Hands-On Exercise 8: Spatial Weights and Applications

Author

Jennifer Poernomo

Published

February 13, 2023

Modified

March 24, 2023

Import Packages

pacman::p_load(sf, spdep, tmap, tidyverse, knitr)

spdep is an older package, so we need to convert data types, unlike the newer sfdep which does it automatically.

Import Data

Geospatial

hunan <- st_read(dsn = "data/geospatial", 
                 layer = "Hunan")

Reading layer `Hunan' from data source 
  `C:\Jenpoer\IS415-GAA\Hands-On-Exercises\chapter-08\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 88 features and 7 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 108.7831 ymin: 24.6342 xmax: 114.2544 ymax: 30.12812
Geodetic CRS:  WGS 84

Aspatial

hunan2012 <- read_csv("data/aspatial/Hunan_2012.csv")

is_tibble(hunan2012)

[1] TRUE

Data Preprocessing

Combining data frame with left join

If you want to retain geometry, the left one must be the geospatial data

hunan <- left_join(hunan,hunan2012)%>%
  select(1:4, 7, 15)

EDA

basemap <- tm_shape(hunan) +
  tm_polygons() +
  tm_text("NAME_3", size=0.5)

gdppc <- qtm(hunan, "GDPPC")
tmap_arrange(basemap, gdppc, asp=1, ncol=2)

Computing contiguity spatial weights

Queen

wm_q <- poly2nb(hunan, queen = TRUE)
summary(wm_q)

Neighbour list object:
Number of regions: 88 
Number of nonzero links: 448 
Percentage nonzero weights: 5.785124 
Average number of links: 5.090909 
Link number distribution:

 1  2  3  4  5  6  7  8  9 11 
 2  2 12 16 24 14 11  4  2  1 
2 least connected regions:
30 65 with 1 link
1 most connected region:
85 with 11 links

List all neighboring polygons for first polygon in the object

wm_q[[1]]

[1]  2  3  4 57 85

hunan$County[1]

[1] "Anxiang"

Reveal county names of the five neighbouring polygons

hunan$NAME_3[c(2,3,4,57,85)]

[1] "Hanshou" "Jinshi"  "Li"      "Nan"     "Taoyuan"

Retrieve GDPPC of five neighbouring counties

nb1 <- wm_q[[1]]
nb1 <- hunan$GDPPC[nb1]
nb1

[1] 20981 34592 24473 21311 22879

Display complete weight matrix

str(wm_q)

List of 88
 $ : int [1:5] 2 3 4 57 85
 $ : int [1:5] 1 57 58 78 85
 $ : int [1:4] 1 4 5 85
 $ : int [1:4] 1 3 5 6
 $ : int [1:4] 3 4 6 85
 $ : int [1:5] 4 5 69 75 85
 $ : int [1:4] 67 71 74 84
 $ : int [1:7] 9 46 47 56 78 80 86
 $ : int [1:6] 8 66 68 78 84 86
 $ : int [1:8] 16 17 19 20 22 70 72 73
 $ : int [1:3] 14 17 72
 $ : int [1:5] 13 60 61 63 83
 $ : int [1:4] 12 15 60 83
 $ : int [1:3] 11 15 17
 $ : int [1:4] 13 14 17 83
 $ : int [1:5] 10 17 22 72 83
 $ : int [1:7] 10 11 14 15 16 72 83
 $ : int [1:5] 20 22 23 77 83
 $ : int [1:6] 10 20 21 73 74 86
 $ : int [1:7] 10 18 19 21 22 23 82
 $ : int [1:5] 19 20 35 82 86
 $ : int [1:5] 10 16 18 20 83
 $ : int [1:7] 18 20 38 41 77 79 82
 $ : int [1:5] 25 28 31 32 54
 $ : int [1:5] 24 28 31 33 81
 $ : int [1:4] 27 33 42 81
 $ : int [1:3] 26 29 42
 $ : int [1:5] 24 25 33 49 54
 $ : int [1:3] 27 37 42
 $ : int 33
 $ : int [1:8] 24 25 32 36 39 40 56 81
 $ : int [1:8] 24 31 50 54 55 56 75 85
 $ : int [1:5] 25 26 28 30 81
 $ : int [1:3] 36 45 80
 $ : int [1:6] 21 41 47 80 82 86
 $ : int [1:6] 31 34 40 45 56 80
 $ : int [1:4] 29 42 43 44
 $ : int [1:4] 23 44 77 79
 $ : int [1:5] 31 40 42 43 81
 $ : int [1:6] 31 36 39 43 45 79
 $ : int [1:6] 23 35 45 79 80 82
 $ : int [1:7] 26 27 29 37 39 43 81
 $ : int [1:6] 37 39 40 42 44 79
 $ : int [1:4] 37 38 43 79
 $ : int [1:6] 34 36 40 41 79 80
 $ : int [1:3] 8 47 86
 $ : int [1:5] 8 35 46 80 86
 $ : int [1:5] 50 51 52 53 55
 $ : int [1:4] 28 51 52 54
 $ : int [1:5] 32 48 52 54 55
 $ : int [1:3] 48 49 52
 $ : int [1:5] 48 49 50 51 54
 $ : int [1:3] 48 55 75
 $ : int [1:6] 24 28 32 49 50 52
 $ : int [1:5] 32 48 50 53 75
 $ : int [1:7] 8 31 32 36 78 80 85
 $ : int [1:6] 1 2 58 64 76 85
 $ : int [1:5] 2 57 68 76 78
 $ : int [1:4] 60 61 87 88
 $ : int [1:4] 12 13 59 61
 $ : int [1:7] 12 59 60 62 63 77 87
 $ : int [1:3] 61 77 87
 $ : int [1:4] 12 61 77 83
 $ : int [1:2] 57 76
 $ : int 76
 $ : int [1:5] 9 67 68 76 84
 $ : int [1:4] 7 66 76 84
 $ : int [1:5] 9 58 66 76 78
 $ : int [1:3] 6 75 85
 $ : int [1:3] 10 72 73
 $ : int [1:3] 7 73 74
 $ : int [1:5] 10 11 16 17 70
 $ : int [1:5] 10 19 70 71 74
 $ : int [1:6] 7 19 71 73 84 86
 $ : int [1:6] 6 32 53 55 69 85
 $ : int [1:7] 57 58 64 65 66 67 68
 $ : int [1:7] 18 23 38 61 62 63 83
 $ : int [1:7] 2 8 9 56 58 68 85
 $ : int [1:7] 23 38 40 41 43 44 45
 $ : int [1:8] 8 34 35 36 41 45 47 56
 $ : int [1:6] 25 26 31 33 39 42
 $ : int [1:5] 20 21 23 35 41
 $ : int [1:9] 12 13 15 16 17 18 22 63 77
 $ : int [1:6] 7 9 66 67 74 86
 $ : int [1:11] 1 2 3 5 6 32 56 57 69 75 ...
 $ : int [1:9] 8 9 19 21 35 46 47 74 84
 $ : int [1:4] 59 61 62 88
 $ : int [1:2] 59 87
 - attr(*, "class")= chr "nb"
 - attr(*, "region.id")= chr [1:88] "1" "2" "3" "4" ...
 - attr(*, "call")= language poly2nb(pl = hunan, queen = TRUE)
 - attr(*, "type")= chr "queen"
 - attr(*, "sym")= logi TRUE

Rook

wm_r <- poly2nb(hunan, queen = FALSE)
summary(wm_r)

Neighbour list object:
Number of regions: 88 
Number of nonzero links: 440 
Percentage nonzero weights: 5.681818 
Average number of links: 5 
Link number distribution:

 1  2  3  4  5  6  7  8  9 10 
 2  2 12 20 21 14 11  3  2  1 
2 least connected regions:
30 65 with 1 link
1 most connected region:
85 with 10 links

Visualising contiguity weights

Get longitude and latitude of each polygon by mapping st_centroid over the geometry column

longitude <- map_dbl(hunan$geometry, ~st_centroid(.x)[[1]])

latitude <- map_dbl(hunan$geometry, ~st_centroid(.x)[[2]])

coords <- cbind(longitude, latitude)

head(coords)

     longitude latitude
[1,]  112.1531 29.44362
[2,]  112.0372 28.86489
[3,]  111.8917 29.47107
[4,]  111.7031 29.74499
[5,]  111.6138 29.49258
[6,]  111.0341 29.79863

plot(hunan$geometry, border="lightgrey")
plot(wm_q, coords, pch = 19, cex = 0.6, add = TRUE, col= "red")

plot(hunan$geometry, border="lightgrey")
plot(wm_r, coords, pch = 19, cex = 0.6, add = TRUE, col = "red")

par(mfrow=c(1,2))
plot(hunan$geometry, border="lightgrey")
plot(wm_q, coords, pch = 19, cex = 0.6, add = TRUE, col= "red", main="Queen Contiguity")
plot(hunan$geometry, border="lightgrey")
plot(wm_r, coords, pch = 19, cex = 0.6, add = TRUE, col = "red", main="Rook Contiguity")

Computing distance based neighbours

Determine the cut-off distance

Return a matrix with the indices of points belonging to the set of the k nearest neighbours of each other by using knearneigh() of spdep.
Convert the knn object returned by knearneigh() into a neighbours list of class nb with a list of integer vectors containing neighbour region number ids by using knn2nb().
Return the length of neighbour relationship edges by using nbdists() of spdep. The function returns in the units of the coordinates if the coordinates are projected, in km otherwise.
Remove the list structure of the returned object by using unlist().

#coords <- coordinates(hunan)
k1 <- knn2nb(knearneigh(coords))
k1dists <- unlist(nbdists(k1, coords, longlat = TRUE))
summary(k1dists)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  24.79   32.57   38.01   39.07   44.52   61.79

We see that the largest first nearest neighbour distance is 61.79 km, so using this as the upper threshold gives certainty that all units will have at least one neighbour.

Fixed distance weight matrix

wm_d62 <- dnearneigh(coords, 0, 62, longlat = TRUE)
wm_d62

Neighbour list object:
Number of regions: 88 
Number of nonzero links: 324 
Percentage nonzero weights: 4.183884 
Average number of links: 3.681818

On average, each point has 3.681818 links (so, 3-4 links)

str(wm_d62)

List of 88
 $ : int [1:5] 3 4 5 57 64
 $ : int [1:4] 57 58 78 85
 $ : int [1:4] 1 4 5 57
 $ : int [1:3] 1 3 5
 $ : int [1:4] 1 3 4 85
 $ : int 69
 $ : int [1:2] 67 84
 $ : int [1:4] 9 46 47 78
 $ : int [1:4] 8 46 68 84
 $ : int [1:4] 16 22 70 72
 $ : int [1:3] 14 17 72
 $ : int [1:5] 13 60 61 63 83
 $ : int [1:4] 12 15 60 83
 $ : int [1:2] 11 17
 $ : int 13
 $ : int [1:4] 10 17 22 83
 $ : int [1:3] 11 14 16
 $ : int [1:3] 20 22 63
 $ : int [1:5] 20 21 73 74 82
 $ : int [1:5] 18 19 21 22 82
 $ : int [1:6] 19 20 35 74 82 86
 $ : int [1:4] 10 16 18 20
 $ : int [1:3] 41 77 82
 $ : int [1:4] 25 28 31 54
 $ : int [1:4] 24 28 33 81
 $ : int [1:4] 27 33 42 81
 $ : int [1:2] 26 29
 $ : int [1:6] 24 25 33 49 52 54
 $ : int [1:2] 27 37
 $ : int 33
 $ : int [1:2] 24 36
 $ : int 50
 $ : int [1:5] 25 26 28 30 81
 $ : int [1:3] 36 45 80
 $ : int [1:6] 21 41 46 47 80 82
 $ : int [1:5] 31 34 45 56 80
 $ : int [1:2] 29 42
 $ : int [1:3] 44 77 79
 $ : int [1:4] 40 42 43 81
 $ : int [1:3] 39 45 79
 $ : int [1:5] 23 35 45 79 82
 $ : int [1:5] 26 37 39 43 81
 $ : int [1:3] 39 42 44
 $ : int [1:2] 38 43
 $ : int [1:6] 34 36 40 41 79 80
 $ : int [1:5] 8 9 35 47 86
 $ : int [1:5] 8 35 46 80 86
 $ : int [1:5] 50 51 52 53 55
 $ : int [1:4] 28 51 52 54
 $ : int [1:6] 32 48 51 52 54 55
 $ : int [1:4] 48 49 50 52
 $ : int [1:6] 28 48 49 50 51 54
 $ : int [1:2] 48 55
 $ : int [1:5] 24 28 49 50 52
 $ : int [1:4] 48 50 53 75
 $ : int 36
 $ : int [1:5] 1 2 3 58 64
 $ : int [1:5] 2 57 64 66 68
 $ : int [1:3] 60 87 88
 $ : int [1:4] 12 13 59 61
 $ : int [1:5] 12 60 62 63 87
 $ : int [1:4] 61 63 77 87
 $ : int [1:5] 12 18 61 62 83
 $ : int [1:4] 1 57 58 76
 $ : int 76
 $ : int [1:5] 58 67 68 76 84
 $ : int [1:2] 7 66
 $ : int [1:4] 9 58 66 84
 $ : int [1:2] 6 75
 $ : int [1:3] 10 72 73
 $ : int [1:2] 73 74
 $ : int [1:3] 10 11 70
 $ : int [1:4] 19 70 71 74
 $ : int [1:5] 19 21 71 73 86
 $ : int [1:2] 55 69
 $ : int [1:3] 64 65 66
 $ : int [1:3] 23 38 62
 $ : int [1:2] 2 8
 $ : int [1:4] 38 40 41 45
 $ : int [1:5] 34 35 36 45 47
 $ : int [1:5] 25 26 33 39 42
 $ : int [1:6] 19 20 21 23 35 41
 $ : int [1:4] 12 13 16 63
 $ : int [1:4] 7 9 66 68
 $ : int [1:2] 2 5
 $ : int [1:4] 21 46 47 74
 $ : int [1:4] 59 61 62 88
 $ : int [1:2] 59 87
 - attr(*, "class")= chr "nb"
 - attr(*, "region.id")= chr [1:88] "1" "2" "3" "4" ...
 - attr(*, "call")= language dnearneigh(x = coords, d1 = 0, d2 = 62, longlat = TRUE)
 - attr(*, "dnn")= num [1:2] 0 62
 - attr(*, "bounds")= chr [1:2] "GE" "LE"
 - attr(*, "nbtype")= chr "distance"
 - attr(*, "sym")= logi TRUE

table(hunan$County, card(wm_d62))

               
                1 2 3 4 5 6
  Anhua         1 0 0 0 0 0
  Anren         0 0 0 1 0 0
  Anxiang       0 0 0 0 1 0
  Baojing       0 0 0 0 1 0
  Chaling       0 0 1 0 0 0
  Changning     0 0 1 0 0 0
  Changsha      0 0 0 1 0 0
  Chengbu       0 1 0 0 0 0
  Chenxi        0 0 0 1 0 0
  Cili          0 1 0 0 0 0
  Dao           0 0 0 1 0 0
  Dongan        0 0 1 0 0 0
  Dongkou       0 0 0 1 0 0
  Fenghuang     0 0 0 1 0 0
  Guidong       0 0 1 0 0 0
  Guiyang       0 0 0 1 0 0
  Guzhang       0 0 0 0 0 1
  Hanshou       0 0 0 1 0 0
  Hengdong      0 0 0 0 1 0
  Hengnan       0 0 0 0 1 0
  Hengshan      0 0 0 0 0 1
  Hengyang      0 0 0 0 0 1
  Hongjiang     0 0 0 0 1 0
  Huarong       0 0 0 1 0 0
  Huayuan       0 0 0 1 0 0
  Huitong       0 0 0 1 0 0
  Jiahe         0 0 0 0 1 0
  Jianghua      0 0 1 0 0 0
  Jiangyong     0 1 0 0 0 0
  Jingzhou      0 1 0 0 0 0
  Jinshi        0 0 0 1 0 0
  Jishou        0 0 0 0 0 1
  Lanshan       0 0 0 1 0 0
  Leiyang       0 0 0 1 0 0
  Lengshuijiang 0 0 1 0 0 0
  Li            0 0 1 0 0 0
  Lianyuan      0 0 0 0 1 0
  Liling        0 1 0 0 0 0
  Linli         0 0 0 1 0 0
  Linwu         0 0 0 1 0 0
  Linxiang      1 0 0 0 0 0
  Liuyang       0 1 0 0 0 0
  Longhui       0 0 1 0 0 0
  Longshan      0 1 0 0 0 0
  Luxi          0 0 0 0 1 0
  Mayang        0 0 0 0 0 1
  Miluo         0 0 0 0 1 0
  Nan           0 0 0 0 1 0
  Ningxiang     0 0 0 1 0 0
  Ningyuan      0 0 0 0 1 0
  Pingjiang     0 1 0 0 0 0
  Qidong        0 0 1 0 0 0
  Qiyang        0 0 1 0 0 0
  Rucheng       0 1 0 0 0 0
  Sangzhi       0 1 0 0 0 0
  Shaodong      0 0 0 0 1 0
  Shaoshan      0 0 0 0 1 0
  Shaoyang      0 0 0 1 0 0
  Shimen        1 0 0 0 0 0
  Shuangfeng    0 0 0 0 0 1
  Shuangpai     0 0 0 1 0 0
  Suining       0 0 0 0 1 0
  Taojiang      0 1 0 0 0 0
  Taoyuan       0 1 0 0 0 0
  Tongdao       0 1 0 0 0 0
  Wangcheng     0 0 0 1 0 0
  Wugang        0 0 1 0 0 0
  Xiangtan      0 0 0 1 0 0
  Xiangxiang    0 0 0 0 1 0
  Xiangyin      0 0 0 1 0 0
  Xinhua        0 0 0 0 1 0
  Xinhuang      1 0 0 0 0 0
  Xinning       0 1 0 0 0 0
  Xinshao       0 0 0 0 0 1
  Xintian       0 0 0 0 1 0
  Xupu          0 1 0 0 0 0
  Yanling       0 0 1 0 0 0
  Yizhang       1 0 0 0 0 0
  Yongshun      0 0 0 1 0 0
  Yongxing      0 0 0 1 0 0
  You           0 0 0 1 0 0
  Yuanjiang     0 0 0 0 1 0
  Yuanling      1 0 0 0 0 0
  Yueyang       0 0 1 0 0 0
  Zhijiang      0 0 0 0 1 0
  Zhongfang     0 0 0 1 0 0
  Zhuzhou       0 0 0 0 1 0
  Zixing        0 0 1 0 0 0

n_comp <- n.comp.nb(wm_d62)
n_comp$nc

[1] 1

table(n_comp$comp.id)


 1 
88

Red lines: links of first nearest neighbours, black lines: links of neighbours within the cut-off distance of 62 km

plot(hunan$geometry, border="lightgrey")
plot(wm_d62, coords, add=TRUE)
plot(k1, coords, add=TRUE, col="red", length=0.08)

par(mfrow=c(1,2))
plot(hunan$geometry, border="lightgrey")
plot(k1, coords, add=TRUE, col="red", length=0.08, main="1st nearest neighbours")
plot(hunan$geometry, border="lightgrey")
plot(wm_d62, coords, add=TRUE, pch = 19, cex = 0.6, main="Distance link")

Adaptive distance weight matrix

Specify the number of neighbours instead, so the distance becomes adaptive to the number of neighbours.

knn6 <- knn2nb(knearneigh(coords, k=6))
knn6

Neighbour list object:
Number of regions: 88 
Number of nonzero links: 528 
Percentage nonzero weights: 6.818182 
Average number of links: 6 
Non-symmetric neighbours list

str(knn6)

List of 88
 $ : int [1:6] 2 3 4 5 57 64
 $ : int [1:6] 1 3 57 58 78 85
 $ : int [1:6] 1 2 4 5 57 85
 $ : int [1:6] 1 3 5 6 69 85
 $ : int [1:6] 1 3 4 6 69 85
 $ : int [1:6] 3 4 5 69 75 85
 $ : int [1:6] 9 66 67 71 74 84
 $ : int [1:6] 9 46 47 78 80 86
 $ : int [1:6] 8 46 66 68 84 86
 $ : int [1:6] 16 19 22 70 72 73
 $ : int [1:6] 10 14 16 17 70 72
 $ : int [1:6] 13 15 60 61 63 83
 $ : int [1:6] 12 15 60 61 63 83
 $ : int [1:6] 11 15 16 17 72 83
 $ : int [1:6] 12 13 14 17 60 83
 $ : int [1:6] 10 11 17 22 72 83
 $ : int [1:6] 10 11 14 16 72 83
 $ : int [1:6] 20 22 23 63 77 83
 $ : int [1:6] 10 20 21 73 74 82
 $ : int [1:6] 18 19 21 22 23 82
 $ : int [1:6] 19 20 35 74 82 86
 $ : int [1:6] 10 16 18 19 20 83
 $ : int [1:6] 18 20 41 77 79 82
 $ : int [1:6] 25 28 31 52 54 81
 $ : int [1:6] 24 28 31 33 54 81
 $ : int [1:6] 25 27 29 33 42 81
 $ : int [1:6] 26 29 30 37 42 81
 $ : int [1:6] 24 25 33 49 52 54
 $ : int [1:6] 26 27 37 42 43 81
 $ : int [1:6] 26 27 28 33 49 81
 $ : int [1:6] 24 25 36 39 40 54
 $ : int [1:6] 24 31 50 54 55 56
 $ : int [1:6] 25 26 28 30 49 81
 $ : int [1:6] 36 40 41 45 56 80
 $ : int [1:6] 21 41 46 47 80 82
 $ : int [1:6] 31 34 40 45 56 80
 $ : int [1:6] 26 27 29 42 43 44
 $ : int [1:6] 23 43 44 62 77 79
 $ : int [1:6] 25 40 42 43 44 81
 $ : int [1:6] 31 36 39 43 45 79
 $ : int [1:6] 23 35 45 79 80 82
 $ : int [1:6] 26 27 37 39 43 81
 $ : int [1:6] 37 39 40 42 44 79
 $ : int [1:6] 37 38 39 42 43 79
 $ : int [1:6] 34 36 40 41 79 80
 $ : int [1:6] 8 9 35 47 78 86
 $ : int [1:6] 8 21 35 46 80 86
 $ : int [1:6] 49 50 51 52 53 55
 $ : int [1:6] 28 33 48 51 52 54
 $ : int [1:6] 32 48 51 52 54 55
 $ : int [1:6] 28 48 49 50 52 54
 $ : int [1:6] 28 48 49 50 51 54
 $ : int [1:6] 48 50 51 52 55 75
 $ : int [1:6] 24 28 49 50 51 52
 $ : int [1:6] 32 48 50 52 53 75
 $ : int [1:6] 32 34 36 78 80 85
 $ : int [1:6] 1 2 3 58 64 68
 $ : int [1:6] 2 57 64 66 68 78
 $ : int [1:6] 12 13 60 61 87 88
 $ : int [1:6] 12 13 59 61 63 87
 $ : int [1:6] 12 13 60 62 63 87
 $ : int [1:6] 12 38 61 63 77 87
 $ : int [1:6] 12 18 60 61 62 83
 $ : int [1:6] 1 3 57 58 68 76
 $ : int [1:6] 58 64 66 67 68 76
 $ : int [1:6] 9 58 67 68 76 84
 $ : int [1:6] 7 65 66 68 76 84
 $ : int [1:6] 9 57 58 66 78 84
 $ : int [1:6] 4 5 6 32 75 85
 $ : int [1:6] 10 16 19 22 72 73
 $ : int [1:6] 7 19 73 74 84 86
 $ : int [1:6] 10 11 14 16 17 70
 $ : int [1:6] 10 19 21 70 71 74
 $ : int [1:6] 19 21 71 73 84 86
 $ : int [1:6] 6 32 50 53 55 69
 $ : int [1:6] 58 64 65 66 67 68
 $ : int [1:6] 18 23 38 61 62 63
 $ : int [1:6] 2 8 9 46 58 68
 $ : int [1:6] 38 40 41 43 44 45
 $ : int [1:6] 34 35 36 41 45 47
 $ : int [1:6] 25 26 28 33 39 42
 $ : int [1:6] 19 20 21 23 35 41
 $ : int [1:6] 12 13 15 16 22 63
 $ : int [1:6] 7 9 66 68 71 74
 $ : int [1:6] 2 3 4 5 56 69
 $ : int [1:6] 8 9 21 46 47 74
 $ : int [1:6] 59 60 61 62 63 88
 $ : int [1:6] 59 60 61 62 63 87
 - attr(*, "region.id")= chr [1:88] "1" "2" "3" "4" ...
 - attr(*, "call")= language knearneigh(x = coords, k = 6)
 - attr(*, "sym")= logi FALSE
 - attr(*, "type")= chr "knn"
 - attr(*, "knn-k")= num 6
 - attr(*, "class")= chr "nb"

plot(hunan$geometry, border="lightgrey")
plot(knn6, coords, pch = 19, cex = 0.6, add = TRUE, col = "red")

Weights based on IDW (Inverse Distance)

dist <- nbdists(wm_q, coords, longlat = TRUE)
ids <- lapply(dist, function(x) 1/(x))
ids

[[1]]
[1] 0.01535405 0.03916350 0.01820896 0.02807922 0.01145113

[[2]]
[1] 0.01535405 0.01764308 0.01925924 0.02323898 0.01719350

[[3]]
[1] 0.03916350 0.02822040 0.03695795 0.01395765

[[4]]
[1] 0.01820896 0.02822040 0.03414741 0.01539065

[[5]]
[1] 0.03695795 0.03414741 0.01524598 0.01618354

[[6]]
[1] 0.015390649 0.015245977 0.021748129 0.011883901 0.009810297

[[7]]
[1] 0.01708612 0.01473997 0.01150924 0.01872915

[[8]]
[1] 0.02022144 0.03453056 0.02529256 0.01036340 0.02284457 0.01500600 0.01515314

[[9]]
[1] 0.02022144 0.01574888 0.02109502 0.01508028 0.02902705 0.01502980

[[10]]
[1] 0.02281552 0.01387777 0.01538326 0.01346650 0.02100510 0.02631658 0.01874863
[8] 0.01500046

[[11]]
[1] 0.01882869 0.02243492 0.02247473

[[12]]
[1] 0.02779227 0.02419652 0.02333385 0.02986130 0.02335429

[[13]]
[1] 0.02779227 0.02650020 0.02670323 0.01714243

[[14]]
[1] 0.01882869 0.01233868 0.02098555

[[15]]
[1] 0.02650020 0.01233868 0.01096284 0.01562226

[[16]]
[1] 0.02281552 0.02466962 0.02765018 0.01476814 0.01671430

[[17]]
[1] 0.01387777 0.02243492 0.02098555 0.01096284 0.02466962 0.01593341 0.01437996

[[18]]
[1] 0.02039779 0.02032767 0.01481665 0.01473691 0.01459380

[[19]]
[1] 0.01538326 0.01926323 0.02668415 0.02140253 0.01613589 0.01412874

[[20]]
[1] 0.01346650 0.02039779 0.01926323 0.01723025 0.02153130 0.01469240 0.02327034

[[21]]
[1] 0.02668415 0.01723025 0.01766299 0.02644986 0.02163800

[[22]]
[1] 0.02100510 0.02765018 0.02032767 0.02153130 0.01489296

[[23]]
[1] 0.01481665 0.01469240 0.01401432 0.02246233 0.01880425 0.01530458 0.01849605

[[24]]
[1] 0.02354598 0.01837201 0.02607264 0.01220154 0.02514180

[[25]]
[1] 0.02354598 0.02188032 0.01577283 0.01949232 0.02947957

[[26]]
[1] 0.02155798 0.01745522 0.02212108 0.02220532

[[27]]
[1] 0.02155798 0.02490625 0.01562326

[[28]]
[1] 0.01837201 0.02188032 0.02229549 0.03076171 0.02039506

[[29]]
[1] 0.02490625 0.01686587 0.01395022

[[30]]
[1] 0.02090587

[[31]]
[1] 0.02607264 0.01577283 0.01219005 0.01724850 0.01229012 0.01609781 0.01139438
[8] 0.01150130

[[32]]
[1] 0.01220154 0.01219005 0.01712515 0.01340413 0.01280928 0.01198216 0.01053374
[8] 0.01065655

[[33]]
[1] 0.01949232 0.01745522 0.02229549 0.02090587 0.01979045

[[34]]
[1] 0.03113041 0.03589551 0.02882915

[[35]]
[1] 0.01766299 0.02185795 0.02616766 0.02111721 0.02108253 0.01509020

[[36]]
[1] 0.01724850 0.03113041 0.01571707 0.01860991 0.02073549 0.01680129

[[37]]
[1] 0.01686587 0.02234793 0.01510990 0.01550676

[[38]]
[1] 0.01401432 0.02407426 0.02276151 0.01719415

[[39]]
[1] 0.01229012 0.02172543 0.01711924 0.02629732 0.01896385

[[40]]
[1] 0.01609781 0.01571707 0.02172543 0.01506473 0.01987922 0.01894207

[[41]]
[1] 0.02246233 0.02185795 0.02205991 0.01912542 0.01601083 0.01742892

[[42]]
[1] 0.02212108 0.01562326 0.01395022 0.02234793 0.01711924 0.01836831 0.01683518

[[43]]
[1] 0.01510990 0.02629732 0.01506473 0.01836831 0.03112027 0.01530782

[[44]]
[1] 0.01550676 0.02407426 0.03112027 0.01486508

[[45]]
[1] 0.03589551 0.01860991 0.01987922 0.02205991 0.02107101 0.01982700

[[46]]
[1] 0.03453056 0.04033752 0.02689769

[[47]]
[1] 0.02529256 0.02616766 0.04033752 0.01949145 0.02181458

[[48]]
[1] 0.02313819 0.03370576 0.02289485 0.01630057 0.01818085

[[49]]
[1] 0.03076171 0.02138091 0.02394529 0.01990000

[[50]]
[1] 0.01712515 0.02313819 0.02551427 0.02051530 0.02187179

[[51]]
[1] 0.03370576 0.02138091 0.02873854

[[52]]
[1] 0.02289485 0.02394529 0.02551427 0.02873854 0.03516672

[[53]]
[1] 0.01630057 0.01979945 0.01253977

[[54]]
[1] 0.02514180 0.02039506 0.01340413 0.01990000 0.02051530 0.03516672

[[55]]
[1] 0.01280928 0.01818085 0.02187179 0.01979945 0.01882298

[[56]]
[1] 0.01036340 0.01139438 0.01198216 0.02073549 0.01214479 0.01362855 0.01341697

[[57]]
[1] 0.028079221 0.017643082 0.031423501 0.029114131 0.013520292 0.009903702

[[58]]
[1] 0.01925924 0.03142350 0.02722997 0.01434859 0.01567192

[[59]]
[1] 0.01696711 0.01265572 0.01667105 0.01785036

[[60]]
[1] 0.02419652 0.02670323 0.01696711 0.02343040

[[61]]
[1] 0.02333385 0.01265572 0.02343040 0.02514093 0.02790764 0.01219751 0.02362452

[[62]]
[1] 0.02514093 0.02002219 0.02110260

[[63]]
[1] 0.02986130 0.02790764 0.01407043 0.01805987

[[64]]
[1] 0.02911413 0.01689892

[[65]]
[1] 0.02471705

[[66]]
[1] 0.01574888 0.01726461 0.03068853 0.01954805 0.01810569

[[67]]
[1] 0.01708612 0.01726461 0.01349843 0.01361172

[[68]]
[1] 0.02109502 0.02722997 0.03068853 0.01406357 0.01546511

[[69]]
[1] 0.02174813 0.01645838 0.01419926

[[70]]
[1] 0.02631658 0.01963168 0.02278487

[[71]]
[1] 0.01473997 0.01838483 0.03197403

[[72]]
[1] 0.01874863 0.02247473 0.01476814 0.01593341 0.01963168

[[73]]
[1] 0.01500046 0.02140253 0.02278487 0.01838483 0.01652709

[[74]]
[1] 0.01150924 0.01613589 0.03197403 0.01652709 0.01342099 0.02864567

[[75]]
[1] 0.011883901 0.010533736 0.012539774 0.018822977 0.016458383 0.008217581

[[76]]
[1] 0.01352029 0.01434859 0.01689892 0.02471705 0.01954805 0.01349843 0.01406357

[[77]]
[1] 0.014736909 0.018804247 0.022761507 0.012197506 0.020022195 0.014070428
[7] 0.008440896

[[78]]
[1] 0.02323898 0.02284457 0.01508028 0.01214479 0.01567192 0.01546511 0.01140779

[[79]]
[1] 0.01530458 0.01719415 0.01894207 0.01912542 0.01530782 0.01486508 0.02107101

[[80]]
[1] 0.01500600 0.02882915 0.02111721 0.01680129 0.01601083 0.01982700 0.01949145
[8] 0.01362855

[[81]]
[1] 0.02947957 0.02220532 0.01150130 0.01979045 0.01896385 0.01683518

[[82]]
[1] 0.02327034 0.02644986 0.01849605 0.02108253 0.01742892

[[83]]
[1] 0.023354289 0.017142433 0.015622258 0.016714303 0.014379961 0.014593799
[7] 0.014892965 0.018059871 0.008440896

[[84]]
[1] 0.01872915 0.02902705 0.01810569 0.01361172 0.01342099 0.01297994

[[85]]
 [1] 0.011451133 0.017193502 0.013957649 0.016183544 0.009810297 0.010656545
 [7] 0.013416965 0.009903702 0.014199260 0.008217581 0.011407794

[[86]]
[1] 0.01515314 0.01502980 0.01412874 0.02163800 0.01509020 0.02689769 0.02181458
[8] 0.02864567 0.01297994

[[87]]
[1] 0.01667105 0.02362452 0.02110260 0.02058034

[[88]]
[1] 0.01785036 0.02058034

Equal weights to each neighbouring polygons

rswm_q <- nb2listw(wm_q, style="W", zero.policy = TRUE)
rswm_q

Characteristics of weights list object:
Neighbour list object:
Number of regions: 88 
Number of nonzero links: 448 
Percentage nonzero weights: 5.785124 
Average number of links: 5.090909 

Weights style: W 
Weights constants summary:
   n   nn S0       S1       S2
W 88 7744 88 37.86334 365.9147

rswm_q$weights[10]

[[1]]
[1] 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125

Row-standardised

rswm_ids <- nb2listw(wm_q, glist=ids, style="B", zero.policy=TRUE)
rswm_ids

Characteristics of weights list object:
Neighbour list object:
Number of regions: 88 
Number of nonzero links: 448 
Percentage nonzero weights: 5.785124 
Average number of links: 5.090909 

Weights style: B 
Weights constants summary:
   n   nn       S0        S1     S2
B 88 7744 8.786867 0.3776535 3.8137

rswm_ids$weights[1]

[[1]]
[1] 0.01535405 0.03916350 0.01820896 0.02807922 0.01145113

summary(unlist(rswm_ids$weights))

    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
0.008218 0.015088 0.018739 0.019614 0.022823 0.040338

Application of Spatial Weight Matrix

Spatial Lag with Row-Standardised Weights

Compute average neighbour GDPPC value for each polygon.

GDPPC.lag <- lag.listw(rswm_q, hunan$GDPPC)
GDPPC.lag

 [1] 24847.20 22724.80 24143.25 27737.50 27270.25 21248.80 43747.00 33582.71
 [9] 45651.17 32027.62 32671.00 20810.00 25711.50 30672.33 33457.75 31689.20
[17] 20269.00 23901.60 25126.17 21903.43 22718.60 25918.80 20307.00 20023.80
[25] 16576.80 18667.00 14394.67 19848.80 15516.33 20518.00 17572.00 15200.12
[33] 18413.80 14419.33 24094.50 22019.83 12923.50 14756.00 13869.80 12296.67
[41] 15775.17 14382.86 11566.33 13199.50 23412.00 39541.00 36186.60 16559.60
[49] 20772.50 19471.20 19827.33 15466.80 12925.67 18577.17 14943.00 24913.00
[57] 25093.00 24428.80 17003.00 21143.75 20435.00 17131.33 24569.75 23835.50
[65] 26360.00 47383.40 55157.75 37058.00 21546.67 23348.67 42323.67 28938.60
[73] 25880.80 47345.67 18711.33 29087.29 20748.29 35933.71 15439.71 29787.50
[81] 18145.00 21617.00 29203.89 41363.67 22259.09 44939.56 16902.00 16930.00

nb1 <- wm_q[[1]]
nb1 <- hunan$GDPPC[nb1]
nb1

[1] 20981 34592 24473 21311 22879

lag.list <- list(hunan$NAME_3, lag.listw(rswm_q, hunan$GDPPC))
lag.res <- as.data.frame(lag.list)
colnames(lag.res) <- c("NAME_3", "lag GDPPC")
hunan <- left_join(hunan,lag.res)

head(hunan)

Simple feature collection with 6 features and 7 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 110.4922 ymin: 28.61762 xmax: 112.3013 ymax: 30.12812
Geodetic CRS:  WGS 84
   NAME_2  ID_3  NAME_3   ENGTYPE_3  County GDPPC lag GDPPC
1 Changde 21098 Anxiang      County Anxiang 23667  24847.20
2 Changde 21100 Hanshou      County Hanshou 20981  22724.80
3 Changde 21101  Jinshi County City  Jinshi 34592  24143.25
4 Changde 21102      Li      County      Li 24473  27737.50
5 Changde 21103   Linli      County   Linli 25554  27270.25
6 Changde 21104  Shimen      County  Shimen 27137  21248.80
                        geometry
1 POLYGON ((112.0625 29.75523...
2 POLYGON ((112.2288 29.11684...
3 POLYGON ((111.8927 29.6013,...
4 POLYGON ((111.3731 29.94649...
5 POLYGON ((111.6324 29.76288...
6 POLYGON ((110.8825 30.11675...

gdppc <- qtm(hunan, "GDPPC")
lag_gdppc <- qtm(hunan, "lag GDPPC")
tmap_arrange(gdppc, lag_gdppc, asp=1, ncol=2)

Spatial Lag as a sum of neighbouring values

b_weights <- lapply(wm_q, function(x) 0*x + 1)
b_weights2 <- nb2listw(wm_q, 
                       glist = b_weights, 
                       style = "B")
b_weights2

Characteristics of weights list object:
Neighbour list object:
Number of regions: 88 
Number of nonzero links: 448 
Percentage nonzero weights: 5.785124 
Average number of links: 5.090909 

Weights style: B 
Weights constants summary:
   n   nn  S0  S1    S2
B 88 7744 448 896 10224

lag_sum <- list(hunan$NAME_3, lag.listw(b_weights2, hunan$GDPPC))
lag.res <- as.data.frame(lag_sum)
colnames(lag.res) <- c("NAME_3", "lag_sum GDPPC")

lag_sum

[[1]]
 [1] "Anxiang"       "Hanshou"       "Jinshi"        "Li"           
 [5] "Linli"         "Shimen"        "Liuyang"       "Ningxiang"    
 [9] "Wangcheng"     "Anren"         "Guidong"       "Jiahe"        
[13] "Linwu"         "Rucheng"       "Yizhang"       "Yongxing"     
[17] "Zixing"        "Changning"     "Hengdong"      "Hengnan"      
[21] "Hengshan"      "Leiyang"       "Qidong"        "Chenxi"       
[25] "Zhongfang"     "Huitong"       "Jingzhou"      "Mayang"       
[29] "Tongdao"       "Xinhuang"      "Xupu"          "Yuanling"     
[33] "Zhijiang"      "Lengshuijiang" "Shuangfeng"    "Xinhua"       
[37] "Chengbu"       "Dongan"        "Dongkou"       "Longhui"      
[41] "Shaodong"      "Suining"       "Wugang"        "Xinning"      
[45] "Xinshao"       "Shaoshan"      "Xiangxiang"    "Baojing"      
[49] "Fenghuang"     "Guzhang"       "Huayuan"       "Jishou"       
[53] "Longshan"      "Luxi"          "Yongshun"      "Anhua"        
[57] "Nan"           "Yuanjiang"     "Jianghua"      "Lanshan"      
[61] "Ningyuan"      "Shuangpai"     "Xintian"       "Huarong"      
[65] "Linxiang"      "Miluo"         "Pingjiang"     "Xiangyin"     
[69] "Cili"          "Chaling"       "Liling"        "Yanling"      
[73] "You"           "Zhuzhou"       "Sangzhi"       "Yueyang"      
[77] "Qiyang"        "Taojiang"      "Shaoyang"      "Lianyuan"     
[81] "Hongjiang"     "Hengyang"      "Guiyang"       "Changsha"     
[85] "Taoyuan"       "Xiangtan"      "Dao"           "Jiangyong"    

[[2]]
 [1] 124236 113624  96573 110950 109081 106244 174988 235079 273907 256221
[11]  98013 104050 102846  92017 133831 158446 141883 119508 150757 153324
[21] 113593 129594 142149 100119  82884  74668  43184  99244  46549  20518
[31] 140576 121601  92069  43258 144567 132119  51694  59024  69349  73780
[41]  94651 100680  69398  52798 140472 118623 180933  82798  83090  97356
[51]  59482  77334  38777 111463  74715 174391 150558 122144  68012  84575
[61] 143045  51394  98279  47671  26360 236917 220631 185290  64640  70046
[71] 126971 144693 129404 284074 112268 203611 145238 251536 108078 238300
[81] 108870 108085 262835 248182 244850 404456  67608  33860

hunan <- left_join(hunan, lag.res)

gdppc <- qtm(hunan, "GDPPC")
lag_sum_gdppc <- qtm(hunan, "lag_sum GDPPC")
tmap_arrange(gdppc, lag_sum_gdppc, asp=1, ncol=2)

Spatial window average

wm_qs <- include.self(wm_q)

wm_qs[[1]]

[1]  1  2  3  4 57 85

wm_qs <- nb2listw(wm_qs)
wm_qs

Characteristics of weights list object:
Neighbour list object:
Number of regions: 88 
Number of nonzero links: 536 
Percentage nonzero weights: 6.921488 
Average number of links: 6.090909 

Weights style: W 
Weights constants summary:
   n   nn S0       S1       S2
W 88 7744 88 30.90265 357.5308

lag_w_avg_gpdpc <- lag.listw(wm_qs, 
                             hunan$GDPPC)
lag_w_avg_gpdpc

 [1] 24650.50 22434.17 26233.00 27084.60 26927.00 22230.17 47621.20 37160.12
 [9] 49224.71 29886.89 26627.50 22690.17 25366.40 25825.75 30329.00 32682.83
[17] 25948.62 23987.67 25463.14 21904.38 23127.50 25949.83 20018.75 19524.17
[25] 18955.00 17800.40 15883.00 18831.33 14832.50 17965.00 17159.89 16199.44
[33] 18764.50 26878.75 23188.86 20788.14 12365.20 15985.00 13764.83 11907.43
[41] 17128.14 14593.62 11644.29 12706.00 21712.29 43548.25 35049.00 16226.83
[49] 19294.40 18156.00 19954.75 18145.17 12132.75 18419.29 14050.83 23619.75
[57] 24552.71 24733.67 16762.60 20932.60 19467.75 18334.00 22541.00 26028.00
[65] 29128.50 46569.00 47576.60 36545.50 20838.50 22531.00 42115.50 27619.00
[73] 27611.33 44523.29 18127.43 28746.38 20734.50 33880.62 14716.38 28516.22
[81] 18086.14 21244.50 29568.80 48119.71 22310.75 43151.60 17133.40 17009.33

lag.list.wm_qs <- list(hunan$NAME_3, lag.listw(wm_qs, hunan$GDPPC))
lag_wm_qs.res <- as.data.frame(lag.list.wm_qs)
colnames(lag_wm_qs.res) <- c("NAME_3", "lag_window_avg GDPPC")

hunan <- left_join(hunan, lag_wm_qs.res)

hunan %>%
  select("County", "lag GDPPC", "lag_window_avg GDPPC") %>%
  kable()

County	lag GDPPC	lag_window_avg GDPPC	geometry
Anxiang	24847.20	24650.50	POLYGON ((112.0625 29.75523…
Hanshou	22724.80	22434.17	POLYGON ((112.2288 29.11684…
Jinshi	24143.25	26233.00	POLYGON ((111.8927 29.6013,…
Li	27737.50	27084.60	POLYGON ((111.3731 29.94649…
Linli	27270.25	26927.00	POLYGON ((111.6324 29.76288…
Shimen	21248.80	22230.17	POLYGON ((110.8825 30.11675…
Liuyang	43747.00	47621.20	POLYGON ((113.9905 28.5682,…
Ningxiang	33582.71	37160.12	POLYGON ((112.7181 28.38299…
Wangcheng	45651.17	49224.71	POLYGON ((112.7914 28.52688…
Anren	32027.62	29886.89	POLYGON ((113.1757 26.82734…
Guidong	32671.00	26627.50	POLYGON ((114.1799 26.20117…
Jiahe	20810.00	22690.17	POLYGON ((112.4425 25.74358…
Linwu	25711.50	25366.40	POLYGON ((112.5914 25.55143…
Rucheng	30672.33	25825.75	POLYGON ((113.6759 25.87578…
Yizhang	33457.75	30329.00	POLYGON ((113.2621 25.68394…
Yongxing	31689.20	32682.83	POLYGON ((113.3169 26.41843…
Zixing	20269.00	25948.62	POLYGON ((113.7311 26.16259…
Changning	23901.60	23987.67	POLYGON ((112.6144 26.60198…
Hengdong	25126.17	25463.14	POLYGON ((113.1056 27.21007…
Hengnan	21903.43	21904.38	POLYGON ((112.7599 26.98149…
Hengshan	22718.60	23127.50	POLYGON ((112.607 27.4689, …
Leiyang	25918.80	25949.83	POLYGON ((112.9996 26.69276…
Qidong	20307.00	20018.75	POLYGON ((111.7818 27.0383,…
Chenxi	20023.80	19524.17	POLYGON ((110.2624 28.21778…
Zhongfang	16576.80	18955.00	POLYGON ((109.9431 27.72858…
Huitong	18667.00	17800.40	POLYGON ((109.9419 27.10512…
Jingzhou	14394.67	15883.00	POLYGON ((109.8186 26.75842…
Mayang	19848.80	18831.33	POLYGON ((109.795 27.98008,…
Tongdao	15516.33	14832.50	POLYGON ((109.9294 26.46561…
Xinhuang	20518.00	17965.00	POLYGON ((109.227 27.43733,…
Xupu	17572.00	17159.89	POLYGON ((110.7189 28.30485…
Yuanling	15200.12	16199.44	POLYGON ((110.9652 28.99895…
Zhijiang	18413.80	18764.50	POLYGON ((109.8818 27.60661…
Lengshuijiang	14419.33	26878.75	POLYGON ((111.5307 27.81472…
Shuangfeng	24094.50	23188.86	POLYGON ((112.263 27.70421,…
Xinhua	22019.83	20788.14	POLYGON ((111.3345 28.19642…
Chengbu	12923.50	12365.20	POLYGON ((110.4455 26.69317…
Dongan	14756.00	15985.00	POLYGON ((111.4531 26.86812…
Dongkou	13869.80	13764.83	POLYGON ((110.6622 27.37305…
Longhui	12296.67	11907.43	POLYGON ((110.985 27.65983,…
Shaodong	15775.17	17128.14	POLYGON ((111.9054 27.40254…
Suining	14382.86	14593.62	POLYGON ((110.389 27.10006,…
Wugang	11566.33	11644.29	POLYGON ((110.9878 27.03345…
Xinning	13199.50	12706.00	POLYGON ((111.0736 26.84627…
Xinshao	23412.00	21712.29	POLYGON ((111.6013 27.58275…
Shaoshan	39541.00	43548.25	POLYGON ((112.5391 27.97742…
Xiangxiang	36186.60	35049.00	POLYGON ((112.4549 28.05783…
Baojing	16559.60	16226.83	POLYGON ((109.7015 28.82844…
Fenghuang	20772.50	19294.40	POLYGON ((109.5239 28.19206…
Guzhang	19471.20	18156.00	POLYGON ((109.8968 28.74034…
Huayuan	19827.33	19954.75	POLYGON ((109.5647 28.61712…
Jishou	15466.80	18145.17	POLYGON ((109.8375 28.4696,…
Longshan	12925.67	12132.75	POLYGON ((109.6337 29.62521…
Luxi	18577.17	18419.29	POLYGON ((110.1067 28.41835…
Yongshun	14943.00	14050.83	POLYGON ((110.0003 29.29499…
Anhua	24913.00	23619.75	POLYGON ((111.6034 28.63716…
Nan	25093.00	24552.71	POLYGON ((112.3232 29.46074…
Yuanjiang	24428.80	24733.67	POLYGON ((112.4391 29.1791,…
Jianghua	17003.00	16762.60	POLYGON ((111.6461 25.29661…
Lanshan	21143.75	20932.60	POLYGON ((112.2286 25.61123…
Ningyuan	20435.00	19467.75	POLYGON ((112.0715 26.09892…
Shuangpai	17131.33	18334.00	POLYGON ((111.8864 26.11957…
Xintian	24569.75	22541.00	POLYGON ((112.2578 26.0796,…
Huarong	23835.50	26028.00	POLYGON ((112.9242 29.69134…
Linxiang	26360.00	29128.50	POLYGON ((113.5502 29.67418…
Miluo	47383.40	46569.00	POLYGON ((112.9902 29.02139…
Pingjiang	55157.75	47576.60	POLYGON ((113.8436 29.06152…
Xiangyin	37058.00	36545.50	POLYGON ((112.9173 28.98264…
Cili	21546.67	20838.50	POLYGON ((110.8822 29.69017…
Chaling	23348.67	22531.00	POLYGON ((113.7666 27.10573…
Liling	42323.67	42115.50	POLYGON ((113.5673 27.94346…
Yanling	28938.60	27619.00	POLYGON ((113.9292 26.6154,…
You	25880.80	27611.33	POLYGON ((113.5879 27.41324…
Zhuzhou	47345.67	44523.29	POLYGON ((113.2493 28.02411…
Sangzhi	18711.33	18127.43	POLYGON ((110.556 29.40543,…
Yueyang	29087.29	28746.38	POLYGON ((113.343 29.61064,…
Qiyang	20748.29	20734.50	POLYGON ((111.5563 26.81318…
Taojiang	35933.71	33880.62	POLYGON ((112.0508 28.67265…
Shaoyang	15439.71	14716.38	POLYGON ((111.5013 27.30207…
Lianyuan	29787.50	28516.22	POLYGON ((111.6789 28.02946…
Hongjiang	18145.00	18086.14	POLYGON ((110.1441 27.47513…
Hengyang	21617.00	21244.50	POLYGON ((112.7144 26.98613…
Guiyang	29203.89	29568.80	POLYGON ((113.0811 26.04963…
Changsha	41363.67	48119.71	POLYGON ((112.9421 28.03722…
Taoyuan	22259.09	22310.75	POLYGON ((112.0612 29.32855…
Xiangtan	44939.56	43151.60	POLYGON ((113.0426 27.8942,…
Dao	16902.00	17133.40	POLYGON ((111.498 25.81679,…
Jiangyong	16930.00	17009.33	POLYGON ((111.3659 25.39472…

w_avg_gdppc <- qtm(hunan, "lag_window_avg GDPPC")
tmap_arrange(lag_gdppc, w_avg_gdppc, asp=1, ncol=2)

Spatial window sum

wm_qs <- include.self(wm_q)
wm_qs

Neighbour list object:
Number of regions: 88 
Number of nonzero links: 536 
Percentage nonzero weights: 6.921488 
Average number of links: 6.090909

b_weights <- lapply(wm_qs, function(x) 0*x + 1)
b_weights[1]

[[1]]
[1] 1 1 1 1 1 1

b_weights2 <- nb2listw(wm_qs, 
                       glist = b_weights, 
                       style = "B")
b_weights2

Characteristics of weights list object:
Neighbour list object:
Number of regions: 88 
Number of nonzero links: 536 
Percentage nonzero weights: 6.921488 
Average number of links: 6.090909 

Weights style: B 
Weights constants summary:
   n   nn  S0   S1    S2
B 88 7744 536 1072 14160

w_sum_gdppc <- list(hunan$NAME_3, lag.listw(b_weights2, hunan$GDPPC))
w_sum_gdppc

[[1]]
 [1] "Anxiang"       "Hanshou"       "Jinshi"        "Li"           
 [5] "Linli"         "Shimen"        "Liuyang"       "Ningxiang"    
 [9] "Wangcheng"     "Anren"         "Guidong"       "Jiahe"        
[13] "Linwu"         "Rucheng"       "Yizhang"       "Yongxing"     
[17] "Zixing"        "Changning"     "Hengdong"      "Hengnan"      
[21] "Hengshan"      "Leiyang"       "Qidong"        "Chenxi"       
[25] "Zhongfang"     "Huitong"       "Jingzhou"      "Mayang"       
[29] "Tongdao"       "Xinhuang"      "Xupu"          "Yuanling"     
[33] "Zhijiang"      "Lengshuijiang" "Shuangfeng"    "Xinhua"       
[37] "Chengbu"       "Dongan"        "Dongkou"       "Longhui"      
[41] "Shaodong"      "Suining"       "Wugang"        "Xinning"      
[45] "Xinshao"       "Shaoshan"      "Xiangxiang"    "Baojing"      
[49] "Fenghuang"     "Guzhang"       "Huayuan"       "Jishou"       
[53] "Longshan"      "Luxi"          "Yongshun"      "Anhua"        
[57] "Nan"           "Yuanjiang"     "Jianghua"      "Lanshan"      
[61] "Ningyuan"      "Shuangpai"     "Xintian"       "Huarong"      
[65] "Linxiang"      "Miluo"         "Pingjiang"     "Xiangyin"     
[69] "Cili"          "Chaling"       "Liling"        "Yanling"      
[73] "You"           "Zhuzhou"       "Sangzhi"       "Yueyang"      
[77] "Qiyang"        "Taojiang"      "Shaoyang"      "Lianyuan"     
[81] "Hongjiang"     "Hengyang"      "Guiyang"       "Changsha"     
[85] "Taoyuan"       "Xiangtan"      "Dao"           "Jiangyong"    

[[2]]
 [1] 147903 134605 131165 135423 134635 133381 238106 297281 344573 268982
[11] 106510 136141 126832 103303 151645 196097 207589 143926 178242 175235
[21] 138765 155699 160150 117145 113730  89002  63532 112988  59330  35930
[31] 154439 145795 112587 107515 162322 145517  61826  79925  82589  83352
[41] 119897 116749  81510  63530 151986 174193 210294  97361  96472 108936
[51]  79819 108871  48531 128935  84305 188958 171869 148402  83813 104663
[61] 155742  73336 112705  78084  58257 279414 237883 219273  83354  90124
[71] 168462 165714 165668 311663 126892 229971 165876 271045 117731 256646
[81] 126603 127467 295688 336838 267729 431516  85667  51028

w_sum_gdppc.res <- as.data.frame(w_sum_gdppc)
colnames(w_sum_gdppc.res) <- c("NAME_3", "w_sum GDPPC")

hunan <- left_join(hunan, w_sum_gdppc.res)

hunan %>%
  select("County", "lag_sum GDPPC", "w_sum GDPPC") %>%
  kable()

County	lag_sum GDPPC	w_sum GDPPC	geometry
Anxiang	124236	147903	POLYGON ((112.0625 29.75523…
Hanshou	113624	134605	POLYGON ((112.2288 29.11684…
Jinshi	96573	131165	POLYGON ((111.8927 29.6013,…
Li	110950	135423	POLYGON ((111.3731 29.94649…
Linli	109081	134635	POLYGON ((111.6324 29.76288…
Shimen	106244	133381	POLYGON ((110.8825 30.11675…
Liuyang	174988	238106	POLYGON ((113.9905 28.5682,…
Ningxiang	235079	297281	POLYGON ((112.7181 28.38299…
Wangcheng	273907	344573	POLYGON ((112.7914 28.52688…
Anren	256221	268982	POLYGON ((113.1757 26.82734…
Guidong	98013	106510	POLYGON ((114.1799 26.20117…
Jiahe	104050	136141	POLYGON ((112.4425 25.74358…
Linwu	102846	126832	POLYGON ((112.5914 25.55143…
Rucheng	92017	103303	POLYGON ((113.6759 25.87578…
Yizhang	133831	151645	POLYGON ((113.2621 25.68394…
Yongxing	158446	196097	POLYGON ((113.3169 26.41843…
Zixing	141883	207589	POLYGON ((113.7311 26.16259…
Changning	119508	143926	POLYGON ((112.6144 26.60198…
Hengdong	150757	178242	POLYGON ((113.1056 27.21007…
Hengnan	153324	175235	POLYGON ((112.7599 26.98149…
Hengshan	113593	138765	POLYGON ((112.607 27.4689, …
Leiyang	129594	155699	POLYGON ((112.9996 26.69276…
Qidong	142149	160150	POLYGON ((111.7818 27.0383,…
Chenxi	100119	117145	POLYGON ((110.2624 28.21778…
Zhongfang	82884	113730	POLYGON ((109.9431 27.72858…
Huitong	74668	89002	POLYGON ((109.9419 27.10512…
Jingzhou	43184	63532	POLYGON ((109.8186 26.75842…
Mayang	99244	112988	POLYGON ((109.795 27.98008,…
Tongdao	46549	59330	POLYGON ((109.9294 26.46561…
Xinhuang	20518	35930	POLYGON ((109.227 27.43733,…
Xupu	140576	154439	POLYGON ((110.7189 28.30485…
Yuanling	121601	145795	POLYGON ((110.9652 28.99895…
Zhijiang	92069	112587	POLYGON ((109.8818 27.60661…
Lengshuijiang	43258	107515	POLYGON ((111.5307 27.81472…
Shuangfeng	144567	162322	POLYGON ((112.263 27.70421,…
Xinhua	132119	145517	POLYGON ((111.3345 28.19642…
Chengbu	51694	61826	POLYGON ((110.4455 26.69317…
Dongan	59024	79925	POLYGON ((111.4531 26.86812…
Dongkou	69349	82589	POLYGON ((110.6622 27.37305…
Longhui	73780	83352	POLYGON ((110.985 27.65983,…
Shaodong	94651	119897	POLYGON ((111.9054 27.40254…
Suining	100680	116749	POLYGON ((110.389 27.10006,…
Wugang	69398	81510	POLYGON ((110.9878 27.03345…
Xinning	52798	63530	POLYGON ((111.0736 26.84627…
Xinshao	140472	151986	POLYGON ((111.6013 27.58275…
Shaoshan	118623	174193	POLYGON ((112.5391 27.97742…
Xiangxiang	180933	210294	POLYGON ((112.4549 28.05783…
Baojing	82798	97361	POLYGON ((109.7015 28.82844…
Fenghuang	83090	96472	POLYGON ((109.5239 28.19206…
Guzhang	97356	108936	POLYGON ((109.8968 28.74034…
Huayuan	59482	79819	POLYGON ((109.5647 28.61712…
Jishou	77334	108871	POLYGON ((109.8375 28.4696,…
Longshan	38777	48531	POLYGON ((109.6337 29.62521…
Luxi	111463	128935	POLYGON ((110.1067 28.41835…
Yongshun	74715	84305	POLYGON ((110.0003 29.29499…
Anhua	174391	188958	POLYGON ((111.6034 28.63716…
Nan	150558	171869	POLYGON ((112.3232 29.46074…
Yuanjiang	122144	148402	POLYGON ((112.4391 29.1791,…
Jianghua	68012	83813	POLYGON ((111.6461 25.29661…
Lanshan	84575	104663	POLYGON ((112.2286 25.61123…
Ningyuan	143045	155742	POLYGON ((112.0715 26.09892…
Shuangpai	51394	73336	POLYGON ((111.8864 26.11957…
Xintian	98279	112705	POLYGON ((112.2578 26.0796,…
Huarong	47671	78084	POLYGON ((112.9242 29.69134…
Linxiang	26360	58257	POLYGON ((113.5502 29.67418…
Miluo	236917	279414	POLYGON ((112.9902 29.02139…
Pingjiang	220631	237883	POLYGON ((113.8436 29.06152…
Xiangyin	185290	219273	POLYGON ((112.9173 28.98264…
Cili	64640	83354	POLYGON ((110.8822 29.69017…
Chaling	70046	90124	POLYGON ((113.7666 27.10573…
Liling	126971	168462	POLYGON ((113.5673 27.94346…
Yanling	144693	165714	POLYGON ((113.9292 26.6154,…
You	129404	165668	POLYGON ((113.5879 27.41324…
Zhuzhou	284074	311663	POLYGON ((113.2493 28.02411…
Sangzhi	112268	126892	POLYGON ((110.556 29.40543,…
Yueyang	203611	229971	POLYGON ((113.343 29.61064,…
Qiyang	145238	165876	POLYGON ((111.5563 26.81318…
Taojiang	251536	271045	POLYGON ((112.0508 28.67265…
Shaoyang	108078	117731	POLYGON ((111.5013 27.30207…
Lianyuan	238300	256646	POLYGON ((111.6789 28.02946…
Hongjiang	108870	126603	POLYGON ((110.1441 27.47513…
Hengyang	108085	127467	POLYGON ((112.7144 26.98613…
Guiyang	262835	295688	POLYGON ((113.0811 26.04963…
Changsha	248182	336838	POLYGON ((112.9421 28.03722…
Taoyuan	244850	267729	POLYGON ((112.0612 29.32855…
Xiangtan	404456	431516	POLYGON ((113.0426 27.8942,…
Dao	67608	85667	POLYGON ((111.498 25.81679,…
Jiangyong	33860	51028	POLYGON ((111.3659 25.39472…

w_sum_gdppc <- qtm(hunan, "w_sum GDPPC")
tmap_arrange(lag_sum_gdppc, w_sum_gdppc, asp=1, ncol=2)