Generalized Linear Models for Spatial Data In R: Free Software to Map Client Needs

The purpose of this workshop is to expose researchers to advanced spatial data analysis techniques in the R environment.  Social Work researchers often work with point data, such as clients in communities or organizations in metro areas, or with polygon data, which often takes the form of aggregate characteristics of a census tract or zip code (Freisthler et al., 2004).  However, Tobbler's law (1987; 1999; 2004) everything is related to everything else, but near objects are more related than the distant.  This spatial dependence violates one of the basic assumption of ordinary least squares regression but researchers often use it anyway.

Spatial data analysis has strategies of modeling or controlling for spatial dependence. One frequently used diagnostic is the Moran's I statistic, a measure of spatial autocorrelation for polygon units. Spatial regression in ordinary least squares is one way to control for spatial autocorrelation by using a connectivity matrix as a weight (Anselin et al., 2005).  However, not all data structures lend themselves to OLS regression.  Spatial filtering an experimental technique that uses the eigenvectors of the spatial connectivity matrix to control for autocorrelation (Tiefelsdorf & Griffith, 2007).  These may then be used in any generalized linear model including binary outcomes and count data models using Poisson or negative binomial link functions.

R can manipulate both point and polygon data (Bivand et al., 2008). The R project is a GNU (GNU is Not UNIX) version of the S system developed by Chambers et al. at Bell Laboratories for statistical and graphical analysis of data.  GNU is the operating system developed by Richard Stallman of MIT and the Free Software Foundation.  GNU software is copy left under the general public license (GPL) so that it may be used, modified and redistributed provided all derivative products also are copyleft GPL.  Accordingly, R is distributed for free, upgrades are free and if a function does not exist, the user may create it. The instructor learned these spatial tools from the authors who wrote them (Bivand, Tiefelsdorf & Griffith).

The workshop will be primarily a demonstration. The instructors will give attendees a chance to install R and workshop data on their laptops. This will allow people to follow along. The workshop does not assume prior knowledge of R. The first section will go over the basics of R. The second section will show how to load spatial data into R from a flat file created by a spreadsheet, any proprietary software package or from the industry standard ESRI shapefile format. The third portion of the workshop, will show an example of plotting points and polygons.  Finally, the instructor will demonstrate an example comparing traditional spatial regression models to spatial filtering with eigenvectors.