Hot spots and how long they last

Counts incidents in square grid cells of side cell (from the corner org) for each period and marks as hot, in each period, the k = ceiling(top * m) busiest of the m cells that ever hold an incident, with every cell tied with the k-th; when a tie would make more than 2 k cells hot the counts do not single them out and the tied cells are left out (counted in tiedout). Each period gets its concentration (the fewest cells holding half its incidents), the share of its incidents in hot cells, and the Jaccard overlap of its hot set with the period before (NA when either is empty); each cell gets the number of periods it was hot and its longest run of successive hot periods, the persistence that tells chronic hot spots from flare-ups (Weisburd, Bushway, Lum and Yang 2004).

Usage

hsper(x, y = NULL, prd, cell, top = 0.05, org = NULL, 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.
prd: The period of each incident: labels (a year, a month, a quarter), taken in sorted order (a factor in the order of its levels), with no missing values.
cell: The side of a cell: positive, in the unit of the coordinates (metres when lonlat = TRUE).
top: The share of the active cells counted hot, above 0 and at most 1.
org: NULL for the lowest x and y, or the grid's corner c(x, y) (projected, as the coordinates are, in metres when lonlat = TRUE).
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 of class hsper: periods, a data frame with one row per period: period, n (incidents), active (cells with any), nhalf and shalf (the fewest cells holding half the incidents, and that number over the active cells of all periods), hot, tiedin (hot cells beyond k from a tie), tiedout, hotshr (the share of incidents in hot cells) and jacc; cells, a data frame with one row per active cell: its centre x, y (in degrees when lonlat = TRUE), n, nhot and run; hot, a logical matrix of cells by periods; cell, each incident's cell (a row of cells); and k.

References

Weisburd, D., Bushway, S., Lum, C. and Yang, S.-M. (2004). Trajectories of crime at places: a longitudinal study of street segments in the city of Seattle. Criminology, 42(2), 283-322. doi:10.1111/j.1745-9125.2004.tb00521.x

Examples

set.seed(1)
n <- 600
p <- cbind(x = c(rnorm(300, 2, 0.3), runif(300, 0, 10)),
           y = c(rnorm(300, 2, 0.3), runif(300, 0, 10)))
h <- hsper(p, prd = rep(2021:2024, length.out = n), cell = 1, top = 0.1)
h
#> hsper: 99 active cells, the 10 busiest hot in each of 4 periods
#>  period   n active nhalf      shalf hot tiedin tiedout    hotshr      jacc
#>    2021 150     57     4 0.04040404  20     10       0 0.7533333       NaN
#>    2022 150     57     4 0.04040404  19      9       0 0.7466667 0.2580645
#>    2023 150     54     4 0.04040404  11      1       0 0.6666667 0.2000000
#>    2024 150     62     4 0.04040404  17      7       0 0.7000000 0.2173913
subset(h$cells, nhot == 4)
#>           x        y  n nhot run
#> 11 1.513147 1.533045 88    4   4
#> 12 1.513147 2.533045 76    4   4
#> 21 2.513147 1.533045 90    4   4
#> 22 2.513147 2.533045 54    4   4