Introduction to Spatial Regression Analysis ICPSR Summer Program University of North Carolina at Chapel Hill. University of Wisconsin-Madison

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1 Introduction to Spatial Regression Analysis ICPSR Summer Program 2012 Paul R. Voss 1 and Katherine J. Curtis 2 1 University of North Carolina at Chapel Hill 2 University of Wisconsin-Madison 1 Odum Institute for Research 2 Department of Community & in Social Science Environmental Sociology Manning Hall, CB # Linden Drive University of North Carolina at Chapel Hill University of Wisconsin-Madison Chapel Hill, NC 2759 Madison WI paul_voss@unc.edu kcurtis@ssc.wisc.edu Objectives The goal of this five-day course is to provide an overview of applied spatial regression analysis (spatial econometrics) that will enable participants to effectively incorporate these tools into their own empirical research. The course will introduce the broader field of spatial data analysis and the range of issues that generally must be dealt with when analyzing georeferenced data on a lattice. Census-type data are among the most commonly encountered data that conform to this description, although the course acknowledges the wider range of data appropriate for spatial regression analysis. In general, this is NOT a course where significant attention can be given to spatial analyses involving so-called geostatistical data or point pattern data. It also is not a GIS course. Course Materials and Organization The course will convene each day from 9:00 a.m. until approximately 4:30 p.m., except for the last day (Friday), when the course likely will wind down earlier to enable participants who must meet Friday evening flights to do so. The course is organized into a format that includes morning lectures (theoretical and conceptual underpinnings) and afternoon computing lab sessions (hands-on applications). We will attempt to set aside the last half hour or more of each day for group discussion of the topics introduced that day. Course materials are organized such that the readings supplement and provide greater detail on the topics covered in the classroom. Many more topics are introduced in the course lectures (assisted by PowerPoint) than can reasonably be absorbed in five intensive days, so the readings provide a point of return for review and deeper understanding of the topics covered, as well as a source of references for further reading. The lab exercises are guided by written, step-by-step tutorial instructions so that they can be repeated (and more fully absorbed) at a later time. Recommended readings and lab exercises are available on-line. The final day will shift attention from the classical econometric perspective and will briefly introduce spatial analytical advances including Bayesian, multi-level, and space-time modeling. We have also designated time on Friday afternoon for participants to present their own work that applies techniques acquired in the workshop.

2 Software The course will use the spatial analysis package OpenGeoDa as well as the open source programming application, R. OUTLINE OF COURSE Day 1, a.m. Introduction to spatial data; why spatial is special and why it matters; classes of spatial data and spatial data modeling; what constitutes a spatial question; overview of normal linear model and OLS estimation; OLS diagnostics; exploratory data analysis and exploratory spatial data analysis. Day 1, p.m. Computing Lab. Exploratory data analysis; brief introduction to GeoDa; running R scripts to prepare data for spatial analysis; variable transformations and data visualization & exploration. Day 1 Readings, Introduction to Spatial Data Analysis: 1. Anselin, Luc Thirty Years of Spatial Econometrics. Papers in Regional Science 89(1):3-25. [A broad, sweeping overview of the development of the field over the past 3 decades by, unquestionably, the premier contributor to that development] 2. Loftin, Colin, and Sally K. Ward A Spatial Autocorrelation Model of the Effects of Population Density on Fertility. American Sociological Review, 48(1): [Together with the following reading, a classic motivational example] 3. Galle, Omer R., Walter R. Gove, & J. Miller McPherson Population Density and Pathology: What Are the Relations for Man? Science (new series) 176: Anselin, Luc What Is Special about Spatial Data? Alternative Perspectives on Spatial Data Analysis. Conference Proceedings, Spatial Statistics: Past, Present, and Future. Institute of Mathematical Geography, Syracuse University. [Now somewhat dated, but a nice overview of why spatial data require special attention] Day 1 Readings, Lab: 1. Anselin, Luc Exploring Spatial Data with GeoDa: A Workbook. [Relevant chapters: 2, 3 and 7-12] 2. Venables, W. N. & D. M. Smith and the R Development Core Team An Introduction to R. [Perhaps the most widely cited introduction to R; there are many!] 3. Anselin, Luc Spatial Regression Analysis in R: A Workbook. [Relevant chapters: 1 & 2] Spatial Regression 2

3 4. Voss, Paul R., David D. Long, Roger B. Hammer, and Samantha Friedman County Child Poverty Rates in the U.S.: A Spatial Regression Approach. Population Research and Policy Review 25: [An introduction to the example used throughout the week] Day 2, a.m. Introduction to spatial autocorrelation; causes of spatial autocorrelation; the language relating to spatial autocorrelation; spatial heterogeneity; spatial dependence; thinking about neighborhood influences; spatial weights matrices; spatial lag operator. Day 2, p.m. Computing Lab. Diagnosing global & local spatial autocorrelation (mostly in R); visualizing spatial autocorrelation; 1 st order queen weights matrix (GeoDa & R); generating other weights matrices. Day 2 Readings, Spatial Autocorrelation: 1. Anselin, Luc The Moran Scatterplot as an ESDA Tool to Assess Local Instability in Spatial Association. Pp in Fischer, Manfred, Henk J. Scholten, and David Unwin (eds.) Spatial Analytical Perspectives on GIS: GISDATA 4 (London: Taylor & Francis). [Introduction to a key diagnostic tool in spatial data analysis] 2. Tolnay, Stewart E., Glenn Deane, & E.M. Beck Vicarious Violence: Spatial Effects on Southern Lynchings, American Journal of Sociology 102(3): [An interesting example of negative spatial autocorrelation arising in a social process] 3. Tobler, Waldo R A Computer Movie Simulating Urban Growth in the Detroit Region. Economic Geography 46(June): [The classic on the concept of positive spatial autocorrelation] 4. Getis, Arthur Reflections on Spatial Autocorrelation. Regional Science and Urban Economics 37: [A brief essay by a quantitative geographer who has contributed much to the spatial autocorrelation literature] 5. Getis, Arthur A History of the Concept of Spatial Autocorrelation: A Geographer s Perspective. Geographical Analysis 40: Day 2 Readings, Lab: 1. Anselin, Luc Exploring Spatial Data with GeoDa: A Workbook. [Relevant chapters: 15-18] 2. Anselin, Luc Spatial Regression Analysis in R: A Workbook. [Relevant chapter: 3] Spatial Regression 3

4 3. Messner, Steven F., Luc Anselin, Robert D. Baller, Darnell F. Hawkins, Glenn Deane, & Stewart E. Tolnay The Spatial Patterning of County Homicide Rates: An Application of Exploratory Spatial Data Analysis. Journal of Quantitative Criminology 15(4): [A nice example of ESDA] Day 3, a.m. Introduction to spatial regression modeling; specifying alternative spatial regression model; spatial lag model; spatial error model; spatial Durbin model; higher-order spatial regression models; disaggregating parameter effects in lag models. Day 3, p.m. Computing Lab. Specifying and estimating spatial model estimation in R; spatial lag model; spatial error model; spatial Durbin model; higher-order spatial regression models; understanding spatial regression model diagnostics; disaggregating parameter effects in lag models. Day 3 Readings, Spatial Regression Models: 1. Anselin, Luc, & Anil Bera Spatial Dependence in Linear Regression Models with An Introduction to Spatial Econometrics. Chapter 7 (pp ) in Aman Ullah & David Giles (eds.) Handbook of Applied Economic Statistics (New York: Marcel Dekker). [A strong, foundational reading] 2. Anselin, Luc Under the Hood: Issues in the Specification and Interpretation of Spatial Regression Models. Agricultural Economics 27(3): [An overview of spatial regression model specifications & interpretation] 3. Anselin, Luc Spatial Externalities and Spatial Econometrics. International Regional Sciences Review 26(2): [Companion to the Hood paper] 4. Baller, Robert D., & Kelly K. Richardson Social Integration, Imitation, and the Geographic Patterning of Suicide. American Sociological Review 67(6): [A good example of theoretically grounded spatial data analysis] 5. Sparks, Patrice Johnelle, & Corey S. Sparks An Application of Spatially Autoregressive Models to the Study of US County Mortality Rates. Population, Space and Place 16: [A nice example of putting it all together and sticking with your theory despite diagnostics to the contrary] 6. Crowder, Kyle and Scott J. South Spatial Dynamics of White Flight: The Effects of Local and Extralocal Racial Conditions on Neighborhood Out-Migration. American Sociological Review 73(5): [A theoretically motivated study incorporating space as a cross-regressive process] 7. Mobley, Lee R., Elisabeth Root, Luc Anselin, Nancy Lozano-Gracia, & Julia Koschinsky International Journal of Health Geographics 5:5-22. [A good article illustrating the disaggregation of direct & indirect effects in a spatial lag model] Spatial Regression 4

5 Day 3 Readings, Lab: 1. Anselin, Luc Exploring Spatial Data with GeoDa: A Workbook. [Relevant chapters: 22-25] 2. Anselin, Luc Spatial Regression Analysis in R: A Workbook. [Relevant chapters: 6 & 7] Day 4, a.m. Local spatial autocorrelation; spatial clustering; Local Moran I statistic, G and G* statistics; comparing local autocorrelation statistics; continuous & discrete spatial heterogeneity. Day 4, p.m. Computing Lab. Deriving local measures of spatial autocorrelation and clustering; spatial heterogeneity; GWR in R; spatial regime analysis in R. Day 4 Readings, Spatial Heterogeneity in Effects: 1. Fotheringham, A. Stewart, & Chris Brunsdon Local forms of Spatial Analysis. Geographical Analysis 31(4): [Understanding GWR] 2. Curtis, Katherine J., Paul R. Voss, & David D. Long Spatial Variation in Poverty- Generating Processes: Child Poverty in the United States. Social Science Research 41: [Very recent application of spatial regime analysis] 3. Wheeler, David, & Michael Tiefelsdorf Multicollinearity and Correlation among Local Regression Coefficients in Geographically Weighted Regression. Journal of Geographical Systems 7: [GWR has its critics] 4. O Loughlin, John, Colin Flint, & Luc Anselin The Geography of the Nazi Vote: Context, Confession, and Class in the Reichstag Election of Annals of the Association of American Geographers 84(3): [Excellent example of regime analysis] 5. Cahill, Meagan, & Gordon Mulligan Using Geographically Weighted Regression to Explore Local Crime Patterns. Social Science Computer Review 25(2): [One of many empirical applications of GWR] Day 4 Readings, Lab: 1. Gros, Daniel, Chris Brunsdon & Richard Harris. No date. Introduction to Geographically Weighted Regression (GWR) and to Grid Enabled GWR. [How to for R] 2. Anselin, Luc Discrete Spatial Heterogeneity & Continuous Spatial Heterogeneity. [Relevant chapters: 8 & 9] Spatial Regression 5

6 Day 5, a.m. Looking to the future of spatial data analysis & additional important topics; introduction to Bayesian perspective; spatial multilevel models; space-time explorations and modeling Day 5, p.m. Participant presentations (applications of techniques acquired in the workshop) Day 5 Readings, frontier topics 1. Besag, Julian, Jeremy York, & Annie Mollié Bayesian Image Restoration with Two Applications in Spatial Statistics. Annals of the Institute of Statistical Mathematics 43(1):1-20. [In the beginning ] 2. Subramanian, S. V., I Delgado, L. Jadue, J. Vega, and I. Kawachi Income Inequality and Health: Multilevel Analysis of Chilean Communities. Journal of Epidemiology and Community Health 57(11): [An often cited application of spatial multilevel modeling] 3. Chaix, Basile, Juan Merlo, and Pierre Chauvin Comparison of a Spatial Approach with the Multilevel Approach for Investigating Place Effects on Health: The Example of Healthcare Utilization in France. Journal of Epidemiology and Community Health 59(6): [For some insight on the spatial and multilevel approaches] 4. Besag, Julian Spatial Interaction and the Statistical Analysis of Lattice Systems. Journal of the Royal Statistical Society. Series B (Methodological) 36(2): [More from the beginning] 5. Zhu, Jun, Yanbing Zheng, Allan L. Carroll, and Brian H. Aukema Autologistic Regression Analysis of Spatial-Temporal Binary Data via Monte Carlo Maximum Likelihood. Journal of Agricultural, Biological, and Environmental Statistics 13(1): [Space-time regression within a maximum likelihood framework] GeoDa: INSTALLING GeoDa & R: GeoDa is a spatial data analysis package developed by Dr. Luc Anselin, Geographer and Regional Scientist at the Arizona State University, Tempe. He and his colleagues maintain a website at: Here you ll find information relating to the GeoDa software package, some wonderfully illustrated tutorials and user guides to the software, and, finally, the software itself. GeoDa is free, but it is not completely open source (at least not quite yet). It began as a Windows application, but today the OpenGeoDa version has been released and will run in all the most common operating systems (Vista, mac, linux, unix, etc.). For this workshop we will be using OpenGeoDa for Windows, version Spatial Regression 6

7 To get started with GeoDa your data must be in a format called a shapefile. A shapefile is actually a small set of interrelated files that have two essential pieces of information: (1) a digital map, and (2) an associated file containing your numerical attribute data. A shapefile MUST be created outside of GeoDa. This is usually accomplished with a GIS package such as ArcGIS. So to get going with GeoDa you must: (1) first learn to use ArcGIS (easy to say; hard to do), or (2) find a shapefile for the geographic area you re interested in using an internet browser (it turns out there are a lot of shapefiles to be found on the Internet), or (3) have a helpful friend who knows how to generate a shapefile in a GIS environment. R R is both a powerful programming language and a particularly strong environment for running statistical analyses on data. It also maintains an impressive capability for graphing and visualizing data. R is a free and open source implementation of the S programming language and has a worldwide community of users, many of whom develop new features (in packages ) that can be downloaded from the Comprehensive R Archive Network (CRAN). There are many good books on using R. In addition, there are many fine online resources documenting R, a variety of R tutorials and other help documentation. Basic Installation. Installation is quick and easy. Go to the R site find the downloadable version and install it following the simple instructions. Adding Packages. Much can be accomplished with the R core package. However, many of the most useful features in R are available through additional packages developed by users to address a specific set of analytical issues. The code for these is maintained at the CRAN and can be found at the site given above. The best way to install these packages is to first load the core R package and then, with R up and running, download the desired packages using the following steps: (1) click on Packages on the menu bar; (2) navigate to Install package(s) ; (3) select a mirror site from which to do the installation (you probably want to choose one of the US sites, but it doesn t really matter), click OK; (4) select the desired packages using the conventional Windows multiple selection method <Ctrl><Enter>; once the desired package are highlighted, click OK, and the most recent version of each package should install. They should automatically install in the library folder under R in the Program Files on your C-drive (or wherever you install your program files). Note that for each R session we carry out, the packages (also called libraries ) required for that session must be loaded. For those of you who are new to R, this will all become clear in the computing lab session of the first day. Here is a list of program files you may wish to install on your laptop before arriving at the workshop. We will actually make use of more packages than this, but many such packages piggyback on the packages listed here. For example, the important package maptools installs when you install spdep. car lmtest sp sphet classint nortest spatstat StatDA graphicsqc RColorBrewer spdep Spatial Regression 7