Spatial regression analysis using eigenvector spatial filtering

__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......Page 1 SPATIALREGRESSIONANALYSIS USINGEIGENVECTORSPATIALFILTERING......Page 3 Copyright......Page 4 Dedication......Page 5 Foreword......Page 6 Moran eigenvector spatial filtering: Multiple origins and convergence......Page 7 A word about the theoretical background for MESF in ecology......Page 8 Extensions and the future of MESF analysis......Page 9 References......Page 10 Preface......Page 12 Data description......Page 15 A preview of the book's content......Page 18 References......Page 22 Chapter outline......Page 24 Defining SA......Page 26 A mathematical formularization of the first law of geography......Page 27 Quantifying spatial relationships: The spatial weights matrix......Page 28 Different measurements for different data types: Quantifying SA......Page 29 The MC: Distributional theory......Page 32 Effects of spatial dependence: Deviating from independent observations......Page 33 SA and the Moran scatterplot......Page 41 SA and histograms......Page 42 The mean and variance of the MC for linear regression residuals......Page 45 References......Page 49 2An introduction to spectral analysis......Page 51 SA: From a spatial frequency to a spatial spectral domain......Page 54 Eigenvalues and eigenvectors......Page 56 Principal components analysis: A reconnaissance......Page 57 The spectral decomposition of a modified SWM......Page 58 Visualizing map patterns with eigenvectors......Page 59 The spectral analysis of one-dimensional data......Page 61 The spectral analysis of two-dimensional data......Page 73 The spectral analysis of three-dimensional data......Page 75 Summary......Page 76 The spectral decomposition of a SWM......Page 77 References......Page 78 Chapter outline......Page 80 A theoretical foundation for ESFs......Page 81 The fundamental theorem of MESF......Page 84 Map pattern and SA: Heterogeneity in map-wide trends......Page 85 Estimating an ESF as an OLS problem: An illustrative linear regression example......Page 86 The selection of eigenvectors to construct an ESF......Page 88 Selected criteria for assessing regression models: The PRESS statistic, residual diagnostics, and multicollinearity......Page 89 Interpreting an ESF and its parameter estimates......Page 92 Comparisons between ESF and SAR model specification results......Page 93 Simulation experiments based upon ESFs......Page 94 ESF prediction with linear regression......Page 96 Summary......Page 98 References......Page 99 4Software implementation for constructing an ESF, with special reference to linear regression......Page 101 Software implementation......Page 102 Geographic scale and resolution issues for ESFs......Page 104 Determining the candidate set of eigenvectors......Page 105 A validation demonstration for approximate ESFs......Page 106 An exploration of a massively large remotely sensed image......Page 110 Correct SWM eigenvectors for a regular square tessellation......Page 111 Summary......Page 114 Appendix 4.A......Page 115 References......Page 116 5MESF and generalized linear regression......Page 117 The logistic regression model specification......Page 118 The binomial regression model specification......Page 121 The Poisson regression model specification......Page 123 Population density......Page 124 Counts of wildfires......Page 125 The negative binomial regression model specification......Page 126 Population density......Page 127 The selection of eigenvectors to construct an ESF for GLMs......Page 128 ESF prediction with generalized linear regression......Page 130 Summary......Page 132 References......Page 133 6Modeling spatial heterogeneity with MESF......Page 134 Spatially varying coefficients......Page 135 An ESF expansion of regression coefficients......Page 139 Local SA ESFs......Page 143 Local versus global SA......Page 145 Local MCs for ESFs......Page 148 Local GRs for ESFs......Page 151 Local Getis-Ord statistics for ESFs......Page 154 Summary......Page 156 Bonferroni adjustment simulation experiment results......Page 157 References......Page 158 7Spatial interaction modeling......Page 160 Initial spatial interaction descriptions of internal Texas migration......Page 162 Spatially autocorrelated origin and destination variables......Page 165 Network autocorrelation in migration flows......Page 168 Spatial and network autocorrelation in journey-to-work flows: A reconnaissance......Page 171 A toy example: Exemplifying the necessary data structures......Page 176 A Corpus Christi toy spatial interaction dataset R code......Page 182 References......Page 184 8Space-time modeling......Page 186 Estimating a SURE term......Page 188 Prediction based on an estimated RE term......Page 193 Space-time data structures: Eigenvector space-time filters......Page 196 The space-time lagged spatial structure specification: Results for Texas population density......Page 198 The space-time contemporaneous spatial structure specification: Results for Texas population density......Page 200 ESTF prediction......Page 201 A toy example: Exemplifying the necessary data structures......Page 203 Summary......Page 208 A Corpus Christi toy space-time dataset R code......Page 212 References......Page 213 9MESF and multivariate statistical analysis......Page 214 Selected mathematical features of PCA......Page 215 Multicollinearity......Page 216 Moving from PCA to FA: Seeking parsimony......Page 225 MANOVA and MESF......Page 227 DFA and MESF......Page 232 The DFA eigenfunction problem......Page 234 CCA and MESF......Page 236 The CCA eigenfunction problem......Page 238 ESFs spanning sets of attribute variables......Page 239 CA and MESF......Page 241 Summary......Page 244 A dendogram from Ward's algorithm for original attribute data......Page 245 Multivariate statistical analysis R code......Page 247 References......Page 255 The toy example: A Dallas-Fort Worth metroplex county geographic resolution dataset......Page 256 Moran scatterplots......Page 257 Normal approximation regression: The spatial linear regression specification......Page 259 Poisson regression: The MESF specification......Page 262 Binomial regression: The MESF specification......Page 264 Spatially varying coefficients: The MESF specification......Page 267 References......Page 269 Epilogue......Page 270 References......Page 271 E......Page 272 L......Page 273 P......Page 274 S......Page 275 W......Page 277 Back Cover......Page 278

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

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