pacman::p_load(sf, spdep, tmap, tidyverse, knitr)Exercise 2A: Spatial Weights and Applications
1. Getting Started
1.1 Install and launching R packages
The code chunk below uses p_load() of pacman package to check if sf, spdep, tmap, tidyverse , and knitr packages are installed into the R environment. If they are, then they will be launched into R.
1.2 Importing the OD data
We will be using two data sets for this exercise. Data were retrieved on 19th Nov 2023. They are :
- Hunan country boundary layer*. (data is in ESRI shapefile format) - Geospatial data
- Hunan_2012.csv*. (data is in csv file) - Attribute table
1.2.1 Importing Hunan country boundary layer
The code chunk below uses st_read() of sf package to import the 1st data set into R. The imported shapefile will be simple features object of sf.
hunan <- st_read(dsn = "data/geospatial",
layer = "Hunan")Reading layer `Hunan' from data source
`/Users/smu/Rworkshop/jiawenoh/ISSS624/Hands-on_Ex/Hands-on_Ex02/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 841.2.2 Importing Hunan_2012.csv
Next, we will import the 2nd dataset (csv) into R. We will use read_csv() of readr package. The output is in R dataframe class.
hunan2012 <- read_csv("data/aspatial/Hunan_2012.csv")1.3 Performing relational join
After importing, we will update the attribute table of hunan’s Spatial Polygons Data Frame with the attribute fields of hunan2012 dataframe. We will performed a left_join() with the aid of dplyr package.
hunan <- left_join(hunan,hunan2012) %>%
select(1:4,7,15)We will be joining both tables by County. By doing the left_join, we will combined the 8 variables from hunan, with 29 variables from hunan2012 and uses select() to filter for the variables that we are interested in.
2. Visualising Regional Development Indicator
In this section, we will be preparing a basemap and a choropleth map to show the distribution of GDPPC 2012 by using qtm() of tmap package.
Show the code
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)
Observations:
Changsha has the highest density.
Based on the geographic location, we could infer that their strategic location could indirectly boost the GDPPC of the nearby cities.
3. Computing Contiguity Spatial Weights
In this section, we will be using poly2nb() of spdep package to compute contiguity weight matrices for the study area. This function builds a neighbors list based on regions with contiguous boundaries.
We are able to pass a ‘queen’ argument with ‘TRUE’ or ‘FALSE’ as options. Without specification, the default will be TRUE. If you do not specify queen - FALSE, the function will return a list of first order neighbors using the queen criteria.
3.1 Computing (QUEEN) contiguity based neighbors
The code chunk below is used to compute 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 linksObservations:
Summary report highlights 88 area units in Hunan.
1 most connected region with 11 neighbors, and
2 least connected regions with only 1 neighbor.
For each polygon in our polygon object, wm_q lists all neighboring polygons. E.g., to see the neighbors of the first polygon in the object, we could use the following code:
wm_q[[1]][1] 2 3 4 57 85From the output, we observed that polygon 1 have 5 neighbors. The respective polygons ID are stored in the hunan Spatial Polygons Data Frame Class.
To retrieve the country name of Polygon ID = 1, we can use the following code:
hunan$County[1][1] "Anxiang"The output shows that Polygon ID = 1 is Anxiang country. To know more about the five neighboring polygons that we have identified with, the below code chunk will be used:
hunan$NAME_3[c(2,3,4,57,85)][1] "Hanshou" "Jinshi" "Li" "Nan" "Taoyuan"Similarly, we are able to retrieve the GDPPC of these five countries by using the code chunk below:
nb1 <- wm_q[[1]]
nb1 <- hunan$GDPPC[nb1]
nb1[1] 20981 34592 24473 21311 22879Additionally, we can display the complete weight matrix by using str() . For the purpose of this exercise, we will add [0:10] to display the first 10 list instead of the full 88.
str(wm_q[0:10])List of 10
$ : 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 72 733.2 Creating (ROOK) contiguity based neighbors
The code chunk below will be used to compute Rook contiguity weight matrix.
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 linksObservations:
Summary report highlights 88 area units in Hunan.
Similar to section 3.1 in terms of area units and least connected regions.
Differs in the most connected area as Rook shows 10 neighbors whereas Queen shows 11 neighbors.
3.3 Visualising contiguity weights
We will be using sf package to get the latitude and longitude of the polygon centroids which allow us to take a point and display a line to each neighboring point. To do so, we would require the coordinates in a separate data frame, and apply a mapping function. The mapping function applies a given function to each element of a vector and returns a vector of the same length.
Our input vector will be geometry column of us.bound while our function will be st_centroid. Additionally, we will be using map_dbl variation of map from the purrr package.
To get our longitude value, we map the st_centroid function over the geometry column of us.bound and access the longitude value through double bracket notation [[]] and 1 which allows us to get the first value in each centroid and the longitude.
longitude <- map_dbl(hunan$geometry, ~st_centroid(.x)[[1]])Similarly, we use the same approach to get latitude. However, we will replace 1 with 2.
latitude <- map_dbl(hunan$geometry, ~st_centroid(.x)[[2]])With longitude and latitude, we can combine them through cbind() to put longitude and latitude into the same object and use head() to check the first few observations.
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 29.798633.4 Plotting Contiguity based neighbors map
We will be plotting the contiguity based neighbors map for Queen, and Rock. Ideally, we are able to plot individually, or combined them together.
Show the code
plot(hunan$geometry, border="lightgrey")
plot(wm_q, coords, pch = 19, cex = 0.6, add = TRUE, col= "red")
Show the code
plot(hunan$geometry, border="lightgrey")
plot(wm_r, coords, pch = 19, cex = 0.6, add = TRUE, col = "red")
Show the code
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")
4. Compute fixed distance based neighbors
In this section, we will be using dnearneigh() of spdep package to derive distance-based weight matrices.
Also, we note that the function identifies neighbours of region points by Euclidean distance with a distance band where d1= lower bound, and d2= upper bound. If unprojected coordinates are used and either specified in the coordinates object x or with x as a two column matrix and longlat=TRUE, great circle distances in km will be calculated assuming the WGS84 reference ellipsoid.
The following steps will be performed :
Determine the cut-off distance
Compute fixed distance weight matrix
Plot fixed distance weight matrix
Note: fixed distance is more useful in smoothing the neighbor relation across multiple neighbors as densely area tends to have more neighbors and vice versa
We will begin the computation by determining the upper limit for the distance band through the following steps :
Return a matrix with the indices of point belonging to the set of the k nearest neighbors by using
knearneigh()of spdep.Convert the knn object return by
knearneigh()into a neighbors list of class nb with a list of integer vectors containing neighbor region number ids by usingknn2nb().Return the length of neighbor relationship edges by using
nbdists()of spdep.Remove the list structure of the return object by using
unlist().
Show the code
#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 As observed, the maximum distance is 61.79km (our upper threshold to ensure that all units have at least one neighbor.
Next, we will compute the distance weight matrix by using dnearneigh() :
Show the code
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 To display the structure of the weight matrix : we can use str() or combine table() and card() of spdep package. In the example below, we wil use the latter:
Show the code
table(hunan$County, card(wm_d62))
1 2 3 4 5 6
Anhua 1 0 0 0 0 0
Anren 0 0 0 1 0 0
Anxiang 0 0 0 0 1 0
Baojing 0 0 0 0 1 0
Chaling 0 0 1 0 0 0
Changning 0 0 1 0 0 0
Changsha 0 0 0 1 0 0
Chengbu 0 1 0 0 0 0
Chenxi 0 0 0 1 0 0
Cili 0 1 0 0 0 0
Dao 0 0 0 1 0 0
Dongan 0 0 1 0 0 0
Dongkou 0 0 0 1 0 0
Fenghuang 0 0 0 1 0 0
Guidong 0 0 1 0 0 0
Guiyang 0 0 0 1 0 0
Guzhang 0 0 0 0 0 1
Hanshou 0 0 0 1 0 0
Hengdong 0 0 0 0 1 0
Hengnan 0 0 0 0 1 0
Hengshan 0 0 0 0 0 1
Hengyang 0 0 0 0 0 1
Hongjiang 0 0 0 0 1 0
Huarong 0 0 0 1 0 0
Huayuan 0 0 0 1 0 0
Huitong 0 0 0 1 0 0
Jiahe 0 0 0 0 1 0
Jianghua 0 0 1 0 0 0
Jiangyong 0 1 0 0 0 0
Jingzhou 0 1 0 0 0 0
Jinshi 0 0 0 1 0 0
Jishou 0 0 0 0 0 1
Lanshan 0 0 0 1 0 0
Leiyang 0 0 0 1 0 0
Lengshuijiang 0 0 1 0 0 0
Li 0 0 1 0 0 0
Lianyuan 0 0 0 0 1 0
Liling 0 1 0 0 0 0
Linli 0 0 0 1 0 0
Linwu 0 0 0 1 0 0
Linxiang 1 0 0 0 0 0
Liuyang 0 1 0 0 0 0
Longhui 0 0 1 0 0 0
Longshan 0 1 0 0 0 0
Luxi 0 0 0 0 1 0
Mayang 0 0 0 0 0 1
Miluo 0 0 0 0 1 0
Nan 0 0 0 0 1 0
Ningxiang 0 0 0 1 0 0
Ningyuan 0 0 0 0 1 0
Pingjiang 0 1 0 0 0 0
Qidong 0 0 1 0 0 0
Qiyang 0 0 1 0 0 0
Rucheng 0 1 0 0 0 0
Sangzhi 0 1 0 0 0 0
Shaodong 0 0 0 0 1 0
Shaoshan 0 0 0 0 1 0
Shaoyang 0 0 0 1 0 0
Shimen 1 0 0 0 0 0
Shuangfeng 0 0 0 0 0 1
Shuangpai 0 0 0 1 0 0
Suining 0 0 0 0 1 0
Taojiang 0 1 0 0 0 0
Taoyuan 0 1 0 0 0 0
Tongdao 0 1 0 0 0 0
Wangcheng 0 0 0 1 0 0
Wugang 0 0 1 0 0 0
Xiangtan 0 0 0 1 0 0
Xiangxiang 0 0 0 0 1 0
Xiangyin 0 0 0 1 0 0
Xinhua 0 0 0 0 1 0
Xinhuang 1 0 0 0 0 0
Xinning 0 1 0 0 0 0
Xinshao 0 0 0 0 0 1
Xintian 0 0 0 0 1 0
Xupu 0 1 0 0 0 0
Yanling 0 0 1 0 0 0
Yizhang 1 0 0 0 0 0
Yongshun 0 0 0 1 0 0
Yongxing 0 0 0 1 0 0
You 0 0 0 1 0 0
Yuanjiang 0 0 0 0 1 0
Yuanling 1 0 0 0 0 0
Yueyang 0 0 1 0 0 0
Zhijiang 0 0 0 0 1 0
Zhongfang 0 0 0 1 0 0
Zhuzhou 0 0 0 0 1 0
Zixing 0 0 1 0 0 0On average, we could see that the all units have 3-4 neighbors.
Thereafter, we will plot the distance weight matrix by using the code below:
Show the code
plot(hunan$geometry, border="lightgrey")
plot(wm_d62, coords, add=TRUE)
plot(k1, coords, add=TRUE, col="red", length=0.08)
As seen above, the red line indicates the 1st nearest neighbors while the black lines indicate the links of neighbors that are within the upper bound (61.79km)
Alternatively, we can plot both lines next to one another:
Show the code
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")
5. Compute adaptive distance weight matrix
Unlike the previous section, we do not do need to perform the first step in determining the cut-off distance. As shown in the code chunk below, we will control the number of neighbors directly using k-nearest neighbors, either by accepting asymmetric neighbors or imposing symmetry.
The following steps will be performed :
Compute adaptive distance weight matrix
Plot adaptive distance weight matrix
We will begin with the following step :
- Return a matrix with the indices of point belonging to the set of the k nearest neighbors by using
knearneigh()of spdep.
Show the code
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 listTo check if all coutry have exactly six neighbors (k= 6), we can display the content of the matrix using str() :
Show the code
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"Thereafter, we will plot the distance weight matrix by using the code below:
Show the code
plot(hunan$geometry, border="lightgrey")
plot(knn6, coords, pch = 19, cex = 0.6, add = TRUE, col = "red")
6. Weights based on IDW
In this section, we will derive a spatial weight matrix based on Inversed Distance method.
The following steps will be performed :
Compute the distances between areas (by using
nbdist()of spdep)Assign weights to each neighboring polygon (by using
nb2listw()of spdep)
Show the code
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 0.02058034Weights are assigned based on the fraction of 1/#no.of neighbors to each neighboring country then summing the weighted income values.
For the example below, we will used style = ‘W’ option (note: there are robust options available). By adding ’Zero.police = TRUE’, we are allowing list of non-neighbors.
Show the code
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 365.9147To see the weight of the first polygon’s eight neighbor type:
rswm_q$weights[10][[1]]
[1] 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125Using the same method, we can derive a row standardize distance weight matrix:
Show the code
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 3.8137To identify the weight of the first list:
rswm_ids$weights[1][[1]]
[1] 0.01535405 0.03916350 0.01820896 0.02807922 0.01145113To view the summary :
summary(unlist(rswm_ids$weights)) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.008218 0.015088 0.018739 0.019614 0.022823 0.040338 7. Application of Spatial Weight Matrix
In this section, we will create four different spatial lagged variables, namely:
spatial lag with row-standardized weights
spatial lag as a sum of neighboring values
spatial window average, and
spatial window sum
7.1 Spatial leg with row-standarized weights
Step 1: Compute average neighbor GDPP value for each polygon. Often, these values are referred to as spatially lagged values.
GDPPC.lag <- lag.listw(rswm_q, hunan$GDPPC)
GDPPC.lag [1] 24847.20 22724.80 24143.25 27737.50 27270.25 21248.80 43747.00 33582.71
[9] 45651.17 32027.62 32671.00 20810.00 25711.50 30672.33 33457.75 31689.20
[17] 20269.00 23901.60 25126.17 21903.43 22718.60 25918.80 20307.00 20023.80
[25] 16576.80 18667.00 14394.67 19848.80 15516.33 20518.00 17572.00 15200.12
[33] 18413.80 14419.33 24094.50 22019.83 12923.50 14756.00 13869.80 12296.67
[41] 15775.17 14382.86 11566.33 13199.50 23412.00 39541.00 36186.60 16559.60
[49] 20772.50 19471.20 19827.33 15466.80 12925.67 18577.17 14943.00 24913.00
[57] 25093.00 24428.80 17003.00 21143.75 20435.00 17131.33 24569.75 23835.50
[65] 26360.00 47383.40 55157.75 37058.00 21546.67 23348.67 42323.67 28938.60
[73] 25880.80 47345.67 18711.33 29087.29 20748.29 35933.71 15439.71 29787.50
[81] 18145.00 21617.00 29203.89 41363.67 22259.09 44939.56 16902.00 16930.00Step 2: Append spatially lag GDPPC values onto hunan sf data frame
lag.list <- list(hunan$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)Step 3: Verify data frame
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...Show the code
gdppc <- qtm(hunan, "GDPPC")
lag_gdppc <- qtm(hunan, "lag GDPPC")
tmap_arrange(gdppc, lag_gdppc, asp=1, ncol=2)
7.2 Spatial lag as sum of neighboring values
To begin, we can calculate spatial lag as a sum of neighboring values by assigning binary weights. This requires us to go back to our neighbors list, then apply a function that will assign binary weights, then we use glist = in the nb2listw() function to explicitly assign these weights.
Step 1: apply lapply() function to assign a value of 1 for each neighbor
Step 2: apply nb2listw() function to explicitly assign these 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 10224Step 3: use lag.listw() to compute a lag variable from our 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")Step 4: examine the result
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 33860Step 5: Append the lag_sum GDPPC into hunan sf data frame
hunan <- left_join(hunan, lag.res)Show the code
gdppc <- qtm(hunan, "GDPPC")
lag_sum_gdppc <- qtm(hunan, "lag_sum GDPPC")
tmap_arrange(gdppc, lag_sum_gdppc, asp=1, ncol=2)
7.3 Spatial window average
The spatial window average uses row-standardized weights and includes the diagonal element.
Step 1: add diagonal element to the neighbor list by using include.self() from spdep
wm_qs <- include.self(wm_q)Step 2: Check neighbor list of area [1]
wm_qs[[1]][1] 1 2 3 4 57 85Step 3: Obtain weights with nb2listw()
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 357.5308Step 4: create lag variable from our weight structure and GDPPC 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 17009.33Step 5: convert lag variable listw object into a dataframe by using as.data.frame()
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")Step 6: append lag_window_avg GDPPC values onto hunan sf data frame using left_join()
hunan <- left_join(hunan, lag_wm_qs.res)Step 7: compare values of lag GDPPC and Spatial window average by using kable() of Knitr package
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 lap_gdppc and w_ave_gdppc maps by using qtm() of tmap package
Show the code
w_avg_gdppc <- qtm(hunan, "lag_window_avg GDPPC")
tmap_arrange(lag_gdppc, w_avg_gdppc, asp=1, ncol=2)
7.4 Spatial window sum
The spatial window sum is the counter part of the window average, but without using row- standardized weights.
Step 1: add diagonal element to the neighbor list by using include.self() from spdep
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 Step 2: Assign binary weights to the neighbor structure that includes the diagonal element
b_weights <- lapply(wm_qs, function(x) 0*x + 1)
b_weights[1][[1]]
[1] 1 1 1 1 1 1Step 3: Explicitly assign weight values by using nb2listw() and glist()
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 14160Step 4: compute lag variable with lag.listw()
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 51028Step 6: convert lag variable listw object into a dataframe by using as.data.frame()
w_sum_gdppc.res <- as.data.frame(w_sum_gdppc)
colnames(w_sum_gdppc.res) <- c("NAME_3", "w_sum GDPPC")Step 7: append w_sum GDPPC values into hunan sf data frame by using left_join()
hunan <- left_join(hunan, w_sum_gdppc.res)Step 8: compare values of lag GDPPC and Spatial window average, kable() of Knitr package is used to prepare a table
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 lap_sum GDPPC and w_sum_gdppc maps by using qtm() of tmap package
Show the code
w_sum_gdppc <- qtm(hunan, "w_sum GDPPC")
tmap_arrange(lag_sum_gdppc, w_sum_gdppc, asp=1, ncol=2)