UID:
edoccha_9960074462202883
Format:
1 online resource (288 pages).
ISBN:
0-12-815692-9
,
0-12-815043-2
Series Statement:
Spatial econometrics and spatial statistics
Content:
"Spatial Regression Analysis Using Eigenvector Spatial Filtering provides both theoretical foundations and guidance on practical implementation for the eigenvector spatial filtering (ESF) technique. ESF is a novel and powerful spatial statistical methodology that allows spatial scientists to account for spatial autocorrelation in georeferenced data analyses. With its flexible structure, ESF can be easily applied to generalized linear regression models. The book discusses ESF specifications for various intermediate-level topics, including spatially varying coefficients models, (non) linear mixed models, local spatial autocorrelation, and spatial interaction models. In addition, it provides a tutorial for ESF model specification and interfaces, including author developed, user-friendly software"--
Note:
Front Cover -- Spatial Regression Analysis Using Eigenvector Spatial Filtering -- Copyright -- Dedication -- Contents -- 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 -- Chapter 1: Spatial autocorrelation -- 1.1. Defining SA -- 1.1.1. A mathematical formularization of the first law of geography -- 1.1.2. Quantifying spatial relationships: The spatial weights matrix -- 1.1.3. Different measurements for different data types: Quantifying SA -- 1.1.4. The MC: Distributional theory -- 1.2. Impacts of SA on attribute statistical distributions -- 1.2.1. Effects of spatial dependence: Deviating from independent observations -- 1.2.2. SA and the Moran scatterplot -- 1.2.3. SA and histograms -- 1.3. Summary -- Appendix 1.A. The mean and variance of the MC for linear regression residuals -- References -- Chapter 2: An introduction to spectral analysis -- 2.1. Representing SA in the spectral domain -- 2.1.1. SA: From a spatial frequency to a spatial spectral domain -- 2.1.2. Eigenvalues and eigenvectors -- 2.1.3. Principal components analysis: A reconnaissance -- 2.1.4. The spectral decomposition of a modified SWM -- 2.1.5. Representing the MC with eigenfunctions -- 2.1.6. Visualizing map patterns with eigenvectors -- 2.2. The spectral analysis of one-dimensional data -- 2.3. The spectral analysis of two-dimensional data -- 2.4. The spectral analysis of three-dimensional data -- 2.5. Summary -- Appendix 2.A. The spectral decomposition of a SWM -- References -- Chapter 3: MESF and linear regression -- 3.1. A theoretical foundation for ESFs -- 3.1.1. The fundamental theorem of MESF.
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3.1.2. Map pattern and SA: Heterogeneity in map-wide trends -- 3.2. Estimating an ESF as an OLS problem: An illustrative linear regression example -- 3.2.1. The selection of eigenvectors to construct an ESF -- 3.2.2. Selected criteria for assessing regression models: The PRESS statistic, residual diagnostics, and multicollinearity -- 3.2.3. Interpreting an ESF and its parameter estimates -- 3.2.4. Comparisons between ESF and SAR model specification results -- 3.3. Simulation experiments based upon ESFs -- 3.4. ESF prediction with linear regression -- 3.5. Summary -- References -- Chapter 4: Software implementation for constructing an ESF, with special reference to linear regression -- 4.1. Software implementation -- 4.2. Geographic scale and resolution issues for ESFs -- 4.3. Determining the candidate set of eigenvectors -- 4.4. Extensions to large georeferenced datasets: Implications for big spatial data -- 4.4.1. A validation demonstration for approximate ESFs -- 4.4.2. An exploration of a massively large remotely sensed image -- 4.4.3. Correct SWM eigenvectors for a regular square tessellation -- 4.5. Summary -- Appendix 4.A. Frequency distributions of the 10,000 NDVI values for the validation analysis, with superimposed theoretica ... -- References -- Chapter 5: MESF and generalized linear regression -- 5.1. The logistic regression model specification -- 5.2. The binomial regression model specification -- 5.3. The Poisson regression model specification -- 5.3.1. Population density -- 5.3.2. Counts of wildfires -- 5.4. The negative binomial regression model specification -- 5.4.1. Population density -- 5.4.2. Counts of wildfires -- 5.5. The selection of eigenvectors to construct an ESF for GLMs -- 5.6. ESF prediction with generalized linear regression -- 5.7. Summary -- References -- Chapter 6: Modeling spatial heterogeneity with MESF.
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6.1. Spatially varying coefficients -- 6.2. An ESF expansion of regression coefficients -- 6.3. Multicollinearity in spatially varying coefficients -- 6.4. Local SA ESFs -- 6.4.1. Local versus global SA -- 6.4.2. Local MCs for ESFs -- 6.4.3. Local GRs for ESFs -- 6.4.4. Local Getis-Ord statistics for ESFs -- 6.5. Summary -- Appendix 6.A. Bonferroni adjustment simulation experiment results -- References -- Chapter : Spatial interaction modeling -- 7.1. Initial spatial interaction descriptions of internal Texas migration -- 7.2. Spatially autocorrelated origin and destination variables -- 7.3. Network autocorrelation in migration flows -- 7.4. Spatial and network autocorrelation in journey-to-work flows: A reconnaissance -- 7.5. A toy example: Exemplifying the necessary data structures -- 7.6. Summary -- Appendix 7.A. A Corpus Christi toy spatial interaction dataset R code -- Appendix 7.B. The functions.R code -- References -- Chapter 8: Space-time modeling -- 8.1. Estimating a SURE term -- 8.1.1. A RE term estimation sensitivity analysis -- 8.1.2. Prediction based on an estimated RE term -- 8.2. Space-time data structures: Eigenvector space-time filters -- 8.2.1. The space-time lagged spatial structure specification: Results for Texas population density -- 8.2.2. The space-time contemporaneous spatial structure specification: Results for Texas population density -- 8.2.3. ESTF prediction -- 8.3. A toy example: Exemplifying the necessary data structures -- 8.4. Summary -- Appendix 8.A. A Corpus Christi toy space-time dataset R code -- References -- Chapter 9: MESF and multivariate statistical analysis -- 9.1. PCA, FA, and MESF -- 9.1.1. Selected mathematical features of PCA -- 9.1.2. Multicollinearity -- 9.1.3. Moving from PCA to FA: Seeking parsimony -- 9.2. MANOVA and MESF -- 9.3. DFA and MESF -- 9.3.1. The DFA eigenfunction problem.
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9.3.2. DFA as a regression problem: Two-regions DFA -- 9.4. CCA and MESF -- 9.4.1. The CCA eigenfunction problem -- 9.4.2. ESFs spanning sets of attribute variables -- 9.5. CA and MESF -- 9.6. Summary -- Appendix 9.A. A dendogram from Ward's algorithm for original attribute data -- Appendix 9.B. Multivariate statistical analysis R code -- References -- Chapter 10: Concluding comments: Toy dataset implementation demonstrations -- 10.1. The toy example: A Dallas-Fort Worth metroplex county geographic resolution dataset -- 10.2. The setup -- 10.3. Moran scatterplots -- 10.4. Normal approximation regression: The spatial linear regression specification -- 10.5. Poisson regression: The MESF specification -- 10.6. Binomial regression: The MESF specification -- 10.7. Spatially varying coefficients: The MESF specification -- 10.8. Summary -- References -- Epilogue -- References -- Index -- Back Cover.
Language:
English
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