sb_vk {WaveSampling}

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)

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).

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.

Author(s)

Raphaël Jauslin [e-mail]

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)