Daniel A. Griffith
Department of Geography, Syracuse University, NY

Position Statement
Curriculum Vitae
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Position Statement

HOW UNSUCCESSFUL HAS GIS BEEN IN HELPING DISSEMINATE SPATIAL STATISTICAL TECHNOLOGY?

Implementation of spatial statistical techniques has been problematic since their initial appearance in the academy. Like GIS databases, spatial statistical analysis is hampered by a need to retain spatial structure (the map to which georeferenced data are linked—as well as selected analytical features of this structure—an ability absent in most standard commercial software packages implementing traditional statistical techniques. Exceptions include, to a limited degree, S+ (the spatial statistical module) and more recently SAS (PROC GIS). Attempts to circumvent this restriction mostly have resulted in dedicated software, such as SAGE (for spatial autoregression, built upon ArcInfo), SpaceStat (with interfaces to GIS packages), and GSLIB (for geostatistics), although some efforts have tricked standard packages into executing spatial statistical procedures (e.g., Griffith’s SAS and MINITAB code developments). The importance of remedying this situation is attested to by an emphasis on the need for promoting spatial statistical skills in such expert statements as the UCGIS education white paper
(http://www.ncgia.ucsb.edu/other/ucgis/ed_priorities/research.html). The question addressed in this paper asks whether or not GIS has helped, is helping, and/or will be helping disseminate spatial statistical technology in order to promote the acquiring of spatial statistical skills by members of the GIS community. Not surprisingly the answer to this question comprises a mixture of yeses and nos.

Underlying the recognition of a need for user-friendly and easy access to spatial statistical technology is an appreciation of what is special about georeferenced data. In other words, what is spatial autocorrelation and why should a spatial scientist not overlook this property of georeferenced data? GIS software holds a privileged position for aiding students in responding to this question. Certainly one simple way of addressing this issue is to provide a tutorial in a GIS that allows a user to discover the answer to this question. Such a tutorial could be modeled after SASIM, EXPLORHO, or USA, for example. Another possibility is to design a tutorial that focuses on the interpretation of spatial autocorrelation as redundant information: the objective would be for a student to decide whether or not a superfund site should undergo remediation, and if so, what sections should be remediated. One of the fascinating features of this illustrative context concerns determination of the effective sample size, which virtually always will be much less than n (the number of sample points); in the extreme, if a student selects all 
points for a sample from essentially the same location, the effective sample size will be only slightly greater than 1! Such a dramatic outcome is highly effective in revealing what is special about spatial data. To date, GIS software at best only allows a user to compute standard spatial autocorrelation indices (Moran Coefficient, Geary Ratio), which sheds little light on this practical issue.

A second part of the question being addressed here concerns spatial structure and its selected analytical properties necessary for executing a spatial statistical analysis. GIS database structures already furnish a means for retaining the necessary geographic structure when a spatial scientist is interested in conducting spatial analysis. This explicit recording of geographic structure can be exploited in order to implement spatial statistical techniques (see, for instance, Zhang and Griffith, 1998a,b). But the selected analytical features needed are eigenfunctions, a concept foreign to or perceived as being highly intimidating by most students of the spatial sciences. A GIS offers a means of redressing this situation. First, spatial statistical techniques can be implemented in a way that requires knowledge of only the extreme eigenvalues characterizing a given geographic structure. Such an implementation alleviates considerable computational and computer memory burdens, and allows massively large georeferenced datasets to be analyzed. Theoretical spatial statistical results already exist for implementing this approach; what remains is for GIS vendors to incorporate these results. In addition, preliminary research suggests that even the extreme eigenvalues may remain unknown; this research needs to be finalized.

Second, the eigenvectors characterizing a geographic structure reveal a kaleidoscope of possible distinct levels and patterns of spatial autocorrelation. A tutorial needs to be developed for inclusion in a GIS that exploits this feature. Pedagogically speaking, it holds considerable promise for sharpening the map-reading skill of inspecting a map pattern and intuitively being able to ascertain the approximate nature and degree of spatial autocorrelation present in the visualized geographic distribution. Experimentally speaking, it holds considerable promise for resampling experiments in which specific levels of nonzero spatial autocorrelation are to be explored.

While a number of GIS packages have embraced spatial autocorrelation indices, to date somewhat more attention seems to have been devoted to geostatistical implementation. In general, though, everyone seems to have begged the question asking what the relationship is between spatial  autoregression and geostatistics. Spatial scientists and students alike continue to puzzle over this question. A GIS environment is the perfect one to foster a far more comprehensive and deeper understanding of this relationship, since both approaches to georeferenced data analysis focus on the property of spatial autocorrelation. Of course, in order to do so spatial autoregression techniques first need to be implemented in GIS packages.

Therefore one answer to the question addressed by this paper may be summarized as follows:

GIS has been, and continues to be, somewhat successful in raising the awareness of spatial scientists and students about selected features of geostatistics and popular indices of spatial autocorrelation, but overall continues to be quite unsuccessful at making spatial statistical technology widely available to this same group. It certainly possesses the potential to do so, however!

Accordingly, one future research endeavor should be to: introduce tutorials into GIS packages that teach about spatial autocorrelation, and implement spatial autoregression procedures in GIS packages, completing these two tasks in such a way that a user can gain a better understanding about the relationship between geostatistics and spatial autoregression. These achievements should be guided by and would  reflect upon the decade-old debate concerning what spatial analysis routines should be incorporated into a GIS. Moreover, while the GIS environment appears to be satisfactory, implementation of spatial statistical procedures remains neglected by GIS vendors, with one result being a failure for spatial scientists to have access to state-of-the-art research methodology


Curriculum Vitae

Daniel A. Griffith, professor of Geography, has been at Syracuse University since 1988, following ten years as a faculty member at SUNY/Buffalo.  He received his doctorate in geography from the University of Toronto, and an M.Sc. in statistics from the Pennsylvania State University.  While at SU he has served as both Chair of and Director of Graduate Studies for the Department of Geography, and Director for the Applied Statistics Program in the College of Arts & Sciences.  His papers have appeared in geography, regional science, and statistics journals, including Annals of the Association of American Geographers, Journal of Regional Science, Environment and Planning, Geographical Analysis, and Journal of Statistical Planning and Inference.  In addition to publishing over 100 articles, book chapters, and discussion papers, he has (co-)authored/edited 14 books and monographs, including Spatial Autocorrelation (1987), Advanced Spatial Statistics (1988), Spatial Regression Analysis on the PC (1993), Statistical Analysis for Geographers  (1991), and Multivariate Analysis for Geographers (1997).  His most recent work concerning pediatric lead poisoning in Syracuse was the topic of a feature article in the Syracuse Herald-Journal.  His research has been funded by the National Science Foundation, the State of New York, NATO Scientific Affairs, the Fulbright Commission, and the Government of Canada.  Dan has been a visiting professor at the University of Rome and Erasmus University Rotterdam, and has given more than 100 invited lectures, including ones to the Tinbergen Institute-Rotterdam, the Max Plank Institute of Solid State Physics-Stuttgart, NCGIA, Cambridge University, University of Paris I, University of Vienna, University of Toronto, Cornell University, and University of Minnesota.  He has been a Fulbright Research Fellow to Canada, received two software awards from the AAG Microcomputer Specialty Group, received an AAG Nystrom award for his doctoral dissertation, and has been listed in a number of biographical references, including Who's Who in American Education.  Dan is a member of Simga Xi, and has received outstanding alumni awards from the University of Toronto’s Geography Department and Indiana University of Pennsylvania.  His areas of interest and expertise include spatial statistics, quantitative-urban-economic geography, and statistical consulting. 


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Daniel A. Griffith
Department of Geography
Syracuse University, NY
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