Illinois Cancer Data set example

We want to compare the default behavior of geostatistical software with the default behavior of ArcView. ArcView has a program called Spatial Analyst, which allows one to interpolate from a set of data. We'll compare the map of SCV1 obtained using ArcView (the defaults) with the map of SCV1 obtained using one particular geostatistical software package (GS+, which we'll be using in lab).

• The first problem was to get the map of Illinois counties and county seats into Cartesian coordinates (meters, say), rather than lat/longs. I used the GIS GRASS to convert the coordinates to UTMs.

• ArcView makes it easy: just load the Spatial Analyst extension, hit the interpolate button, choose the defaults, and you have a map (which you can contour, for example). We'll compare contours of the two maps.

• The variogram was computed for the data by the software GS+. I took the defaults all the way through. Here's the variogram:

  

  Note that the software gives us four directional variograms too, so that we can decide if an isotropic model is a good idea. In this case, it doesn't look too bad. Note also the sample mean, which is shown with the straight dashed line in the plots. The model that was plotted (and additional possible models) are shown in another screen:

  

  Note that the exponential model was chosen - don't know why GS+ took that one, but guess that it's the r-squared it calculates.

• We now go ahead and krig the data to produce a surface or a contour of a surface (to be compared in a moment). It offers three-d plots, as well as contour plots.

• Kriging produces a kriging variance as well, which was discussed earlier in this module.

• One of the cross-validation results presented is a plot of the cross-validated values against the true values. We would like to see the point cloud hug the regression line, and see the regression line overlap the line y=x (not quite in this case!).

• Okay, now to the comparison of the plots:

  

  Can you guess which is which? They are obviously not the same! The ArcView map (on the left), created using Inverse Distance Weighting, has much more "confidence" in the data than does the kriging map. See how the IDW map swoops up to meet the data points: the kriged map won't do that, because of the nugget in the model.

• Conclusion: it really does make a difference what type of mapping you do! Don't be too casual, and consider doing it the hard way....