Introduction to sfhotspot

sfhotspot is a package for understanding patterns in data that represent points in space. You can use it to count points in different places, estimate the density of points, show changes in the distribution of points over time, identify places with more points than would be expected by chance, and classify areas based on the number of points in them during different periods.

The specific motivation for this package was to analyse the locations of crimes, but the functions should be useful for understanding patterns in points representing other features or events. The package is called sfhotspot because it works with (and – where relevant – produces) SF objects as produced by the sf package. sfhotspot also produces data that is tidy, making it easy to use functions from packages such as dplyr to filter the results, etc.

All the functions in sfhotspot work on an SF data frame or tibble in which each row in the data represents a single point (e.g. the location of an event). In this introduction we will use the built-in memphis_robberies dataset to show how each of the hotspot_*() family of functions works. memphis_robberies contains details of 2,245 robberies in Memphis, Tennessee, in 2019.

We can plot this raw data, but the resulting plot is not very informative (even with the points made semi-transparent), since there are too many points to see clear patterns.

The included `memphis_robberies` dataset
uid	offense_type	date	geometry
15213800	personal robbery	2019-01-01 03:30:00	POINT (-89.942 35.149)
15214030	personal robbery	2019-01-01 22:00:00	POINT (-89.86 35.059)
15214042	personal robbery	2019-01-01 23:58:00	POINT (-89.929 35.058)
15214050	personal robbery	2019-01-02 00:30:00	POINT (-90.018 35.201)
15214118	personal robbery	2019-01-02 11:38:00	POINT (-89.96 35.14)
15214242	personal robbery	2019-01-02 20:50:00	POINT (-89.953 35.159)
15214290	personal robbery	2019-01-03 01:30:00	POINT (-89.95 35.026)
15214295	personal robbery	2019-01-03 02:00:00	POINT (-89.932 35.076)
15214319	personal robbery	2019-01-03 05:00:00	POINT (-90.021 35.033)
15214428	personal robbery	2019-01-03 16:45:00	POINT (-90.032 35.165)

Counting points

The hotspot_count() produces an SF object with counts for the number of points in (by default) each cell in a grid of cells. As with all the functions in the package, this can be customised in various ways – see Common arguments, below.

point_counts <- hotspot_count(memphis_robberies)
#> Cell size set to 0.00524 degrees automatically

point_counts
#> Simple feature collection with 2926 features and 1 field
#> Geometry type: POLYGON
#> Dimension:     XY
#> Bounding box:  xmin: -90.1261 ymin: 34.99475 xmax: -89.72786 ymax: 35.26199
#> Geodetic CRS:  WGS 84
#> # A tibble: 2,926 × 2
#>        n                                                                geometry
#>  * <dbl>                                                           <POLYGON [°]>
#>  1     0 ((-90.08418 34.99475, -90.07894 34.99475, -90.07894 34.99999, -90.0841…
#>  2     0 ((-90.07894 34.99475, -90.0737 34.99475, -90.0737 34.99999, -90.07894 …
#>  3     0 ((-90.0737 34.99475, -90.06846 34.99475, -90.06846 34.99999, -90.0737 …
#>  4     0 ((-90.06846 34.99475, -90.06322 34.99475, -90.06322 34.99999, -90.0684…
#>  5     0 ((-90.06322 34.99475, -90.05798 34.99475, -90.05798 34.99999, -90.0632…
#>  6     0 ((-90.05798 34.99475, -90.05274 34.99475, -90.05274 34.99999, -90.0579…
#>  7     0 ((-90.05274 34.99475, -90.0475 34.99475, -90.0475 34.99999, -90.05274 …
#>  8     0 ((-90.0475 34.99475, -90.04226 34.99475, -90.04226 34.99999, -90.0475 …
#>  9     0 ((-90.04226 34.99475, -90.03702 34.99475, -90.03702 34.99999, -90.0422…
#> 10     0 ((-90.03702 34.99475, -90.03178 34.99475, -90.03178 34.99999, -90.0370…
#> # ℹ 2,916 more rows

We can then plot that grid of cells.

ggplot() +
  geom_sf(
    mapping = aes(fill = n),
    data = point_counts,
    alpha = 0.75,
    colour = NA
  ) +
  scale_fill_distiller(direction = 1)

A basic map showing the count of robberies in each cell in a grid covering Memphis, TN. Grid cells with more robberies are shown in darker shades of blue, while those with fewer robberies are shown in lighter shades.

Calculating kernel density

The hotspot_kde() function can be used to calculate kernel density estimates for each cell in a grid. The kernel density estimation (KDE) can be customised using the bandwidth and bandwidth_adjust arguments. This function also accepts the argument explained in the Common arguments section, below.

If you do not specify any optional arguments, hotspot_kde() will try to choose reasonable default values. The KDE algorithm requires projected co-ordinates (i.e. not longitudes and latitudes), so we must first transform the data to use an appropriate local projected co-ordinate system.

robbery_kde <- memphis_robberies |> 
  st_transform("EPSG:2843") |> 
  hotspot_kde()

robbery_kde

#> Simple feature collection with 3301 features and 2 fields
#> Geometry type: POLYGON
#> Dimension:     XY
#> Bounding box:  xmin: 223497.9 ymin: 80772.86 xmax: 260497.9 ymax: 110272.9
#> Projected CRS: NAD83(HARN) / Tennessee
#> # A tibble: 3,301 × 3
#>        n   kde                                                          geometry
#>  * <dbl> <dbl>                                                     <POLYGON [m]>
#>  1     0  20.7 ((229497.9 80772.86, 229497.9 81272.86, 229997.9 81272.86, 22999…
#>  2     0  25.1 ((229997.9 80772.86, 229997.9 81272.86, 230497.9 81272.86, 23049…
#>  3     0  30.2 ((230497.9 80772.86, 230497.9 81272.86, 230997.9 81272.86, 23099…
#>  4     0  35.6 ((230997.9 80772.86, 230997.9 81272.86, 231497.9 81272.86, 23149…
#>  5     0  40.7 ((231497.9 80772.86, 231497.9 81272.86, 231997.9 81272.86, 23199…
#>  6     0  45.2 ((231997.9 80772.86, 231997.9 81272.86, 232497.9 81272.86, 23249…
#>  7     0  48.4 ((232497.9 80772.86, 232497.9 81272.86, 232997.9 81272.86, 23299…
#>  8     0  50.1 ((232997.9 80772.86, 232997.9 81272.86, 233497.9 81272.86, 23349…
#>  9     0  50.2 ((233497.9 80772.86, 233497.9 81272.86, 233997.9 81272.86, 23399…
#> 10     1  48.6 ((233997.9 80772.86, 233997.9 81272.86, 234497.9 81272.86, 23449…
#> # ℹ 3,291 more rows

Again, we can plot the result.

ggplot() +
  geom_sf(
    mapping = aes(fill = kde),
    data = robbery_kde,
    alpha = 0.75,
    colour = NA
  ) +
  scale_fill_distiller(direction = 1)

A hotspot map showing the density of robberies in each cell in a grid covering Memphis, TN. Grid cells with higher densitites of robberies are shown in darker shades of blue, while those with lower densities are shown in lighter shades.

We can adjust the appearance of the KDE layer on this map by specifying optional arguments to hotspot_kde(). In particular, the bandwidth_adjust argument is useful for controlling the level of detail visible in the density layer – use values of bandwidth_adjust below 1 to show more detail, and values above 1 to show a smoother density surface.

Common arguments

All the functions in this package work on a grid of cells, which can be customised using one or more of these common arguments:

cell_size specifies the size of each equally spaced grid cell, using the same units (metres, degrees, etc.) as used in the sf data frame given in the data argument. Ignored if grid is not NULL. If this argument and grid are both NULL (the default), the cell size will be calculated automatically.
grid_type specifies whether the grid should be made up of squares (“rect”, the default) or hexagons (“hex”). Ignored if grid is not NULL.
grid specifies an sf data frame containing polygons, which will be used as the grid for which counts are made.
quiet whether messages should be printed reporting the values of any parameters (such as cell_size) that have been set automatically.

Automatic cell-size selection

If grid and cell_size are both NULL, the cell size will be set so that there are 50 cells on the shorter side of the grid. If the data SF object is projected in metres or feet, the number of cells will be adjusted upwards so that the cell size is a multiple of 100.