sbi: Spatial Balance Index

In Spbsampling: Spatially Balanced Sampling

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)

Spbsampling documentation built on Aug. 24, 2022, 5:06 p.m.