__Spatial Regression Analysis Using Eigenvector Spatial Filtering__ provides theoretical foundations and guides practical implementation of the Moran eigenvector spatial filtering (MESF) technique. MESF is a novel and powerful spatial statistical methodology that allows spatial scientists to account for spatial autocorrelation in their georeferenced data analyses. Its appeal is in its simplicity, yet its implementation drawbacks include serious complexities associated with constructing an eigenvector spatial filter. This book discusses MESF specifications for various intermediate-level topics, including spatially varying coefficients models, (non) linear mixed models, local spatial autocorrelation, space-time models, and spatial interaction models. __Spatial Regression Analysis Using Eigenvector Spatial Filtering__ is accompanied by sample R codes and a Windows application with illustrative datasets so that readers can replicate the examples in the book and apply the methodology to their own application projects. It also includes a Foreword by Pierre Legendre. 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 Back Cover
Spatial Regression Analysis Using Eigenvector Spatial Filtering provides theoretical foundations and guides practical implementation of the Moran eigenvector spatial filtering (MESF) technique. MESF is a novel and powerful spatial statistical methodology that allows spatial scientists to account for spatial autocorrelation in their georeferenced data analyses. Its appeal is in its simplicity, yet its implementation drawbacks include serious complexities associated with constructing an eigenvector spatial filter.
This book discusses MESF specifications for various intermediate-level topics, including spatially varying coefficients models, (non) linear mixed models, local spatial autocorrelation, space-time models, and spatial interaction models. Spatial Regression Analysis Using Eigenvector Spatial Filtering is accompanied by sample R codes and a Windows application with illustrative datasets so that readers can replicate the examples in the book and apply the methodology to their own application projects. It also includes a Foreword by Pierre Legendre.
- Reviews the uses of ESF across linear regression, generalized linear regression, spatial autocorrelation measurement, and spatially varying coefficient models
- Includes computer code and template datasets for further modeling
- Provides comprehensive coverage of related concepts in spatial data analysis and spatial statistics
