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Columns 

Mapematical GIS Models: Doing the Math 
By: Joe Berry
(
(Note: the following thoughts
were compiled from a series of discussions grappling with map analysis
approaches between Joe Berry the Principal of Berry and Associates and Craig
Von Hagen a GIS Specialist with FAO – Africover,
Nairobi, Kenya)
There are two primary
approaches to potential/propensity modeling for spatial information:
Suitability Modeling and Mathematical Modeling.
Suitability Modeling involves expert
opinion of criteria and model logic such as a management model for locating the
best areas to locate a proposed campground. (For an example, go
; select "Identifying Campground
Suitability" example) HERE. In this approach, model logic is
developed by "those in the know" then implemented. It has advantages
in communicating model assumptions and results to nontechnical
decisionmakers... not a "mapematical black
box."
Mathematical Modeling (specifically Spatial
Data Mining) derives a numerical relationship among map layers. However, it has
a major drawback in the availability of appropriate data. Most GIS data are
discrete vector maps composed of polygons representing the typical (…arithmetic
average? or just categorical data?) condition with no reference to the variance
or its spatial distribution within a parcel. It is tough to generate a good
spatial model from "generalized chunky" data. They are great for
humancompatible map displays but limited for spatial data mining. Standard
multivariate analysis prefers continuous data in both numeric and geographic
space, which is not the case in typical GIS maps.
Given that, it does
not mean that you cannot derive a mapematical model
with generic GIS data (computer won't crash and burn). It just suggests that
you had better do a lot of "empirical verification" to see how well
the prediction equation is working. Two ways to do that are:
1) Error Analysis
 run the model on the data used to derive the prediction equation for error
surface analysis
http://www.innovativegis.com/basis/MapAnalysis/Topic16/Topic16.htm
and...
2) Residual
Analysis  run the model under some "known" conditions not used
in developing the model and compare model predictions...
http://www.innovativegis.com/basis/MapAnalysis/Topic2/Topic2.htm
Suggestions
For most of my consulting, I use MapCalc, an inexpensive yet powerful
gridbased map analysis package I helped develop (see www.redhensystems.com) . For advanced
statistical processing, I use standard JMP software (www.jmpdiscovery.com) . On rare occasions, SPlus (www.insightful.com) can be used for some
aspects of spatial statistics but they do not provide for predictive
statistics.
Other sources of
information:
Precision Farming
Primer, particularly the case study of a corn field... http://www.innovativegis.com/basis/pfprimer/Appendix_D/Appendix_D.htm
http://www.innovativegis.com/basis/MapAnalysis/Topic10/Topic10.htm,
Select "Understanding Map Correlation" and "Predictable
Maps" topics
http://www.innovativegis.com/basis/MapAnalysis/Topic16/Topic16.htm,
Select "Predictable Maps" and "Stratifying Maps for better
predictions" topics
From the Beyond
Mapping column in GEOWorld with online archives of the columns at... www.geoplace.com,
Select “Archives,” “GeoWorld,”
any year (19952002), then search on the phrase “Beyond Mapping.”