Spatial Regression Course
The course will introduce spatial data analysis of geo-referenced data, spatial auto-correlation, spatial heterogeneity and spatial dependence. A focus on spatial auto-correlation extends ordinary multiple regression to methods of spatial regression. This course is hands-on: afternoons will be computer sessions based on morning theory lectures. The computer sessions will introduce the GeoDa, GWR & R software. The lab exercises will use UK and European datasets.
Dates: 19-23/11/2007
Duration: 5 days
Level: Intermediate
Course Fee: £525/ £375 academic (£200 postgraduate
research students)
Course Leader: Paul
Voss, University of Wisconsin
Course Requirements:Prerequisites for maximizing learning in this course are
a solid grounding in standard multivariate regression techniques and a
minimal level of comfort with matrix notation and algebra. Some acquaintance with the course software of
ArcGIS and GeoDa for exploratory spatial data analysis is
helpful but not a pre-requisite.
The intended audience is all those wishing to effectively incorporate spatial analysis into their own empirical research.
The computer tutorials will use data from the UK Census and Eurostat, and will be supported by Susan Ramsay and Paul Widdop. Improvements may be made to the syllabus before November.
Introduction to Spatial Regression Analysis
Cathie Marsh Centre for Census and Survey Research, Manchester, UK
November 19th-23rd 2007
Paul R. Voss University of Wisconsin-Madison
Applied Population Laboratory
Center for Demography and Ecology
Departments of Rural Sociology and Sociology
University of Wisconsin-Madison
Madison WI 53706
voss@ssc.wisc.edu
Summary:
The role of spatial autocorrelation in spatial data sets is a central focus. This five-day course will address the following questions: how does spatial autocorrelation arise; how is it measured and understood; how does it relate to issues of spatial heterogeneity and spatial dependence; and how should it inform the specification and estimation of regression models. The course is structured around a combined lecture format (mornings) and computing lab exercises (afternoons). Although we will use mapping software, the focus of the course is on spatial analysis, not Geographic Information Systems (GIS). Software emphasis will be given to ArcGIS 9 and GeoDa for exploratory spatial data analysis (ESDA) and modeling. The course will also introduce particular spatial analysis techniques that are available in GWR and R. Some acquaintance with this software is helpful but is not a prerequisite. Prerequisites for maximizing learning in this course are a solid grounding in standard multivariate regression techniques and a minimal level of comfort with matrix notation and algebra.
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. 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.
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 will likely 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. All recommended readings and lab exercises are available on-line.
OUTLINE OF COURSE
Day 1 Morning:
1. Welcome and introductions
2. Review of objectives and overview of week
3. Goal and overview of the day
4. Motivational example
5. Understanding spatial data
a. Overview of spatial data and spatial data analysis
b. Spatial analysis vs. spatial data analysis
c Classes of problems in spatial data analysis
d. Spatial vs. non-spatial data analysis
5. Why spatial is special
a. Characteristics of spatial data
b. Problems caused by spatial data
6. Review OLS assumptions
a. Assumptions of the classical linear regression model
b. Consequences of violation of the assumptions
7. Visualizing spatial data
8. Orientation to afternoon lab: Introduction to shapeflies (attribute data and digital map married up)
Day 1 Afternoon:
1. Constructing/finding a shapefile
2. Introduction to “our” shapefile; your task: Begin thinking now about hypotheses, models, and analyses
3. Simple mapping operations using ArcGIS
4. Reading a shapefile into GeoDa
5. Simple mapping operations using GeoDa
Day 1 Readings:
1. Anselin, Luc. 1989. “What is Special About Spatial Data? Alternative Perspectives on Spatial Data Analysis.” NCGIA Technical Paper 89-4.
2. Anselin, Luc. 1999. “The Future of Spatial Analysis in the Social Sciences.” Geographic Information Sciences 5(2):67-76.
3. Goodchild, Michael F., Luc Anselin, Richard P. Applebaum, and Barbara Herr Harthorn. 2000. “Toward Spatially Integrated Social Science.” International Regional Science Review 23:139-159.
4. Loftin, Colin and Sally K. Ward. 1983. “A Spatial Autocorrelation Model of the Effects of Population Density on Fertility.” American Sociological Review, 48(1):121-128.
5. Galle, Omer R., Walter R. Gove, J. Miller McPherson. 1972. “Population Density and Pathology: What Are the Relations for Man?” Science (new series) 176:23-30
Day 2 Morning:
1. Q&A from readings or 1st day lecture or lab
2. Goal for the day: ESDA & spatial autocorrelation
3. Data exploration:
a. Distribution aspects of dependent variable
b. QQ Plots
c. Linearity between dependent variable and independent variables
d. Variable transformations
4. Global spatial autocorrelation & weights matrices
a. What it is
b. How it arises; Spatial processes
i. Spatial heterogeneity
ii. Spatial dependence
c. Consequences of spatial autocorrelation
d. How to measure it
i. Weights Matrices
ii. Global measures of spatial autocorrelation
a. Global Moran statistic
b. Global Geary statistic
d. Problems with global measures
5. Local measures of spatial autocorrelation
a. Local Moran
b. Moran scatterplot
c. LISA mapping
7. Orientation to afternoon lab: ESDA and spatial autocorrelation with GeoDa
Day 2 Afternoon:
1. Introduction to ESDA
2. ESDA with GeoDa
3. Creating and comparing weights matrices
4. Global spatial autocorrelation in GeoDa
5. Local spatial autocorrelation in GeoDa
Day 2 Readings:
1. Anselin, Luc. 1996. “The Moran Scatterplot as an ESDA Tool to Assess Local Instability in Spatial Association.” Pp. 111-125 in Fischer, Manfred, Henk J. Scholten, and David Unwin (eds.) Spatial Analytical Perspectives on GIS: GISDATA 4 (London: Taylor & Francis).
2. Anselin, Luc. 1995. “Local Indicators of Spatial Association – LISA.” Geographical Analysis 27(2):93-115.
3. Messner, Steven F., et al. 1999. “The Spatial Patterning of County Homicide Rates: An Application of Exploratory Spatial Data Analysis.” Journal of Quantitative Criminology 15(4):423-450
Day 3 Morning:
1. Q&A from readings or 2nd day lecture, lab or readings
2. Goal for the day: understanding spatial regression
3. Spatial processes
a. Spatial heterogeneity
i. Define
ii. Causes of
iii. Problems arising from
iv. Analogue to time-series analysis
a. Corrections for
v. GWR priview
b. Spatial dependence
i. Define
ii. Causes of
a. True contagion vs. false contagion
iii. Expressions of
a. Lagged dependent variable
b. Unresolved heterogeneity; error lag
iv. Corrections for
a. Spatial lag model
b. Spatial error model
c. What these models mean/imply
d. Relationship between the two models
e. Higher order models
4. Common modeling strategy
a. Specify and estimate OLS model
b. Analyze the regression diagnostics
c. Specify spatial model
d. MLE fundamentals
5. Understanding the regression diagnostics provided by GeoDa
a. Information criteria statistics
b. Normality of errors
c. Heteroskedasticity
d. Lagrange multiplier statistics
6. Orientation to afternoon lab: OLS & spatial regression modeling with Geoda
Day 3 Afternoon:
1. OLS regression in GeoDa
2. GeoDa diagnostics and implications of these
3. Spatial regression models in GeoDa
4. Possible corrections for heterogeneity
Day 3 Readings:
1. Anselin, Luc, and Anil Bera. 1998. “Spatial Dependence in Linear Regression Models with an Introduction to Spatial Econometrics.” Chapter 7 (pp. 237-289) in Aman Ullah and David Giles (eds.) Handbook of Applied Economic Statistics (New York: Marcel Dekker).
2. Anselin, Luc. 2002. “Under the Hood: Issues in the Specification and Interpretation of Spatial Regression Models.” Agricultural Economics 27(3):247-267.
3. Voss, Paul R., David D. Long, Roger B. Hammer, and Samantha Friedman. 2006. “County Child Poverty Rates in the U.S.: A Spatial Regression Approach.” Population Research and Policy Review 25:369-391.
4. Baller, Robert D., and Kelly K. Richardson. 2002. “Social Integration, Imitation, and the Geographic Patterning of Suicide.” American Sociological Review 67(6):873-888.
Day 4 Morning:
1. Q&A from readings or 3rd day lecture, lab or readings
2. Goal for the day: understanding GWR
3. Introduction to GWR
a. Theory and concept
b. Local multivariate methods for spatial data analysis
i. Spatial expansion model
ii. Spatial adaptive filtering
iii. Multilevel modeling
iv. Random coefficient models
c. GWR approach
d GWR software
4. GWR analytical steps
5. What it means
a. Spatial regimes
b. Clues to interaction effects
c. Clues to public policy messages in GWR maps
6. Cautions with GWR
7. Putting it all together: Example of a concrete spatial data analysis
8. Orientation to afternoon lab: GWR
Day 4 Afternoon:
1. GWR hands on
Day 4 Readings:
1. Fotheringham, A. Stewart, and Chris Brunsdon. 1999. “Local forms of Spatial Analysis.” Geographical Analysis 31(4):340-358.
2. Wheeler, David, and Michael Tiefelsdorf. 2005. “Multicollinearity and Correlation among Local Regression Coefficients in Geographically Weighted Regression.” Journal of Geographical Systems 7:161-187.
3. Messner, Steven F., and Luc Anselin. 2004. “Spatial Analyses of Homicide with Areal Data.” Pp. 127-144 in Michael F. Goodchild and Donald G. Janelle (eds.) Spatially Integrated Social Science. (Oxford: Oxford University Press).
Day 5 Morning:
1. Q&A from readings or 4th day lecture, lab or readings
2. Goal for the day: Wrapping things up & introduction to spatial data analysis in R
3. Spatial data analysis in R
a. Why R?
b. Representing spatial data in R
c. Visualizing spatial data in R
d. Accessing spatial data in R
e. Analyzing spatial data in R
4. Other software
5. Textbook resources for spatial data analysis
6. Useful websites and listserves
7. Orientation to afternoon: No lab, per se
Day 5 Afternoon:
1. Last chance to ask software questions
2. Hands on with R
3. Possible brief student presentations
Day 5 Readings:
1. Anselin, Luc. 2005. Spatial Regression Analysis in R: A Workbook. (Urbana-Champaign, IL: University of Illinois, Spatial Analysis Laboratory).
2. Bhati, Avinash Singh. 2005. “Robust Spatial Analysis of Rare Crimes: An Information-Theoretic Approach.” Sociological Methodology 35 (1) 239-302