sb {BalancedSampling}

Spatial balance

Description

Calculates the spatial balance of a sample.

Usage

sb(prob, x, sample, type = "kdtree2", bucketSize = 10)

sblb(prob, x, sample, type = "kdtree2", bucketSize = 10)

Arguments

prob

A vector of length N with inclusion probabilities, or an integer > 1. If an integer n, then the sample will be drawn with equal probabilities n / N.

x

An N by p matrix of (standardized) auxiliary variables. Squared euclidean distance is used in the x space.

sample

A vector of sample indices.

type

The method used in finding nearest neighbours. Must be one of "kdtree0", "kdtree1", "kdtree2", and "notree".

bucketSize

The maximum size of the terminal nodes in the k-d-trees.

Details

About voronoi and sumofsquares

Value

The balance measure of the provided sample.

Functions

• sblb(): Spatial balance using local balance

k-d-trees

The types "kdtree" creates k-d-trees with terminal node bucket sizes according to bucketSize.

• "kdtree0" creates a k-d-tree using a median split on alternating variables.

• "kdtree1" creates a k-d-tree using a median split on the largest range.

• "kdtree2" creates a k-d-tree using a sliding-midpoint split.

• "notree" does a naive search for the nearest neighbour.

References

Friedman, J. H., Bentley, J. L., & Finkel, R. A. (1977). An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software (TOMS), 3(3), 209-226.

Maneewongvatana, S., & Mount, D. M. (1999, December). It’s okay to be skinny, if your friends are fat. In Center for geometric computing 4th annual workshop on computational geometry (Vol. 2, pp. 1-8).

Stevens Jr, D. L., & Olsen, A. R. (2004). Spatially balanced sampling of natural resources. Journal of the American statistical Association, 99(465), 262-278.

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

Prentius, W, & Grafström A. (2023). Manuscript.

See Also

Other measure: vsb()

Other measure: vsb()

Examples

## Not run: 
set.seed(12345);
N = 500;
n = 70;
prob = rep(n / N, N);
x = matrix(runif(N * 2), ncol = 2);
s = lpm2(prob, x);
b = sb(prob, x, s);

## End(Not run)