Take home ex1

1 Data Preparation

1.1 Import data

First of all we load the package that needed: sf, spdep, tmap, tidyverse,dplyr, funModeling

pacman::p_load(sf, spdep, tmap, tidyverse,dplyr, funModeling)

There are two dataset we used:

• geo_export:

• nga_admbnda_adm2_osgof_20190417

change it to shorter name

1.1.1 import waterpoint

wp<- st_read(dsn="geodata",
             layer="geo_export",
             crs=4326) %>%
  filter(clean_coun=="Nigeria")

I saved it into wp_nga.rds. In this way I can delete geo_export data which is too large to git push.

I add #eval: false to make sure the code chunk will only display

ref

wp_nga<-write_rds(wp,"geodata/wp_nga.rds")

1.1.2 import Nigeria LGA boundary data

nga<- st_read(dsn="geodata",
             layer="geoBoundaries-NGA-ADM2",
             crs=4326)

Reading layer `geoBoundaries-NGA-ADM2' from data source 
  `D:\Xu-Siyi\ISSS624\Take-home Exercise\geodata' using driver `ESRI Shapefile'
Simple feature collection with 774 features and 5 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2.668534 ymin: 4.273007 xmax: 14.67882 ymax: 13.89442
Geodetic CRS:  WGS 84

1.2 Data Wrangling

1.2.1 Recoding NA values into string

In the code chunk below, replace_na() is used to recode all the NA values in status_cle field into Unknown.

wp_nga <- read_rds("geodata/wp_nga.rds") %>%
  mutate(status_cle = replace_na(status_cle, "Unknown"))

1.2.2 EDA

In the code chunk below, freq() of funModeling package is used to display the distribution of status_cle field in wp_nga.

freq(data=wp_nga, 
     input = 'status_cle')

Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
of ggplot2 3.3.4.
ℹ The deprecated feature was likely used in the funModeling package.
  Please report the issue at <https://github.com/pablo14/funModeling/issues>.

                        status_cle frequency percentage cumulative_perc
1                       Functional     16919      83.29           83.29
2      Functional but needs repair      2102      10.35           93.64
3        Functional but not in use       579       2.85           96.49
4                          Unknown       396       1.95           98.44
5         Abandoned/Decommissioned       234       1.15           99.59
6                        Abandoned        76       0.37           99.96
7                   Non-Functional         5       0.02           99.98
8 Non functional due to dry season         2       0.01          100.00

1.3 Extracting Water Point Data

In this section, we will extract the water point records by using classes in status_cle field.

1.3.1 Extracting the functional water point data

in this code chunk below, filter() is used to select functional water points

wpt_functional <- wp_nga %>%
  filter(status_cle %in%
           c("Functional", 
             "Functional but not in use",
             "Functional but needs repair"))

freq(data=wpt_functional, 
     input = 'status_cle')

                   status_cle frequency percentage cumulative_perc
1                  Functional     16919      86.32           86.32
2 Functional but needs repair      2102      10.72           97.04
3   Functional but not in use       579       2.95          100.00

1.3.2 Extracting non-funtional water point

In the code chunk below, filter() of dplyr is used to select non-functional water points.

wpt_nonfunctional <- wp_nga %>%
  filter(status_cle %in%
           c("Abandoned/Decommissioned", 
             "Abandoned",
             "Non-Functional",
             "Non functional due to dry season",
             "Non-Functional due to dry season"))

freq(data=wpt_nonfunctional, 
     input = 'status_cle')

                        status_cle frequency percentage cumulative_perc
1         Abandoned/Decommissioned       234      73.82           73.82
2                        Abandoned        76      23.97           97.79
3                   Non-Functional         5       1.58           99.37
4 Non functional due to dry season         2       0.63          100.00

1.3.3 Extracting water point with Unknown class

In the code chunk below, filter() of dplyr is used to select water points with unknown status.

wpt_unknown <- wp_nga %>%
  filter(status_cle == "Unknown")

freq(data=wpt_unknown, 
     input = 'status_cle')

  status_cle frequency percentage cumulative_perc
1    Unknown       396        100             100

1.4 Performing Point-in-Polygon Count

The point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon.

nga_wp <- nga %>% 
  mutate(`total wpt` = lengths(
    st_intersects(nga, wp_nga))) %>%
  mutate(`wpt functional` = lengths(
    st_intersects(nga, wpt_functional))) %>%
  mutate(`wpt non-functional` = lengths(
    st_intersects(nga, wpt_nonfunctional))) %>%
  mutate(`wpt unknown` = lengths(
    st_intersects(nga, wpt_unknown)))

1.5 Saving the Analytical Data Table

nga_wp <- nga_wp %>%
  mutate(pct_functional = `wpt functional`/`total wpt`) %>%
  mutate(`pct_non-functional` = `wpt non-functional`/`total wpt`) %>%
  select(3:4, 9:10, 18:23)

Things to learn from the code chunk above:

mutate() of dplyr package is used to derive two fields namely pct_functional and pct_non-functional.

to keep the file size small, select() of dplyr is used to retain only field 3,4,9,10, 18,19,20,21,22,and 23.

Now, you have the tidy sf data table subsequent analysis. We will save the sf data table into rds format.

write_rds(nga_wp, "geodata/nga_wp.rds")

There is only data file we use, nga_wp.rds, which is the combination of the geospatial and aspatial data.

1.6 Visualising the spatial dsitribution of water points

nga_wp <- read_rds("geodata/nga_wp.rds")
total <- qtm(nga_wp, "total wpt")
wp_functional <- qtm(nga_wp, "wpt functional")
wp_nonfunctional <- qtm(nga_wp, "wpt non-functional")
unknown <- qtm(nga_wp, "wpt unknown")

tmap_arrange(total, wp_functional, wp_nonfunctional, unknown, asp=1, ncol=2)

2 Outliers/Clusters Analysis

2.1 Global Spatial Autocorrelation

2.1.1 Computing Contiguity Spatial Weights

wm_q <- poly2nb(nga_wp, 
                queen=TRUE)
summary(wm_q)

Neighbour list object:
Number of regions: 774 
Number of nonzero links: 4440 
Percentage nonzero weights: 0.7411414 
Average number of links: 5.736434 
1 region with no links:
86
Link number distribution:

  0   1   2   3   4   5   6   7   8   9  10  11  12  14 
  1   2  14  57 125 182 140 122  72  41  12   4   1   1 
2 least connected regions:
138 560 with 1 link
1 most connected region:
508 with 14 links

The summary report above shows that there are 774 area units in Hunan. The most connected area unit has 14 neighbours. There are two area units (138 and 560) with only one neighbours.

2.1.2 Row-standardised weights matrix

Now we calculate

Because there is 1 region with no links in the NGA data, I use set.ZeroPolicyOption(TRUE) to create the Weights Matrix.

set.ZeroPolicyOption(TRUE)

[1] FALSE

rswm_q <- nb2listw(wm_q, 
                   style="W", 
                   zero.policy = TRUE
                   )
rswm_q

Characteristics of weights list object:
Neighbour list object:
Number of regions: 774 
Number of nonzero links: 4440 
Percentage nonzero weights: 0.7411414 
Average number of links: 5.736434 
1 region with no links:
86

Weights style: W 
Weights constants summary:
    n     nn  S0       S1       S2
W 773 597529 773 285.0658 3198.414

2.1.3 Global Spatial Autocorrelation: Moran’s I

Moran’s I is a measure of spatial autocorrelation

I use moran.test() of spdep to do Moran’s I statistics testing

2.1.3.1 Maron’s I test

(1) Funtional waterpoint

moran.test(nga_wp$`wpt functional`, 
           listw=rswm_q, 
           zero.policy = TRUE, 
           na.action=na.omit)

    Moran I test under randomisation

data:  nga_wp$`wpt functional`  
weights: rswm_q  n reduced by no-neighbour observations
  

Moran I statistic standard deviate = 27.729, p-value < 2.2e-16
alternative hypothesis: greater
sample estimates:
Moran I statistic       Expectation          Variance 
      0.597453820      -0.001295337       0.000466245 

p-value<0.01, means we reject Null hypothesis.

The code chunk below performs 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(nga_wp$`wpt functional`, 
                listw=rswm_q, 
                nsim=999, 
                zero.policy = TRUE, 
                na.action=na.omit)
bperm

    Monte-Carlo simulation of Moran I

data:  nga_wp$`wpt functional` 
weights: rswm_q  
number of simulations + 1: 1000 

statistic = 0.59745, observed rank = 1000, p-value = 0.001
alternative hypothesis: greater

In the code chunk below we use hist() and abline() to visualize Monte Carlo Moran’s I

mean(bperm$res[1:999])

[1] -0.001937958

var(bperm$res[1:999])

[1] 0.0004471542

summary(bperm$res[1:999])

     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-0.066100 -0.016121 -0.002669 -0.001938  0.011703  0.077458 

hist(bperm$res, 
     freq=TRUE, 
     breaks=20, 
     xlab="Simulated Moran's I")
abline(v=0, 
       col="red") 

(2) Water-non fuctional

moran.test(nga_wp$`wpt non-functional`, 
           listw=rswm_q, 
           zero.policy = TRUE, 
           na.action=na.omit)

    Moran I test under randomisation

data:  nga_wp$`wpt non-functional`  
weights: rswm_q  n reduced by no-neighbour observations
  

Moran I statistic standard deviate = 10.244, p-value < 2.2e-16
alternative hypothesis: greater
sample estimates:
Moran I statistic       Expectation          Variance 
     0.2144866157     -0.0012953368      0.0004437415 

set.seed(1234)
bperm= moran.mc(nga_wp$`wpt non-functional`, 
                listw=rswm_q, 
                nsim=999, 
                zero.policy = TRUE, 
                na.action=na.omit)
bperm

    Monte-Carlo simulation of Moran I

data:  nga_wp$`wpt non-functional` 
weights: rswm_q  
number of simulations + 1: 1000 

statistic = 0.21449, observed rank = 1000, p-value = 0.001
alternative hypothesis: greater

In the code chunk below we use hist() and abline() to visualize Monte Carlo Moran’s I

mean(bperm$res[1:999])

[1] -0.002834731

var(bperm$res[1:999])

[1] 0.0003851432

summary(bperm$res[1:999])

     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-0.046615 -0.016790 -0.005141 -0.002835  0.009189  0.093353 

hist(bperm$res, 
     freq=TRUE, 
     breaks=20, 
     xlab="Simulated Moran's I")
abline(v=0, 
       col="red") 

2.2 Spatial Correlogram

2.2.1 Compute Moran’s I correlogram

(1) Functional water points

MI_corr <- sp.correlogram(wm_q, 
                          nga_wp$`wpt functional`, 
                          order=6, 
                          method="I", 
                          style="W")
plot(MI_corr)

print(MI_corr)

Spatial correlogram for nga_wp$`wpt functional` 
method: Moran's I
           estimate expectation    variance standard deviate Pr(I) two sided
1 (773)  5.9745e-01 -1.2953e-03  4.6625e-04           27.729       < 2.2e-16
2 (773)  4.9033e-01 -1.2953e-03  1.9980e-04           34.781       < 2.2e-16
3 (773)  3.9305e-01 -1.2953e-03  1.2053e-04           35.920       < 2.2e-16
4 (773)  3.2632e-01 -1.2953e-03  8.6612e-05           35.202       < 2.2e-16
5 (773)  2.3144e-01 -1.2953e-03  6.8012e-05           28.221       < 2.2e-16
6 (773)  1.4209e-01 -1.2953e-03  5.6741e-05           19.035       < 2.2e-16
           
1 (773) ***
2 (773) ***
3 (773) ***
4 (773) ***
5 (773) ***
6 (773) ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(2) Not Functional water points

MI_corr <- sp.correlogram(wm_q, 
                          nga_wp$`wpt non-functional`, 
                          order=6, 
                          method="I", 
                          style="W")
plot(MI_corr)

print(MI_corr)

Spatial correlogram for nga_wp$`wpt non-functional` 
method: Moran's I
           estimate expectation    variance standard deviate Pr(I) two sided
1 (773)  2.1449e-01 -1.2953e-03  4.4374e-04          10.2435       < 2.2e-16
2 (773)  1.0322e-01 -1.2953e-03  1.9016e-04           7.5792       3.478e-14
3 (773)  7.7266e-02 -1.2953e-03  1.1471e-04           7.3351       2.216e-13
4 (773)  5.8938e-02 -1.2953e-03  8.2437e-05           6.6341       3.266e-11
5 (773)  4.0501e-02 -1.2953e-03  6.4736e-05           5.1948       2.049e-07
6 (773)  2.4576e-02 -1.2953e-03  5.4011e-05           3.5203        0.000431
           
1 (773) ***
2 (773) ***
3 (773) ***
4 (773) ***
5 (773) ***
6 (773) ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

2.3 Cluster and Outlier Analysis

I use Local Indicators for Spatial Association (LISA) to detect cluster and/or outlier from functional waterpoint and Not Functional water points of Nigeria

2.3.1 Functional water points

2.3.1.1 Computing local Moran’s I

I use shapeID column because there are duplication “Bassa, Ifelodun, Irepodun, Nasarawa, Obi, Surulere” in shapename column

fips <- order(nga_wp$shapeID)
localMI <- localmoran(nga_wp$`wpt functional`, rswm_q)
head(localMI)

            Ii          E.Ii       Var.Ii       Z.Ii Pr(z != E(Ii))
1  0.072133151 -3.070532e-04 0.0591657387  0.2978136   7.658454e-01
2 -0.042519745 -1.241765e-05 0.0031954141 -0.7519695   4.520694e-01
3  0.453434964 -5.865912e-04 0.1508598995  1.1689329   2.424307e-01
4 -0.162429843 -9.740804e-05 0.0106857965 -1.5703695   1.163292e-01
5  0.006090939 -4.911403e-06 0.0007563421  0.2216538   8.245834e-01
6  2.719950590 -2.940625e-03 0.3216733273  4.8009012   1.579532e-06

localmoran() function returns a matrix of values whose columns are:

Ii: the local Moran’s I statistics

E.Ii: the expectation of local moran statistic under the randomisation hypothesis

Var.Ii: the variance of local moran statistic under the randomisation hypothesis

Z.Ii:the standard deviate of local moran statistic

Pr(): the p-value of local moran statistic

printCoefmat(data.frame(
  localMI[fips,], 
  row.names=nga_wp$shapeID[fips]),
  check.names=FALSE)

                                    Ii        E.Ii      Var.Ii        Z.Ii
NGA-ADM2-72505758B10049836  4.5343e-01 -5.8659e-04  2.2658e-01  9.5381e-01
NGA-ADM2-72505758B10063467 -9.6710e-02 -4.8993e-05  9.4429e-03 -9.9471e-01
NGA-ADM2-72505758B10065661 -2.8800e-01 -5.6662e-03  6.1813e-01 -3.5910e-01
NGA-ADM2-72505758B10302610  2.9115e-01 -4.9757e-04  6.3739e-02  1.1552e+00
NGA-ADM2-72505758B10682130  4.5343e-01 -5.8659e-04  9.0281e-02  1.5110e+00
NGA-ADM2-72505758B11317593 -9.3856e-03 -6.0372e-04  9.2915e-02 -2.8810e-02
NGA-ADM2-72505758B1132196   1.3739e-01 -3.0705e-04  3.3677e-02  7.5033e-01
NGA-ADM2-72505758B11373444  4.4896e-01 -5.8659e-04  1.1300e-01  1.3373e+00
NGA-ADM2-72505758B11735424  4.5343e-01 -5.8659e-04  6.4318e-02  1.7902e+00
NGA-ADM2-72505758B11870040  4.5343e-01 -5.8659e-04  9.0281e-02  1.5110e+00
NGA-ADM2-72505758B11997780  4.5343e-01 -5.8659e-04  5.6205e-02  1.9151e+00
NGA-ADM2-72505758B122892   -7.1407e-02 -1.0067e-05  1.9404e-03 -1.6208e+00
NGA-ADM2-72505758B12413588  4.5343e-01 -5.8659e-04  7.5136e-02  1.6564e+00
NGA-ADM2-72505758B1244901   1.8731e-01 -5.4117e-04  5.9340e-02  7.7114e-01
NGA-ADM2-72505758B12596325  4.5343e-01 -5.8659e-04  6.4318e-02  1.7902e+00
NGA-ADM2-72505758B12674914  9.2220e-01 -9.7765e-04  1.5041e-01  2.3804e+00
NGA-ADM2-72505758B12680831  4.5343e-01 -5.8659e-04  9.0281e-02  1.5110e+00
NGA-ADM2-72505758B12769973  4.5343e-01 -5.8659e-04  7.5136e-02  1.6564e+00
NGA-ADM2-72505758B12816297 -1.8706e-02 -1.5863e-06  2.4429e-04 -1.1967e+00
NGA-ADM2-72505758B13021078  4.5343e-01 -5.8659e-04  6.4318e-02  1.7902e+00
NGA-ADM2-72505758B13075745  4.5343e-01 -5.8659e-04  4.4847e-02  2.1439e+00
NGA-ADM2-72505758B13233811  2.2813e-02 -6.5905e-06  1.6959e-03  5.5413e-01
NGA-ADM2-72505758B13380599  6.1078e-02 -1.6230e-04  2.0797e-02  4.2466e-01
NGA-ADM2-72505758B13427126  5.1892e-01 -1.4413e-03  2.2163e-01  1.1053e+00
NGA-ADM2-72505758B13487741  4.5343e-01 -5.8659e-04  7.5136e-02  1.6564e+00
NGA-ADM2-72505758B13685756  2.0082e-01 -1.6230e-04  3.1277e-02  1.1365e+00
NGA-ADM2-72505758B139854    4.5343e-01 -5.8659e-04  1.1300e-01  1.3506e+00
NGA-ADM2-72505758B14016122  4.5343e-01 -5.8659e-04  6.4318e-02  1.7902e+00
NGA-ADM2-72505758B14174427  2.2439e-01 -3.0705e-04  5.9166e-02  9.2378e-01
NGA-ADM2-72505758B14213332  2.1590e-01 -4.1587e-04  8.0125e-02  7.6421e-01
NGA-ADM2-72505758B14369579 -2.3397e-02 -1.6230e-04  2.4989e-02 -1.4698e-01
NGA-ADM2-72505758B14654508 -9.9657e-02 -3.7777e-04  7.2787e-02 -3.6799e-01
NGA-ADM2-72505758B14842261 -1.5058e-01 -1.1721e-04  1.1236e-02 -1.4195e+00
NGA-ADM2-72505758B15135669  4.5343e-01 -5.8659e-04  5.6205e-02  1.9151e+00
NGA-ADM2-72505758B15152925  1.5866e-01 -1.2418e-05  1.9123e-03  3.6285e+00
NGA-ADM2-72505758B15168871  4.1985e-01 -5.8659e-04  5.6205e-02  1.7734e+00
NGA-ADM2-72505758B15269567 -2.6156e-01 -2.7444e-04  2.3351e-02 -1.7099e+00
NGA-ADM2-72505758B15283345 -6.5138e-02 -5.4031e-05  6.9244e-03 -7.8214e-01
NGA-ADM2-72505758B15329511  1.9968e-03 -9.1702e-08  1.4122e-05  5.3138e-01
NGA-ADM2-72505758B15626765  4.4627e-01 -5.8659e-04  9.0281e-02  1.4872e+00
NGA-ADM2-72505758B15745475  1.6682e-01 -1.9733e-04  1.8914e-02  1.2144e+00
NGA-ADM2-72505758B15928088  8.6339e+00 -4.1790e-02  4.3932e+00  4.1391e+00
NGA-ADM2-72505758B1616690   3.1706e+00 -2.6376e-03  4.0511e-01  4.9856e+00
NGA-ADM2-72505758B16281923 -1.0863e-01 -9.7408e-05  1.4999e-02 -8.8618e-01
NGA-ADM2-72505758B16283774  4.5343e-01 -5.8659e-04  1.1300e-01  1.3506e+00
NGA-ADM2-72505758B16331092 -1.1025e-01 -4.9757e-04  6.3739e-02 -4.3471e-01
NGA-ADM2-72505758B16408752 -1.6556e-01 -9.7408e-05  1.2483e-02 -1.4809e+00
NGA-ADM2-72505758B16424915  1.9150e+00 -3.5961e-03  4.5924e-01  2.8312e+00
NGA-ADM2-72505758B16610760  4.5343e-01 -5.8659e-04  6.4318e-02  1.7902e+00
NGA-ADM2-72505758B16696559  4.9135e-01 -8.0641e-04  8.8402e-02  1.6553e+00
NGA-ADM2-72505758B16765159 -2.4029e-01 -4.1587e-04  3.9854e-02 -1.2016e+00
NGA-ADM2-72505758B16773759  4.5343e-01 -5.8659e-04  9.0281e-02  1.5110e+00
NGA-ADM2-72505758B17259178  1.4667e+00 -9.1874e-04  1.7692e-01  3.4891e+00
NGA-ADM2-72505758B17453237  1.7848e-02 -5.4031e-05  8.3202e-03  1.9626e-01
NGA-ADM2-72505758B17534332  4.5343e-01 -5.8659e-04  9.0281e-02  1.5110e+00
NGA-ADM2-72505758B17563771  4.5343e-01 -5.8659e-04  1.1300e-01  1.3506e+00
NGA-ADM2-72505758B17614134  1.7009e+00 -3.2601e-03  5.0042e-01  2.4091e+00
NGA-ADM2-72505758B17633838  1.1906e-03 -2.5869e-05  9.9982e-03  1.2166e-02
NGA-ADM2-72505758B17736122  1.8383e-01 -1.8759e-04  2.4037e-02  1.1869e+00
NGA-ADM2-72505758B1782277   3.8763e-03 -4.2752e-07  5.4793e-05  5.2373e-01
NGA-ADM2-72505758B18027142  4.4896e-01 -5.8659e-04  1.1300e-01  1.3373e+00
NGA-ADM2-72505758B18156007  4.5343e-01 -5.8659e-04  9.0281e-02  1.5110e+00
NGA-ADM2-72505758B18272004  1.0956e-01 -1.8759e-04  2.4037e-02  7.0783e-01
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NGA-ADM2-72505758B95606818  2.8015e-02 -4.9114e-06  4.1800e-04  1.3705e+00
NGA-ADM2-72505758B95781523  4.5343e-01 -5.8659e-04  6.4318e-02  1.7902e+00
NGA-ADM2-72505758B9585780   1.0670e+00 -3.7118e-03  4.0571e-01  1.6810e+00
NGA-ADM2-72505758B95859729  3.8315e-01 -4.9690e-03  1.2723e+00  3.4409e-01
NGA-ADM2-72505758B95872281 -1.7815e-01 -2.4366e-04  4.6953e-02 -8.2105e-01
NGA-ADM2-72505758B95999274  4.5343e-01 -5.8659e-04  9.0281e-02  1.5110e+00
NGA-ADM2-72505758B9609327   4.5343e-01 -5.8659e-04  9.0281e-02  1.5110e+00
NGA-ADM2-72505758B9615674   2.0317e-01 -4.9757e-04  4.7680e-02  9.3273e-01
NGA-ADM2-72505758B96206882  2.0661e+00 -2.5402e-03  4.8838e-01  2.9601e+00
NGA-ADM2-72505758B96230569  1.6304e-02 -4.8993e-05  6.2789e-03  2.0638e-01
NGA-ADM2-72505758B9625976   2.1125e+00 -3.1518e-03  4.8384e-01  3.0416e+00
NGA-ADM2-72505758B96315687  6.1722e-02 -3.4150e-04  5.2572e-02  2.7068e-01
NGA-ADM2-72505758B96375167  2.6565e-02 -5.8659e-04  7.5136e-02  9.9054e-02
NGA-ADM2-72505758B96655345  4.5343e-01 -5.8659e-04  9.0281e-02  1.5110e+00
NGA-ADM2-72505758B9668183   1.8003e-02 -2.0075e-05  1.9246e-03  4.1083e-01
NGA-ADM2-72505758B96685701  4.5343e-01 -5.8659e-04  6.4318e-02  1.7902e+00
NGA-ADM2-72505758B96746323 -3.0735e-02 -5.3818e-03  1.0318e+00 -2.4960e-02
NGA-ADM2-72505758B9692286   4.5343e-01 -5.8659e-04  1.1300e-01  1.3506e+00
NGA-ADM2-72505758B96981662  4.5343e-01 -5.8659e-04  1.1300e-01  1.3506e+00
NGA-ADM2-72505758B97139317  4.5343e-01 -5.8659e-04  1.1300e-01  1.3506e+00
NGA-ADM2-72505758B97184317  2.6031e-02 -9.7408e-05  9.3379e-03  2.7039e-01
NGA-ADM2-72505758B9725515   4.5343e-01 -5.8659e-04  1.5086e-01  1.1689e+00
NGA-ADM2-72505758B97294598  1.6467e-01 -4.0882e-05  4.4850e-03  2.4595e+00
NGA-ADM2-72505758B97405906  8.4213e-03 -3.0705e-04  3.9341e-02  4.4005e-02
NGA-ADM2-72505758B97448934  4.5343e-01 -5.8659e-04  1.1300e-01  1.3506e+00
NGA-ADM2-72505758B9755199   3.3742e-02 -2.0075e-05  3.8694e-03  5.4276e-01
NGA-ADM2-72505758B98057596 -9.5767e-02 -2.5869e-05  2.2016e-03 -2.0404e+00
NGA-ADM2-72505758B98072407 -6.4016e-02 -1.0067e-05  1.5503e-03 -1.6256e+00
NGA-ADM2-72505758B98086722  1.3948e-01 -2.1471e-04  1.8270e-02  1.0335e+00
NGA-ADM2-72505758B98116860 -2.3258e-02 -2.5869e-05  2.4801e-03 -4.6650e-01
NGA-ADM2-72505758B98120163  4.5343e-01 -5.8659e-04  1.1300e-01  1.3506e+00
NGA-ADM2-72505758B98218468  4.5343e-01 -5.8659e-04  7.5136e-02  1.6564e+00
NGA-ADM2-72505758B98262124  1.9079e-01 -8.5820e-05  1.0998e-02  1.8201e+00
NGA-ADM2-72505758B98593855  4.5140e-01 -2.2512e-04  2.1578e-02  3.0745e+00
NGA-ADM2-72505758B98658548  2.2782e-02 -6.3301e-05  5.3871e-03  3.1126e-01
NGA-ADM2-72505758B98737176  4.5343e-01 -5.8659e-04  1.1300e-01  1.3506e+00
NGA-ADM2-72505758B98765613 -9.7229e-02 -2.5869e-05  3.3154e-03 -1.6882e+00
NGA-ADM2-72505758B99221548  1.0190e-01 -2.2512e-04  2.8846e-02  6.0127e-01
NGA-ADM2-72505758B99270352 -3.4152e-02 -1.7053e-05  1.6349e-03 -8.4423e-01
NGA-ADM2-72505758B99641746  4.4985e-01 -5.8659e-04  9.0281e-02  1.4991e+00
NGA-ADM2-72505758B99650649  3.0292e+00 -1.7465e-03  2.2344e-01  6.4119e+00
NGA-ADM2-72505758B99764805  4.5343e-01 -5.8659e-04  9.0281e-02  1.5110e+00
NGA-ADM2-72505758B9986554   6.7927e-02 -1.7136e-04  4.4090e-02  3.2431e-01
NGA-ADM2-72505758B99970923 -3.0153e-02 -2.5869e-05  6.6568e-03 -3.6926e-01
                           Pr.z....E.Ii..
NGA-ADM2-72505758B10049836         0.3402
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NGA-ADM2-72505758B10065661         0.7195
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NGA-ADM2-72505758B11317593         0.9770
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NGA-ADM2-72505758B25708171            NaN
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NGA-ADM2-72505758B8622199          0.0106
NGA-ADM2-72505758B86358915         0.4523
NGA-ADM2-72505758B8652160          0.0345
NGA-ADM2-72505758B86583227         0.0060
NGA-ADM2-72505758B86734523         0.0421
NGA-ADM2-72505758B86763634         0.1308
NGA-ADM2-72505758B86773608         0.9139
NGA-ADM2-72505758B86821483         0.1444
NGA-ADM2-72505758B8687564          0.0977
NGA-ADM2-72505758B86879364         0.0555
NGA-ADM2-72505758B8726241          0.0523
NGA-ADM2-72505758B8775504          0.0000
NGA-ADM2-72505758B87811615         0.0001
NGA-ADM2-72505758B87995813         0.1768
NGA-ADM2-72505758B88150775         0.0007
NGA-ADM2-72505758B88452088         0.5211
NGA-ADM2-72505758B88587475         0.1308
NGA-ADM2-72505758B88727897         0.0579
NGA-ADM2-72505758B88761962         0.9704
NGA-ADM2-72505758B88921590         0.0977
NGA-ADM2-72505758B88925335         0.1768
NGA-ADM2-72505758B8918259          0.0263
NGA-ADM2-72505758B89235976         0.7863
NGA-ADM2-72505758B89515171         0.0000
NGA-ADM2-72505758B8960534          0.0200
NGA-ADM2-72505758B89722002         0.2957
NGA-ADM2-72505758B89731144         0.0011
NGA-ADM2-72505758B89894474         0.6032
NGA-ADM2-72505758B90027140         0.0977
NGA-ADM2-72505758B90250628         0.0134
NGA-ADM2-72505758B90811761         0.0485
NGA-ADM2-72505758B91050715         0.8449
NGA-ADM2-72505758B91135250         0.0000
NGA-ADM2-72505758B913149           0.2759
NGA-ADM2-72505758B91510140         0.0000
NGA-ADM2-72505758B91579398         0.0057
NGA-ADM2-72505758B91650930         0.0000
NGA-ADM2-72505758B91687942         0.0977
NGA-ADM2-72505758B92105435         0.3930
NGA-ADM2-72505758B92139849         0.2817
NGA-ADM2-72505758B92277191         0.3806
NGA-ADM2-72505758B92576019         0.1020
NGA-ADM2-72505758B92786354         0.7691
NGA-ADM2-72505758B92819273         0.0977
NGA-ADM2-72505758B92921679         0.7442
NGA-ADM2-72505758B92954057         0.7957
NGA-ADM2-72505758B93424331         0.0977
NGA-ADM2-72505758B93427284         0.1351
NGA-ADM2-72505758B93593012         0.0002
NGA-ADM2-72505758B93638472         0.3217
NGA-ADM2-72505758B93649439         0.1338
NGA-ADM2-72505758B93709657         0.0977
NGA-ADM2-72505758B93737389         0.5076
NGA-ADM2-72505758B93761587         0.0734
NGA-ADM2-72505758B93767969         0.0555
NGA-ADM2-72505758B94189690         0.6446
NGA-ADM2-72505758B94509825         0.1308
NGA-ADM2-72505758B94606913         0.0001
NGA-ADM2-72505758B94629448         0.1308
NGA-ADM2-72505758B94685339         0.1768
NGA-ADM2-72505758B94886311         0.0000
NGA-ADM2-72505758B94925970         0.0000
NGA-ADM2-72505758B94954595         0.0555
NGA-ADM2-72505758B95154533         0.0016
NGA-ADM2-72505758B95191090         0.1768
NGA-ADM2-72505758B95323810         0.1308
NGA-ADM2-72505758B95411855         0.2955
NGA-ADM2-72505758B95429572         0.7436
NGA-ADM2-72505758B95534398         0.4686
NGA-ADM2-72505758B95566521         0.9052
NGA-ADM2-72505758B95606818         0.1705
NGA-ADM2-72505758B95781523         0.0734
NGA-ADM2-72505758B9585780          0.0928
NGA-ADM2-72505758B95859729         0.7308
NGA-ADM2-72505758B95872281         0.4116
NGA-ADM2-72505758B95999274         0.1308
NGA-ADM2-72505758B9609327          0.1308
NGA-ADM2-72505758B9615674          0.3510
NGA-ADM2-72505758B96206882         0.0031
NGA-ADM2-72505758B96230569         0.8365
NGA-ADM2-72505758B9625976          0.0024
NGA-ADM2-72505758B96315687         0.7866
NGA-ADM2-72505758B96375167         0.9211
NGA-ADM2-72505758B96655345         0.1308
NGA-ADM2-72505758B9668183          0.6812
NGA-ADM2-72505758B96685701         0.0734
NGA-ADM2-72505758B96746323         0.9801
NGA-ADM2-72505758B9692286          0.1768
NGA-ADM2-72505758B96981662         0.1768
NGA-ADM2-72505758B97139317         0.1768
NGA-ADM2-72505758B97184317         0.7869
NGA-ADM2-72505758B9725515          0.2424
NGA-ADM2-72505758B97294598         0.0139
NGA-ADM2-72505758B97405906         0.9649
NGA-ADM2-72505758B97448934         0.1768
NGA-ADM2-72505758B9755199          0.5873
NGA-ADM2-72505758B98057596         0.0413
NGA-ADM2-72505758B98072407         0.1040
NGA-ADM2-72505758B98086722         0.3014
NGA-ADM2-72505758B98116860         0.6409
NGA-ADM2-72505758B98120163         0.1768
NGA-ADM2-72505758B98218468         0.0977
NGA-ADM2-72505758B98262124         0.0687
NGA-ADM2-72505758B98593855         0.0021
NGA-ADM2-72505758B98658548         0.7556
NGA-ADM2-72505758B98737176         0.1768
NGA-ADM2-72505758B98765613         0.0914
NGA-ADM2-72505758B99221548         0.5477
NGA-ADM2-72505758B99270352         0.3985
NGA-ADM2-72505758B99641746         0.1338
NGA-ADM2-72505758B99650649         0.0000
NGA-ADM2-72505758B99764805         0.1308
NGA-ADM2-72505758B9986554          0.7457
NGA-ADM2-72505758B99970923         0.7119

• Mapping the local Moran’s I: I append the local Moran’s I dataframe onto Nigeria spatial polygon dataframe

nga_wp.localMI <- cbind(nga_wp,localMI) %>%
  rename(Pr.Ii = Pr.z....E.Ii..)

• Mapping local Moran’s I values: Using choropleth mapping functions of tmap package,I plot the local Moran’s I values by using the code chinks below

tm_shape(nga_wp.localMI) +
  tm_fill(col = "Ii", 
          style = "pretty",
          palette = "RdBu",
          title = "local moran statistics") +
  tm_borders(alpha = 0.5)

Variable(s) "Ii" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

• Mapping local Moran’s I p-values

tm_shape(nga_wp.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(nga_wp.localMI) +
  tm_fill(col = "Ii", 
          style = "pretty", 
          title = "local moran statistics") +
  tm_borders(alpha = 0.5)

pvalue.map <- tm_shape(nga_wp.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)

Variable(s) "Ii" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

2.3.1.2 Creating a LISA Cluster Map

(1) Plotting Moran scatterplot

nci <- moran.plot(nga_wp$`wpt functional`, rswm_q,
                  labels=as.character(nga_wp$shapeName), 
                  xlab="GDPPC 2012", 
                  ylab="Spatially Lag GDPPC 2012")

the plot is split in 4 quadrants.

(2) Plotting Moran scatterplot with standardised variable

nga_wp$Z.wpt_functional <- scale(nga_wp$`wpt functional`) %>% 
  as.vector 

nci2 <- moran.plot(nga_wp$Z.wpt_functional, rswm_q,
                   labels=as.character(nga_wp$shapeName),
                   xlab="z-GDPPC 2012", 
                   ylab="Spatially Lag z-GDPPC 2012")

(3) Preparing LISA map classes

quadrant <- vector(mode="numeric",length=nrow(localMI))

nga_wp$lag_wpt_functional <- lag.listw(rswm_q, nga_wp$`wpt functional`)
DV <- nga_wp$lag_wpt_functional - mean(nga_wp$lag_wpt_functional)     

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] <- 0

quadrant <- vector(mode="numeric",length=nrow(localMI))
nga_wp$lag_wpt_functional <- lag.listw(rswm_q, nga_wp$`wpt functional`)
DV <- nga_wp$lag_wpt_functional - mean(nga_wp$lag_wpt_functional)     
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] <- 0

(4) Plotting LISA map

nga_wp.localMI$quadrant <- quadrant
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high")

tm_shape(nga_wp.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(nga_wp, "wpt functional")

nga_wp.localMI$quadrant <- quadrant
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high")

LISAmap <- tm_shape(nga_wp.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)

2.3.2 Not Functional water points

2.3.1.1 Computing local Moran’s I

I use shapeID column because there are duplication “Bassa, Ifelodun, Irepodun, Nasarawa, Obi, Surulere” in shapename column

fips <- order(nga_wp$shapeID)
localMI <- localmoran(nga_wp$`wpt non-functional`, rswm_q)
head(localMI)

            Ii          E.Ii     Var.Ii        Z.Ii Pr(z != E(Ii))
1 -0.743259879 -0.0001170554 0.02255956 -4.94774157   7.507950e-07
2  1.164028068 -0.0002485396 0.06394121  4.60432271   4.138104e-06
3  0.090483811 -0.0001170554 0.03011852  0.52205410   6.016327e-01
4 -0.004801182 -0.0001170554 0.01284088 -0.04133626   9.670278e-01
5  3.475006771 -0.0017934796 0.27569679  6.62161433   3.552971e-11
6  0.058722147 -0.0001170554 0.01284088  0.51924139   6.035924e-01

localmoran() function returns a matrix of values whose columns are:

Ii: the local Moran’s I statistics

E.Ii: the expectation of local moran statistic under the randomisation hypothesis

Var.Ii: the variance of local moran statistic under the randomisation hypothesis

Z.Ii:the standard deviate of local moran statistic

Pr(): the p-value of local moran statistic

printCoefmat(data.frame(
  localMI[fips,], 
  row.names=nga_wp$shapeID[fips]),
  check.names=FALSE)

                                    Ii        E.Ii      Var.Ii        Z.Ii
NGA-ADM2-72505758B10049836 -0.46534532 -0.00011706  0.04523646 -2.18736768
NGA-ADM2-72505758B10063467 -0.02068201 -0.00011706  0.02255956 -0.13691863
NGA-ADM2-72505758B10065661  0.09048381 -0.00011706  0.01284088  0.79953022
NGA-ADM2-72505758B10302610 -0.02068201 -0.00011706  0.01500059 -0.16790888
NGA-ADM2-72505758B10682130  0.09048381 -0.00011706  0.01802418  0.67484594
NGA-ADM2-72505758B11317593  0.00155115 -0.00011706  0.01802418  0.01242573
NGA-ADM2-72505758B1132196   0.02696048 -0.00011706  0.01284088  0.23895257
NGA-ADM2-72505758B11373444  0.09048381 -0.00011706  0.02255956  0.60320797
NGA-ADM2-72505758B11735424  0.09048381 -0.00011706  0.01284088  0.79953022
NGA-ADM2-72505758B11870040  0.09048381 -0.00011706  0.01802418  0.67484594
NGA-ADM2-72505758B11997780  0.09048381 -0.00011706  0.01122111  0.85529222
NGA-ADM2-72505758B122892    0.09048381 -0.00011706  0.02255956  0.60320797
NGA-ADM2-72505758B12413588  0.09048381 -0.00011706  0.01500059  0.73973844
NGA-ADM2-72505758B1244901   0.05872215 -0.00011706  0.01284088  0.51924139
NGA-ADM2-72505758B12596325  0.09048381 -0.00011706  0.01284088  0.79953022
NGA-ADM2-72505758B12674914  0.04601748 -0.00011706  0.01802418  0.34363584
NGA-ADM2-72505758B12680831  0.09048381 -0.00011706  0.01802418  0.67484594
NGA-ADM2-72505758B12769973  0.09048381 -0.00011706  0.01500059  0.73973844
NGA-ADM2-72505758B12816297  0.00155115 -0.00011706  0.01802418  0.01242573
NGA-ADM2-72505758B13021078  0.09048381 -0.00011706  0.01284088  0.79953022
NGA-ADM2-72505758B13075745  0.09048381 -0.00011706  0.00895342  0.95749822
NGA-ADM2-72505758B13233811  0.01637326 -0.00011706  0.03011852  0.09501937
NGA-ADM2-72505758B13380599 -0.46534532 -0.00011706  0.01500059 -3.79849820
NGA-ADM2-72505758B13427126  0.09048381 -0.00011706  0.01802418  0.67484594
NGA-ADM2-72505758B13487741  9.31089499 -0.17183549 18.23884152  2.22041822
NGA-ADM2-72505758B13685756  0.03490090 -0.00011706  0.02255956  0.23314467
NGA-ADM2-72505758B139854    0.09048381 -0.00011706  0.02255956  0.60320797
NGA-ADM2-72505758B14016122 -0.13184784 -0.00024854  0.02726102 -0.79704443
NGA-ADM2-72505758B14174427  0.03490090 -0.00011706  0.02255956  0.23314467
NGA-ADM2-72505758B14213332  0.19212114 -0.00024854  0.04789363  0.87901798
NGA-ADM2-72505758B14369579  1.03825188 -0.00179348  0.27569679  1.98078082
NGA-ADM2-72505758B14654508  0.09048381 -0.00011706  0.02255956  0.60320797
NGA-ADM2-72505758B14842261  0.06269236 -0.00011706  0.01122111  0.59293473
NGA-ADM2-72505758B15135669 -0.13184784 -0.00024854  0.02382225 -0.85263307
NGA-ADM2-72505758B15152925  0.04601748 -0.00011706  0.01802418  0.34363584
NGA-ADM2-72505758B15168871  0.09048381 -0.00011706  0.01122111  0.85529222
NGA-ADM2-72505758B15269567  0.06578029 -0.00011706  0.00996128  0.66025305
NGA-ADM2-72505758B15283345  9.22196233 -0.06503740  7.79336848  3.32669379
NGA-ADM2-72505758B15329511  0.37887972 -0.00912373  1.39221583  0.32883823
NGA-ADM2-72505758B15626765  0.09048381 -0.00011706  0.01802418  0.67484594
NGA-ADM2-72505758B15745475  0.06269236 -0.00011706  0.01122111  0.59293473
NGA-ADM2-72505758B15928088 -0.03656285 -0.00011706  0.01284088 -0.32162508
NGA-ADM2-72505758B1616690   0.38650252 -0.00024854  0.03826508  1.97710724
NGA-ADM2-72505758B16281923  0.04601748 -0.00011706  0.01802418  0.34363584
NGA-ADM2-72505758B16283774  0.09048381 -0.00011706  0.02255956  0.60320797
NGA-ADM2-72505758B16331092  0.01637326 -0.00011706  0.01500059  0.13464022
NGA-ADM2-72505758B16408752 -0.13184784 -0.00011706  0.01500059 -1.07555621
NGA-ADM2-72505758B16424915 -0.24301366 -0.00011706  0.01500059 -1.98320354
NGA-ADM2-72505758B16610760  0.09048381 -0.00011706  0.01284088  0.79953022
NGA-ADM2-72505758B16696559 -0.03928527 -0.00024854  0.02726102 -0.23642992
NGA-ADM2-72505758B16765159  0.00710944 -0.00011706  0.01122111  0.06821974
NGA-ADM2-72505758B16773759  0.09048381 -0.00011706  0.01802418  0.67484594
NGA-ADM2-72505758B17259178  0.09048381 -0.00011706  0.02255956  0.60320797
NGA-ADM2-72505758B17453237  0.25691493 -0.00024854  0.03826508  1.31464348
NGA-ADM2-72505758B17534332  0.09048381 -0.00011706  0.01802418  0.67484594
NGA-ADM2-72505758B17563771  0.09048381 -0.00011706  0.02255956  0.60320797
NGA-ADM2-72505758B17614134  0.04601748 -0.00011706  0.01802418  0.34363584
NGA-ADM2-72505758B17633838 -0.13184784 -0.00011706  0.04523646 -0.61935975
NGA-ADM2-72505758B17736122 -0.09479256 -0.00011706  0.01500059 -0.77300710
NGA-ADM2-72505758B1782277   0.01637326 -0.00011706  0.01500059  0.13464022
NGA-ADM2-72505758B18027142  0.09048381 -0.00011706  0.02255956  0.60320797
NGA-ADM2-72505758B18156007  0.09048381 -0.00011706  0.01802418  0.67484594
NGA-ADM2-72505758B18272004  0.05342854 -0.00011706  0.01500059  0.43718933
NGA-ADM2-72505758B1827434   0.23840242 -0.00024854  0.02726102  1.44541361
NGA-ADM2-72505758B18295427  0.04601748 -0.00011706  0.01802418  0.34363584
NGA-ADM2-72505758B18326272 -0.20595839 -0.00011706  0.03011852 -1.18608482
NGA-ADM2-72505758B18376242  0.09048381 -0.00011706  0.01500059  0.73973844
NGA-ADM2-72505758B18447698 -0.04291518 -0.00011706  0.01802418 -0.31878437
NGA-ADM2-72505758B18534598  0.08413148 -0.00024854  0.03184604  0.47283746
NGA-ADM2-72505758B18548676  0.12732734 -0.00024854  0.03826508  0.65217972
NGA-ADM2-72505758B18747813  0.03490090 -0.00011706  0.02255956  0.23314467
NGA-ADM2-72505758B18888506  0.09048381 -0.00011706  0.01802418  0.67484594
NGA-ADM2-72505758B18960886  0.02696048 -0.00011706  0.01284088  0.23895257
NGA-ADM2-72505758B19119765  0.06578029 -0.00011706  0.00996128  0.66025305
NGA-ADM2-72505758B19327087  0.09048381 -0.00011706  0.01802418  0.67484594
NGA-ADM2-72505758B19376786 -0.02068201 -0.00011706  0.01500059 -0.16790888
NGA-ADM2-72505758B19458752  0.05872215 -0.00011706  0.01284088  0.51924139
NGA-ADM2-72505758B19462210  0.09048381 -0.00011706  0.01802418  0.67484594
NGA-ADM2-72505758B19539344 -0.03656285 -0.00011706  0.01284088 -0.32162508
NGA-ADM2-72505758B196939   -0.02512865 -0.03072001  4.58548780  0.00261111
NGA-ADM2-72505758B19914513  0.09048381 -0.00011706  0.03011852  0.52205410
NGA-ADM2-72505758B20050296  0.05872215 -0.00011706  0.01284088  0.51924139
NGA-ADM2-72505758B20351569  0.09048381 -0.00011706  0.01500059  0.73973844
NGA-ADM2-72505758B20421162 10.97838237 -0.00912373  3.49413543  5.87799567
NGA-ADM2-72505758B20535362  0.09048381 -0.00011706  0.01802418  0.67484594
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NGA-ADM2-72505758B72340078         0.6620
NGA-ADM2-72505758B72369186         0.2440
NGA-ADM2-72505758B72408011         0.8208
NGA-ADM2-72505758B72527598         0.3924
NGA-ADM2-72505758B72583543         0.7311
NGA-ADM2-72505758B72901624         0.4254
NGA-ADM2-72505758B72996990         0.4998
NGA-ADM2-72505758B73155659         0.3924
NGA-ADM2-72505758B73169585         0.0000
NGA-ADM2-72505758B7318634          0.6092
NGA-ADM2-72505758B7324564          0.9901
NGA-ADM2-72505758B73267274         0.8156
NGA-ADM2-72505758B73302858         0.4998
NGA-ADM2-72505758B73332929         0.4240
NGA-ADM2-72505758B73850861         0.7311
NGA-ADM2-72505758B74167895         0.4595
NGA-ADM2-72505758B74224076         0.9670
NGA-ADM2-72505758B74273353         0.8156
NGA-ADM2-72505758B74442045         0.7311
NGA-ADM2-72505758B74527534         0.4998
NGA-ADM2-72505758B74576641         0.8929
NGA-ADM2-72505758B74718112         0.4595
NGA-ADM2-72505758B7490938          0.0000
NGA-ADM2-72505758B75034141         0.4364
NGA-ADM2-72505758B75040986         0.6711
NGA-ADM2-72505758B75230852         0.8131
NGA-ADM2-72505758B7553151          0.0082
NGA-ADM2-72505758B75536077         0.9918
NGA-ADM2-72505758B75784992         0.4998
NGA-ADM2-72505758B75801679         0.4998
NGA-ADM2-72505758B75908239         0.4240
NGA-ADM2-72505758B75983929         0.4998
NGA-ADM2-72505758B76052259         0.0003
NGA-ADM2-72505758B76392163         0.6036
NGA-ADM2-72505758B76566778         0.4595
NGA-ADM2-72505758B7691229          0.5464
NGA-ADM2-72505758B77062793         0.6016
NGA-ADM2-72505758B7732292          0.6637
NGA-ADM2-72505758B77767589         0.0000
NGA-ADM2-72505758B77907079         0.4998
NGA-ADM2-72505758B78258316         0.0001
NGA-ADM2-72505758B783054           0.9243
NGA-ADM2-72505758B78395267         0.5157
NGA-ADM2-72505758B7845389          0.3924
NGA-ADM2-72505758B78492046         0.4240
NGA-ADM2-72505758B78527113         0.4240
NGA-ADM2-72505758B78527729         0.4240
NGA-ADM2-72505758B78555816         0.9670
NGA-ADM2-72505758B7855953          0.3383
NGA-ADM2-72505758B78597532         0.4998
NGA-ADM2-72505758B78619683         0.4705
NGA-ADM2-72505758B78698197         0.7634
NGA-ADM2-72505758B78741094         0.4998
NGA-ADM2-72505758B79155077         0.4595
NGA-ADM2-72505758B79178637         0.9243
NGA-ADM2-72505758B79193959         0.8111
NGA-ADM2-72505758B79316383         0.6711
NGA-ADM2-72505758B79444654         0.3805
NGA-ADM2-72505758B79493017         0.4998
NGA-ADM2-72505758B7968540          0.7311
NGA-ADM2-72505758B79803896         0.6016
NGA-ADM2-72505758B79815894         0.0000
NGA-ADM2-72505758B79902123         0.5464
NGA-ADM2-72505758B79945925         0.8896
NGA-ADM2-72505758B79983056         0.0001
NGA-ADM2-72505758B80057854         0.7458
NGA-ADM2-72505758B80290097         0.9281
NGA-ADM2-72505758B8045942          0.4595
NGA-ADM2-72505758B80517430         0.3924
NGA-ADM2-72505758B80733792         0.7327
NGA-ADM2-72505758B80737371         0.0000
NGA-ADM2-72505758B80966644         0.4595
NGA-ADM2-72505758B81144344         0.4998
NGA-ADM2-72505758B8143254          0.6637
NGA-ADM2-72505758B8152058          0.9256
NGA-ADM2-72505758B81562716         0.9670
NGA-ADM2-72505758B81594808         0.9243
NGA-ADM2-72505758B81600634         0.4240
NGA-ADM2-72505758B81840583         0.6028
NGA-ADM2-72505758B8232613          0.3640
NGA-ADM2-72505758B82571199         0.4240
NGA-ADM2-72505758B82611067         0.5532
NGA-ADM2-72505758B82612540         0.7499
NGA-ADM2-72505758B82650021         0.5464
NGA-ADM2-72505758B82952463         0.7311
NGA-ADM2-72505758B82980400         0.9243
NGA-ADM2-72505758B83115922         0.5486
NGA-ADM2-72505758B83213265         0.8965
NGA-ADM2-72505758B83356374         0.4595
NGA-ADM2-72505758B83595220         0.9243
NGA-ADM2-72505758B83712041         0.4595
NGA-ADM2-72505758B83816053         0.7311
NGA-ADM2-72505758B83963728         0.8006
NGA-ADM2-72505758B83971794         0.9650
NGA-ADM2-72505758B84114048         0.5472
NGA-ADM2-72505758B84194123         0.5464
NGA-ADM2-72505758B84339715         0.6711
NGA-ADM2-72505758B84457876         0.6016
NGA-ADM2-72505758B84478450         0.8929
NGA-ADM2-72505758B84831958         0.5464
NGA-ADM2-72505758B84865629         0.9901
NGA-ADM2-72505758B85138406         0.5464
NGA-ADM2-72505758B85275479         0.0000
NGA-ADM2-72505758B85519087         0.4998
NGA-ADM2-72505758B86064137         0.4240
NGA-ADM2-72505758B86185926         0.6480
NGA-ADM2-72505758B8622199          0.0029
NGA-ADM2-72505758B86358915         0.6620
NGA-ADM2-72505758B8652160          0.7342
NGA-ADM2-72505758B86583227         0.4240
NGA-ADM2-72505758B86734523         0.5091
NGA-ADM2-72505758B86763634         0.4998
NGA-ADM2-72505758B86773608         0.6016
NGA-ADM2-72505758B86821483         0.4998
NGA-ADM2-72505758B8687564          0.4595
NGA-ADM2-72505758B86879364         0.3924
NGA-ADM2-72505758B8726241          0.6620
NGA-ADM2-72505758B8775504          0.7311
NGA-ADM2-72505758B87811615         0.8166
NGA-ADM2-72505758B87995813         0.5464
NGA-ADM2-72505758B88150775         0.6609
NGA-ADM2-72505758B88452088         0.6620
NGA-ADM2-72505758B88587475         0.0483
NGA-ADM2-72505758B88727897         0.4998
NGA-ADM2-72505758B88761962         0.4595
NGA-ADM2-72505758B88921590         0.4595
NGA-ADM2-72505758B88925335         0.5464
NGA-ADM2-72505758B8918259          0.4998
NGA-ADM2-72505758B89235976         0.3805
NGA-ADM2-72505758B89515171         0.2409
NGA-ADM2-72505758B8960534          0.1321
NGA-ADM2-72505758B89722002         0.4998
NGA-ADM2-72505758B89731144         0.7327
NGA-ADM2-72505758B89894474         0.4998
NGA-ADM2-72505758B90027140         0.4595
NGA-ADM2-72505758B90250628         0.6036
NGA-ADM2-72505758B90811761         0.5637
NGA-ADM2-72505758B91050715         0.4395
NGA-ADM2-72505758B91135250         0.3777
NGA-ADM2-72505758B913149           0.5532
NGA-ADM2-72505758B91510140         0.6620
NGA-ADM2-72505758B91579398         0.8929
NGA-ADM2-72505758B91650930         0.8710
NGA-ADM2-72505758B91687942         0.4595
NGA-ADM2-72505758B92105435         0.7311
NGA-ADM2-72505758B92139849         0.6016
NGA-ADM2-72505758B92277191         0.9901
NGA-ADM2-72505758B92576019         0.4595
NGA-ADM2-72505758B92786354         0.4240
NGA-ADM2-72505758B92819273         0.4595
NGA-ADM2-72505758B92921679         0.0000
NGA-ADM2-72505758B92954057         0.5126
NGA-ADM2-72505758B93424331         0.4595
NGA-ADM2-72505758B93427284         0.4395
NGA-ADM2-72505758B93593012         0.8156
NGA-ADM2-72505758B93638472         0.8156
NGA-ADM2-72505758B93649439         0.4998
NGA-ADM2-72505758B93709657         0.4595
NGA-ADM2-72505758B93737389         0.7311
NGA-ADM2-72505758B93761587         0.4240
NGA-ADM2-72505758B93767969         0.3924
NGA-ADM2-72505758B94189690         0.3254
NGA-ADM2-72505758B94509825         0.4998
NGA-ADM2-72505758B94606913         0.3805
NGA-ADM2-72505758B94629448         0.4998
NGA-ADM2-72505758B94685339         0.5464
NGA-ADM2-72505758B94886311         0.8439
NGA-ADM2-72505758B94925970         0.5637
NGA-ADM2-72505758B94954595         0.3924
NGA-ADM2-72505758B95154533         0.4595
NGA-ADM2-72505758B95191090         0.5464
NGA-ADM2-72505758B95323810         0.4998
NGA-ADM2-72505758B95411855         0.8461
NGA-ADM2-72505758B95429572         0.8929
NGA-ADM2-72505758B95534398         0.9499
NGA-ADM2-72505758B95566521         0.1682
NGA-ADM2-72505758B95606818         0.7394
NGA-ADM2-72505758B95781523         0.4240
NGA-ADM2-72505758B9585780          0.6053
NGA-ADM2-72505758B95859729         0.6016
NGA-ADM2-72505758B95872281         0.6122
NGA-ADM2-72505758B95999274         0.4998
NGA-ADM2-72505758B9609327          0.4998
NGA-ADM2-72505758B9615674          0.5532
NGA-ADM2-72505758B96206882         0.5476
NGA-ADM2-72505758B96230569         0.1682
NGA-ADM2-72505758B9625976          0.9901
NGA-ADM2-72505758B96315687         0.9901
NGA-ADM2-72505758B96375167         0.4595
NGA-ADM2-72505758B96655345         0.4998
NGA-ADM2-72505758B9668183          0.5532
NGA-ADM2-72505758B96685701         0.6036
NGA-ADM2-72505758B96746323         0.8156
NGA-ADM2-72505758B9692286          0.5464
NGA-ADM2-72505758B96981662         0.5464
NGA-ADM2-72505758B97139317         0.5464
NGA-ADM2-72505758B97184317         0.0048
NGA-ADM2-72505758B9725515          0.6016
NGA-ADM2-72505758B97294598         0.7477
NGA-ADM2-72505758B97405906         0.0928
NGA-ADM2-72505758B97448934         0.5464
NGA-ADM2-72505758B9755199          0.2124
NGA-ADM2-72505758B98057596         0.7415
NGA-ADM2-72505758B98072407         0.7311
NGA-ADM2-72505758B98086722         0.5109
NGA-ADM2-72505758B98116860         0.4705
NGA-ADM2-72505758B98120163         0.8156
NGA-ADM2-72505758B98218468         0.6620
NGA-ADM2-72505758B98262124         0.8929
NGA-ADM2-72505758B98593855         0.3924
NGA-ADM2-72505758B98658548         0.3640
NGA-ADM2-72505758B98737176         0.5464
NGA-ADM2-72505758B98765613         0.6620
NGA-ADM2-72505758B99221548         0.6322
NGA-ADM2-72505758B99270352         0.7410
NGA-ADM2-72505758B99641746         0.4998
NGA-ADM2-72505758B99650649         0.0223
NGA-ADM2-72505758B99764805         0.7311
NGA-ADM2-72505758B9986554          0.9243
NGA-ADM2-72505758B99970923         0.6016

• Mapping the local Moran’s I: I append the local Moran’s I dataframe onto Nigeria spatial polygon dataframe

nga_wp.localMI <- cbind(nga_wp,localMI) %>%
  rename(Pr.Ii = Pr.z....E.Ii..)

• Mapping local Moran’s I values: Using choropleth mapping functions of tmap package,I plot the local Moran’s I values by using the code chinks below

tm_shape(nga_wp.localMI) +
  tm_fill(col = "Ii", 
          style = "pretty",
          palette = "RdBu",
          title = "local moran statistics") +
  tm_borders(alpha = 0.5)

Variable(s) "Ii" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

• Mapping local Moran’s I p-values

tm_shape(nga_wp.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(nga_wp.localMI) +
  tm_fill(col = "Ii", 
          style = "pretty", 
          title = "local moran statistics") +
  tm_borders(alpha = 0.5)

pvalue.map <- tm_shape(nga_wp.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)

Variable(s) "Ii" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

2.3.1.2 Creating a LISA Cluster Map

(1) Plotting Moran scatterplot

nci <- moran.plot(nga_wp$`wpt non-functional`, rswm_q,
                  labels=as.character(nga_wp$shapeName), 
                  xlab="GDPPC 2012", 
                  ylab="Spatially Lag GDPPC 2012")

the plot is split in 4 quadrants.

(2) Plotting Moran scatterplot with standardised variable

nga_wp$Z.wpt_nonfunctional <- scale(nga_wp$`wpt non-functional`) %>% 
  as.vector 

nci2 <- moran.plot(nga_wp$Z.wpt_nonfunctional, rswm_q,
                   labels=as.character(nga_wp$shapeName),
                   xlab="z-GDPPC 2012", 
                   ylab="Spatially Lag z-GDPPC 2012")

(3) Preparing LISA map classes

quadrant <- vector(mode="numeric",length=nrow(localMI))

nga_wp$lag_wpt_nonfunctional <- lag.listw(rswm_q, nga_wp$`wpt non-functional`)
DV <- nga_wp$lag_wpt_nonfunctional - mean(nga_wp$lag_wpt_nonfunctional)     

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] <- 0

quadrant <- vector(mode="numeric",length=nrow(localMI))
nga_wp$lag_wpt_nonfunctional <- lag.listw(rswm_q, nga_wp$`wpt non-functional`)
DV <- nga_wp$lag_wpt_nonfunctional - mean(nga_wp$lag_wpt_nonfunctional)     
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] <- 0

(4) Plotting LISA map

nga_wp.localMI$quadrant <- quadrant
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high")

tm_shape(nga_wp.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(nga_wp, "wpt non-functional")

nga_wp.localMI$quadrant <- quadrant
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high")

LISAmap <- tm_shape(nga_wp.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)

3 Hot Spot Area and Cold Spot Analysis

3.1 Getis and Ord’s G-Statistics

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

3.2 Deriving distance-based weight matrix

First, I 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.

3.2.1 Deriving the centroid

To get our longitude values we map the st_centroid() function over the geometry column of us.bound and access the longitude value through double bracket notation [[]] and 1. This allows us to get only the longitude, which is the first value in each centroid.

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

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

coords <- cbind(longitude, latitude)

3.2.2 Determine the cut-off distance

Firstly, we need to determine the upper limit for distance band by using the steps below:

• Return a matrix with the indices of points belonging to the set of the k nearest neighbours of each other by using knearneigh() of spdep.

• Convert the knn object returned by knearneigh() into a neighbours list of class nb with a list of integer vectors containing neighbour region number ids by using knn2nb().

• Return the length of neighbour relationship edges by using nbdists() of spdep. The function returns in the units of the coordinates if the coordinates are projected, in km otherwise.

• Remove the list structure of the returned object by using unlist().

#coords <- coordinates(hunan)
k1 <- knn2nb(knearneigh(coords))
k1dists <- unlist(nbdists(k1, coords, longlat = TRUE))
summary(k1dists)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  2.662  12.815  20.242  22.031  27.706  71.661 

The summary report shows that the largest first nearest neighbour distance is 71.66 km, so using this as the upper threshold gives certainty that all units will have at least one neighbour.

3.2.3 Computing fixed distance weight matrix

wm_d72 <- dnearneigh(coords, 0, 72, longlat = TRUE)
wm_d72

Neighbour list object:
Number of regions: 774 
Number of nonzero links: 18112 
Percentage nonzero weights: 3.023323 
Average number of links: 23.40052 

wm72_lw <- nb2listw(wm_d72, style = 'B')
summary(wm72_lw)

Characteristics of weights list object:
Neighbour list object:
Number of regions: 774 
Number of nonzero links: 18112 
Percentage nonzero weights: 3.023323 
Average number of links: 23.40052 
Link number distribution:

 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 
 5  8 12 21 32 35 33 35 28 36 25 21 19 23 16 14 10 13 15 17 16 11 13 10  6 12 
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 
12  5 16 13 12  7  9  9 12  7 12 15 13  9 10  4  5  4  7  8  8  8  6  5  3  2 
53 54 55 56 57 58 59 60 61 62 63 64 65 67 68 70 
 3  4  5  3  6  5  2  6  4  8  8  4  4  3  1  1 
5 least connected regions:
90 112 123 237 670 with 1 link
1 most connected region:
585 with 70 links

Weights style: B 
Weights constants summary:
    n     nn    S0    S1      S2
B 774 599076 18112 36224 2614072

3.3 Computing adaptive distance weight matrix

knn <- knn2nb(knearneigh(coords, k=8))
knn

Neighbour list object:
Number of regions: 774 
Number of nonzero links: 6192 
Percentage nonzero weights: 1.033592 
Average number of links: 8 
Non-symmetric neighbours list

knn_lw <- nb2listw(knn, style = 'B')
summary(knn_lw)

Characteristics of weights list object:
Neighbour list object:
Number of regions: 774 
Number of nonzero links: 6192 
Percentage nonzero weights: 1.033592 
Average number of links: 8 
Non-symmetric neighbours list
Link number distribution:

  8 
774 
774 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 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 with 8 links
774 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 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 with 8 links

Weights style: B 
Weights constants summary:
    n     nn   S0    S1     S2
B 774 599076 6192 11152 201942

3.4 Computing Gi statistics and Visualize Hot Spot Area

3.4.1 Functional water points

(1) Gi statistics using fixed distance

fips <- order(nga_wp$shapeName)
gi.fixed <- localG(nga_wp$`wpt functional`
, wm72_lw)
gi.fixed

  [1] -1.0632673035 -1.0670096865 -0.9538105219  0.6908253119 -1.4739182231
  [6]  8.4571951096  1.4115942694  2.8124345967  4.9221743543 -1.7723969977
 [11]  0.0001560952  0.8207039699  1.5598357554  3.3082321808  1.4495775297
 [16]  6.2907428360  6.7130205396  3.3774154110  2.6439754805  0.9856048585
 [21]  0.0992864076  1.7695155282 -2.2749800220 -1.3322220573 -2.1722927254
 [26]  0.0933609976  0.4024302684  7.7088908966  8.9342921266  4.7865872442
 [31]  0.2147079291  2.3699399139 -3.6973182236  1.6991586730  5.8720382946
 [36] -1.9056438031  2.6062293079  3.0701904493  3.2292064569  3.1746521879
 [41]  3.3755894496 -0.4446495103 -0.6013327048  5.3823065919  4.9004828685
 [46]  1.8718083746 -3.3522701675 -2.3516495094  1.2618878904 -1.2173447139
 [51]  1.9945170537 -2.8963151965 -2.3795294466 -2.7217034589 -0.5921487653
 [56]  1.8638332462 -1.8774170252 -2.0124418252 -1.5110495030 -0.8862870333
 [61] -0.2071057962  2.3898614683 -0.2428407217 -1.7902304320 -2.2500551193
 [66]  1.2996488317  9.9946841605 -1.0484644454 -1.9150872995  8.7974713163
 [71] 10.0874741382  5.5560861962  2.5823513363 -2.5434161821 -2.6344218933
 [76]  2.8709446373  0.0169928152 -2.8149729571 -2.8345198930 -2.3284259862
 [81] -2.9727981889  1.1682703870 -1.6563505010 -1.1689328537 -4.2581644413
 [86] -0.1820610289 -2.9727981889 -1.5110495030 -2.3439186891  0.9827453453
 [91] -1.1689328537 -0.8605786455  0.3114933949  0.2020462150 -0.4100138578
 [96] -2.8082635505 -2.4492841959 -1.3373243809 -2.8915924154 -2.3439186891
[101] -4.0783091288  6.4028633481  0.2304692202  2.8921603918 -4.3747406190
[106]  1.3387322056 -1.9056438031 -3.5627616473 -2.3516495094 -2.1439370584
[111] -2.6344218933 -0.6739592159 -2.1439370584 -2.1439370584 -1.6454603170
[116] -2.7226157453 -1.0165548390  3.1418882478  1.3178640772 10.1116645865
[121] -1.5986155968 -0.8200419409 -0.6733282075 10.7960395837 -0.7180373730
[126] -0.5925332794 -2.6344218933 -1.6563505010 -1.7902304320 -4.0783091288
[131] -1.9150872995 -1.3506447225  3.7499348968 -1.5897420230  0.2770421599
[136] -0.3577783669 -0.3150203699 -0.7571591551 -3.3522701675 -1.1689328537
[141] -1.3840959001 -4.3747406190 -1.3506447225 -1.9150872995 -4.0783091288
[146] -1.3506447225 -2.6344218933 -1.5110495030 -2.6344218933 -2.5434161821
[151] -2.9727981889 -1.9150872995 -1.4875625231 -3.0520511651 -4.2581644413
[156] -4.2581644413 -0.7893138881 -0.5612925929 -1.9960317784 -1.5110495030
[161] -1.7801415017  0.8711692692  3.2193921963 -1.6563505010 -2.8360994887
[166] -2.9727981889 -3.2794996320 -3.1295005143 -1.4984048673  6.7477496429
[171]  2.4508127103 10.1665688475 10.0714638316  5.7843899693  8.3458844490
[176]  2.6945019663  1.9756135480  6.5684218569 10.6308499194 -0.1569289100
[181] -2.0720537157  9.3099508980 -1.4084038355 -1.0032573605  5.4619126681
[186]  3.7048885942  6.9194236586  7.8949716964 -2.2297469487 -1.0198972137
[191] -0.3827080897  4.3037903081  1.8677597667  1.4084688677  1.1667232394
[196]  0.4252974336 -0.8294671812 -1.0991345181 -1.4830668445 -0.5753777952
[201]  0.2985420427 -0.7361554330 -1.5371523487 -1.1467628533 -1.5139746076
[206] -0.9764232608  2.2548347939 -1.1875217576 -1.2793183652 -0.8278089178
[211] -0.2525846649 -0.2551189552  4.4891635919  1.9670557894 -2.4339821036
[216] -2.0044792131  4.6645897747  4.4886828471 -4.3747406190 -1.6563505010
[221] -2.3516495094 -1.9150872995 -1.6345701330 -2.0325857459 -1.5110495030
[226] -2.6344218933 -4.0783091288 -1.5110495030 -2.5434161821 -2.1439370584
[231] -1.3506447225 -0.6708925773 -3.0520511651 -3.6973182236 -4.0783091288
[236] -0.6308035252  2.5993935954 -3.7630546080  0.2685122946  3.8050213822
[241] -1.1689328537 -4.1989069936 -2.1439370584 -1.6563505010 -2.7159029934
[246] -1.0088442604 -2.1439370584 -1.6454603170 -2.2500551193 -1.5110495030
[251] -1.3506447225 -1.3506447225 -1.7902304320  1.8510379215 -2.4492841959
[256] -1.7902304320 -0.0133692508 -2.3516495094 -2.0325857459 -2.1354794757
[261] -1.6563505010 -2.4492841959  0.5127045193 -4.3167666596 -2.5434161821
[266] -2.1439370584 -4.0169048035  4.5162590822  1.5668734268 -3.3522701675
[271] -1.1689328537 -2.6344218933 -1.6454603170 -1.9150872995  5.8594650963
[276]  5.6953449622  5.2660558639  4.7281326811  4.6143993534 -1.4553837194
[281]  2.2813649171  3.1491714091  2.1462656822  1.4833490452 -0.6687443617
[286] -1.1291208531  1.7679593468 -1.1283070357 -0.7701456812  3.1618557369
[291] -2.2945754241 -2.1683023813 -2.6385720883 -2.2244054096  3.7867931680
[296]  7.5439666417  1.8624642789 10.2335722131  9.2322081224  8.0371449309
[301]  6.9681943350  9.4987689863  5.6814362239  5.9333683624 10.0880375648
[306]  1.7459767472 -2.0236765072 -1.0457911061 -0.6319667101 -1.0252062498
[311] -1.3234299832 -1.0211509778 -2.1563851407 -1.7627295698  2.5911165138
[316]  3.9629547723  2.9244040096  1.3150582597  7.9287201079  3.1415040765
[321] -1.0582913698 -1.5116031280 -1.3213325672 -3.1295005143 -2.0162075597
[326]  2.3184552303  2.1881395727  6.2888692398  4.8861907505  6.1349551833
[331] -1.1794814101  1.6026625621 -1.3027385048 -1.1172022474 -0.7716666771
[336] -0.9259245188  6.3656211921 -1.2826642753 10.7093954744  0.4405987720
[341]  6.7869686328  7.8488702920  9.9425429345 10.1938572365 -2.0325857459
[346]  8.7462943801  8.4117773837  8.6504758633  2.7902710631 -3.8278348710
[351] -0.0316408439  1.4296841366  0.8599975618  1.2320280653  9.0906675375
[356] 10.9388129247  7.1267016086  7.4628307351 -1.6563505010  5.0870129700
[361]  4.0124347905  3.2958037502  2.4218470810 -1.3175432333 -1.9618741734
[366] -2.4607402920  7.9483367559 -0.8871555410  6.6978038451 -0.7487385134
[371] -0.8863704779 -2.1393812426 -2.5434161821  2.7731030767 -0.9014386689
[376]  0.9340595951  2.0044591212  8.4899062279  7.7959272575  1.3632407377
[381] -1.1007330352 -3.1295005143 -1.7902304320 -0.0646749063 -2.5434161821
[386] -2.1439370584  1.0988522711 -1.5110495030 -2.3516495094 -1.5008751002
[391] -1.3811485108 -0.3494288804  1.2933470021 -4.3167666596 -0.0087186839
[396] -1.6562283328 -1.6454603170 -2.7226157453 -3.3522701675 -1.5110495030
[401]  0.1519013671 -0.0109993558 -2.6344218933  2.5439408115 -0.4242659287
[406] -1.1689328537 -2.1439370584 -2.2419858410 -1.2087827890 -2.8082635505
[411] -0.9410346434 -3.4236826784 -4.3167666596 -1.5110495030 -4.0169048035
[416] -0.2983377402  0.6782758292 -2.4492841959  0.3995646133 -2.8082635505
[421]  2.2905227590 -2.5434161821  0.3431833423 -1.7902304320 -0.2668019574
[426] -3.6305730497  2.8526099674 -2.0325857459  1.9182309506 -0.9645376878
[431] -3.7630546080 -1.7801415017 -2.3516495094 -3.9547169953 -2.6344218933
[436]  2.0438812059 -1.6563505010  2.0875336455 -1.1586579214 -1.5110495030
[441]  5.9246461434 -1.1535618391  2.2547023906 -1.8187640183 -2.8082635505
[446]  1.3382943358 -1.1689328537 -4.2581644413 -4.3167666596 -4.2581644413
[451] -2.8915924154  2.1760903433 -3.6973182236  0.4089337254 -1.9150872995
[456]  3.3942631425 -2.6344218933 -2.1354794757  1.3374113134  6.9931549916
[461]  2.1445971690  2.1303454343 -2.1354794757 -0.1848224157  1.3502066712
[466]  0.8654852388 -0.7399783166  0.4687944808 -0.2949862633  2.8289063227
[471]  0.6649046179 -1.9150872995 -1.3506447225 -4.1989069936 -1.7902304320
[476] -1.4991276733 -1.5110495030 -2.7226157453 -1.5110495030 -2.4492841959
[481] -1.3506447225 -2.2500551193 -4.2581644413  1.3124888815 -2.7226157453
[486] -3.2794996320 -0.5826566417 -3.3522701675 -1.7902304320 -0.9538105219
[491] -3.0520511651 -1.3506447225 -1.1689328537 -0.8614333295 -2.7226157453
[496] -3.2794996320 -1.3380814261 -2.1091607582 -0.4758398089 -1.6563505010
[501] -2.9727981889  0.0206843077 -4.1389655025 -1.9150872995 -1.4732052913
[506]  8.4166576354 -0.9538105219  1.4495095008 -1.6563505010  4.0381438008
[511]  6.1207930405 -1.6563505010 -1.5110495030 -3.2052777742  2.3618746785
[516] -0.8092899885 -1.7902304320 -1.7902304320 -4.4889033722  1.1729497802
[521]  2.1723239517 -1.7215586522 -1.5585271578 -1.0571541438 -1.3506447225
[526] -1.7902304320 -1.5110495030 -1.2656864229 -2.0325857459 -1.9150872995
[531] -2.1676086219 -2.7176310405  2.9809544955  1.1450446966 -2.1944913261
[536] -2.2326145665 -2.2011410222 -0.9346421737 -1.2338219766 -1.0395789334
[541] -1.0724879697 -1.6790681487 -2.2749800220  2.7025410943  3.2510615622
[546]  4.3883340713  2.3454032851 -1.3129683782 -0.9159581714 10.2388189666
[551] -1.3849119185 -1.6476981229  6.7042031311  4.4870476718  1.8900958142
[556]  1.7470130836 10.2836194351  2.0812712794 -0.4685014316 10.9854467360
[561] -0.7501455289 -1.1232443955  0.2085210397 -2.1518025919 -1.3060565786
[566]  8.9130474945  9.1898147295  8.9698348181  6.8126047839  2.6220195285
[571] -0.9619571538  1.1194708981 -2.0346595471  2.2943467622 -1.8365549811
[576]  2.9891291323  5.5508140243  1.2144535835 -1.6230813934  1.9705503041
[581]  4.6362865328  6.5910050128  2.2172948436  1.6887960939 -1.4725666829
[586]  0.9198497075 -0.7961651515 -1.4356397026  2.1773120070 -1.1155004965
[591]  9.5277257691 -1.0017638226 10.9738098691  3.4334540972  3.2012232519
[596]  0.7011765976 -1.2009960898  5.5929839759  5.6618403963  4.6613119000
[601]  3.3919463402 -2.6786478465 -2.6588307198 -1.1799813004 -0.7557185182
[606] -0.1231260932  1.9279845606 -1.1401502289  7.1510513224  7.7469359467
[611] -2.2025423334 10.8506206963 -0.5263700492 -2.1436413468 -2.0519621520
[616] -2.0336306891 -1.3426015247 -2.4365278427 -1.8015613815  2.8479954422
[621] -2.3973989379 -2.7118475181  2.0367411481 -1.1750303747 10.1260907067
[626]  2.0566833970  0.3357640162  0.5058522092  2.0559015524  1.8371077698
[631] -1.6333045334 -1.5725203818 -1.5280510788  3.6678033304  5.7520113207
[636] -2.8720995274 -1.0485449620  7.3882521836  6.1678150146 10.5149836580
[641] -0.7327969709  0.0572066684 -1.4864750763  0.6875506895 -1.4772817963
[646] -1.6563505010  1.5211676324 -2.4492841959 -0.3246749821 -3.9547169953
[651]  2.8579269001 -1.7902304320 -3.2052777742 -4.3167666596 -3.6305730497
[656]  0.1032543571 -3.2794996320 -3.9547169953 -2.6344218933 -1.3506447225
[661] -2.1354794757 -2.7226157453 -1.4949308110 -1.3506447225  1.8932382855
[666]  1.4917063261 -3.1295005143  1.1526039539 -1.0937227768  1.4000757262
[671]  2.1715782775 -2.4492841959 -1.6563505010 -2.1437789270 -4.1989069936
[676] -2.3439186891  0.5685312893 -1.5110495030 -2.1439370584 -0.8896548347
[681] -1.9150872995  2.4229518786 -2.6344218933 -2.2500551193 -2.7226157453
[686] -2.7226157453 -1.9150872995 -1.1585922308 -2.3516495094  0.5638531049
[691] -2.8915924154 -2.0325857459  2.0454593444  9.4708994953  0.5410025850
[696] -1.3955655534 -1.1056043786 -2.8082635505  1.8474850765 -1.7902304320
[701] -2.4492841959 -2.1439370584 -4.3167666596  2.7375307820 -1.3506447225
[706] -2.8915924154 -4.2581644413 -1.3322220573  1.7150919527  0.6078045237
[711] -2.1439370584 -4.1389655025 -2.8915924154 -2.1439370584 -0.1295463387
[716] -1.3316122414 -1.5698228802 -0.5176850227 -1.4964293761 -1.7857827138
[721] -1.2994836650 -0.3876727976 -1.0245708554  2.9424997357 -1.2643102407
[726] -1.1087310344 -1.6338206948 -0.4210525847 -1.1538301305 -1.4723676498
[731] -4.4321116070 -2.1578903294 -0.8395204074 -0.6437273597  4.2867547887
[736]  2.2781822259 -1.5533967318 -1.1742762754 -1.6599276463  5.0522210888
[741] -2.6344218933  1.7953476495 -4.1989069936 -1.9150872995 -0.3494263283
[746] -1.2755262672 -1.4011565950 -1.5110495030 -0.2181946307 -3.8917074465
[751]  0.9547193253 -2.3516495094 -0.2446358077 -2.5434161821  4.2947671841
[756]  5.2300334810  4.4330276859  7.3405457235 -2.2419858410 -3.1295005143
[761] -1.5110495030 -0.4975991205 -1.8867568105 -2.0058580299 -0.2915590759
[766] -0.9538105219 -1.1689328537 -2.1439370584 -2.7226157453 -0.5461415291
[771] -2.5362494095 -0.8874323615 -1.9150872995 -1.6563505010
attr(,"cluster")
  [1] Low  High Low  Low  Low  High Low  High High Low  Low  High High High High
 [16] High High High Low  Low  Low  High Low  Low  Low  Low  Low  High High High
 [31] High Low  Low  High High Low  High High High High High High Low  Low  High
 [46] High Low  Low  High Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low 
 [61] Low  Low  High Low  Low  Low  High High Low  High High High High Low  Low 
 [76] High Low  Low  Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low  High
 [91] Low  Low  High High Low  Low  Low  Low  Low  Low  Low  High Low  High Low 
[106] High Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low  High
[121] Low  Low  Low  High High Low  Low  Low  Low  Low  Low  Low  High Low  Low 
[136] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
[151] Low  Low  Low  Low  Low  Low  Low  High Low  Low  Low  High High Low  Low 
[166] Low  Low  Low  Low  High High High High High Low  Low  High High High Low 
[181] Low  High Low  High High High High High Low  Low  Low  High Low  Low  Low 
[196] High Low  Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low  Low  Low 
[211] Low  High High Low  Low  Low  High High Low  Low  Low  Low  Low  Low  Low 
[226] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High High Low  Low  High
[241] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low 
[256] Low  Low  Low  Low  Low  Low  Low  High Low  Low  Low  Low  High Low  Low 
[271] Low  Low  Low  Low  Low  High High Low  High Low  High High High High Low 
[286] Low  High Low  Low  High Low  Low  Low  Low  High Low  High High High High
[301] High High High High High Low  Low  Low  Low  Low  Low  Low  High Low  Low 
[316] Low  High High High High Low  Low  Low  Low  Low  Low  Low  High High High
[331] High High Low  Low  High High High Low  High Low  High Low  High High Low 
[346] High High High Low  Low  Low  Low  High Low  High High High High Low  Low 
[361] High High Low  Low  Low  High High Low  High Low  Low  Low  Low  High Low 
[376] Low  High High High Low  Low  Low  Low  Low  Low  Low  High Low  Low  Low 
[391] Low  Low  High Low  High Low  Low  Low  Low  Low  Low  High Low  High Low 
[406] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low  Low  Low 
[421] High Low  High Low  Low  Low  High Low  High Low  Low  Low  Low  Low  Low 
[436] High Low  High Low  Low  High Low  High Low  Low  High Low  Low  Low  Low 
[451] Low  High Low  High Low  Low  Low  Low  High High High High Low  Low  Low 
[466] High Low  Low  Low  High High Low  Low  Low  Low  Low  Low  Low  Low  Low 
[481] Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
[496] Low  Low  Low  Low  Low  Low  High Low  Low  High Low  Low  High Low  High
[511] High Low  Low  Low  Low  Low  Low  Low  Low  High High High Low  Low  Low 
[526] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High
[541] Low  Low  Low  Low  High High Low  High High High Low  Low  High High Low 
[556] High High High High High Low  High High Low  Low  High High High High Low 
[571] Low  High Low  Low  High High High High Low  Low  High High Low  High Low 
[586] Low  Low  Low  Low  Low  High Low  High High High Low  Low  High High High
[601] High Low  Low  High Low  High Low  High High High Low  High Low  Low  Low 
[616] Low  Low  Low  Low  High High Low  High Low  High Low  High High High Low 
[631] Low  Low  High High High Low  Low  High Low  High Low  Low  Low  High High
[646] Low  High Low  Low  Low  Low  Low  Low  Low  Low  High Low  Low  Low  Low 
[661] Low  Low  Low  Low  High High Low  Low  Low  Low  Low  Low  Low  Low  Low 
[676] Low  High Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
[691] Low  Low  High High Low  Low  Low  Low  High Low  Low  Low  Low  High Low 
[706] Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low 
[721] Low  High Low  High Low  High Low  Low  High Low  Low  Low  Low  Low  High
[736] High Low  High Low  High Low  High Low  Low  Low  Low  Low  Low  Low  Low 
[751] High Low  Low  Low  Low  High High High Low  Low  Low  Low  Low  Low  High
[766] Low  Low  Low  Low  High Low  High Low  Low 
Levels: Low High
attr(,"gstari")
[1] FALSE
attr(,"call")
localG(x = nga_wp$`wpt functional`, listw = wm72_lw)
attr(,"class")
[1] "localG"

The Gi statistics is represented as a Z-score. Greater values represent a greater intensity of clustering and the direction (positive or negative) indicates high or low clusters.

nga_wp.gi <- cbind(nga_wp, as.matrix(gi.fixed)) %>%
  rename(gstat_fixed = as.matrix.gi.fixed.)

(2) Mapping Gi values with fixed distance weights

The code chunk below shows the functions used to map the Gi values derived using fixed distance weight matrix.

gdppc <- qtm(nga_wp, "wpt functional")

Gimap <-tm_shape(nga_wp.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)

Variable(s) "gstat_fixed" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

(3) Gi statistics using adaptive distance

The code chunk below are used to compute the Gi values for GDPPC2012 by using an adaptive distance weight matrix (i.e knb_lw).

fips <- order(nga_wp$shapeName)
gi.adaptive <- localG(nga_wp$`wpt functional`
, knn_lw)
nga_wp.gi <- cbind(nga_wp, as.matrix(gi.adaptive)) %>%
  rename(gstat_adaptive = as.matrix.gi.adaptive.)

(4) Mapping Gi values with adaptive distance weights

Now I visualize the location of hot spot and cold spot area. The code chunk below shows the functions used to map the Gi values derived using fixed distance weight matrix.

gdppc<- qtm(nga_wp, "wpt functional")

Gimap <- tm_shape(nga_wp.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)

Variable(s) "gstat_adaptive" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

3.4.2 Not Functional water points

(1) Gi statistics using fixed distance

fips <- order(nga_wp$shapeName)
gi.fixed <- localG(nga_wp$`wpt non-functional`
, wm72_lw)
gi.fixed

  [1]  6.5337259052  6.5319238447 -0.4259788679 -0.9574982243  8.5418861626
  [6]  1.5421779468 -1.1561964353 -1.4660718555  0.9482850743  3.1371777082
 [11]  0.0101223889 -0.7807121168  0.3515338167 -0.2677616718 -1.1573062867
 [16] -0.2584017581 -1.0170909209  0.4446715383  1.3378478253 -0.7995302161
 [21] -0.1652233639 -1.1682290936 -1.0675886676 -0.6748459383  2.8393327487
 [26]  1.0688312184 -0.2724969192 -0.2922325892 -0.5987050168 -0.4433604372
 [31]  0.7645059144 -1.1951232807  1.8419524289  2.5819762168 -0.9383484409
 [36]  1.7682827270 -0.0822593181 -0.6285091267 -0.2896071988  0.0722598791
 [41] -0.4734487746  5.4940324367 -0.1273324547 -1.0126897720 -0.4342237134
 [46] -0.4026277306  2.1768067849 -1.0502641487 -1.2629400262  0.8770452407
 [51] -1.1573062867 -0.9058386602 -0.5071496523 -0.7695234874  5.0634636910
 [56] -0.7254639953  0.0244573516 -0.0037008912 -0.6748459383 -0.7310976572
 [61] -0.1081744501 -1.1951232807 -0.6748459383 -0.7995302161 -1.0048913390
 [66]  5.9829622963  1.0273896998  2.0366041740 -0.8552922211 -0.3357900293
 [71] -0.1054445086 -0.5871686734 -0.7397384440 -1.1359085699 -0.9840709148
 [76] -0.1623522360 -0.9721623909 -1.0463396400 -1.2422799228 -0.7148217202
 [81] -1.3276737654 -1.2343339588 -0.7397384440 -0.5220541001  1.1685220223
 [86]  2.1856421836 -1.3276737654 -0.6748459383  0.0236170510 -0.3010173971
 [91] -0.5220541001  0.1160047722 -0.5191748831  0.0464515956 -0.7225311997
 [96] -1.2541913730 -1.0938685253 -0.6032079712 -1.2914066634  0.0236170510
[101]  1.3712150830  0.4624961174  2.4766728230  5.6054061853  1.0427975403
[106] -0.5929347263 -0.5847132984 -1.5911558306 -1.0502641487 -0.9574982243
[111] -1.1765523969 -0.3010173971 -0.9574982243 -0.9574982243 -0.7397384440
[116] -1.2159404267 -0.1652233639  2.8255127830  0.7885424389  0.6496970397
[121]  2.2297832866  3.2392333195 -0.3010173971 -0.2359945688 -0.7995302161
[126]  3.6559580389 -1.1765523969 -0.7397384440 -0.7995302161  1.3712150830
[131] -0.8552922211 -0.6032079712 -0.9077679005  0.4569391844 -0.7225311997
[136]  5.8086033301  5.8086033301 -0.9077679005 -1.4971487713 -0.5220541001
[141] -0.7397384440  1.0427975403 -0.2331446682 -0.8552922211  1.3712150830
[146] -0.6032079712 -1.1765523969 -0.6748459383 -1.1765523969 -1.1359085699
[151] -1.3276737654 -0.3305772315 -0.7995302161 -1.3630687336 -0.7689824162
[156]  1.1685220223  2.1214506764  0.4564952529 -1.0502641487 -0.6748459383
[161] -0.7995302161 -0.9574982243 -0.3415159238  0.7783566342 -1.0801429459
[166]  2.7877821570 -1.4646489093 -1.3976581886  8.0933467102  0.3249279766
[171] -0.5192413921 -0.1054445086 -0.3643423211  0.4704579945  0.1584146108
[176] -0.7915894327 -1.1185484438 -0.9192479158 -0.3164953046  0.5615293857
[181]  0.3360363194 -0.5535268727  2.8080212184  7.2040350668 -0.4122764763
[186] -0.0003741695 -0.7556085716  0.2052582683 -0.4220506910  3.9703124427
[191]  2.1836339455 -0.9526093523 -0.5384899266 -0.7964379195 -0.8334298447
[196] -1.1121501755  0.6438877065  0.3137427980 -0.0876396328  0.3870995356
[201]  0.7216154088  7.2962403214  7.2566694439  3.4311214203  0.8137253622
[206]  1.0567117486 -1.2320655304  7.6369662945  9.4696028861  0.3093949665
[211]  0.2931288141 -0.0467996625  4.4119933424 -1.3035566958 -0.7570326281
[216]  3.6536087596  0.7959964909  0.5843996273  1.0427975403 -0.7397384440
[221] -1.0502641487 -0.5929347263 -0.7397384440  0.8248360183 -0.6727478048
[226] -1.1765523969  1.3712150830 -0.6748459383 -1.1359085699 -0.7225311997
[231] -0.6032079712 -0.6032079712 -0.0250977735  1.8419524289  1.3712150830
[236] -0.4246544759 -0.3010173971  1.7561910619 -0.9077679005 -0.6602530550
[241] -0.5220541001  1.2340856069 -0.9574982243 -0.7397384440 -1.2159404267
[246]  5.5896818913  1.8621060705 -0.7397384440 -1.0048913390 -0.6748459383
[251] -0.6032079712 -0.6032079712 -0.7995302161 -0.4875641752 -1.0938685253
[256] -0.7995302161 -1.0048913390 -0.8354879087 -0.9077679005 -0.9574982243
[261] -0.7397384440 -1.0938685253 -1.0048913390  1.1047958090 -1.1359085699
[266] -0.9574982243 -1.6644981030 -0.3291851856  0.3401839944 -1.4971487713
[271] -0.5220541001 -0.9840709148 -0.7397384440 -0.8552922211 -0.9664650390
[276] -0.9274700573 -1.0170909209 -0.9781671913 -1.0170909209 -0.2724969192
[281] -0.9840709148 -1.2658211310 -0.8354879087 -1.2969567904  6.1552940600
[286]  8.5583598510  0.1369186347  7.4050351682 -0.1367816582 -0.0250977735
[291] -1.0369866160 -0.9708223130 -0.7961347537 -0.9379938720 -1.3035566958
[296]  0.3236161289 -1.1682290936 -0.2144132320 -0.1960384792 -0.2211914895
[301] -0.1612416772  0.4028313845 -0.6720605973  1.8235544408  0.2372026697
[306] -1.3035566958 -0.9077679005 -0.9352494592 -0.5334250851  0.2156222055
[311]  0.0055772761  0.0441448754 -0.1247274277  1.9625016132 -0.7443612696
[316] -0.9932483120 -1.1185484438 -0.9958399624  0.2530701708 -0.8090801364
[321]  7.6953701018  0.7227084037  1.0224680449 -1.3976581886  2.1806554737
[326] -1.2049207837 -1.3870458035 -0.8404610797 -0.1142408180  2.3915031649
[331]  8.3232385900 -1.2982149465  8.3034986120  7.6464261358  1.0219689776
[336]  1.5492545793  1.1456268165  6.4258988306  0.6955968289  1.1624915524
[341] -0.5330073048  0.4195785142 -0.2682345828 -0.0616294039 -0.9077679005
[346]  1.7969361586  0.5715437867  0.7231261765 -0.7995302161 -1.7095395023
[351]  6.9955319102 -1.2343339588  0.8827220107 -0.0124257347  0.5670220430
[356] -0.0616294039  0.0130252915 -0.3648907393 -0.7397384440 -1.2320655304
[361] -1.3630687336 -0.4915910827 -0.7626240766  5.9514605000  4.7951541484
[366]  0.0658019412  0.7294177399  0.3228949164 -0.6736279231  0.6507876137
[371]  0.8793958255 -0.8079638602 -0.9368026006 -0.9077679005  6.8788604991
[376]  0.2672244065 -0.8552922211 -0.4918710922  1.7016047941 -0.6602530550
[381] -0.7397384440 -1.3976581886 -0.5192413921 -0.7397384440 -1.1359085699
[386] -0.9574982243 -0.4127382095 -0.6748459383 -1.0502641487 -0.2525971506
[391] -0.2525971506 -0.4845563588 -0.2525971506  1.1047958090 -0.7397384440
[396] -0.7397384440 -0.7397384440 -1.0294479763 -1.4971487713 -0.6748459383
[401] -0.9077679005 -0.4259788679 -1.1765523969 -1.0938685253 -0.6748459383
[406] -0.5220541001 -0.9574982243  0.1160047722 -0.7397384440 -1.2541913730
[411] -0.0682197367 -1.5290421294  1.1047958090 -0.6748459383 -1.6644981030
[416] -0.2331446682 -0.4875641752 -0.8873824764 -0.8552922211 -1.2541913730
[421] -0.7995302161 -1.1359085699 -0.5565328945 -0.7995302161 -0.7995302161
[426] -1.6214409069 -0.2389525680 -0.9077679005 -0.5167371774  7.4529312093
[431]  1.7561910619  1.1624915524 -0.8354879087  0.4665706284 -1.1765523969
[436] -0.0628420131 -0.7397384440 -0.2389525680  1.8146122966 -0.6748459383
[441]  0.6679457707 -0.5220541001 -1.1682290936 -0.9077679005 -1.2541913730
[446] -0.2525971506 -0.5220541001  1.0518184165 -1.8065922377  1.1685220223
[451] -1.2914066634  0.0966904414 -1.6512497976 -0.3323536723 -0.3193723174
[456]  0.3298063272 -1.1765523969 -0.9574982243  0.1968659159 -0.9948831255
[461] -1.2681922493 -1.2681922493  0.2173368985 -0.5929347263 -0.4371893343
[466] -0.3305772315 -0.7225311997 -0.7397384440 -0.7397384440 -0.5929347263
[471]  0.0413362561 -0.8552922211 -0.6032079712  1.2340856069 -0.7995302161
[476] -0.6748459383 -0.6748459383 -1.2159404267 -0.6748459383 -1.0938685253
[481] -0.6032079712 -1.0048913390  1.1685220223 -0.4875641752 -1.0294479763
[486] -1.4646489093 -0.2611981899 -1.4971487713 -0.7995302161 -0.4259788679
[491] -1.3630687336 -0.6032079712 -0.5220541001 -0.5220541001 -1.2159404267
[496] -1.4646489093 -1.0048913390 -0.5505031914  5.6840449105 -0.7397384440
[501] -1.3276737654  0.0822914816  1.3016062299 -0.8552922211  9.3439953613
[506]  0.4316620441 -0.4259788679 -0.6748459383 -0.7397384440  0.6560451536
[511] -0.2318760335 -0.7397384440 -0.6748459383 -1.4315008760 -1.1307202807
[516] -0.8552922211  1.1624915524 -0.5192413921  0.9235918006 -0.2389525680
[521]  0.1941377581  0.4093024002  0.4722086802  3.2423385006 -0.6032079712
[526] -0.7995302161 -0.6748459383  3.1999870901 -0.9077679005 -0.8552922211
[531] -0.8308762929 -1.0801429459 -0.6720605973 -1.0316248954 -0.7738549514
[536] -0.8832154198 -0.8079638602  7.9418067757  8.7520860737  7.8750209492
[541] -0.3707613664 -1.0502641487 -0.8748867318 -1.4506725453  1.1685479513
[546]  0.4645408950  0.1941377581  6.6426608315  2.3241472968 -0.1054445086
[551]  6.9433005476  3.3879178027  2.0087119489  1.3198657094 -1.3019228013
[556]  0.0623374036  0.3720071210 -1.2533933348  7.7833588383  0.3963686530
[561]  0.0587272458  0.1531114649  0.4033718712 -0.1678620285  2.5477299264
[566]  0.2439994063  0.1279409304 -0.3508982143  1.8594525393  0.0441448754
[571]  4.2754248803 -0.1081744501 -0.1047006520  2.9964787298  0.7285925680
[576]  0.0130252915 -0.0281537916  1.0219689776 -1.2662733555 -1.1521096114
[581]  0.8551511229 -0.0729482666 -0.5385906621  0.3632994597 -0.2336376467
[586]  0.4523039231  7.3135879554  0.7300418099  0.5585768657  3.3852779170
[591] -0.3502901959  0.4691883116  0.0483926035  0.1160047722 -1.3035566958
[596]  0.4564952529  4.0406955085 -1.1771746866 -0.6266997791 -0.6786956109
[601]  0.0244573516 -0.2563942129 -0.2816734186  8.2346116549  6.9405918512
[606]  1.0542570922 -0.1346402247  1.1919351234  0.0055772761 -0.4203316951
[611] -0.9956985058  0.0751082610  6.4688887040 -0.7392926370 -0.7042594728
[616] -0.1648047591  8.7490398102 -1.4845051520 -1.0990801163 -0.0207719370
[621]  0.1343331268 -0.1958644065 -1.0923374414  6.4579160149 -0.1891980010
[626]  0.3550297591  0.7645059144  0.2489735181  0.2198514985  0.6452478091
[631]  2.2376471532  2.1127391914  1.6098934371 -0.6898014070 -0.1107208661
[636] -1.1130698515  7.0898010737 -1.0046454406 -0.8680732574  0.4497117801
[641] -0.8552922211 -0.2495738837  2.1491050366 -0.3415159238  3.0313765732
[646] -0.4371893343  0.5802411276 -1.0938685253 -0.6032079712  1.5172890427
[651] -1.4191037264 -0.7995302161 -1.4315008760  1.1047958090  1.9312059781
[656] -0.0614382810 -1.4646489093 -1.7662060021 -1.1765523969 -0.6032079712
[661] -0.9574982243 -1.2159404267  1.4596757626 -0.6032079712 -0.4127382095
[666] -0.6032079712 -1.3976581886 -0.4059354289  0.9223772918  0.4376697392
[671] -1.3105842474 -1.0938685253 -0.7397384440 -0.9574982243 -1.7508891231
[676] -1.0502641487  0.0413362561 -0.6748459383 -0.9574982243 -0.6748459383
[681]  0.1968659159 -1.1682290936 -1.1765523969 -1.0048913390 -1.2159404267
[686] -1.2159404267 -0.8552922211  1.1635025404 -1.0502641487 -1.0502641487
[691]  2.9340212766 -0.9077679005 -1.2320655304  0.4195785142 -1.0502641487
[696] -0.0682197367  5.3659514506  3.0908615406 -0.3436358365 -0.7995302161
[701] -1.0938685253 -0.9574982243  1.1047958090 -0.7225311997 -0.2331446682
[706] -1.2914066634  1.1685220223 -0.6748459383  0.4728374605  0.0966904414
[711] -0.9574982243 -1.7224887953  1.5255452966 -0.9574982243  0.0055772761
[716] -0.3955652826  1.3128731865  5.9654506308  1.0356654745  1.3128731865
[721]  6.4740652149  0.7343173160  7.9179789515 -0.1346402247  7.6038144640
[726]  4.8989514737  0.0250683904 -1.1528916318  2.7864500485  3.7194431134
[731]  0.9824269172 -1.0034056873  7.5348120376  7.2390075406  0.1160047722
[736] -0.3436358365  1.5421779468  7.7695889303 -0.3936969961  1.0127216611
[741] -1.1765523969  0.1192027412  0.2927287130 -0.8552922211  0.4645408950
[746]  0.2759991762  0.3515338167 -0.6748459383 -0.6032079712  1.5940888158
[751] -0.0102840429 -1.0502641487 -0.7995302161 -1.1359085699  0.6560451536
[756]  0.8393918473  0.7684673204  1.8506809693  1.0127216611 -1.3976581886
[761] -0.6748459383  1.6473659266 -0.8552922211 -0.9077679005 -0.7397384440
[766] -0.4259788679 -0.5220541001 -0.9545213091 -1.2159404267 -0.7807121168
[771] -1.1359085699 -0.9077679005 -0.8552922211 -0.7397384440
attr(,"cluster")
  [1] Low  High Low  Low  High Low  Low  High High Low  High Low  Low  High Low 
 [16] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low 
 [31] Low  Low  Low  Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low  Low 
 [46] High Low  Low  High Low  Low  Low  Low  Low  Low  Low  High High Low  High
 [61] Low  Low  Low  Low  Low  Low  High High Low  Low  Low  Low  Low  Low  Low 
 [76] High Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
 [91] Low  Low  High High Low  Low  Low  Low  Low  Low  Low  High Low  Low  Low 
[106] Low  High Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low  Low 
[121] Low  Low  Low  High Low  High Low  Low  Low  Low  Low  Low  Low  Low  Low 
[136] High High Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
[151] Low  Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low  High High Low 
[166] Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low  Low  Low  High High
[181] Low  High High Low  High Low  Low  Low  High Low  Low  Low  Low  Low  Low 
[196] Low  Low  High Low  Low  High Low  High Low  High High Low  High High Low 
[211] Low  High High Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High
[226] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low  Low  Low  Low 
[241] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
[256] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low  Low 
[271] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low 
[286] Low  Low  High High Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low 
[301] Low  Low  Low  Low  Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low 
[316] Low  Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low  Low  Low  High
[331] Low  High High High Low  Low  Low  Low  Low  Low  High Low  High Low  Low 
[346] Low  High Low  Low  Low  High Low  Low  Low  High Low  Low  Low  Low  Low 
[361] Low  Low  High Low  High Low  High Low  Low  High Low  Low  Low  Low  Low 
[376] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
[391] Low  High Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
[406] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
[421] Low  Low  Low  Low  Low  Low  Low  Low  High High Low  Low  Low  Low  Low 
[436] High Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low  Low 
[451] Low  Low  Low  Low  High Low  Low  Low  High Low  Low  Low  Low  Low  Low 
[466] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
[481] Low  Low  Low  Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low  Low 
[496] Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
[511] High Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High High Low  Low 
[526] Low  Low  Low  Low  Low  High Low  Low  Low  Low  High Low  High High Low 
[541] Low  Low  Low  Low  High High Low  High High Low  High High High Low  Low 
[556] High High Low  High High Low  Low  High Low  Low  Low  Low  Low  High Low 
[571] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low  Low  Low 
[586] Low  High High Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low  High
[601] High Low  Low  Low  Low  Low  Low  Low  Low  Low  High Low  High Low  Low 
[616] Low  Low  High Low  High Low  Low  Low  High High High Low  High High Low 
[631] Low  High Low  High Low  High Low  Low  Low  High Low  High Low  High Low 
[646] Low  High Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
[661] Low  Low  High Low  Low  Low  Low  Low  High Low  Low  Low  Low  Low  Low 
[676] Low  Low  Low  Low  Low  High Low  Low  Low  Low  Low  Low  High Low  Low 
[691] Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low  Low 
[706] Low  Low  Low  High Low  Low  Low  Low  Low  Low  Low  Low  High Low  Low 
[721] High High High Low  High High High High Low  Low  Low  Low  High High Low 
[736] Low  Low  High Low  Low  Low  High High Low  High Low  Low  Low  Low  Low 
[751] High Low  Low  Low  Low  High High Low  Low  Low  Low  Low  Low  Low  Low 
[766] Low  Low  High Low  Low  Low  Low  Low  Low 
Levels: Low High
attr(,"gstari")
[1] FALSE
attr(,"call")
localG(x = nga_wp$`wpt non-functional`, listw = wm72_lw)
attr(,"class")
[1] "localG"

The Gi statistics is represented as a Z-score. Greater values represent a greater intensity of clustering and the direction (positive or negative) indicates high or low clusters.

nga_wp.gi <- cbind(nga_wp, as.matrix(gi.fixed)) %>%
  rename(gstat_fixed = as.matrix.gi.fixed.)

(2) Mapping Gi values with fixed distance weights

The code chunk below shows the functions used to map the Gi values derived using fixed distance weight matrix.

gdppc <- qtm(nga_wp, "wpt non-functional")

Gimap <-tm_shape(nga_wp.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)

Variable(s) "gstat_fixed" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

(3) Gi statistics using adaptive distance

The code chunk below are used to compute the Gi values for GDPPC2012 by using an adaptive distance weight matrix (i.e knb_lw).

fips <- order(nga_wp$shapeName)
gi.adaptive <- localG(nga_wp$`wpt non-functional`
, knn_lw)
nga_wp.gi <- cbind(nga_wp, as.matrix(gi.adaptive)) %>%
  rename(gstat_adaptive = as.matrix.gi.adaptive.)

(4) Mapping Gi values with adaptive distance weights

Now I visualize the location of hot spot and cold spot area. The code chunk below shows the functions used to map the Gi values derived using fixed distance weight matrix.

gdppc<- qtm(nga_wp, "wpt non-functional")

Gimap <- tm_shape(nga_wp.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)

Variable(s) "gstat_adaptive" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.