Premise

Wanted to make something akin to an interpolated surface for some spatially auto-correlated categorical data (presence/absence). I quickly generated some fake spatially auto-correlated data to work with using r.surf.fractal in GRASS. These data were converted into a binary map using an arbitrary threshold that looked about right-- splitting the data into something that looked 'spatially clumpy'.

Fig. 1: Simulated auto-correlated, categorical variable, with sampling points and derived voronoi polygons.

I had used voronoi polygons in the past to display connectivity of categorical data recorded at points, even though sparsely sampled areas tend to be over emphasized. Figure 1 shows the fake spatially auto-correlated data (grey = presence /white = not present), sample points (yellow boxes), and voronoi polygons. The polygons with thicker, red boundaries represent the "voronoi interpolation" of the categorical feature.

Interpolation by RST

Wanting something a little more interesting, I tried interpolating the presence/absence data by via RST. Numerical interpolation of categorical data is usually not preferred as it creates a continuum between discreet classes-- i.e. values that do not have a sensible interpretation. Throwing that aside for the sake of making a neat map, a color scheme was selected to emphasize the categorical nature of the interpolated surface (Figure 2).

Fig. 2: RST interpolation of 0-1 continuum: red=1, blue=0.

Conditional Indicator Simulation

Finally, I gave conditional indicator simulation a try-- this required two steps: 1) fitting a model variogram, 2) simulation. This approach generates different output on each simulation, however, the output represents the original spatial pattern and variability. A more interesting map could be generated by running 1000 simulations and converting them into a single probability map.

Indicator Variogram: Empirical semi-variogram for indicator=1, with spherical model fit.

Categorical Interpolation 3: Single conditional indicator simulation.

Comparison

Code Snippets

Generate Some Data in GRASS

Perform Indicator Simulation in R

Make Some Maps in GRASS