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constructs spatial weight matrices based on distance

Source: R/spdep_helpers.R
spdep_distance_swm.Rd

Constructs spatial weight matrices based on distance via spdep package.

Usage

spdep_distance_swm(
  sfj,
  kernel = NULL,
  k = NULL,
  bandwidth = NULL,
  power = 1,
  style = "W",
  zero.policy = TRUE
)

Arguments

sfj

An sf object or can be converted to sf by sf::st_as_sf().

kernel

(optional) The kernel function, can be one of uniform, triangular,quadratic(epanechnikov),quartic and gaussian. Default is NULL.

k

(optional) The number of nearest neighbours. Default is NULL. Only useful when kernel is provided.

bandwidth

(optional) The bandwidth, default is NULL. When the spatial reference of sf object is the geographical coordinate system, the unit of bandwidth is km. The unit used in the projection coordinate system are consistent with those used in the sf object coordinate system.

power

(optional) Default is 1. Useful when kernel is not provided.

style

(optional) style can take values W, B, C, and S. More to see spdep::nb2mat(). Default is W. For spatial weights based on distance functions, a style of B means using the original value of the calculated distance function.

zero.policy

(optional) if FALSE stop with error for any empty neighbour sets, if TRUE permit the weights list to be formed with zero-length weights vectors. Default is TRUE.

Value

A matrix

Details

five different kernel weight functions:

  • uniform: \(K_{(z)} = 1/2\),for \(\lvert z \rvert < 1\)

  • triangular \(K_{(z)} = 1 - \lvert z \rvert\),for \(\lvert z \rvert < 1\)

  • quadratic (epanechnikov) \(K_{(z)} = \frac{3}{4} \left( 1 - z^2 \right)\),for \(\lvert z \rvert < 1\)

  • quartic \(K_{(z)} = \frac{15}{16} {\left( 1 - z^2 \right)}^2\),for \(\lvert z \rvert < 1\)

  • gaussian \(K_{(z)} = \frac{1}{\sqrt{2 \pi}} e^{- \frac{z^2}{2}}\)

For the equation above, \(z = d_{ij} / h_i\) where \(h_i\) is the bandwidth

Note

When kernel is setting, using distance weight based on kernel function, Otherwise the inverse distance weight will be used.

Examples

pts = sf::read_sf(system.file('extdata/pts.gpkg',package = 'sdsfun'))
wt1 = spdep_distance_swm(pts, style = 'B')
wt2 = spdep_distance_swm(pts, kernel = 'gaussian')
wt3 = spdep_distance_swm(pts, k = 3, kernel = 'gaussian')
wt4 = spdep_distance_swm(pts, k = 3, kernel = 'gaussian', bandwidth = 10000)