[GRASSLIST:1586] Re: interpolate nominal values

[Edzer J. Pebesma]

Rich Shepard wrote:
> 
>   Soil maps (and soil taxonomy in general) are best represented either by
> vector polygons (the way they're drawn on paper maps) or raster regions that
> more accurately reflect the transition zone between one soil type and the
> adjacent one.

I disagree here. It depends on how the data were obtained: were they
mapped in the field as polygons (in which case vector seems most appropriate)
or were they interpolated (estimated) from point samples (e.g. in the case
of chemical composition)? In the latter case, raster representation seems
the obvious way to go -- most interpolation programs output raster maps.
> 
>   Now, if you had ratio data representing, for example, samples of plant
> species' densities and height (just to pick some arbitrary parameters for
> the sake of this discussion) you could interpolate those data and drape the
> soils layer over them to see if there were meaningful patters in the
> relationship.
> 
>   Perhaps my point will be better understood if I present an absurd example.
> (Don't try this at home! It can be done only by experts on a closed course.)
> Suppose you had point (sites) data of fast-food restaurants (i.e., junk food
> vendors) from a typical American medium size city. The nominal data
> categories include "McDonalds", "Burger King", "Taco John", etc. Now,

Like the confusion about "nominal" vs. "interval/ratio" data, you're mixing
two spatial data types here -- geostatistical data vs. point pattern data
(using Cressie's "Statistics for spatial data" terminology). Geostatistical
data are obtained (measured) at a limited number of locations, but takes on
a value (could be measured) at any location in the region of interest. Point
pattern data are patterns of occurences of specific items (cities, fast food
stores, trees,...) in a region. The latter can be "transformed" to the former
by using the concept of local density.

One typical problem for geostatistical data is interpolation. E.g., soil type
is measured at a limited number of sites, and now we want to make a soil map
from it. For nominal data, the way to go is define an indicator variable
for each soil type, give it a 1 if the soil type is present and else a 0.
Interpolated values may be interpreted as _estimated_ probabilities of 
occurence for that soil type. (Note that they are not real probabilities).

For further clues, look into the geostats literature for indicator kriging,
indicator cokriging and indicator simulation. There's a lot written about this.
--
Edzer