Non-standard Spatial Statistics and Spatial Econometrics (eBook)

Preface 4
Prologue 5
Contents 28
Part I Non-standard Spatial Statistics 33
1 Introduction: Spatial Statistics 34
2 Individual Versus Ecological Analyses 35
2.1 Introduction 35
2.2 Spatial Autocorrelation Effects 35
2.3 Aggregation Impacts 36
2.3.1 The Syracuse Data 38
2.3.2 Previous Findings for Syracuse 40
2.4 Spatial Autocorrelation in the Syracuse Data 41
2.4.1 Spatial Autocorrelation in the Syracuse Data: LN(BLL + 1) Values 41
2.4.2 Spatial Autocorrelation in the Syracuse Data: Appraised House Value 43
2.5 Spatial Autocorrelation in the Syracuse Data: Other Sources 46
2.6 Bayesian Analysis Using Gibbs Sampling (BUGS) and Model Prediction Experiments 47
2.6.1 Results for the 2000 Census Tracts 50
2.7 Discussion and Implications 52
3 Statistical Models for Spatial Data: Some Linkages and Communalities 54
3.1 Introduction 54
3.2 Background: Quantifying Spatial Autocorrelation 55
3.2.1 The Moran Scatterplot 56
3.2.2 The Semivariogram Plot 57
3.3 Specifications of Spatial Autoregressive and Geostatistical Models 57
3.3.1 Spatial Autoregressive Models 58
3.4 Geostatistical Models 60
3.5 Linkages Between Spatial Autoregression and Geostatistics 61
3.6 A Major Commonality of Spatial Autoregression and Geostatistics 62
3.7 Implications for Quantitative Human Geography 64
4 Frequency Distributions for Simulated Spatially Autocorrelated Random Variables 65
4.1 Introduction 65
4.2 The Normal Probability Model 66
4.2.1 Simulating Spatially Autocorrelated Normal RVs 67
4.2.2 Simulation Results for an Ideal Regular Hexagonal Surface Partitioning 69
4.2.3 Simulation Results for the China County Geographic Configuration 73
4.2.4 Implications 76
4.3 The Poisson Probability Model 78
4.3.1 Simulating Spatially Autocorrelated Poisson RVs 80
4.3.1.1 MCMC Map Simulation 81
4.3.1.2 SF Map Simulation 83
4.3.2 Simulation Results for an Ideal Regular Hexagonal Surface Partitioning 83
4.3.3 Simulation Results for the China County Geographic Configuration 84
4.3.4 Implications 88
4.4 The Binomial Probability Model, N > 1
4.4.1 Simulating Spatially Autocorrelated Binomial RVs 91
4.4.2 Simulation Results for an Ideal Regular Hexagonal Surface Partitioning 93
4.4.3 Simulation Results for the China County Geographic Configuration 96
4.4.4 Implications 98
4.5 Discussion 99
5 Understanding Correlations Among Spatial Processes 102
5.1 Introduction 102
5.2 Two Illustrative Examples 102
5.3 Geostatistical Semivariogram Model Implications 104
5.4 Spatial Autoregressive Model Implications 109
5.4.1 Variance and Covariance Inflation Attributable to Spatial Autocorrelation 112
5.4.2 Effective Sample Size as a Function of .X and .Y 114
5.5 Spatial Filtering Model Implications 116
5.5.1 Correlation Coefficient Decomposition 117
5.5.2 Variance Inflation 120
5.6 Discussion 120
6 Spatially Structured Random Effects: A Comparison of Three Popular Specifications 123
6.1 Introduction 123
6.2 Modeling Spatial Structure 123
6.3 Linear Mixed Models 125
6.4 Generalized Linear Mixed Models 131
6.5 Degrees of Freedom for GLMM Random Effects 136
6.6 Extensions to Space-Time Data Sets 137
6.7 Discussion and Implications 140
7 Spatial Filter Versus Conventional Spatial Model Specifications: Some Comparisons 142
7.1 Introduction 142
7.1.1 Background 142
7.2 Variation and Covariation Considerations for Poisson Random Variables 145
7.2.1 Heterogeneity in Counts Data 146
7.2.2 Spatial Autocorrelation in Poisson Random Variables 149
7.2.3 Spatial Autocorrelation-induced Correlation Inflation 151
7.3 Principal Spatial Statistical Model Specifications 155
7.3.1 The Log-normal Approximation 155
7.3.2 A Winsorized Auto-Poisson Model 156
7.3.3 A Proper CAR Model Specification via GeoBUGS 159
7.4 Spatial Filter Model Specifications 161
7.4.1 The Log-normal Approximation Spatial Filter Model 161
7.4.2 A Poisson Spatial Filter Model 162
7.4.3 A Spatial Filter Model Specification via BUGS 164
7.5 Discussion 165
7.5.1 Cross-validation Results for the Poisson Spatial Filter Model 166
7.5.2 A Simulation Experiment Based Upon the Poisson Spatial Filter Model 166
7.5.3 Impacts of Incorporating Additional Information 168
7.5.4 Implications for Data Mapping 169
7.6 Concluding Comments 172
8 The Role of Spatial Autocorrelation in Prioritizing Sites Within a Geographic Landscape 175
8.1 Introduction: The Problem 175
8.2 The Murray Superfund Site: Part I 176
8.2.1 State-of-the-Art Practice 177
8.2.2 A Spatial Methodology: Stage 1, Spatial Sampling Data Collection and Preprocessing 178
8.3 The Murray Superfund Site: Part II 180
8.3.1 A Spatial Methodology: Stage 2, Spatial Statistics for Calculating UCLs 183
8.4 The Murray Superfund Site: Part III 185
8.4.1 A Spatial Methodology: Stage 3, Prioritizing Subregions for Remediation 187
8.5 The Murray Superfund Site: Part IV 187
8.5.1 A Spatial Methodology: Stage 4, Covariation of Contaminants and Joint Pollutant Analyses 188
8.6 The Murray Superfund Site: Part V 192
8.7 Implications 194
9 General Conclusions: Spatial Statistics 195
Part II Non-standard Spatial Econometrics 198
10 Introduction: Spatial Econometrics 199
11 A Mixed Linear-Logarithmic Specification forINTnl Lotka-Volterra Models with Endogenously Generated SDLS-Variables
11.1 Lotka-Volterra Models 200
11.1.1 A General Specification 200
11.1.2 Applications 201
11.1.3 Simultaneous Dynamic Least Squares (SDLS) Estimation 202
11.2 Mixed Specification 203
11.2.1 Equations 203
11.2.2 Stability 204
11.3 Application 204
11.4 Conclusion 207
12 Selecting Spatial Regimes by Threshold Analysis 209
12.1 Method 209
12.2 Spatial Income Generating Model 210
12.3 A Spatial Activity Complex Model 213
12.4 Conclusion 217
12.5 Appendix 217
13 Finite Automata 218
13.1 A Finite Automaton Bi-regional Dynamic Model 218
13.2 An Empirical Application 222
13.3 Conclusion 224
14 Learning from Residuals 226
14.1 Residuals 226
14.2 Multiple Regimes 228
14.3 Spatial Interpolation 231
14.4 Composite Parameters 232
14.5 Conclusion 234
15 Verhulst and Poisson Distributions 235
15.1 Robust Estimation in the Binary Case: A Linear Logistic Estimator (LLE) 235
15.2 A Logistic Dynamic Share Model 237
15.3 A Linear Poisson Distribution Estimator 239
15.4 Conclusion 243
16 Qualireg, A Qualitative Regression Method 244
16.1 Qualiflex 244
16.2 Qualireg 247
16.3 Spatial Setting 248
16.4 Conclusion 250
17 Filtering Complexity for Observational Errors and Spatial Bias 251
17.1 Complexity, Estimation and Testing 251
17.2 Filtering for Observational Errors 253
17.3 Further Filtering for Spatial Bias 256
17.4 Conclusions 257
18 General Spatial Econometric Conclusions 259
Epilogue 260
References 262
Author Index 272
Subject Index 273