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Information to Users INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9* black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMtdirectty to order. ProQuest Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600 UMI i r SPATIAL ASSOCIATION MEASURES FOR AN ESDA-GIS FRAMEWORK: DEVELOPMENTS, SIGNMCANCE TESTS, AND APPLICATIONS TO SPATIO-TEMPORAL INCOME DYNAMICS OF U.S. LABOR MARKET AREAS, 1969-1999 DISSERTATION Presented in Partial Fulfillment of the Requirements for The Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Sang-Il Lee, M.A. ***** The Ohio State University 2001 Dissertation Conunittee: pproved Professor Lawrence A. Brown, Adviser Professor Mei-Po Kwan Adviser Professor Michael Tiefelsdorf Department of Geography UMI Number: 3031220 Copyright 2002 by Lee, Sang-Il All rights reserved. UMI* UMI Microform 3031220 Copyright 2002 by Bell & Howell Information and Learning Company. Ali rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 . - "k ■ ABSTRACT This study is concerned with developing new spatial association measures (SAMs), elaborating generalized significance testing methods, proposing associated graphical and mapping techniques for an ESDA-GIS (Exploratory Spatial Data Analysis- Geographic Information Systems) fiamework, and applying those techniques to spatio- temporal income dynamics across U.S. labor market areas, 1969-1999. It is argued that SAMs play a central role in obtaining a seamless integration between ESDA and GIS where the cross-fertilization between them is highly achieved in such a way that ESDA takes advantage of GIS’s data manipulation and visualization capabilities and a GIS utilizes ESDA’s statistical integrity and computational efficiency. Two sets of new SAMs are developed: global S and local Si as univariate SAMs, and global L and local L{ as bivariate SAMs. Global S, spatial smoothing scalar, captures the degree of spatial smoothing when» geographicafvariableis transformed to its spatially smoothed vector in which each observation is re computed in conjunction with its neighbors as defined in a spatial w ei^ts matrix. If a spatial pattern is more spatially clustered, it is given a higher value of S. Local St, defined as an observation’s relative contribution to the corresponding global 5, allows a researcher to detect spatial clusters 11 with efFectively avoiding the tyranny of refen»nrg nhservarinns that pn»<»Yisting iinivariarg SAMs have suffered from. Global L and local Li are devised to conform to two concepts of association involved in comparing two spatial patterns in a simultaneous fashion: pairwise point-to- point association and univariate spatial association. Whereas aspatial bivariate association measure, such as Pearson’s correlation coefficient, is dedicated solely to the first type of association, global L captures numerical co-variances conditioned by topological relationships among observations to parameterize bivariate spatial dependence and to calibrate the degree of spatial co-patteming. Local £/, a localized spatial correlation, captures the degree to which each location conforms to or deviats from the corresponding global I , and allows for exploring spatial heterogeneity in a bivariate relation. Two sets of generalized significance testing methods are elaborated: one based on normality assumption and the other on randomization assumption. It is demonstrated that a transformation of SAMs to ratio of quadratic forms allows for a derivation of first four moments for global and local univariate SAMs including S and Si under normality assumption. The Extended Mantel Test and the generalized vector randomization test are elaborated to compute first two moments of SAMs under randomization assumption. It is evidenced that the devised randomization test procedures can be applied to all the SAMs, whether global or local, whether univariate or bivariate, or whether a zero-diagonal in a spatial weights matrix or not. ui geographical inquiries is illustrated with a hypothetical data set For univariate situations, local s significance map and Geary significance map are devised in comparison with the preexisting Moran significance map. For bivariate situations, local L and local-r maps, local-L and local-r scatterplots, and local-L and local-r significance maps are proposed. When various significance levels are applied to those significance maps, probability maps can be created where higher p-value areas are expected to surround lower /r value areas, resulting in a probability surface. Those ESDA techniques are expected to accomplish various ESDA purposes. The ESDA techniques are applied to an empirical study on spatio-temporal income dynamics across the U.S. labor market areas from 1969 to 1999. A series of local-S significance maps identify spatial clusters in regional per capital personal distribution, and show that spatial integration within the spatial clusters has been eroded. A notion of o-convergence is not evidence. Rather, a trend toward income divergence is detected since the late 70s. Two distinctive trends towards regional income divergence observed in the late 1980s and the late 1990s seem to be associated with different spatial processes: the former with contagious spatial processes; the latter with sporadic spatial processes. A spatial autoregressive model concludes that there is no statistical evidence of P-convergence between 1969 income levels and income growth rate between 1969 and 1999. Various local-L scatterplot maps and significance maps report that spatial heterogeneity in P-convergence is evident during the entire period and varies sub-period to sub-period in terms of strength and locations. iv Dedicated to my parents, Yong-Woo Lee and Chun-Ja Kwon, and my sisters, In-Sun, Sung-Mi, and Hye-Sun ACKNOWLEDGMENTS I wish to thank my advisor. Dr. Lawrence A. Brown, for his support, encouragement, and endorsement. It has been an honor to work with him not only as a great scholar but also as a wonderful person. I have owed him everything during my stay at the Ohio State University. I wish to express special thanks to Dr. Michael Tiefelsdorf for guiding me to the amazing world of spatial statistics and for consistently stimulating discussions. He has been a beacon for me to navigate the world without getting lost, although any errors found in this dissertation are utterly pertinent to me. I am grateful to Dr. Mei-Po Kwan for allowing me to develop crucial ideas for the dissertation in her classes and for always encouraging me. I also wish to thank faculty members and colleagues at the Ohio State University who have supported and encouraged me in pursuing the degree, among others. Dr. Kevin Cox, Dr. Nancy Ettlinger, Dr. Linda Lobao, Dr. Allan Murray, Dr. Bae-Gyoon Park, Dr. Joe Weber, Jon Moore, and Philip Hisnay. I am grateful to faculQr members in Department of Geognq>hy Education in Seoul National University, Dr. Jae-Ki Hwang, Dr. Ki-Suk Lee, Dr. Manik Hwang, Dr. Jong- VI Wook Kim, and Dr>Jaft-Myong-Ryu,.foc.having.gotmfcJKeU.preparedia.pupaiing for my^ final degree in this institution. I am enormously indebted to a group of mentors in Korea who made my life here possible, among others, Dr. Sangcheol Kwon, Dr. Tae-Yeol Seo, Dr. Jung-Hwa Kwon, and Dr. Young-Min Lee. I won’t be able to repay them. My special thanks go to my wife, Hyun-Mi Kim, who is the best colleague and firiend as well as the loveliest woman on this planet. vu VITA November 27,1966 .................................. Bom - Pohang, Korea 1989 ........................................................... B.A., Geography Education, Seoul National University 1991 ........................................................... M.A., Geography Education, Seoul National University 1993 -1 9 9 5 .............................................. Ph D. Program, Geography Education, Seoul National University 1996 - present .......................................... Graduate Teaching and Research Associate, The Ohio State University PUBLICATIONS Research Publication 1. Sang-Il Lee, “A generalized significance testing method for spatial association measures: an extension of the Mantel test.” Environment and Planning A, forthcoming (2002). 2. Sang-Il Lee, “Developing a bivariate spatial association
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