Journey-to-crime surface

Ranks the cells of a grid as candidate bases of an offender from the locations of a series of incidents. mode = "sum" gives the classic aggregate surface, the sum over incidents of the decay of their distance to the cell (Canter et al. 2000; Levine 2009); mode = "lik" gives the sum of the logarithms, the log-likelihood of the cell as base when the decay function is the planar density of an incident about the base and the incidents are independent (O'Leary 2009), so that prob is the posterior over cells under a uniform prior. The sum surface is not a likelihood.

Usage

jtsurf(
  x,
  y = NULL,
  win,
  nx,
  ny,
  type,
  par,
  tab = NULL,
  metric = "euclid",
  mode = "sum"
)

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 grid's rectangle c(xmin, xmax, ymin, ymax).

nx, ny

The numbers of cells across and up: whole numbers from 1, with at most 1e9 cells.

type

The form: one of the names above.

par

The parameters of the form, of the length given above.

tab

For type = "table": at least two values from 0.

metric

"euclid" (straight-line distance) or "manhattan" (|dx| + |dy|, a street grid aligned with the axes).

mode

"sum" or "lik".

Value

A list. raw and prob, matrices of nx rows (across) and ny columns (up), cell [i, j] centred at (xmin + (i - 1/2) dx, ymin + (j - 1/2) dy): the surface and its normalised version (summing to 1). peak, a named vector: cell (the first cell of maximum value, numbered down the columns of the matrix), x and y (its centre).

Details

What this does not license: the surface ranks places to search under the assumptions that the series is one offender's, that the offender travelled from one fixed base inside the grid, and that the decay function, which describes offenders in general, fits this one. It is a search priority, not evidence that any person lives anywhere. Accuracy on solved series in the same place (jtacc()) is the only guide to its worth.

References

Canter, D., Coffey, T., Huntley, M. and Missen, C. (2000). Predicting serial killers' home base using a decision support system. Journal of Quantitative Criminology, 16(4), 457-478. doi:10.1023/A:1007551316253

O'Leary, M. (2009). The mathematics of geographic profiling. Journal of Investigative Psychology and Offender Profiling, 6(3), 253-265. doi:10.1002/jip.111

Examples

s <- jtsurf(c(2, 3, 4), c(2, 4, 3), win = c(0, 6, 0, 6), nx = 30,
            ny = 30, type = "negexp", par = c(1, 1), mode = "lik")
s$peak
#>  cell     x     y 
#> 467.0   3.3   3.1