#pacman:: is for introducing pacman without installing it into R environment
pacman::p_load(sf, sfdep, knitr, tmap, tidyverse, plotly)In-class Ex2:Spatial Weights
Overview
This in-class introduces an alternative R package called sfdep. According to Josiah Parry, the developer of the package, “sfdep builds on the great shoulders of spdep package for spatial dependence. sfdep creates an sf and tidyverse friendly interface to the package as well as introduces new functionality that is not present in spdep. sfdep utilizes list columns extensively to make this interface possible.”
Getting Started
Installing and Loading the R packages
Install and load sf,tmap, sfdep, tidyverse and knitr packages into R environment for preparation.
Data Importing
For the purpose of in-class exercise, two data sets will be used:
Hunan county boundary layer. This is a geospatial data set in ESRI shapefile format.
Hunan_2012.csv: This csv file contains selected Hunan’s local development indicators in 2012.
hunan <- st_read(dsn = "data/geospatial",
layer = "Hunan")Reading layer `Hunan' from data source
`D:\KathyChiu77\ISSS624\In-class Ex\In-class_Ex2\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")Combining Both Data Frame by Using Left Join
Check and grasp the basic structure of data.
head(hunan,5)Simple feature collection with 5 features and 7 fields
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 111.2145 ymin: 28.61762 xmax: 112.3013 ymax: 29.95847
Geodetic CRS: WGS 84
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
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...head(hunan2012,5)# A tibble: 5 × 29
County City avg_wage deposite FAI Gov_Rev Gov_Exp GDP GDPPC GIO Loan
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Anhua Yiya… 30544 10967 6832. 457. 2703 13225 14567 9277. 3955.
2 Anren Chen… 28058 4599. 6386. 221. 1455. 4941. 12761 4189. 2555.
3 Anxiang Chan… 31935 5517. 3541 244. 1780. 12482 23667 5109. 2807.
4 Baojing Huna… 30843 2250 1005. 193. 1379. 4088. 14563 3624. 1254.
5 Chaling Zhuz… 31251 8241. 6508. 620. 1947 11585 20078 9158. 4287.
# ℹ 18 more variables: 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>hunan_GDPPC <- left_join(hunan,hunan2012) %>%
select(1:4,7,15)By using left_join, the selected column (1, 2, 3, 4, 7, 15) of data frame hunan will be retained in the new one. Notably, the column geometry will be auto-saved for geospatial data.
Plotting a choropleth map
tmap_mode("plot")
tm_shape(hunan_GDPPC) +
tm_fill("GDPPC",
style = "quantile",
palette = "Blues",
title = "GDPPC") +
tm_borders(alpha = 0.5) +
tm_layout(main.title = "Distribution of GDP per capita by district, Hunan Province",
main.title.position = "center",
main.title.size = 1.2,
legend.height = 0.45,
legend.width = 0.35,
frame = TRUE) +
tm_compass(type="8star", size = 2) +
tm_scale_bar() +
tm_grid(alpha =0.2)
Deriving Contiguity Spatial Weights
By and large, there are two types of spatial weights, they are contiguity wights and distance-based weights. In this section, you will learn how to derive contiguity spatial weights by using sfdep.
Two steps are required to derive a contiguity spatial weights, they are:
identifying contiguity neighbour list by
st_contiguity()of sfdep package, andderiving the contiguity spatial weights by using
st_weights()of sfdep package
In this section, we will learn how to derive the contiguity neighbour list and contiguity spatial weights separately. Then, we will learn how to combine both steps into a single process.
Identifying contiguity neighbours: Queen’s method
In the code chunk below st_contiguity() is used to derive a contiguity neighbour list by using Queen’s method.
nb_queen <- hunan_GDPPC %>%
mutate(nb = st_contiguity(geometry),
.before = 1)The code chunk below is used to print the summary of the first lag neighbour list (i.e. nb) .
summary(nb_queen$nb)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 linksThe summary report above shows that there are 88 area units in Hunan province. The most connected area unit has 11 neighbours. There are two are units with only one neighbour.
To view the content of the data table, you can either display the output data frame on RStudio data viewer or by printing out the first ten records by using the code chunk below.
nb_queenSimple 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:
nb NAME_2 ID_3 NAME_3 ENGTYPE_3
1 2, 3, 4, 57, 85 Changde 21098 Anxiang County
2 1, 57, 58, 78, 85 Changde 21100 Hanshou County
3 1, 4, 5, 85 Changde 21101 Jinshi County City
4 1, 3, 5, 6 Changde 21102 Li County
5 3, 4, 6, 85 Changde 21103 Linli County
6 4, 5, 69, 75, 85 Changde 21104 Shimen County
7 67, 71, 74, 84 Changsha 21109 Liuyang County City
8 9, 46, 47, 56, 78, 80, 86 Changsha 21110 Ningxiang County
9 8, 66, 68, 78, 84, 86 Changsha 21111 Wangcheng County
10 16, 17, 19, 20, 22, 70, 72, 73 Chenzhou 21112 Anren County
County GDPPC geometry
1 Anxiang 23667 POLYGON ((112.0625 29.75523...
2 Hanshou 20981 POLYGON ((112.2288 29.11684...
3 Jinshi 34592 POLYGON ((111.8927 29.6013,...
4 Li 24473 POLYGON ((111.3731 29.94649...
5 Linli 25554 POLYGON ((111.6324 29.76288...
6 Shimen 27137 POLYGON ((110.8825 30.11675...
7 Liuyang 63118 POLYGON ((113.9905 28.5682,...
8 Ningxiang 62202 POLYGON ((112.7181 28.38299...
9 Wangcheng 70666 POLYGON ((112.7914 28.52688...
10 Anren 12761 POLYGON ((113.1757 26.82734...The print shows that polygon 1 has five neighbours. They are polygons number 2, 3, 4, 57,and 85.
One of the advantage of sfdep over spdep is that the output is an sf tibble data frame.
kable(head(nb_queen,
n=10))| nb | NAME_2 | ID_3 | NAME_3 | ENGTYPE_3 | County | GDPPC | geometry |
|---|---|---|---|---|---|---|---|
| 2, 3, 4, 57, 85 | Changde | 21098 | Anxiang | County | Anxiang | 23667 | POLYGON ((112.0625 29.75523… |
| 1, 57, 58, 78, 85 | Changde | 21100 | Hanshou | County | Hanshou | 20981 | POLYGON ((112.2288 29.11684… |
| 1, 4, 5, 85 | Changde | 21101 | Jinshi | County City | Jinshi | 34592 | POLYGON ((111.8927 29.6013,… |
| 1, 3, 5, 6 | Changde | 21102 | Li | County | Li | 24473 | POLYGON ((111.3731 29.94649… |
| 3, 4, 6, 85 | Changde | 21103 | Linli | County | Linli | 25554 | POLYGON ((111.6324 29.76288… |
| 4, 5, 69, 75, 85 | Changde | 21104 | Shimen | County | Shimen | 27137 | POLYGON ((110.8825 30.11675… |
| 67, 71, 74, 84 | Changsha | 21109 | Liuyang | County City | Liuyang | 63118 | POLYGON ((113.9905 28.5682,… |
| 9, 46, 47, 56, 78, 80, 86 | Changsha | 21110 | Ningxiang | County | Ningxiang | 62202 | POLYGON ((112.7181 28.38299… |
| 8, 66, 68, 78, 84, 86 | Changsha | 21111 | Wangcheng | County | Wangcheng | 70666 | POLYGON ((112.7914 28.52688… |
| 16, 17, 19, 20, 22, 70, 72, 73 | Chenzhou | 21112 | Anren | County | Anren | 12761 | POLYGON ((113.1757 26.82734… |
Identify contiguity neighbours: Rooks’ method
nb_rook <- hunan_GDPPC %>%
mutate(nb = st_contiguity(geometry,
queen = FALSE),
.before = 1)Identifying higher order neighbors
There are times that we need to identify high order contiguity neighbours. To accomplish the task, st_nb_lag_cumul() should be used as shown in the code chunk below.
nb2_queen <- hunan_GDPPC %>%
mutate(nb = st_contiguity(geometry),
nb2 = st_nb_lag_cumul(nb, 2),
.before = 1)Note that if the order is 2, the result contains both 1st and 2nd order neighbors as shown on the print below.
nb2_queenSimple feature collection with 88 features and 8 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:
nb
1 2, 3, 4, 57, 85
2 1, 57, 58, 78, 85
3 1, 4, 5, 85
4 1, 3, 5, 6
5 3, 4, 6, 85
6 4, 5, 69, 75, 85
7 67, 71, 74, 84
8 9, 46, 47, 56, 78, 80, 86
9 8, 66, 68, 78, 84, 86
10 16, 17, 19, 20, 22, 70, 72, 73
nb2
1 2, 3, 4, 5, 6, 32, 56, 57, 58, 64, 69, 75, 76, 78, 85
2 1, 3, 4, 5, 6, 8, 9, 32, 56, 57, 58, 64, 68, 69, 75, 76, 78, 85
3 1, 2, 4, 5, 6, 32, 56, 57, 69, 75, 78, 85
4 1, 2, 3, 5, 6, 57, 69, 75, 85
5 1, 2, 3, 4, 6, 32, 56, 57, 69, 75, 78, 85
6 1, 2, 3, 4, 5, 32, 53, 55, 56, 57, 69, 75, 78, 85
7 9, 19, 66, 67, 71, 73, 74, 76, 84, 86
8 2, 9, 19, 21, 31, 32, 34, 35, 36, 41, 45, 46, 47, 56, 58, 66, 68, 74, 78, 80, 84, 85, 86
9 2, 7, 8, 19, 21, 35, 46, 47, 56, 58, 66, 67, 68, 74, 76, 78, 80, 84, 85, 86
10 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 70, 71, 72, 73, 74, 82, 83, 86
NAME_2 ID_3 NAME_3 ENGTYPE_3 County GDPPC
1 Changde 21098 Anxiang County Anxiang 23667
2 Changde 21100 Hanshou County Hanshou 20981
3 Changde 21101 Jinshi County City Jinshi 34592
4 Changde 21102 Li County Li 24473
5 Changde 21103 Linli County Linli 25554
6 Changde 21104 Shimen County Shimen 27137
7 Changsha 21109 Liuyang County City Liuyang 63118
8 Changsha 21110 Ningxiang County Ningxiang 62202
9 Changsha 21111 Wangcheng County Wangcheng 70666
10 Chenzhou 21112 Anren County Anren 12761
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...Deriving contiguity weights: Queen’s method
Now, you are ready to compute the contiguity weights by using st_weights() of sfdep package.
Deriving contiguity weights: Queen’s method
In the code chunk below, queen method is used to derive the contiguity weights.
wm_q <- hunan_GDPPC %>%
mutate(nb = st_contiguity(geometry),
wt = st_weights(nb,
style = "W"),
.before = 1) Notice that st_weights() provides tree arguments, they are:
nb: A neighbor list object as created by st_neighbors().
style: Default “W” for row standardized weights. This value can also be “B”, “C”, “U”, “minmax”, and “S”. B is the basic binary coding, W is row standardised (sums over all links to n), C is globally standardised (sums over all links to n), U is equal to C divided by the number of neighbours (sums over all links to unity), while S is the variance-stabilizing coding scheme proposed by Tiefelsdorf et al. 1999, p. 167-168 (sums over all links to n).
allow_zero: If TRUE, assigns zero as lagged value to zone without neighbors.
wm_qSimple feature collection with 88 features and 8 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:
nb
1 2, 3, 4, 57, 85
2 1, 57, 58, 78, 85
3 1, 4, 5, 85
4 1, 3, 5, 6
5 3, 4, 6, 85
6 4, 5, 69, 75, 85
7 67, 71, 74, 84
8 9, 46, 47, 56, 78, 80, 86
9 8, 66, 68, 78, 84, 86
10 16, 17, 19, 20, 22, 70, 72, 73
wt
1 0.2, 0.2, 0.2, 0.2, 0.2
2 0.2, 0.2, 0.2, 0.2, 0.2
3 0.25, 0.25, 0.25, 0.25
4 0.25, 0.25, 0.25, 0.25
5 0.25, 0.25, 0.25, 0.25
6 0.2, 0.2, 0.2, 0.2, 0.2
7 0.25, 0.25, 0.25, 0.25
8 0.1428571, 0.1428571, 0.1428571, 0.1428571, 0.1428571, 0.1428571, 0.1428571
9 0.1666667, 0.1666667, 0.1666667, 0.1666667, 0.1666667, 0.1666667
10 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125
NAME_2 ID_3 NAME_3 ENGTYPE_3 County GDPPC
1 Changde 21098 Anxiang County Anxiang 23667
2 Changde 21100 Hanshou County Hanshou 20981
3 Changde 21101 Jinshi County City Jinshi 34592
4 Changde 21102 Li County Li 24473
5 Changde 21103 Linli County Linli 25554
6 Changde 21104 Shimen County Shimen 27137
7 Changsha 21109 Liuyang County City Liuyang 63118
8 Changsha 21110 Ningxiang County Ningxiang 62202
9 Changsha 21111 Wangcheng County Wangcheng 70666
10 Chenzhou 21112 Anren County Anren 12761
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...Distance-based Weights
There are three popularly used distance-based spatial weights, they are:
fixed distance weights,
adaptive distance weights, and
inverse distance weights (IDW).
Deriving fixed distance weights
Before we can derive the fixed distance weights, we need to determine the upper limit for distance band by using the steps below:
geo <- sf::st_geometry(hunan_GDPPC)
nb <- st_knn(geo, longlat = TRUE)
dists <- unlist(st_nb_dists(geo, nb))Now, we will go ahead to derive summary statistics of the nearest neighbour distances vector (i.e. dists) by usign the coced chunk below.
summary(dists) Min. 1st Qu. Median Mean 3rd Qu. Max.
21.56 29.11 36.89 37.34 43.21 65.80 The summary statistics report above shows that the maximum nearest neighbour distance is 65.80km. By using a threshold value of 66km will ensure that each area will have at least one neighbour.
Now we will go ahead to compute the fixed distance weights by using the code chunk below.
wm_fd <- hunan_GDPPC %>%
mutate(nb = st_dist_band(geometry,
upper = 66),
wt = st_weights(nb),
.before = 1)Deriving adaptive distance weights
In this section, you will derive an adaptive spatial weights by using the code chunk below.
wm_ad <- hunan_GDPPC %>%
mutate(nb = st_knn(geometry,
k=8),
wt = st_weights(nb),
.before = 1)Calculate inverse distance weights
In this section, you will derive an inverse distance weights by using the code chunk below.
wm_idw <- hunan_GDPPC %>%
mutate(nb = st_contiguity(geometry),
wts = st_inverse_distance(nb, geometry,
scale = 1,
alpha = 1),
.before = 1)