Introduction to Spatial Regression Analysis Paul R. Voss and ... - icpsr

Introduction to Spatial Regression Analysis
Paul R. Voss 1 and Katherine Curtis 2
1
University of North Carolina at Chapel Hill
2
University of Wisconsin-Madison
1
Odum Institute for Research in Social Science
2 Department of Rural Sociology
Manning Hall, CB #3355
1450 Linden Drive
University of North Carolina at Chapel Hill University of Wisconsin-Madison
Chapel Hill, NC 27599 Madison WI 53706
voss@ssc.wisc.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.
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. All recommended readings and
lab exercises are available on-line.
Software
The course will use primarily the spatial analysis package GeoDa TM and the open source
programming language R.

OUTLINE OF COURSE
Day 1 Morning:
1. Welcome and introductions
2. Review of objectives and overview of week
3. Goal and overview for Day 1
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 often caused by spatial data
6. Review OLS estimation
a. Assumptions of the classical linear regression model
b. Consequences of violation of the assumptions
7. The importance of exploratory data analysis (EDA) and exploratory spatial data
analysis (ESDA)
8. Orientation to afternoon lab: Introduction to shapefiles (attribute data and digital map
married up) and elementary ESDA using GeoDa. TM Orientation to univariate EDA
using R
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 TM
4. Reading a shapefile into GeoDa TM
5. Simple mapping operations using GeoDa TM
6. Univariate EDA using R.
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. Ward, Michael D., and Kristian Skrede Gleditsch. 2008. Spatial Regression
Models. Quantitative Applications in the Social Sciences, No. 155. Thousand
Oaks, CA: Sage. Chapter 1. [This small book may be found as a downloadable
PDF at: http://faculty.washington.edu/mdw/ ]
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 1 st day lecture or lab
2. Goal for Day 2: 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; Box-Cox 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
c. 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 TM and
similar work in R.
Day 2 Afternoon:
1. Introduction to ESDA
2. ESDA with GeoDa TM and R
3. Creating and comparing weights matrices
4. Global spatial autocorrelation in GeoDa TM and R
5. Local spatial autocorrelation in GeoDa TM and R
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 2 nd day lecture, lab or readings
2. Goal for Day 3: Understanding spatial regression
3. Spatial processes
a. Spatial heterogeneity
i. Define
ii. Causes of
iii. Problems arising from
iv. Analogue to time-series analysis
v. Correcting for spatial heterogeneity
vi. GWR preview
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 TM and
R

Day 3 Afternoon:
1. OLS regression in GeoDa TM and R
2. GeoDa TM diagnostics and implications of these
3. Spatial regression models in GeoDa TM and R
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.
5. Ward, Michael D., and Kristian Skrede Gleditsch. 2008. Spatial Regression Models.
Quantitative Applications in the Social Sciences, No. 155. Thousand Oaks, CA:
Sage. Chapters 2 & 3.
Day 4 Morning:
1. Q&A from readings or 3 rd day lecture, lab or readings
2. Goal for Day 4: 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, and GWR in R
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 4 th day lecture, lab or readings
2. Goal for the day: Wrapping things up & introduction to spatial data analysis in R
3. Where the field of spatial data analysis is heading in the short term
4. Resources:
a. Other software
b. Textbook resources for spatial data analysis
c. Useful websites and listserves
5. Orientation to afternoon: No lab, per se
Day 5 Afternoon:
1. Last chance to ask software questions
2. Review data analysis in GeoDa and R
2. Consultations regarding your own data, data issues, and plans
Day 5 Readings:
1. Anselin, Luc. 2005. Spatial Regression Analysis in R: A Workbook. (Urbana-
Champaign, IL: University of Illinois, Spatial Analysis Laboratory).
2. Ward, Michael D., and Kristian Skrede Gleditsch. 2008. Spatial Regression Models.
Quantitative Applications in the Social Sciences, No. 155. Thousand Oaks, CA:
Sage. Chapter 4.