Tugas Kelompok Regspas

Pada Kesempatan Kali ini , Kami dari Kelompok 7 ingin melihat ada tidaknya hubungan secara spasial pada Kasus Stunting di Sumba Tengah

library(readxl)
## Warning: package 'readxl' was built under R version 4.3.2
library(sf)
## Warning: package 'sf' was built under R version 4.3.3
## Linking to GEOS 3.11.2, GDAL 3.8.2, PROJ 9.3.1; sf_use_s2() is TRUE
library(spdep)
## Warning: package 'spdep' was built under R version 4.3.3
## Loading required package: spData
## Warning: package 'spData' was built under R version 4.3.3
## To access larger datasets in this package, install the spDataLarge
## package with: `install.packages('spDataLarge',
## repos='https://nowosad.github.io/drat/', type='source')`
library(spatialreg)
## Warning: package 'spatialreg' was built under R version 4.3.3
## Loading required package: Matrix
## 
## Attaching package: 'spatialreg'
## The following objects are masked from 'package:spdep':
## 
##     get.ClusterOption, get.coresOption, get.mcOption,
##     get.VerboseOption, get.ZeroPolicyOption, set.ClusterOption,
##     set.coresOption, set.mcOption, set.VerboseOption,
##     set.ZeroPolicyOption
library(sp)
## Warning: package 'sp' was built under R version 4.3.3
library(tmap)
## Warning: package 'tmap' was built under R version 4.3.3
## Breaking News: tmap 3.x is retiring. Please test v4, e.g. with
## remotes::install_github('r-tmap/tmap')
library(dplyr)
## Warning: package 'dplyr' was built under R version 4.3.2
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.3.2
library(tidyverse)
## Warning: package 'tidyverse' was built under R version 4.3.2
## Warning: package 'tibble' was built under R version 4.3.2
## Warning: package 'tidyr' was built under R version 4.3.2
## Warning: package 'readr' was built under R version 4.3.2
## Warning: package 'purrr' was built under R version 4.3.2
## Warning: package 'forcats' was built under R version 4.3.2
## Warning: package 'lubridate' was built under R version 4.3.2
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats   1.0.0     ✔ stringr   1.5.1
## ✔ lubridate 1.9.3     ✔ tibble    3.2.1
## ✔ purrr     1.0.2     ✔ tidyr     1.3.0
## ✔ readr     2.1.4
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ tidyr::expand() masks Matrix::expand()
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ✖ tidyr::pack()   masks Matrix::pack()
## ✖ tidyr::unpack() masks Matrix::unpack()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
shp <- st_read("C:/Users/Admin/Downloads/Adriano Excel Putra/SHP/idn_admbnda_adm4_ID5_bps_20200401.shp")
## Reading layer `idn_admbnda_adm4_ID5_bps_20200401' from data source 
##   `C:\Users\Admin\Downloads\Adriano Excel Putra\SHP\idn_admbnda_adm4_ID5_bps_20200401.shp' 
##   using driver `ESRI Shapefile'
## Simple feature collection with 5183 features and 18 fields
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: 114.4316 ymin: -11.00762 xmax: 125.1933 ymax: -8.061396
## Geodetic CRS:  WGS 84

Data SHP Sumba Tengah

shp_sumba_tengah<- shp %>% filter(ADM2_EN == "Sumba Tengah")

shp_sumba_tengah
## Simple feature collection with 65 features and 18 fields
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: 119.4156 ymin: -9.84415 xmax: 119.9263 ymax: -9.343454
## Geodetic CRS:  WGS 84
## First 10 features:
##            ADM4_EN   ADM4_PCODE ADM4_REF ADM4ALT1EN ADM4ALT2EN
## 1         Anajiaka ID5316020006     <NA>       <NA>       <NA>
## 2        Anakalang ID5316010008     <NA>       <NA>       <NA>
## 3          Anapalu ID5316020014     <NA>       <NA>       <NA>
## 4        Bolubokat ID5316030007     <NA>       <NA>       <NA>
## 5  Bolubokat Barat ID5316030018     <NA>       <NA>       <NA>
## 6  Bolubokat Utara ID5316030008     <NA>       <NA>       <NA>
## 7      Bondo Sulla ID5316040010     <NA>       <NA>       <NA>
## 8          Cendana ID5316040004     <NA>       <NA>       <NA>
## 9    Cendana Barat ID5316040013     <NA>       <NA>       <NA>
## 10        Daha Elu ID5316020015     <NA>       <NA>       <NA>
##                  ADM3_EN ADM3_PCODE      ADM2_EN ADM2_PCODE             ADM1_EN
## 1  Umbu Ratu Nggay Barat  ID5316020 Sumba Tengah     ID5316 Nusa Tenggara Timur
## 2             Katikutana  ID5316010 Sumba Tengah     ID5316 Nusa Tenggara Timur
## 3  Umbu Ratu Nggay Barat  ID5316020 Sumba Tengah     ID5316 Nusa Tenggara Timur
## 4        Umbu Ratu Nggay  ID5316030 Sumba Tengah     ID5316 Nusa Tenggara Timur
## 5        Umbu Ratu Nggay  ID5316030 Sumba Tengah     ID5316 Nusa Tenggara Timur
## 6        Umbu Ratu Nggay  ID5316030 Sumba Tengah     ID5316 Nusa Tenggara Timur
## 7                Mamboro  ID5316040 Sumba Tengah     ID5316 Nusa Tenggara Timur
## 8                Mamboro  ID5316040 Sumba Tengah     ID5316 Nusa Tenggara Timur
## 9                Mamboro  ID5316040 Sumba Tengah     ID5316 Nusa Tenggara Timur
## 10 Umbu Ratu Nggay Barat  ID5316020 Sumba Tengah     ID5316 Nusa Tenggara Timur
##    ADM1_PCODE   ADM0_EN ADM0_PCODE       date    validOn    validTo Shape_Leng
## 1        ID53 Indonesia         ID 2019-12-20 2020-04-01 -001-11-30 0.05340610
## 2        ID53 Indonesia         ID 2019-12-20 2020-04-01 -001-11-30 0.08168241
## 3        ID53 Indonesia         ID 2019-12-20 2020-04-01 -001-11-30 0.11753300
## 4        ID53 Indonesia         ID 2019-12-20 2020-04-01 -001-11-30 0.12347702
## 5        ID53 Indonesia         ID 2019-12-20 2020-04-01 -001-11-30 0.32236466
## 6        ID53 Indonesia         ID 2019-12-20 2020-04-01 -001-11-30 0.30182614
## 7        ID53 Indonesia         ID 2019-12-20 2020-04-01 -001-11-30 0.25315111
## 8        ID53 Indonesia         ID 2019-12-20 2020-04-01 -001-11-30 0.23894156
## 9        ID53 Indonesia         ID 2019-12-20 2020-04-01 -001-11-30 0.24107028
## 10       ID53 Indonesia         ID 2019-12-20 2020-04-01 -001-11-30 0.16364761
##      Shape_Area                       geometry
## 1  0.0001545420 MULTIPOLYGON (((119.5912 -9...
## 2  0.0002911557 MULTIPOLYGON (((119.5759 -9...
## 3  0.0007973376 MULTIPOLYGON (((119.6062 -9...
## 4  0.0007122808 MULTIPOLYGON (((119.6899 -9...
## 5  0.0024054681 MULTIPOLYGON (((119.6511 -9...
## 6  0.0018686310 MULTIPOLYGON (((119.7112 -9...
## 7  0.0024328930 MULTIPOLYGON (((119.4716 -9...
## 8  0.0021984290 MULTIPOLYGON (((119.5959 -9...
## 9  0.0021056805 MULTIPOLYGON (((119.5367 -9...
## 10 0.0008922374 MULTIPOLYGON (((119.5962 -9...
nrow(shp_sumba_tengah)
## [1] 65

Data Stunting Sumba Tengah

data <- read_excel("C:/Users/Admin/Downloads/Adriano Excel Putra/DataStunting.xlsx.", sheet=3)

data
## # A tibble: 65 × 5
##    `Kode Kec` `NAMA KECAMATAN`      `KODE DESA` `NAMA DESA`  Stunting
##         <dbl> <chr>                       <dbl> <chr>           <dbl>
##  1     531701 KATIKU TANA            5320000000 MAKATA KERI        18
##  2     531701 KATIKU TANA            5320000000 KABELA WUNTU        4
##  3     531701 KATIKU TANA            5320000000 MATA WOGA           3
##  4     531701 KATIKU TANA            5320000000 UMBU RIRI           0
##  5     531701 KATIKU TANA            5320000000 ANAKALANG           7
##  6     531701 KATIKU TANA            5320000000 DEWA JARA           2
##  7     531701 KATIKU TANA            5320000000 MATA REDI           4
##  8     531702 UMBU RATU NGGAY BARAT  5320000000 PRAI MADETA         5
##  9     531702 UMBU RATU NGGAY BARAT  5320000000 PONDOK              5
## 10     531702 UMBU RATU NGGAY BARAT  5320000000 MADERI              0
## # ℹ 55 more rows

Merge Data

library(dplyr)

#Buat ADM4EN pada data shp_sumbawa_barat menjadi Huruf Kapital
shp_sumba_tengah$ADM4_EN <- toupper(shp_sumba_tengah$ADM4_EN)

#Merge data shp_sumbawa_barat dengan data

mapSumba <- full_join(shp_sumba_tengah, data, by = c("ADM4_EN" = "NAMA DESA"))
library(ggplot2)

library(ggplot2)
library(viridis)
## Warning: package 'viridis' was built under R version 4.3.3
## Loading required package: viridisLite
## Warning: package 'viridisLite' was built under R version 4.3.2
mapBogor <- st_as_sf(mapSumba)
Stuntingbre <- ggplot(mapSumba) +  
  geom_sf(aes(fill = Stunting)) + 
  scale_fill_viridis_c(option = "D", name = "Stunting") +  # Menggunakan palet warna kontinyu
  theme_minimal()

Stuntingbre

Bila dilakukan Visualisasi secara sekilas, dapat terlihat bahwa pola penyebaran Stunting di Kabupaten Sumba Tengah terlihat bergerombol dengan angka disekitar 0 sampai 25 Kasus Stunting. Bila dilihat juga terdapat satu dearah dengan Kasus Stunting yang sangat tinggi ditandai dengan warna Kuning sebagai outlier dari data tersebut. Untuk memastikan pola penyebarannya, maka analisis lebih lanjut akan dilakukan

Pembobot Contuguity

Moran Test Pembobot Queen

# Membuat matriks pembobot spasial dengan metode queen
W <- poly2nb(mapBogor, queen = TRUE)
W.queen <- nb2listw(W, style='W')

IM <- moran.test(mapBogor$Stunting, W.queen,randomisation=T, alternative="greater", zero.policy = FALSE)
IM #Greater untuk Hipotesis adanya autokorelasi lokal 
## 
##  Moran I test under randomisation
## 
## data:  mapBogor$Stunting  
## weights: W.queen    
## 
## Moran I statistic standard deviate = 1.0127, p-value = 0.1556
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.033479343      -0.015625000       0.002351223

Dilihat dari Uji Morannya, didapatkan nilai p-valuenya yang lebih besar dari alpha 5%, Hal ini mengindikasikan bahwa Tak Tolak H0, dimana berarti dari Matrix pembobot queen, dapat dikatakan bahwa sebaran jumlah kasus stunting di Sumba Tengah menyebar secara acak.

# Plot geometri dari mapSumba
plot(st_geometry(mapSumba), border = "blue", col = 'gray')

# Membuat centroid dari geometri
coords <- st_coordinates(st_centroid(st_geometry(mapSumba)))



# Plotkan pembobot spasial W.queen
plot(W.queen, coords, add = TRUE, col = "red")

# Menambahkan judul
title(main = "Pembobot Queen")

Gettis Ord Test Global

GO <- globalG.test(mapBogor$Stunting, W.queen, alternative = "greater")
## Warning in globalG.test(mapBogor$Stunting, W.queen, alternative = "greater"):
## Binary weights recommended (especially for distance bands)
GO
## 
##  Getis-Ord global G statistic
## 
## data:  mapBogor$Stunting 
## weights: W.queen   
## 
## standard deviate = 1.2381, p-value = 0.1078
## alternative hypothesis: greater
## sample estimates:
## Global G statistic        Expectation           Variance 
##       2.060140e-02       1.562500e-02       1.615449e-05

Dari Uji Gettis ORd Global, Didapatkan P-value yang lebih besar dari alpha 5%. Hal ini mengindikasikan tak tolak H0, artinya dapat dikatakan bahwa tidak terdapat adanya indikasi hot-spot / cold-spot secara global

Moran TestPembobot Rook

# Membuat matriks pembobot spasial dengan metode rook
W <- poly2nb(mapSumba, queen = FALSE)

W.rook <- nb2listw(W, style='B')

IM <- moran.test(mapBogor$Stunting, W.rook,randomisation=T, alternative="greater", zero.policy = FALSE)
IM
## 
##  Moran I test under randomisation
## 
## data:  mapBogor$Stunting  
## weights: W.rook    
## 
## Moran I statistic standard deviate = 1.1872, p-value = 0.1176
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.039202101      -0.015625000       0.002132834

Dilihat dari Uji Morannya, didapatkan nilai p-valuenya yang lebih besar dari alpha 5%, Hal ini mengindikasikan bahwa Tak Tolak H0, dimana berarti dari Matrix pembobot Rook, dapat dikatakan bahwa sebaran jumlah kasus stunting di Sumba Tengah menyebar secara acak.

# Plot geometri dari mapBogor
plot(st_geometry(mapSumba), border = "blue", col = 'gray')

# Membuat centroid dari geometri
coords <- st_coordinates(st_centroid(st_geometry(mapSumba)))


# Plotkan pembobot spasial W.queen
plot(W.rook, coords, add = TRUE, col = "red")

# Menambahkan judul
title(main = "Pembobot Rook")

Gettis Ord Test Global

W.rook2 <- nb2listw(W, style='B')
GO <- globalG.test(mapSumba$Stunting, W.rook2, alternative = "greater")
GO
## 
##  Getis-Ord global G statistic
## 
## data:  mapSumba$Stunting 
## weights: W.rook2   
## 
## standard deviate = 0.78228, p-value = 0.217
## alternative hypothesis: greater
## sample estimates:
## Global G statistic        Expectation           Variance 
##       0.0945650010       0.0774038462       0.0004812478

Dari Uji Gettis ORd Global, Didapatkan P-value yang lebih besar dari alpha 5%. Hal ini mengindikasikan tak tolak H0, artinya dapat dikatakan bahwa tidak terdapat adanya indikasi hot-spot / cold-spot secara global

Local Moran

LM <- localmoran(mapSumba$Stunting, W.queen, alternative = "greater")
head(LM)
##             Ii          E.Ii      Var.Ii       Z.Ii Pr(z > E(Ii))
## 1  0.092218199 -0.0034467881 0.053159287  0.4149191     0.3391006
## 2 -0.005852652 -0.0002213997 0.002207651 -0.1198505     0.5476992
## 3  0.078407574 -0.0023229179 0.023113910  0.5310078     0.2977067
## 4  0.161343867 -0.0034467881 0.053159287  0.7147316     0.2373874
## 5  0.062592913 -0.0034467881 0.021657487  0.4487465     0.3268073
## 6  0.062592913 -0.0002775082 0.004293578  0.9594817     0.1686581
# Pastikan Local Moran's I sudah dihitung
mapSumba$lmI <- LM[, "Ii"]  # local Moran's I

# Tambahkan juga variabel lain yang relevan jika perlu
mapSumba$lmZ <- LM[, "Z.Ii"]  # z-scores
mapSumba$lmp <- LM[, "Pr(z > E(Ii))"]  # p-values


p1 <- tm_shape(mapSumba) +
  tm_polygons(col = "lmI", title = "Local Moran's I",
              style = "quantile") +
  tm_layout(legend.outside = TRUE)
p1
## Variable(s) "lmI" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

p2 <- tm_shape(mapSumba) +
  tm_polygons(col = "lmp", title = "p-value",
              breaks = c(-Inf, 0.05, Inf)) +
  tm_layout(legend.outside = TRUE)
p2

Dapat diliahat bila diuji Indeks Morannya secara lokal, hampir keseluruhan desa di Sumba Tengah tidak singinfikan, hanya terdapat 2 desa yayng indeks morannya nyata ( terima H1, dimana H1 adalah terjadinya penggerombolan kasus stunting/ autokorelasi lokal)

tmap_mode("plot")
## tmap mode set to plotting
tm_shape(mapSumba) + tm_polygons(col = "lmZ",
title = "Local Moran's I", style = "fixed",
breaks = c(-Inf, -1.96, 1.96, Inf),
labels = c("Negative SAC", "No SAC", "Positive SAC"),
palette =  c("blue", "white", "red")) +
tm_layout(legend.outside = TRUE)

Dapat dilihat Indeks moran yang tadi nyata merupakan Autokorelasi positif, sedangkan yang lainnya menyebar acak dan ada beberapa desa yang memiliki autokorelasi negatif walau tidak nyata dalam taraf 5 %

Moran Plot

moran.plot(mapSumba$Stunting, W.queen)

Dari Moran Plot, didapatkan garis korelasi yang positif yang mengindikasikan adanya autokorelasi global walaupun garis ini dapat dilihat sangat lemah karena hanya bergeser sedikit dari titik rataannya.

Hotspot

Local_M <- localG(mapSumba$Stunting, W.queen, alternative = "greater")
Local_M
##  [1] -0.41491912 -0.11985050 -0.53100779 -0.71473164 -0.44874649 -0.95948173
##  [7]  0.38836488 -0.21984334  0.21790820  0.23864914  4.89064390  0.04771959
## [13] -0.23800199 -0.05879127  0.22678525  0.18976861  0.15499518 -0.54341020
## [19] -0.70925798  0.14116319  2.58434761  4.42491160 -0.39061777 -0.28362265
## [25] -1.08632595 -1.01472324 -1.03260319 -0.23643993 -0.34411070  0.14970296
## [31] -0.59336221 -0.85475980 -0.34411070 -0.48636418 -0.13537936  0.93294140
## [37] -0.08006911 -0.61320437 -0.67863695 -0.76564119 -0.36864841 -0.82088213
## [43]  0.03910352 -0.65688576 -0.11510659  0.14638116  0.18651135 -0.47418101
## [49] -0.57021037 -0.94522767 -0.69298312 -0.85380133 -0.47746644  3.91094728
## [55]  0.94199309  3.65846744  0.16429944 -0.73934058 -0.82574245  0.57804427
## [61] -0.46350434  0.28343790 -0.25009227 -0.03668020 -0.47509112
## attr(,"internals")
##                Gi    E(Gi)        V(Gi)       Z(Gi) Pr(z > E(Gi))
##  [1,] 0.008953168 0.015625 2.585612e-04 -0.41491912  6.608994e-01
##  [2,] 0.014044944 0.015625 1.738063e-04 -0.11985050  5.476992e-01
##  [3,] 0.008747698 0.015625 1.677391e-04 -0.53100779  7.022933e-01
##  [4,] 0.004132231 0.015625 2.585612e-04 -0.71473164  7.626126e-01
##  [5,] 0.011019284 0.015625 1.053397e-04 -0.44874649  6.731927e-01
##  [6,] 0.000000000 0.015625 2.651958e-04 -0.95948173  8.313419e-01
##  [7,] 0.022079772 0.015625 2.762370e-04  0.38836488  3.488730e-01
##  [8,] 0.012711864 0.015625 1.755880e-04 -0.21984334  5.870034e-01
##  [9,] 0.018732782 0.015625 2.034015e-04  0.21790820  4.137503e-01
## [10,] 0.019101124 0.015625 2.121635e-04  0.23864914  4.056888e-01
## [11,] 0.132478632 0.015625 5.708899e-04  4.89064390  5.025333e-07
## [12,] 0.016248839 0.015625 1.709040e-04  0.04771959  4.809699e-01
## [13,] 0.011772853 0.015625 2.619657e-04 -0.23800199  5.940602e-01
## [14,] 0.014664804 0.015625 2.667434e-04 -0.05879127  5.234408e-01
## [15,] 0.020949721 0.015625 5.512696e-04  0.22678525  4.102954e-01
## [16,] 0.018105850 0.015625 1.709040e-04  0.18976861  4.247452e-01
## [17,] 0.018156425 0.015625 2.667434e-04  0.15499518  4.384126e-01
## [18,] 0.006887052 0.015625 2.585612e-04 -0.54341020  7.065763e-01
## [19,] 0.005509642 0.015625 2.034015e-04 -0.70925798  7.609178e-01
## [20,] 0.017447199 0.015625 1.666283e-04  0.14116319  4.438705e-01
## [21,] 0.045289855 0.015625 1.317597e-04  2.58434761  4.878170e-03
## [22,] 0.086776860 0.015625 2.585612e-04  4.42491160  4.824089e-06
## [23,] 0.010000000 0.015625 2.073677e-04 -0.39061777  6.519601e-01
## [24,] 0.005830904 0.015625 1.192468e-03 -0.28362265  6.116502e-01
## [25,] 0.002754821 0.015625 1.403618e-04 -1.08632595  8.613326e-01
## [26,] 0.001104972 0.015625 2.047574e-04 -1.01472324  8.448811e-01
## [27,] 0.002295684 0.015625 1.666283e-04 -1.03260319  8.491052e-01
## [28,] 0.011142061 0.015625 3.594876e-04 -0.23643993  5.934543e-01
## [29,] 0.009182736 0.015625 3.504940e-04 -0.34411070  6.346185e-01
## [30,] 0.018055556 0.015625 2.636030e-04  0.14970296  4.404995e-01
## [31,] 0.007162534 0.015625 2.034015e-04 -0.59336221  7.235306e-01
## [32,] 0.004591368 0.015625 1.666283e-04 -0.85475980  8.036579e-01
## [33,] 0.009182736 0.015625 3.504940e-04 -0.34411070  6.346185e-01
## [34,] 0.007681564 0.015625 2.667434e-04 -0.48636418  6.866455e-01
## [35,] 0.013957307 0.015625 1.517495e-04 -0.13537936  5.538440e-01
## [36,] 0.033149171 0.015625 3.528306e-04  0.93294140  1.754251e-01
## [37,] 0.013774105 0.015625 5.343598e-04 -0.08006911  5.319089e-01
## [38,] 0.010242086 0.015625 7.705919e-05 -0.61320437  7.301294e-01
## [39,] 0.005665722 0.015625 2.153677e-04 -0.67863695  7.513160e-01
## [40,] 0.005586592 0.015625 1.719013e-04 -0.76564119  7.780551e-01
## [41,] 0.011083744 0.015625 1.517495e-04 -0.36864841  6.438051e-01
## [42,] 0.004721435 0.015625 1.764312e-04 -0.82088213  7.941433e-01
## [43,] 0.016528926 0.015625 5.343598e-04  0.03910352  4.844039e-01
## [44,] 0.000000000 0.015625 5.657966e-04 -0.65688576  7.443728e-01
## [45,] 0.013774105 0.015625 2.585612e-04 -0.11510659  5.458197e-01
## [46,] 0.018365473 0.015625 3.504940e-04  0.14638116  4.418102e-01
## [47,] 0.018390805 0.015625 2.199037e-04  0.18651135  4.260219e-01
## [48,] 0.008839779 0.015625 2.047574e-04 -0.47418101  6.823146e-01
## [49,] 0.008264463 0.015625 1.666283e-04 -0.57021037  7.157325e-01
## [50,] 0.004352988 0.015625 1.422100e-04 -0.94522767  8.277287e-01
## [51,] 0.005586592 0.015625 2.098381e-04 -0.69298312  7.558399e-01
## [52,] 0.005509642 0.015625 1.403618e-04 -0.85380133  8.033925e-01
## [53,] 0.008815427 0.015625 2.034015e-04 -0.47746644  6.834850e-01
## [54,] 0.078512397 0.015625 2.585612e-04  3.91094728  4.596742e-05
## [55,] 0.023529412 0.015625 7.041151e-05  0.94199309  1.730981e-01
## [56,] 0.068144044 0.015625 2.060797e-04  3.65846744  1.268640e-04
## [57,] 0.017458101 0.015625 1.244802e-04  0.16429944  4.347477e-01
## [58,] 0.007352941 0.015625 1.251809e-04 -0.73934058  7.701499e-01
## [59,] 0.002100840 0.015625 2.682448e-04 -0.82574245  7.955249e-01
## [60,] 0.026897214 0.015625 3.802737e-04  0.57804427  2.816171e-01
## [61,] 0.009641873 0.015625 1.666283e-04 -0.46350434  6.784985e-01
## [62,] 0.019283747 0.015625 1.666283e-04  0.28343790  3.884206e-01
## [63,] 0.012396694 0.015625 1.666283e-04 -0.25009227  5.987420e-01
## [64,] 0.015151515 0.015625 1.666283e-04 -0.03668020  5.146300e-01
## [65,] 0.004273504 0.015625 5.708899e-04 -0.47509112  6.826390e-01
## attr(,"cluster")
##  [1] Low  High Low  Low  Low  Low  High High Low  High High Low  Low  Low  Low 
## [16] Low  Low  Low  Low  Low  High Low  Low  High Low  Low  Low  Low  Low  Low 
## [31] Low  Low  Low  Low  High Low  Low  Low  High Low  High High Low  High Low 
## [46] Low  High Low  Low  Low  Low  Low  Low  Low  High Low  Low  High High High
## [61] Low  Low  Low  Low  High
## Levels: Low High
## attr(,"gstari")
## [1] FALSE
## attr(,"call")
## localG(x = mapSumba$Stunting, listw = W.queen, alternative = "greater")
## attr(,"class")
## [1] "localG"
mapSumba$lmZ2 <- Local_M
tmap_mode("plot")
## tmap mode set to plotting
tm_shape(mapSumba) + tm_polygons(col = "lmZ2",
title = "Local Gi", style = "fixed",
breaks = c(-Inf, -1.96, 1.96, Inf),
labels = c("Coldspot", "No SAC", "Hostpot"),
palette =  c("blue", "white", "red")) +
tm_layout(legend.outside = TRUE)

Dapat dilihat bahwa Secara Hot-spot lokal, ada beberapa daearah yang diindikasikan sebagai hot-spot. Hal ini kontradiktif dengan argumen sebelumnya di Gettis Ord Globalnya yang menandakan tidak adanya Indikasi hot-spot/cold-spot secara global. Bila diperhatikan pula, desa yang menjadi hot-spot ini salah dua nya adalah desa yang terindikasi secara lokal memiliki autokorelasi positif.

Pembobot Jarak

Radial Near ( Jarak 10 KM)

coords <- st_coordinates(st_centroid(st_geometry(mapSumba)))
w.rdw <-dnearneigh(coords,0,10,longlat=TRUE) # Treshold Jarak 10 Km
w.rdw.s <- nb2listw(w.rdw,style='W')
summary(w.rdw.s)
## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 65 
## Number of nonzero links: 810 
## Percentage nonzero weights: 19.1716 
## Average number of links: 12.46154 
## 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 
##  1  3  2  4  2  3  7  3  1  3  4  1  1  4  2  3  3  1  1  3  3  5  3  2 
## 1 least connected region:
## 17 with 1 link
## 2 most connected regions:
## 3 29 with 24 links
## 
## Weights style: W 
## Weights constants summary:
##    n   nn S0       S1     S2
## W 65 4225 65 16.17648 265.34

Moran Test

IM <- moran.test(mapSumba$Stunting, w.rdw.s,randomisation=T, alternative="greater", zero.policy = FALSE) #Greater artinya mengecek ada tidaknya autokorelasi positif
IM
## 
##  Moran I test under randomisation
## 
## data:  mapSumba$Stunting  
## weights: w.rdw.s    
## 
## Moran I statistic standard deviate = 1.4399, p-value = 0.07495
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.034835080      -0.015625000       0.001228138

Dilihat dari Uji Morannya, didapatkan nilai p-valuenya yang lebih besar dari alpha 5%, Hal ini mengindikasikan bahwa Tak Tolak H0, dimana berarti dari Matrix pembobot Radial Near , dapat dikatakan bahwa sebaran jumlah kasus stunting di Sumba Tengah menyebar secara acak.

Gettis Ord Global

GO <- globalG.test(mapSumba$Stunting, w.rdw.s, alternative = "greater")
## Warning in globalG.test(mapSumba$Stunting, w.rdw.s, alternative = "greater"):
## Binary weights recommended (especially for distance bands)
GO
## 
##  Getis-Ord global G statistic
## 
## data:  mapSumba$Stunting 
## weights: w.rdw.s   
## 
## standard deviate = 1.5387, p-value = 0.06194
## alternative hypothesis: greater
## sample estimates:
## Global G statistic        Expectation           Variance 
##       2.001585e-02       1.562500e-02       8.143486e-06

Dari Uji Gettis ORd Global, Didapatkan P-value yang lebih besar dari alpha 5%. Hal ini mengindikasikan tak tolak H0, artinya dapat dikatakan bahwa tidak terdapat adanya indikasi hot-spot / cold-spot secara global

Local Moran

LM <- localmoran(mapSumba$Stunting, w.rdw.s,alternative = "greater")
head(LM)
##            Ii          E.Ii      Var.Ii       Z.Ii Pr(z > E(Ii))
## 1 -0.08510417 -0.0034467881 0.006317480 -1.0273620     0.8478750
## 2  0.01852224 -0.0002213997 0.000407108  0.9289644     0.1764538
## 3 -0.07427101 -0.0023229179 0.003985157 -1.1397159     0.8727977
## 4  0.12068171 -0.0034467881 0.009797986  1.2540160     0.1049181
## 5  0.11196839 -0.0034467881 0.010631857  1.1193305     0.1314996
## 6  0.03270465 -0.0002775082 0.001240367  0.9364919     0.1745100
# Pastikan Local Moran's I sudah dihitung
mapSumba$lm.EDW <- LM[, "Ii"]  # local Moran's I

# Tambahkan juga variabel lain yang relevan jika perlu
mapSumba$lmZ <- LM[, "Z.Ii"]  # z-scores
mapSumba$lmp <- LM[, "Pr(z > E(Ii))"]  # p-values


p1 <- tm_shape(mapSumba) +
  tm_polygons(col = "lmI", title = "Local Moran's I",
              style = "quantile") +
  tm_layout(legend.outside = TRUE)
p1
## Variable(s) "lmI" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

p2 <- tm_shape(mapSumba) +
  tm_polygons(col = "lmp", title = "p-value",
              breaks = c(-Inf, 0.05, Inf)) +
  tm_layout(legend.outside = TRUE)
p2

Dapat dilihat bahwa terdapat beberapa desa yang terindikasi memilliki autokorelasi secara lokal

tmap_mode("plot")
## tmap mode set to plotting
tm_shape(mapSumba) + tm_polygons(col = "lmZ",
title = "Local Moran's I", style = "fixed",
breaks = c(-Inf, -1.96, 1.96, Inf),
labels = c("Negative SAC", "No SAC", "Positive SAC"),
palette =  c("blue", "white", "red")) +
tm_layout(legend.outside = TRUE)

Dapat dilihat Indeks moran yang tadi nyata merupakan Autokorelasi positif, sedangkan yang lainnya menyebar acak dan ada beberapa desa yang memiliki autokorelasi negatif walau tidak nyata dalam taraf 5 %

Exponential

D<-dist(coords, method = "euclidean")# Metode Jarak Euclidean
D<-as.matrix(D)

Moran Global

alpha=1
w.edw<-exp((-alpha)*D)
diag(w.edw)<-0
rtot<-rowSums(w.edw,na.rm=TRUE)
w.edw.sd<-w.edw/rtot #row-normalized
w.edw.s = mat2listw(w.edw.sd,style='W')


w.edw.s <- mat2listw(w.edw.sd,style='W') #untuk melihat matriks W

summary(w.edw.s)
## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 65 
## Number of nonzero links: 4160 
## Percentage nonzero weights: 98.46154 
## Average number of links: 64 
## Link number distribution:
## 
## 64 
## 65 
## 65 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 with 64 links
## 65 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 with 64 links
## 
## Weights style: W 
## Weights constants summary:
##    n   nn S0       S1       S2
## W 65 4225 65 2.041734 260.1077
IM <- moran.test(mapSumba$Stunting, w.edw.s,randomisation=T, alternative="greater", zero.policy = FALSE)
IM
## 
##  Moran I test under randomisation
## 
## data:  mapSumba$Stunting  
## weights: w.edw.s    
## 
## Moran I statistic standard deviate = 2.1621, p-value = 0.0153
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##     -1.344167e-02     -1.562500e-02      1.019690e-06
#Ambil Kurtosis dan Index Moran dari pembobotot exponensial

moran(mapSumba$Stunting, w.edw.s, n=length(w.edw.s$neighbours), S0=Szero(w.edw.s))
## $I
## [1] -0.01344167
## 
## $K
## [1] 41.07314

Dapat dilihat bahwa dari Moran testnya, P-valuenya lebih kecil dari alpha 5 persen. Hal ini mengindikasikan bahwa terdapat autokorelasi secara Global, namun bila dilihat dari Indeks Morannya yaitu sebesar -0,013 ~~ Dimana akan mendekati 0, hal ini mengindikasikan bahwa pola penyebaran kasusnya menyebar secara acak.

Local Moran

#Cari Local Moran dari matrix pembobot jarak exponential

LM <- localmoran(mapSumba$Stunting, w.edw.s, alternative = "greater")
head(LM)
##              Ii          E.Ii       Var.Ii       Z.Ii Pr(z > E(Ii))
## 1 -0.0081592191 -0.0034467881 1.870019e-05 -1.0897379    0.86208568
## 2  0.0011529013 -0.0002213997 1.290038e-06  1.2099868    0.11314197
## 3 -0.0045214140 -0.0023229179 1.142283e-05 -0.6504874    0.74231128
## 4  0.0008855662 -0.0034467881 1.116320e-05  1.2966704    0.09737231
## 5  0.0012422610 -0.0034467881 1.173064e-05  1.3690643    0.08548959
## 6  0.0014525657 -0.0002775082 9.883626e-07  1.7402294    0.04090937
# Pastikan Local Moran's I sudah dihitung
mapSumba$lmI <- LM[, "Ii"]  # local Moran's I

# Tambahkan juga variabel lain yang relevan jika perlu

mapSumba$lmZ <- LM[, "Z.Ii"]  # z-scores

mapSumba$lmp <- LM[, "Pr(z > E(Ii))"]  # p-values

p1 <- tm_shape(mapSumba) +
  tm_polygons(col = "lmI", title = "Local Moran's I",
              style = "quantile") +
  tm_layout(legend.outside = TRUE)


p2 <- tm_shape(mapSumba) +
  
  tm_polygons(col = "lmp", title = "p-value",
              breaks = c(-Inf, 0.05, Inf)) +
  tm_layout(legend.outside = TRUE)

p1
## Variable(s) "lmI" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

p2

Dapat diliahat bila diuji Indeks Morannya secara lokal, hampir keseluruhan desa di Sumba Tengah tidak singinfikan, hanya terdapat beberapa desa yayng indeks morannya nyata ( terima H1, dimana H1 adalah terjadinya penggerombolan kasus stunting/ autokorelasi lokal)

tmap_mode("plot")
## tmap mode set to plotting
tm_shape(mapSumba) + tm_polygons(col = "lmZ",
title = "Local Moran's I", style = "fixed",
breaks = c(-Inf, -1.96, 1.96, Inf),
labels = c("Negative SAC", "No SAC", "Positive SAC"),
palette =  c("blue", "white", "red")) +
tm_layout(legend.outside = TRUE)

Dapat dilihat Indeks moran yang tadi nyata merupakan Autokorelasi positif, sedangkan yang lainnya menyebar acak dan ada beberapa desa yang memiliki autokorelasi negatif walau tidak nyata dalam taraf 5 %

Gettis Ord Global

w.edw.s = mat2listw(w.edw.sd,style='B')
GO <- globalG.test(mapSumba$Stunting, w.edw.s,alternative = "greater")
GO
## 
##  Getis-Ord global G statistic
## 
## data:  mapSumba$Stunting 
## weights: w.edw.s   
## 
## standard deviate = 1.1454, p-value = 0.126
## alternative hypothesis: greater
## sample estimates:
## Global G statistic        Expectation           Variance 
##       1.581048e-02       1.562500e-02       2.622256e-08

Dari Uji Gettis ORd Global, Didapatkan P-value yang lebih besar dari alpha 5%. Hal ini mengindikasikan tak tolak H0, artinya dapat dikatakan bahwa tidak terdapat adanya indikasi hot-spot / cold-spot secara global

Hotspot Gettis Ord Local

# Cari Hotspot dengan Gettis Ord

Local_M <- localG(mapSumba$Stunting, w.rdw.s, alternative = "greater")

Local_M
##  [1]  1.027361959  0.928964397  1.139715863 -1.254016024 -1.119330542
##  [6] -0.936491919 -0.212399965 -0.236426231  0.441231739 -0.716555558
## [11]  2.270882348  2.291828768  1.219103443 -0.340978615 -0.776816691
## [16]  1.179405786 -0.049550626 -0.675932227 -1.068171868 -0.929805839
## [21]  1.437546451  3.291691649 -0.043401974  3.106657403 -1.164504125
## [26] -1.300239224 -1.152761558  1.890012834 -0.666547482  2.285345271
## [31] -0.570210373 -0.322316492 -0.457749476 -0.430308068 -0.022399309
## [36] -0.045099420 -0.080069107 -0.001361946 -0.678636953 -0.747552192
## [41] -0.928712986 -0.320910900  0.056214848 -0.656885762 -0.543410196
## [46]  0.146381164  2.817143879 -1.277019339 -0.977501821 -0.943418156
## [51]  1.208571562 -1.382702434 -0.436529447  2.764786005  1.584031599
## [56]  3.401886323  1.334294097 -1.192372410 -0.184389091  0.135008161
## [61] -0.621276716  0.176731870  0.016745870  0.008030693 -0.877123572
## attr(,"internals")
##                Gi    E(Gi)        V(Gi)        Z(Gi) Pr(z > E(Gi))
##  [1,] 0.021319919 0.015625 3.072756e-05  1.027361959  0.1521250286
##  [2,] 0.020884221 0.015625 3.205123e-05  0.928964397  0.1764537688
##  [3,] 0.021754144 0.015625 2.892054e-05  1.139715863  0.1272023481
##  [4,] 0.006968076 0.015625 4.765637e-05 -1.254016024  0.8950819093
##  [5,] 0.007575758 0.015625 5.171223e-05 -1.119330542  0.8685004246
##  [6,] 0.007428041 0.015625 7.661212e-05 -0.936491919  0.8254900143
##  [7,] 0.013024013 0.015625 1.499573e-04 -0.212399965  0.5841024935
##  [8,] 0.013720743 0.015625 6.487241e-05 -0.236426231  0.5934490280
##  [9,] 0.019086974 0.015625 6.156218e-05  0.441231739  0.3295226188
## [10,] 0.010767790 0.015625 4.594878e-05 -0.716555558  0.7631758124
## [11,] 0.033238367 0.015625 6.015829e-05  2.270882348  0.0115770506
## [12,] 0.034711806 0.015625 6.935890e-05  2.291828768  0.0109577630
## [13,] 0.022664316 0.015625 3.334109e-05  1.219103443  0.1114024666
## [14,] 0.013567438 0.015625 3.641259e-05 -0.340978615  0.6334401598
## [15,] 0.009951117 0.015625 5.334867e-05 -0.776816691  0.7813665361
## [16,] 0.022980501 0.015625 3.889538e-05  1.179405786  0.1191183161
## [17,] 0.013966480 0.015625 1.120322e-03 -0.049550626  0.5197597535
## [18,] 0.000000000 0.015625 5.343598e-04 -0.675932227  0.7504581621
## [19,] 0.001836547 0.015625 1.666283e-04 -1.068171868  0.8572785040
## [20,] 0.010101010 0.015625 3.529565e-05 -0.929805839  0.8237641887
## [21,] 0.024242424 0.015625 3.593446e-05  1.437546451  0.0752813920
## [22,] 0.047382920 0.015625 9.308202e-05  3.291691649  0.0004979337
## [23,] 0.015000000 0.015625 2.073677e-04 -0.043401974  0.5173094480
## [24,] 0.051384840 0.015625 1.324965e-04  3.106657403  0.0009460777
## [25,] 0.003673095 0.015625 1.053397e-04 -1.164504125  0.8778901137
## [26,] 0.003038674 0.015625 9.370255e-05 -1.300239224  0.9032405045
## [27,] 0.001967729 0.015625 1.403618e-04 -1.152761558  0.8754958666
## [28,] 0.027855153 0.015625 4.187302e-05  1.890012834  0.0293781218
## [29,] 0.012052342 0.015625 2.872902e-05 -0.666547482  0.7474693877
## [30,] 0.033730159 0.015625 6.276261e-05  2.285345271  0.0111462952
## [31,] 0.008264463 0.015625 1.666283e-04 -0.570210373  0.7157324893
## [32,] 0.011806375 0.015625 1.403618e-04 -0.322316492  0.6263935296
## [33,] 0.008264463 0.015625 2.585612e-04 -0.457749476  0.6764337809
## [34,] 0.010824022 0.015625 1.244802e-04 -0.430308068  0.6665142204
## [35,] 0.015412748 0.015625 8.979117e-05 -0.022399309  0.5089352843
## [36,] 0.015285451 0.015625 5.668426e-05 -0.045099420  0.5179859683
## [37,] 0.013774105 0.015625 5.343598e-04 -0.080069107  0.5319088534
## [38,] 0.015617064 0.015625 3.394915e-05 -0.001361946  0.5005433376
## [39,] 0.005665722 0.015625 2.153677e-04 -0.678636953  0.7513160388
## [40,] 0.011416080 0.015625 3.169994e-05 -0.747552192  0.7726348446
## [41,] 0.008958756 0.015625 5.152279e-05 -0.928712986  0.8234810754
## [42,] 0.009442871 0.015625 3.711139e-04 -0.320910900  0.6258610431
## [43,] 0.016528926 0.015625 2.585612e-04  0.056214848  0.4775853265
## [44,] 0.000000000 0.015625 5.657966e-04 -0.656885762  0.7443728129
## [45,] 0.006887052 0.015625 2.585612e-04 -0.543410196  0.7065762966
## [46,] 0.018365473 0.015625 3.504940e-04  0.146381164  0.4418102479
## [47,] 0.042319749 0.015625 8.979117e-05  2.817143879  0.0024226407
## [48,] 0.007734807 0.015625 3.817511e-05 -1.277019339  0.8992022902
## [49,] 0.010017531 0.015625 3.290779e-05 -0.977501821  0.8358396117
## [50,] 0.005193906 0.015625 1.222507e-04 -0.943418156  0.8272664699
## [51,] 0.023184358 0.015625 3.912236e-05  1.208571562  0.1134137437
## [52,] 0.005681818 0.015625 5.171223e-05 -1.382702434  0.9166219373
## [53,] 0.012199921 0.015625 6.156218e-05 -0.436529447  0.6687736806
## [54,] 0.040821438 0.015625 8.305298e-05  2.764786005  0.0028480075
## [55,] 0.022058824 0.015625 1.649721e-05  1.584031599  0.0565932642
## [56,] 0.056193114 0.015625 1.422100e-04  3.401886323  0.0003346123
## [57,] 0.023676510 0.015625 3.641259e-05  1.334294097  0.0910537457
## [58,] 0.008658009 0.015625 3.414025e-05 -1.192372410  0.8834423732
## [59,] 0.012605042 0.015625 2.682448e-04 -0.184389091  0.5731458864
## [60,] 0.017291066 0.015625 1.522876e-04  0.135008161  0.4463027109
## [61,] 0.008264463 0.015625 1.403618e-04 -0.621276716  0.7327912144
## [62,] 0.017906336 0.015625 1.666283e-04  0.176731870  0.4298595031
## [63,] 0.015777611 0.015625 8.305298e-05  0.016745870  0.4933196768
## [64,] 0.015702479 0.015625 9.308202e-05  0.008030693  0.4967962516
## [65,] 0.004884005 0.015625 1.499573e-04 -0.877123572  0.8097902386
## attr(,"cluster")
##  [1] Low  High Low  Low  Low  Low  High High Low  High High Low  Low  Low  Low 
## [16] Low  Low  Low  Low  Low  High Low  Low  High Low  Low  Low  Low  Low  Low 
## [31] Low  Low  Low  Low  High Low  Low  Low  High Low  High High Low  High Low 
## [46] Low  High Low  Low  Low  Low  Low  Low  Low  High Low  Low  High High High
## [61] Low  Low  Low  Low  High
## Levels: Low High
## attr(,"gstari")
## [1] FALSE
## attr(,"call")
## localG(x = mapSumba$Stunting, listw = w.rdw.s, alternative = "greater")
## attr(,"class")
## [1] "localG"
mapSumba$lmZ2 <- Local_M
tmap_mode("plot")
## tmap mode set to plotting
#Gettis Ord
teserahdeh<- tm_shape(mapSumba) + tm_polygons(col = "lmZ2",
title = "Local Gi", style = "fixed",
breaks = c(-Inf, -1.96, 1.96, Inf),
labels = c("Coldspot", "No SAC", "Hostpot"),
palette =  c("blue", "white", "red")) +
tm_layout(legend.outside = TRUE)

teserahdeh

Dapat dilihat bahwa Secara Hot-spot lokal, ada beberapa daearah yang diindikasikan sebagai hot-spot. Hal ini kontradiktif dengan argumen sebelumnya di Gettis Ord Globalnya yang menandakan tidak adanya Indikasi hot-spot/cold-spot secara global. Bila diperhatikan pula, desa yang menjadi hot-spot ini salah dua nya adalah desa yang terindikasi secara lokal memiliki autokorelasi positif.

KNN ( 3 Tetangga)

Moran Global

w.knn<-knn2nb(knearneigh(coords,k=3,longlat=TRUE))
w.knn.s <- nb2listw(w.knn,style='W')
summary(w.knn.s)
## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 65 
## Number of nonzero links: 195 
## Percentage nonzero weights: 4.615385 
## Average number of links: 3 
## Non-symmetric neighbours list
## Link number distribution:
## 
##  3 
## 65 
## 65 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 with 3 links
## 65 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 with 3 links
## 
## Weights style: W 
## Weights constants summary:
##    n   nn S0       S1       S2
## W 65 4225 65 38.33333 269.3333
IM <- moran.test(mapBogor$Stunting, w.knn.s,randomisation=T, alternative="greater", zero.policy = FALSE)# Greater untuk menguji autokreolasi positif
IM
## 
##  Moran I test under randomisation
## 
## data:  mapBogor$Stunting  
## weights: w.knn.s    
## 
## Moran I statistic standard deviate = 2.3709, p-value = 0.008873
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.117381172      -0.015625000       0.003147262
moran(mapBogor$Stunting, w.knn.s, n=length(w.knn.s$neighbours), S0=Szero(w.knn.s))
## $I
## [1] 0.1173812
## 
## $K
## [1] 41.07314

Dapat dilihat bahwa dari Moran testnya, P-valuenya lebih kecil dari alpha 5 persen. Hal ini mengindikasikan bahwa terdapat autokorelasi secara Global, namun bila dilihat dari Indeks Morannya yaitu sebesar 0.1 ~~ Dimana akan mendekati 0, hal ini mengindikasikan bahwa pola penyebaran kasusnya menyebar secara acak. Namun bila dibandingkan dengan beberapa pembobot sebelumnya, ini yang paling mendekati 1, sehingga bila dilihat secara perbandingan pembobot, KNN mengindikasikan adanya autokorelasi global positif ( penggerombolan)

Gettis Ord Global W.KNN

w.knn.s <- nb2listw(w.knn,style='B')
GO <- globalG.test(mapBogor$Stunting, w.edw.s,alternative = "greater")
GO
## 
##  Getis-Ord global G statistic
## 
## data:  mapBogor$Stunting 
## weights: w.edw.s   
## 
## standard deviate = 1.1454, p-value = 0.126
## alternative hypothesis: greater
## sample estimates:
## Global G statistic        Expectation           Variance 
##       1.581048e-02       1.562500e-02       2.622256e-08

Dari Uji Gettis ORd Global, Didapatkan P-value yang lebih besar dari alpha 5%. Hal ini mengindikasikan tak tolak H0, artinya dapat dikatakan bahwa tidak terdapat adanya indikasi hot-spot / cold-spot secara global

Local Moran

LM <- localmoran(mapBogor$Stunting, w.knn.s , alternative = "greater")
head(LM)
##           Ii          E.Ii     Var.Ii      Z.Ii Pr(z > E(Ii))
## 1 0.14827836 -0.0103403643 0.64854330 0.1969631     0.4219282
## 2 0.05251985 -0.0006641990 0.04179311 0.2601531     0.3973728
## 3 0.47842755 -0.0069687538 0.43757022 0.7337913     0.2315380
## 4 0.42478103 -0.0103403643 0.64854330 0.5403074     0.2944925
## 5 0.26677950 -0.0103403643 0.64854330 0.3441107     0.3653815
## 6 0.13173825 -0.0008325245 0.05238165 0.5792396     0.2812138
# Pastikan Local Moran's I sudah dihitung
mapSumba$lmI <- LM[, "Ii"]  # local Moran's I

# Tambahkan juga variabel lain yang relevan jika perlu

mapSumba$lmZ <- LM[, "Z.Ii"]  # z-scores

mapSumba$lmp <- LM[, "Pr(z > E(Ii))"]  # p-values

p1 <- tm_shape(mapSumba) +
  tm_polygons(col = "lmI", title = "Local Moran's I",
              style = "quantile") +
  tm_layout(legend.outside = TRUE)


p2 <- tm_shape(mapSumba) +
  
  tm_polygons(col = "lmp", title = "p-value",
              breaks = c(-Inf, 0.05, Inf)) +
  tm_layout(legend.outside = TRUE)

p1
## Variable(s) "lmI" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

p2

Dapat diliahat bila diuji Indeks Morannya secara lokal, hampir keseluruhan desa di Sumba Tengah tidak singinfikan, hanya terdapat beberapa desa yayng indeks morannya nyata ( terima H1, dimana H1 adalah terjadinya penggerombolan kasus stunting/ autokorelasi lokal)

tmap_mode("plot")
## tmap mode set to plotting
tm_shape(mapSumba) + tm_polygons(col = "lmZ",
title = "Local Moran's I", style = "fixed",
breaks = c(-Inf, -1.96, 1.96, Inf),
labels = c("Negative SAC", "No SAC", "Positive SAC"),
palette =  c("blue", "white", "red")) +
tm_layout(legend.outside = TRUE)

Dapat dilihat Indeks moran yang tadi nyata merupakan Autokorelasi positif, sedangkan yang lainnya menyebar acak dan ada beberapa desa yang memiliki autokorelasi negatif walau tidak nyata dalam taraf 5 %

Moran Plot

moran.plot(mapBogor$Stunting, w.knn.s)

Dari Moran Plot, didapatkan garis korelasi yang positif yang mengindikasikan adanya autokorelasi global positif.

Hotspot

w.knn.s <- nb2listw(w.knn,style='W')
Local_M <- localG(mapSumba$Stunting, w.knn.s, alternative = "greater")
Local_M
##  [1] -0.19696314  0.26015314 -0.73379135 -0.54030744 -0.34411070 -0.57923957
##  [7]  0.71390713 -0.22507617  0.34257791  0.16221314  4.54186026 -0.08952580
## [13] -0.24116885 -0.23411633  0.25553874 -0.18746855  0.35346975 -0.34411070
## [19] -0.83460255 -0.24601232  4.04124963  0.19543035  0.05510550 -0.10294347
## [25] -0.78555337 -0.83183445 -0.78555337 -0.38335406 -0.54030744 -0.43472117
## [31] -0.24601232 -0.34411070 -0.34411070 -0.52790937  0.03382927  0.93294140
## [37] -0.34411070 -0.42997836 -0.32091090 -0.77273690 -0.21220182 -0.32091090
## [43]  0.34257791 -0.81108507 -0.34411070  0.14638116 -0.50743912 -0.58672669
## [49] -0.73650418 -0.58416455 -0.52790937 -0.54030744 -0.29506151  4.36461115
## [55]  2.25294061  0.88581702 -0.23411633 -0.57457424 -0.67250434  0.57804427
## [61] -0.29506151 -0.24601232  0.19543035  0.04828279 -0.66022990
## attr(,"internals")
##                 Gi    E(Gi)        V(Gi)       Z(Gi) Pr(z > E(Gi))
##  [1,] 0.0119375574 0.015625 0.0003504940 -0.19696314  5.780718e-01
##  [2,] 0.0205992509 0.015625 0.0003655925  0.26015314  3.973728e-01
##  [3,] 0.0018416206 0.015625 0.0003528306 -0.73379135  7.684620e-01
##  [4,] 0.0055096419 0.015625 0.0003504940 -0.54030744  7.055075e-01
##  [5,] 0.0091827365 0.015625 0.0003504940 -0.34411070  6.346185e-01
##  [6,] 0.0046425255 0.015625 0.0003594876 -0.57923957  7.187862e-01
##  [7,] 0.0294396961 0.015625 0.0003744547  0.71390713  2.376423e-01
##  [8,] 0.0112994350 0.015625 0.0003693402 -0.22507617  5.890400e-01
##  [9,] 0.0220385675 0.015625 0.0003504940  0.34257791  3.659580e-01
## [10,] 0.0187265918 0.015625 0.0003655925  0.16221314  4.355690e-01
## [11,] 0.1035137702 0.015625 0.0003744547  4.54186026  2.788000e-06
## [12,] 0.0139275766 0.015625 0.0003594876 -0.08952580  5.356680e-01
## [13,] 0.0110803324 0.015625 0.0003551091 -0.24116885  5.952879e-01
## [14,] 0.0111731844 0.015625 0.0003615854 -0.23411633  5.925527e-01
## [15,] 0.0204841713 0.015625 0.0003615854  0.25553874  3.991535e-01
## [16,] 0.0120705664 0.015625 0.0003594876 -0.18746855  5.743534e-01
## [17,] 0.0223463687 0.015625 0.0003615854  0.35346975  3.618682e-01
## [18,] 0.0091827365 0.015625 0.0003504940 -0.34411070  6.346185e-01
## [19,] 0.0000000000 0.015625 0.0003504940 -0.83460255  7.980292e-01
## [20,] 0.0110192837 0.015625 0.0003504940 -0.24601232  5.971637e-01
## [21,] 0.0946859903 0.015625 0.0003827306  4.04124963  2.658356e-05
## [22,] 0.0192837466 0.015625 0.0003504940  0.19543035  4.225280e-01
## [23,] 0.0166666667 0.015625 0.0003573285  0.05510550  4.780272e-01
## [24,] 0.0136054422 0.015625 0.0003848708 -0.10294347  5.409961e-01
## [25,] 0.0009182736 0.015625 0.0003504940 -0.78555337  7.839354e-01
## [26,] 0.0000000000 0.015625 0.0003528306 -0.83183445  7.972488e-01
## [27,] 0.0009182736 0.015625 0.0003504940 -0.78555337  7.839354e-01
## [28,] 0.0083565460 0.015625 0.0003594876 -0.38335406  6.492714e-01
## [29,] 0.0055096419 0.015625 0.0003504940 -0.54030744  7.055075e-01
## [30,] 0.0074074074 0.015625 0.0003573285 -0.43472117  6.681176e-01
## [31,] 0.0110192837 0.015625 0.0003504940 -0.24601232  5.971637e-01
## [32,] 0.0091827365 0.015625 0.0003504940 -0.34411070  6.346185e-01
## [33,] 0.0091827365 0.015625 0.0003504940 -0.34411070  6.346185e-01
## [34,] 0.0055865922 0.015625 0.0003615854 -0.52790937  7.012189e-01
## [35,] 0.0162835249 0.015625 0.0003789300  0.03382927  4.865066e-01
## [36,] 0.0331491713 0.015625 0.0003528306  0.93294140  1.754251e-01
## [37,] 0.0091827365 0.015625 0.0003504940 -0.34411070  6.346185e-01
## [38,] 0.0074487896 0.015625 0.0003615854 -0.42997836  6.663943e-01
## [39,] 0.0094428706 0.015625 0.0003711139 -0.32091090  6.258610e-01
## [40,] 0.0009310987 0.015625 0.0003615854 -0.77273690  7.801609e-01
## [41,] 0.0114942529 0.015625 0.0003789300 -0.21220182  5.840252e-01
## [42,] 0.0094428706 0.015625 0.0003711139 -0.32091090  6.258610e-01
## [43,] 0.0220385675 0.015625 0.0003504940  0.34257791  3.659580e-01
## [44,] 0.0000000000 0.015625 0.0003711139 -0.81108507  7.913416e-01
## [45,] 0.0091827365 0.015625 0.0003504940 -0.34411070  6.346185e-01
## [46,] 0.0183654729 0.015625 0.0003504940  0.14638116  4.418102e-01
## [47,] 0.0057471264 0.015625 0.0003789300 -0.50743912  6.940766e-01
## [48,] 0.0046040516 0.015625 0.0003528306 -0.58672669  7.213064e-01
## [49,] 0.0018365473 0.015625 0.0003504940 -0.73650418  7.692880e-01
## [50,] 0.0046168052 0.015625 0.0003551091 -0.58416455  7.204452e-01
## [51,] 0.0055865922 0.015625 0.0003615854 -0.52790937  7.012189e-01
## [52,] 0.0055096419 0.015625 0.0003504940 -0.54030744  7.055075e-01
## [53,] 0.0101010101 0.015625 0.0003504940 -0.29506151  6.160266e-01
## [54,] 0.0973370064 0.015625 0.0003504940  4.36461115  6.367454e-06
## [55,] 0.0404411765 0.015625 0.0001213306  2.25294061  1.213145e-02
## [56,] 0.0323176362 0.015625 0.0003551091  0.88581702  1.878581e-01
## [57,] 0.0111731844 0.015625 0.0003615854 -0.23411633  5.925527e-01
## [58,] 0.0046685341 0.015625 0.0003636208 -0.57457424  7.172104e-01
## [59,] 0.0028011204 0.015625 0.0003636208 -0.67250434  7.493687e-01
## [60,] 0.0268972142 0.015625 0.0003802737  0.57804427  2.816171e-01
## [61,] 0.0101010101 0.015625 0.0003504940 -0.29506151  6.160266e-01
## [62,] 0.0110192837 0.015625 0.0003504940 -0.24601232  5.971637e-01
## [63,] 0.0192837466 0.015625 0.0003504940  0.19543035  4.225280e-01
## [64,] 0.0165289256 0.015625 0.0003504940  0.04828279  4.807454e-01
## [65,] 0.0028490028 0.015625 0.0003744547 -0.66022990  7.454468e-01
## attr(,"cluster")
##  [1] Low  High Low  Low  Low  Low  High High Low  High High Low  Low  Low  Low 
## [16] Low  Low  Low  Low  Low  High Low  Low  High Low  Low  Low  Low  Low  Low 
## [31] Low  Low  Low  Low  High Low  Low  Low  High Low  High High Low  High Low 
## [46] Low  High Low  Low  Low  Low  Low  Low  Low  High Low  Low  High High High
## [61] Low  Low  Low  Low  High
## Levels: Low High
## attr(,"gstari")
## [1] FALSE
## attr(,"call")
## localG(x = mapSumba$Stunting, listw = w.knn.s, alternative = "greater")
## attr(,"class")
## [1] "localG"
mapSumba$lmZ2 <- Local_M

tmap_mode("plot")
## tmap mode set to plotting
tm_shape(mapSumba) + tm_polygons(col = "lmZ2",
title = "Local Gi", style = "fixed",
breaks = c(-Inf, -1.96, 1.96, Inf),
labels = c("Coldspot", "No SAC", "Hostpot"),
palette =  c("blue", "white", "red")) +
tm_layout(legend.outside = TRUE)

# Kasih nama buat Hotspot dan Coldspotnya berdasarkan namadesanya

Dapat dilihat bahwa Secara Hot-spot lokal, ada beberapa daearah yang diindikasikan sebagai hot-spot. Hal ini kontradiktif dengan argumen sebelumnya di Gettis Ord Globalnya yang menandakan tidak adanya Indikasi hot-spot/cold-spot secara global. Bila diperhatikan pula, desa yang menjadi hot-spot ini salah dua nya adalah desa yang terindikasi secara lokal memiliki autokorelasi positif.

Kesimpulan

Pola penyebaran kasus Stunting di Sumba Tengah yang didapat dari perbandingan beberapa uji yang dipakai dapat dikatakan menyebar secara positif walaupun sangat lemah. Pengujian ini bisa saja menghasilkan dugaan korelasi yang kurang kuat karena jarak yang dipakai masih menggunakan jarak Euclidian dan belum mencoba jarak lainnya, selain itu juga Distirbusi Data yang tidak normal ( Kurtosis 40) juga bisa menjadi dasar dalam hasil autokorelasi yang tidak singinfikan ini walaupun sudah dilakukan randomized pada pengujian. Untuk itu Penelitian ini bisa menjadi acuan bagi pemerintah dalam melakukan penananganan Kasus Stunting utamanya di Sumba Tengah, dimana pemerintah bisa langsung mengutamakan titik-tiik kasus stunting yang bergerombol tersebut ( utamanya di desa dengan tingkat stunting paling tinggi tadi.

Authorized by Kelompok 7

  1. Adriano Excel Putra
  2. Sintong M. Purba
  3. Sherinda Engelina
  4. Thariq Hambali
  5. M. Abdan Rofi
  6. M. Tsaqif Nadjmuddin.