hpwd {Spbsampling}

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 \pi_{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 \beta for the algorithm. The higher \beta 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