WaveSampling (version 0.1.4)

sb_vk: Values \(v_k\) to compute the Spatial balance

Description

Calculates the \(v_k\) values of the spatial balance developped by Stevens and Olsen (2004) and suggested by Grafström et al. (2012).

Usage

sb_vk(pik, X, s)

Value

A vector of size \(N\) with elements equal to the \(v_k\) values. If the unit is not selected then the value is equal to 0.

Arguments

pik

vector of the inclusion probabilities. The length should be equal to \(N\).

X

matrix representing the spatial coordinates.

s

A vector of size \(N\) with elements equal 0 or 1. The value 1 indicates that the unit is selected while the value 0 is for non-chosen unit.

Details

The spatial balance measure based on the Voronoï polygons is defined by

$$B(S) = \frac{1}{n}\sum_{k\in S} (v_k -1)^2 .$$

The function return the \(v_k\) values and is mainly based on the function sb of the package BalancedSampling Grafström and Lisic (2019).

References

Grafström, A., Lundström, N.L.P. and Schelin, L. (2012). Spatially balanced sampling through the Pivotal method. Biometrics, 68(2), 514-520

Grafström, A., Lisic J. (2019). BalancedSampling: Balanced and Spatially Balanced Sampling. R package version 1.5.5. https://CRAN.R-project.org/package=BalancedSampling

Stevens, D. L. Jr. and Olsen, A. R. (2004). Spatially balanced sampling of natural resources. Journal of the American Statistical Association 99, 262-278

See Also

BalancedSampling::sb

Examples

N <- 50
n <- 10
X <- as.matrix(cbind(runif(N),runif(N)))
pik <- rep(n/N,N)
s <- wave(X,pik)
v <- sb_vk(pik,X,s)