pacman::p_load(sf, spdep, tmap, tidyverse, knitr)Hands-On Exercise 6: Spatial Weights & Applications
Danger
This Hands-On Exercise is based spdep rather than sf.
For In-Class Ex and Take Home Ex will use sfdep. This will cut down conversion form sf to sp (that we had in TH Ex1).
Imports
Packages
Data
hunan <- st_read(dsn = "data/geospatial",
layer = "Hunan")Reading layer `Hunan' from data source
`/Users/michelle/Desktop/IS415/shelle-mim/IS415-GAA/Hands-on_Exercise/Wk6/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 84hunan2012 <- read_csv("data/aspatial/Hunan_2012.csv")# Relational join
hunan <- left_join(hunan,hunan2012)%>%
select(1:4, 7, 15)Visualise Regional Development Indicator
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
Computing contiguity based neighbours
Queen
# Computer Queen contiguity weight matrix
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# Lists all neighbouring polygons
wm_qNeighbour list object:
Number of regions: 88
Number of nonzero links: 448
Percentage nonzero weights: 5.785124
Average number of links: 5.090909 # List neighbours of first polygon
wm_q[[1]][1] 2 3 4 57 85# Retrieve county name of polygon 1
hunan$County[1][1] "Anxiang"# Reveal county names of Anxiangs's 5 neighbours
hunan$NAME_3[c(2,3,4,57,85)][1] "Hanshou" "Jinshi" "Li" "Nan" "Taoyuan"# Retrieve GDPCC of these 5 counties
nb1 <- wm_q[[1]]
nb1 <- hunan$GDPPC[nb1]
nb1[1] 20981 34592 24473 21311 22879# Display complete weight of matrix using str()
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 TRUERook
wm_r <- poly2nb(hunan, queen=FALSE) # just add a queen=FALSE, is queen=TRUE by default
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 linksVisualising contiguity weights
Get coordinates of polygons
longitude <- map_dbl(hunan$geometry, ~st_centroid(.x)[[1]])
latitude <- map_dbl(hunan$geometry, ~st_centroid(.x)[[2]])
# Combine lat and long with cbind
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 29.79863Plot QUeen contiguity based neighbours map
plot(hunan$geometry, border="lightgrey")
plot(wm_q, coords, pch = 19, cex = 0.6, add = TRUE, col= "red")
Plot Rook contiguity based neighbours map
plot(hunan$geometry, border="lightgrey")
plot(wm_r, coords, pch = 19, cex = 0.6, add = TRUE, col = "red")
Plot both
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 cut-off distance
#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 # Compute fixed dist weight matrix
wm_d62 <- dnearneigh(coords, 0, 62, longlat = TRUE)
wm_d62Neighbour list object:
Number of regions: 88
Number of nonzero links: 324
Percentage nonzero weights: 4.183884
Average number of links: 3.681818 # Display content of matrix
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# Display in table
table(hunan$County, card(wm_d62))
1 2 3 4 5 6
Anhua 1 0 0 0 0 0
Anren 0 0 0 1 0 0
Anxiang 0 0 0 0 1 0
Baojing 0 0 0 0 1 0
Chaling 0 0 1 0 0 0
Changning 0 0 1 0 0 0
Changsha 0 0 0 1 0 0
Chengbu 0 1 0 0 0 0
Chenxi 0 0 0 1 0 0
Cili 0 1 0 0 0 0
Dao 0 0 0 1 0 0
Dongan 0 0 1 0 0 0
Dongkou 0 0 0 1 0 0
Fenghuang 0 0 0 1 0 0
Guidong 0 0 1 0 0 0
Guiyang 0 0 0 1 0 0
Guzhang 0 0 0 0 0 1
Hanshou 0 0 0 1 0 0
Hengdong 0 0 0 0 1 0
Hengnan 0 0 0 0 1 0
Hengshan 0 0 0 0 0 1
Hengyang 0 0 0 0 0 1
Hongjiang 0 0 0 0 1 0
Huarong 0 0 0 1 0 0
Huayuan 0 0 0 1 0 0
Huitong 0 0 0 1 0 0
Jiahe 0 0 0 0 1 0
Jianghua 0 0 1 0 0 0
Jiangyong 0 1 0 0 0 0
Jingzhou 0 1 0 0 0 0
Jinshi 0 0 0 1 0 0
Jishou 0 0 0 0 0 1
Lanshan 0 0 0 1 0 0
Leiyang 0 0 0 1 0 0
Lengshuijiang 0 0 1 0 0 0
Li 0 0 1 0 0 0
Lianyuan 0 0 0 0 1 0
Liling 0 1 0 0 0 0
Linli 0 0 0 1 0 0
Linwu 0 0 0 1 0 0
Linxiang 1 0 0 0 0 0
Liuyang 0 1 0 0 0 0
Longhui 0 0 1 0 0 0
Longshan 0 1 0 0 0 0
Luxi 0 0 0 0 1 0
Mayang 0 0 0 0 0 1
Miluo 0 0 0 0 1 0
Nan 0 0 0 0 1 0
Ningxiang 0 0 0 1 0 0
Ningyuan 0 0 0 0 1 0
Pingjiang 0 1 0 0 0 0
Qidong 0 0 1 0 0 0
Qiyang 0 0 1 0 0 0
Rucheng 0 1 0 0 0 0
Sangzhi 0 1 0 0 0 0
Shaodong 0 0 0 0 1 0
Shaoshan 0 0 0 0 1 0
Shaoyang 0 0 0 1 0 0
Shimen 1 0 0 0 0 0
Shuangfeng 0 0 0 0 0 1
Shuangpai 0 0 0 1 0 0
Suining 0 0 0 0 1 0
Taojiang 0 1 0 0 0 0
Taoyuan 0 1 0 0 0 0
Tongdao 0 1 0 0 0 0
Wangcheng 0 0 0 1 0 0
Wugang 0 0 1 0 0 0
Xiangtan 0 0 0 1 0 0
Xiangxiang 0 0 0 0 1 0
Xiangyin 0 0 0 1 0 0
Xinhua 0 0 0 0 1 0
Xinhuang 1 0 0 0 0 0
Xinning 0 1 0 0 0 0
Xinshao 0 0 0 0 0 1
Xintian 0 0 0 0 1 0
Xupu 0 1 0 0 0 0
Yanling 0 0 1 0 0 0
Yizhang 1 0 0 0 0 0
Yongshun 0 0 0 1 0 0
Yongxing 0 0 0 1 0 0
You 0 0 0 1 0 0
Yuanjiang 0 0 0 0 1 0
Yuanling 1 0 0 0 0 0
Yueyang 0 0 1 0 0 0
Zhijiang 0 0 0 0 1 0
Zhongfang 0 0 0 1 0 0
Zhuzhou 0 0 0 0 1 0
Zixing 0 0 1 0 0 0n_comp <- n.comp.nb(wm_d62)
n_comp$nc[1] 1table(n_comp$comp.id)
1
88 Plot fixed dist weight matrix
plot(hunan$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")
Compute adaptive dist weight matrix
# Control num of neighbours using k-nearest neighbours
knn6 <- knn2nb(knearneigh(coords, k=6))
knn6Neighbour 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# Display content
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
plot(hunan$geometry, border="lightgrey")
plot(knn6, coords, pch = 19, cex = 0.6, add = TRUE, col = "red")
Weights based on in Inversed Distance (IDW)
Compute distances
# Compute using nbdists() of spdep
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 0.02058034Row-standardised weights matrix
# Assign weights to neighboring polygons
rswm_q <- nb2listw(wm_q, style="W", zero.policy = TRUE)
rswm_qCharacteristics 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# See weight of first polygon's eight neighbours type
rswm_q$weights[10][[1]]
[1] 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125# row standardised dist weight matrix
rswm_ids <- nb2listw(wm_q, glist=ids, style="B", zero.policy=TRUE)
rswm_idsCharacteristics 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 3.8137rswm_ids$weights[1][[1]]
[1] 0.01535405 0.03916350 0.01820896 0.02807922 0.01145113summary(unlist(rswm_ids$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
Types of spatial lagged variables:
spatial lag with row-standardised weights
spatial lag as a sum of neighbouring values
spatial window average
spatial window sum
Spatial Lag with row-standardised weights
(Compute ave neighbor GDPCC values for each polygon)
GDPPC.lag <- lag.listw(rswm_q, hunan$GDPPC)
GDPPC.lag [1] 24847.20 22724.80 24143.25 27737.50 27270.25 21248.80 43747.00 33582.71
[9] 45651.17 32027.62 32671.00 20810.00 25711.50 30672.33 33457.75 31689.20
[17] 20269.00 23901.60 25126.17 21903.43 22718.60 25918.80 20307.00 20023.80
[25] 16576.80 18667.00 14394.67 19848.80 15516.33 20518.00 17572.00 15200.12
[33] 18413.80 14419.33 24094.50 22019.83 12923.50 14756.00 13869.80 12296.67
[41] 15775.17 14382.86 11566.33 13199.50 23412.00 39541.00 36186.60 16559.60
[49] 20772.50 19471.20 19827.33 15466.80 12925.67 18577.17 14943.00 24913.00
[57] 25093.00 24428.80 17003.00 21143.75 20435.00 17131.33 24569.75 23835.50
[65] 26360.00 47383.40 55157.75 37058.00 21546.67 23348.67 42323.67 28938.60
[73] 25880.80 47345.67 18711.33 29087.29 20748.29 35933.71 15439.71 29787.50
[81] 18145.00 21617.00 29203.89 41363.67 22259.09 44939.56 16902.00 16930.00# Retrieve GDPPC of 5 countries (done earlier)
nb1 <- wm_q[[1]]
nb1 <- hunan$GDPPC[nb1]
nb1[1] 20981 34592 24473 21311 22879# Append spatially lag GDPPC values
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...# Plot
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
(Sum neighboring values by assigning binary weights)
b_weights <- lapply(wm_q, function(x) 0*x + 1)
b_weights2 <- nb2listw(wm_q,
glist = b_weights,
style = "B")
b_weights2Characteristics 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# Compute a lag var from weight and GDPPC
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 33860hunan <- 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
(Uses row-standardized weights + includes diagonal element)
# Add diagonal element
wm_qs <- include.self(wm_q)wm_qs[[1]][1] 1 2 3 4 57 85# Obtain weights
wm_qs <- nb2listw(wm_qs)
wm_qsCharacteristics 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# Compute the lag variable
lag_w_avg_gpdpc <- lag.listw(wm_qs,
hunan$GDPPC)
lag_w_avg_gpdpc [1] 24650.50 22434.17 26233.00 27084.60 26927.00 22230.17 47621.20 37160.12
[9] 49224.71 29886.89 26627.50 22690.17 25366.40 25825.75 30329.00 32682.83
[17] 25948.62 23987.67 25463.14 21904.38 23127.50 25949.83 20018.75 19524.17
[25] 18955.00 17800.40 15883.00 18831.33 14832.50 17965.00 17159.89 16199.44
[33] 18764.50 26878.75 23188.86 20788.14 12365.20 15985.00 13764.83 11907.43
[41] 17128.14 14593.62 11644.29 12706.00 21712.29 43548.25 35049.00 16226.83
[49] 19294.40 18156.00 19954.75 18145.17 12132.75 18419.29 14050.83 23619.75
[57] 24552.71 24733.67 16762.60 20932.60 19467.75 18334.00 22541.00 26028.00
[65] 29128.50 46569.00 47576.60 36545.50 20838.50 22531.00 42115.50 27619.00
[73] 27611.33 44523.29 18127.43 28746.38 20734.50 33880.62 14716.38 28516.22
[81] 18086.14 21244.50 29568.80 48119.71 22310.75 43151.60 17133.40 17009.33# Convert lag varioable obj into dataframe
lag.list.wm_qs <- list(hunan$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")# Append
hunan <- left_join(hunan, lag_wm_qs.res)# compare vals of lag and spatial window ave
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… |
# Plot for comparison
w_avg_gdppc <- qtm(hunan, "lag_window_avg GDPPC")
tmap_arrange(lag_gdppc, w_avg_gdppc, asp=1, ncol=2)
Spatial window sum
(window ave, but without row-standardized weights)
# Add diagonal element
wm_qs <- include.self(wm_q)
wm_qsNeighbour list object:
Number of regions: 88
Number of nonzero links: 536
Percentage nonzero weights: 6.921488
Average number of links: 6.090909 # Assign binary weights
b_weights <- lapply(wm_qs, function(x) 0*x + 1)
b_weights[1][[1]]
[1] 1 1 1 1 1 1# Assign weight values
b_weights2 <- nb2listw(wm_qs,
glist = b_weights,
style = "B")
b_weights2Characteristics 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# Compute lag variable
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# Convert to dataframe
w_sum_gdppc.res <- as.data.frame(w_sum_gdppc)
colnames(w_sum_gdppc.res) <- c("NAME_3", "w_sum GDPPC")# Append
hunan <- left_join(hunan, w_sum_gdppc.res)# Compare
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… |
# Plot comparison
w_sum_gdppc <- qtm(hunan, "w_sum GDPPC")
tmap_arrange(lag_sum_gdppc, w_sum_gdppc, asp=1, ncol=2)