pacman::p_load(sf, spdep,
tmap,
tidyverse,
DT, knitr, kableExtra)
# - Creates a package list containing the necessary R packages
# - Checks if the R packages in the package list have been installed
# - If not installed, will installed the missing packages & launch into R environment.
1 Overview
Learning how to compute Global Measure of Spatial Autocorrelation (GLSA) by using spdep package, including:
- import geospatial data using appropriate function(s) of sf package
- import csv file using appropriate function of readr package
- perform relational join using appropriate join function of dplyr package
- compute Global Spatial Autocorrelation (GSA) statistics by using appropriate functions of spdep package
- plot Moran scatterplot
- compute and plot spatial correlogram using appropriate function of spdep package
- compute Local Indicator of Spatial Association (LISA) statistics for detecting clusters and outliers by using appropriate functions spdep package
- compute Getis-Ord’s Gi-statistics for detecting hot spot or/and cold spot area by using appropriate functions of spdep package
- visualise the analysis output by using tmap package.
The Analytical Question
In spatial policy, one of the main development objective of the local government and planners is to ensure equal distribution of development in the province. Our task in this study, hence, is to apply appropriate spatial statistical methods to discover if development are even distributed geographically. If the answer is No, then, our next question will be “is there sign of spatial clustering?” And, if the answer for this question is Yes, then our next question will be “where are these clusters?”
In this case study, we are interested to examine the spatial pattern of a selected development indicator (i.e. GDP per capita) of Hunan Provice, People Republic of China.
2 The Packages
| Package | Description |
|---|---|
| spdep | To compute spatial weights, Global and Local Spatial Autocorrelation statistics (eg plot Moran scatterplot, compute and plot correlogram) |
| sf | For importing, managing, and processing geospatial data |
| tidyverse | A collection of functions for performing data science task such as importing, tidying, wrangling data and visualising data. |
| tmap | To prepare cartographic quality choropleth map |
| DT, knitr and kableExtra | For building tables |
3 The Data
Two data sets will be used in this hands-on exercise, they are:
| Type | Name | Details |
|---|---|---|
| Geospatial | Hunan |
|
| Aspatial | Hunan_2012 |
|
3.1 Loading the Data
In this section, you will learn how to bring a geospatial data and its associated attribute table into R environment. The geospatial data is in ESRI shapefile format and the attribute table is in csv fomat.
The code chunk below uses st_read() of sf package to import Hunan shapefile into R.
#output: simple features object
hunan <- st_read(dsn = "data/geospatial",
layer = "Hunan")Reading layer `Hunan' from data source
`C:\kytjy\ISSS626-GAA\Hands-on_Ex\Hands-on_Ex05\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 88 features and 7 fields
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 108.7831 ymin: 24.6342 xmax: 114.2544 ymax: 30.12812
Geodetic CRS: WGS 84| NAME_2 | ID_3 | NAME_3 | ENGTYPE_3 | Shape_Leng | Shape_Area | County | geometry |
|---|---|---|---|---|---|---|---|
| Changde | 21098 | Anxiang | County | 1.8690742 | 0.1005619 | Anxiang | POLYGON ((112.0625 29.75523... |
| Changde | 21100 | Hanshou | County | 2.3606914 | 0.1997875 | Hanshou | POLYGON ((112.2288 29.11684... |
| Changde | 21101 | Jinshi | County City | 1.4256199 | 0.0530241 | Jinshi | POLYGON ((111.8927 29.6013,... |
| Changde | 21102 | Li | County | 3.4743245 | 0.1890812 | Li | POLYGON ((111.3731 29.94649... |
| Changde | 21103 | Linli | County | 2.2895061 | 0.1145036 | Linli | POLYGON ((111.6324 29.76288... |
| Changde | 21104 | Shimen | County | 4.1719181 | 0.3719471 | Shimen | POLYGON ((110.8825 30.11675... |
| Changsha | 21109 | Liuyang | County City | 4.0605788 | 0.4601679 | Liuyang | POLYGON ((113.9905 28.5682,... |
| Changsha | 21110 | Ningxiang | County | 3.3237542 | 0.2661420 | Ningxiang | POLYGON ((112.7181 28.38299... |
| Changsha | 21111 | Wangcheng | County | 2.2920930 | 0.1304916 | Wangcheng | POLYGON ((112.7914 28.52688... |
| Chenzhou | 21112 | Anren | County | 2.2407387 | 0.1334394 | Anren | POLYGON ((113.1757 26.82734... |
| Chenzhou | 21115 | Guidong | County | 2.0467289 | 0.1285299 | Guidong | POLYGON ((114.1799 26.20117... |
| Chenzhou | 21117 | Jiahe | County | 1.5038242 | 0.0631237 | Jiahe | POLYGON ((112.4425 25.74358... |
| Chenzhou | 21118 | Linwu | County | 2.0512481 | 0.1244964 | Linwu | POLYGON ((112.5914 25.55143... |
| Chenzhou | 21119 | Rucheng | County | 2.7155640 | 0.2176296 | Rucheng | POLYGON ((113.6759 25.87578... |
| Chenzhou | 21120 | Yizhang | County | 3.2765386 | 0.1935418 | Yizhang | POLYGON ((113.2621 25.68394... |
| Chenzhou | 21121 | Yongxing | County | 2.9211528 | 0.1767181 | Yongxing | POLYGON ((113.3169 26.41843... |
| Chenzhou | 21122 | Zixing | County City | 2.6995368 | 0.2476280 | Zixing | POLYGON ((113.7311 26.16259... |
| Hengyang | 21123 | Changning | County City | 2.4013569 | 0.1863642 | Changning | POLYGON ((112.6144 26.60198... |
| Hengyang | 21124 | Hengdong | County | 2.7098301 | 0.1756985 | Hengdong | POLYGON ((113.1056 27.21007... |
| Hengyang | 21125 | Hengnan | County | 3.7804926 | 0.2408050 | Hengnan | POLYGON ((112.7599 26.98149... |
| Hengyang | 21126 | Hengshan | County | 2.3513543 | 0.0899128 | Hengshan | POLYGON ((112.607 27.4689, ... |
| Hengyang | 21129 | Leiyang | County | 2.7427498 | 0.2426073 | Leiyang | POLYGON ((112.9996 26.69276... |
| Hengyang | 21130 | Qidong | County | 3.0714217 | 0.1733332 | Qidong | POLYGON ((111.7818 27.0383,... |
| Huaihua | 21131 | Chenxi | County | 3.0228314 | 0.1821929 | Chenxi | POLYGON ((110.2624 28.21778... |
| Huaihua | 21134 | Zhongfang | County | 2.9023763 | 0.1994978 | Zhongfang | POLYGON ((109.9431 27.72858... |
| Huaihua | 21135 | Huitong | County | 3.1096821 | 0.2053454 | Huitong | POLYGON ((109.9419 27.10512... |
| Huaihua | 21136 | Jingzhou | County | 2.8584583 | 0.1988991 | Jingzhou | POLYGON ((109.8186 26.75842... |
| Huaihua | 21137 | Mayang | Autonomous County | 2.3274351 | 0.1462606 | Mayang | POLYGON ((109.795 27.98008,... |
| Huaihua | 21138 | Tongdao | Autonomous County | 2.5711292 | 0.2021613 | Tongdao | POLYGON ((109.9294 26.46561... |
| Huaihua | 21139 | Xinhuang | Autonomous County | 2.1443973 | 0.1377764 | Xinhuang | POLYGON ((109.227 27.43733,... |
| Huaihua | 21140 | Xupu | County | 4.0350213 | 0.3136471 | Xupu | POLYGON ((110.7189 28.30485... |
| Huaihua | 21141 | Yuanling | County | 4.1642914 | 0.5345233 | Yuanling | POLYGON ((110.9652 28.99895... |
| Huaihua | 21142 | Zhijiang | Autonomous County | 2.4452310 | 0.1906027 | Zhijiang | POLYGON ((109.8818 27.60661... |
| Loudi | 21143 | Lengshuijiang | County City | 0.9753557 | 0.0372343 | Lengshuijiang | POLYGON ((111.5307 27.81472... |
| Loudi | 21146 | Shuangfeng | County | 2.4012680 | 0.1565776 | Shuangfeng | POLYGON ((112.263 27.70421,... |
| Loudi | 21147 | Xinhua | County | 3.3284533 | 0.3361624 | Xinhua | POLYGON ((111.3345 28.19642... |
| Shaoyang | 21148 | Chengbu | Autonomous County | 2.9374722 | 0.2362023 | Chengbu | POLYGON ((110.4455 26.69317... |
| Yongzhou | 21149 | Dongan | District | 3.2132100 | 0.1983914 | Dongan | POLYGON ((111.4531 26.86812... |
| Shaoyang | 21150 | Dongkou | County | 2.9425568 | 0.1971258 | Dongkou | POLYGON ((110.6622 27.37305... |
| Shaoyang | 21151 | Longhui | County | 2.7208650 | 0.2578820 | Longhui | POLYGON ((110.985 27.65983,... |
| Shaoyang | 21152 | Shaodong | County | 2.3029031 | 0.1701016 | Shaodong | POLYGON ((111.9054 27.40254... |
| Shaoyang | 21155 | Suining | County | 3.3043615 | 0.2659378 | Suining | POLYGON ((110.389 27.10006,... |
| Shaoyang | 21156 | Wugang | County City | 2.2565865 | 0.1400498 | Wugang | POLYGON ((110.9878 27.03345... |
| Shaoyang | 21157 | Xinning | County | 3.3414094 | 0.2487593 | Xinning | POLYGON ((111.0736 26.84627... |
| Shaoyang | 21158 | Xinshao | County | 2.2955891 | 0.1658312 | Xinshao | POLYGON ((111.6013 27.58275... |
| Xiangtan | 21159 | Shaoshan | County City | 0.7722034 | 0.0212792 | Shaoshan | POLYGON ((112.5391 27.97742... |
| Xiangtan | 21162 | Xiangxiang | County City | 3.0755761 | 0.1840808 | Xiangxiang | POLYGON ((112.4549 28.05783... |
| Xiangxi Tujia and Miao | 21163 | Baojing | County | 2.5569785 | 0.1606901 | Baojing | POLYGON ((109.7015 28.82844... |
| Xiangxi Tujia and Miao | 21164 | Fenghuang | County | 2.2928893 | 0.1596618 | Fenghuang | POLYGON ((109.5239 28.19206... |
| Xiangxi Tujia and Miao | 21165 | Guzhang | County | 1.7973808 | 0.1202073 | Guzhang | POLYGON ((109.8968 28.74034... |
| Xiangxi Tujia and Miao | 21166 | Huayuan | County | 1.7921938 | 0.1025162 | Huayuan | POLYGON ((109.5647 28.61712... |
| Xiangxi Tujia and Miao | 21167 | Jishou | County City | 1.8826069 | 0.0973363 | Jishou | POLYGON ((109.8375 28.4696,... |
| Xiangxi Tujia and Miao | 21168 | Longshan | County | 2.9782522 | 0.2919091 | Longshan | POLYGON ((109.6337 29.62521... |
| Xiangxi Tujia and Miao | 21169 | Luxi | County | 2.2051733 | 0.1434018 | Luxi | POLYGON ((110.1067 28.41835... |
| Xiangxi Tujia and Miao | 21170 | Yongshun | County | 3.0959707 | 0.3551324 | Yongshun | POLYGON ((110.0003 29.29499... |
| Yiyang | 21171 | Anhua | County | 4.5835050 | 0.4510648 | Anhua | POLYGON ((111.6034 28.63716... |
| Yiyang | 21172 | Nan | County | 2.3011103 | 0.1247939 | Nan | POLYGON ((112.3232 29.46074... |
| Yiyang | 21176 | Yuanjiang | County City | 2.3268236 | 0.1886048 | Yuanjiang | POLYGON ((112.4391 29.1791,... |
| Yongzhou | 21178 | Jianghua | Autonomous County | 3.3360379 | 0.2927690 | Jianghua | POLYGON ((111.6461 25.29661... |
| Yongzhou | 21180 | Lanshan | County | 2.3556792 | 0.1603531 | Lanshan | POLYGON ((112.2286 25.61123... |
| Yongzhou | 21183 | Ningyuan | County | 3.3322291 | 0.2266737 | Ningyuan | POLYGON ((112.0715 26.09892... |
| Yongzhou | 21185 | Shuangpai | County | 2.3877440 | 0.1540255 | Shuangpai | POLYGON ((111.8864 26.11957... |
| Yongzhou | 21186 | Xintian | County | 1.7274574 | 0.0894019 | Xintian | POLYGON ((112.2578 26.0796,... |
| Yueyang | 21187 | Huarong | County | 2.8178435 | 0.1678359 | Huarong | POLYGON ((112.9242 29.69134... |
| Yueyang | 21188 | Linxiang | County City | 2.5975997 | 0.1568525 | Linxiang | POLYGON ((113.5502 29.67418... |
| Yueyang | 21189 | Miluo | County City | 2.4474057 | 0.1497881 | Miluo | POLYGON ((112.9902 29.02139... |
| Yueyang | 21190 | Pingjiang | County | 3.2177944 | 0.3786800 | Pingjiang | POLYGON ((113.8436 29.06152... |
| Yueyang | 21191 | Xiangyin | County | 2.3515063 | 0.1491429 | Xiangyin | POLYGON ((112.9173 28.98264... |
| Zhangjiajie | 21194 | Cili | County | 2.8940385 | 0.3232206 | Cili | POLYGON ((110.8822 29.69017... |
| Zhuzhou | 21197 | Chaling | County | 2.2375615 | 0.2278921 | Chaling | POLYGON ((113.7666 27.10573... |
| Zhuzhou | 21198 | Liling | County City | 2.2435440 | 0.1960655 | Liling | POLYGON ((113.5673 27.94346... |
| Zhuzhou | 21199 | Yanling | County | 2.1078954 | 0.1849090 | Yanling | POLYGON ((113.9292 26.6154,... |
| Zhuzhou | 21200 | You | County | 2.8904505 | 0.2436366 | You | POLYGON ((113.5879 27.41324... |
| Zhuzhou | 21201 | Zhuzhou | District | 0.9331877 | 0.0373488 | Zhuzhou | POLYGON ((113.2493 28.02411... |
| Zhangjiajie | 21196 | Sangzhi | County | 3.3475449 | 0.3216362 | Sangzhi | POLYGON ((110.556 29.40543,... |
| Yueyang | 21192 | Yueyang | District | 2.5710437 | 0.1047594 | Yueyang | POLYGON ((113.343 29.61064,... |
| Yongzhou | 21184 | Qiyang | County | 3.1835301 | 0.2275458 | Qiyang | POLYGON ((111.5563 26.81318... |
| Yiyang | 21173 | Taojiang | County | 2.6080229 | 0.1905982 | Taojiang | POLYGON ((112.0508 28.67265... |
| Shaoyang | 21153 | Shaoyang | County City | 0.9765399 | 0.0316779 | Shaoyang | POLYGON ((111.5013 27.30207... |
| Loudi | 21144 | Lianyuan | County City | 2.8007253 | 0.2057341 | Lianyuan | POLYGON ((111.6789 28.02946... |
| Huaihua | 21132 | Hongjiang | District | 3.3031522 | 0.1994795 | Hongjiang | POLYGON ((110.1441 27.47513... |
| Hengyang | 21127 | Hengyang | County City | 0.9035944 | 0.0349171 | Hengyang | POLYGON ((112.7144 26.98613... |
| Chenzhou | 21116 | Guiyang | County | 3.6939698 | 0.2668106 | Guiyang | POLYGON ((113.0811 26.04963... |
| Changsha | 21107 | Changsha | District | 0.9536480 | 0.0320942 | Changsha | POLYGON ((112.9421 28.03722... |
| Changde | 21105 | Taoyuan | County | 4.1225866 | 0.4126555 | Taoyuan | POLYGON ((112.0612 29.32855... |
| Xiangtan | 21160 | Xiangtan | County City | 0.8480602 | 0.0253653 | Xiangtan | POLYGON ((113.0426 27.8942,... |
| Yongzhou | 21177 | Dao | County | 2.7674949 | 0.2206642 | Dao | POLYGON ((111.498 25.81679,... |
| Yongzhou | 21179 | Jiangyong | County | 2.2995970 | 0.1473782 | Jiangyong | POLYGON ((111.3659 25.39472... |
Next, we will import Hunan_2012.csv into R by using read_csv() of readr package.
#output: R dataframe class
hunan2012 <- read_csv("data/aspatial/Hunan_2012.csv")| County | City | avg_wage | deposite | FAI | Gov_Rev | Gov_Exp | GDP | GDPPC | GIO | Loan | NIPCR | Bed | Emp | EmpR | EmpRT | Pri_Stu | Sec_Stu | Household | Household_R | NOIP | Pop_R | RSCG | Pop_T | Agri | Service | Disp_Inc | RORP | ROREmp |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Anhua | Yiyang | 30544 | 10967.0 | 6831.7 | 456.72 | 2703.00 | 13225.0 | 14567 | 9276.90 | 3954.90 | 3528.3 | 2718 | 494.310 | 441.4 | 338.0 | 54.175 | 32.830 | 290.400 | 234.5 | 101 | 670.3 | 5760.60 | 910.8 | 4942.253 | 5414.5 | 12373 | 0.7359464 | 0.8929619 |
| Anren | Chenzhou | 28058 | 4598.9 | 6386.1 | 220.57 | 1454.70 | 4941.2 | 12761 | 4189.20 | 2555.30 | 3271.8 | 970 | 290.820 | 255.4 | 99.4 | 33.171 | 17.505 | 104.600 | 121.9 | 34 | 243.2 | 2386.40 | 388.7 | 2357.764 | 3814.1 | 16072 | 0.6256753 | 0.8782065 |
| Anxiang | Changde | 31935 | 5517.2 | 3541.0 | 243.64 | 1779.50 | 12482.0 | 23667 | 5108.90 | 2806.90 | 7693.7 | 1931 | 336.390 | 270.5 | 205.9 | 19.584 | 17.819 | 148.100 | 135.4 | 53 | 346.0 | 3957.90 | 528.3 | 4524.410 | 14100.0 | 16610 | 0.6549309 | 0.8041262 |
| Baojing | Hunan West | 30843 | 2250.0 | 1005.4 | 192.59 | 1379.10 | 4087.9 | 14563 | 3623.50 | 1253.70 | 4191.3 | 927 | 195.170 | 145.6 | 116.4 | 19.249 | 11.831 | 73.200 | 69.9 | 18 | 184.1 | 768.04 | 281.3 | 1118.561 | 541.8 | 13455 | 0.6544614 | 0.7460163 |
| Chaling | Zhuzhou | 31251 | 8241.4 | 6508.4 | 620.19 | 1947.00 | 11585.0 | 20078 | 9157.70 | 4287.40 | 3887.7 | 1449 | 330.290 | 299.0 | 154.0 | 33.906 | 20.548 | 148.700 | 139.4 | 106 | 301.6 | 4009.50 | 578.4 | 3793.550 | 5444.0 | 20461 | 0.5214385 | 0.9052651 |
| Changning | Hengyang | 28518 | 10860.0 | 7920.0 | 769.86 | 2631.60 | 19886.0 | 24418 | 37392.00 | 4242.80 | 9528.0 | 3605 | 548.610 | 415.1 | 273.7 | 81.831 | 44.485 | 211.200 | 211.7 | 115 | 448.2 | 5220.40 | 816.3 | 6430.782 | 13074.6 | 20868 | 0.5490628 | 0.7566395 |
| Changsha | Changsha | 54540 | 24332.0 | 33624.0 | 5350.00 | 7885.50 | 88009.0 | 88656 | 51361.00 | 40534.00 | 17070.0 | 3310 | 670.820 | 452.0 | 219.4 | 59.151 | 39.685 | 300.300 | 248.4 | 214 | 475.1 | 22604.00 | 998.6 | 13107.148 | 17726.6 | 183252 | 0.4757661 | 0.6738022 |
| Chengbu | Shaoyang | 28597 | 2580.6 | 1922.3 | 160.73 | 1191.60 | 2569.5 | 10132 | 1681.40 | 1232.00 | 3271.8 | 582 | 162.480 | 127.6 | 94.4 | 18.751 | 7.869 | 76.100 | 59.6 | 17 | 189.6 | 1173.80 | 256.7 | 1356.950 | 1215.1 | 12379 | 0.7386054 | 0.7853274 |
| Chenxi | Huaihua | 33580 | 4990.0 | 5818.4 | 460.49 | 1724.20 | 7755.2 | 17026 | 6644.50 | 3220.00 | 4777.0 | 2170 | 308.430 | 214.4 | 174.8 | 26.706 | 14.591 | 139.500 | 110.5 | 55 | 311.7 | 2570.60 | 456.7 | 2257.520 | 1306.3 | 14595 | 0.6825049 | 0.6951334 |
| Cili | Zhangjiajie | 33099 | 8116.9 | 4498.1 | 499.77 | 2306.20 | 11378.0 | 18714 | 5843.30 | 5503.40 | 5031.8 | 2179 | 381.200 | 334.8 | 264.3 | 34.918 | 27.020 | 211.400 | 174.5 | 70 | 379.4 | 3116.90 | 610.4 | 3112.731 | 5005.6 | 15603 | 0.6215596 | 0.8782791 |
| Dao | Yongzhou | 32541 | 7245.0 | 7922.0 | 461.66 | 2013.50 | 11034.0 | 18059 | 2393.80 | 2873.50 | 9000.0 | 1588 | 381.530 | 344.3 | 178.3 | 65.790 | 31.430 | 158.700 | 157.9 | 44 | 388.2 | 2898.80 | 613.6 | 5602.035 | 8411.1 | 16305 | 0.6326597 | 0.9024192 |
| Dongan | Yongzhou | 36713 | 6549.3 | 9158.0 | 434.07 | 1720.60 | 11495.0 | 20901 | 11597.00 | 3320.60 | 9116.7 | 1305 | 322.250 | 278.1 | 163.6 | 39.419 | 20.661 | 166.500 | 163.0 | 84 | 366.0 | 3106.30 | 551.2 | 4866.481 | 6784.4 | 20265 | 0.6640058 | 0.8629946 |
| Dongkou | Shaoyang | 31483 | 9489.6 | 8703.2 | 374.96 | 2209.50 | 10286.0 | 13240 | 10568.00 | 4120.30 | 3792.5 | 1620 | 583.560 | 499.2 | 263.2 | 69.845 | 43.194 | 262.400 | 220.4 | 74 | 523.1 | 3229.10 | 780.9 | 6025.184 | 9116.8 | 15375 | 0.6698681 | 0.8554390 |
| Fenghuang | Hunan West | 31608 | 4008.7 | 2550.0 | 406.51 | 1763.60 | 4681.2 | 13382 | 848.99 | 2863.00 | 4681.2 | 1212 | 250.730 | 195.4 | 151.8 | 33.379 | 17.690 | 90.100 | 80.5 | 17 | 255.5 | 2605.40 | 351.3 | 1206.261 | 651.1 | 14281 | 0.7272986 | 0.7793244 |
| Guidong | Chenzhou | 30149 | 2200.1 | 2512.9 | 111.19 | 880.00 | 1955.9 | 8497 | 1202.60 | 1437.20 | 3130.4 | 567 | 138.530 | 115.2 | 56.9 | 13.437 | 7.091 | 64.800 | 65.4 | 14 | 150.1 | 486.10 | 231.8 | 630.016 | 911.1 | 12290 | 0.6475410 | 0.8315888 |
| Guiyang | Chenzhou | 41394 | 9664.8 | 15712.0 | 1309.20 | 2727.50 | 23023.0 | 32853 | 36820.00 | 4860.10 | 10271.0 | 2237 | 517.180 | 430.9 | 242.0 | 69.344 | 33.568 | 231.800 | 217.5 | 127 | 420.4 | 6281.80 | 704.1 | 8804.639 | 14791.5 | 64517 | 0.5970743 | 0.8331722 |
| Guzhang | Hunan West | 28610 | 1563.8 | 1021.7 | 108.40 | 959.60 | 1490.4 | 11580 | 513.95 | 849.56 | 3595.9 | 392 | 98.421 | 74.6 | 56.7 | 8.718 | 6.288 | 35.200 | 31.4 | 10 | 85.2 | 354.48 | 129.0 | 527.230 | 504.0 | 11954 | 0.6604651 | 0.7579683 |
| Hanshou | Changde | 32265 | 7979.0 | 8665.0 | 386.13 | 2062.40 | 15788.0 | 20981 | 13491.00 | 4550.00 | 8269.9 | 2560 | 456.780 | 388.8 | 246.7 | 42.097 | 33.029 | 240.200 | 208.7 | 95 | 553.2 | 4460.50 | 804.6 | 6545.350 | 17727.0 | 18925 | 0.6875466 | 0.8511756 |
| Hengdong | Hengyang | 30992 | 8661.0 | 6665.0 | 542.25 | 1937.40 | 17409.0 | 27485 | 17305.00 | 4118.00 | 10829.0 | 1859 | 388.340 | 284.5 | 201.0 | 48.983 | 36.120 | 164.400 | 167.4 | 96 | 426.4 | 5127.00 | 634.9 | 5972.961 | 11278.5 | 19800 | 0.6716018 | 0.7326054 |
| Hengnan | Hengyang | 28031 | 3288.9 | 9531.4 | 804.91 | 2894.40 | 21019.0 | 21911 | 20953.00 | 4013.00 | 9872.9 | 2173 | 601.570 | 503.6 | 354.0 | 76.933 | 57.519 | 256.000 | 274.3 | 118 | 629.1 | 5752.60 | 961.4 | 8624.680 | 15914.0 | 18683 | 0.6543582 | 0.8371428 |
| Hengshan | Hengyang | 28688 | 5944.6 | 4871.1 | 451.46 | 1393.70 | 9718.9 | 25172 | 8571.50 | 2221.50 | 10619.0 | 966 | 291.120 | 261.9 | 158.8 | 28.997 | 20.909 | 103.700 | 101.0 | 89 | 256.4 | 1713.70 | 387.0 | 3505.269 | 6233.5 | 17732 | 0.6625323 | 0.8996290 |
| Hengyang | Hengyang | 27760 | 14680.0 | 11145.0 | 597.66 | 2778.80 | 21495.0 | 19382 | 18288.00 | 5549.60 | 10313.0 | 2632 | 686.520 | 500.2 | 313.6 | 88.917 | 64.674 | 299.200 | 247.7 | 120 | 733.4 | 5386.30 | 1111.6 | 12451.938 | 23139.2 | 124392 | 0.6597697 | 0.7286022 |
| Hongjiang | Huaihua | 37686 | 5966.0 | 6515.5 | 623.95 | 2067.80 | 7355.5 | 17733 | 13750.00 | 3272.20 | 6553.5 | 1161 | 229.400 | 199.9 | 132.0 | 23.614 | 18.837 | 136.100 | 124.7 | 76 | 260.9 | 1744.20 | 415.8 | 2588.250 | 202.8 | 27334 | 0.6274651 | 0.8714037 |
| Huarong | Yueyang | 26832 | 8116.4 | 14292.0 | 365.84 | 1933.90 | 21654.0 | 30413 | 40193.00 | 4564.80 | 10367.0 | 1500 | 442.970 | 359.2 | 252.9 | 31.601 | 26.933 | 202.300 | 170.2 | 151 | 430.3 | 6348.90 | 714.1 | 7690.520 | 10050.6 | 21501 | 0.6025767 | 0.8108901 |
| Huayuan | Hunan West | 31708 | 3669.8 | 2200.0 | 331.78 | 1503.70 | 5905.9 | 20337 | 9257.60 | 2463.60 | 4353.8 | 1240 | 214.790 | 149.8 | 94.9 | 23.831 | 14.031 | 76.900 | 59.9 | 74 | 188.1 | 1024.70 | 291.1 | 883.722 | 533.2 | 15467 | 0.6461697 | 0.6974254 |
| Huitong | Huaihua | 33693 | 4615.0 | 2617.4 | 295.00 | 1306.70 | 4588.3 | 14334 | 2095.60 | 1369.30 | 4631.9 | 1194 | 246.150 | 193.5 | 143.7 | 20.603 | 13.337 | 96.700 | 114.4 | 25 | 234.5 | 1061.70 | 320.9 | 1580.090 | 5.2 | 13989 | 0.7307572 | 0.7861060 |
| Jiahe | Chenzhou | 36023 | 5493.1 | 4864.3 | 453.68 | 1331.50 | 9608.2 | 32091 | 14882.00 | 1906.50 | 7903.3 | 719 | 242.800 | 198.9 | 83.0 | 36.054 | 19.497 | 99.000 | 108.5 | 100 | 179.6 | 1365.90 | 301.3 | 2276.272 | 3230.2 | 17744 | 0.5960836 | 0.8191928 |
| Jianghua | Yongzhou | 34378 | 4586.4 | 4631.5 | 309.70 | 1651.40 | 6555.9 | 15801 | 3357.10 | 2976.00 | 3225.3 | 1663 | 306.310 | 272.7 | 188.9 | 37.494 | 20.644 | 109.900 | 116.1 | 33 | 285.1 | 2384.80 | 416.7 | 3272.511 | 10533.8 | 16274 | 0.6841853 | 0.8902746 |
| Jiangyong | Yongzhou | 30250 | 3198.2 | 3942.5 | 187.23 | 1009.10 | 4012.2 | 17168 | 2022.70 | 1201.20 | 3253.9 | 720 | 153.580 | 132.8 | 94.3 | 21.936 | 11.093 | 68.300 | 61.2 | 25 | 163.5 | 1238.20 | 234.3 | 2862.901 | 9773.3 | 16634 | 0.6978233 | 0.8646959 |
| Jingzhou | Huaihua | 33870 | 3592.8 | 2031.4 | 237.51 | 1129.00 | 5007.7 | 20348 | 4534.10 | 1566.50 | 5397.3 | 1054 | 163.910 | 112.6 | 85.8 | 16.978 | 11.446 | 69.100 | 56.1 | 32 | 140.6 | 1611.50 | 246.7 | 1769.328 | 337.5 | 12859 | 0.5699230 | 0.6869624 |
| Jinshi | Changde | 28692 | 4581.7 | 4777.0 | 373.31 | 1148.40 | 8706.9 | 34592 | 10935.00 | 2242.00 | 8169.9 | 848 | 122.780 | 82.1 | 61.7 | 8.723 | 7.592 | 81.900 | 43.7 | 77 | 92.4 | 3683.00 | 251.8 | 2562.460 | 7525.0 | 19498 | 0.3669579 | 0.6686757 |
| Jishou | Hunan West | 39816 | 9586.2 | 5235.0 | 470.22 | 1738.20 | 9631.5 | 31537 | 6345.70 | 8282.90 | 4823.0 | 3790 | 213.420 | 97.0 | 62.4 | 25.454 | 21.941 | 99.200 | 46.5 | 49 | 85.2 | 5651.00 | 306.6 | 849.010 | 611.6 | 17980 | 0.2778865 | 0.4545029 |
| Lanshan | Yongzhou | 33756 | 4236.0 | 3986.7 | 296.68 | 1194.60 | 6627.2 | 20088 | 5392.10 | 1599.40 | 8672.1 | 1144 | 233.390 | 201.5 | 131.6 | 32.448 | 16.299 | 83.300 | 90.7 | 52 | 198.2 | 2234.20 | 330.9 | 2262.021 | 10341.9 | 19161 | 0.5989725 | 0.8633618 |
| Leiyang | Hengyang | 32814 | 15393.0 | 18687.0 | 1535.20 | 3819.00 | 30213.0 | 26105 | 42707.00 | 7409.20 | 10611.0 | 2531 | 750.120 | 553.7 | 405.8 | 112.200 | 56.350 | 338.100 | 281.2 | 155 | 629.3 | 7268.10 | 1160.2 | 8349.199 | 19981.6 | 19634 | 0.5424065 | 0.7381486 |
| Lengshuijiang | Loudi | 35647 | 6805.3 | 9746.8 | 1054.20 | 2105.30 | 21243.0 | 64257 | 36926.00 | 8936.60 | 10441.0 | 1413 | 191.320 | 101.8 | 61.8 | 29.639 | 20.113 | 112.400 | 56.9 | 118 | 78.4 | 5750.60 | 332.6 | 1277.869 | 991.8 | 23120 | 0.2357186 | 0.5320928 |
| Li | Changde | 32541 | 13487.0 | 16066.0 | 709.61 | 2459.50 | 20322.0 | 24473 | 18402.00 | 6748.00 | 8377.0 | 2038 | 513.440 | 426.8 | 227.1 | 38.975 | 33.938 | 268.500 | 256.0 | 96 | 539.7 | 7110.20 | 832.5 | 7562.340 | 53160.0 | 18985 | 0.6482883 | 0.8312558 |
| Lianyuan | Loudi | 30320 | 8059.7 | 9255.3 | 707.45 | 3298.60 | 18340.0 | 18346 | 20515.00 | 7243.20 | 4307.7 | 2260 | 706.840 | 612.9 | 344.1 | 71.232 | 53.597 | 316.200 | 298.7 | 154 | 712.6 | 6889.00 | 1001.5 | 7642.158 | 5965.4 | 38131 | 0.7115327 | 0.8670986 |
| Liling | Zhuzhou | 42896 | 12865.0 | 19125.0 | 2602.60 | 4221.40 | 39553.0 | 41491 | 57146.00 | 9398.10 | 13347.0 | 2797 | 639.830 | 513.1 | 212.1 | 53.992 | 33.705 | 248.400 | 229.7 | 482 | 473.2 | 11213.00 | 958.0 | 5373.990 | 17378.0 | 24185 | 0.4939457 | 0.8019318 |
| Linli | Changde | 32667 | 564.1 | 7781.2 | 336.86 | 1538.70 | 10355.0 | 25554 | 8214.00 | 358.00 | 8143.1 | 1440 | 307.360 | 272.2 | 100.8 | 23.286 | 18.943 | 129.100 | 157.2 | 99 | 246.6 | 3604.90 | 409.3 | 3583.910 | 7031.0 | 18604 | 0.6024921 | 0.8856065 |
| Linwu | Chenzhou | 32031 | 5984.0 | 5734.3 | 478.92 | 1435.20 | 8191.1 | 23986 | 6250.70 | 2152.70 | 7102.2 | 959 | 215.300 | 184.1 | 90.2 | 41.913 | 13.238 | 101.500 | 88.0 | 67 | 227.5 | 2023.30 | 342.8 | 1606.947 | 2632.2 | 17966 | 0.6636523 | 0.8550859 |
| Linxiang | Yueyang | 31669 | 5850.5 | 10852.0 | 319.20 | 1609.00 | 15968.0 | 31897 | 29988.00 | 3788.20 | 9739.0 | 1289 | 293.500 | 212.5 | 98.8 | 36.202 | 23.831 | 138.600 | 136.7 | 123 | 286.1 | 4598.80 | 502.3 | 3357.477 | 2994.6 | 20628 | 0.5695799 | 0.7240204 |
| Liuyang | Changsha | 40446 | 21415.0 | 43599.0 | 2473.10 | 4605.50 | 81113.0 | 63118 | 99254.00 | 23408.00 | 15719.0 | 6225 | 919.620 | 721.4 | 300.1 | 90.978 | 58.819 | 374.800 | 369.8 | 733 | 642.7 | 16233.00 | 1285.5 | 10844.470 | 26617.8 | 27345 | 0.4999611 | 0.7844544 |
| Longhui | Shaoyang | 33615 | 11925.0 | 8723.9 | 425.06 | 2741.60 | 10511.0 | 9572 | 9317.90 | 3985.50 | 3177.6 | 2726 | 709.990 | 604.4 | 436.7 | 95.163 | 54.211 | 344.600 | 298.8 | 85 | 834.1 | 2819.60 | 1098.2 | 4320.396 | 3264.6 | 12049 | 0.7595156 | 0.8512796 |
| Longshan | Hunan West | 34203 | 5557.0 | 2810.0 | 218.53 | 2052.40 | 4933.6 | 9754 | 893.45 | 2128.20 | 4164.0 | 1505 | 334.420 | 266.7 | 167.5 | 42.189 | 30.946 | 148.200 | 126.1 | 18 | 345.8 | 2293.90 | 508.3 | 2248.709 | 921.5 | 13138 | 0.6803069 | 0.7975001 |
| Luxi | Hunan West | 32680 | 2946.8 | 1772.0 | 184.25 | 1337.60 | 4878.3 | 17472 | 7085.60 | 1626.60 | 4089.1 | 664 | 197.490 | 149.7 | 80.9 | 21.683 | 17.160 | 82.400 | 71.1 | 42 | 174.3 | 917.41 | 280.3 | 1036.088 | 540.8 | 13247 | 0.6218337 | 0.7580131 |
| Mayang | Huaihua | 32772 | 3456.0 | 2703.1 | 215.86 | 1461.00 | 4738.8 | 13744 | 3876.90 | 2242.00 | 4299.8 | 975 | 216.850 | 160.0 | 148.1 | 24.173 | 15.207 | 90.300 | 87.8 | 33 | 245.0 | 1581.70 | 345.6 | 1865.938 | 5.2 | 14487 | 0.7089120 | 0.7378372 |
| Miluo | Yueyang | 36113 | 4749.3 | 15828.0 | 1068.60 | 2446.50 | 29548.0 | 42497 | 66342.00 | 3330.60 | 9421.3 | 965 | 451.270 | 303.3 | 162.8 | 40.221 | 30.662 | 204.900 | 193.6 | 269 | 351.4 | 5817.70 | 697.0 | 5688.717 | 8978.5 | 23379 | 0.5041607 | 0.6721032 |
| Nan | Yiyang | 35272 | 8921.7 | 3367.5 | 300.00 | 1987.10 | 15568.0 | 21311 | 11804.00 | 4928.10 | 8369.8 | 1877 | 366.100 | 325.6 | 226.1 | 35.487 | 29.444 | 259.200 | 201.3 | 91 | 455.9 | 5266.20 | 732.8 | 7783.359 | 6781.7 | 17691 | 0.6221343 | 0.8893745 |
| Ningxiang | Changsha | 40744 | 18662.0 | 49234.0 | 2448.90 | 4812.20 | 73250.0 | 62202 | 114145.00 | 18435.00 | 13763.0 | 4351 | 852.960 | 757.6 | 318.3 | 80.715 | 68.853 | 391.700 | 369.6 | 552 | 655.5 | 15623.00 | 1186.5 | 12804.480 | 18447.7 | 24020 | 0.5524652 | 0.8882011 |
| Ningyuan | Yongzhou | 34190 | 7351.4 | 7716.5 | 514.24 | 2234.40 | 8984.3 | 12697 | 5627.80 | 4249.40 | 4151.5 | 1753 | 444.920 | 401.3 | 157.8 | 68.336 | 32.471 | 185.500 | 157.8 | 64 | 460.9 | 3097.50 | 710.2 | 4283.431 | 9958.4 | 19742 | 0.6489721 | 0.9019599 |
| Pingjiang | Yueyang | 30017 | 8718.4 | 10627.0 | 461.62 | 2827.00 | 16444.0 | 17252 | 25647.00 | 5201.20 | 3780.8 | 2205 | 601.380 | 512.8 | 278.3 | 73.943 | 43.548 | 260.900 | 269.9 | 136 | 612.5 | 3448.30 | 957.5 | 5060.948 | 8789.3 | 14883 | 0.6396867 | 0.8527054 |
| Qidong | Hengyang | 30990 | 13633.0 | 6875.7 | 463.91 | 2413.20 | 17718.0 | 18001 | 26260.00 | 4246.10 | 9020.6 | 2055 | 607.640 | 529.2 | 311.0 | 80.694 | 51.474 | 289.200 | 287.3 | 115 | 627.8 | 6076.00 | 986.4 | 7380.180 | 15451.7 | 18256 | 0.6364558 | 0.8709104 |
| Qiyang | Yongzhou | 32059 | 14432.0 | 14439.0 | 499.51 | 2710.50 | 17705.0 | 20638 | 11567.00 | 6388.30 | 8816.0 | 2799 | 594.100 | 495.2 | 257.9 | 75.936 | 45.318 | 241.900 | 255.1 | 107 | 519.9 | 3832.70 | 860.7 | 6273.597 | 13568.8 | 19776 | 0.6040432 | 0.8335297 |
| Rucheng | Chenzhou | 35575 | 4777.6 | 3816.6 | 343.00 | 1492.70 | 3756.0 | 11286 | 4492.20 | 2426.20 | 2993.7 | 1130 | 232.280 | 197.3 | 127.8 | 33.101 | 14.478 | 111.300 | 101.6 | 43 | 235.7 | 751.80 | 333.2 | 2079.963 | 1744.7 | 13755 | 0.7073830 | 0.8494059 |
| Sangzhi | Zhangjiajie | 33916 | 3920.0 | 3081.3 | 248.06 | 1856.10 | 5615.4 | 14624 | 1694.80 | 2981.20 | 3405.9 | 1999 | 267.150 | 234.5 | 139.8 | 31.278 | 18.993 | 127.900 | 122.8 | 28 | 256.9 | 1803.30 | 385.5 | 3607.897 | 17585.8 | 45167 | 0.6664073 | 0.8777840 |
| Shaodong | Shaoyang | 31507 | 16184.0 | 12214.0 | 771.60 | 2757.00 | 22898.0 | 25246 | 29175.00 | 7855.30 | 10089.0 | 3080 | 724.310 | 547.7 | 310.0 | 99.082 | 59.009 | 363.200 | 297.8 | 148 | 524.9 | 8576.30 | 912.1 | 5704.602 | 4679.3 | 18296 | 0.5754851 | 0.7561679 |
| Shaoshan | Xiangtan | 33314 | 2626.4 | 4500.0 | 258.64 | 683.65 | 4956.8 | 55570 | 9717.60 | 1649.00 | 14916.0 | 488 | 73.652 | 62.0 | 33.6 | 5.910 | 3.201 | 27.147 | 30.4 | 48 | 57.7 | 1200.80 | 92.3 | 807.714 | 1630.3 | 24991 | 0.6251354 | 0.8417966 |
| Shaoyang | Shaoyang | 31783 | 8345.7 | 7237.3 | 376.42 | 2780.80 | 9031.2 | 9653 | 7887.80 | 2425.30 | 3499.3 | 2294 | 655.130 | 569.2 | 385.0 | 71.417 | 43.525 | 265.400 | 247.9 | 65 | 657.6 | 3406.30 | 942.3 | 5518.299 | 21656.5 | 65431 | 0.6978669 | 0.8688352 |
| Shimen | Changde | 33261 | 8334.4 | 10531.0 | 548.33 | 2178.80 | 16293.0 | 27137 | 17795.00 | 6026.50 | 6156.0 | 2502 | 392.050 | 329.6 | 193.8 | 29.245 | 26.104 | 190.600 | 184.7 | 122 | 399.2 | 6490.70 | 600.5 | 5266.510 | 6981.0 | 19275 | 0.6647794 | 0.8407091 |
| Shuangfeng | Loudi | 33684 | 11455.0 | 7904.9 | 470.59 | 2657.50 | 15225.0 | 17755 | 16665.00 | 3914.00 | 5470.3 | 1862 | 559.470 | 488.5 | 309.6 | 57.966 | 41.575 | 244.300 | 245.6 | 129 | 644.6 | 4596.00 | 859.4 | 7943.893 | 2613.1 | 14994 | 0.7500582 | 0.8731478 |
| Shuangpai | Yongzhou | 33302 | 1918.0 | 3572.0 | 226.37 | 881.96 | 3728.0 | 21942 | 2646.30 | 2056.40 | 4568.1 | 408 | 86.264 | 68.0 | 46.2 | 11.339 | 6.890 | 57.600 | 39.5 | 34 | 111.6 | 567.21 | 174.1 | 1866.171 | 9092.1 | 18479 | 0.6410109 | 0.7882778 |
| Suining | Shaoyang | 31750 | 4307.1 | 3605.6 | 222.40 | 1442.50 | 5658.1 | 16069 | 11150.00 | 1566.40 | 4990.4 | 802 | 264.080 | 208.9 | 145.2 | 26.200 | 14.261 | 108.800 | 86.3 | 54 | 268.4 | 1761.50 | 352.9 | 2064.499 | 1413.5 | 15004 | 0.7605554 | 0.7910482 |
| Taojiang | Yiyang | 35184 | 8657.4 | 8743.0 | 417.37 | 2276.80 | 15162.0 | 19509 | 18691.00 | 4656.80 | 8687.9 | 2504 | 472.800 | 411.4 | 194.0 | 48.047 | 33.234 | 260.900 | 208.8 | 153 | 504.5 | 5355.90 | 779.7 | 13878.842 | 13439.3 | 79214 | 0.6470437 | 0.8701354 |
| Taoyuan | Changde | 31877 | 11948.0 | 8656.0 | 710.08 | 2625.10 | 19603.0 | 22879 | 16529.00 | 4735.00 | 7682.6 | 2070 | 558.770 | 479.9 | 300.5 | 44.429 | 36.630 | 274.500 | 272.0 | 60 | 607.4 | 8926.00 | 857.1 | 18328.460 | 50619.0 | 60461 | 0.7086688 | 0.8588507 |
| Tongdao | Huaihua | 35400 | 2578.0 | 1525.4 | 165.59 | 1046.50 | 2653.2 | 12781 | 2514.50 | 1021.00 | 3696.4 | 882 | 144.490 | 105.5 | 82.2 | 15.913 | 7.776 | 57.900 | 49.7 | 27 | 154.2 | 749.14 | 208.1 | 981.418 | 644.2 | 12424 | 0.7409899 | 0.7301543 |
| Wangcheng | Changsha | 45171 | 12122.0 | 48829.0 | 2285.50 | 3802.30 | 37488.0 | 70666 | 148976.00 | 10330.00 | 16495.0 | 1678 | 361.480 | 268.6 | 131.2 | 28.838 | 24.815 | 161.300 | 154.8 | 314 | 266.6 | 5623.30 | 533.4 | 5222.356 | 6648.6 | 27690 | 0.4998125 | 0.7430563 |
| Wugang | Shaoyang | 30573 | 8618.0 | 7373.3 | 486.85 | 2346.00 | 9046.7 | 12112 | 5346.00 | 3852.00 | 4864.4 | 2250 | 483.620 | 402.5 | 271.4 | 70.758 | 43.683 | 243.900 | 194.0 | 52 | 502.9 | 3476.00 | 752.3 | 4613.704 | 1734.7 | 15126 | 0.6684833 | 0.8322650 |
| Xiangtan | Xiangtan | 35274 | 15516.0 | 10121.0 | 1236.60 | 3050.10 | 22728.0 | 27060 | 30730.00 | 12217.00 | 10135.0 | 2022 | 610.490 | 551.9 | 347.1 | 46.556 | 54.439 | 248.590 | 239.1 | 187 | 574.0 | 4889.10 | 845.2 | 10688.618 | 40758.0 | 69261 | 0.6791292 | 0.9040279 |
| Xiangxiang | Xiangtan | 33040 | 13298.0 | 9819.0 | 975.59 | 2942.80 | 23175.0 | 29361 | 39630.00 | 7900.30 | 9264.3 | 2451 | 586.400 | 492.0 | 324.5 | 47.743 | 39.612 | 231.710 | 242.0 | 189 | 535.7 | 5891.80 | 787.8 | 6852.943 | 17531.9 | 22297 | 0.6799949 | 0.8390177 |
| Xiangyin | Yueyang | 33169 | 5466.1 | 14714.0 | 520.53 | 2318.80 | 23265.0 | 33983 | 49507.00 | 5222.90 | 8824.5 | 1550 | 466.110 | 357.4 | 169.4 | 44.878 | 30.752 | 193.800 | 190.1 | 152 | 408.4 | 4273.20 | 686.9 | 6000.857 | 8175.0 | 19945 | 0.5945552 | 0.7667718 |
| Xinhua | Loudi | 32496 | 11075.0 | 6725.3 | 576.47 | 3599.50 | 14940.0 | 13398 | 12152.00 | 6121.20 | 3342.4 | 1542 | 755.140 | 677.9 | 451.6 | 96.224 | 57.670 | 316.600 | 313.8 | 112 | 817.4 | 5743.50 | 1116.7 | 6919.849 | 3145.3 | 13834 | 0.7319782 | 0.8977143 |
| Xinhuang | Huaihua | 31891 | 2373.1 | 2075.8 | 170.11 | 1069.30 | 3782.1 | 15412 | 3405.70 | 1265.20 | 3935.6 | 1350 | 149.710 | 105.6 | 104.0 | 15.938 | 8.781 | 72.000 | 72.5 | 36 | 178.6 | 873.45 | 246.0 | 1130.322 | 785.8 | 12732 | 0.7260163 | 0.7053637 |
| Xinning | Shaoyang | 32067 | 6126.3 | 5978.8 | 390.67 | 1830.60 | 6064.6 | 10732 | 3857.70 | 2899.90 | 3287.7 | 1565 | 429.840 | 347.8 | 227.4 | 41.633 | 22.005 | 171.400 | 146.5 | 38 | 383.6 | 1445.90 | 566.7 | 2415.712 | 2364.9 | 13031 | 0.6769014 | 0.8091383 |
| Xinshao | Shaoyang | 34199 | 7344.2 | 8313.8 | 384.19 | 2229.20 | 8590.9 | 11514 | 10829.00 | 5042.50 | 3986.4 | 2319 | 577.690 | 477.4 | 265.8 | 68.131 | 39.034 | 234.100 | 213.0 | 79 | 533.6 | 2941.60 | 749.0 | 3003.553 | 5679.2 | 13778 | 0.7124166 | 0.8263948 |
| Xintian | Yongzhou | 33609 | 3851.6 | 3401.9 | 250.31 | 1280.20 | 4776.4 | 14426 | 3357.40 | 1334.90 | 2894.9 | 1264 | 236.520 | 217.1 | 116.9 | 32.138 | 15.970 | 93.800 | 107.1 | 42 | 226.6 | 1329.80 | 332.1 | 2530.482 | 3134.3 | 16925 | 0.6823246 | 0.9178928 |
| Xupu | Huaihua | 29873 | 8675.5 | 6112.2 | 457.86 | 2452.00 | 10314.0 | 13863 | 6720.40 | 4588.00 | 5453.1 | 2106 | 512.610 | 400.9 | 292.3 | 53.793 | 29.166 | 226.100 | 211.2 | 71 | 516.0 | 3427.30 | 745.9 | 4308.431 | 242.6 | 16558 | 0.6917817 | 0.7820760 |
| Yanling | Zhuzhou | 34156 | 3274.4 | 5835.0 | 402.90 | 1038.20 | 4250.5 | 21021 | 5855.80 | 2379.60 | 3608.4 | 545 | 116.180 | 99.0 | 54.0 | 10.838 | 6.682 | 52.200 | 46.0 | 75 | 112.2 | 1241.20 | 202.2 | 971.500 | 6851.0 | 18652 | 0.5548961 | 0.8521260 |
| Yizhang | Chenzhou | 33508 | 7938.8 | 9992.5 | 750.40 | 2142.60 | 10455.0 | 17814 | 19120.00 | 3697.00 | 3788.6 | 2280 | 348.830 | 279.9 | 128.8 | 63.564 | 25.843 | 161.300 | 142.5 | 169 | 363.4 | 5037.50 | 588.9 | 2521.831 | 3584.6 | 19318 | 0.6170827 | 0.8023966 |
| Yongshun | Hunan West | 31234 | 4516.9 | 2464.1 | 220.66 | 2021.70 | 4142.1 | 9590 | 1061.00 | 2839.90 | 3963.1 | 1801 | 312.990 | 259.4 | 195.7 | 38.686 | 24.854 | 115.700 | 113.9 | 23 | 292.5 | 2247.30 | 433.3 | 2018.756 | 845.8 | 12650 | 0.6750519 | 0.8287805 |
| Yongxing | Chenzhou | 33278 | 7097.6 | 13456.0 | 1294.50 | 2476.00 | 21382.0 | 37651 | 43700.00 | 3053.70 | 9856.1 | 1969 | 375.500 | 304.9 | 133.5 | 52.440 | 19.765 | 172.500 | 145.7 | 175 | 333.5 | 4807.10 | 562.6 | 3174.984 | 4540.5 | 19960 | 0.5927835 | 0.8119840 |
| You | Zhuzhou | 36791 | 9541.6 | 15611.0 | 1533.30 | 2803.00 | 25153.0 | 36264 | 32738.00 | 6316.20 | 13021.0 | 1992 | 472.320 | 418.0 | 254.3 | 42.124 | 31.908 | 186.400 | 196.9 | 248 | 344.4 | 7654.80 | 693.7 | 6071.620 | 27443.0 | 22732 | 0.4964682 | 0.8849932 |
| Yuanjiang | Yiyang | 33302 | 7763.4 | 10486.0 | 509.45 | 2381.20 | 17603.0 | 26258 | 21082.00 | 6464.20 | 10060.0 | 1856 | 401.220 | 335.2 | 203.3 | 34.220 | 27.932 | 260.300 | 161.0 | 105 | 366.7 | 5125.10 | 672.5 | 6644.520 | 5899.6 | 20552 | 0.5452788 | 0.8354519 |
| Yuanling | Huaihua | 37762 | 5627.0 | 5466.8 | 677.40 | 2202.60 | 14156.0 | 24194 | 14835.00 | 2485.30 | 4265.4 | 2501 | 382.530 | 283.9 | 210.2 | 33.935 | 21.278 | 166.500 | 155.9 | 56 | 397.0 | 3092.50 | 586.5 | 2508.387 | 637.8 | 15165 | 0.6768968 | 0.7421640 |
| Yueyang | Yueyang | 31470 | 4946.6 | 15084.0 | 330.43 | 1971.60 | 18974.0 | 26360 | 36800.00 | 3668.70 | 10377.0 | 1616 | 411.260 | 293.3 | 173.0 | 40.218 | 30.051 | 201.500 | 150.9 | 158 | 435.3 | 5836.60 | 721.7 | 11279.478 | 15381.2 | 88494 | 0.6031592 | 0.7131741 |
| Zhijiang | Huaihua | 33582 | 4306.1 | 2802.2 | 356.96 | 1470.00 | 6992.5 | 20518 | 4491.80 | 2477.30 | 4535.1 | 935 | 223.750 | 175.5 | 116.1 | 23.693 | 14.726 | 101.800 | 94.3 | 56 | 247.6 | 2133.30 | 341.6 | 2576.470 | 90.8 | 13589 | 0.7248244 | 0.7843575 |
| Zhongfang | Huaihua | 34941 | 1296.3 | 7594.6 | 348.83 | 1048.00 | 7332.1 | 30846 | 8608.50 | 968.44 | 6082.5 | 662 | 170.250 | 103.1 | 89.3 | 12.709 | 8.563 | 71.100 | 70.9 | 56 | 173.8 | 1064.90 | 238.3 | 2917.158 | 1938.6 | 37231 | 0.7293328 | 0.6055800 |
| Zhuzhou | Zhuzhou | 37191 | 5395.6 | 4777.7 | 507.04 | 1408.80 | 7962.1 | 27589 | 6768.90 | 2970.20 | 11407.0 | 1032 | 210.380 | 177.0 | 106.0 | 12.436 | 11.824 | 92.200 | 85.2 | 82 | 210.6 | 2538.40 | 289.6 | 4236.370 | 10883.0 | 103228 | 0.7272099 | 0.8413347 |
| Zixing | Chenzhou | 34163 | 7873.2 | 14891.0 | 1556.00 | 2679.00 | 22261.0 | 65706 | 51921.00 | 5014.70 | 10838.0 | 1159 | 261.980 | 177.9 | 76.0 | 22.316 | 14.760 | 114.000 | 86.3 | 155 | 140.2 | 4835.80 | 340.2 | 2761.164 | 3636.3 | 21600 | 0.4121105 | 0.6790595 |
The code chunk below will be used to update the attribute table of hunan’s SpatialPolygonsDataFrame with the attribute fields of hunan2012 dataframe. This is performed by using left_join() of dplyr package.
colnames(hunan)[1] "NAME_2" "ID_3" "NAME_3" "ENGTYPE_3" "Shape_Leng"
[6] "Shape_Area" "County" "geometry" colnames(hunan2012) [1] "County" "City" "avg_wage" "deposite" "FAI"
[6] "Gov_Rev" "Gov_Exp" "GDP" "GDPPC" "GIO"
[11] "Loan" "NIPCR" "Bed" "Emp" "EmpR"
[16] "EmpRT" "Pri_Stu" "Sec_Stu" "Household" "Household_R"
[21] "NOIP" "Pop_R" "RSCG" "Pop_T" "Agri"
[26] "Service" "Disp_Inc" "RORP" "ROREmp" hunan <- left_join(hunan,hunan2012) %>%
select(1:4, 7, 15)3.2 Visualising Regional Development Indicator
Now, we are going to prepare a basemap and a choropleth map showing 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=0.3) +
tm_layout(bg.color = "#E4D5C9",
frame = F)
gdppc <- qtm(hunan, "GDPPC") +
tm_layout(bg.color = "#E4D5C9",
frame = F,
legend.title.size = 0.9,
legend.text.size = 0.5)
tmap_arrange(basemap, gdppc, asp=1, ncol=2)
4 Global Spatial Autocorrelation
This section is where we will compute global spatial autocorrelation statistics and perform spatial complete randomness test for global spatial autocorrelation.
4.1 Computing Contiguity Spatial Weights
Before we can compute the global spatial autocorrelation statistics, we need to construct a spatial weights of the study area. The spatial weights is used to define the neighbourhood relationships between the geographical units (i.e. county) in the study area.
poly2nb()of spdep package to compute contiguity weight matrices for the study area.- This function builds a neighbours list based on regions with contiguous boundaries. If you look at the documentation you will see that you can pass a “queen” argument that takes TRUE or FALSE as options.
- Default: Queen = TRUE, but if you change it to FALSE, you are using ROOK method.
- The output that you will get is a list.
The code chunk below will be 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 linksInterpretation
- There are 88 area units in Hunan.
- Most connected area unit has 11 neighbours.
- There are 2 area units with only 1 neighbour.
4.2 Row-standardised weights matrix
Assign weights to each neighboring polygon. In our case, each neighboring polygon will be assigned equal weight (style=“W”).
This is accomplished by assigning the fraction 1/(# of neighbors) to each neighboring county then summing the weighted income values.
While this is the most intuitive way to summaries the neighbors’ values it has one drawback in that polygons along the edges of the study area will base their lagged values on fewer polygons thus potentially over- or under-estimating the true nature of the spatial autocorrelation in the data.
Style=“W” option used for this example for simplicity’s sake but more robust options are available, notably style=“B”.
- Styles:
- W: row standardised (sums over all links to n)
- B: basic binary coding
- C: globally standardised (sums over all links to n)
- U: equal to C divided by the number of neighbours (sums over all links to unity)
- S: variance-stabilizing coding scheme (sums over all links to n)
- minmax: divides the weights by min of the max row sums and max column sums of the input weights; similar to C/U
- Styles:
The input of
*nb2listw()must be an object of class nb. The syntax of the function has two major arguments, namely style and zero.poly.
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 365.9147zero.policy = TRUE allows for lists of non-neighbors. This should be used with caution since the user may not be aware of missing neighbors in their dataset however, a zero.policy = FALSE would return an error.
If zero policy = TRUE, weights vectors of zero length are inserted for regions without neighbour in the neighbours list. These will in turn generate lag values of zero, equivalent to the sum of products of the zero row t(rep(0, length = length(neighbours))) %*% x, for arbitrary numerical vector x of length length(neighbours). The spatially lagged value of x for the zero-neighbour region will then be zero, which may (or may not) be a sensible choice.
4.3 Global Spatial Autocorrelation: Moran’s I
Describe how features differ from the values in the study area as a whole
Hypothesis:
\(H_0\): Observed spatial patterns of values is equally likely as any other spatial pattern i.e. data is randomly disbursed, no spatial pattern
\(H_1\): Data is more spatially clustered than expected by chance alone.
Moran I (\(Z\) value) is:
- positive (I>0): Clustered, observations tend to be similar;
- negative(I<0): Dispersed, observations tend to be dissimilar;
- approximately zero: observations are arranged randomly over space.
Moran’s I statistical testing using moran.test() of spdep.
moran.test(hunan$GDPPC,
listw=rswm_q,
zero.policy = TRUE,
na.action=na.omit)
Moran I test under randomisation
data: hunan$GDPPC
weights: rswm_q
Moran I statistic standard deviate = 4.7351, p-value = 1.095e-06
alternative hypothesis: greater
sample estimates:
Moran I statistic Expectation Variance
0.300749970 -0.011494253 0.004348351 Question: What statistical conclusion can you draw from the output above?
- The p-value which is 1.095e-06, or 0.0000001095 which is very small
- We will reject the null hypothesis at 99.9% as the p-value is smaller than our alpha value.
- Since the Moran I statistic 0.300749970 is > 0 and is approaching 1 which is positive autocorrelation, we can infer that spatial patterns that we observed resemble a cluster.
Note:
- When we accept or reject the null hypothesis, we have to mention at what confidence interval.
- Once you select a confidence interval, it will translate into the alpha value or significance value.
- Confidence intervals:
- 90% alpha value is 0.1, number of simulations: 100
- 95 % alpha value 0.05,
- 99 % alpha value 0.01,
- 99.9 alpha value is 0.001 , number of simulations: 1000
Permutation test for Moran’s I statistic by using moran.mc() of spdep. A total of 1000 simulation will be performed.
set.seed(1234)
bperm= moran.mc(hunan$GDPPC,
listw=rswm_q,
nsim=999,
zero.policy = TRUE,
na.action=na.omit)
bperm
Monte-Carlo simulation of Moran I
data: hunan$GDPPC
weights: rswm_q
number of simulations + 1: 1000
statistic = 0.30075, observed rank = 1000, p-value = 0.001
alternative hypothesis: greaterQuestion: What statistical conclusion can you draw from the output above?
- After 999 simulations, our P-value is 0.001.
- We will accept / do not reject the null hypothesis at 99.9% as the p-value is equal to our alpha value 0.001.
- Since the Monte Carlo statistic 0.30075 is > 0 and is approaching 1 which is positive autocorrelation, we can infer that spatial patterns that we observed resemble a cluster.
Using hist()
Plot the distribution of the statistical values as histogram to examine the simulated Moran’s I test statistics in greater detail: hist() and abline() of R Graphics are used.
Show the code
par(bg = '#E4D5C9')
mean(bperm$res[1:999])[1] -0.01504572Show the code
var(bperm$res[1:999])[1] 0.004371574Show the code
summary(bperm$res[1:999]) Min. 1st Qu. Median Mean 3rd Qu. Max.
-0.18339 -0.06168 -0.02125 -0.01505 0.02611 0.27593 Show the code
hist(bperm$res,
freq=TRUE,
breaks=20,
col = "#efe7df",
xlab="Simulated Moran's I")
abline(v=0,
col="#800200",
lwd = 3,
lty = 2) 
Using ggplot
plot2 <- bperm$res
mu <- mean(plot2)
ggplot(data=data.frame(plot2),
aes(x=plot2)
) +
geom_histogram(
bins=30,
fill="#efe7df",
color="black",
size=0.2
) +
geom_vline(
xintercept = mu,
color="#800200",
linetype = "longdash",
size = 1
) +
labs(title ="Histogram of Monte Carlo Moran's Is",
x = "Simulated Moran's I",
y = "Frequency"
) +
theme(
plot.title = element_text(face = "bold", size = 10, hjust = 0.5),
axis.title.x = element_text(size = 8),
axis.title.y = element_text(hjust=1, angle=0, size = 8),
axis.ticks = element_blank(),
axis.text = element_text(size = 6),
plot.background = element_rect(fill = "#E4D5C9", color = "#E4D5C9"),
panel.background = element_rect(fill = "#E4D5C9", color = "#E4D5C9")
)
4.5 Global Spatial Autocorrelation: Geary’s
In this section, you will learn how to perform Geary’s c statistics testing by using appropriate functions of spdep package.
Describes how features differ from their immediate neighbours.
Geary c (\(Z\) value) is:
- Large c value (>1) : Dispersed, observations tend to be dissimilar;
- Small c value (<1) : Clustered, observations tend to be similar;
- c = 1: observations are arranged randomly over space.
The code chunk below performs Geary’s C test for spatial autocorrelation by using geary.test() of spdep.
geary.test(hunan$GDPPC,
listw = rswm_q)
Geary C test under randomisation
data: hunan$GDPPC
weights: rswm_q
Geary C statistic standard deviate = 3.6108, p-value = 0.0001526
alternative hypothesis: Expectation greater than statistic
sample estimates:
Geary C statistic Expectation Variance
0.6907223 1.0000000 0.0073364 Question: What statistical conclusion can you draw from the output above?
- Here, the p-value is 0.0001526.
- We will reject the null hypothesis at 99.9% as the p-value is smaller than our alpha value, 0.001.
- The Geary C statistic is 0.6907223 which is < 1, hence the spatial pattern is “clustered”.
Performs permutation test for Geary’s C statistic by using geary.mc() of spdep.
set.seed(1234)
bperm=geary.mc(hunan$GDPPC,
listw=rswm_q,
nsim=999)
bperm
Monte-Carlo simulation of Geary C
data: hunan$GDPPC
weights: rswm_q
number of simulations + 1: 1000
statistic = 0.69072, observed rank = 1, p-value = 0.001
alternative hypothesis: greaterQuestion: What statistical conclusion can you draw from the output above?
- After running 1000 simulations, the p-value is now = 0.001.
- Hence, we will accept / cannot reject the null hypothesis at 99.9% as the p-value is equal to our alpha value, 0.001.
- The Geary C statistic is now, 0.69072, which is still < 1, hence the spatial pattern is “clustered”.
Plot a histogram to reveal the distribution of the simulated values by using the code chunk below.
Show the code
par(bg = '#E4D5C9')
mean(bperm$res[1:999])[1] 1.004402Show the code
var(bperm$res[1:999])[1] 0.007436493Show the code
summary(bperm$res[1:999]) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.7142 0.9502 1.0052 1.0044 1.0595 1.2722 Show the code
hist(bperm$res,
freq=TRUE,
breaks=20,
col = "#efe7df",
xlab="Simulated Geary c")
abline(v=1,
col="#800200",
lwd = 3,
lty = 2) 
plot2 <- bperm$res
mu <- mean(plot2)
ggplot(data=data.frame(plot2),
aes(x=plot2)
) +
geom_histogram(
bins=30,
fill="#efe7df",
color="black",
size=0.2
) +
geom_vline(
xintercept = mu,
color="#800200",
linetype = "longdash",
size = 1
) +
labs(title ="Histogram of Monte Carlo Geary's Cs",
x = "Simulated Geary's C",
y = "Frequency"
) +
theme(
plot.title = element_text(face = "bold", size = 10, hjust = 0.5),
axis.title.x = element_text(size = 8),
axis.title.y = element_text(hjust=1, angle=0, size = 8),
axis.ticks = element_blank(),
axis.text = element_text(size = 6),
plot.background = element_rect(fill = "#E4D5C9", color = "#E4D5C9"),
panel.background = element_rect(fill = "#E4D5C9", color = "#E4D5C9")
)
Question: What statistical observation can you draw from the output?
The distribution is close to a normal distribution, with more values in the center of the histogram.
5 Spatial Correlogram
- Spatial correlograms are for examining patterns of spatial autocorrelation in the data or model residuals.
- They show how correlated are pairs of spatial observations when you increase the distance (lag) between them
- they are plots of some index of autocorrelation (Moran’s I or Geary’s c) against distance.
- Although correlograms are not as fundamental as variograms (a keystone concept of geostatistics), they are very useful as an exploratory and descriptive tool.
- For this purpose they actually provide richer information than variograms.
sp.correlogram()of spdep package: computes a 6-lag spatial correlogram of GDPPC.- The global spatial autocorrelation used in Moran’s I.
- The
plot()of base Graph is then used to plot the output.
MI_corr <- sp.correlogram(wm_q,
hunan$GDPPC,
order=6,
method="I",
style="W")
print(MI_corr)Spatial correlogram for hunan$GDPPC
method: Moran's I
estimate expectation variance standard deviate Pr(I) two sided
1 (88) 0.3007500 -0.0114943 0.0043484 4.7351 2.189e-06 ***
2 (88) 0.2060084 -0.0114943 0.0020962 4.7505 2.029e-06 ***
3 (88) 0.0668273 -0.0114943 0.0014602 2.0496 0.040400 *
4 (88) 0.0299470 -0.0114943 0.0011717 1.2107 0.226015
5 (88) -0.1530471 -0.0114943 0.0012440 -4.0134 5.984e-05 ***
6 (88) -0.1187070 -0.0114943 0.0016791 -2.6164 0.008886 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1par(bg = '#E4D5C9')
plot(MI_corr)
sp.correlogram()of spdep package: used to compute a 6-lag spatial correlogram of GDPPC.- The global spatial autocorrelation used in Geary’s C.
- The
plot()of base Graph is then used to plot the output.
GC_corr <- sp.correlogram(wm_q,
hunan$GDPPC,
order=6,
method="C",
style="W")
print(GC_corr)Spatial correlogram for hunan$GDPPC
method: Geary's C
estimate expectation variance standard deviate Pr(I) two sided
1 (88) 0.6907223 1.0000000 0.0073364 -3.6108 0.0003052 ***
2 (88) 0.7630197 1.0000000 0.0049126 -3.3811 0.0007220 ***
3 (88) 0.9397299 1.0000000 0.0049005 -0.8610 0.3892612
4 (88) 1.0098462 1.0000000 0.0039631 0.1564 0.8757128
5 (88) 1.2008204 1.0000000 0.0035568 3.3673 0.0007592 ***
6 (88) 1.0773386 1.0000000 0.0058042 1.0151 0.3100407
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1par(bg = '#E4D5C9')
plot(GC_corr)
6 Reference
Kam, T. S. Global Measures of Spatial Autocorrelation. R for Geospatial Data Science and Analytics. https://r4gdsa.netlify.app/chap09.html