HIP {spbal}

Halton Iterative Partitioning (HIP).

Description

HIP draws spatially balanced samples and over-samples from point resources by partitioning the resource into boxes with the same nested structure as Halton boxes. The spbal parameter iterations defines the number of boxes used in the HIP partition and should be larger than the sample size but less than the population size. The iterations parameter also defines the number of units available in the HIP over-sample, where the over-sample contains one unit from each box in the HIP partition.

Usage

HIP(
  population = NULL,
  n = 20,
  iterations = 7,
  minRadius = NULL,
  panels = NULL,
  panel_overlap = NULL,
  verbose = FALSE
)

Arguments

population

A population of point pairs.

n

The number of points to draw from the population. Default 20.

iterations

The levels of partitioning required. Default 7.

minRadius

If specified, the minimum distance, in meters, allowed between sample points. This is applied to the $overSample.

panels

A list of integers that define the size of each panel in a non-overlapping panels design. The length of the list determines the number of panels required. The sum of the integers in the panels parameter will determine the total number of samples selected, n. The default value for panels is NULL, this indicates that a non-overlapping panel design is not wanted.

panel_overlap

A list of integers that define the overlap into the previous panel. Is only used when the panels parameter is not NULL. The default value for panel_overlap is NULL. The length of panel_overlap must be equal to the length of panels. The first value is always forced to zero as the first panel never overlaps any region.

verbose

Boolean if you want to see any output printed to screen. Helpful if taking a long time. Default is FALSE i.e. no informational messages are displayed.

Details

Halton iterative partitioning (HIP) extends Basic acceptance sampling (BAS) to point resources. It partitions the resource into $B >= n$ boxes that have the same nested structure as in BAS, but different sizes. These boxes are then uniquely numbered using a random-start Halton sequence of length $B$. The HIP sample is obtained by randomly drawing one point from each of the boxes numbered $1, 2, . . . , n$.

Value

Return a list containing the following five variables:

• Population Original population point pairs as an sf object.

• HaltonIndex The Halton index for the point. Points will be spread equally across all Halton indices.

• sample The sample from the population of size n.

• overSample The overSample contains one point from each Halton box. All contiguous sub-samples from oversample are spatially balanced, and the first n points are identical to sample.

• minRadius This result variable contains the sample created using the minRadius parameter. If the minRadius parameter is not specified then the minRadius variable will contain NULL.

Author(s)

Phil Davies, Blair Robertson.

Examples

# generating 20 points from a population of 5,000 (random) points with 7
# levels of partitioning (4 in the first dimension and 3 in the second) to
# give (2^4) * (3^3) = 32 * 27, resulting in 864 boxes ----------------------

# set random seed
set.seed(511)

# define HIP parameters.
pop <- matrix(runif(5000*2), nrow = 5000, ncol = 2)
n <- 20
its <- 7

# Convert the population matrix to an sf point object.
sf_points <- sf::st_as_sf(data.frame(pop), coords = c("X1", "X2"))
dim(sf::st_coordinates(sf_points))

# generate HIP sample.
result <- spbal::HIP(population = sf_points,
                     n = n,
                     iterations =  its)

# HaltonIndex
HaltonIndex <- result$HaltonIndex
table(HaltonIndex)

# Population Sample
HIPsample <- result$sample
HIPsample