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Day 5

Spatial Regression Modeling

Paul Voss & Katherine Curtis

The Center for Spatially Integrated Social ScienceSanta Barbara, CAJuly 12-17, 2009

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Plan for today• Alternative spatial processes

– Point pattern analysis– Geostatistics– Higher order spatial regression models

• Some thoughts about where spatial data analysis is headed over the next couple years

• What are the big unanswered questions? Frontiers?• Resources

– Textbooks– Software

• What opportunities lie ahead?– Training– Publishing

• Lab:– Presentations– Open forum

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Recall from Monday:Types of Spatial Data

• Event data (point data)• Spatially continuous data (geostatistical

data)• Lattice data (regionalized data)• Spatial interaction data (flow data)

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Event Data• Interest is in pattern of point locations

– Observed attributes often not of interest; focus is on the locations where the attribute has value

– But can be “marked” with attributes, one of which may be temporal

• Objective: Investigate whether the proximity of events, i.e., their locations in relation to each other, represents a systematic pattern– In particular, indications of departure from randomness

(some form of regularity or clustering)– Is there perhaps a process at work that we might

identify? Are the data random (CSR)?– Estimate how intensity of events varies over the study

region, and seek models which account for this

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Origins of Event Data Analysis• 1930s: plant ecology• 1940s onward: plant and animal ecology (mostly analysis

of the spatial distribution of individual species and the interrelationships of two or more species; aim: understand individual or environmental factors influencing such patterns)

• 1960s: “Quantitative revolution” in Geography (examination of settlement location patterns; central place theory; spatial patterning of physical features)

• 1970s: extensions to archeology, anthropology, astronomy and materials science (distributions of artifacts at archeological sites, galaxies in universe, particles in metals)

• 1980s - present: crime pattern analysis and epidemiology

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Event DataSome Analytical issues:

• What’s a point?• Handling edge effects• Objective? Study of…

– dispersion: location of points wrt the study region (modeling the geographic variation in “intensity”)

• Intensity analysis• Scan statistics

– arrangement: location of points wrt each other

• Nearest neighbor distances

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• When we see a map like this, the question we should be asking is: Why do these points have this particular pattern?

• Is it because this is where the people are? In which case the null hypothesis changes from CSR/HPP to something else:HetPP ≡ IPP ≡ Constant (individual-level) Risk Hypothesis

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For social scientists, the principal areas of research where tools and

methodologies of event analysis are important are medical geography,

public health research and criminology

To some extent, it has led to development of specialized

“toolboxes” and highly specific software applications

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Spatially Continuous Data• Data are points (as with event data), but attached

to each is a measurement on some assumed continuous spatial process

• Problem is not one of asking whether there is a pattern in the locations themselves; i.e., the pattern of the locations is not itself the subject of analysis

• Objective: Understand the pattern in the values• Use this understanding (possibly in conjunction

with other covariates) to “model” (predict) values at locations not part of the spatial sample; “Kriging”

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Very occasionally one runs across the use of tools and methodologies of geostatistics in conjunction with

the analysis of data on a latticee.g., use of semivariogram to

determine the range over which neighboring influences occur

Higher order regression models, e.g., the SARAR(1,1) model:

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1,1where

1 210

<<

+=++++=

λρελ

βββρMuu

uWXXWyy n

[ ] [ ]1,1

,,,,,,,1where 210

<<

==+=

+=

λρρβββδ

ελδ

WYWXXZMuu

uZyor

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Other disturbance specifications. Recall the Spatial Error Model from Wednesday

y X uu Wu= += +

βλ ε

This is the most common specification for expressing spatial error dependence. But it is not the only such. Other

specifications are widely discussed if less widely used

We said, first-order variation comes only through Xβ; second-order variation is represented as an

autoregressive, interactive effect through λWu; thus, the disturbance vector u consists of an iid location-

specific innovation, ε, and an autoregressive smoother on the neighboring disturbances, Wu

εεγ += Wu A “moving average” specification. Each disturbance term consists of a location-specific innovation and a

smoothing filter on neighboring innovations

εξ +=Wu An “error components” model. Disturbance is a sum of 2 independent error terms (a location-specific

innovation and a smoothing of neighboring errors)

Models in Space & Time• Presently one of the leading-edge

development areas in spatial data analysis• For many years as been dealt with using

SUR and Spatial SUR models (Zellner, 1962), where a limited degree of simultaneity is present in the form of error dependence in different equations

• Probably best discussed in the context of the next several slides…

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Some exciting near-term developments

• GeoDa• R• Other software developments• Training opportunities

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• PySAL/PySpace – mostly for programmers– Analytical interface to ArcGIS

• OpenGeoDa – alpha version available; bugs being repaired– This is/will be “truly cross-platform”; will run natively on Windows,

Vista & XP, mac, unix, linux, etc

• GeoDaSpace – for spatial regression using GMM; out soon• GeoDaNet – for point pattern analysis on networks; out this

summer• Legacy GeoDa – 0.95i• STARS• Video of AAG presentations (April 17) presently viewable

from the GeoDa Center website

GeoDa & Team Anselin

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• Constant upgrading of tools and functionality• New package: splm -- Spatial Panel Linear Models

– Collaboration of Gianfranco Piras & Giovanni Millo– Presently on R-Forge site– Based mainly on Kapoor, Mudit, Harry H. Kelejian, and Ingmar R.

Prucha. 2007. " Panel Data Models with Spatially Correlated Error Components. " Journal of Econometrics 140:97-130.

• Additions to spdep (spdep2)– K-P HAC. Based mainly on Kelejian, Harry H. & Ingmar R. Prucha.

2007. "HAC Estimation in a Spatial Framework." Journal of Econometrics 140:131-154.

– GS2SLS. Based mainly on Kelejian, Harry H. & Ingmar R. Prucha. 1998. "A Generalized Spatial Two Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances." Journal of Real Estate Finance and Economics, 17: 99-121.

R & Team Bivand

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Team Kelejian & Prucha

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Spatial Econometrics Association

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May 25 – June 19, 2009

Other training opportunities

• ICPSR Summer Program• CSISS/PRI• Bayesian modeling

– UK– Andrew Lawson

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Rather male dominated field, it would appear?

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Carol GotwayCrawford

Julie Le Gallo

Katherine Curtis

Nancy Lozano-Gracia

Julia KoschinskyLee Mobley

Rosina Moreno Serrano

Mobley & AnselinProposal: “Spatial Analysis of

Health and Social Data”

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“… to develop web-based spatial analysis tools, multilevel databases and

user support infrastructure”

Meetings• AAG

– 2010 Annual Meeting (Washington, DC, April 14-18)

• RSAI– Regional meetings– NARSC (San Francisco, Nov. 18-21, 2009)– Spatial Economics Research Centre (London)

• SEA– Founding conference 2006 – Rome– 1st World Conference 2007 – Cambridge– 2nd World Conference 2008 – NYC– 3rd World Conference 2009 – Barcelona (July 8-10)

• Spatial Econometrics & Statistics (France)– 8th Annual Workshop, Besançon, Fr., June 2-3, 2009

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The Frontiers…• HAC estimators• Limited dependent variables

– Spatial logistic– Spatial poisson– Spatial probit– Spatial Tobit

• Modeling in space & time• Bayesian disease modeling• Bayesian spatial modeling for non-point data• Integrated spatial modeling• More R

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Available chapter-by-chapter as PDF files at:http://www.springerlink.com/content/978-0-387-78170-9

Best of all…

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Other useful book resources…

Roughly chronological order

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http://faculty.washington.edu/mdw/pdfs/SRMbook.pdf

Michael D. Ward

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Recent Books

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Some software resources…

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GIS• ESRI ArcGIS 9

– Geostatistical Analyst Extension– Spatial Statistics Toolbox

• MapInfo (now Pitney Bowes Business Insight)– http://www.pbinsight.com/

• Manifold– http://www.manifold.net/

• GRASS 6.4 (open source; free) – http://grass.osgeo.org/

• Quantum GIS (open source; Switzerland?)– http://www.qgis.org/

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Three specialized spatial data analysis software programs

• SpaceStat– http://www.terraseer.com/products/spacestat.html

• GeoDa– http://geodacenter.asu.edu

• GWR– http://ncg.nuim.ie/ncg/GWR/

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Toolboxes for spatial data analysis• ArcGIS 9

– Spatial Analyst Toolbox– Spatial Statistics Toolbox

• MATLAB– James LeSage: http://www.spatial-econometrics.com/– R. Kelley Pace: http://www.spatial-statistics.com/

• Stata– http://www.stata.com/

• S+SpatialStats (now part of TIBCO, Inc.?)– http://www.insightful.com/products/spatial/default.asp

• R– http://cran.r-project.org/

• GeoBUGS– http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/geobugs.shtml

• GeoVista Studio– http://www.geovistastudio.psu.edu/jsp/index.jsp

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Other specialized software of potential interest

• CrimeStat– http://www.icpsr.umich.edu/CRIMESTAT/

• SANET– http://okabe.t.u-tokyo.ac.jp/okabelab/atsu/sanet/sanet-

index.html

• STARS– http://regal.sdsu.edu/index.php/Main/STARS

• STIS– http://www.terraseer.com/products/STIS.html

• and lots more…

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Great websites…

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Other favorites?

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Readings for today• Anselin, Luc. 2005. Spatial Regression Analysis in R:

A Workbook. (Urbana-Champaign, IL: University of Illinois, Spatial Analysis Laboratory).

• 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.

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THANKS!To Don & Stephen and the UCSB support team!!Thanks to you for your participation & interest!!

Thanks for your enthusiasmHappy spatial analyzing

See you this afternoon in the LabSafe travels

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Thanks, Katherine!

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Remainder of today…Final lunch together

Last chance for questionsAfternoon: Presentations & Open ForumClosing comments by Stephen & Don,

and certificates of completion

Questions?

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