Spatial weights

Builds the neighbours and weights the autocorrelation statistics (gearc(), gorg(), lmorn(), locgi()) use: the k nearest neighbours of each point (type = "knn", ties broken by the lower row number), the points within distance d ("band", the distance itself included), or a contiguity list nb ("contig", one element per unit giving its neighbours' numbers, as spdep's poly2nb() returns). Weights are 1, or the inverse distance to the power idw; style = "row" divides each unit's weights by their sum (a unit without neighbours keeps none), "raw" leaves them.

Usage

spwt(
  x = NULL,
  y = NULL,
  type = "knn",
  k = 4,
  d = NULL,
  nb = NULL,
  idw = 0,
  style = "row",
  metric = "euclid",
  lonlat = FALSE
)

Arguments

x, y

The points: x and y numeric vectors of equal length; or x a matrix or data frame with columns named x and y (or X and Y, as sf::st_coordinates() names them, or lon and lat with lonlat = TRUE) and y NULL; or x an sf or sfc object of POINT geometries, whose coordinate reference system must agree with lonlat. An unnamed two-column matrix is read as x then y; other columns are never taken by position. Vectors given separately (x, y, and w or t where a function takes them) are matched by name when every one is named and no name repeats, as elsewhere in the package; otherwise by position. No missing or infinite values.

type

"knn", "band" or "contig".

k

For "knn": the number of neighbours, from 1 to the number of points less 1.

d

For "band": the distance, positive, in the unit of the coordinates (metres when lonlat = TRUE).

nb

For "contig": a list with one element per unit, each a vector of neighbour numbers (from 1; 0 alone for none).

idw

The power of the inverse distance: 0 (binary weights) or more; above 0 it needs the points.

style

"row" or "raw".

metric

"euclid" or "manhattan" (|dx| + |dy|).

lonlat

FALSE (the default) when x and y are planar coordinates in one length unit; TRUE when they are longitude and latitude in degrees, which are then projected to metres by eqproj() about their own centre, and centres are returned in degrees. It is never guessed.

Value

A list: n (the number of units), and one element per neighbour pair, in order of unit then neighbour: i, j (integer unit numbers), d (their distance, NA for contiguity without points) and w (the weight). x may be NULL for contiguity with binary weights.

References

Cliff, A. D. and Ord, J. K. (1981). Spatial Processes: Models and Applications. Pion, London.

Examples

set.seed(1)
p <- cbind(x = runif(20), y = runif(20))
w <- spwt(p, k = 3)
str(w)
#> List of 5
#>  $ n: int 20
#>  $ i: int [1:60] 1 1 1 2 2 2 3 3 3 4 ...
#>  $ j: int [1:60] 12 16 19 5 11 14 13 16 17 6 ...
#>  $ d: num [1:60] 0.347 0.353 0.24 0.179 0.317 ...
#>  $ w: num [1:60] 0.333 0.333 0.333 0.333 0.333 ...
spwt(nb = list(2, c(1, 3), 2), type = "contig")$w
#> [1] 1.0 0.5 0.5 1.0