tidyrgeoda provides following methods for spatial
weights by invoking rgeoda:
- Queen
- Rook
- Distance based
- K-Nearest Neighbor
- Kernel
- Read GAL/GWT/SWM weights
Load spatial data and nessary r package.
library(sf)
library(dplyr)
library(tidyrgeoda)
guerry = read_sf(system.file("extdata","Guerry.shp",package = "rgeoda"))
head(guerry)## Simple feature collection with 6 features and 29 fields
## Geometry type: MULTIPOLYGON
## Dimension: XY
## Bounding box: xmin: 595532 ymin: 1858801 xmax: 975716 ymax: 2564568
## Projected CRS: NTF (Paris) / Lambert zone II
## # A tibble: 6 × 30
## CODE_DE COUNT AVE_ID_ dept Region Dprtmnt Crm_prs Crm_prp Litercy Donatns
## <chr> <dbl> <dbl> <dbl> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
## 1 01 1 49 1 E Ain 28870 15890 37 5098
## 2 02 1 812 2 N Aisne 26226 5521 51 8901
## 3 03 1 1418 3 C Allier 26747 7925 13 10973
## 4 04 1 1603 4 E Basses-Alp… 12935 7289 46 2733
## 5 05 1 1802 5 E Hautes-Alp… 17488 8174 69 6962
## 6 07 1 2249 7 S Ardeche 9474 10263 27 3188
## # ℹ 20 more variables: Infants <dbl>, Suicids <dbl>, MainCty <dbl>,
## # Wealth <dbl>, Commerc <dbl>, Clergy <dbl>, Crm_prn <dbl>, Infntcd <dbl>,
## # Dntn_cl <dbl>, Lottery <dbl>, Desertn <dbl>, Instrct <dbl>, Prsttts <dbl>,
## # Distanc <dbl>, Area <dbl>, Pop1831 <dbl>, TopCrm <dbl>, TopLit <dbl>,
## # TopWealth <dbl>, geometry <MULTIPOLYGON [m]>Contiguity Weights
Contiguity means that two spatial units share a common border of non-zero length. Operationally, we can further distinguish between a rook and a queen criterion of contiguity, in analogy to the moves allowed for the such-named pieces on a chess board. The queen criterion is somewhat more encompassing and defines neighbors as spatial units sharing a common edge or a common vertex.The rook criterion defines neighbors by the existence of a common edge between two spatial units.
To create a Queen contiguity weights, one can call the function
st_contiguity_weights(sfj,queen = TRUE)
qw = st_contiguity_weights(guerry)
st_summary(qw)## # A tibble: 8 × 2
## name value
## <chr> <chr>
## 1 "number of observations:" 85
## 2 "is symmetric: " TRUE
## 3 "sparsity:" 0.0581314878892734
## 4 "min neighbors:" 2
## 5 "max neighbors:" 8
## 6 "mean neighbors:" 4.94117647058824
## 7 "median neighbors:" 5
## 8 "has isolates:" FALSEIf queen is assigned to
FALSE,tidyrgeoda will invoke
rgeoda to create a Rook contiguity weights.
rw = st_contiguity_weights(guerry,queen = F)
st_summary(rw)## # A tibble: 8 × 2
## name value
## <chr> <chr>
## 1 "number of observations:" 85
## 2 "is symmetric: " TRUE
## 3 "sparsity:" 0.0581314878892734
## 4 "min neighbors:" 2
## 5 "max neighbors:" 8
## 6 "mean neighbors:" 4.94117647058824
## 7 "median neighbors:" 5
## 8 "has isolates:" FALSEYou can also create high order of contiguity weights by changing
order to more than 1.
rw = st_contiguity_weights(guerry,queen = F,order = 2)
st_summary(rw)## # A tibble: 8 × 2
## name value
## <chr> <chr>
## 1 "number of observations:" 85
## 2 "is symmetric: " TRUE
## 3 "sparsity:" 0.104636678200692
## 4 "min neighbors:" 2
## 5 "max neighbors:" 14
## 6 "mean neighbors:" 8.89411764705882
## 7 "median neighbors:" 9
## 8 "has isolates:" FALSECreate contiguity weights with 1-order and 2-order together:
rw2 = st_contiguity_weights(guerry,queen = F,order = 2,
include_lower_order = T)
st_summary(rw2)## # A tibble: 8 × 2
## name value
## <chr> <chr>
## 1 "number of observations:" 85
## 2 "is symmetric: " TRUE
## 3 "sparsity:" 0.162768166089965
## 4 "min neighbors:" 4
## 5 "max neighbors:" 21
## 6 "mean neighbors:" 13.8352941176471
## 7 "median neighbors:" 14
## 8 "has isolates:" FALSEDistance Based Weights
The most straightforward spatial weights matrix constructed from a
distance measure is obtained when i and j are considered neighbors
whenever j falls within a critical distance band from i.You can use
st_distance_weights() to achieve the Distance Based
Weights.
dw = st_distance_weights(guerry)
st_summary(dw)## # A tibble: 8 × 2
## name value
## <chr> <chr>
## 1 "number of observations:" 85
## 2 "is symmetric: " TRUE
## 3 "sparsity:" 0.0434602076124567
## 4 "min neighbors:" 1
## 5 "max neighbors:" 7
## 6 "mean neighbors:" 3.69411764705882
## 7 "median neighbors:" 4
## 8 "has isolates:" FALSEThe distance threshold default is generate use
rgeoda::min_distthreshold(),but you can assign
dist_thres argument by hand.
dw2 = st_distance_weights(guerry,dist_thres = 1.5e5)
st_summary(dw2)## # A tibble: 8 × 2
## name value
## <chr> <chr>
## 1 "number of observations:" 85
## 2 "is symmetric: " TRUE
## 3 "sparsity:" 0.0968858131487889
## 4 "min neighbors:" 2
## 5 "max neighbors:" 13
## 6 "mean neighbors:" 8.23529411764706
## 7 "median neighbors:" 9
## 8 "has isolates:" FALSEK-Nearest Neighbor Weights
A special case of distance based weights is K-Nearest neighbor
weights, in which every observation will have exactly k neighbors. It
can be used to avoid the problem of isolate in distance-band weights
when a smaller cut-off distance is used. To create a KNN weights, we can
call the function st_knn_weights():
knn6_w = st_knn_weights(guerry, 6)
st_summary(knn6_w)## # A tibble: 8 × 2
## name value
## <chr> <chr>
## 1 "number of observations:" 85
## 2 "is symmetric: " FALSE
## 3 "sparsity:" 0.0705882352941176
## 4 "min neighbors:" 6
## 5 "max neighbors:" 6
## 6 "mean neighbors:" 6
## 7 "median neighbors:" 6
## 8 "has isolates:" FALSEKernel Weights
Kernel weights apply kernel function to determine the distance decay in the derived continuous weights kernel. The kernel weights are defined as a function \(K_{z}\) of the ratio between the distance \(d_{ij}\) from \(i\) to \(j\), and the bandwidth \(h_i\), with \(z = \frac{d_{ij}}{h_i}\).
The kernel functions include
triangularuniformquadraticepanechnikovquarticgaussian
Two functions are provided in tidyrgeoda to create
kernel weights.
Use st_kernel_weights() for Kernel Weights with
afixedbandwidth
kernel_w = st_kernel_weights(guerry,"uniform")
st_summary(kernel_w)## # A tibble: 8 × 2
## name value
## <chr> <chr>
## 1 "number of observations:" 85
## 2 "is symmetric: " FALSE
## 3 "sparsity:" 0.0434602076124567
## 4 "min neighbors:" 1
## 5 "max neighbors:" 7
## 6 "mean neighbors:" 3.69411764705882
## 7 "median neighbors:" 4
## 8 "has isolates:" FALSEUse st_kernel_knn_weights() for Kernel Weights with
adaptive bandwidth
adptkernel_w = st_kernel_knn_weights(guerry, 6, "uniform")
st_summary(adptkernel_w)## # A tibble: 8 × 2
## name value
## <chr> <chr>
## 1 "number of observations:" 85
## 2 "is symmetric: " FALSE
## 3 "sparsity:" 0.0705882352941176
## 4 "min neighbors:" 6
## 5 "max neighbors:" 6
## 6 "mean neighbors:" 6
## 7 "median neighbors:" 6
## 8 "has isolates:" FALSECreate Spatial Weights object by st_weights()
st_weights() is a wrapper function for all above
st_*_weights,you can use it like:
qw = st_weights(guerry,weight = 'contiguity')
qw## Reference class object of class "Weight"
## Field "gda_w":
## An object of class "p_GeoDaWeight"
## Slot "pointer":
## <pointer: 0x55b97d5db280>
##
## Field "is_symmetric":
## [1] TRUE
## Field "sparsity":
## [1] 0.05813149
## Field "min_neighbors":
## [1] 2
## Field "max_neighbors":
## [1] 8
## Field "num_obs":
## [1] 85
## Field "mean_neighbors":
## [1] 4.941176
## Field "median_neighbors":
## [1] 5
## Field "has_isolates":
## [1] FALSE
st_summary(qw)## # A tibble: 8 × 2
## name value
## <chr> <chr>
## 1 "number of observations:" 85
## 2 "is symmetric: " TRUE
## 3 "sparsity:" 0.0581314878892734
## 4 "min neighbors:" 2
## 5 "max neighbors:" 8
## 6 "mean neighbors:" 4.94117647058824
## 7 "median neighbors:" 5
## 8 "has isolates:" FALSE