In Class ex 1 - Chap 3 Spatial Weights and Applications

Overview

Step 1: Check and load packages

In this chapter, we will learn how to compute spatial weights using R.

Check if we have required packages:

packages = c('sf', 'spdep', 'tmap', 'tidyverse', 'here')
for (p in packages){
  if(!require(p, character.only = T)){
    install.packages(p)
  }
  library(p,character.only = T)
}

Loading required package: sf

Linking to GEOS 3.9.3, GDAL 3.5.2, PROJ 8.2.1; sf_use_s2() is TRUE

Loading required package: spdep

Loading required package: sp

Loading required package: spData

To access larger datasets in this package, install the spDataLarge
package with: `install.packages('spDataLarge',
repos='https://nowosad.github.io/drat/', type='source')`

Loading required package: tmap

Loading required package: tidyverse

── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
✔ ggplot2 3.4.0      ✔ purrr   0.3.5 
✔ tibble  3.1.8      ✔ dplyr   1.0.10
✔ tidyr   1.2.1      ✔ stringr 1.4.1 
✔ readr   2.1.3      ✔ forcats 0.5.2 
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
Loading required package: here

here() starts at D:/f4sared/ISSS624

Import the required packages:

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

Step 2: Loading the data into R

Create the shapefile path:

shapefile_path <- here("data", "dataHunan", "geospatial")
shapefile_path

[1] "D:/f4sared/ISSS624/data/dataHunan/geospatial"

We will first load the shapefile into the environment:

hunan <- st_read(dsn = shapefile_path, layer = "Hunan")

Reading layer `Hunan' from data source 
  `D:\f4sared\ISSS624\data\dataHunan\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

We will then check the loaded file:

list(hunan)

[[1]]
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
First 10 features:
     NAME_2  ID_3    NAME_3   ENGTYPE_3 Shape_Leng Shape_Area    County
1   Changde 21098   Anxiang      County   1.869074 0.10056190   Anxiang
2   Changde 21100   Hanshou      County   2.360691 0.19978745   Hanshou
3   Changde 21101    Jinshi County City   1.425620 0.05302413    Jinshi
4   Changde 21102        Li      County   3.474325 0.18908121        Li
5   Changde 21103     Linli      County   2.289506 0.11450357     Linli
6   Changde 21104    Shimen      County   4.171918 0.37194707    Shimen
7  Changsha 21109   Liuyang County City   4.060579 0.46016789   Liuyang
8  Changsha 21110 Ningxiang      County   3.323754 0.26614198 Ningxiang
9  Changsha 21111 Wangcheng      County   2.292093 0.13049161 Wangcheng
10 Chenzhou 21112     Anren      County   2.240739 0.13343936     Anren
                         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...
7  POLYGON ((113.9905 28.5682,...
8  POLYGON ((112.7181 28.38299...
9  POLYGON ((112.7914 28.52688...
10 POLYGON ((113.1757 26.82734...

Create the csv path:

csv_path <- here("data", "dataHunan", "aspatial", "Hunan_2012.csv")
csv_path

[1] "D:/f4sared/ISSS624/data/dataHunan/aspatial/Hunan_2012.csv"

Next we will Import the CSV file:

hunan2012 <- read_csv(csv_path)

Rows: 88 Columns: 29
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr  (2): County, City
dbl (27): avg_wage, deposite, FAI, Gov_Rev, Gov_Exp, GDP, GDPPC, GIO, Loan, ...

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

After the CSV files is imported, we will check it:

list(hunan2012)

[[1]]
# A tibble: 88 × 29
   County    City     avg_w…¹ depos…²    FAI Gov_Rev Gov_Exp    GDP GDPPC    GIO
   <chr>     <chr>      <dbl>   <dbl>  <dbl>   <dbl>   <dbl>  <dbl> <dbl>  <dbl>
 1 Anhua     Yiyang     30544  10967   6832.    457.   2703  13225  14567  9277.
 2 Anren     Chenzhou   28058   4599.  6386.    221.   1455.  4941. 12761  4189.
 3 Anxiang   Changde    31935   5517.  3541     244.   1780. 12482  23667  5109.
 4 Baojing   Hunan W…   30843   2250   1005.    193.   1379.  4088. 14563  3624.
 5 Chaling   Zhuzhou    31251   8241.  6508.    620.   1947  11585  20078  9158.
 6 Changning Hengyang   28518  10860   7920     770.   2632. 19886  24418 37392 
 7 Changsha  Changsha   54540  24332  33624    5350    7886. 88009  88656 51361 
 8 Chengbu   Shaoyang   28597   2581.  1922.    161.   1192.  2570. 10132  1681.
 9 Chenxi    Huaihua    33580   4990   5818.    460.   1724.  7755. 17026  6644.
10 Cili      Zhangji…   33099   8117.  4498.    500.   2306. 11378  18714  5843.
# … with 78 more rows, 19 more variables: Loan <dbl>, NIPCR <dbl>, Bed <dbl>,
#   Emp <dbl>, EmpR <dbl>, EmpRT <dbl>, Pri_Stu <dbl>, Sec_Stu <dbl>,
#   Household <dbl>, Household_R <dbl>, NOIP <dbl>, Pop_R <dbl>, RSCG <dbl>,
#   Pop_T <dbl>, Agri <dbl>, Service <dbl>, Disp_Inc <dbl>, RORP <dbl>,
#   ROREmp <dbl>, and abbreviated variable names ¹​avg_wage, ²​deposite

After the CSV file is imported, we need to perform a relational join using dplyr:

**Note: Here it seems relational join magically detects the common feature to join by. WOW !

hunan <- left_join(hunan,hunan2012)

Joining, by = "County"

Step 3: Visualize using plots

Next we will make use of the tmap package (tm_shape, tm_text, qtm):

basemap <- tm_shape(hunan) +
  tm_polygons() +
  tm_text("NAME_3", size=0.2)

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

Step 4: Computing the Contiguity Spatial Weights

Queen:

Compute the (QUEEN) contiguity based neighbors 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

Next we want to see the neighbor for the first polygon:
**Note: Both syntax below seem to work

wm_q[1]

[[1]]
[1]  2  3  4 57 85

wm_q[[1]]

[1]  2  3  4 57 85

Next we will retrieve the name of polygon 1:

hunan$County[1]

[1] "Anxiang"

We will next reveal the neighbouring counties of Anxiang:

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

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

We can also retrieve the neighbouring GDPPC of the five countries by code chunk below:

**Note: we can save the neighbor as a list.

**Then we will just use that as the input for filtering

nb_1 <- wm_q[[1]]
nb_1 <- hunan$GDPPC[nb_1]
nb_1

[1] 20981 34592 24473 21311 22879

Using str(), we will then display the 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:

Create the weight matrix based on the 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

Step 5: Visualize the contiguity weights:

Data preparation:

Store the longitude:

**~ means shorthand for writing a function

** .x means a vector input

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

Store the latitude:

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

Bind the 2 above together:

coords <- cbind(longitude, latitude)

Check the head of the newly created data:

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 QUEEN:

Next we will plot the contiguity based neighbors map:

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

Plot ROOK:

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

Plotting both maps together:

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")

Step 6: Compute distance based neighbors:

Compute the neighbors:

Calculate the nearest neighbor:

**k is default value 1

k1 <- knn2nb(knearneigh(coords))

Here we see that each polygon only has 1 neighbor:

str(k1)

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

compute the distance between all neighbors:

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 

Summary report shows that the max value is 61.79, so this value will be used as the upper threshold

Compute the weight matrix:

We compute the distance weight matrix as follow:

**0 is min threshold

**62 is max threshold

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 

**Average number of links here refers to the average number of nearest neighbor per polygon

Display the weight 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

An alternative way to present the data:

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

Find number of disjoint sub graph:

https://r4gdsa.netlify.app/chap03.html#computing-distance-based-neighbours

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

[1] 1

table(n_comp$comp.id)

 1 
88 

Plot the distance based weight matrix:

Plot the distance based neighbor + K1 nearest neighbor:

**Note it is an overlap of 2 plots on 1

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

Plot the distance based + K nearest neighbor on 2 separate plots:

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 distance weight matrix:

Recalculate the N nearest neighbors, this time using K = 6

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

Check the output:

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 the new K = 6:

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

Step 7: Inversed Distance method

First we will compute the distance between all polygons:

dist <- nbdists(wm_q, coords, longlat = TRUE)

Apply a simple function:

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

Get the row standardized weight matrix:

**Note , here we use style W

**But style W may not be that robust. We can also use style B

**zero policy is set to true for list of non-neighbors

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

We check the output:

rswm_q$weights[10]

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

Next we will compute the row standardized distance weight matrix:

**Note here we will need to use “ids” which is the inversed distance

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

Check the output:

rswm_ids$weights[1]

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

Check 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 

Step 8: Apply spatial weight matrix:

Spatial lag with row-standardized weights:

Compute the spatial lag:

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

The lag for the first polygon is:

GDPPC.lag[1]

[1] 24847.2

The GDPPC of the first polygon’s neighbor are:

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

[1] 20981 34592 24473 21311 22879

Their total is:

sum(nb1)

[1] 124236

Their average is:

sum(nb1)/5

[1] 24847.2

So their weighted averaged is the value of the lag of the first polygon.

Append the 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)

Joining, by = "NAME_3"

head(hunan)

Simple feature collection with 6 features and 36 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 Shape_Leng Shape_Area  County    City
1 Changde 21098 Anxiang      County   1.869074 0.10056190 Anxiang Changde
2 Changde 21100 Hanshou      County   2.360691 0.19978745 Hanshou Changde
3 Changde 21101  Jinshi County City   1.425620 0.05302413  Jinshi Changde
4 Changde 21102      Li      County   3.474325 0.18908121      Li Changde
5 Changde 21103   Linli      County   2.289506 0.11450357   Linli Changde
6 Changde 21104  Shimen      County   4.171918 0.37194707  Shimen Changde
  avg_wage deposite     FAI Gov_Rev Gov_Exp     GDP GDPPC     GIO   Loan  NIPCR
1    31935   5517.2  3541.0  243.64  1779.5 12482.0 23667  5108.9 2806.9 7693.7
2    32265   7979.0  8665.0  386.13  2062.4 15788.0 20981 13491.0 4550.0 8269.9
3    28692   4581.7  4777.0  373.31  1148.4  8706.9 34592 10935.0 2242.0 8169.9
4    32541  13487.0 16066.0  709.61  2459.5 20322.0 24473 18402.0 6748.0 8377.0
5    32667    564.1  7781.2  336.86  1538.7 10355.0 25554  8214.0  358.0 8143.1
6    33261   8334.4 10531.0  548.33  2178.8 16293.0 27137 17795.0 6026.5 6156.0
   Bed    Emp  EmpR EmpRT Pri_Stu Sec_Stu Household Household_R NOIP Pop_R
1 1931 336.39 270.5 205.9  19.584  17.819     148.1       135.4   53 346.0
2 2560 456.78 388.8 246.7  42.097  33.029     240.2       208.7   95 553.2
3  848 122.78  82.1  61.7   8.723   7.592      81.9        43.7   77  92.4
4 2038 513.44 426.8 227.1  38.975  33.938     268.5       256.0   96 539.7
5 1440 307.36 272.2 100.8  23.286  18.943     129.1       157.2   99 246.6
6 2502 392.05 329.6 193.8  29.245  26.104     190.6       184.7  122 399.2
    RSCG Pop_T    Agri Service Disp_Inc      RORP    ROREmp lag GDPPC
1 3957.9 528.3 4524.41   14100    16610 0.6549309 0.8041262  24847.20
2 4460.5 804.6 6545.35   17727    18925 0.6875466 0.8511756  22724.80
3 3683.0 251.8 2562.46    7525    19498 0.3669579 0.6686757  24143.25
4 7110.2 832.5 7562.34   53160    18985 0.6482883 0.8312558  27737.50
5 3604.9 409.3 3583.91    7031    18604 0.6024921 0.8856065  27270.25
6 6490.7 600.5 5266.51    6981    19275 0.6647794 0.8407091  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 the lag GDPPPC:

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

Spatial lag as sum of neighbouring values:

Calculate the weights:

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

Compute lag variable:

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")

Examine the output:

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

Join the data:

hunan <- left_join(hunan, lag.res)

Joining, by = "NAME_3"

Plot the lag sum:

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:

Assign to new variable:

wm_q1 <- wm_q

Next we will use include.self() to set the attribute to include self in neighbor calculation.

include.self(wm_q1)

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

Obtain the weights:

wm_q1 <- nb2listw(wm_q1)
wm_q1

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

Create lag variable:

lag_w_avg_gpdpc <- lag.listw(wm_q1, 
                             hunan$GDPPC)
lag_w_avg_gpdpc

 [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

Convert to dataframe:

lag.list.wm_q1 <- list(hunan$NAME_3, lag.listw(wm_q1, hunan$GDPPC))
lag_wm_q1.res <- as.data.frame(lag.list.wm_q1)
colnames(lag_wm_q1.res) <- c("NAME_3", "lag_window_avg GDPPC")

Join to mainframe:

hunan <- left_join(hunan, lag_wm_q1.res)

Joining, by = "NAME_3"

Plot the outcome:

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

Spatial Window Sum:

We will not proceed without row standardized weights:

Copy new variable

wm_q1 <- wm_q

Set attribute:

include.self(wm_q1)

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

wm_q1

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

Apply function:

b_weights <- lapply(wm_q1, function(x) 0*x + 1)
b_weights[1]

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

Get weight values:

b_weights2 <- nb2listw(wm_q1, 
                       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

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] 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

Convert result into dataframe:

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

Join to main frame:

hunan <- left_join(hunan, w_sum_gdppc.res)

Joining, by = "NAME_3"

Plot the results:

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