pacman::p_load(sf, spdep, tmap, tidyverse)Hands-on exercise 7
Import
Import packages
Import data
Import shapefile
hunan <- st_read(dsn = "data/geospatial",
layer = "Hunan")Reading layer `Hunan' from data source
`C:\Study\Y3\S2\IS415\ELAbishek\IS415-GAA\hands-on-exercise\wk7\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 84Import CSV file
hunan2012 <- read_csv("data/aspatial/Hunan_2012.csv")Performing relational join
hunan <- left_join(hunan,hunan2012) %>%
select(1:4, 7, 15)Visualising Regional Development Indicator
equal <- tm_shape(hunan) +
tm_fill("GDPPC",
n = 5,
style = "equal") +
tm_borders(alpha = 0.5) +
tm_layout(main.title = "Equal interval classification")
quantile <- tm_shape(hunan) +
tm_fill("GDPPC",
n = 5,
style = "quantile") +
tm_borders(alpha = 0.5) +
tm_layout(main.title = "Equal quantile classification")
tmap_arrange(equal,
quantile,
asp=1,
ncol=2)
Global spatial autocorrelation
Computing contiguity spatial weights
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 linksRow standardised weights matrix
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 365.9147Global Spatial Autocorrelation: Moran’s I
Moran’s I test
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 Computing Monte Carlo Moran’s I
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: greaterVisualising Monte Carlo Moran’s I
mean(bperm$res[1:999])[1] -0.01504572var(bperm$res[1:999])[1] 0.004371574summary(bperm$res[1:999]) Min. 1st Qu. Median Mean 3rd Qu. Max.
-0.18339 -0.06168 -0.02125 -0.01505 0.02611 0.27593 hist(bperm$res,
freq=TRUE,
breaks=20,
xlab="Simulated Moran's I")
abline(v=0,
col="red") 
Global Spatial Autocorrelation: Geary’s
Geary’s C test
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 Computing Monte Carlo Geary’s C
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: greaterVisualising the Monte Carlo Geary’s C
mean(bperm$res[1:999])[1] 1.004402var(bperm$res[1:999])[1] 0.007436493summary(bperm$res[1:999]) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.7142 0.9502 1.0052 1.0044 1.0595 1.2722 hist(bperm$res, freq=TRUE, breaks=20, xlab="Simulated Geary c")
abline(v=1, col="red") 
Spatial Correlogram
Compute Moran’s I correlogram
MI_corr <- sp.correlogram(wm_q,
hunan$GDPPC,
order=6,
method="I",
style="W")
plot(MI_corr)
print(MI_corr)Spatial correlogram for hunan$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 ' ' 1Compute Geary’s C correlogram and plot
GC_corr <- sp.correlogram(wm_q,
hunan$GDPPC,
order=6,
method="C",
style="W")
plot(GC_corr)
print(GC_corr)Spatial correlogram for hunan$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 ' ' 1Cluster and outlier analysis
Computing local Moran’s I
fips <- order(hunan$County)
localMI <- localmoran(hunan$GDPPC, rswm_q)
head(localMI) Ii E.Ii Var.Ii Z.Ii Pr(z != E(Ii))
1 -0.001468468 -2.815006e-05 4.723841e-04 -0.06626904 0.9471636
2 0.025878173 -6.061953e-04 1.016664e-02 0.26266425 0.7928094
3 -0.011987646 -5.366648e-03 1.133362e-01 -0.01966705 0.9843090
4 0.001022468 -2.404783e-07 5.105969e-06 0.45259801 0.6508382
5 0.014814881 -6.829362e-05 1.449949e-03 0.39085814 0.6959021
6 -0.038793829 -3.860263e-04 6.475559e-03 -0.47728835 0.6331568printCoefmat(data.frame(
localMI[fips,],
row.names=hunan$County[fips]),
check.names=FALSE) Ii E.Ii Var.Ii Z.Ii Pr.z....E.Ii..
Anhua -2.2493e-02 -5.0048e-03 5.8235e-02 -7.2467e-02 0.9422
Anren -3.9932e-01 -7.0111e-03 7.0348e-02 -1.4791e+00 0.1391
Anxiang -1.4685e-03 -2.8150e-05 4.7238e-04 -6.6269e-02 0.9472
Baojing 3.4737e-01 -5.0089e-03 8.3636e-02 1.2185e+00 0.2230
Chaling 2.0559e-02 -9.6812e-04 2.7711e-02 1.2932e-01 0.8971
Changning -2.9868e-05 -9.0010e-09 1.5105e-07 -7.6828e-02 0.9388
Changsha 4.9022e+00 -2.1348e-01 2.3194e+00 3.3590e+00 0.0008
Chengbu 7.3725e-01 -1.0534e-02 2.2132e-01 1.5895e+00 0.1119
Chenxi 1.4544e-01 -2.8156e-03 4.7116e-02 6.8299e-01 0.4946
Cili 7.3176e-02 -1.6747e-03 4.7902e-02 3.4200e-01 0.7324
Dao 2.1420e-01 -2.0824e-03 4.4123e-02 1.0297e+00 0.3032
Dongan 1.5210e-01 -6.3485e-04 1.3471e-02 1.3159e+00 0.1882
Dongkou 5.2918e-01 -6.4461e-03 1.0748e-01 1.6338e+00 0.1023
Fenghuang 1.8013e-01 -6.2832e-03 1.3257e-01 5.1198e-01 0.6087
Guidong -5.9160e-01 -1.3086e-02 3.7003e-01 -9.5104e-01 0.3416
Guiyang 1.8240e-01 -3.6908e-03 3.2610e-02 1.0305e+00 0.3028
Guzhang 2.8466e-01 -8.5054e-03 1.4152e-01 7.7931e-01 0.4358
Hanshou 2.5878e-02 -6.0620e-04 1.0167e-02 2.6266e-01 0.7928
Hengdong 9.9964e-03 -4.9063e-04 6.7742e-03 1.2742e-01 0.8986
Hengnan 2.8064e-02 -3.2160e-04 3.7597e-03 4.6294e-01 0.6434
Hengshan -5.8201e-03 -3.0437e-05 5.1076e-04 -2.5618e-01 0.7978
Hengyang 6.2997e-02 -1.3046e-03 2.1865e-02 4.3486e-01 0.6637
Hongjiang 1.8790e-01 -2.3019e-03 3.1725e-02 1.0678e+00 0.2856
Huarong -1.5389e-02 -1.8667e-03 8.1030e-02 -4.7503e-02 0.9621
Huayuan 8.3772e-02 -8.5569e-04 2.4495e-02 5.4072e-01 0.5887
Huitong 2.5997e-01 -5.2447e-03 1.1077e-01 7.9685e-01 0.4255
Jiahe -1.2431e-01 -3.0550e-03 5.1111e-02 -5.3633e-01 0.5917
Jianghua 2.8651e-01 -3.8280e-03 8.0968e-02 1.0204e+00 0.3076
Jiangyong 2.4337e-01 -2.7082e-03 1.1746e-01 7.1800e-01 0.4728
Jingzhou 1.8270e-01 -8.5106e-04 2.4363e-02 1.1759e+00 0.2396
Jinshi -1.1988e-02 -5.3666e-03 1.1334e-01 -1.9667e-02 0.9843
Jishou -2.8680e-01 -2.6305e-03 4.4028e-02 -1.3543e+00 0.1756
Lanshan 6.3334e-02 -9.6365e-04 2.0441e-02 4.4972e-01 0.6529
Leiyang 1.1581e-02 -1.4948e-04 2.5082e-03 2.3422e-01 0.8148
Lengshuijiang -1.7903e+00 -8.2129e-02 2.1598e+00 -1.1623e+00 0.2451
Li 1.0225e-03 -2.4048e-07 5.1060e-06 4.5260e-01 0.6508
Lianyuan -1.4672e-01 -1.8983e-03 1.9145e-02 -1.0467e+00 0.2952
Liling 1.3774e+00 -1.5097e-02 4.2601e-01 2.1335e+00 0.0329
Linli 1.4815e-02 -6.8294e-05 1.4499e-03 3.9086e-01 0.6959
Linwu -2.4621e-03 -9.0703e-06 1.9258e-04 -1.7676e-01 0.8597
Linxiang 6.5904e-02 -2.9028e-03 2.5470e-01 1.3634e-01 0.8916
Liuyang 3.3688e+00 -7.7502e-02 1.5180e+00 2.7972e+00 0.0052
Longhui 8.0801e-01 -1.1377e-02 1.5538e-01 2.0787e+00 0.0376
Longshan 7.5663e-01 -1.1100e-02 3.1449e-01 1.3690e+00 0.1710
Luxi 1.8177e-01 -2.4855e-03 3.4249e-02 9.9561e-01 0.3194
Mayang 2.1852e-01 -5.8773e-03 9.8049e-02 7.1663e-01 0.4736
Miluo 1.8704e+00 -1.6927e-02 2.7925e-01 3.5715e+00 0.0004
Nan -9.5789e-03 -4.9497e-04 6.8341e-03 -1.0988e-01 0.9125
Ningxiang 1.5607e+00 -7.3878e-02 8.0012e-01 1.8274e+00 0.0676
Ningyuan 2.0910e-01 -7.0884e-03 8.2306e-02 7.5356e-01 0.4511
Pingjiang -9.8964e-01 -2.6457e-03 5.6027e-02 -4.1698e+00 0.0000
Qidong 1.1806e-01 -2.1207e-03 2.4747e-02 7.6396e-01 0.4449
Qiyang 6.1966e-02 -7.3374e-04 8.5743e-03 6.7712e-01 0.4983
Rucheng -3.6992e-01 -8.8999e-03 2.5272e-01 -7.1814e-01 0.4727
Sangzhi 2.5053e-01 -4.9470e-03 6.8000e-02 9.7972e-01 0.3272
Shaodong -3.2659e-02 -3.6592e-05 5.0546e-04 -1.4510e+00 0.1468
Shaoshan 2.1223e+00 -5.0227e-02 1.3668e+00 1.8583e+00 0.0631
Shaoyang 5.9499e-01 -1.1253e-02 1.3012e-01 1.6807e+00 0.0928
Shimen -3.8794e-02 -3.8603e-04 6.4756e-03 -4.7729e-01 0.6332
Shuangfeng 9.2835e-03 -2.2867e-03 3.1516e-02 6.5174e-02 0.9480
Shuangpai 8.0591e-02 -3.1366e-04 8.9838e-03 8.5358e-01 0.3933
Suining 3.7585e-01 -3.5933e-03 4.1870e-02 1.8544e+00 0.0637
Taojiang -2.5394e-01 -1.2395e-03 1.4477e-02 -2.1002e+00 0.0357
Taoyuan 1.4729e-02 -1.2039e-04 8.5103e-04 5.0903e-01 0.6107
Tongdao 4.6482e-01 -6.9870e-03 1.9879e-01 1.0582e+00 0.2900
Wangcheng 4.4220e+00 -1.1067e-01 1.3596e+00 3.8873e+00 0.0001
Wugang 7.1003e-01 -7.8144e-03 1.0710e-01 2.1935e+00 0.0283
Xiangtan 2.4530e-01 -3.6457e-04 3.2319e-03 4.3213e+00 0.0000
Xiangxiang 2.6271e-01 -1.2703e-03 2.1290e-02 1.8092e+00 0.0704
Xiangyin 5.4525e-01 -4.7442e-03 7.9236e-02 1.9539e+00 0.0507
Xinhua 1.1810e-01 -6.2649e-03 8.6001e-02 4.2409e-01 0.6715
Xinhuang 1.5725e-01 -4.1820e-03 3.6648e-01 2.6667e-01 0.7897
Xinning 6.8928e-01 -9.6674e-03 2.0328e-01 1.5502e+00 0.1211
Xinshao 5.7578e-02 -8.5932e-03 1.1769e-01 1.9289e-01 0.8470
Xintian -7.4050e-03 -5.1493e-03 1.0877e-01 -6.8395e-03 0.9945
Xupu 3.2406e-01 -5.7468e-03 5.7735e-02 1.3726e+00 0.1699
Yanling -6.9021e-02 -5.9211e-04 9.9306e-03 -6.8667e-01 0.4923
Yizhang -2.6844e-01 -2.2463e-03 4.7588e-02 -1.2202e+00 0.2224
Yongshun 6.3064e-01 -1.1350e-02 1.8830e-01 1.4795e+00 0.1390
Yongxing 4.3411e-01 -9.0735e-03 1.5088e-01 1.1409e+00 0.2539
You 7.8750e-02 -7.2728e-03 1.2116e-01 2.4714e-01 0.8048
Yuanjiang 2.0004e-04 -1.7760e-04 2.9798e-03 6.9181e-03 0.9945
Yuanling 8.7298e-03 -2.2981e-06 2.3221e-05 1.8121e+00 0.0700
Yueyang 4.1189e-02 -1.9768e-04 2.3113e-03 8.6085e-01 0.3893
Zhijiang 1.0476e-01 -7.8123e-04 1.3100e-02 9.2214e-01 0.3565
Zhongfang -2.2685e-01 -2.1455e-03 3.5927e-02 -1.1855e+00 0.2358
Zhuzhou 3.2864e-01 -5.2432e-04 7.2391e-03 3.8688e+00 0.0001
Zixing -7.6849e-01 -8.8210e-02 9.4057e-01 -7.0144e-01 0.4830Mapping the local Moran’s I
hunan.localMI <- cbind(hunan,localMI) %>%
rename(Pr.Ii = Pr.z....E.Ii..)Mapping local Moran’s I values
tm_shape(hunan.localMI) +
tm_fill(col = "Ii",
style = "pretty",
palette = "RdBu",
title = "local moran statistics") +
tm_borders(alpha = 0.5)
Mapping local Moran’s I p-values
tm_shape(hunan.localMI) +
tm_fill(col = "Pr.Ii",
breaks=c(-Inf, 0.001, 0.01, 0.05, 0.1, Inf),
palette="-Blues",
title = "local Moran's I p-values") +
tm_borders(alpha = 0.5)
Mapping both local Moran’s I values and p-values
localMI.map <- tm_shape(hunan.localMI) +
tm_fill(col = "Ii",
style = "pretty",
title = "local moran statistics") +
tm_borders(alpha = 0.5)
pvalue.map <- tm_shape(hunan.localMI) +
tm_fill(col = "Pr.Ii",
breaks=c(-Inf, 0.001, 0.01, 0.05, 0.1, Inf),
palette="-Blues",
title = "local Moran's I p-values") +
tm_borders(alpha = 0.5)
tmap_arrange(localMI.map, pvalue.map, asp=1, ncol=2)
Creating a LISA Cluster Map
Plotting Moran scatterplot
nci <- moran.plot(hunan$GDPPC, rswm_q,
labels=as.character(hunan$County),
xlab="GDPPC 2012",
ylab="Spatially Lag GDPPC 2012")
Plotting Moran scatterplot with standardised variable
hunan$Z.GDPPC <- scale(hunan$GDPPC) %>%
as.vector nci2 <- moran.plot(hunan$Z.GDPPC, rswm_q,
labels=as.character(hunan$County),
xlab="z-GDPPC 2012",
ylab="Spatially Lag z-GDPPC 2012")
Preparing LISA map classes
quadrant <- vector(mode="numeric",length=nrow(localMI))hunan$lag_GDPPC <- lag.listw(rswm_q, hunan$GDPPC)
DV <- hunan$lag_GDPPC - mean(hunan$lag_GDPPC) LM_I <- localMI[,1] - mean(localMI[,1]) signif <- 0.05 quadrant[DV <0 & LM_I>0] <- 1
quadrant[DV >0 & LM_I<0] <- 2
quadrant[DV <0 & LM_I<0] <- 3
quadrant[DV >0 & LM_I>0] <- 4 quadrant[localMI[,5]>signif] <- 0quadrant <- vector(mode="numeric",length=nrow(localMI))
hunan$lag_GDPPC <- lag.listw(rswm_q, hunan$GDPPC)
DV <- hunan$lag_GDPPC - mean(hunan$lag_GDPPC)
LM_I <- localMI[,1]
signif <- 0.05
quadrant[DV <0 & LM_I>0] <- 1
quadrant[DV >0 & LM_I<0] <- 2
quadrant[DV <0 & LM_I<0] <- 3
quadrant[DV >0 & LM_I>0] <- 4
quadrant[localMI[,5]>signif] <- 0Plotting LISA map
hunan.localMI$quadrant <- quadrant
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high")
tm_shape(hunan.localMI) +
tm_fill(col = "quadrant",
style = "cat",
palette = colors[c(sort(unique(quadrant)))+1],
labels = clusters[c(sort(unique(quadrant)))+1],
popup.vars = c("")) +
tm_view(set.zoom.limits = c(11,17)) +
tm_borders(alpha=0.5)
gdppc <- qtm(hunan, "GDPPC")
hunan.localMI$quadrant <- quadrant
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high")
LISAmap <- tm_shape(hunan.localMI) +
tm_fill(col = "quadrant",
style = "cat",
palette = colors[c(sort(unique(quadrant)))+1],
labels = clusters[c(sort(unique(quadrant)))+1],
popup.vars = c("")) +
tm_view(set.zoom.limits = c(11,17)) +
tm_borders(alpha=0.5)
tmap_arrange(gdppc, LISAmap,
asp=1, ncol=2)
Hot spot and cold spot analysis
Getis and Ord’s G-statistics
An alternative spatial statistics to detect spatial anomalies is the Getis and Ord’s G-statistics (Getis and Ord, 1972; Ord and Getis, 1995). It looks at neighbours within a defined proximity to identify where either high or low values clutser spatially. Here, statistically significant hot-spots are recognised as areas of high values where other areas within a neighbourhood range also share high values too.
The analysis consists of three steps:
Deriving spatial weight matrix
Computing Gi statistics
Mapping Gi statistics
Deriving distance-based weight matrix
First, we need to define a new set of neighbours. Whist the spatial autocorrelation considered units which shared borders, for Getis-Ord we are defining neighbours based on distance.
There are two type of distance-based proximity matrix, they are:
fixed distance weight matrix; and
adaptive distance weight matrix.
Deriving the centroid
longitude <- map_dbl(hunan$geometry, ~st_centroid(.x)[[1]])latitude <- map_dbl(hunan$geometry, ~st_centroid(.x)[[2]])coords <- cbind(longitude, latitude)Determining cut-off distance
#coords <- coordinates(hunan)
k1 <- knn2nb(knearneigh(coords))
k1dists <- unlist(nbdists(k1, coords, longlat = TRUE))
summary(k1dists) Min. 1st Qu. Median Mean 3rd Qu. Max.
24.79 32.57 38.01 39.07 44.52 61.79 Computing fixed distance weight matrix
wm_d62 <- dnearneigh(coords, 0, 62, longlat = TRUE)
wm_d62Neighbour list object:
Number of regions: 88
Number of nonzero links: 324
Percentage nonzero weights: 4.183884
Average number of links: 3.681818 wm62_lw <- nb2listw(wm_d62, style = 'B')
summary(wm62_lw)Characteristics of weights list object:
Neighbour list object:
Number of regions: 88
Number of nonzero links: 324
Percentage nonzero weights: 4.183884
Average number of links: 3.681818
Link number distribution:
1 2 3 4 5 6
6 15 14 26 20 7
6 least connected regions:
6 15 30 32 56 65 with 1 link
7 most connected regions:
21 28 35 45 50 52 82 with 6 links
Weights style: B
Weights constants summary:
n nn S0 S1 S2
B 88 7744 324 648 5440Computing adaptive distance weight matrix
knn <- knn2nb(knearneigh(coords, k=8))
knnNeighbour list object:
Number of regions: 88
Number of nonzero links: 704
Percentage nonzero weights: 9.090909
Average number of links: 8
Non-symmetric neighbours listknn_lw <- nb2listw(knn, style = 'B')
summary(knn_lw)Characteristics of weights list object:
Neighbour list object:
Number of regions: 88
Number of nonzero links: 704
Percentage nonzero weights: 9.090909
Average number of links: 8
Non-symmetric neighbours list
Link number distribution:
8
88
88 least connected regions:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 with 8 links
88 most connected regions:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 with 8 links
Weights style: B
Weights constants summary:
n nn S0 S1 S2
B 88 7744 704 1300 23014Computing Gi statistics
Gi statistics using fixed distance
fips <- order(hunan$County)
gi.fixed <- localG(hunan$GDPPC, wm62_lw)
gi.fixed [1] 0.436075843 -0.265505650 -0.073033665 0.413017033 0.273070579
[6] -0.377510776 2.863898821 2.794350420 5.216125401 0.228236603
[11] 0.951035346 -0.536334231 0.176761556 1.195564020 -0.033020610
[16] 1.378081093 -0.585756761 -0.419680565 0.258805141 0.012056111
[21] -0.145716531 -0.027158687 -0.318615290 -0.748946051 -0.961700582
[26] -0.796851342 -1.033949773 -0.460979158 -0.885240161 -0.266671512
[31] -0.886168613 -0.855476971 -0.922143185 -1.162328599 0.735582222
[36] -0.003358489 -0.967459309 -1.259299080 -1.452256513 -1.540671121
[41] -1.395011407 -1.681505286 -1.314110709 -0.767944457 -0.192889342
[46] 2.720804542 1.809191360 -1.218469473 -0.511984469 -0.834546363
[51] -0.908179070 -1.541081516 -1.192199867 -1.075080164 -1.631075961
[56] -0.743472246 0.418842387 0.832943753 -0.710289083 -0.449718820
[61] -0.493238743 -1.083386776 0.042979051 0.008596093 0.136337469
[66] 2.203411744 2.690329952 4.453703219 -0.340842743 -0.129318589
[71] 0.737806634 -1.246912658 0.666667559 1.088613505 -0.985792573
[76] 1.233609606 -0.487196415 1.626174042 -1.060416797 0.425361422
[81] -0.837897118 -0.314565243 0.371456331 4.424392623 -0.109566928
[86] 1.364597995 -1.029658605 -0.718000620
attr(,"cluster")
[1] Low Low High High High High High High High Low Low High Low Low Low
[16] High High High High Low High High Low Low High Low Low Low Low Low
[31] Low Low Low High Low Low Low Low Low Low High Low Low Low Low
[46] High High Low Low Low Low High Low Low Low Low Low High Low Low
[61] Low Low Low High High High Low High Low Low High Low High High Low
[76] High Low Low Low Low Low Low High High Low High Low Low
Levels: Low High
attr(,"gstari")
[1] FALSE
attr(,"call")
localG(x = hunan$GDPPC, listw = wm62_lw)
attr(,"class")
[1] "localG"hunan.gi <- cbind(hunan, as.matrix(gi.fixed)) %>%
rename(gstat_fixed = as.matrix.gi.fixed.)Mapping Gi values with fixed distance weights
gdppc <- qtm(hunan, "GDPPC")
Gimap <-tm_shape(hunan.gi) +
tm_fill(col = "gstat_fixed",
style = "pretty",
palette="-RdBu",
title = "local Gi") +
tm_borders(alpha = 0.5)
tmap_arrange(gdppc, Gimap, asp=1, ncol=2)
Gi statistics using adaptive distance
fips <- order(hunan$County)
gi.adaptive <- localG(hunan$GDPPC, knn_lw)
hunan.gi <- cbind(hunan, as.matrix(gi.adaptive)) %>%
rename(gstat_adaptive = as.matrix.gi.adaptive.)Mapping Gi values with adaptive distance weights
gdppc<- qtm(hunan, "GDPPC")
Gimap <- tm_shape(hunan.gi) +
tm_fill(col = "gstat_adaptive",
style = "pretty",
palette="-RdBu",
title = "local Gi") +
tm_borders(alpha = 0.5)
tmap_arrange(gdppc,
Gimap,
asp=1,
ncol=2)