hpwd: Heuristic Product Within Distance (Spatially Balanced...

In Spbsampling: Spatially Balanced Sampling

Heuristic Product Within Distance (Spatially Balanced Sampling Design)

Description

Selects spatially balanced samples through the use of Heuristic Product Within Distance design (HPWD). To have constant inclusion probabilities π_{i}=n/N, where n is sample size and N is population size, the distance matrix has to be standardized with function stprod.

Usage

hpwd(dis, n, beta = 10, nrepl = 1L)

Arguments

dis	A distance matrix NxN that specifies how far all the pairs of units in the population are.
n	Sample size.
beta	Parameter β for the algorithm. The higher β is, the more the sample is going to be spread (default = 10).
nrepl	Number of samples to draw (default = 1).

Details

The HPWD design generates samples approximately with the same probabilities of the pwd but with a significantly smaller number of steps. In fact, this algorithm randomly selects a sample of size n exactly with n steps, updating at each step the selection probability of not-selected units, depending on their distance from the units that were already selected in the previous steps.

Value

Returns a matrix nrepl x n, which contains the nrepl selected samples, each of them stored in a row. In particular, the i-th row contains all labels of units selected in the i-th sample.

References

Benedetti R, Piersimoni F (2017). A spatially balanced design with probability function proportional to the within sample distance. Biometrical Journal, 59(5), 1067-1084. doi: 10.1002/bimj.201600194

Benedetti R, Piersimoni F (2017). Fast Selection of Spatially Balanced Samples. arXiv. https://arxiv.org/abs/1710.09116

Examples

# Example 1
# Draw 1 sample of dimension 10 without constant inclusion probabilities
dis <- as.matrix(dist(cbind(lucas_abruzzo$x, lucas_abruzzo$y))) # distance matrix
s <- hpwd(dis = dis, n = 10) # drawn sample

# Example 2
# Draw 1 sample of dimension 15 with constant inclusion probabilities
# equal to n/N, with N = population size
dis <- as.matrix(dist(cbind(lucas_abruzzo$x, lucas_abruzzo$y))) # distance matrix
con <- rep(1, nrow(dis)) # vector of constraints
stand_dist <- stprod(mat = dis, con = con) # standardized matrix
s <- hpwd(dis = stand_dist$mat, n = 15) # drawn sample

# Example 3
# Draw 2 samples of dimension 15 with constant inclusion probabilities
# equal to n/N, with N = population size, and an increased level of spread, beta = 20
dis <- as.matrix(dist(cbind(lucas_abruzzo$x, lucas_abruzzo$y))) # distance matrix
con <- rep(0, nrow(dis)) # vector of constraints
stand_dist <- stprod(mat = dis, con = con) # standardized matrix
s <- hpwd(dis = stand_dist$mat, n = 15, beta = 20, nrepl = 2) # drawn samples

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