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

by Daniel A. Griffith

Overview

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 auorrelation - 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.

Product Details

ISBN-13:	9783540009320
Publisher:	Springer Berlin Heidelberg
Publication date:	08/13/2003
Series:	Advances in Spatial Science
Edition description:	2003
Pages:	250
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1 Introduction.- 1.1 Scientific Visualization.- 1.2 What Is Spatial Auorrelation?.- 1.3 Selected Visualization Tools: An Overview.- 1.4 The Sample Georeferenced Datasets.- 2 Salient Properties of Geographic Connectivity Underlying Spatial Auorrelation.- 2.1 Eigenfunctions Associated with Geographic Connectivity Matrices.- 2.2 Generalized Eigenvalue Frequency Distributions.- 2.3 The Auto-Gaussian Jacobian Term Normalizing Factor.- 2.4 Eigenfunctions Associated with the GR.- 2.5 Remarks and Discussion.- 3 Sampling Distributions Associated with Spatial Auorrelation.- 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.- 3.4 Samples as Outcomes of a Multivariate Drawing: Extending the Simple Random Samnling Persnective.- 3.5 Effective Sample Size.- 3.6. Remarks and Discussion.- 4 Spatial Filtering.- 4.1 Eigenvector-based Spatial Filtering.- 4.2 Coefficients for Single and Linear Combinations of Distinct Map Patterns.- 4.3 Eigenvector Selection Criteria.- 4.4 Regression Analysis: Standard Errors Based upon Simulation Experiments and Resampling.- 4.5 The MC Local Statistic and Illuminating Diagnostics.- 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.- 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.- 8.3 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.

Editorial Reviews

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)

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