedback.350 10.3.3.2 Calculating the Direct and Indirect Effects in the Presence of Spatial Feedback.351 10.3.3.3 Some Properties of Direct and Indirect Effects. 351 10.3.3.4 A Property (Limitation) of the Average Direct and Average Indirect Effects Under the SLM Model.354 10.3.3.5 Summary. 354 10.3.4 The Estimated Effects from the Cigarette Sales Data. 355 10.4 Model Fitting in
WinBUGS. 356 10.4.1 Derivation of the Likelihood Function.357 10.4.2 Simplifications to the Likelihood Computation. 361 10.4.3 The Zeros-Trick in WinBUGS. 361 10.4.4 Calculating the Covariate Effects in WinBUGS. 362 10.5 Concluding Remarks.365 10.5.1 Other Spatial Econometric Models and the Two Problems of Identifiability. 365 10.5.2 Comparing the Hierarchical Modelling Approach and the Spatial Econometric Approach: A Summary.367 10.6 Exercises. 370 11 Spatial Econometric Modelling: Applications. 373 11.1 Application 1: Modelling the Voting Outcomes at the Local Authority District Level in England from the 2016 EU Referendum. 373 11.1.1 Introduction.373 11.1.2 Data.374 11.1.3 Exploratory
Data Analysis. 375 11.1.4 Modelling Using Spatial Econometric Models. 375 11.1.5 Results.378 11.1.6 Conclusion and Discussion. 381 11.2 Application 2: Modelling Price Competition Between Petrol Retail Outlets in a Large City. 382 11.2.1 Introduction.382 11.2.2 Data. 383 11.2.3 Exploratory Data Analysis.383 11.2.4 Spatial Econometric Modelling and Results. 384 11.2.5 A Spatial Hierarchical Model with /4 Likelihood. 385 11.2.6 Conclusion and Discussion.388 11.3 Final Remarks on Spatial Econometric Modelling of Spatial Data.388 11.4 Exercises. 389 Appendix: Petrol Retail Price Data.390
Contents XIV Part III Modelling Spatial-Temporal Data 12 Modelling Spatial-Temporal Data: An Introduction. 395 12.1 Introduction.395 12.2 Modelling Annual Counts of Burglary Cases at the Small Area Level: A Motivating Example and Frameworks for Modelling Spatial-Temporal Data. 398 12.3 Modelling Small Area Temporal Data. 401 12.3.1 Issues to Consider When Modelling Temporal Patterns in the Small Area Setting.403 12.3.1.1 Issues Relating to Temporal Dependence. 403 12.3.1.2 Issues Relating to Temporal Heterogeneity and Spatial Heterogeneity in Modelling Small Area Temporal Patterns. 404 12.3.1.3 Issues Relating to Flexibility of a Temporal Model. 404 12.3.2 Modelling Small Area Temporal Patterns: Setting the Scene. 406 12.3.3 A Linear Time Trend Model. 407 12.3.3.1 Model Formulations. 407 12.3.3.2 Modelling Trends in the PeterboroughBurglary Data.411 12.3.4 Random Walk Models. 416 12.3.4.1 Model
Formulations. 417 12.3.4.2 The RW1 Model: Its Formulation Via the Full Conditionals and Its Properties. 418 12.3.4.3 WinBUGS Implementation of the RW1Model. 421 12.3.4.4 Example: Modelling Burglary Trends Using the Peterborough Data. 421 12.3.4.5 The Random Walk Model of Order 2. 424 12.3.5 Interrupted Time Series (ITS) Models.426 12.3.5.1 Quasi-Experimental Designs and the Purpose of ITS Modelling. 426 12.3.5.2 Model Formulations. 428 12.3.5.3 WinBUGS Implementation.429 12.3.5.4 Results. 432 12.4 Concluding Remarks. 434 12.5 Exercises. 435 Appendix: Three Different Forms for Specifying the Impact Function/. 436 13 Exploratory Analysis of Spatial-Temporal Data.439 13.1
Introduction.439 13.2 Patterns of Spatial-Temporal Data.440 13.3 Visualising Spatial-Temporal Data. 443 13.4 Tests of Space-Time Interaction.448 13.4.1 The Knox Test. 449 13.4.1.1 An Instructive Example of the Knox Test and Different Methods to Derive a p-Value.451 13.4.1.2 Applying the Knox Test to the MalariaData.453 13.4.2 Kulldorff's Space-Time Scan Statistic.454 13.4.2.1 Application: The Simulated Small Area COPD Mortality Data.456 13.4.3 Assessing Space-Time Interaction in the Form of Varying Local Time Trend Patterns.459 Contents XV 13.4.3.1 Exploratory Analysis of the Local Trends in the Peterborough Burglary Data. 460 13.4.3.2 Exploratory Analysis of the Local Time Trends in the England COPD Mortality Data.460 13.5 Concluding
Remarks.463 13.6 Exercises. 464 14 Bayesian Hierarchical Models for Spatial-Temporal Data I: Space-Time Separable Models.465 14.1 Introduction. 465 14.2 Estimating Small Area Burglary Rates Over Time: Setting the Scene. 465 14.3 The Space-Time Separable Modelling Framework.467 14.3.1 Model Formulations. 467 14.3.2 Do We Combine the Space and Time Components Additively or Multiplicatively?. 469 14.3.3 Analysing the Peterborough Burglary Data Using a Space-Time Separable Model. 470 14.3.4 Results.474 14.4 Concluding Remarks. 478 14.5 Exercises. 479 15 Bayesian Hierarchical Models for Spatial-Temporal Data
II: Space-Time Inseparable Models.481 15.1 Introduction.481 15.2 From Space-Time Separability to Space-Time Inseparability: The Big Picture. 481 15.3 Type I Space-Time Interaction. 484 15.3.1 Example: A Space-Time Model with Type I Space-Time Interaction. 484 15.3.2 WinBUGS Implementation.486 15.4 Type II Space-Time Interaction. 486 15.4.1 Example: Two Space-Time Models with Type II Space-Time Interaction.489 15.4.2 WinBUGS Implementation.490 15.5 Type III Space-Time Interaction.490 15.5.1 Example: A Space-Time Model with Type III Space-Time Interaction.491 15.5.2 WinBUGS Implementation.492 15.6 Results from Analysing the Peterborough Burglary Data. 493 15.7 Type IV Space-Time
Interaction.498 15.7.1 Strategy 1: Extending Type II to Type IV.499 15.7.2 Strategy 2: Extending Type III to Type IV.501 15.7.2.1 Examples of Strategy 2. 502 15.7.3 Strategy 3: Clayton's Rule.504 15.7.3.1 Structure Matrices and Gaussian Markov Random Fields.505 15.7.3.2 Taking the Kronecker Product.506 15.7.3.3 Exploring the Induced Space-Time Dependence Structure via the Full Conditionals. 508 15.7.4 Summary on Type IV Space-Time Interaction. 512 15.8 Concluding Remarks. 513 15.9 Exercises. 515
Contents XVI 16 Applications in Modelling Spatial-Temporal Data. 517 16.1 Introduction.517 16.2 Application 1: Evaluating a Targeted Crime Reduction Intervention. 518 16.2.1 Background and Data. 518 16.2.2 Constructing Different Control Groups.520 16.2.3 Evaluation Using ITS.521 16.2.4 WinBUGS Implementation. 523 16.2.5 Results. 523 16.2.6 Some Remarks. 526 16.3 Application 2: Assessing the Stability of Risk in Space and Time.527 16.3.1 Studying the Temporal Dynamics of Crime Hotspots and Coldspots: Background, Data and the Modelling Idea.527 16.3.2 Model Formulations. 530 16.3.3 Classification of Areas.531 16.3.4 Model Implementation and Area Classification. 532 16.3.5 Interpreting the Statistical Results.
535 16.4 Application 3: Detecting Unusual Local Time Patterns in Small Area Data.539 16.4.1 Small Area Disease Surveillance: Background and Modelling Idea. 539 16.4.2 Model Formulation. 540 16.4.3 Detecting Unusual Areas with a Control of the False Discovery Rate. 543 16.4.4 Fitting BaySTDetect in WinBUGS. 543 16.4.5 A Simulated Dataset to Illustrate the Use of BaySTDetect.546 16.4.6 Results from the Simulated Dataset. 546 16.4.7 General Results from Li et al. (2012) and an Extension of BaySTDetect. 548 16.5 Application 4: Investigating the Presence of Spatial-Temporal Spillover Effects on Village-Level Malaria Risk in Kalaburagi, Karnataka, India.550 16.5.1 Background and Study Objective. 550 16.5.2 Data.551 16.5.3 Modelling.552 16.5.4
Results.553 16.5.5 Concluding Remarks.556 16.6 Conclusions.558 16.7 Exercises. 560 Part IV Addendum 17 Modelling Spatial and Spatial-Temporal Data: Future Agendas?. 565 17.1 Topic 1: Modelling Multiple Related Outcomes Over Space and Time. 565 17.2 Topic 2: Joint Modelling of Georeferenced Longitudinal and Time-to-Event Data. 567 17.3 Topic 3: Multiscale Modelling.567 17.4 Topic 4: Using Survey Data for Small Area Estimation. 568 17.5 Topic 5: Combining Data at Both Aggregate and Individual Levels to Improve Ecological Inference.571 Contents XVII 17.6 Topic 6: Geostatistical Modelling.572 17.6.1 Spatial Dependence. 573 17.6.2 Mapping to Reduce Visual Bias.
574 17.6.3 Modelling Scale Effects.574 17.7 Topic 7: Modelling Count Data in Spatial Econometrics. 575 17.8 Topic 8: Computation. 575 References. 577 Index.597 |
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| any_adam_object_boolean | 1 |
| author | Haining, Robert P. 1948- Li, Guangquan 1982- |
| author_GND | (DE-588)14116607X (DE-588)1210514494 |
| author_facet | Haining, Robert P. 1948- Li, Guangquan 1982- |
| author_role | aut aut |
| author_sort | Haining, Robert P. 1948- |
| author_variant | r p h rp rph g l gl |
| building | Verbundindex |
| bvnumber | BV047707304 |
| classification_rvk | SK 850 CM 4000 |
| ctrlnum | (OCoLC)1310248081 (DE-599)BVBBV047707304 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Psychologie Mathematik |
| discipline_str_mv | Psychologie Mathematik |
| edition | First issued in paperback 2021 |
| format | Book |
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| id | DE-604.BV047707304 |
| illustrated | Illustrated |
| index_date | 2024-07-03T18:59:32Z |
| indexdate | 2024-07-10T09:19:43Z |
| institution | BVB |
| isbn | 9781032175003 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033091160 |
| oclc_num | 1310248081 |
| open_access_boolean | |
| owner | DE-824 DE-19 DE-BY-UBM DE-739 |
| owner_facet | DE-824 DE-19 DE-BY-UBM DE-739 |
| physical | xxvi, 608 Seiten Illustrationen, Diagramme, Karten |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Chapman and Hall/CRC, Statistics in the social and behavioral sciences |
| spelling | Haining, Robert P. 1948- (DE-588)14116607X aut Modelling spatial and spatial-temporal data a Bayesian approach by Robert Haining and Guangquan Li First issued in paperback 2021 Boca Raton ; London ; New York CRC Press [2021] © 2021 xxvi, 608 Seiten Illustrationen, Diagramme, Karten txt rdacontent n rdamedia nc rdacarrier Chapman and Hall/CRC, Statistics in the social and behavioral sciences References S. 577-596, Index S. 597-608 Spatial analysis (Statistics) Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Räumliche Statistik (DE-588)4386767-4 gnd rswk-swf Raumdaten (DE-588)4206012-6 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 s Räumliche Statistik (DE-588)4386767-4 s Raumdaten (DE-588)4206012-6 s DE-604 Li, Guangquan 1982- Verfasser (DE-588)1210514494 aut Erscheint auch als Online-Ausgabe 978-1-4822-3743-6 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033091160&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Haining, Robert P. 1948- Li, Guangquan 1982- Modelling spatial and spatial-temporal data a Bayesian approach Spatial analysis (Statistics) Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Räumliche Statistik (DE-588)4386767-4 gnd Raumdaten (DE-588)4206012-6 gnd |
| subject_GND | (DE-588)4144220-9 (DE-588)4386767-4 (DE-588)4206012-6 |
| title | Modelling spatial and spatial-temporal data a Bayesian approach |
| title_auth | Modelling spatial and spatial-temporal data a Bayesian approach |
| title_exact_search | Modelling spatial and spatial-temporal data a Bayesian approach |
| title_exact_search_txtP | Modelling spatial and spatial-temporal data a Bayesian approach |
| title_full | Modelling spatial and spatial-temporal data a Bayesian approach by Robert Haining and Guangquan Li |
| title_fullStr | Modelling spatial and spatial-temporal data a Bayesian approach by Robert Haining and Guangquan Li |
| title_full_unstemmed | Modelling spatial and spatial-temporal data a Bayesian approach by Robert Haining and Guangquan Li |
| title_short | Modelling spatial and spatial-temporal data |
| title_sort | modelling spatial and spatial temporal data a bayesian approach |
| title_sub | a Bayesian approach |
| topic | Spatial analysis (Statistics) Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Räumliche Statistik (DE-588)4386767-4 gnd Raumdaten (DE-588)4206012-6 gnd |
| topic_facet | Spatial analysis (Statistics) Bayes-Entscheidungstheorie Räumliche Statistik Raumdaten |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033091160&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hainingrobertp modellingspatialandspatialtemporaldataabayesianapproach AT liguangquan modellingspatialandspatialtemporaldataabayesianapproach |