From the online “Directions Magazine,” Wednesday May 22, 2002

http://www.directionsmag.com/, main page

 Columns

 Map-ematical GIS Models: Doing the Math

By: Joe Berry
(Apr 30, 2002

(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 non-technical decision-makers... not a "map-ematical 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 human-compatible 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 map-ematical 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 grid-based 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, S-Plus (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 (1995-2002), then search on the phrase “Beyond Mapping.”