Spatial Autocorrelation and Spatial Filtering: Gaining Understanding Through Theory and Scientific Visualization

ISBN-13: 9783540009320 / Angielski / Twarda / 2003 / 250 str.

Daniel A. Griffith

Opis

Exploiting the old maxim that "a picture is worth a thousand words," scientific visualization may be defined as the transformation of numerical scientific data into informative graphical displays. It introduces a nonverbal model into subdisciplines that hitherto employed mostly or only mathematical or verbal-conceptual models. The focus of this monograph is on how scientific visualization can help revolutionize the manner in which the tendencies for (dis)similar numerical values to cluster together in location on a map are explored and analyzed, affording spatial data analyses that are better understood, presented, and used. In doing so, the concept known as spatial autocorrelation - which characterizes these tendencies and is one of the key features of georeferenced data, or data tagged to the earth's surface - is further de-mystified. This self-correlation arises from relative locations in geographic space.

Recenzje

From the reviews:

"Daniel Griffith here makes an effort to expand the methodological toolbox of spatial analysis by presenting, analyzing, and meticulously demonstrating with numerous examples, the applications of spatial filtering ... . In sum, many readers will find the book an appealing source of geographic and statistical material, richly supplemented by the use of scientific visualization ... . Conceivably, spatial researchers will appreciate its invigorating introduction to mathematical-geographical properties of spatial datasets, and the statisticians will enjoy its many witty and challenging examples." (Oleg Smirnov, Journal of Regional Science, Vol. 44 (3), 2004)

Spis treści

1 Introduction.- 1.1 Scientific Visualization.- 1.2 What Is Spatial Autocorrelation?.- 1.3 Selected Visualization Tools: An Overview.- 1.3.1 Graphical Portrayals of Spatial Autocorrelation.- 1.4 The Sample Georeferenced Datasets.- 1.4.1 Selected Interval/Ratio Datasets.- 1.4.2 Selected Counts Datasets.- 1.4.3 Selected Binomial Datasets.- 2 Salient Properties of Geographic Connectivity Underlying Spatial Autocorrelation.- 2.1 Eigenfunctions Associated with Geographic Connectivity Matrices.- 2.1.1 Eigenvalue Decompositions.- 2.1.2 Eigenvectors Associated with Geographic Connectivity Matrices.- 2.1.3 The Maximum MC Value (MCmax).- 2.1.4 Moments of Eigenvalue Distributions.- 2.2 Generalized Eigenvalue Frequency Distributions.- 2.2.1 The Extreme Eigenvalues of Matrices C and W.- 2.2.2 Spectrum Results for Matrices C and W.- 2.2.3 Spectrum Results for Matrix (I - 11T/n)C(I - 11T/n).- 2.3 The Auto-Gaussian Jacobian Term Normalizing Factor.- 2.3.1 Simplification of the Auto-Gaussian Jacobian Term Based upon Matrix W for a Regular Square Tessellation and the Rook’s Definition of Connectivity.- 2.4 Eigenfunctions Associated with the GR.- 2.5 Remarks and Discussion.- 3 Sampling Distributions Associated with Spatial Autocorrelation.- 3.1 Samples as Random Permutations of Values across Locations on a Man: Randomization.- 3.2 Simple Random Samples at Each Location on a Map: Unconstrained Selection.- 3.3 Samples as Ordered Random Drawings from a Parent Frequency Distribution: Extending the Permutation Perspective.- 3.3.1 The Samnling Distribution fnr MC.- 3.3.2 The Distribution of p for an Auto-normal SAR Model.- 3.4 Samples as Outcomes of a Multivariate Drawing: Extending the Simple Random Samnling Persnective.- 3.4.1 The Auto-normal Model: ML Estimation.- 3.4.2 The Auto-logistic/binomial Model.- 3.4.3 Embedding Spatial Autocorrelation through the Mean Response.- 3.5 Effective Sample Size.- 3.5.1 Estimates Based upon a Single Mean Response.- 3.5.2 Estimates Based upon Multiple Mean Responses.- 3.5.3 Estimates Based upon a Difference of Means for Correlated (Paired) Samples.- 3.5.4 Relationships between Effective Sample Size and the Configuration of Sample Points.- 3.6. Remarks and Discussion.- 4 Spatial Filtering.- 4.1 Eigenvector-based Spatial Filtering.- 4.1.1 Map Patterns Depicted by Eigenvectors of Matrix (I-?C)T(I-? C).- 4.1.2 Similarities with Conventional PCA.- 4.1.3 Orthogonality and Uncorrelatedness of the Eigenvectors.- 4.1.4 Linear Combinations of Eigenvectors of Matrix (I - 11T/n)C(I - 11T/n).- 4.2 Coefficients for Single and Linear Combinations of Distinct Map Patterns.- 4.2.1 Decomposition of Regressor and Regressand Attribute Variables.- 4.2.2 The Sampling Distributions of y? and r.- 4.3 Eigenvector Selection Criteria.- 4.3.1 The Auto-normal Model.- 4.3.2 The Auto-logistic/binomial Model.- 4.3.3 The Auto-Poisson Model.- 4.3.4 The Case of Negative Spatial Autocorrelation.- 4.4 Regression Analysis: Standard Errors Based upon Simulation Experiments and Resampling.- 4.4.1 Simulating Error for Georeferenced Data.- 4.4.2 Bootstrapping Georeferenced Data.- 4.5 The MC Local Statistic and Illuminating Diagnostics.- 4.5.1 The MCis.- 4.5.2 Diagnostics Based upon Eigenvectors of Matrix (I-11T/n)C(I-11T/n).- 4.6 Remarks and Discussion.- 5 Spatial Filtering Applications: Selected Interval/Ratio Datasets.- 5.1 Geographic Distributions of Settlement Size in Peru.- 5.2 The Geographic Distribution of Lyme Disease in Georgia.- 5.3 The Geographic Distribution or Biomass in the Hign Peak District.- 5.4 The Geographic Distribution of Agricultural and Topographic Variables in Puerto Rico.- 5.5 Remarks and Discussion.- 5.5.1 Relationship between the SAR and Eigenvector Spatial Filtering Specifications.- 5.5.2 Computing Back-transformations.- 6 Spatial Filtering Applications: Selected Counts Datasets.- 6.1 Geographic Distributions of Settlement Counts in Pennsylvania.- 6.2 The Geographic Distribution of Farms in Loiza, Puerto Rico.- 6.3 The Geographic Distribution of Volcanoes in Uganda.- 6.4 The Geographic Distribution of Cholera Deaths in London.- 6.5 The Geographic Distribution of Drumlins in Ireland.- 6.6 Remarks and Discussion.- 7 Spatial Filtering Applications: Selected Percentage Datasets.- 7.1 The Geographic Distribution of the Presence/Absence of Plant Disease in an Agricultural Field.- 7.2 The Geographic Distribution of Plant Disease in an Agricultural Field.- 7.3 The Geographic Distribution of Blood Group A in Eire.- 7.4 The Geographic Distribution of Urbanization across the Island of Puerto Rico.- 7.5 Remarks and Discussion.- 8 Concluding Comments.- 8.1 Spatial Filtering versus Spatial Autoregression.- 8.2 Some Numerical Issues in Spatial Filtering.- 8.2.1 Covariation of Spatial Filter and SAR Spatial Autocorrelation Measures.- 8.2.2 Exploding Georeferenced Data with a Spatial Filter When Maps Have Holes or Gaps: Estimating Missing Data Values.- 8.2.3 Rotation and Theoretical Eigenvectors Given by Theorem 2.5 for Regular Square Tessellations Forming Rectangular Regions.- 8.2.4 Effective Sample Size Revisited.- 8.3 Stepwise Selection of Eigenvectors for an Auto-Poisson Model.- 8.4 Binomial and Poisson Overdispersion.- 8.5 Future Research: What Next?.- List of Symbols.- List of Tables.- List of Figures.- References.- Author Index.- Place Index.

Blurb

Advances in Spatial Science

This series of books is dedicated to reporting on recent advances in spatial science. It contains scientific studies focusing on spatial phenomena, utilising theoretical frameworks, analytical methods, and empirical procedures specifically designed for spatial analysis. The series brings together innovative spatial research utilising concepts, perspectives, and methods with a relevance to both basic science and policy making. The aim is to present advances in spatial science to an informed readership in universities, research organisations, and policy-making institutions throughout the world.

 

The type of material considered for publication in the series includes:

 

- Monographs of theoretical and applied research in spatial science;

- State-of-the-art volumes in areas of basic research;

- Reports of innovative theories and methods in spatial science;

- Tightly edited reports form specially organised research seminars.

 

Manuscripts must be prepared in accordance with the guidelines for authors and editors that may be obtained from Springer-Verlag. Manuscripts considered for the series will be reviewed by independent experts to ensure their originality, scientific level, and international policy relevance.