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Book Cover
Author Griffith, Daniel A.

Title Spatial regression analysis using Eigenvector spatial filtering / Daniel A. Griffith, Yongwan Chun, Bin Li
Published [Place of publication not identified] : Academic Press, 2019
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Description 1 online resource
Contents 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 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
3.1.2. Map pattern and SA: Heterogeneity in map-wide trends3.2. 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 regression4.1. 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
Subject Eigenvectors.
Regression analysis.
Spatial analysis (Statistics)
Regression analysis.
Spatial analysis (Statistics)
Form Electronic book
Author Chun, Yongwan.
Li, Bin.
ISBN 0128150432