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Kernel intensity surface of incidents

Source: R/kdsurf.R
kdsurf.Rd

Where incidents cluster: the intensity lambda(u) = sum_j w_j k(u - p_j) with the product normal kernel of standard deviations h (along x and y), in incidents per unit area, on a regular grid or at given locations. On a grid it is the surface of MASS::kde2d() times the number of points, with the same default bandwidth (the normal reference 1.06 min(sd, IQR / 1.34) n^(-1/5) on each axis, a quarter of MASS::bandwidth.nrd()). With a study rectangle win the edge corrections of spatstat.explore::density.ppp() apply: "uniform" divides the intensity at u by e(u), the share of the kernel centred at u inside win (Diggle 1985), and "diggle" divides each point's kernel by its own share e(p_j) (Jones 1993). On a grid the smallest sets of cells holding each share cover of the surface's mass (highest density regions, Hyndman 1996) are reported with their area: half the incidents in a few per cent of the map is concentration. The bandwidth decides how sharp the surface is and should be reported with any map.

Usage

kdsurf(
  x,
  y = NULL,
  w = NULL,
  h = NULL,
  win = NULL,
  nx = 100,
  ny = nx,
  edge = "none",
  at = NULL,
  cover = c(0.5, 0.9)
)

Arguments

x, y

The points in planar coordinates (project longitude and latitude with eqproj() first): x and y numeric vectors of equal length, or x a matrix or data frame with columns named x and y. At least two points; no missing values.

w

NULL, or one weight from 0 per point.

h

NULL for the normal reference bandwidths, or one or two positive numbers: the kernel's standard deviations along x and y.

win

NULL, or the study rectangle c(xmin, xmax, ymin, ymax): the grid's extent (otherwise the points' range widened by 3 h), and needed by an edge correction.

nx, ny

The grid's number of columns and rows: whole numbers from 2.

edge

"none", "uniform" or "diggle".

at

NULL for the grid; "points" for the intensity at each point, leaving the point itself out; or coordinates (as for x) to evaluate at.

cover

Shares between 0 and 1 of the surface's mass for the regions.

Value

A list of class kdsurf: x, y (the grid's coordinates, or the evaluation points), z (the intensity: a matrix with one row per x and one column per y on a grid, NaN where win holds none of the kernel, otherwise a vector), h (the standard deviations used) and regions (NULL off the grid): a data frame of cover, level (the lowest intensity in the region), area and share (of the grid's area).

References

Diggle, P. J. (1985). A kernel method for smoothing point process data. Journal of the Royal Statistical Society, Series C, 34(2), 138-147. doi:10.2307/2347366

Jones, M. C. (1993). Simple boundary correction for kernel density estimation. Statistics and Computing, 3(3), 135-146. doi:10.1007/BF00147776

Hyndman, R. J. (1996). Computing and graphing highest density regions. The American Statistician, 50(2), 120-126. doi:10.1080/00031305.1996.10474359

Examples

set.seed(1)
p <- cbind(x = c(rnorm(80, 2, 0.5), runif(40, 0, 6)),
           y = c(rnorm(80, 3, 0.5), runif(40, 0, 6)))
k <- kdsurf(p, win = c(0, 6, 0, 6), nx = 50, edge = "uniform")
k
#> kdsurf: 50 x 50 grid, sd 0.2794 by 0.2655, peak 49.54
#>  cover     level      area  share
#>    0.5 13.021117  2.413994 0.0644
#>    0.9  1.626066 15.773428 0.4208
image(k$x, k$y, k$z)

kdsurf(p, h = 0.4, at = "points")$z[1:5]
#> [1] 27.05935 34.01434 21.47548 14.47467 30.98250