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.

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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 SA1.1.4. 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 eigenvectors2.1.3. Principal…