Spatial Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 158

+s
+}
> srs_grts < - GRTS(rep(n/N,N),x ¼ framepop$xc,y ¼ framepop$yc)
Stratum: None
Current number of levels: 4
Final number of levels: 4
> table(srs_grts)
srs_grts
01
900 100
> library(tripack)
> par(mar ¼ c(1,1,1,1),xaxs ¼ "i",yaxs ¼ "i")
> plot(framepop$xc,framepop$yc, axes ¼ F,cex ¼ 0.5,pch ¼ 19,
+ xlim ¼ c(0,1),ylim ¼ c(0,1))
> points(framepop$xc[srs_grts ¼¼ 1],framepop$yc[srs_grts ¼¼ 1],
+ pch¼1,
+ cex¼2)
> vorgrts < - voronoi.mosaic(framepop$xc[srs_grts ¼¼ 1],
+ framepop$yc[srs_grts ¼¼ 1])
> plot(vorgrts,add¼T,all¼T,do.points¼F)
> box()

The Voronoi polygons could represent a basic tool for defining a measure that
provides information on the spatial distribution of the selected samples. This index
could be very helpful for comparing how well two or more algorithms spread a set
of points over the study region. Given a finite set of points, the Voronoi polygons
partition the region so that for each point k that defines the polygon , every point of
this polygon is closer to k than to any other point in the set.
Intuitively, we could expect that the spread of a set of points may reflect the
variability of the size of these polygons, because we will have the same area for
each polygon if the distribution of the points is exactly systematic over the plane.
Such a measure can be easily evaluated in R . In the following, we have compared
the outcome of GRTS (vorgrts) with the SRS (vorsrs) and maximal stratifi-
cation (vorstr) methods described in Chap. 6 (results are 1,000 to increase the
readability).

> vorsrs < -voronoi.mosaic(framepop$xc[srs ¼¼ 1],framepop$yc[srs ¼¼
+ 1])
> vorstr < -voronoi.mosaic(framepop$xc[str[,1]],framepop$yc[str
+ [,1]])
> summary(vorsrs$area[vorsrs$area > 0])*1000
Min. 1st Qu. Median Mean 3rd Qu. Max.