SPATIAL ANALYSIS USING BIG DATA......Page 2
Copyright......Page 3
Contributors......Page 4
Preface......Page 5
References......Page 10
1.1 The definition of spatial data......Page 12
1.2.1 Spatial autocorrelation......Page 14
1.2.2 Spatial heterogenity......Page 15
References......Page 16
2.1 Definitions of notations......Page 17
2.2.1 The classical linear regression model and violation of typical assumptions......Page 18
2.2.2 Endogeneity......Page 20
2.2.3 Spatial autocorrelation of error term and heteroskedastic variance......Page 24
2.3 The generalized linear model......Page 25
2.4 The additive model......Page 27
2.5.1 Bayes' theorem......Page 31
2.5.2 The Markov chain Monte Carlo method......Page 32
2.5.3 Bayesian estimation of the classical linear regression model......Page 36
References......Page 38
3.1 Spatial weight matrix......Page 40
3.1.1 Definition of the spatial weight matrix......Page 41
3.1.2 Specification of the spatial weight matrix......Page 44
3.1.3 Standardization of the spatial weight matrix......Page 45
3.2.1 Testing for global spatial autocorrelation......Page 46
3.2.2 Testing for local spatial autocorrelation......Page 50
3.2.2.1 Local Moran statistic......Page 51
3.2.2.3 Gi and Giβ statistics......Page 52
3.2.3.1 Japanese income data: an application of local Moran......Page 54
3.2.3.2 Japanese population data: an application of local Geary......Page 56
3.3.2 Testing for local spatial heterogeneity: Hi statistic......Page 58
References......Page 60
FOUR - Geostatistics and Gaussian process models......Page 64
4.1 What is geostatistics?......Page 65
4.2.1 Spatial data and spatial process......Page 66
4.2.2.1 Assumptions......Page 67
4.2.2.2 Covariance function and semivariogram......Page 68
4.2.2.3 Anisotropy......Page 75
4.3 Parameter estimation......Page 76
4.3.1 Nonlinear least squares method......Page 79
4.3.3 Restricted maximum likelihood method......Page 81
4.4.1 Spatial prediction and Kriging......Page 83
4.4.1.1 Ordinary Kriging......Page 85
4.5 Universal Kriging......Page 88
4.5.1.2 Trans-Gaussian Kriging......Page 92
4.5.1.3 Indicator Kriging......Page 94
4.5.2 Block Kriging......Page 95
4.6.1 Spatial generalized linear model......Page 97
4.6.2 Geo-additive model......Page 100
4.7.1 Data model, process model, and parameter model......Page 102
4.7.2 Bayesian geostatistical model......Page 104
4.7.3 Bayesian spatial prediction......Page 105
4.8.2 Approaches that view time axis as continuous......Page 106
4.8.3 Approaches that view time axis as discrete......Page 108
4.9.1 Outline......Page 109
4.9.2 Low-rank approximation......Page 110
4.9.3.1 Covariance tapering method......Page 111
4.9.3.2 Composite likelihood approach......Page 112
4.9.3.4 Approximation by Gaussian Markov random field......Page 113
References......Page 114
FIVE -Spatial econometric models......Page 120
5.1 What is spatial econometrics?......Page 121
5.2.1 Spatial lag model and spatial error model......Page 122
5.2.2 Spatial Durbin model and generalized spatial model......Page 126
5.2.3 Impact measures......Page 127
5.3.1 Ordinary least squares method......Page 129
5.3.2 Maximum likelihood method......Page 131
5.3.3 Bayesian method......Page 136
5.4 Testing spatial autocorrelation based on the spatial econometric models......Page 138
5.4.3 Lagrangean multiplier test......Page 139
5.5.1 Spatially adjusted Breusch-Pagan test......Page 142
5.5.2 Spatial chow test......Page 143
5.6.2 Spatial discrete choice models......Page 144
5.6.3 Spatial panel models......Page 149
5.7.1 Outline......Page 150
5.7.2 Generalized spatial two stage least squares method......Page 151
5.7.3.1 Approximation of log of Jacobian......Page 155
5.7.3.2 Matrix exponential spatial specification method......Page 156
5.7.3.3 Spatiotemporal autoregressive model......Page 157
5.7.5 Sampling-based method......Page 158
References......Page 159
6.1 Introduction......Page 166
6.2.1 Concept of the geographically weighted regression models......Page 167
6.2.2 Parameter estimation of the geographically weighted regression model......Page 169
6.2.3 Example: application of the geographically weighted regression model......Page 170
6.2.4 Geographically weighted regression and collinearity......Page 172
6.2.5 Extended geographically weighted regression models......Page 174
6.3.2 Moran eigenvectors......Page 176
6.3.3 Eigenvector spatial filtering approach......Page 178
6.3.4 Example: application of the eigenvector spatial filtering approach......Page 180
6.4.2 Fast eigenvector spatial filtering modeling......Page 181
References......Page 183
SEVEN -Implementation with R language......Page 186
7.2 Housing price data in Lucas County (Ohio, USA)......Page 187
7.3 R package for spatial features: sf......Page 189
7.4.1 Define spatial weight matrix......Page 191
7.4.2 Testing for global spatial autocorrelation......Page 193
7.4.3 Testing for local spatial autocorrelation......Page 195
7.5.1 Assumptions......Page 197
7.5.2 Classical geostatistical modeling......Page 198
7.5.3 Low-rank approximations......Page 204
7.5.4 Sparse approximations......Page 205
7.6.1 Spatial econometric models in R......Page 207
7.6.2 Generalized spatial two-stage least squares method......Page 208
7.6.3.1 Approximation of log of Jacobian......Page 212
7.6.3.2 Matrix exponential spatial specification approach......Page 213
7.7.1 Geographically weighted regression-based approaches......Page 215
7.7.2 Spatial filtering approaches......Page 219
References......Page 227
G......Page 229
M......Page 230
S......Page 231
W......Page 232