Spatial analysis using big data: methods and urban applications

SPATIAL ANALYSIS USING BIG DATA
Copyright
Contributors
Preface
	References
ONE - Introduction
	1.1 The definition of spatial data
	1.2 Characteristics of spatial data: spatial autocorrelation and spatial heterogeneity
		1.2.1 Spatial autocorrelation
		1.2.2 Spatial heterogenity
	References
TWO - Mathematical preparation
	2.1 Definitions of notations
	2.2 The classical linear regression model
		2.2.1 The classical linear regression model and violation of typical assumptions
		2.2.2 Endogeneity
		2.2.3 Spatial autocorrelation of error term and heteroskedastic variance
	2.3 The generalized linear model
	2.4 The additive model
	2.5 The basics of Bayesian statistics
		2.5.1 Bayes\' theorem
		2.5.2 The Markov chain Monte Carlo method
		2.5.3 Bayesian estimation of the classical linear regression model
	References
THREE - Global and local indicators of spatial associations
	3.1 Spatial weight matrix
		3.1.1 Definition of the spatial weight matrix
		3.1.2 Specification of the spatial weight matrix
		3.1.3 Standardization of the spatial weight matrix
	3.2 Testing for spatial autocorrelation
		3.2.1 Testing for global spatial autocorrelation
		3.2.2 Testing for local spatial autocorrelation
			3.2.2.1 Local Moran statistic
			3.2.2.2 Local Geary statistic
			3.2.2.3 Gi and Gi∗ statistics
		3.2.3 Examples
			3.2.3.1 Japanese income data: an application of local Moran
			3.2.3.2 Japanese population data: an application of local Geary
	3.3 Testing for spatial heterogeneity
		3.3.1 Testing for global spatial heterogeneity
		3.3.2 Testing for local spatial heterogeneity: Hi statistic
	References
FOUR - Geostatistics and Gaussian process models
	4.1 What is geostatistics?
	4.2 Geostatistical model
		4.2.1 Spatial data and spatial process
		4.2.2 Stationary spatial process
			4.2.2.1 Assumptions
			4.2.2.2 Covariance function and semivariogram
			4.2.2.3 Anisotropy
	4.3 Parameter estimation
		4.3.1 Nonlinear least squares method
		4.3.2 Maximum likelihood method
		4.3.3 Restricted maximum likelihood method
	4.4 Kriging
		4.4.1 Spatial prediction and Kriging
			4.4.1.1 Ordinary Kriging
	4.5 Universal Kriging
		4.5.1 Nonlinear Kriging
			4.5.1.1 Lognormal Kriging
			4.5.1.2 Trans-Gaussian Kriging
			4.5.1.3 Indicator Kriging
		4.5.2 Block Kriging
	4.6 Extended model
		4.6.1 Spatial generalized linear model
			4.6.2 Geo-additive model
	4.7 Hierarchical Bayesian model
		4.7.1 Data model, process model, and parameter model
		4.7.2 Bayesian geostatistical model
		4.7.3 Bayesian spatial prediction
	4.8 Spatiotemporal model
		4.8.1 Outline
		4.8.2 Approaches that view time axis as continuous
		4.8.3 Approaches that view time axis as discrete
	4.9 Methods for large data
		4.9.1 Outline
		4.9.2 Low-rank approximation
		4.9.3 Sparse approximation
			4.9.3.1 Covariance tapering method
			4.9.3.2 Composite likelihood approach
			4.9.3.3 Nearest-neighbor Gaussian process
			4.9.3.4 Approximation by Gaussian Markov random field
	References
FIVE -
Spatial econometric models
	5.1 What is spatial econometrics?
	5.2 Spatial econometric models
		5.2.1 Spatial lag model and spatial error model
		5.2.2 Spatial Durbin model and generalized spatial model
		5.2.3 Impact measures
		5.2.4 Models for spatial heterogeneity: varying coefficient models in space
	5.3 Parameter estimation of the spatial econometric models
		5.3.1 Ordinary least squares method
		5.3.2 Maximum likelihood method
		5.3.3 Bayesian method
	5.4 Testing spatial autocorrelation based on the spatial econometric models
		5.4.1 Wald test
		5.4.2 Likelihood ratio test
		5.4.3 Lagrangean multiplier test
	5.5 Testing spatial heterogeneity based on the spatial econometric models
		5.5.1 Spatially adjusted Breusch-Pagan test
		5.5.2 Spatial chow test
	5.6 Related methods
		5.6.1 Conditional autoregressive model
		5.6.2 Spatial discrete choice models
		5.6.3 Spatial panel models
	5.7 Methods for large data
		5.7.1 Outline
		5.7.2 Generalized spatial two stage least squares method
		5.7.3 Maximum likelihood–based methods
			5.7.3.1 Approximation of log of Jacobian
			5.7.3.2 Matrix exponential spatial specification method
			5.7.3.3 Spatiotemporal autoregressive model
		5.7.4 Bayesian method
		5.7.5 Sampling-based method
	References
SIX  -
Models in quantitative geography
	6.1 Introduction
	6.2 Geographically weighted regression models
		6.2.1 Concept of the geographically weighted regression models
		6.2.2 Parameter estimation of the geographically weighted regression model
		6.2.3 Example: application of the geographically weighted regression model
		6.2.4 Geographically weighted regression and collinearity
		6.2.5 Extended geographically weighted regression models
	6.3 Spatial filtering approach
		6.3.1 Types of spatial filtering
		6.3.2 Moran eigenvectors
		6.3.3 Eigenvector spatial filtering approach
		6.3.4 Example: application of the eigenvector spatial filtering approach
	6.4 Methods for large data
		6.4.1 Fast geographically weighted regression modeling
		6.4.2 Fast eigenvector spatial filtering modeling
	References
SEVEN -
Implementation with R language
	7.1 Implementation of spatial (geo-)statistical and spatial econometric methods with R
	7.2 Housing price data in Lucas County (Ohio, USA)
	7.3 R package for spatial features: sf
	7.4 Global and local indicators of spatial associations
		7.4.1 Define spatial weight matrix
		7.4.2 Testing for global spatial autocorrelation
		7.4.3 Testing for local spatial autocorrelation
		7.4.4 Testing for local spatial heterogeneity
	7.5 Geostatistics
		7.5.1 Assumptions
		7.5.2 Classical geostatistical modeling
		7.5.3 Low-rank approximations
		7.5.4 Sparse approximations
	7.6 Spatial econometrics
		7.6.1 Spatial econometric models in R
		7.6.2 Generalized spatial two-stage least squares method
		7.6.3 Maximum likelihood–based methods
			7.6.3.1 Approximation of log of Jacobian
			7.6.3.2 Matrix exponential spatial specification approach
	7.7 Quantitative geography
		7.7.1 Geographically weighted regression-based approaches
		7.7.2 Spatial filtering approaches
	References
Index
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	C
	D
	E
	F
	G
	H
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	L
	M
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	O
	P
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	T
	U
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