sabre.Rmd
The sabre (Spatial Association Between REgionalizations) is an R package for calculating a degree of spatial association between regionalizations or categorical maps. This package offers support for sf
spatial objects, and the following methods:
Two simple regionalizations would be used to show the basic concept of sabre.
The first map, regions1
, has four regions (“r1”, “r2”, “r3”, “r4”) of the same size and shape. The second one, regions2
, contains three irregular regions where “z1” is the smallest and “z3” being the largest. Our goal is to compare these two regionalizations and calculate a degree of spatial association between them.
It can be done with vmeasure_calc()
, which calculates “V-measure”, “Homogeneity”, and “Completeness” and returns two preprocessed input maps. This function requires, at least, four arguments:
x
- an sf
object containing the first regionalizationy
- an sf
object containing the second regionalizationx_name
- a name of the column with regions names of the first regionalizationy_name
- a name of the column with regions names of the second regionalizationImportantly, both x
and y
must contain POLYGON
s or MULTIPOLYGON
s and have the same coordinate reference system.
There are also two additional arguments - B
and precision
. If B
> 1 then completeness is weighted more strongly than homogeneity, and if B
< 1 then homogeneity is weighted more strongly than completeness. By default this value is 1. The vmeasure_calc()
function calculates intersections of the input geometries internally using sf::st_intersection()
, which depends on the coordinates values precision. The precision
argument can be used when vmeasure_calc
produces an error. For example, precision = 1000
rounds values to the third decimal places and precision = 0.001
uses values rounded to the nearest 1000.
regions_vm = vmeasure_calc(x = regions1, y = regions2, x_name = z, y_name = z)
regions_vm
#> The SABRE results:
#>
#> V-measure: 0.36
#> Homogeneity: 0.32
#> Completeness: 0.42
#>
#> The spatial objects can be retrieved with:
#> $map1 - the first map
#> $map2 - the second map
The result is a list with three metrics of spatial association - V-measure
, Homogeneity
, Completeness
- and two sf
objects with preprocessed input maps - $map1
and $map2
. All of the above metrics are between 0 and 1, where larger values are desired. V-measure
is a measure of an overall spatial correspondence between input maps. Homogeneity
shows an average homogeneity of the regions in the second map with respect to the regions in the first map. Completeness
is a function of homogeneity of the regions in the first map with respect to the regions in the second map. The spatial outputs, $map1
and $map2
, have two columns. The first one contains regions’ names and the second one (rih
) describes regions’ inhomogeneities. Geometries of these spatial outputs show intersections of the two input regionalizations.
For example, “Map1” shows that three regions have the same inhomogeneity of 0.48. This is due a fact that all of these three have two regions from the second map. The upper left region has a larger inhomogeneity of 0.86 as its area “belongs” to three different regions in the second map. More information about this method and its applications can be found in Nowosad and Stepinski (2018).
The sabre also allows for calculating a degree of spatial association between regionalizations using the MapCurve method (Hargrove et al., 2006). The mapcurves_calc()
function also requires four arguments, x
, x_name
, y
, and y_name
. It also accepts an additional argument - precision
. All of these arguments are explained in the previous section.
regions_mc = mapcurves_calc(x = regions1, y = regions2, x_name = z, y_name = z)
regions_mc
#> The MapCurves results:
#>
#> The goodness of fit: 0.61
#> Reference map: x
#>
#> The spatial objects can be retrieved with:
#> $map1 - the first map
#> $map2 - the second map
The mapcurves_calc()
returns a list with a value of the goodness of fit (GOF), the map used as a reference, and two sf
objects with preprocessed input maps - $map1
and $map2
. Read Hargrove et al. (2006) to learn more about this method.