Spatial Regression Analysis Using Eigenvector Spatial Filtering

By Daniel Griffith, Yongwan Chun and Bin Li

Spatial Regression Analysis Using Eigenvector Spatial Filtering provides theoretical foundations and guides practical implementation of the Moran eigenvector spatial filtering (MESF) technique. MESF is a novel and powerful spatial statistical methodology that allows spatial scientists to account for spatial autocorrelation in their georeferenced data analyses. Its appeal is in its simplicity, yet its implementation drawbacks include serious complexities associated with constructing an eigenvector spatial filter.

This book discusses MESF specifications for various intermediate-level topics, including spatially varying coefficients models, (non) linear mixed models, local spatial autocorrelation, space-time models, and spatial interaction models. Spatial Regression Analysis Using Eigenvector Spatial Filtering is accompanied by sample R codes and a Windows application with illustrative datasets so that readers can replicate the examples in the book and apply the methodology to their own application projects. It also includes a Foreword by Pierre Legendre.

• Reviews the uses of ESF across linear regression, generalized linear regression, spatial autocorrelation measurement, and spatially varying coefficient models
• Includes computer code and template datasets for further modeling
• Provides comprehensive coverage of related concepts in spatial data analysis and spatial statistics

• Language: English
• Publisher: Academic Press
• Release date: Sep 14, 2019
• ISBN: 9780128156926

Daniel Griffith

Daniel A. Griffith is an Ashbel Smith Professor of Geospatial Information Sciences at the University of Texas at Dallas, affiliated professor in the College of Public Health at the University of South Florida, and adjunct professor in the Department of Resource Economics and Environmental Sociology at the University of Alberta. He holds degrees in Mathematics, Statistics, and Geography, and arguably is the inventor of Moran eigenvector spatial filtering. He is a two-time Fulbright Senior Specialist, an AAG Distinguished Research Honors awardee, and an elected fellow of the Royal Society of Canada, UCGIS, AAG, American Association for the Advancement of Science, American Statistical Association, Regional Science Association International, and Spatial Econometrics Association.

Book preview

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Preface

Daniel A. Griffith, Richardson, TX

Yongwan Chun, Richardson, TX

Bin Li, Mt. Pleasant, MI

Moran eigenvector spatial filtering (MESF) is a relatively recent novel and powerful statistical methodology that accounts for spatial autocorrelation (SA) in its georeferenced data analyses. Its appeal is its simplicity in terms of regression analysis. Its implementation drawbacks include serious complexities associated with constructing an eigenvector spatial filter (ESF). The principal goal of this book is to provide an accessible reference book for applying MESF to spatial regression modeling by including ESFs in spatial regression model specifications. It interfaces with user-friendly software primarily developed by Dr. Hyeongmo Koo. The purpose of this preamble is to furnish an overview of the history of and motivation for developing MESF, as well as an overview of the georeferenced Texas dataset used for empirical illustrations throughout this book.

Setting the stage for MESF, Cliff and Ord (1973) published their book entitled Spatial Autocorrelation, initiating a popularization of this fundamental concept as well as the spatial auto-normal probability model in geographic information science (GIScience) and the geographic/geospatial sciences. Besag (1974) published Spatial interaction and the statistical analysis of lattice systems, extending the spatial auto-models beyond the auto-normal specification. These two publications highlighted important emerging spatial statistical methodology challenges: (1) the intractability of the auto-normal model log-Jacobian term (i.e., the normalizing constant); (2) the difficulty of specifying auto-models for nonnormal data (which eventually were implemented with the numerically intensive Markov chain Monte Carlo [MCMC] technique); and (3) the failure of certain auto-models to account for positive SA (PSA; e.g., the auto-Poisson and the auto-negative binomial). Meanwhile, considerable work in the late 1970s demonstrated that SA mattered and contrasted georeferenced data analyses ignoring SA with those acknowledging SA.

This latter theme became the topic of Griffith's doctoral dissertation, in which he established the rudimentary foundation of MESF (Griffith, 1978a). This foundation involved the spatial auto-normal model, in its simultaneous autoregressive (SAR) specification, and filtered SA from georeferenced data in a way that parallels the Cochrane–Orcutt filtering of time-series data containing serial correlation (i.e., temporal autocorrelation). Comparisons of analysis results for georeferenced data based on original and filtered data reveal data analytic complications attributable to SA. Three journal articles derived from this dissertation highlight this approach: a 1978 Geographical Analysis paper about ANOVA, a 1979 Economic Geography paper involving an empirical data analysis, and a 1981 Geographical Analysis rejoinder reporting before and after spatial filtering results for multivariate statistical analyses of georeferenced data (Griffith, 1978b, 1979, 1981). The idea of spatial filtering was formulated at this time but without being directly linked to the notion of a spatial weights matrix (SWM) or the Moran coefficient (MC).

Next, Griffith turned his research attention and efforts to SWMs, applying his knowledge about principal components analysis (PCA) to them. Inspiration for this work mostly derived from exposure to PCA applications to spatial interaction data done by his former University of Toronto professors, James Simmons and Larry Bourne, during and shortly after his doctoral program of study. In his attempt to further articulate spatial filtering, Griffith (1984) published a PCA study of a SWM. His results were disappointing but did emphasize that the principal eigenfunction of a SWM, which already had been promoted in transportation geography as a quantification of topological accessibility associated with a geographic configuration of areal units (based upon the dual graph of its corresponding surface partitioning), offered promise. Accordingly, Griffith (1988) published a chapter in his spatial statistics book showing that the principal eigenvector of a SWM highlights a dimension that spans socioeconomic/demographic, spatial interaction, and land use data. Interestingly, Boots and Kanaroglou (1988) had exactly the same idea about the principal eigenvector being a useful regression analysis covariate, also publishing their paper in that same