Search-circle hot-spot areas

Hot-spot areas from search circles (Block and Block 1995): circles of radius r are centred on the nodes of an nx by ny grid spanning the rectangle win (corners included), the points in each are counted, the circles holding at least two points are ranked by count and the first top are kept; kept circles that share a point are merged, repeatedly, and a hot-spot area is the set of points in a merged group, kept if it has at least minpts. Descriptions differ on the circle's radius and on the grid; both are the caller's choice here.

Usage

stacel(
  x,
  y = NULL,
  win,
  nx = 20,
  ny = 20,
  r,
  top = 25,
  minpts = 5,
  k = 1,
  c = 1,
  count = NULL
)

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 (an unnamed two-column matrix is read as x then y). At least two points, all inside win; no missing values.

win

The rectangle the grid spans, c(xmin, xmax, ymin, ymax); points may lie outside it.

nx, ny

The numbers of grid nodes across and up: whole numbers from 2 to 10000.

r

The search radius, positive, in the unit of the coordinates.

top

The number of busiest circles kept: one whole number from 1.

minpts

The fewest points a hot-spot area keeps: a whole number from 2.

k

The divisor offset: 0, 1 or 2; the total weight must exceed it.

c

The multiplier of each cluster's standard deviational ellipse (see sdell()).

count

NULL for points, or for zones: one whole count from 0 per zone, the points x, y being the zones' centroids. A zone is taken as count incidents at its centroid, which these hot-spot rules treat exactly as coincident points. Zones with count 0 get NA; the random-expectation threshold counts incidents, not zones.

Value

A list. cl, the hot-spot area of each point (zone) (a row of clusters) or NA, in input order. clusters, a data frame with one row per area, by size: points, mx, my (mean centre), wx, wy (centre of minimum distance), a, b and angle (the standard deviational ellipse of its points).

References

Block, R. L. and Block, C. R. (1995). Space, place and crime: hot spot areas and hot places of liquor-related crime. In J. E. Eck and D. Weisburd (eds.), Crime and Place, Crime Prevention Studies 4, 145-183. Criminal Justice Press.

Examples

set.seed(1)
x <- c(rnorm(30, 2, 0.2), runif(60, 0, 10))
y <- c(rnorm(30, 2, 0.2), runif(60, 0, 10))
stacel(x, y, win = c(0, 10, 0, 10), r = 0.75, top = 5, minpts = 5)$clusters
#>   points       mx       my       wx       wy         a         b     angle
#> 1     35 2.027899 2.025648 2.055272 2.024903 0.3233517 0.2532551 0.1950933