Spatio-temporal grids and spacetime
Unlike {spacetime}, sfdep does not make explicit
distinctions between spatio-temporal full and sparse grids. Rather, the
approach is more laissez faire. The design of the spacetime interface is
very flexible and is designed to let the user clean their data with
whatever tools are familiar and to their own specification.
The distinction between sparse and full grids is important when it comes to analyzing data. For example emerging hot spot analysis requires a spatio-temporal full-grid. sfdep utilizes the phrase “spacetime cube” as popularized by ESRI to refer to a spatio-temporal full grid.
Spacetime Cubes
A spacetime object is a spacetime cube if every location has a value for every time index. Another way of saying this is that each location contains a regular time-series.
In ESRI terminology, the basic unit of a spacetime cube is a bin. A bin is the unique combination of a location and time index. For each time index, the collection of every location is called a time slice. In every location, the collection of every bin at each time index is referred to as a a bin time-series.
We can test if an object is a spacetime cube with
is_spacetime_cube()
is_spacetime_cube(spt)
#> [1] TRUEHere we take a sample of 800 of the 850 rows of spt
which makes this a sparse grid.
sparse_spt <- dplyr::slice_sample(spt, n = 800)
is_spacetime_cube(sparse_spt)
#> ! Number of rows does not equal `n time-periods x n locations`
#> [1] FALSEIf an object is a spare spatio-temporal grid we can make it a full
one using complete_spacetime_cube(). This works similarly
to [tidyr::complete()].
complete_spacetime_cube() ensures that there is a row for
each combination of location and time. New rows will contain missing
values
spt_complete <- complete_spacetime_cube(sparse_spt)
#> ! Vars(s) `crime_pers` is missing 50 value(s).
is_spacetime_cube(spt_complete)
#> [1] TRUEOne of the conditions of being a spactime cube is that the time-series must be regular (only one observation for each time index). Here we can create a sample of our data with replacement to create an irregular time-series at multiple locations.
set.seed(0)
sparse_spt <- dplyr::slice_sample(spt, n = 800, replace = TRUE)
complete_spacetime_cube(sparse_spt)
#> Error in `complete_spacetime_cube()`:
#> ! Location and time combinations are not unique.
#> ℹ There should only be one observation per time and location combination.This error is informative. We do not have unique bins in our spacetime data. We can check this.
dplyr::count(sparse_spt, time_period, code_dept)
#> spacetime ────
#> Context:`data`
#> 85 locations `code_dept`
#> 10 time periods `time_period`
#> ── data context ────────────────────────────────────────────────────────────────
#> # A tibble: 517 × 3
#> time_period code_dept n
#> <int> <fct> <int>
#> 1 1 01 1
#> 2 1 03 1
#> 3 1 05 1
#> 4 1 07 1
#> 5 1 09 1
#> 6 1 12 1
#> 7 1 16 1
#> 8 1 17 2
#> 9 1 18 1
#> 10 1 21 2
#> # … with 507 more rows
#> # ℹ Use `print(n = ...)` to see more rowsSpacetime cubes are used for emerging hot spot analysis as below.
emerging_hotspot_analysis(spt, "crime_pers", threshold = 0.05)
#> # A tibble: 85 × 4
#> location tau p_value classification
#> <fct> <dbl> <dbl> <chr>
#> 1 01 0.111 0.721 sporadic hotspot
#> 2 02 0.378 0.152 sporadic hotspot
#> 3 03 0.378 0.152 sporadic hotspot
#> 4 04 -0.0667 0.858 sporadic coldspot
#> 5 05 0.156 0.592 sporadic coldspot
#> 6 07 -0.467 0.0736 sporadic coldspot
#> 7 08 -0.0222 1 sporadic hotspot
#> 8 09 -0.333 0.210 sporadic coldspot
#> 9 10 -0.422 0.107 no pattern detected
#> 10 11 -0.333 0.210 consecutive coldspot
#> # … with 75 more rows
#> # ℹ Use `print(n = ...)` to see more rows