Agriculture Reference
In-Depth Information
> library(BalancedSampling)
> n < - 100
> N < - 1000
> set.seed(200694)
> p ¼ rep(n/N,N)
> X < - cbind(framepop$xc,framepop$yc)
> sam_scps < - scps(p,X)
> length(sam_scps)
[1] 100
> spbalance(ds,rep(n/N,N),sam_scps)
[1] 0.1022222
> 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$xc[sam_scps],framepop$yc[sam_scps],
+ pch¼1, cex¼2)
> box()
The output (sam_scps) is the vector of the codes of the selected units. It is
worthwhile noting the excellent performance of the SB index, which is even lower
than in the maximal stratification. In fact, in the previous exercise we obtained a SB
value of 0.1022222.
The approach that inspired the SCPS method is based on a careful adjustment of
a procedure for selecting
π k , obtained by introducing the
correlation between selection probabilities or by modifying the
π
ps samples with fixed
π kl s (which remain
unknown and cannot be fixed in advance).
Using a similar technique, Grafstr ¨ m et al. ( 2012 ) derived two alternative pro-
cedures for selecting samples with fixed
ˀ k s and correlated inclusion probabilities,
as an extension of the pivotal method for selecting
ps samples (Deville and Till ´
1998 ). They are essentially based on an updating rule for the probabilities
π
π l .
At each step, the rules state that the sum of the updated probabilities is as locally
constant as possible, and that they differ from each other in the way that the two
nearby units k and l are chosen. These two methods are referred to as the local
pivotal method 1 (LPM 1), which the authors suggest is better spatially balanced ,
and the local pivotal method 2 (LPM 2), which is simpler and faster.
A sample is obtained in N steps. At each step, the inclusion probabilities for two
units are updated, and the sampling outcome is decided for at least one of the units.
When the updated inclusion probability
π k and
π k is equal to 0 or 1, a label representing
“not selected” or “selected” is assigned to the unit k . It is then removed from the
population, and cannot be chosen again. The updating procedure is repeated with
updated inclusion probabilities, until a label is assigned to all the units of the
population. Deville and Till´ ( 1998 ) suggested randomly choosing a pair of units
at each step to maximize the entropy of the selected units. Grafstr¨m et al. ( 2012 )
introduced LPMs that update the inclusion probabilities according to the same
updating rule of Deville and Till´ ( 1998 ) but for two nearby units, improving the
spatial balance .
Search WWH ::




Custom Search