| sbi {Spbsampling} | R Documentation |
Spatial Balance Index
Description
Computes the Spatial Balance Index (SBI), which is a measure of spatial balance of a sample. The lower it is, the better the spread.
Usage
sbi(dis, pi, s)
Arguments
dis |
A distance matrix NxN that specifies how far all the pairs of units in the population are. |
pi |
A vector of first order inclusion probabilities of the units of the population. |
s |
A vector of labels of the sample. |
Details
The SBI is based on Voronoi polygons. Given a sample s, each unit i
in the sample has its own Voronoi polygon, which is composed by all
population units closer to i than to any other sample unit j.
Then, per each Voronoi polygon, define v_{i} as the sum of the
inclusion probabilities of all units in the i-th Voronoi polygon.
Finally, the variance of v_{i} is the SBI.
Value
Returns the Spatial Balance Index.
References
Stevens DL, Olsen AR (2004). Spatially Balanced Sampling of Natural Resources. Journal of the American Statistical Association, 99(465), 262-278. doi:10.1198/016214504000000250
Examples
dis <- as.matrix(dist(cbind(simul1$x, simul1$y))) # distance matrix
con <- rep(0, nrow(dis)) # vector of constraints
stand_dist <- stprod(mat = dis, con = con) # standardized matrix
pi <- rep(100 / nrow(dis), nrow(dis)) # vector of probabilities inclusion
s <- pwd(dis = stand_dist$mat, n = 100)$s # sample
sbi(dis = dis, pi = pi, s = s)