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
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
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