Spatial regression analysis using eigenvector spatial filtering

Cover
SPATIAL
REGRESSION
ANALYSIS USING
EIGENVECTOR
SPATIAL
FILTERING
Copyright
Dedication
Foreword
	Moran eigenvector spatial filtering: Multiple origins and convergence
	A word about the theoretical background for MESF in ecology
	Extensions and the future of MESF analysis
	References
Preface
	Data description
	A preview of the book\'s content
	References
1
Spatial autocorrelation
	Chapter outline
	Defining SA
		A mathematical formularization of the first law of geography
		Quantifying spatial relationships: The spatial weights matrix
		Different measurements for different data types: Quantifying SA
		The MC: Distributional theory
	Impacts of SA on attribute statistical distributions
		Effects of spatial dependence: Deviating from independent observations
		SA and the Moran scatterplot
		SA and histograms
	Summary
	The mean and variance of the MC for linear regression residuals
	References
2
An introduction to spectral analysis
	Representing SA in the spectral domain
		SA: From a spatial frequency to a spatial spectral domain
		Eigenvalues and eigenvectors
		Principal components analysis: A reconnaissance
		The spectral decomposition of a modified SWM
		Representing the MC with eigenfunctions
		Visualizing map patterns with eigenvectors
	The spectral analysis of one-dimensional data
	The spectral analysis of two-dimensional data
	The spectral analysis of three-dimensional data
	Summary
	The spectral decomposition of a SWM
	References
3
MESF and linear regression
	Chapter outline
	A theoretical foundation for ESFs
		The fundamental theorem of MESF
		Map pattern and SA: Heterogeneity in map-wide trends
	Estimating an ESF as an OLS problem: An illustrative linear regression example
		The selection of eigenvectors to construct an ESF
		Selected criteria for assessing regression models: The PRESS statistic, residual diagnostics, and multicollinearity
		Interpreting an ESF and its parameter estimates
		Comparisons between ESF and SAR model specification results
	Simulation experiments based upon ESFs
	ESF prediction with linear regression
	Summary
	References
4
Software implementation for constructing an ESF, with special reference to linear regression
	Software implementation
	Geographic scale and resolution issues for ESFs
	Determining the candidate set of eigenvectors
	Extensions to large georeferenced datasets: Implications for big spatial data
		A validation demonstration for approximate ESFs
		An exploration of a massively large remotely sensed image
		Correct SWM eigenvectors for a regular square tessellation
	Summary
	Appendix 4.A
	References
5
MESF and generalized linear regression
	The logistic regression model specification
	The binomial regression model specification
	The Poisson regression model specification
		Population density
		Counts of wildfires
	The negative binomial regression model specification
		Population density
		Counts of wildfires
	The selection of eigenvectors to construct an ESF for GLMs
	ESF prediction with generalized linear regression
	Summary
	References
6
Modeling spatial heterogeneity with MESF
	Spatially varying coefficients
	An ESF expansion of regression coefficients
	Multicollinearity in spatially varying coefficients
	Local SA ESFs
		Local versus global SA
		Local MCs for ESFs
		Local GRs for ESFs
		Local Getis-Ord statistics for ESFs
	Summary
	Bonferroni adjustment simulation experiment results
	References
7
Spatial interaction modeling
	Initial spatial interaction descriptions of internal Texas migration
	Spatially autocorrelated origin and destination variables
	Network autocorrelation in migration flows
	Spatial and network autocorrelation in journey-to-work flows: A reconnaissance
	A toy example: Exemplifying the necessary data structures
	Summary
	A Corpus Christi toy spatial interaction dataset R code
	The functions.R code
	References
8
Space-time modeling
	Estimating a SURE term
		A RE term estimation sensitivity analysis
		Prediction based on an estimated RE term
	Space-time data structures: Eigenvector space-time filters
		The space-time lagged spatial structure specification: Results for Texas population density
		The space-time contemporaneous spatial structure specification: Results for Texas population density
		ESTF prediction
	A toy example: Exemplifying the necessary data structures
	Summary
	A Corpus Christi toy space-time dataset R code
	References
9
MESF and multivariate statistical analysis
	PCA, FA, and MESF
		Selected mathematical features of PCA
		Multicollinearity
		Moving from PCA to FA: Seeking parsimony
	MANOVA and MESF
	DFA and MESF
		The DFA eigenfunction problem
		DFA as a regression problem: Two-regions DFA
	CCA and MESF
		The CCA eigenfunction problem
		ESFs spanning sets of attribute variables
	CA and MESF
	Summary
	A dendogram from Ward\'s algorithm for original attribute data
	Multivariate statistical analysis R code
	References
10
Concluding comments: Toy dataset implementation demonstrations
	The toy example: A Dallas-Fort Worth metroplex county geographic resolution dataset
	The setup
	Moran scatterplots
	Normal approximation regression: The spatial linear regression specification
	Poisson regression: The MESF specification
	Binomial regression: The MESF specification
	Spatially varying coefficients: The MESF specification
	Summary
	References
Epilogue
	References
Index
	A
	B
	C
	D
	E
	F
	G
	H
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
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