Advances in Spatial Science

Transcription

1 Advances in Spatial Science Editorial Board Manfred M. Fischer Geoffrey J.D. Hewings Peter Nijkamp Folke Snickars (Coordinating Editor) For further volumes:

2 Arthur Getis

3 Luc Anselin Editors l Sergio J. Rey Perspectives on Spatial Data Analysis 123

4 Editors Prof. Dr. Luc Anselin Prof. Dr. Sergio J. Rey School of Geographical Sciences Arizona State University Coor Hall 975 S Myrtle Avenue Tempe, AZ USA Luc.Anselin@asu.edu Sergio.Rey@asu.edu ISBN e-isbn DOI: / Springer Heidelberg Dordrecht London New York Library of Congress Control Number: # Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: SPi Publisher Services Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 To Arthur Getis

6 Preface Spatial data analysis has seen explosive growth in recent years. Both in mainstream statistics and econometrics as well as in many applied fields, the attention to space, location, and interaction has become an important feature of scholarly work. The methods developed to deal with problems of spatial pattern recognition, spatial autocorrelation, and spatial heterogeneity have seen greatly increased adoption, in part due to the availability of user friendly desktop software. Through his theoretical and applied work, Arthur Getis has been a major contributing figure in this development. In this volume, we take both a retrospective and a prospective view of the field. We use the occasion of the retirement and move to emeritus status of Arthur Getis to highlight the contributions of his work. In addition, we aim to place it into perspective in light of the current state of the art and future directions in spatial data analysis. To this end, we elected to combine reprints of selected classic contributions by Getis with chapters written by key spatial scientists. These scholars were specifically invited to react to the earlier work by Getis with an eye toward assessing its impact, tracing out the evolution of related research, and to reflect on the future broadening of spatial analysis. The organization of the book follows four main themes in Getis contributions: Spatial analysis Pattern analysis Local statistics Applications For each of these themes, the chapters provide a historical perspective on early methodological developments and theoretical insights, assessments of these contributions in light of the current state of the art, as well as descriptions of new techniques and applications. Putting together a volume such as this would not be possible without the efforts of many individuals. We feel most fortunate to have been in the skilled hands of the Springer-Verlag team and in particular wish to extend our gratitude to Katharina Wetzel-Vandai and Barbara Fess for their continued support during this project and to Manfred Fischer for his editorial suggestions. We are indebted to the authors of both the original pieces as well as the new contributions and the referees. The vii

7 viii Preface project benefited enormously from the technical typesetting skills of Xinyue Ye of the Department of Geography at San Diego State University and David Folch of the School of Geographical Sciences at Arizona State University, without whose dedicated efforts this volume would not have been completed. The Spatial Analysis Laboratory at the University of Illinois Champaign-Urbana and the Department of Geography at San Diego State University both provided institutional support during the early phases of this project. The GeoDa Center for Geospatial Analysis and Computation in the School of Geographical Sciences at Arizona State University provided critical support to bring the project to closure. Finally, we would like to dedicate this volume to Arthur Getis whose contributions have impacted so many. We feel fortunate to not only count ourselves among those, but also to call him a valued friend. Tempe, AZ, USA August 2009 Luc Anselin Sergio Rey

8 Foreword Born in Philadelphia in 1934 Arthur Getis received his undergraduate degrees from Pennsylvania State University and his Ph.D. in Geography from the University of Washington in Until his retirement, he held the Stephen and Mary Birch Foundation Endowed Chair on Geographical Studies at San Diego State University. Prior to joining San Diego University, he was the Chairman of the Geography Department and Director of the School of Social Sciences at the University of Illinois. He has also served on the board, or as chairman of scientific societies, most notably the Regional Science Association. Getis research studies in social science have included work in location theory, urban geography, mathematical pattern analysis, spatial analysis, geographical information science, and most recently, clustering analysis of disease or crime. Some of this material is reflected in his books: Models of Spatial Processes Approaches to the Study of Point, Line, and Area Patterns (with B. Boots, Cambridge University Press 1978); Point Pattern Analysis (with B. Boots, Sage Publications, 1987); The Tyranny of Data (San Diego State University Press, 1995); Recent Developments in Spatial Analysis Spatial Statistics, Behavioral Modeling, and Computational Intelligence (with M. Fischer, Springer 1997); and Spatial Econometrics and Spatial Statistics (edited with others, Palgrave, 2003). Related work has been published in over 80 articles and in worldwide lectures. With J. Getis, he has also contributed to geographic education in the United States. To summarize, Arthur Getis outstanding contributions have been to the rigorous study of spatial patterns including the effect of autocorrelation and the introduction of local statistics. The latter include numerous original developments that allow the recognition of variations from place to place in contradistinction to more conventional global analyses that are not aware of spatial detail. The introduction of these methods has revolutionized recent spatial analysis. For this, we need to thank the editors Luc Anselin and Sergio Rey. Santa Barbara, CA, USA January 2009 Waldo Tobler ix

9 Contents 1 Perspectives on Spatial Data Analysis... 1 Luc Anselin and Sergio J. Rey Part I Spatial Analysis 2 Spatial Interaction and Spatial Autocorrelation: A Cross-Product Approach Arthur Getis 3 Spatial Statistical Analysis and Geographic Information Systems Luc Anselin and Arthur Getis 4 Whose Hand on the Tiller? Revisiting Spatial Statistical Analysis and GIS Michael F. Goodchild 5 Spatial Interaction and Spatial Autocorrelation Manfred M. Fischer, Martin Reismann, and Thomas Scherngell Part II Pattern Analysis 6 Second-Order Analysis of Point Patterns: The Case of Chicago as a Multi-center Urban Region Arthur Getis 7 Second-Order Neighborhood Analysis of Mapped Point Patterns Arthur Getis and Janet Franklin 8 A Class of Local and Global K Functions and Their Exact Statistical Methods Atsu Okabe, Barry Boots and Toshiaki Satoh xi

10 xii Contents 9 Spatial Point Pattern Analysis of Plants Janet Franklin Part III Local Statistics 10 The Analysis of Spatial Association by Use of Distance Statistics Arthur Getis and J. Keith Ord 11 Constructing the Spatial Weights Matrix Using a Local Statistic Arthur Getis and Jared Aldstadt 12 Spatial Autocorrelation: A Statistician s Reflections J. Keith Ord 13 Health Surveillance Around Prespecified Locations Using Case-Control Data Peter A. Rogerson Part IV Applications 14 Spatial Filtering in a Regression Framework: Examples Using Data on Urban Crime, Regional Inequality, and government Expenditures Arthur Getis 15 Characteristics of the Spatial Pattern of the Dengue Vector, Aedes aegypti, in Iquitos, Peru Arthur Getis, Amy C. Morrison, Kenneth Gray, and Thomas W. Scott 16 Spatial Filtering and Missing Georeferenced Data Imputation: A Comparison of the Getis and Griffith Methods Daniel Griffith 17 Spatial Patterns of Fertility in Rural Egypt John R. Weeks References Author Index Index Contributors...287

11 List of Tables 1.1 Samples of empirical workby Getis in epidemiology Most cited articles A comparison of various spatial models and the cross-product statistic The log-additive spatial interaction model: parameter estimates and performance measures (N =12,432) Spatial econometric flow models based on different spatial weights matrix specifications: ML estimates using Ng and Peyton s Cholesky algorithm (N =12,432observations) Characteristics of G i statistics Standard normal variates for G(d) and I(d) under varying circumstances for a specified d value Spatial association among counties: SIDS rates by county in North Carolina, Highest positive and negative standard normal variates by county for G i (d) and G i(d): SIDS rates in North Carolina, (d =33miles) Spatial association among zip code districts: dwelling unit prices in San Diego county, September Highest positive and negative standard normal variates by zip code district for G i (d) and G i(d): dwelling unit prices in San Diego county, September 1989 (d =5miles) Data set descriptions AIC results Estimated autocorrelationcoefficientvalues Moran s Z(I)of residuals Asymptoticrelative efficiencies fordifferentpatternsof weights Relative magnitudes of the G and LISA coefficients: major differencesare in boldand moderatedifferencesare in italics Summaryof clusteringstatistics L(d) values for distances m for houses and adult mosquitoes in Maynas a* xiii

12 xiv List of Tables 15.3 L(d) values for distances m for houses and adult mosquitoes in Maynas a* ˆL(d) values for distances for houses, adult mosquitoes, pupae, water-holding containers, positive water-holding containers in Maynas a* ˆL(d) values for distances m for houses, adult mosquitoes, pupae, water-holding containers, positive water-holding containers in Maynas a* Number of members of clusters in Maynas and Tupac Amaru in time periods a and b One or more adult mosquitoes and/or pupae present in houses in Maynas and Tupac Amaru in time periods a and b Spearman s rank correlations of the number of containers per house with the number of mosquitoes and pupae per house ˆL(d) values for 10 m for Maynas and Tupac Amaru for time periods a and b* Sources of data forusing (16.1)to constructfig Selected model-based imputations for two selected empirical data sets containing missing values: Pennsylvaniacoal ash, andvandalizedturnipfield plots Comparisonsof the two spatial filter estimators Fertility decline in Egypt and Menoufia, Regression models for fertility in Menoufia, Regression models for fertility in Menoufia, Regression models for fertility in Menoufia, Regression models of fertility change between 1976 and Results for Menoufia from the 1988 and 1995 Egyptian demographicand health surveys...255

13 List of Figures 1.1 Annual citation patterns for Arthur Getis Concept co-citationnetwork Authorco-citationnetwork Journalco-citationnetwork Functionsof a GIS Origin-based and destination-based similarity. The flows (i, j) and (r, s) are origin-based similar in Case A since the origin regions i and r are contiguous spatial units, and destination-based similar in Case B since the destination regions j and s are contiguous spatial units Flows with selected significant G ij ( o W ) statistic: (a) indicating high residual flows from neighbours of origin i to the destination region Île-de-France; and (b) indicating low residual flows from neighbours of the region Leipzig to a destination region j A border correction is needed when the distance xy is greater than the distance of x to the nearest border Population distribution in the Chicago region A plot of ˆL for the population of the Chicago region. The straight line is the mean for a Poisson process. The portion of the diagram from t =0to t =0.06 is enlargedon Fig A plot of ˆL for the population of the Chicago region. The dashed lines are the 95% confidencebands of the Poisson process Cumulative distribution curve (heavy line) ofˆl i (d) for hypothetical tree in a square of area 1. L i (d) is the number of points within distance d of point i corrected for the boundary effect, and scaled such that L i (d) =d when L i (d) represents a pattern produced by a Poisson process in the plane. Dashed lines represent 0.01 significance levels around the line representing Poisson process Point pattern representation of tree locations in the study area. The letters A, B, and C mark particular individual trees, which are referredto in Fig.7.4.Northis up xv

14 xvi List of Figures 7.3 Values for ˆL(d) over the range 0.01 d L(d) is the number of points within distance d of all points i corrected for the boundary effect, and scaled such that L(d) =d when L(d) represents a pattern produced by a Poisson process in the plane. ˆL(d) may be interpreted as the average for all 108 points (from Fig. 7.2) taken together. Solid line shows expected values given a Poisson distribution. Solid dots showobservedvalues Values for ˆL i (d) over the range 0.01 d 0.30 when i = A Pattern created by assigning to each tree its ˆL(d) value Points of P (the white circles), points of Q (the black circles) andadiskd i (t) centered at a point of Q with radius t The edge effect: (a) the first case, (b) the second case, (c) adjustment Disks are not overlapped, t t max (a), and they are overlapped, t>t max (b) Local Voronoi cross K function (a) and global Voronoi cross K function(b) Locations of 440 Torrey pine trees (Pinus torreyana) in the East Grove area of Torrey Pines State Reserve, La Jolla, CA, USA (E. Santos and J. Franklin, unpublished data). Map on left shows tree locations scaled by size (DBH, trunk diameter at 1.3 m height), and center map shown the tree locations scaled by the local value of L(t) at lag of 14 m (see Fig. 9.2). Negative values shown as squares, positive values as circles. Map on right shown tree locations scaled by the values of local Gi* (see text) where neighborhood contiguity is based on a lag distance of 25 m (maximum nearest neighbor distance used to avoid islands). These analyses were carried out using the spatstat package in the R statistical environment (R Development Core Team, 2004) Global L(t) for the trees shown in Fig. 9.1 at lags of m showing significant clumping at all scales and a peak in L(t) at m; (b) Moran s I as a measure of spatial autocorrelation of tree size (DBH, see Fig. 9.1 caption) where neighborhood contiguity is based on a lag distance of 10 m, indicating significant positive spatial association of tree size at lag 1 (10 m). These analyses were carried out using the splancs package (Rowlingson and Diggle, 1993) in the R statistical environment (R Development Core Team, 2004) Sudden infant death rates for counties of North Carolina,

15 List of Figures xvii 10.2 Z[G i (d = furthest nearest neighbor = 33 miles)] for SIDS rates of counties of North Carolina, San Diego house prices, September Z[G i (d = furthest nearest neighbor = 5 miles)] for house prices of San Diego county zip code districts, September Random data set. Shading values are in random normal deviates Two cluster data set. Shading values are in random normal deviates Six cluster data set. Shading values are in random normal deviates d c s calculated for data sets in Figs. 11.1, 11.2, and Distances are based on one unit separating centers of rook s case neighbors True andtest pattern foran interior cell on a regulargrid Normal probability plot for G statistics with two clusters of extremevalues (Minitabplot) Example of a partitioned study area Components of spatial model building There is no discernible spatial pattern of the residuals of the trial equation. One might get the impression from this that there is no spatial autocorrelationin the data The dependent variable. Log Y,ishighinthewestand low in the east. AH other variables in the trial equation act similarly Map of Iquitos, Peru and location of the Maynas and Tupac Amarustudy areas Mosquitoes per house in the Maynas a study Clusters of Aedes aegypti adults in the Maynas a study based on the number of mosquitoes in houses Clusters of Aedes aegypti adults in the Maynas a study based on presenceor absenceof mosquitoes Clusters of Aedes aegypti pupae in the Maynas a study based on presence or absence of pupae Scatter plot of EM algorithm results: reported published vs. (16.1)generatedestimates Spherical model plots (denoted by asterisks) superimposed on experimental semivariograms (denoted by solid circles). (a) left: coal ash data (n = 208). (b) right: vandalized turnip field plot residuals (n =33) The study site of Menoufia governorate, Egypt Situations improvedbydasymetricmapping Fertility levels in Menoufia in Spatial pattern of fertility in Spatial pattern of fertility in Spatial pattern of fertility change between 1976 and Spatial pattern of illiteracy change between 1976 and