Take Home Exe01
MELANIE TAN
5/10/2020
Take Home Assignment 1 for IS415 - Geospatial Analytics and Applications
Overview
In view of this, we are going to conduct a use-case to demonstrate the potential contribution of geospatial analytics in R to integrate, analyse and communicate the analysis results by using open data provided by different government agencies. The specific objectives of the study are as follow:
Calibrating a simple linear regression to reveal the relation between public bus commuters’ flows (i.e. tap-in or tap-out) data and residential population at the planning sub-zone level.
Performing spatial autocorrelation analysis on the residual of the regression model to test if the model conforms to the randomization assumption.
Performing localized geospatial statistics analysis by using commuters’ tap-in and tap-out data to identify geographical clustering.
For the purpose of this study, the passenger volume by bus-stop data set of Land Transport Authority (LTA) has been provided. This data set is extracted using the dynamic API provided at LTA DataMall. The remaining data from the government open data portal.
Loading required package
packages = c('rgdal', 'sf', 'spdep', 'sp','tmap', 'tidyverse')
for (p in packages){
if(!require(p, character.only = T)){
install.packages(p)
}
library(p,character.only = T)
}## Loading required package: rgdal## Loading required package: sp## rgdal: version: 1.4-8, (SVN revision 845)
## Geospatial Data Abstraction Library extensions to R successfully loaded
## Loaded GDAL runtime: GDAL 2.4.2, released 2019/06/28
## Path to GDAL shared files: /Library/Frameworks/R.framework/Versions/3.6/Resources/library/rgdal/gdal
## GDAL binary built with GEOS: FALSE
## Loaded PROJ.4 runtime: Rel. 5.2.0, September 15th, 2018, [PJ_VERSION: 520]
## Path to PROJ.4 shared files: /Library/Frameworks/R.framework/Versions/3.6/Resources/library/rgdal/proj
## Linking to sp version: 1.3-2## Loading required package: sf## Linking to GEOS 3.7.2, GDAL 2.4.2, PROJ 5.2.0## Loading required package: spdep## Loading required package: spData## To access larger datasets in this package, install the spDataLarge
## package with: `install.packages('spDataLarge',
## repos='https://nowosad.github.io/drat/', type='source')`## Loading required package: tmap## Loading required package: tidyverse## ── Attaching packages ─────────────────────────────────────────────────────────── tidyverse 1.3.0 ──## ✓ ggplot2 3.3.0 ✓ purrr 0.3.3
## ✓ tibble 2.1.3 ✓ dplyr 0.8.4
## ✓ tidyr 1.0.2 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.5.0## ── Conflicts ────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()Question 1
Importing data population
data_pop <- read_csv("data/aspatial/respopagesextod2011to2019.csv")## Parsed with column specification:
## cols(
## PA = col_character(),
## SZ = col_character(),
## AG = col_character(),
## Sex = col_character(),
## TOD = col_character(),
## Pop = col_double(),
## Time = col_double()
## )Importing data volume
data_volume <- read_csv("data/aspatial/passenger volume by busstop.csv")## Parsed with column specification:
## cols(
## YEAR_MONTH = col_character(),
## DAY_TYPE = col_character(),
## TIME_PER_HOUR = col_double(),
## PT_TYPE = col_character(),
## PT_CODE = col_character(),
## TOTAL_TAP_IN_VOLUME = col_double(),
## TOTAL_TAP_OUT_VOLUME = col_double()
## )Importing data bustop
Since we are extracting the data from a Singapore database, there is no need to transform the data. We can just set the CRS to 3414.
data_busstop <- st_read(dsn = "data/geospatial", layer = "BusStop")## Reading layer `BusStop' from data source `/Users/mel/Desktop/Take_home_ex1/data/geospatial' using driver `ESRI Shapefile'
## Simple feature collection with 5040 features and 3 fields
## geometry type: POINT
## dimension: XY
## bbox: xmin: 4427.938 ymin: 26482.1 xmax: 48282.5 ymax: 52983.82
## epsg (SRID): NA
## proj4string: +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +datum=WGS84 +units=m +no_defsImporting Planning Area Subzone
st_transform does not need to change the polygon due to its nature of being set in the Singapore context.
data_mpsz <- st_read(dsn = "data/geospatial", layer = "MP14_SUBZONE_WEB_PL")## Reading layer `MP14_SUBZONE_WEB_PL' from data source `/Users/mel/Desktop/Take_home_ex1/data/geospatial' using driver `ESRI Shapefile'
## Simple feature collection with 323 features and 15 fields
## geometry type: MULTIPOLYGON
## dimension: XY
## bbox: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
## epsg (SRID): NA
## proj4string: +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +datum=WGS84 +units=m +no_defsFiltering and sum of population according to subzone category
data_pop2019 <- data_pop %>%
filter(Time == 2019) %>%
group_by (SZ) %>%
summarise(Pop = sum(Pop)) %>%
mutate_at(.vars = vars(SZ), .funs = funs(toupper))## Warning: funs() is soft deprecated as of dplyr 0.8.0
## Please use a list of either functions or lambdas:
##
## # Simple named list:
## list(mean = mean, median = median)
##
## # Auto named with `tibble::lst()`:
## tibble::lst(mean, median)
##
## # Using lambdas
## list(~ mean(., trim = .2), ~ median(., na.rm = TRUE))
## This warning is displayed once per session.Left join SG map with the subzone layer
data_mpsz_2019 <- left_join(data_mpsz,data_pop2019, c("SUBZONE_N" = "SZ"))## Warning: Column `SUBZONE_N`/`SZ` joining factor and character vector, coercing
## into character vectorSum of total volume of tap in and tap out
data_volumeC <- data_volume %>%
group_by(PT_CODE) %>%
summarise(TOTAL_TAP_OUT_VOLUME = sum(TOTAL_TAP_OUT_VOLUME),TOTAL_TAP_IN_VOLUME = sum(TOTAL_TAP_IN_VOLUME)) Left join bus stop layer and volumeC by common factor (bus code)
final_bus <- left_join(data_busstop,data_volumeC, c("BUS_STOP_N" = "PT_CODE"))## Warning: Column `BUS_STOP_N`/`PT_CODE` joining factor and character vector,
## coercing into character vectorRemove fields with “NA”
#final_bus <- final_bus %>%
#select(BUS_STOP_N,TOTAL_TAP_IN_VOLUME, TOTAL_TAP_OUT_VOLUME) %>%
final_bus = subset(final_bus, select = -c(LOC_DESC, BUS_ROOF_N))
final_bus <- na.omit(final_bus)Join Sg map layer with bus information
final_q1 <- st_join(data_mpsz_2019,final_bus)Summation of tapin and tapout according to subzone area
final_q1 <- final_q1 %>%
group_by(SUBZONE_N, Pop)%>%
summarise(TOTAL_TAP_IN_VOLUME = sum(TOTAL_TAP_IN_VOLUME), TOTAL_TAP_OUT_VOLUME = sum(TOTAL_TAP_OUT_VOLUME))Before removing unnecessary datas
qtm(final_q1)## Warning: The shape final_q1 is invalid. See sf::st_is_valid
Omit rows with missing values
final_q1 <- na.omit(final_q1)Consolidated Data with no missing values
qtm(final_q1)## Warning: The shape final_q1 is invalid. See sf::st_is_valid
Question 2
Hypothesis test Null hypothesis : Tapin and Tapout volume is randomly distributed Alternative hypothesis : Tapin and Tapout volume is not randomly distributed Confidence Interval : 95%
Calculating predicted value and residual value for total_tap_in_volume
final_q1 <- final_q1
fit1 <- lm(final_q1$TOTAL_TAP_IN_VOLUME ~ final_q1$Pop)
final_q1$predicted_in <- predict(fit1)
final_q1$residuals_in <- residuals(fit1)Performing Linear Regression for Tapin values
ggplot(final_q1, aes(x = Pop, y = TOTAL_TAP_IN_VOLUME)) +
geom_point(color = 'red') +
geom_smooth(method = "lm", se = TRUE)## `geom_smooth()` using formula 'y ~ x'
Predicted_in against residual_in
plot(final_q1$predicted_in,final_q1$residuals_in, xlab = "predicted_In", ylab = "residuals_In")
Residual Map
tm_shape(final_q1) +
tm_fill(col = "residuals_in",
style = "pretty")+
tm_borders(alpha = 0.5)## Warning: The shape final_q1 is invalid. See sf::st_is_valid## Variable "residuals_in" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
Summary
summary(final_q1)## SUBZONE_N Pop TOTAL_TAP_IN_VOLUME TOTAL_TAP_OUT_VOLUME
## Length:305 Min. : 0 Min. : 70 Min. : 154
## Class :character 1st Qu.: 70 1st Qu.: 91448 1st Qu.: 92241
## Mode :character Median : 6510 Median : 227690 Median : 224722
## Mean : 13207 Mean : 378572 Mean : 377915
## 3rd Qu.: 19460 3rd Qu.: 485104 3rd Qu.: 468349
## Max. :132900 Max. :3754337 Max. :3660297
## geometry predicted_in residuals_in
## MULTIPOLYGON :305 Min. : 124455 Min. :-863762
## epsg:NA : 0 1st Qu.: 125802 1st Qu.:-123199
## +proj=tmer...: 0 Median : 249717 Median : -63290
## Mean : 378572 Mean : 0
## 3rd Qu.: 498894 3rd Qu.: 34580
## Max. :2681643 Max. :1950650Information on tapin
summary(fit1)##
## Call:
## lm(formula = final_q1$TOTAL_TAP_IN_VOLUME ~ final_q1$Pop)
##
## Residuals:
## Min 1Q Median 3Q Max
## -863762 -123199 -63290 34580 1950650
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.245e+05 2.107e+04 5.907 9.34e-09 ***
## final_q1$Pop 1.924e+01 9.370e-01 20.535 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 297800 on 303 degrees of freedom
## Multiple R-squared: 0.5819, Adjusted R-squared: 0.5805
## F-statistic: 421.7 on 1 and 303 DF, p-value: < 2.2e-16Calculating predicted value and residual value for total_tap_out_volume
final_q1 <- final_q1
fit2 <- lm(final_q1$TOTAL_TAP_OUT_VOLUME ~ final_q1$Pop)
final_q1$predicted_out <- predict(fit2)
final_q1$residuals_out <- residuals(fit2)Performing Linear Regression for Tapout values
ggplot(final_q1, aes(x = Pop, y = TOTAL_TAP_OUT_VOLUME)) +
geom_point(color = 'red') +
geom_smooth(method = "lm", se = TRUE)## `geom_smooth()` using formula 'y ~ x'
Predicted_out against residual_out
plot(final_q1$predicted_out,final_q1$residuals_out, xlab = "predicted_out", ylab = "residuals_Out")
Residual Map
tm_shape(final_q1) +
tm_fill(col = "residuals_in",
style = "pretty")+
tm_borders(alpha = 0.5)## Warning: The shape final_q1 is invalid. See sf::st_is_valid## Variable "residuals_in" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
Summary
summary(final_q1)## SUBZONE_N Pop TOTAL_TAP_IN_VOLUME TOTAL_TAP_OUT_VOLUME
## Length:305 Min. : 0 Min. : 70 Min. : 154
## Class :character 1st Qu.: 70 1st Qu.: 91448 1st Qu.: 92241
## Mode :character Median : 6510 Median : 227690 Median : 224722
## Mean : 13207 Mean : 378572 Mean : 377915
## 3rd Qu.: 19460 3rd Qu.: 485104 3rd Qu.: 468349
## Max. :132900 Max. :3754337 Max. :3660297
## geometry predicted_in residuals_in predicted_out
## MULTIPOLYGON :305 Min. : 124455 Min. :-863762 Min. : 124937
## epsg:NA : 0 1st Qu.: 125802 1st Qu.:-123199 1st Qu.: 126278
## +proj=tmer...: 0 Median : 249717 Median : -63290 Median : 249637
## Mean : 378572 Mean : 0 Mean : 377915
## 3rd Qu.: 498894 3rd Qu.: 34580 3rd Qu.: 497697
## Max. :2681643 Max. :1950650 Max. :2670666
## residuals_out
## Min. :-823156
## 1st Qu.:-122534
## Median : -58009
## Mean : 0
## 3rd Qu.: 31081
## Max. :1644315Information on tapout
summary(fit2)##
## Call:
## lm(formula = final_q1$TOTAL_TAP_OUT_VOLUME ~ final_q1$Pop)
##
## Residuals:
## Min 1Q Median 3Q Max
## -823156 -122534 -58009 31081 1644315
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.249e+05 2.040e+04 6.125 2.81e-09 ***
## final_q1$Pop 1.916e+01 9.072e-01 21.114 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 288300 on 303 degrees of freedom
## Multiple R-squared: 0.5954, Adjusted R-squared: 0.594
## F-statistic: 445.8 on 1 and 303 DF, p-value: < 2.2e-16Question 2
Modelling Spatial Neighbours
In this section, we will use “spdep” package to compute contiguity weight matrix for the study area. This helps to build a neighbours list based on regions with contiguous boundaires.
Note: If we do not specify the arguement (True/False) when passing a “queen” argument, the default is set to “True”. If we set the argument to queen = FALSE, this function will return us a list of first order neighbours using the Queen criteria.
Creating (QUEEN) conriguirt based neighbours
The summary report shows that there are 305 area units. The most connected area unit has 17 neighbours. There are 6 area units with only 2 neighbours.
final_q2 <- final_q1
wm_q <- poly2nb(final_q2, queen = TRUE)
summary(wm_q)## Neighbour list object:
## Number of regions: 305
## Number of nonzero links: 1844
## Percentage nonzero weights: 1.982263
## Average number of links: 6.045902
## Link number distribution:
##
## 2 3 4 5 6 7 8 9 10 11 12 14 17
## 6 11 27 79 76 50 36 13 2 2 1 1 1
## 6 least connected regions:
## 2 41 132 170 228 275 with 2 links
## 1 most connected region:
## 39 with 17 linksDisplaying weight matrix by using str()
For each polygon in our polygon object, wm_q lists all the neighbouring polygons.
str(wm_q)## List of 305
## $ : int [1:6] 215 216 218 219 220 262
## $ : int [1:2] 64 195
## $ : int [1:8] 4 36 65 122 148 157 200 202
## $ : int [1:6] 3 35 43 89 148 202
## $ : int [1:9] 23 80 81 111 112 116 143 162 254
## $ : int [1:6] 33 91 93 165 243 244
## $ : int [1:4] 60 75 155 221
## $ : int [1:8] 44 50 120 233 269 295 296 298
## $ : int [1:5] 38 47 52 70 253
## $ : int [1:6] 18 114 125 144 160 265
## $ : int [1:4] 39 63 72 102
## $ : int [1:5] 38 58 149 151 241
## $ : int [1:4] 16 78 235 293
## $ : int [1:8] 15 16 78 109 121 236 250 293
## $ : int [1:6] 14 109 121 185 236 250
## $ : int [1:5] 13 14 78 236 293
## $ : int [1:7] 28 66 74 133 211 242 282
## $ : int [1:8] 10 80 110 114 125 129 197 224
## $ : int [1:7] 87 88 103 134 209 234 276
## $ : int [1:5] 104 137 224 280 292
## $ : int [1:9] 27 50 135 137 154 230 266 269 292
## $ : int [1:6] 46 51 53 188 193 201
## $ : int [1:5] 5 80 110 111 112
## $ : int [1:7] 45 94 108 124 247 284 305
## $ : int [1:5] 27 125 135 189 265
## $ : int [1:8] 84 131 163 172 173 184 239 251
## $ : int [1:5] 21 25 135 265 266
## $ : int [1:5] 17 51 66 77 282
## $ : int [1:5] 31 34 86 95 260
## $ : int [1:5] 51 62 113 207 282
## $ : int [1:5] 29 32 33 34 86
## $ : int [1:4] 31 33 86 91
## $ : int [1:8] 6 31 32 34 91 243 267 268
## $ : int [1:7] 29 31 33 260 267 303 304
## $ : int [1:7] 4 43 89 188 206 263 264
## $ : int [1:7] 3 65 89 115 202 259 264
## $ : int [1:5] 38 47 156 201 253
## $ : int [1:9] 9 12 37 52 58 151 201 241 253
## $ : int [1:17] 11 63 72 79 90 145 147 161 165 166 ...
## $ : int [1:3] 41 42 293
## $ : int [1:2] 40 42
## $ : int [1:7] 40 41 76 140 141 248 293
## $ : int [1:9] 4 35 131 148 172 184 204 206 251
## $ : int [1:7] 8 50 214 230 232 269 296
## $ : int [1:6] 24 94 108 124 247 276
## $ : int [1:6] 22 47 53 188 193 201
## $ : int [1:10] 9 37 46 70 156 188 192 201 237 253
## $ : int [1:5] 49 119 190 256 286
## $ : int [1:6] 48 79 190 256 286 294
## $ : int [1:8] 8 21 44 137 154 230 232 269
## $ : int [1:11] 22 28 30 53 58 62 77 113 149 201 ...
## $ : int [1:8] 9 38 70 115 153 228 241 258
## $ : int [1:6] 22 46 51 77 188 206
## $ : int [1:5] 55 56 57 71 285
## $ : int [1:6] 54 57 71 238 243 268
## $ : int [1:6] 54 57 175 177 196 285
## $ : int [1:7] 54 55 56 67 164 177 238
## $ : int [1:5] 12 38 51 149 201
## $ : int [1:5] 92 130 148 157 252
## $ : int [1:7] 7 75 97 98 205 221 270
## $ : int [1:6] 73 90 93 130 244 278
## $ : int [1:8] 30 51 112 113 129 149 207 254
## $ : int [1:6] 11 39 83 91 102 165
## $ : int [1:9] 2 109 116 117 136 138 187 195 246
## $ : int [1:6] 3 36 122 200 257 259
## $ : int [1:7] 17 28 77 101 174 211 239
## $ : int [1:5] 57 82 164 171 238
## $ : int [1:5] 90 144 161 163 278
## $ : int [1:4] 150 152 162 235
## $ : int [1:6] 9 47 52 115 237 258
## $ : int [1:5] 54 55 100 268 285
## $ : int [1:5] 11 39 79 102 210
## $ : int [1:4] 61 130 204 278
## $ : int [1:6] 17 114 129 133 142 211
## $ : int [1:8] 7 60 155 212 213 214 222 270
## $ : int [1:5] 42 140 141 180 248
## $ : int [1:7] 28 51 53 66 99 174 206
## $ : int [1:8] 13 14 16 81 118 121 152 235
## $ : int [1:10] 39 49 72 147 176 210 223 256 277 294
## $ : int [1:7] 5 18 23 110 111 197 224
## $ : int [1:8] 5 78 109 116 118 121 143 162
## $ : int [1:5] 67 92 171 238 279
## $ : int [1:9] 63 86 91 95 102 119 223 256 260
## $ : int [1:6] 26 144 160 163 167 173
## $ : int [1:6] 158 168 227 288 289 291
## $ : int [1:6] 29 31 32 83 91 95
## $ : int [1:4] 19 88 194 234
## $ : int [1:7] 19 87 103 194 261 271 272
## $ : int [1:6] 4 35 36 115 202 264
## $ : int [1:6] 39 61 68 161 244 278
## $ : int [1:7] 6 32 33 63 83 86 165
## $ : int [1:6] 59 82 130 171 252 279
## $ : int [1:6] 6 61 130 243 244 279
## $ : int [1:7] 24 45 128 247 260 284 304
## $ : int [1:5] 29 83 86 119 260
## $ : int [1:5] 97 98 117 126 136
## $ : int [1:5] 60 96 98 117 205
## $ : int [1:7] 60 96 97 126 230 231 270
## $ : int [1:4] 77 131 174 206
## [list output truncated]
## - attr(*, "class")= chr "nb"
## - attr(*, "region.id")= chr [1:305] "1" "2" "3" "4" ...
## - attr(*, "call")= language poly2nb(pl = final_q2, queen = TRUE)
## - attr(*, "type")= chr "queen"
## - attr(*, "sym")= logi TRUEConverting sf to sp format
final_q2 <- as(final_q2, "Spatial")Plotting Queen contiguity based neighhbours maps
plot(final_q2, border = "lightgrey")
plot(wm_q, coordinates(final_q2), pch = 19, cex = 0.6, add = TRUE, col = "red")
Creating (ROOK) contiguity based neighbours
wm_r <- poly2nb(final_q2, queen = FALSE)
summary(wm_r)## Neighbour list object:
## Number of regions: 305
## Number of nonzero links: 1586
## Percentage nonzero weights: 1.704918
## Average number of links: 5.2
## Link number distribution:
##
## 1 2 3 4 5 6 7 8 9 10 13 14
## 1 5 25 70 94 59 31 12 4 2 1 1
## 1 least connected region:
## 170 with 1 link
## 1 most connected region:
## 39 with 14 linksPlotting Rook contiguity based neighbours maps
plot(final_q2, border = "lightgrey")
plot(wm_r, coordinates(final_q2), pch =19, cex = 0.6 , add =TRUE, col = "red")
Computing distance based neighbours
Using the “spdep” package, this function identifies neighbours of region points by its Euclidean distance with a distance band with lower d1= and upper d2= bounds controlled by the bounds= argument. If unprojected coordinates are used and either specified in the coordinates object x or with x as a two column matrix and longlat=TRUE, great circle distances in km will be calculated assuming the WGS84 reference ellipsoid. # 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().
coords1 <- coordinates(final_q2)
k1 <- knn2nb(knearneigh(coords1))
k1dists <- unlist(nbdists(k1, coords1, longlat = FALSE))
summary(k1dists)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 182.5 616.7 891.7 941.4 1169.9 5403.9Computing fixed distance weight matrix using 4505 metres
now we will compute the distance weight matrix by using the function dnearneigh()
wm_d5405 <- dnearneigh(coords1, 0, 5405, longlat = FALSE)
wm_d5405## Neighbour list object:
## Number of regions: 305
## Number of nonzero links: 16620
## Percentage nonzero weights: 17.86617
## Average number of links: 54.4918Plotting fixed distance weight matrix
As shown in the diagram below, the red lines show the links of 1st nearest neighbours and the black lines show the links of neighbours within the cut-off distance of 62km.
plot(final_q2, border = "lightgrey")
plot(wm_d5405,coords1, add = TRUE)
plot(k1, coords1, add =TRUE, col = "red", length = 0.08)
Plotting based on the nearest neighbour
plot(final_q2, border = "lightgrey")
plot(k1, coordinates(final_q2), add = TRUE, col = "red", length= 0.08, main = "1st nearest neighbours")
Computing adaptive distance weight matrix when k = 25
When choosing to use adaptive distance weight matrix over fixed distance weight matrix, we are ideally controlling the maximum number of neighbours which we want to have
wm_knn25 <- knn2nb(knearneigh(coords1, k = 25))
wm_knn25## Neighbour list object:
## Number of regions: 305
## Number of nonzero links: 7625
## Percentage nonzero weights: 8.196721
## Average number of links: 25
## Non-symmetric neighbours listPlotting distance based neighbours
plot(final_q2, border = "lightgrey")
plot(wm_knn25, coords1, pch =19, cex = 0.6, add =TRUE, col = "red")
Weights based on IDW
This step shows how to compute the distance between areas by using nbdists() of spdep
dis <- nbdists(wm_q, coordinates(coords1),longlat = FALSE)
ids <- lapply(dis, function(x) 1/(x))
ids## [[1]]
## [1] 0.0008844646 0.0010479991 0.0008884163 0.0007273849 0.0007193983
## [6] 0.0008145135
##
## [[2]]
## [1] 0.0054804712 0.0005914389
##
## [[3]]
## [1] 0.0007684273 0.0008535163 0.0016794719 0.0005228567 0.0009209275
## [6] 0.0010335223 0.0008362313 0.0011858756
##
## [[4]]
## [1] 0.0007684273 0.0008561566 0.0015861182 0.0015851372 0.0006885765
## [6] 0.0016141745
##
## [[5]]
## [1] 0.0007967047 0.0005944779 0.0005997133 0.0006629205 0.0006203687
## [6] 0.0004515623 0.0006945162 0.0006050635 0.0005702379
##
## [[6]]
## [1] 0.0006512433 0.0004671180 0.0005523321 0.0005380965 0.0007563099
## [6] 0.0004293567
##
## [[7]]
## [1] 0.0009454441 0.0007069296 0.0007923248 0.0010038960
##
## [[8]]
## [1] 0.0012338838 0.0007347920 0.0012417764 0.0009286863 0.0011898358
## [6] 0.0007053164 0.0007185553 0.0008303685
##
## [[9]]
## [1] 0.0009959629 0.0014465086 0.0008333699 0.0012148870 0.0028731128
##
## [[10]]
## [1] 0.0007966394 0.0007643972 0.0009104748 0.0005199707 0.0007906804
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## [[11]]
## [1] 0.0003340443 0.0010083234 0.0010893058 0.0011046871
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## [[12]]
## [1] 0.0009203502 0.0020296371 0.0010516944 0.0011788831 0.0007483077
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## [[13]]
## [1] 0.0010456738 0.0003182144 0.0003952133 0.0003518128
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## [[14]]
## [1] 0.0006604971 0.0007274440 0.0004081409 0.0003335133 0.0004247956
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## [[15]]
## [1] 0.0006604971 0.0005181608 0.0004845093 0.0005729590 0.0003245967
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## [[16]]
## [1] 0.0010456738 0.0007274440 0.0003591730 0.0004215166 0.0003491228
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## [[17]]
## [1] 0.001494780 0.001309997 0.001254359 0.001634425 0.005480303 0.001374095
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##
## [[18]]
## [1] 0.0007966394 0.0010681721 0.0010154354 0.0006284152 0.0008854919
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## [[19]]
## [1] 0.0004808385 0.0005021102 0.0008552618 0.0004146824 0.0004872308
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## [[20]]
## [1] 0.0010407629 0.0006501128 0.0011361197 0.0015437033 0.0010316891
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## [[21]]
## [1] 0.0009133602 0.0006159278 0.0009185349 0.0008728608 0.0009670193
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## [[22]]
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## [[23]]
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## [[24]]
## [1] 0.0008162825 0.0008398420 0.0008406863 0.0004617106 0.0005947800
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## [[25]]
## [1] 0.001435649 0.001373958 0.001301113 0.001553837 0.001196836
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## [[26]]
## [1] 0.0010772114 0.0011926100 0.0007632171 0.0013811557 0.0017409189
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## [[27]]
## [1] 0.0009133602 0.0014356489 0.0011960458 0.0010402196 0.0011480012
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## [[28]]
## [1] 0.001494780 0.001688439 0.001806303 0.002215290 0.001827225
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## [[29]]
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## [[30]]
## [1] 0.001238038 0.001127684 0.001875890 0.001768612 0.002907612
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## [[31]]
## [1] 0.0008033522 0.0012456515 0.0008676965 0.0010995633 0.0011008015
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## [[32]]
## [1] 0.0012456515 0.0011139187 0.0012296235 0.0009886271
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## [[33]]
## [1] 0.0006512433 0.0008676965 0.0011139187 0.0005251520 0.0005749060
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## [[34]]
## [1] 0.0011060344 0.0010995633 0.0005251520 0.0004251748 0.0008437823
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## [[35]]
## [1] 0.0008561566 0.0008849290 0.0010580384 0.0009130871 0.0013190889
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## [[36]]
## [1] 0.0008535163 0.0008953932 0.0014430880 0.0009473669 0.0015587598
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## [[37]]
## [1] 0.001945131 0.001681760 0.002867186 0.001639452 0.002216870
##
## [[38]]
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##
## [[39]]
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##
## [[40]]
## [1] 0.0001928089 0.0002883642 0.0002455784
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## [[41]]
## [1] 0.0001928089 0.0004024258
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## [[42]]
## [1] 0.0002883642 0.0004024258 0.0006129229 0.0019940506 0.0008011982
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##
## [[43]]
## [1] 0.0015861182 0.0008849290 0.0008398056 0.0005903989 0.0014993606
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##
## [[44]]
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##
## [[45]]
## [1] 0.0008162825 0.0005354544 0.0007349304 0.0005731750 0.0011214057
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##
## [[46]]
## [1] 0.002786005 0.001655110 0.001585079 0.001188246 0.004539138 0.002151225
##
## [[47]]
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## [[48]]
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## [[49]]
## [1] 0.0012058406 0.0004999170 0.0005894044 0.0006608109 0.0001555721
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##
## [[50]]
## [1] 0.0007347920 0.0006159278 0.0010523062 0.0005157678 0.0006160934
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## [[51]]
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## [[52]]
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## [[53]]
## [1] 0.0021175583 0.0015850790 0.0009940277 0.0019383743 0.0013815042
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##
## [[54]]
## [1] 0.0012679380 0.0009472779 0.0009463488 0.0007722726 0.0009961000
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## [[55]]
## [1] 0.0012679380 0.0006445618 0.0008307086 0.0007361763 0.0010745010
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##
## [[56]]
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##
## [[57]]
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## [[58]]
## [1] 0.0020296371 0.0008909215 0.0012837830 0.0011211216 0.0021805706
##
## [[59]]
## [1] 0.0014706766 0.0007308071 0.0007947858 0.0007562421 0.0018549035
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## [[60]]
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## [[61]]
## [1] 0.0009569472 0.0008914289 0.0005038005 0.0009232508 0.0005109660
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## [[62]]
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## [[63]]
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## [[64]]
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##
## [[65]]
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##
## [[66]]
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## [[67]]
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## [[68]]
## [1] 0.0006551399 0.0006323491 0.0007688645 0.0006923416 0.0006630296
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## [[69]]
## [1] 0.0003576751 0.0027288080 0.0005130452 0.0004573750
##
## [[70]]
## [1] 0.0012148870 0.0010095743 0.0009365227 0.0009376301 0.0017858303
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##
## [[71]]
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## [[72]]
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## [[73]]
## [1] 0.0009569472 0.0010927189 0.0006092117 0.0011052717
##
## [[74]]
## [1] 0.001254359 0.001847165 0.001246546 0.002947284 0.001905506 0.001215211
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## [[75]]
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## [[76]]
## [1] 0.0006129229 0.0008043174 0.0004952084 0.0007646180 0.0005671129
##
## [[77]]
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##
## [[78]]
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##
## [[79]]
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## [[80]]
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##
## [[81]]
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## [[82]]
## [1] 0.0008486986 0.0011616417 0.0006850879 0.0008707460 0.0010969618
##
## [[83]]
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## [[84]]
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##
## [[85]]
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##
## [[86]]
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##
## [[87]]
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## [[88]]
## [1] 0.0005021102 0.0006797906 0.0006095651 0.0005423136 0.0003218864
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## [[89]]
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## [[90]]
## [1] 0.0002052066 0.0008914289 0.0006551399 0.0004331565 0.0005114755
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##
## [[91]]
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## [[92]]
## [1] 0.0014706766 0.0011616417 0.0010185613 0.0008388284 0.0012334400
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##
## [[93]]
## [1] 0.0005523321 0.0005038005 0.0005434111 0.0005945843 0.0005624447
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##
## [[94]]
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##
## [[95]]
## [1] 0.0009886344 0.0007803539 0.0009712084 0.0007024667 0.0004659997
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## [[96]]
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##
## [[97]]
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## [[98]]
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## [[99]]
## [1] 0.001054214 0.001728934 0.002081466 0.003270785
##
## [[100]]
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## [[101]]
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## [[102]]
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##
## [[103]]
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##
## [[104]]
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##
## [[105]]
## [1] 0.0010416579 0.0008205729 0.0016225886 0.0010939092
##
## [[106]]
## [1] 0.0005738362 0.0005950200 0.0004109096 0.0005459857
##
## [[107]]
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##
## [[108]]
## [1] 0.0008406863 0.0007349304 0.0009415369 0.0005528355 0.0010636285
##
## [[109]]
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## [[110]]
## [1] 0.001015435 0.001308456 0.001009708 0.001162548 0.001263436
##
## [[111]]
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##
## [[112]]
## [1] 0.0006203687 0.0012994766 0.0009055964 0.0011625483 0.0007706987
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##
## [[113]]
## [1] 0.0018758898 0.0007652248 0.0020375810 0.0032176173
##
## [[114]]
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##
## [[115]]
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##
## [[116]]
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##
## [[117]]
## [1] 0.0004999113 0.0013302139 0.0013386176 0.0004791146 0.0005220051
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##
## [[118]]
## [1] 0.0004590628 0.0008634903 0.0013106572 0.0007257594
##
## [[119]]
## [1] 0.0009429093 0.0007113341 0.0007024667 0.0010310895 0.0008670194
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##
## [[120]]
## [1] 0.0012417764 0.0010061634 0.0016064245 0.0007500777 0.0006527161
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##
## [[121]]
## [1] 0.0004247956 0.0004845093 0.0008120822 0.0004740970 0.0007308826
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##
## [[122]]
## [1] 0.0005228567 0.0005532175 0.0004659838 0.0006848329 0.0007154684
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##
## [[123]]
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## [[124]]
## [1] 0.0004617106 0.0005731750 0.0004655908 0.0009415369 0.0005971033
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##
## [[125]]
## [1] 0.0009104748 0.0008854919 0.0013739575 0.0018447344 0.0012660904
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##
## [[126]]
## [1] 0.0007079950 0.0007633509 0.0004791146 0.0010600826 0.0006155883
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##
## [[127]]
## [1] 0.0003347486 0.0003706924 0.0007000023 0.0005612734 0.0004524634
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##
## [[128]]
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##
## [[129]]
## [1] 0.0007727715 0.0008137706 0.0012465457 0.0012634360 0.0007706987
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##
## [[130]]
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##
## [[131]]
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##
## [[132]]
## [1] 0.0003268225 0.0001588970
##
## [[133]]
## [1] 0.001634425 0.002947284 0.001385731 0.001410822 0.003151084 0.001256117
##
## [[134]]
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##
## [[135]]
## [1] 0.0009185349 0.0013011130 0.0011960458 0.0009251157 0.0020739748
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##
## [[136]]
## [1] 0.0008559948 0.0006583517 0.0005220051 0.0010600826 0.0005421815
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##
## [[137]]
## [1] 0.0006501128 0.0008728608 0.0005157678 0.0009251157 0.0010775191
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##
## [[138]]
## [1] 0.0004577414 0.0015436485 0.0011808249 0.0006359459 0.0005019429
##
## [[139]]
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##
## [[140]]
## [1] 0.0019940506 0.0008043174 0.0009596504
##
## [[141]]
## [1] 0.0008011982 0.0004952084 0.0009596504 0.0006448811 0.0005569009
##
## [[142]]
## [1] 0.001905506 0.002155110 0.001173341 0.002117198
##
## [[143]]
## [1] 0.0006945162 0.0005368678 0.0009348921 0.0009737749 0.0007756161
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##
## [[144]]
## [1] 0.0005199707 0.0006323491 0.0009472419 0.0008631691 0.0007656277
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##
## [[145]]
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##
## [[146]]
## [1] 0.0009737087 0.0007442446 0.0012016582
##
## [[147]]
## [1] 0.0002010500 0.0003195914 0.0003007833 0.0002794956 0.0004319575
## [6] 0.0007285740 0.0006137274
##
## [[148]]
## [1] 0.0009209275 0.0006885765 0.0005903989 0.0007947858 0.0003973116
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##
## [[149]]
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##
## [[150]]
## [1] 0.0003576751 0.0003565208 0.0007828211 0.0007434300
##
## [[151]]
## [1] 0.0011788831 0.0006389516 0.0007072448 0.0007820725
##
## [[152]]
## [1] 0.0027288080 0.0005132010 0.0013106572 0.0003565208 0.0005498480
## [6] 0.0004522272
##
## [[153]]
## [1] 0.0003834344 0.0004289498 0.0002314672 0.0003612755 0.0009749956
## [6] 0.0007359933 0.0008145372
##
## [[154]]
## [1] 0.0009670193 0.0006160934 0.0005988950 0.0006123168 0.0007815553
## [6] 0.0006897687
##
## [[155]]
## [1] 0.0007923248 0.0004114382 0.0005517146 0.0011535647 0.0005293790
## [6] 0.0005392759 0.0008134370 0.0005051222
##
## [[156]]
## [1] 0.002867186 0.004067640 0.002561179
##
## [[157]]
## [1] 0.0010335223 0.0007562421 0.0014487345 0.0006895592 0.0013707402
## [6] 0.0008877129
##
## [[158]]
## [1] 0.0009052426 0.0007286437 0.0005374007 0.0008571714 0.0012635235
## [6] 0.0008494279
##
## [[159]]
## [1] 0.0023549597 0.0008659158 0.0009323011 0.0019315136 0.0012191250
##
## [[160]]
## [1] 0.0007906804 0.0009530039 0.0010628247 0.0008631691 0.0009323011
## [6] 0.0012216629
##
## [[161]]
## [1] 0.0001768116 0.0007688645 0.0004331565 0.0007656277 0.0005266164
## [6] 0.0006332031
##
## [[162]]
## [1] 0.0006050635 0.0005130452 0.0005367892 0.0007257594 0.0007828211
## [6] 0.0005498480 0.0005835155
##
## [[163]]
## [1] 0.0007632171 0.0006923416 0.0009036664 0.0006757887 0.0012700407
## [6] 0.0005433935 0.0009875630 0.0007858092
##
## [[164]]
## [1] 0.0007772129 0.0010756576 0.0004659838 0.0006138709 0.0009035572
##
## [[165]]
## [1] 0.0005380965 0.0002737692 0.0005635119 0.0006391097 0.0004653883
##
## [[166]]
## [1] 0.0002683471 0.0005147621 0.0004677178 0.0002794956 0.0008020971
## [6] 0.0003635218
##
## [[167]]
## [1] 0.001897502 0.001931514 0.001221663
##
## [[168]]
## [1] 0.0016882588 0.0003347486 0.0003440179 0.0005632418 0.0006394116
##
## [[169]]
## [1] 0.0007863728 0.0006765787 0.0007936833 0.0006766479 0.0009144844
##
## [[170]]
## [1] 0.0010237594 0.0005317834
##
## [[171]]
## [1] 0.0007005273 0.0006850879 0.0008388284 0.0006848329 0.0006895592
## [6] 0.0006138709 0.0007246327 0.0014065835
##
## [[172]]
## [1] 0.001381156 0.001499361 0.001143942 0.002013965 0.002670398
##
## [[173]]
## [1] 0.001740919 0.001698319 0.001270041
##
## [[174]]
## [1] 0.001810937 0.001428451 0.002081466 0.001378924 0.002105425
##
## [[175]]
## [1] 0.0008804997 0.0006080385 0.0002383559 0.0006806064 0.0010994341
##
## [[176]]
## [1] 0.0004659262 0.0003706924 0.0004714539 0.0005463079 0.0001363250
## [6] 0.0007572657
##
## [[177]]
## [1] 0.0003870761 0.0004282372 0.0007154684 0.0009035572 0.0005264662
## [6] 0.0008237961
##
## [[178]]
## [1] 0.0011606057 0.0004289498 0.0005264662 0.0004718708 0.0006285525
##
## [[179]]
## [1] 0.0007549420 0.0008548606 0.0008288357 0.0005041493 0.0008457051
##
## [[180]]
## [1] 0.0007646180 0.0006448811 0.0007549420 0.0007522091 0.0005443625
## [6] 0.0004372572
##
## [[181]]
## [1] 0.0005569009 0.0008548606 0.0007522091 0.0003250143 0.0005951552
##
## [[182]]
## [1] 0.0003250143 0.0006141783 0.0005673003 0.0003760981 0.0004890464
## [6] 0.0003790195 0.0003634948 0.0004832907
##
## [[183]]
## [1] 0.0008288357 0.0005951552 0.0006141783 0.0006921830
##
## [[184]]
## [1] 0.0021359847 0.0009754817 0.0021872901 0.0020139648 0.0012233764
##
## [[185]]
## [1] 0.0005729590 0.0003674989 0.0005117418 0.0007198150 0.0004840856
## [6] 0.0006385265
##
## [[186]]
## [1] 0.0005673003 0.0005117418 0.0006083621 0.0004240125 0.0006027871
##
## [[187]]
## [1] 0.0003484138 0.0011808249 0.0003760981 0.0006083621 0.0005976192
##
## [[188]]
## [1] 0.0010053075 0.0009130871 0.0011882456 0.0012752370 0.0013815042
## [6] 0.0025427862 0.0014707896 0.0011895686 0.0010944296
##
## [[189]]
## [1] 0.001553837 0.001844734 0.002073975 0.001130309 0.001077185
##
## [[190]]
## [1] 0.0008453700 0.0005894044 0.0010310895 0.0004911556 0.0001835135
##
## [[191]]
## [1] 0.0004109096 0.0004658607 0.0006080385 0.0007957366
##
## [[192]]
## [1] 0.002409536 0.002542786 0.001346056
##
## [[193]]
## [1] 0.004246161 0.004539138 0.003190765
##
## [[194]]
## [1] 0.0006710641 0.0005423136 0.0003598823
##
## [[195]]
## [1] 0.0005914389 0.0005391132 0.0004111056 0.0006359459 0.0007198150
## [6] 0.0004240125 0.0005976192
##
## [[196]]
## [1] 0.0003140761 0.0002314672 0.0002383559 0.0008237961 0.0004718708
##
## [[197]]
## [1] 0.0007862832 0.0007337944 0.0012660904 0.0007783442 0.0011303087
## [6] 0.0011249032 0.0012898124
##
## [[198]]
## [1] 0.0005517146 0.0004890464 0.0005237190 0.0009521368 0.0006454913
## [6] 0.0012202319
##
## [[199]]
## [1] 0.0011535647 0.0010237594 0.0005237190 0.0004482638 0.0005900300
##
## [[200]]
## [1] 0.0008362313 0.0007800422 0.0012516009 0.0013707402 0.0007246327
##
## [[201]]
## [1] 0.001961539 0.001639452 0.001106800 0.002151225 0.001093929 0.001006755
## [7] 0.002180571 0.003190765
##
## [[202]]
## [1] 0.0011858756 0.0016141745 0.0015587598 0.0017085086 0.0006863876
##
## [[203]]
## [1] 0.0007000023 0.0003268225 0.0004714539 0.0004247967 0.0001192015
##
## [[204]]
## [1] 0.0006645138 0.0006092117 0.0004535521 0.0012854630 0.0005433935
## [6] 0.0006242597 0.0008038044
##
## [[205]]
## [1] 0.0005882390 0.0006622107 0.0004699321 0.0005019429 0.0005293790
## [6] 0.0003790195 0.0009521368 0.0010807381
##
## [[206]]
## [1] 0.0013190889 0.0006068059 0.0011669967 0.0009593690 0.0032707849
## [6] 0.0012376668 0.0014707896
##
## [[207]]
## [1] 0.001768612 0.001264616 0.003217617 0.001295627 0.004856986 0.001431092
##
## [[208]]
## [1] 0.0009296548 0.0005971033 0.0001885392 0.0005864060
##
## [[209]]
## [1] 0.0004872308 0.0005459857 0.0007655114 0.0006898052
##
## [[210]]
## [1] 0.0017640729 0.0006380445 0.0008793455 0.0015652694
##
## [[211]]
## [1] 0.005480303 0.001620773 0.001215211 0.001410822 0.002117198
##
## [[212]]
## [1] 0.0006135425 0.0005392759 0.0004482638 0.0005809040 0.0003945316
##
## [[213]]
## [1] 0.0004537707 0.0004402317 0.0005809040 0.0005271964
##
## [[214]]
## [1] 0.0005522971 0.0005824524 0.0007244036 0.0007850873 0.0010231873
## [6] 0.0005897557 0.0006931955 0.0004085692
##
## [[215]]
## [1] 0.0008844646 0.0004484147 0.0008353430 0.0009941599 0.0007224240
## [6] 0.0005402766
##
## [[216]]
## [1] 0.0010479991 0.0007863728 0.0009848841 0.0007364310 0.0005525449
##
## [[217]]
## [1] 0.0003031692 0.0010061634 0.0008851363 0.0007331820 0.0005283529
## [6] 0.0007911726
##
## [[218]]
## [1] 0.0008884163 0.0008353430 0.0006392394 0.0010130442 0.0008182666
##
## [[219]]
## [1] 0.0007273849 0.0004853275 0.0006765787 0.0009941599 0.0009848841
## [6] 0.0007850817
##
## [[220]]
## [1] 0.0007193983 0.0007364310 0.0006477397
##
## [[221]]
## [1] 0.0010038960 0.0008816404 0.0008134370 0.0006454913 0.0010807381
##
## [[222]]
## [1] 0.0006725425 0.0004161279 0.0003945316 0.0005271964 0.0007244036
## [6] 0.0005478535
##
## [[223]]
## [1] 0.0006422761 0.0005287836 0.0007728916 0.0015652694 0.0012445817
##
## [[224]]
## [1] 0.0005582520 0.0011361197 0.0007472384 0.0009646208 0.0011551931
## [6] 0.0006925429 0.0011249032 0.0009030283
##
## [[225]]
## [1] 0.0003440179 0.0006392394 0.0008143613 0.0006328711 0.0004385271
##
## [[226]]
## [1] 0.0003315311 0.0007224240 0.0010130442 0.0008143613 0.0008089463
## [6] 0.0006705818
##
## [[227]]
## [1] 0.0007239239 0.0007286437 0.0005632418 0.0006328711 0.0008089463
## [6] 0.0008042633
##
## [[228]]
## [1] 0.0005281460 0.0003612755
##
## [[229]]
## [1] 0.0006155883 0.0005421815 0.0010775191 0.0008035399 0.0010567762
##
## [[230]]
## [1] 0.0004796635 0.0005613861 0.0008084859 0.0004080881 0.0006409791
## [6] 0.0006159787 0.0008035399 0.0006716230 0.0007414247
##
## [[231]]
## [1] 0.0007176809 0.0006648233 0.0007850873 0.0006716230 0.0010406266
## [6] 0.0008628066
##
## [[232]]
## [1] 0.0008274338 0.0006482015 0.0010231873 0.0007414247 0.0010406266
## [6] 0.0006297648
##
## [[233]]
## [1] 0.0009286863 0.0016064245 0.0005988950 0.0008851363 0.0008631945
## [6] 0.0007535726
##
## [[234]]
## [1] 0.0008520536 0.0005866016 0.0004130312 0.0006898052
##
## [[235]]
## [1] 0.0003952133 0.0004573750 0.0008547691 0.0004522272
##
## [[236]]
## [1] 0.0004347218 0.0003245967 0.0004215166 0.0006440951 0.0004568226
## [6] 0.0004757994
##
## [[237]]
## [1] 0.0009929414 0.0017858303 0.0012115781 0.0011895686 0.0013460559
## [6] 0.0017106449
##
## [[238]]
## [1] 0.0007361763 0.0007855978 0.0011515406 0.0008707460 0.0005253427
## [6] 0.0013972447
##
## [[239]]
## [1] 0.001173259 0.001357015 0.001313398 0.001546939 0.001219125 0.002105425
## [7] 0.001223376
##
## [[240]]
## [1] 0.0002675416 0.0005251301 0.0003815210 0.0003264227 0.0008020971
## [6] 0.0005940005 0.0004117503
##
## [[241]]
## [1] 0.0007483077 0.0011632481 0.0003948806 0.0007820725
##
## [[242]]
## [1] 0.001374095 0.001590313 0.003151084 0.004856986 0.001274897
##
## [[243]]
## [1] 0.0007563099 0.0004975931 0.0010745010 0.0005945843 0.0005253427
## [6] 0.0006668607 0.0005599372
##
## [[244]]
## [1] 0.0004293567 0.0002436984 0.0005109660 0.0005114755 0.0005624447
## [6] 0.0004653883
##
## [[245]]
## [1] 0.0003102613 0.0003144920 0.0003635218 0.0007331820 0.0005940005
## [6] 0.0004993617 0.0004552439 0.0006941456
##
## [[246]]
## [1] 0.0007922509 0.0010121205 0.0005388047 0.0006904133 0.0005453621
## [6] 0.0008220713
##
## [[247]]
## [1] 0.0005947800 0.0011214057 0.0005878204 0.0005344496 0.0008493880
## [6] 0.0004338263 0.0006055212
##
## [[248]]
## [1] 0.0002990772 0.0005671129 0.0005041493 0.0005443625 0.0006440951
## [6] 0.0005306800 0.0005488483 0.0002922396
##
## [[249]]
## [1] 0.0008457051 0.0004372572 0.0003634948 0.0006921830 0.0004840856
## [6] 0.0006027871 0.0005306800 0.0005028560
##
## [[250]]
## [1] 0.0004995999 0.0007023772 0.0006385265 0.0004568226 0.0005488483
## [6] 0.0005028560
##
## [[251]]
## [1] 0.0013218127 0.0011098536 0.0009875630 0.0026703982 0.0006242597
##
## [[252]]
## [1] 0.0018549035 0.0012334400 0.0007389812 0.0008877129 0.0014065835
##
## [[253]]
## [1] 0.002873113 0.002216870 0.001372912 0.001948109 0.002561179
##
## [[254]]
## [1] 0.0005702379 0.0007443998 0.0009696900 0.0007434300 0.0005835155
##
## [[255]]
## [1] 0.0007230473 0.0005967835 0.0004077862 0.0006806064 0.0007957366
## [6] 0.0007478291
##
## [[256]]
## [1] 0.0011247779 0.0006608109 0.0004497876 0.0007192723 0.0007086270
## [6] 0.0008670194 0.0012445817
##
## [[257]]
## [1] 0.0016215648 0.0004898232 0.0009749956 0.0006285525 0.0007735384
##
## [[258]]
## [1] 0.0006004213 0.0007647918 0.0017618804 0.0007359933 0.0016947708
##
## [[259]]
## [1] 0.0018066249 0.0006991914 0.0012938630 0.0008145372 0.0007735384
## [6] 0.0016947708
##
## [[260]]
## [1] 0.0005712184 0.0004251748 0.0003073434 0.0005670438 0.0004659997
## [6] 0.0004247849 0.0004911556 0.0003887738 0.0002088315 0.0003541975
## [11] 0.0005275901
##
## [[261]]
## [1] 0.0003218864 0.0002975343 0.0008291338 0.0005049506 0.0001542695
##
## [[262]]
## [1] 0.0008145135 0.0008182666 0.0006477397 0.0004385271
##
## [[263]]
## [1] 0.001540560 0.001318513 0.001094430 0.001710645 0.001966668
##
## [[264]]
## [1] 0.001346865 0.001060021 0.001686860 0.001587403 0.001966668
##
## [[265]]
## [1] 0.0010308952 0.0011968356 0.0010402196 0.0007090567 0.0005871395
## [6] 0.0005266164 0.0010746232
##
## [[266]]
## [1] 0.0006021494 0.0011480012 0.0001645843 0.0006123168 0.0006332031
## [6] 0.0010746232 0.0004485587
##
## [[267]]
## [1] 0.0007172715 0.0008437823 0.0007987667 0.0016225886 0.0007671798
## [6] 0.0011476771
##
## [[268]]
## [1] 0.0009562278 0.0005206350 0.0009217813 0.0009121779 0.0006668607
## [6] 0.0007671798
##
## [[269]]
## [1] 0.0011898358 0.0005586148 0.0009741019 0.0012375030 0.0007500777
## [6] 0.0007815553 0.0008631945
##
## [[270]]
## [1] 0.0009588311 0.0006052788 0.0010333581 0.0005897557 0.0008628066
##
## [[271]]
## [1] 0.0003581628 0.0003598823 0.0008084706 0.0005519974 0.0004484270
##
## [[272]]
## [1] 0.0004299816 0.0003175116 0.0008291338 0.0008084706 0.0005240650
##
## [[273]]
## [1] 0.0005049506 0.0005519974 0.0005240650 0.0002929857 0.0001134911
## [6] 0.0001213027
##
## [[274]]
## [1] 0.0004484270 0.0002929857 0.0001850521
##
## [[275]]
## [1] 0.0001134911 0.0001850521
##
## [[276]]
## [1] 0.0003744015 0.0008919877 0.0003022496 0.0004382548 0.0007045348
## [6] 0.0012109373 0.0006055212
##
## [[277]]
## [1] 0.0001596115 0.0004809745 0.0005612734 0.0004319575 0.0005463079
## [6] 0.0004247967 0.0004915467 0.0004053952
##
## [[278]]
## [1] 0.0005691920 0.0006630296 0.0011052717 0.0004718208 0.0005543262
## [6] 0.0007858092 0.0008038044
##
## [[279]]
## [1] 0.0010969618 0.0005743429 0.0008207514 0.0005751480 0.0013972447
## [6] 0.0005599372
##
## [[280]]
## [1] 0.0015437033 0.0008005437 0.0006428544 0.0006438739 0.0010567762
## [6] 0.0008220713 0.0007157379
##
## [[281]]
## [1] 0.0002470680 0.0006897687 0.0005283529 0.0007535726 0.0004485587
##
## [[282]]
## [1] 0.003113330 0.001827225 0.002907612 0.001250838 0.001256117 0.001431092
## [7] 0.001274897
##
## [[283]]
## [1] 0.0005051222 0.0005317834 0.0004832907 0.0012202319 0.0005900300
##
## [[284]]
## [1] 0.0008492056 0.0005945526 0.0005528355 0.0003887738 0.0002856042
## [6] 0.0005447012
##
## [[285]]
## [1] 0.0009961000 0.0005674316 0.0015195815 0.0007359605 0.0010994341
## [6] 0.0007478291
##
## [[286]]
## [1] 0.0001549935 0.0001555721 0.0001574317 0.0001588970 0.0001363250
## [6] 0.0001835135 0.0001192015 0.0001885392 0.0002088315 0.0001542695
## [11] 0.0001213027 0.0002856042 0.0001471878 0.0002385428
##
## [[287]]
## [1] 0.0004524634 0.0007285740 0.0005374007 0.0004915467 0.0008148493
## [6] 0.0005866930 0.0010408045
##
## [[288]]
## [1] 0.0004968948 0.0004951369 0.0008571714 0.0005402766 0.0006705818
## [6] 0.0008042633 0.0006335360
##
## [[289]]
## [1] 0.0010395985 0.0012635235 0.0008148493 0.0006916773 0.0010034146
##
## [[290]]
## [1] 0.0004649255 0.0006137274 0.0008494279 0.0005866930 0.0006335360
## [6] 0.0006916773
##
## [[291]]
## [1] 0.0006690619 0.0005409661 0.0006394116 0.0004053952 0.0010408045
## [6] 0.0010034146
##
## [[292]]
## [1] 0.0010316891 0.0005457459 0.0009728851 0.0010063404 0.0010771852
## [6] 0.0012898124 0.0009030283 0.0007157379
##
## [[293]]
## [1] 0.0003518128 0.0002714655 0.0003491228 0.0002455784 0.0002256594
## [6] 0.0004757994 0.0002922396
##
## [[294]]
## [1] 0.0010814935 0.0005992600 0.0007572657 0.0001471878
##
## [[295]]
## [1] 0.0007053164 0.0006527161 0.0004993617 0.0012130822 0.0011116356
## [6] 0.0011896411
##
## [[296]]
## [1] 0.0007185553 0.0008390341 0.0006931955 0.0006297648 0.0012130822
## [6] 0.0007434539
##
## [[297]]
## [1] 0.0005848096 0.0004085692 0.0005478535 0.0004552439 0.0011116356
## [6] 0.0007434539
##
## [[298]]
## [1] 0.0008303685 0.0011552884 0.0007911726 0.0006941456 0.0011896411
##
## [[299]]
## [1] 0.0007195245 0.0007936833 0.0009976951 0.0010966976 0.0011267504
##
## [[300]]
## [1] 0.0004822651 0.0006766479 0.0009976951 0.0006996752
##
## [[301]]
## [1] 0.0009792549 0.0007151468 0.0004117503 0.0010966976 0.0006996752
## [6] 0.0006275951
##
## [[302]]
## [1] 0.0006772965 0.0004851766 0.0012016582 0.0009144844 0.0005525449
## [6] 0.0007850817 0.0011267504 0.0006275951
##
## [[303]]
## [1] 0.0011504312 0.0010939092 0.0009326884 0.0003541975 0.0011476771
## [6] 0.0009467193
##
## [[304]]
## [1] 0.0008727454 0.0007970945 0.0006865491 0.0005275901 0.0009467193
##
## [[305]]
## [1] 0.0005505365 0.0010636285 0.0006752464 0.0005864060 0.0005447012
## [6] 0.0002385428Row-standardised weights matrix
We need to assign weights to each neighbouring polygon. In this case, each neighbouring polygon will be assigned equal weight (style=“W”). This is accomplished by assigning the fraction 1/(#ofneighbors) to each neighboring county then summing the weighted income values. While this is the most intuitive way to summaries the neighbors’ values it has one drawback in that polygons along the edges of the study area will base their lagged values on fewer polygons thus potentially over- or under-estimating the true nature of the spatial autocorrelation in the data. For this example, we’ll stick with the style=“W” option for simplicity’s sake but note that other more robust options are available, notably style=“B”.
If zero policy is set to TRUE, weights vectors of zero length are inserted for regions without neighbour in the neighbours list. These will in turn generate lag values of zero, equivalent to the sum of products of the zero row t(rep(0, length=length(neighbours))) %*% x, for arbitraty numerical vector x of length length(neighbours). The spatially lagged value of x for the zero-neighbour region will then be zero, which may (or may not) be a sensible choice.
rswm_knn25 <-nb2listw(wm_knn25, style = "W", zero.policy = TRUE)
rswm_knn25## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 305
## Number of nonzero links: 7625
## Percentage nonzero weights: 8.196721
## Average number of links: 25
## Non-symmetric neighbours list
##
## Weights style: W
## Weights constants summary:
## n nn S0 S1 S2
## W 305 93025 305 22.0144 1244.109Performing Moran’s I on residual_in
moran.test(final_q2$residuals_in, listw = rswm_knn25,zero.policy = TRUE, na.action = na.omit)##
## Moran I test under randomisation
##
## data: final_q2$residuals_in
## weights: rswm_knn25
##
## Moran I statistic standard deviate = 0.71206, p-value = 0.2382
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## 0.0069605892 -0.0032894737 0.0002072123Computing Monte Carlo Moran’s I (tapin)
set.seed(1234)
Monte_C_residuals_in <- moran.mc(final_q2$residuals_in, listw = rswm_knn25, nsim = 999,zero.policy = TRUE, na.action = na.omit)
Monte_C_residuals_in##
## Monte-Carlo simulation of Moran I
##
## data: final_q2$residuals_in
## weights: rswm_knn25
## number of simulations + 1: 1000
##
## statistic = 0.0069606, observed rank = 783, p-value = 0.217
## alternative hypothesis: greaterComputing Monte Carlo Moran’s I (tapout)
moran.test(final_q2$residuals_out, listw = rswm_knn25,zero.policy = TRUE, na.action = na.omit)##
## Moran I test under randomisation
##
## data: final_q2$residuals_out
## weights: rswm_knn25
##
## Moran I statistic standard deviate = 0.95813, p-value = 0.169
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## 0.0105538387 -0.0032894737 0.0002087508Monte Carlo simulation approach of Geary’s C
set.seed(1234)
Monte_C_residuals_out <- moran.mc(final_q2$residuals_out, listw = rswm_knn25, nsim = 999,zero.policy = TRUE, na.action = na.omit)
Monte_C_residuals_in##
## Monte-Carlo simulation of Moran I
##
## data: final_q2$residuals_in
## weights: rswm_knn25
## number of simulations + 1: 1000
##
## statistic = 0.0069606, observed rank = 783, p-value = 0.217
## alternative hypothesis: greaterSince p-value = 0.5821 of tapin and tapout are greater than significance level of 0.05. Therefore, there is no statisitical evidence to reject null hypothesis. Concluding that tapin and tapout are randomly distributed. Rejection of alternative hypothesis, also means that Moran’s I calculation is irrelevent in determining the pattern.
Question 3
Computing local Moran’s I
To compute local Moran’s I, the localmoran() function of spdep will be used.
fips <- order(final_q2$SUBZONE_N)
localMI_tapin <- localmoran(final_q2$TOTAL_TAP_IN_VOLUME,rswm_knn25)
head(localMI_tapin)## Ii E.Ii Var.Ii Z.Ii Pr(z > 0)
## 1 -0.16881464 -0.003289474 0.03508884 -0.8836484 0.8115570
## 2 -0.15039076 -0.003289474 0.03508884 -0.7852934 0.7838592
## 3 -0.06614555 -0.003289474 0.03508884 -0.3355542 0.6313965
## 4 0.17162098 -0.003289474 0.03508884 0.9337514 0.1752161
## 5 -0.21327111 -0.003289474 0.03508884 -1.1209772 0.8688512
## 6 -0.05765667 -0.003289474 0.03508884 -0.2902367 0.6141824Code chunk that lists the content of local Moran matrix derived by using printCoefmat()
printCoefmat(data.frame(localMI_tapin[fips,],row.names = final_q2$SUBZONE_N[fips]), check.names =FALSE)## Ii E.Ii Var.Ii Z.Ii
## ADMIRALTY -0.16881464 -0.00328947 0.03508884 -0.88364843
## AIRPORT ROAD -0.15039076 -0.00328947 0.03508884 -0.78529340
## ALEXANDRA HILL -0.06614555 -0.00328947 0.03508884 -0.33555422
## ALEXANDRA NORTH 0.17162098 -0.00328947 0.03508884 0.93375136
## ALJUNIED -0.21327111 -0.00328947 0.03508884 -1.12097720
## ANAK BUKIT -0.05765667 -0.00328947 0.03508884 -0.29023674
## ANCHORVALE 0.03063218 -0.00328947 0.03508884 0.18108918
## ANG MO KIO TOWN CENTRE 0.17107574 -0.00328947 0.03508884 0.93084061
## ANSON 0.29550362 -0.00328947 0.03508884 1.59509305
## BALESTIER -0.30277248 -0.00328947 0.03508884 -1.59877611
## BANGKIT 0.01310647 -0.00328947 0.03508884 0.08752898
## BAYFRONT SUBZONE 0.30881794 -0.00328947 0.03508884 1.66617094
## BAYSHORE -0.47319777 -0.00328947 0.03508884 -2.50858364
## BEDOK NORTH 3.49931070 -0.00328947 0.03508884 18.69846841
## BEDOK RESERVOIR 0.33611802 -0.00328947 0.03508884 1.81191116
## BEDOK SOUTH 0.95213001 -0.00328947 0.03508884 5.10046255
## BENCOOLEN 0.21974903 -0.00328947 0.03508884 1.19068068
## BENDEMEER -0.06350007 -0.00328947 0.03508884 -0.32143148
## BENOI SECTOR 0.02849933 -0.00328947 0.03508884 0.16970308
## BIDADARI -0.03098880 -0.00328947 0.03508884 -0.14787155
## BISHAN EAST 0.34958891 -0.00328947 0.03508884 1.88382488
## BOAT QUAY 0.30845686 -0.00328947 0.03508884 1.66424334
## BOON KENG 0.00243131 -0.00328947 0.03508884 0.03054015
## BOON LAY PLACE 0.12207318 -0.00328947 0.03508884 0.66924271
## BOON TECK -0.04275652 -0.00328947 0.03508884 -0.21069302
## BOULEVARD -0.39123392 -0.00328947 0.03508884 -2.07102340
## BRADDELL -0.05493385 -0.00328947 0.03508884 -0.27570112
## BRAS BASAH 0.09211260 -0.00328947 0.03508884 0.50929952
## BRICKWORKS -0.05246374 -0.00328947 0.03508884 -0.26251453
## BUGIS -0.04683962 -0.00328947 0.03508884 -0.23249043
## BUKIT BATOK CENTRAL 0.00740259 -0.00328947 0.03508884 0.05707908
## BUKIT BATOK EAST -0.00818749 -0.00328947 0.03508884 -0.02614785
## BUKIT BATOK SOUTH -0.00541558 -0.00328947 0.03508884 -0.01135012
## BUKIT BATOK WEST -0.04000037 -0.00328947 0.03508884 -0.19597941
## BUKIT HO SWEE 0.11160279 -0.00328947 0.03508884 0.61334700
## BUKIT MERAH 0.01390381 -0.00328947 0.03508884 0.09178556
## CECIL 0.25060902 -0.00328947 0.03508884 1.35542533
## CENTRAL SUBZONE 0.30557284 -0.00328947 0.03508884 1.64884710
## CENTRAL WATER CATCHMENT 0.03339007 -0.00328947 0.03508884 0.19581202
## CHANGI AIRPORT 0.50888234 -0.00328947 0.03508884 2.73420544
## CHANGI POINT -0.36276075 -0.00328947 0.03508884 -1.91902069
## CHANGI WEST -0.19489087 -0.00328947 0.03508884 -1.02285518
## CHATSWORTH 0.09654258 -0.00328947 0.03508884 0.53294879
## CHENG SAN 0.23225262 -0.00328947 0.03508884 1.25743051
## CHIN BEE -0.11952312 -0.00328947 0.03508884 -0.62050790
## CHINA SQUARE 0.25714785 -0.00328947 0.03508884 1.39033257
## CHINATOWN -0.12008796 -0.00328947 0.03508884 -0.62352329
## CHOA CHU KANG CENTRAL -0.06096877 -0.00328947 0.03508884 -0.30791825
## CHOA CHU KANG NORTH 0.00011826 -0.00328947 0.03508884 0.01819203
## CHONG BOON 0.11064648 -0.00328947 0.03508884 0.60824181
## CITY HALL 0.02811475 -0.00328947 0.03508884 0.16764997
## CITY TERMINALS 0.24270849 -0.00328947 0.03508884 1.31324872
## CLARKE QUAY 0.12587051 -0.00328947 0.03508884 0.68951457
## CLEMENTI CENTRAL -0.32570183 -0.00328947 0.03508884 -1.72118340
## CLEMENTI NORTH -0.07489425 -0.00328947 0.03508884 -0.38225876
## CLEMENTI WEST 0.01357083 -0.00328947 0.03508884 0.09000797
## CLEMENTI WOODS -0.00826071 -0.00328947 0.03508884 -0.02653871
## CLIFFORD PIER 0.27482263 -0.00328947 0.03508884 1.48468854
## COMMONWEALTH 0.09208956 -0.00328947 0.03508884 0.50917656
## COMPASSVALE -0.02913086 -0.00328947 0.03508884 -0.13795306
## CORONATION ROAD 0.11650506 -0.00328947 0.03508884 0.63951754
## CRAWFORD 0.08858515 -0.00328947 0.03508884 0.49046841
## DAIRY FARM -0.05541745 -0.00328947 0.03508884 -0.27828279
## DEFU INDUSTRIAL PARK -0.08237334 -0.00328947 0.03508884 -0.42218554
## DEPOT ROAD 0.12276307 -0.00328947 0.03508884 0.67292567
## DHOBY GHAUT 0.04944891 -0.00328947 0.03508884 0.28154141
## DOVER 0.05509000 -0.00328947 0.03508884 0.31165613
## DUNEARN 0.09862278 -0.00328947 0.03508884 0.54405382
## EAST COAST -0.39866297 -0.00328947 0.03508884 -2.11068305
## EVERTON PARK 0.16082548 -0.00328947 0.03508884 0.87612008
## FABER -0.01596425 -0.00328947 0.03508884 -0.06766370
## FAJAR -0.00844749 -0.00328947 0.03508884 -0.02753585
## FARRER COURT 0.25188867 -0.00328947 0.03508884 1.36225665
## FARRER PARK -0.04830663 -0.00328947 0.03508884 -0.24032198
## FERNVALE 0.04231431 -0.00328947 0.03508884 0.24345367
## FLORA DRIVE -0.28070507 -0.00328947 0.03508884 -1.48097027
## FORT CANNING 0.27343903 -0.00328947 0.03508884 1.47730228
## FRANKEL 0.67752875 -0.00328947 0.03508884 3.63451646
## GALI BATU -0.05704619 -0.00328947 0.03508884 -0.28697774
## GEYLANG BAHRU 0.00949426 -0.00328947 0.03508884 0.06824536
## GEYLANG EAST 0.16714410 -0.00328947 0.03508884 0.90985171
## GHIM MOH 0.09003496 -0.00328947 0.03508884 0.49820816
## GOMBAK -0.01613193 -0.00328947 0.03508884 -0.06855884
## GOODWOOD PARK 0.24923367 -0.00328947 0.03508884 1.34808310
## GREENWOOD PARK -0.11373365 -0.00328947 0.03508884 -0.58960112
## GUILIN -0.04420645 -0.00328947 0.03508884 -0.21843340
## GUL BASIN 0.06136697 -0.00328947 0.03508884 0.34516544
## GUL CIRCLE 0.05327315 -0.00328947 0.03508884 0.30195696
## HENDERSON HILL -0.00497603 -0.00328947 0.03508884 -0.00900361
## HILLCREST 0.18884474 -0.00328947 0.03508884 1.02569957
## HILLVIEW -0.01260092 -0.00328947 0.03508884 -0.04970875
## HOLLAND DRIVE 0.09579285 -0.00328947 0.03508884 0.52894638
## HOLLAND ROAD -0.03376095 -0.00328947 0.03508884 -0.16267056
## HONG KAH 0.46784056 -0.00328947 0.03508884 2.51510580
## HONG KAH NORTH 0.03490772 -0.00328947 0.03508884 0.20391395
## HOUGANG CENTRAL 0.27377814 -0.00328947 0.03508884 1.47911259
## HOUGANG EAST 0.00653823 -0.00328947 0.03508884 0.05246472
## HOUGANG WEST 0.30256578 -0.00328947 0.03508884 1.63279406
## INSTITUTION HILL 0.24504637 -0.00328947 0.03508884 1.32572937
## INTERNATIONAL BUSINESS PARK -0.08643041 -0.00328947 0.03508884 -0.44384401
## ISTANA NEGARA 0.27499681 -0.00328947 0.03508884 1.48561840
## JELEBU 0.01922961 -0.00328947 0.03508884 0.12021709
## JOO KOON -0.01186348 -0.00328947 0.03508884 -0.04577191
## JOO SENG -0.07960155 -0.00328947 0.03508884 -0.40738845
## JURONG GATEWAY 0.13695537 -0.00328947 0.03508884 0.74869058
## JURONG PORT -0.10659759 -0.00328947 0.03508884 -0.55150556
## JURONG RIVER -0.14417707 -0.00328947 0.03508884 -0.75212186
## JURONG WEST CENTRAL -0.30309828 -0.00328947 0.03508884 -1.60051537
## KAKI BUKIT 0.60226073 -0.00328947 0.03508884 3.23270166
## KALLANG BAHRU 0.01214038 -0.00328947 0.03508884 0.08237156
## KALLANG WAY -0.07298420 -0.00328947 0.03508884 -0.37206207
## KAMPONG BUGIS 0.06870158 -0.00328947 0.03508884 0.38432091
## KAMPONG GLAM 0.22900537 -0.00328947 0.03508884 1.24009525
## KAMPONG JAVA 0.08370177 -0.00328947 0.03508884 0.46439871
## KAMPONG TIONG BAHRU 0.08973796 -0.00328947 0.03508884 0.49662264
## KAMPONG UBI 0.13742821 -0.00328947 0.03508884 0.75121480
## KANGKAR 0.05498025 -0.00328947 0.03508884 0.31107019
## KATONG -0.08971734 -0.00328947 0.03508884 -0.46139116
## KEAT HONG -0.00093957 -0.00328947 0.03508884 0.01254488
## KEBUN BAHRU 0.00285166 -0.00328947 0.03508884 0.03278418
## KEMBANGAN 0.49428731 -0.00328947 0.03508884 2.65629055
## KENT RIDGE 0.13696907 -0.00328947 0.03508884 0.74876372
## KHATIB 0.00702143 -0.00328947 0.03508884 0.05504429
## KIAN TECK -0.04750707 -0.00328947 0.03508884 -0.23605358
## KIM KEAT -0.06598789 -0.00328947 0.03508884 -0.33471258
## KOVAN 0.03730851 -0.00328947 0.03508884 0.21673047
## KRANJI -0.08280362 -0.00328947 0.03508884 -0.42448260
## LAKESIDE -0.09182333 -0.00328947 0.03508884 -0.47263387
## LAVENDER -0.10479824 -0.00328947 0.03508884 -0.54189984
## LEEDON PARK 0.16507142 -0.00328947 0.03508884 0.89878679
## LEONIE HILL 0.26883279 -0.00328947 0.03508884 1.45271206
## LIM CHU KANG -0.16932897 -0.00328947 0.03508884 -0.88639414
## LITTLE INDIA 0.22322965 -0.00328947 0.03508884 1.20926180
## LIU FANG -0.07509736 -0.00328947 0.03508884 -0.38334307
## LORONG 8 TOA PAYOH -0.05129276 -0.00328947 0.03508884 -0.25626330
## LORONG AH SOO 0.04537975 -0.00328947 0.03508884 0.25981838
## LORONG CHUAN -0.20320912 -0.00328947 0.03508884 -1.06726173
## LORONG HALUS -0.20798929 -0.00328947 0.03508884 -1.09278046
## LOWER SELETAR -0.03331478 -0.00328947 0.03508884 -0.16028870
## LOYANG EAST -0.39817332 -0.00328947 0.03508884 -2.10806908
## LOYANG WEST -0.37982465 -0.00328947 0.03508884 -2.01011555
## MACKENZIE 0.15155903 -0.00328947 0.03508884 0.82665154
## MACPHERSON 0.05041039 -0.00328947 0.03508884 0.28667424
## MALCOLM 0.08554472 -0.00328947 0.03508884 0.47423724
## MANDAI EAST -0.18781641 -0.00328947 0.03508884 -0.98508847
## MANDAI ESTATE -0.08711068 -0.00328947 0.03508884 -0.44747562
## MANDAI WEST -0.11335767 -0.00328947 0.03508884 -0.58759395
## MARGARET DRIVE 0.06178732 -0.00328947 0.03508884 0.34740946
## MARINA CENTRE 0.17782558 -0.00328947 0.03508884 0.96687432
## MARINA EAST (MP) 0.06560445 -0.00328947 0.03508884 0.36778702
## MARINA SOUTH 0.38590509 -0.00328947 0.03508884 2.07769709
## MARINE PARADE 0.43386464 -0.00328947 0.03508884 2.33372695
## MARITIME SQUARE -0.28295326 -0.00328947 0.03508884 -1.49297215
## MARYMOUNT 0.19466414 -0.00328947 0.03508884 1.05676615
## MATILDA 0.03897715 -0.00328947 0.03508884 0.22563839
## MAXWELL 0.39819503 -0.00328947 0.03508884 2.14330636
## MEI CHIN 0.08073606 -0.00328947 0.03508884 0.44856640
## MIDVIEW 0.04767366 -0.00328947 0.03508884 0.27206433
## MONK'S HILL 0.32516789 -0.00328947 0.03508884 1.75345438
## MOULMEIN -0.03743677 -0.00328947 0.03508884 -0.18229373
## MOUNT PLEASANT 0.01013131 -0.00328947 0.03508884 0.07164623
## MOUNTBATTEN -0.06734329 -0.00328947 0.03508884 -0.34194834
## NASSIM 0.12277169 -0.00328947 0.03508884 0.67297166
## NATIONAL UNIVERSITY OF S'PORE 0.06161402 -0.00328947 0.03508884 0.34648430
## NATURE RESERVE 0.02011873 -0.00328947 0.03508884 0.12496362
## NEE SOON -0.15582926 -0.00328947 0.03508884 -0.81432658
## NEWTON CIRCUS 0.09188862 -0.00328947 0.03508884 0.50810383
## NORTH COAST 0.15908976 -0.00328947 0.03508884 0.86685400
## NORTHLAND 0.02447383 -0.00328947 0.03508884 0.14821308
## NORTHSHORE -0.09162169 -0.00328947 0.03508884 -0.47155743
## ONE NORTH 0.04625246 -0.00328947 0.03508884 0.26447731
## ONE TREE HILL 0.23733354 -0.00328947 0.03508884 1.28455476
## ORANGE GROVE 0.33932017 -0.00328947 0.03508884 1.82900565
## OXLEY 0.28657788 -0.00328947 0.03508884 1.54744343
## PANDAN 0.02453059 -0.00328947 0.03508884 0.14851614
## PANG SUA -0.20359834 -0.00328947 0.03508884 -1.06933956
## PASIR PANJANG 1 0.02537539 -0.00328947 0.03508884 0.15302602
## PASIR PANJANG 2 0.07244438 -0.00328947 0.03508884 0.40430169
## PASIR RIS CENTRAL 0.62208106 -0.00328947 0.03508884 3.33851157
## PASIR RIS DRIVE 0.62283390 -0.00328947 0.03508884 3.34253056
## PASIR RIS PARK -0.29739250 -0.00328947 0.03508884 -1.57005537
## PASIR RIS WAFER FAB PARK -0.36367053 -0.00328947 0.03508884 -1.92387756
## PASIR RIS WEST 0.18682745 -0.00328947 0.03508884 1.01493036
## PATERSON 0.14688127 -0.00328947 0.03508884 0.80167954
## PAYA LEBAR EAST -0.66204030 -0.00328947 0.03508884 -3.51671070
## PAYA LEBAR NORTH -0.34204311 -0.00328947 0.03508884 -1.80842055
## PAYA LEBAR WEST -0.26719836 -0.00328947 0.03508884 -1.40886531
## PEARL'S HILL 0.10272359 -0.00328947 0.03508884 0.56594584
## PEI CHUN -0.05577657 -0.00328947 0.03508884 -0.28019994
## PENG SIANG 0.03925530 -0.00328947 0.03508884 0.22712330
## PENJURU CRESCENT 0.06196807 -0.00328947 0.03508884 0.34837434
## PEOPLE'S PARK 0.10640058 -0.00328947 0.03508884 0.58557526
## PHILLIP 0.34090959 -0.00328947 0.03508884 1.83749071
## PIONEER SECTOR 0.06694171 -0.00328947 0.03508884 0.37492593
## PLAB -0.15109315 -0.00328947 0.03508884 -0.78904307
## PORT 0.05325207 -0.00328947 0.03508884 0.30184438
## POTONG PASIR -0.04244897 -0.00328947 0.03508884 -0.20905113
## PUNGGOL FIELD 0.09307041 -0.00328947 0.03508884 0.51441277
## PUNGGOL TOWN CENTRE -0.05685758 -0.00328947 0.03508884 -0.28597083
## QUEENSWAY 0.11047748 -0.00328947 0.03508884 0.60733962
## RAFFLES PLACE 0.30092759 -0.00328947 0.03508884 1.62404865
## REDHILL 0.02490492 -0.00328947 0.03508884 0.15051445
## RESERVOIR VIEW -0.25324335 -0.00328947 0.03508884 -1.33436716
## RIDOUT 0.20668247 -0.00328947 0.03508884 1.12092548
## RIVERVALE 0.16656144 -0.00328947 0.03508884 0.90674120
## ROBERTSON QUAY 0.13715608 -0.00328947 0.03508884 0.74976209
## ROCHOR CANAL 0.21378652 -0.00328947 0.03508884 1.15885010
## SAFTI 0.03333761 -0.00328947 0.03508884 0.19553199
## SAMULUN -0.09607726 -0.00328947 0.03508884 -0.49534328
## SAUJANA 0.00164746 -0.00328947 0.03508884 0.02635557
## SELEGIE 0.23218241 -0.00328947 0.03508884 1.25705571
## SELETAR -0.10439804 -0.00328947 0.03508884 -0.53976341
## SELETAR AEROSPACE PARK -0.24814115 -0.00328947 0.03508884 -1.30712933
## SELETAR HILLS -0.15426093 -0.00328947 0.03508884 -0.80595413
## SEMBAWANG CENTRAL 0.35989827 -0.00328947 0.03508884 1.93886090
## SEMBAWANG EAST -0.12310358 -0.00328947 0.03508884 -0.63962203
## SEMBAWANG HILLS -0.00933314 -0.00328947 0.03508884 -0.03226383
## SEMBAWANG NORTH -0.02981167 -0.00328947 0.03508884 -0.14158751
## SEMBAWANG SPRINGS -0.12022961 -0.00328947 0.03508884 -0.62427948
## SEMBAWANG STRAITS -0.22476584 -0.00328947 0.03508884 -1.18234131
## SENGKANG TOWN CENTRE 0.12688061 -0.00328947 0.03508884 0.69490694
## SENGKANG WEST -0.23593266 -0.00328947 0.03508884 -1.24195484
## SENJA 0.00186077 -0.00328947 0.03508884 0.02749434
## SENNETT -0.02563695 -0.00328947 0.03508884 -0.11930097
## SENOKO NORTH -0.18707889 -0.00328947 0.03508884 -0.98115124
## SENOKO SOUTH -0.16271726 -0.00328947 0.03508884 -0.85109785
## SENOKO WEST -0.11998880 -0.00328947 0.03508884 -0.62299396
## SENTOSA 0.22476657 -0.00328947 0.03508884 1.21746658
## SERANGOON CENTRAL 0.13503816 -0.00328947 0.03508884 0.73845567
## SERANGOON GARDEN 0.19358583 -0.00328947 0.03508884 1.05100967
## SERANGOON NORTH 0.04205382 -0.00328947 0.03508884 0.24206306
## SERANGOON NORTH IND ESTATE -0.23546687 -0.00328947 0.03508884 -1.23946825
## SHANGRI-LA -0.02654247 -0.00328947 0.03508884 -0.12413503
## SHIPYARD 0.04088521 -0.00328947 0.03508884 0.23582450
## SIGLAP -0.45649703 -0.00328947 0.03508884 -2.41942748
## SIMEI 0.66955046 -0.00328947 0.03508884 3.59192477
## SINGAPORE GENERAL HOSPITAL 0.12384315 -0.00328947 0.03508884 0.67869161
## SINGAPORE POLYTECHNIC 0.03685339 -0.00328947 0.03508884 0.21430081
## SOMERSET -0.12628707 -0.00328947 0.03508884 -0.65661697
## SPRINGLEAF -0.09004539 -0.00328947 0.03508884 -0.46314245
## STRAITS VIEW 0.35654492 -0.00328947 0.03508884 1.92095919
## SUNGEI ROAD 0.16035836 -0.00328947 0.03508884 0.87362635
## SUNSET WAY -0.01151062 -0.00328947 0.03508884 -0.04388822
## SWISS CLUB 0.13979799 -0.00328947 0.03508884 0.76386581
## TAGORE -0.03235607 -0.00328947 0.03508884 -0.15517067
## TAI SENG -0.00781742 -0.00328947 0.03508884 -0.02417223
## TAMAN JURONG 0.23226724 -0.00328947 0.03508884 1.25750857
## TAMPINES EAST 1.99180318 -0.00328947 0.03508884 10.65070947
## TAMPINES NORTH -0.22505857 -0.00328947 0.03508884 -1.18390402
## TAMPINES WEST 1.27780414 -0.00328947 0.03508884 6.83905876
## TANGLIN 0.27448560 -0.00328947 0.03508884 1.48288936
## TANGLIN HALT 0.07831424 -0.00328947 0.03508884 0.43563764
## TANJONG PAGAR 0.37834667 -0.00328947 0.03508884 2.03734681
## TANJONG RHU 0.08135540 -0.00328947 0.03508884 0.45187271
## TEBAN GARDENS -0.00125950 -0.00328947 0.03508884 0.01083693
## TECK WHYE 0.00161187 -0.00328947 0.03508884 0.02616562
## TELOK BLANGAH DRIVE -0.00484984 -0.00328947 0.03508884 -0.00832992
## TELOK BLANGAH RISE 0.04635339 -0.00328947 0.03508884 0.26501613
## TELOK BLANGAH WAY 0.06346200 -0.00328947 0.03508884 0.35634966
## TENGAH -0.35993852 -0.00328947 0.03508884 -1.90395436
## TENGEH 0.04104825 -0.00328947 0.03508884 0.23669490
## THE WHARVES -0.33232118 -0.00328947 0.03508884 -1.75652049
## TIONG BAHRU 0.13130939 -0.00328947 0.03508884 0.71854979
## TIONG BAHRU STATION -0.25837049 -0.00328947 0.03508884 -1.36173817
## TOA PAYOH CENTRAL -0.30654737 -0.00328947 0.03508884 -1.61892822
## TOA PAYOH WEST -0.01320861 -0.00328947 0.03508884 -0.05295284
## TOH GUAN -0.00091264 -0.00328947 0.03508884 0.01268864
## TOH TUCK -0.02251748 -0.00328947 0.03508884 -0.10264783
## TOWNSVILLE 0.02360066 -0.00328947 0.03508884 0.14355175
## TRAFALGAR 0.41174649 -0.00328947 0.03508884 2.21565023
## TUAS BAY 0.03792017 -0.00328947 0.03508884 0.21999577
## TUAS NORTH 0.03873354 -0.00328947 0.03508884 0.22433791
## TUAS PROMENADE 0.03561127 -0.00328947 0.03508884 0.20766979
## TUAS VIEW 0.10974909 -0.00328947 0.03508884 0.60345112
## TUAS VIEW EXTENSION 0.14396527 -0.00328947 0.03508884 0.78611259
## TUKANG -0.11719240 -0.00328947 0.03508884 -0.60806549
## TURF CLUB -0.07672574 -0.00328947 0.03508884 -0.39203612
## TYERSALL 0.15521424 -0.00328947 0.03508884 0.84616474
## ULU PANDAN 0.08937903 -0.00328947 0.03508884 0.49470653
## UPPER PAYA LEBAR -0.02981154 -0.00328947 0.03508884 -0.14158682
## UPPER THOMSON 0.11781276 -0.00328947 0.03508884 0.64649867
## VICTORIA -0.11606191 -0.00328947 0.03508884 -0.60203040
## WATERWAY EAST -0.05681019 -0.00328947 0.03508884 -0.28571784
## WENYA -0.14089006 -0.00328947 0.03508884 -0.73457435
## WEST COAST -0.02584070 -0.00328947 0.03508884 -0.12038868
## WESTERN WATER CATCHMENT 0.04735404 -0.00328947 0.03508884 0.27035807
## WOODGROVE 0.02402704 -0.00328947 0.03508884 0.14582796
## WOODLANDS EAST 0.52658337 -0.00328947 0.03508884 2.82870157
## WOODLANDS REGIONAL CENTRE 0.00078437 -0.00328947 0.03508884 0.02174805
## WOODLANDS SOUTH 0.04837088 -0.00328947 0.03508884 0.27578639
## WOODLANDS WEST 0.04197694 -0.00328947 0.03508884 0.24165263
## WOODLEIGH -0.13377132 -0.00328947 0.03508884 -0.69657129
## XILIN -0.32708588 -0.00328947 0.03508884 -1.72857209
## YEW TEE -0.02488937 -0.00328947 0.03508884 -0.11531002
## YIO CHU KANG 0.04280239 -0.00328947 0.03508884 0.24605925
## YIO CHU KANG EAST -0.11842411 -0.00328947 0.03508884 -0.61464091
## YIO CHU KANG NORTH -0.07362081 -0.00328947 0.03508884 -0.37546055
## YIO CHU KANG WEST -0.00155465 -0.00328947 0.03508884 0.00926130
## YISHUN CENTRAL -0.04088662 -0.00328947 0.03508884 -0.20071062
## YISHUN EAST -0.09930833 -0.00328947 0.03508884 -0.51259220
## YISHUN SOUTH 0.02356272 -0.00328947 0.03508884 0.14334920
## YISHUN WEST -0.00570797 -0.00328947 0.03508884 -0.01291104
## YUHUA EAST 0.01678666 -0.00328947 0.03508884 0.10717551
## YUHUA WEST 0.09337107 -0.00328947 0.03508884 0.51601784
## YUNNAN -0.12660838 -0.00328947 0.03508884 -0.65833225
## Pr.z...0.
## ADMIRALTY 0.8116
## AIRPORT ROAD 0.7839
## ALEXANDRA HILL 0.6314
## ALEXANDRA NORTH 0.1752
## ALJUNIED 0.8689
## ANAK BUKIT 0.6142
## ANCHORVALE 0.4281
## ANG MO KIO TOWN CENTRE 0.1760
## ANSON 0.0553
## BALESTIER 0.9451
## BANGKIT 0.4651
## BAYFRONT SUBZONE 0.0478
## BAYSHORE 0.9939
## BEDOK NORTH 0.0000
## BEDOK RESERVOIR 0.0350
## BEDOK SOUTH 0.0000
## BENCOOLEN 0.1169
## BENDEMEER 0.6261
## BENOI SECTOR 0.4326
## BIDADARI 0.5588
## BISHAN EAST 0.0298
## BOAT QUAY 0.0480
## BOON KENG 0.4878
## BOON LAY PLACE 0.2517
## BOON TECK 0.5834
## BOULEVARD 0.9808
## BRADDELL 0.6086
## BRAS BASAH 0.3053
## BRICKWORKS 0.6035
## BUGIS 0.5919
## BUKIT BATOK CENTRAL 0.4772
## BUKIT BATOK EAST 0.5104
## BUKIT BATOK SOUTH 0.5045
## BUKIT BATOK WEST 0.5777
## BUKIT HO SWEE 0.2698
## BUKIT MERAH 0.4634
## CECIL 0.0876
## CENTRAL SUBZONE 0.0496
## CENTRAL WATER CATCHMENT 0.4224
## CHANGI AIRPORT 0.0031
## CHANGI POINT 0.9725
## CHANGI WEST 0.8468
## CHATSWORTH 0.2970
## CHENG SAN 0.1043
## CHIN BEE 0.7325
## CHINA SQUARE 0.0822
## CHINATOWN 0.7335
## CHOA CHU KANG CENTRAL 0.6209
## CHOA CHU KANG NORTH 0.4927
## CHONG BOON 0.2715
## CITY HALL 0.4334
## CITY TERMINALS 0.0945
## CLARKE QUAY 0.2452
## CLEMENTI CENTRAL 0.9574
## CLEMENTI NORTH 0.6489
## CLEMENTI WEST 0.4641
## CLEMENTI WOODS 0.5106
## CLIFFORD PIER 0.0688
## COMMONWEALTH 0.3053
## COMPASSVALE 0.5549
## CORONATION ROAD 0.2612
## CRAWFORD 0.3119
## DAIRY FARM 0.6096
## DEFU INDUSTRIAL PARK 0.6636
## DEPOT ROAD 0.2505
## DHOBY GHAUT 0.3891
## DOVER 0.3777
## DUNEARN 0.2932
## EAST COAST 0.9826
## EVERTON PARK 0.1905
## FABER 0.5270
## FAJAR 0.5110
## FARRER COURT 0.0866
## FARRER PARK 0.5950
## FERNVALE 0.4038
## FLORA DRIVE 0.9307
## FORT CANNING 0.0698
## FRANKEL 0.0001
## GALI BATU 0.6129
## GEYLANG BAHRU 0.4728
## GEYLANG EAST 0.1815
## GHIM MOH 0.3092
## GOMBAK 0.5273
## GOODWOOD PARK 0.0888
## GREENWOOD PARK 0.7223
## GUILIN 0.5865
## GUL BASIN 0.3650
## GUL CIRCLE 0.3813
## HENDERSON HILL 0.5036
## HILLCREST 0.1525
## HILLVIEW 0.5198
## HOLLAND DRIVE 0.2984
## HOLLAND ROAD 0.5646
## HONG KAH 0.0059
## HONG KAH NORTH 0.4192
## HOUGANG CENTRAL 0.0696
## HOUGANG EAST 0.4791
## HOUGANG WEST 0.0513
## INSTITUTION HILL 0.0925
## INTERNATIONAL BUSINESS PARK 0.6714
## ISTANA NEGARA 0.0687
## JELEBU 0.4522
## JOO KOON 0.5183
## JOO SENG 0.6581
## JURONG GATEWAY 0.2270
## JURONG PORT 0.7094
## JURONG RIVER 0.7740
## JURONG WEST CENTRAL 0.9453
## KAKI BUKIT 0.0006
## KALLANG BAHRU 0.4672
## KALLANG WAY 0.6451
## KAMPONG BUGIS 0.3504
## KAMPONG GLAM 0.1075
## KAMPONG JAVA 0.3212
## KAMPONG TIONG BAHRU 0.3097
## KAMPONG UBI 0.2263
## KANGKAR 0.3779
## KATONG 0.6777
## KEAT HONG 0.4950
## KEBUN BAHRU 0.4869
## KEMBANGAN 0.0040
## KENT RIDGE 0.2270
## KHATIB 0.4781
## KIAN TECK 0.5933
## KIM KEAT 0.6311
## KOVAN 0.4142
## KRANJI 0.6644
## LAKESIDE 0.6818
## LAVENDER 0.7061
## LEEDON PARK 0.1844
## LEONIE HILL 0.0732
## LIM CHU KANG 0.8123
## LITTLE INDIA 0.1133
## LIU FANG 0.6493
## LORONG 8 TOA PAYOH 0.6011
## LORONG AH SOO 0.3975
## LORONG CHUAN 0.8571
## LORONG HALUS 0.8628
## LOWER SELETAR 0.5637
## LOYANG EAST 0.9825
## LOYANG WEST 0.9778
## MACKENZIE 0.2042
## MACPHERSON 0.3872
## MALCOLM 0.3177
## MANDAI EAST 0.8377
## MANDAI ESTATE 0.6727
## MANDAI WEST 0.7216
## MARGARET DRIVE 0.3641
## MARINA CENTRE 0.1668
## MARINA EAST (MP) 0.3565
## MARINA SOUTH 0.0189
## MARINE PARADE 0.0098
## MARITIME SQUARE 0.9323
## MARYMOUNT 0.1453
## MATILDA 0.4107
## MAXWELL 0.0160
## MEI CHIN 0.3269
## MIDVIEW 0.3928
## MONK'S HILL 0.0398
## MOULMEIN 0.5723
## MOUNT PLEASANT 0.4714
## MOUNTBATTEN 0.6338
## NASSIM 0.2505
## NATIONAL UNIVERSITY OF S'PORE 0.3645
## NATURE RESERVE 0.4503
## NEE SOON 0.7923
## NEWTON CIRCUS 0.3057
## NORTH COAST 0.1930
## NORTHLAND 0.4411
## NORTHSHORE 0.6814
## ONE NORTH 0.3957
## ONE TREE HILL 0.0995
## ORANGE GROVE 0.0337
## OXLEY 0.0609
## PANDAN 0.4410
## PANG SUA 0.8575
## PASIR PANJANG 1 0.4392
## PASIR PANJANG 2 0.3430
## PASIR RIS CENTRAL 0.0004
## PASIR RIS DRIVE 0.0004
## PASIR RIS PARK 0.9418
## PASIR RIS WAFER FAB PARK 0.9728
## PASIR RIS WEST 0.1551
## PATERSON 0.2114
## PAYA LEBAR EAST 0.9998
## PAYA LEBAR NORTH 0.9647
## PAYA LEBAR WEST 0.9206
## PEARL'S HILL 0.2857
## PEI CHUN 0.6103
## PENG SIANG 0.4102
## PENJURU CRESCENT 0.3638
## PEOPLE'S PARK 0.2791
## PHILLIP 0.0331
## PIONEER SECTOR 0.3539
## PLAB 0.7850
## PORT 0.3814
## POTONG PASIR 0.5828
## PUNGGOL FIELD 0.3035
## PUNGGOL TOWN CENTRE 0.6125
## QUEENSWAY 0.2718
## RAFFLES PLACE 0.0522
## REDHILL 0.4402
## RESERVOIR VIEW 0.9090
## RIDOUT 0.1312
## RIVERVALE 0.1823
## ROBERTSON QUAY 0.2267
## ROCHOR CANAL 0.1233
## SAFTI 0.4225
## SAMULUN 0.6898
## SAUJANA 0.4895
## SELEGIE 0.1044
## SELETAR 0.7053
## SELETAR AEROSPACE PARK 0.9044
## SELETAR HILLS 0.7899
## SEMBAWANG CENTRAL 0.0263
## SEMBAWANG EAST 0.7388
## SEMBAWANG HILLS 0.5129
## SEMBAWANG NORTH 0.5563
## SEMBAWANG SPRINGS 0.7338
## SEMBAWANG STRAITS 0.8815
## SENGKANG TOWN CENTRE 0.2436
## SENGKANG WEST 0.8929
## SENJA 0.4890
## SENNETT 0.5475
## SENOKO NORTH 0.8367
## SENOKO SOUTH 0.8026
## SENOKO WEST 0.7334
## SENTOSA 0.1117
## SERANGOON CENTRAL 0.2301
## SERANGOON GARDEN 0.1466
## SERANGOON NORTH 0.4044
## SERANGOON NORTH IND ESTATE 0.8924
## SHANGRI-LA 0.5494
## SHIPYARD 0.4068
## SIGLAP 0.9922
## SIMEI 0.0002
## SINGAPORE GENERAL HOSPITAL 0.2487
## SINGAPORE POLYTECHNIC 0.4152
## SOMERSET 0.7443
## SPRINGLEAF 0.6784
## STRAITS VIEW 0.0274
## SUNGEI ROAD 0.1912
## SUNSET WAY 0.5175
## SWISS CLUB 0.2225
## TAGORE 0.5617
## TAI SENG 0.5096
## TAMAN JURONG 0.1043
## TAMPINES EAST 0.0000
## TAMPINES NORTH 0.8818
## TAMPINES WEST 0.0000
## TANGLIN 0.0691
## TANGLIN HALT 0.3315
## TANJONG PAGAR 0.0208
## TANJONG RHU 0.3257
## TEBAN GARDENS 0.4957
## TECK WHYE 0.4896
## TELOK BLANGAH DRIVE 0.5033
## TELOK BLANGAH RISE 0.3955
## TELOK BLANGAH WAY 0.3608
## TENGAH 0.9715
## TENGEH 0.4064
## THE WHARVES 0.9605
## TIONG BAHRU 0.2362
## TIONG BAHRU STATION 0.9134
## TOA PAYOH CENTRAL 0.9473
## TOA PAYOH WEST 0.5211
## TOH GUAN 0.4949
## TOH TUCK 0.5409
## TOWNSVILLE 0.4429
## TRAFALGAR 0.0134
## TUAS BAY 0.4129
## TUAS NORTH 0.4112
## TUAS PROMENADE 0.4177
## TUAS VIEW 0.2731
## TUAS VIEW EXTENSION 0.2159
## TUKANG 0.7284
## TURF CLUB 0.6525
## TYERSALL 0.1987
## ULU PANDAN 0.3104
## UPPER PAYA LEBAR 0.5563
## UPPER THOMSON 0.2590
## VICTORIA 0.7264
## WATERWAY EAST 0.6125
## WENYA 0.7687
## WEST COAST 0.5479
## WESTERN WATER CATCHMENT 0.3934
## WOODGROVE 0.4420
## WOODLANDS EAST 0.0023
## WOODLANDS REGIONAL CENTRE 0.4913
## WOODLANDS SOUTH 0.3914
## WOODLANDS WEST 0.4045
## WOODLEIGH 0.7570
## XILIN 0.9581
## YEW TEE 0.5459
## YIO CHU KANG 0.4028
## YIO CHU KANG EAST 0.7306
## YIO CHU KANG NORTH 0.6463
## YIO CHU KANG WEST 0.4963
## YISHUN CENTRAL 0.5795
## YISHUN EAST 0.6959
## YISHUN SOUTH 0.4430
## YISHUN WEST 0.5052
## YUHUA EAST 0.4573
## YUHUA WEST 0.3029
## YUNNAN 0.7448Mapping the local Moran’s I
final_q2.localMI_tapin <- cbind(final_q2,localMI_tapin)Mapping both local Moran’s I values and p-values (Tapin)
localMI_tapin.map <- tm_shape(final_q2.localMI_tapin) +
tm_fill(col = "Ii",
style = "pretty",
title = "local moran statistics") +
tm_borders(alpha = 0.5)
P_value_tapin.map <- tm_shape(final_q2.localMI_tapin) +
tm_fill(col = "Pr.z...0.",
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_tapin.map, P_value_tapin.map, asp=1, ncol=2)## Warning: The shape final_q2.localMI_tapin is invalid. See sf::st_is_valid## Variable "Ii" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Warning: The shape final_q2.localMI_tapin is invalid. See sf::st_is_valid
Creating a LISA Cluster Map
nci <- moran.plot(final_q2$TOTAL_TAP_IN_VOLUME, rswm_knn25, labels=as.character(final_q2$SUBZONE_N), xlab="TOTAL_TAP_IN_VOLUME", ylab="Spatially Lag TOTAL_TAP_IN_VOLUME")
Plotting Moran scatterplot with standardised variable
final_q2$Z.TOTAL_TAP_IN_VOLUME <- scale(final_q2$TOTAL_TAP_IN_VOLUME) %>% as.vectorPlot Moran scatterplot again
as.vector() is added to the end ensuring data type obtained in out of the vector
nci2 <- moran.plot(final_q2$Z.TOTAL_TAP_IN_VOLUME, rswm_knn25, labels=as.character(final_q2$SUBZONE_N), xlab="z-TOTAL_TAP_IN_VOLUME", ylab="Spatially Lag z-TOTAL_TAP_IN_VOLUME")
Steps to prepare a LISA cluster map
quadrant <- vector(mode="numeric",length=nrow(localMI_tapin))##Center the variable of interest around its mean
DV <- final_q2$TOTAL_TAP_IN_VOLUME - mean(final_q2$TOTAL_TAP_IN_VOLUME) Center the local Moran’s around the mean
C_mI <- localMI_tapin[,1] - mean(localMI_tapin[,1]) Setting satistical significance level for the local Moran
signif <- 0.054 types of commands defining ; High-high, low-low, low-high, high-low categories
quadrant[DV >0 & C_mI>0] <- 4
quadrant[DV <0 & C_mI<0] <- 1
quadrant[DV <0 & C_mI>0] <- 2
quadrant[DV >0 & C_mI<0] <- 3Placing non-significant Moran in the category 0
quadrant[localMI_tapin[,5]>signif] <- 0Combining all the above steps into one single code chunk
quadrant <- vector(mode="numeric",length=nrow(localMI_tapin))
DV <- final_q2$TOTAL_TAP_IN_VOLUME - mean(final_q2$TOTAL_TAP_IN_VOLUME)
C_mI <- localMI_tapin[,1] - mean(localMI_tapin[,1])
signif <- 0.05
quadrant[DV >0 & C_mI>0] <- 4
quadrant[DV <0 & C_mI<0] <- 1
quadrant[DV <0 & C_mI>0] <- 2
quadrant[DV >0 & C_mI<0] <- 3
quadrant[localMI_tapin[,5]>signif] <- 0Building the LISA map
Based on the LISA map, we can see several clusters which primarily align with the initial observation of Local Moran’s I scores. However, it is also evident that we see certain subzones in the north-east and west that fall within the High-High quadrants which indicates a positive auto-correlation with neighbouring and a small portion in the central region falling into the low-high quadrant also indicating a positive auto-correlation but is relatively weaker as compared to the regions in the high-high quadrants.
final_q2.localMI_tapin$quadrant <- quadrant
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high")
tm_shape(final_q2.localMI_tapin) +
tm_fill(col = "quadrant", style = "cat", palette = colors[c(sort(unique(quadrant)))+1], labels = clusters[c(sort(unique(quadrant)))+1], popup.vars = c("Postal.Code")) +
tm_view(set.zoom.limits = c(11,17)) +
tm_borders(alpha=0.5)## Warning: The shape final_q2.localMI_tapin is invalid. See sf::st_is_valid
Computing local Moran I
fips <- order(final_q2$SUBZONE_N)
localMI_tapout <- localmoran(final_q2$TOTAL_TAP_OUT_VOLUME,rswm_knn25)
head(localMI_tapout)## Ii E.Ii Var.Ii Z.Ii Pr(z > 0)
## 1 -0.11927615 -0.003289474 0.03513481 -0.6187843 0.7319708
## 2 -0.16022262 -0.003289474 0.03513481 -0.8372321 0.7987689
## 3 -0.12874399 -0.003289474 0.03513481 -0.6692948 0.7483463
## 4 0.18223529 -0.003289474 0.03513481 0.9897672 0.1611440
## 5 -0.28043986 -0.003289474 0.03513481 -1.4785862 0.9303745
## 6 -0.05630789 -0.003289474 0.03513481 -0.2828511 0.6113545Code chunk that lists the content of local Moran matrix derived by using printCoefmat()
printCoefmat(data.frame(localMI_tapout[fips,],row.names = final_q2$SUBZONE_N[fips]), check.names =FALSE)## Ii E.Ii Var.Ii Z.Ii
## ADMIRALTY -1.1928e-01 -3.2895e-03 3.5135e-02 -6.1878e-01
## AIRPORT ROAD -1.6022e-01 -3.2895e-03 3.5135e-02 -8.3723e-01
## ALEXANDRA HILL -1.2874e-01 -3.2895e-03 3.5135e-02 -6.6929e-01
## ALEXANDRA NORTH 1.8224e-01 -3.2895e-03 3.5135e-02 9.8977e-01
## ALJUNIED -2.8044e-01 -3.2895e-03 3.5135e-02 -1.4786e+00
## ANAK BUKIT -5.6308e-02 -3.2895e-03 3.5135e-02 -2.8285e-01
## ANCHORVALE 3.4385e-02 -3.2895e-03 3.5135e-02 2.0099e-01
## ANG MO KIO TOWN CENTRE 1.6175e-01 -3.2895e-03 3.5135e-02 8.8046e-01
## ANSON 3.1644e-01 -3.2895e-03 3.5135e-02 1.7058e+00
## BALESTIER -3.0532e-01 -3.2895e-03 3.5135e-02 -1.6113e+00
## BANGKIT 8.2216e-03 -3.2895e-03 3.5135e-02 6.1411e-02
## BAYFRONT SUBZONE 3.1579e-01 -3.2895e-03 3.5135e-02 1.7023e+00
## BAYSHORE -6.0856e-01 -3.2895e-03 3.5135e-02 -3.2291e+00
## BEDOK NORTH 3.6560e+00 -3.2895e-03 3.5135e-02 1.9522e+01
## BEDOK RESERVOIR 2.6590e-01 -3.2895e-03 3.5135e-02 1.4361e+00
## BEDOK SOUTH 9.9802e-01 -3.2895e-03 3.5135e-02 5.3419e+00
## BENCOOLEN 2.4764e-01 -3.2895e-03 3.5135e-02 1.3387e+00
## BENDEMEER -7.2083e-02 -3.2895e-03 3.5135e-02 -3.6701e-01
## BENOI SECTOR 2.7601e-02 -3.2895e-03 3.5135e-02 1.6480e-01
## BIDADARI -5.2609e-02 -3.2895e-03 3.5135e-02 -2.6312e-01
## BISHAN EAST 4.2443e-01 -3.2895e-03 3.5135e-02 2.2819e+00
## BOAT QUAY 2.6157e-01 -3.2895e-03 3.5135e-02 1.4130e+00
## BOON KENG 3.6243e-03 -3.2895e-03 3.5135e-02 3.6885e-02
## BOON LAY PLACE 1.2516e-01 -3.2895e-03 3.5135e-02 6.8527e-01
## BOON TECK -2.1001e-02 -3.2895e-03 3.5135e-02 -9.4492e-02
## BOULEVARD -5.2046e-01 -3.2895e-03 3.5135e-02 -2.7591e+00
## BRADDELL -6.2529e-02 -3.2895e-03 3.5135e-02 -3.1604e-01
## BRAS BASAH 9.9563e-02 -3.2895e-03 3.5135e-02 5.4871e-01
## BRICKWORKS -4.2124e-02 -3.2895e-03 3.5135e-02 -2.0718e-01
## BUGIS -6.5870e-02 -3.2895e-03 3.5135e-02 -3.3387e-01
## BUKIT BATOK CENTRAL 1.8634e-02 -3.2895e-03 3.5135e-02 1.1696e-01
## BUKIT BATOK EAST -1.5096e-02 -3.2895e-03 3.5135e-02 -6.2987e-02
## BUKIT BATOK SOUTH -3.0059e-03 -3.2895e-03 3.5135e-02 1.5126e-03
## BUKIT BATOK WEST -2.9130e-02 -3.2895e-03 3.5135e-02 -1.3786e-01
## BUKIT HO SWEE 1.2455e-01 -3.2895e-03 3.5135e-02 6.8204e-01
## BUKIT MERAH -1.2720e-02 -3.2895e-03 3.5135e-02 -5.0312e-02
## CECIL 2.6083e-01 -3.2895e-03 3.5135e-02 1.4091e+00
## CENTRAL SUBZONE 2.4721e-01 -3.2895e-03 3.5135e-02 1.3364e+00
## CENTRAL WATER CATCHMENT 3.8559e-02 -3.2895e-03 3.5135e-02 2.2326e-01
## CHANGI AIRPORT 5.7924e-01 -3.2895e-03 3.5135e-02 3.1078e+00
## CHANGI POINT -3.6230e-01 -3.2895e-03 3.5135e-02 -1.9153e+00
## CHANGI WEST -2.9606e-01 -3.2895e-03 3.5135e-02 -1.5619e+00
## CHATSWORTH 1.1162e-01 -3.2895e-03 3.5135e-02 6.1306e-01
## CHENG SAN 1.7260e-01 -3.2895e-03 3.5135e-02 9.3837e-01
## CHIN BEE -1.2104e-01 -3.2895e-03 3.5135e-02 -6.2819e-01
## CHINA SQUARE 2.2323e-01 -3.2895e-03 3.5135e-02 1.2085e+00
## CHINATOWN -1.9429e-02 -3.2895e-03 3.5135e-02 -8.6103e-02
## CHOA CHU KANG CENTRAL -5.2579e-02 -3.2895e-03 3.5135e-02 -2.6296e-01
## CHOA CHU KANG NORTH -5.1266e-05 -3.2895e-03 3.5135e-02 1.7276e-02
## CHONG BOON 1.7638e-01 -3.2895e-03 3.5135e-02 9.5854e-01
## CITY HALL -3.1880e-03 -3.2895e-03 3.5135e-02 5.4115e-04
## CITY TERMINALS 2.3567e-01 -3.2895e-03 3.5135e-02 1.2749e+00
## CLARKE QUAY 2.2080e-01 -3.2895e-03 3.5135e-02 1.1955e+00
## CLEMENTI CENTRAL -2.7299e-01 -3.2895e-03 3.5135e-02 -1.4389e+00
## CLEMENTI NORTH -8.4517e-02 -3.2895e-03 3.5135e-02 -4.3335e-01
## CLEMENTI WEST 3.0193e-03 -3.2895e-03 3.5135e-02 3.3657e-02
## CLEMENTI WOODS -2.7648e-03 -3.2895e-03 3.5135e-02 2.7990e-03
## CLIFFORD PIER 2.8709e-01 -3.2895e-03 3.5135e-02 1.5492e+00
## COMMONWEALTH 1.4189e-01 -3.2895e-03 3.5135e-02 7.7455e-01
## COMPASSVALE -2.9560e-02 -3.2895e-03 3.5135e-02 -1.4015e-01
## CORONATION ROAD 1.4596e-01 -3.2895e-03 3.5135e-02 7.9625e-01
## CRAWFORD 7.1620e-02 -3.2895e-03 3.5135e-02 3.9964e-01
## DAIRY FARM -5.0279e-02 -3.2895e-03 3.5135e-02 -2.5069e-01
## DEFU INDUSTRIAL PARK -6.1091e-02 -3.2895e-03 3.5135e-02 -3.0837e-01
## DEPOT ROAD 1.1457e-01 -3.2895e-03 3.5135e-02 6.2875e-01
## DHOBY GHAUT 1.9527e-02 -3.2895e-03 3.5135e-02 1.2173e-01
## DOVER 4.1791e-02 -3.2895e-03 3.5135e-02 2.4050e-01
## DUNEARN 1.4798e-01 -3.2895e-03 3.5135e-02 8.0702e-01
## EAST COAST -4.2261e-01 -3.2895e-03 3.5135e-02 -2.2371e+00
## EVERTON PARK 1.3778e-01 -3.2895e-03 3.5135e-02 7.5259e-01
## FABER -1.1074e-02 -3.2895e-03 3.5135e-02 -4.1528e-02
## FAJAR -3.2033e-03 -3.2895e-03 3.5135e-02 4.5954e-04
## FARRER COURT 2.5341e-01 -3.2895e-03 3.5135e-02 1.3695e+00
## FARRER PARK -3.5074e-02 -3.2895e-03 3.5135e-02 -1.6957e-01
## FERNVALE 3.4067e-02 -3.2895e-03 3.5135e-02 1.9929e-01
## FLORA DRIVE -2.4810e-01 -3.2895e-03 3.5135e-02 -1.3060e+00
## FORT CANNING 2.6962e-01 -3.2895e-03 3.5135e-02 1.4560e+00
## FRANKEL 9.2867e-01 -3.2895e-03 3.5135e-02 4.9719e+00
## GALI BATU -4.8720e-02 -3.2895e-03 3.5135e-02 -2.4237e-01
## GEYLANG BAHRU 6.7870e-03 -3.2895e-03 3.5135e-02 5.3758e-02
## GEYLANG EAST 1.9495e-01 -3.2895e-03 3.5135e-02 1.0576e+00
## GHIM MOH 9.1559e-02 -3.2895e-03 3.5135e-02 5.0601e-01
## GOMBAK -3.6072e-02 -3.2895e-03 3.5135e-02 -1.7489e-01
## GOODWOOD PARK 2.6345e-01 -3.2895e-03 3.5135e-02 1.4231e+00
## GREENWOOD PARK -1.0149e-01 -3.2895e-03 3.5135e-02 -5.2392e-01
## GUILIN -1.2011e-02 -3.2895e-03 3.5135e-02 -4.6527e-02
## GUL BASIN 5.2006e-02 -3.2895e-03 3.5135e-02 2.9500e-01
## GUL CIRCLE 5.0748e-02 -3.2895e-03 3.5135e-02 2.8829e-01
## HENDERSON HILL 2.6949e-02 -3.2895e-03 3.5135e-02 1.6132e-01
## HILLCREST 2.0355e-01 -3.2895e-03 3.5135e-02 1.1035e+00
## HILLVIEW -1.0130e-02 -3.2895e-03 3.5135e-02 -3.6496e-02
## HOLLAND DRIVE 1.0280e-01 -3.2895e-03 3.5135e-02 5.6599e-01
## HOLLAND ROAD -1.9487e-02 -3.2895e-03 3.5135e-02 -8.6414e-02
## HONG KAH 4.9819e-01 -3.2895e-03 3.5135e-02 2.6754e+00
## HONG KAH NORTH 9.3067e-05 -3.2895e-03 3.5135e-02 1.8046e-02
## HOUGANG CENTRAL 3.0676e-01 -3.2895e-03 3.5135e-02 1.6541e+00
## HOUGANG EAST 3.5817e-03 -3.2895e-03 3.5135e-02 3.6657e-02
## HOUGANG WEST 2.9687e-01 -3.2895e-03 3.5135e-02 1.6013e+00
## INSTITUTION HILL 2.5583e-01 -3.2895e-03 3.5135e-02 1.3824e+00
## INTERNATIONAL BUSINESS PARK -9.4105e-02 -3.2895e-03 3.5135e-02 -4.8450e-01
## ISTANA NEGARA 3.0259e-01 -3.2895e-03 3.5135e-02 1.6319e+00
## JELEBU 4.5374e-03 -3.2895e-03 3.5135e-02 4.1756e-02
## JOO KOON 1.3272e-03 -3.2895e-03 3.5135e-02 2.4630e-02
## JOO SENG -8.1733e-02 -3.2895e-03 3.5135e-02 -4.1849e-01
## JURONG GATEWAY 1.4383e-01 -3.2895e-03 3.5135e-02 7.8486e-01
## JURONG PORT -1.0934e-01 -3.2895e-03 3.5135e-02 -5.6575e-01
## JURONG RIVER -1.5861e-01 -3.2895e-03 3.5135e-02 -8.2863e-01
## JURONG WEST CENTRAL -2.3749e-01 -3.2895e-03 3.5135e-02 -1.2494e+00
## KAKI BUKIT 7.2933e-01 -3.2895e-03 3.5135e-02 3.9085e+00
## KALLANG BAHRU -9.6846e-04 -3.2895e-03 3.5135e-02 1.2382e-02
## KALLANG WAY -9.3287e-02 -3.2895e-03 3.5135e-02 -4.8014e-01
## KAMPONG BUGIS 6.3161e-02 -3.2895e-03 3.5135e-02 3.5451e-01
## KAMPONG GLAM 2.3283e-01 -3.2895e-03 3.5135e-02 1.2597e+00
## KAMPONG JAVA 7.8659e-02 -3.2895e-03 3.5135e-02 4.3719e-01
## KAMPONG TIONG BAHRU 7.0648e-02 -3.2895e-03 3.5135e-02 3.9445e-01
## KAMPONG UBI 1.8059e-01 -3.2895e-03 3.5135e-02 9.8100e-01
## KANGKAR 4.3608e-02 -3.2895e-03 3.5135e-02 2.5020e-01
## KATONG -7.8443e-02 -3.2895e-03 3.5135e-02 -4.0094e-01
## KEAT HONG 4.2198e-02 -3.2895e-03 3.5135e-02 2.4267e-01
## KEBUN BAHRU -3.0820e-03 -3.2895e-03 3.5135e-02 1.1071e-03
## KEMBANGAN 5.0834e-01 -3.2895e-03 3.5135e-02 2.7295e+00
## KENT RIDGE 1.3989e-01 -3.2895e-03 3.5135e-02 7.6388e-01
## KHATIB 7.2276e-02 -3.2895e-03 3.5135e-02 4.0314e-01
## KIAN TECK -3.9615e-02 -3.2895e-03 3.5135e-02 -1.9380e-01
## KIM KEAT -1.0823e-01 -3.2895e-03 3.5135e-02 -5.5985e-01
## KOVAN 3.4720e-02 -3.2895e-03 3.5135e-02 2.0278e-01
## KRANJI -7.2599e-02 -3.2895e-03 3.5135e-02 -3.6976e-01
## LAKESIDE -7.7179e-02 -3.2895e-03 3.5135e-02 -3.9420e-01
## LAVENDER -9.0353e-02 -3.2895e-03 3.5135e-02 -4.6448e-01
## LEEDON PARK 1.8518e-01 -3.2895e-03 3.5135e-02 1.0055e+00
## LEONIE HILL 2.9949e-01 -3.2895e-03 3.5135e-02 1.6153e+00
## LIM CHU KANG -1.6761e-01 -3.2895e-03 3.5135e-02 -8.7666e-01
## LITTLE INDIA 2.3891e-01 -3.2895e-03 3.5135e-02 1.2921e+00
## LIU FANG -8.4230e-02 -3.2895e-03 3.5135e-02 -4.3181e-01
## LORONG 8 TOA PAYOH -3.9111e-02 -3.2895e-03 3.5135e-02 -1.9110e-01
## LORONG AH SOO 4.8096e-02 -3.2895e-03 3.5135e-02 2.7414e-01
## LORONG CHUAN -1.9591e-01 -3.2895e-03 3.5135e-02 -1.0276e+00
## LORONG HALUS -2.1889e-01 -3.2895e-03 3.5135e-02 -1.1502e+00
## LOWER SELETAR -3.3564e-02 -3.2895e-03 3.5135e-02 -1.6151e-01
## LOYANG EAST -4.3647e-01 -3.2895e-03 3.5135e-02 -2.3110e+00
## LOYANG WEST -3.0489e-01 -3.2895e-03 3.5135e-02 -1.6090e+00
## MACKENZIE 1.9685e-01 -3.2895e-03 3.5135e-02 1.0678e+00
## MACPHERSON 5.4115e-02 -3.2895e-03 3.5135e-02 3.0625e-01
## MALCOLM 8.6808e-02 -3.2895e-03 3.5135e-02 4.8067e-01
## MANDAI EAST -2.1330e-01 -3.2895e-03 3.5135e-02 -1.1204e+00
## MANDAI ESTATE -1.0054e-01 -3.2895e-03 3.5135e-02 -5.1882e-01
## MANDAI WEST -1.0987e-01 -3.2895e-03 3.5135e-02 -5.6860e-01
## MARGARET DRIVE 1.0862e-01 -3.2895e-03 3.5135e-02 5.9706e-01
## MARINA CENTRE 1.6958e-01 -3.2895e-03 3.5135e-02 9.2226e-01
## MARINA EAST (MP) 7.3665e-02 -3.2895e-03 3.5135e-02 4.1055e-01
## MARINA SOUTH 3.9794e-01 -3.2895e-03 3.5135e-02 2.1405e+00
## MARINE PARADE 3.8075e-01 -3.2895e-03 3.5135e-02 2.0488e+00
## MARITIME SQUARE -2.8045e-01 -3.2895e-03 3.5135e-02 -1.4786e+00
## MARYMOUNT 1.2889e-01 -3.2895e-03 3.5135e-02 7.0518e-01
## MATILDA 4.4216e-02 -3.2895e-03 3.5135e-02 2.5344e-01
## MAXWELL 3.9551e-01 -3.2895e-03 3.5135e-02 2.1276e+00
## MEI CHIN 3.1479e-02 -3.2895e-03 3.5135e-02 1.8549e-01
## MIDVIEW 4.8578e-02 -3.2895e-03 3.5135e-02 2.7671e-01
## MONK'S HILL 3.5143e-01 -3.2895e-03 3.5135e-02 1.8924e+00
## MOULMEIN -3.1067e-02 -3.2895e-03 3.5135e-02 -1.4819e-01
## MOUNT PLEASANT 1.5414e-02 -3.2895e-03 3.5135e-02 9.9782e-02
## MOUNTBATTEN -7.5838e-02 -3.2895e-03 3.5135e-02 -3.8705e-01
## NASSIM 1.6619e-01 -3.2895e-03 3.5135e-02 9.0416e-01
## NATIONAL UNIVERSITY OF S'PORE 7.6971e-02 -3.2895e-03 3.5135e-02 4.2819e-01
## NATURE RESERVE 2.3068e-02 -3.2895e-03 3.5135e-02 1.4062e-01
## NEE SOON -1.5075e-01 -3.2895e-03 3.5135e-02 -7.8670e-01
## NEWTON CIRCUS 1.5878e-01 -3.2895e-03 3.5135e-02 8.6464e-01
## NORTH COAST 1.3222e-01 -3.2895e-03 3.5135e-02 7.2293e-01
## NORTHLAND 2.6611e-02 -3.2895e-03 3.5135e-02 1.5952e-01
## NORTHSHORE -9.5402e-02 -3.2895e-03 3.5135e-02 -4.9142e-01
## ONE NORTH 5.6333e-03 -3.2895e-03 3.5135e-02 4.7603e-02
## ONE TREE HILL 2.6500e-01 -3.2895e-03 3.5135e-02 1.4313e+00
## ORANGE GROVE 3.5859e-01 -3.2895e-03 3.5135e-02 1.9306e+00
## OXLEY 3.1692e-01 -3.2895e-03 3.5135e-02 1.7083e+00
## PANDAN 2.8646e-02 -3.2895e-03 3.5135e-02 1.7038e-01
## PANG SUA -1.8401e-01 -3.2895e-03 3.5135e-02 -9.6411e-01
## PASIR PANJANG 1 1.8847e-02 -3.2895e-03 3.5135e-02 1.1810e-01
## PASIR PANJANG 2 9.1049e-02 -3.2895e-03 3.5135e-02 5.0329e-01
## PASIR RIS CENTRAL 6.9566e-01 -3.2895e-03 3.5135e-02 3.7289e+00
## PASIR RIS DRIVE 6.0658e-01 -3.2895e-03 3.5135e-02 3.2536e+00
## PASIR RIS PARK -2.6010e-01 -3.2895e-03 3.5135e-02 -1.3701e+00
## PASIR RIS WAFER FAB PARK -3.5270e-01 -3.2895e-03 3.5135e-02 -1.8641e+00
## PASIR RIS WEST 1.5912e-01 -3.2895e-03 3.5135e-02 8.6645e-01
## PATERSON 2.8224e-01 -3.2895e-03 3.5135e-02 1.5233e+00
## PAYA LEBAR EAST -6.9401e-01 -3.2895e-03 3.5135e-02 -3.6850e+00
## PAYA LEBAR NORTH -3.5063e-01 -3.2895e-03 3.5135e-02 -1.8531e+00
## PAYA LEBAR WEST -2.7189e-01 -3.2895e-03 3.5135e-02 -1.4330e+00
## PEARL'S HILL 1.6397e-01 -3.2895e-03 3.5135e-02 8.9233e-01
## PEI CHUN -4.3184e-02 -3.2895e-03 3.5135e-02 -2.1283e-01
## PENG SIANG 2.1800e-02 -3.2895e-03 3.5135e-02 1.3385e-01
## PENJURU CRESCENT 5.5902e-02 -3.2895e-03 3.5135e-02 3.1578e-01
## PEOPLE'S PARK 5.4849e-02 -3.2895e-03 3.5135e-02 3.1017e-01
## PHILLIP 3.4500e-01 -3.2895e-03 3.5135e-02 1.8581e+00
## PIONEER SECTOR 6.6780e-02 -3.2895e-03 3.5135e-02 3.7382e-01
## PLAB -1.9137e-01 -3.2895e-03 3.5135e-02 -1.0034e+00
## PORT 5.5353e-02 -3.2895e-03 3.5135e-02 3.1286e-01
## POTONG PASIR -3.2930e-02 -3.2895e-03 3.5135e-02 -1.5813e-01
## PUNGGOL FIELD 7.2965e-02 -3.2895e-03 3.5135e-02 4.0682e-01
## PUNGGOL TOWN CENTRE -7.1078e-02 -3.2895e-03 3.5135e-02 -3.6165e-01
## QUEENSWAY 1.1448e-01 -3.2895e-03 3.5135e-02 6.2830e-01
## RAFFLES PLACE 3.2904e-01 -3.2895e-03 3.5135e-02 1.7730e+00
## REDHILL 3.1603e-02 -3.2895e-03 3.5135e-02 1.8615e-01
## RESERVOIR VIEW -2.5623e-01 -3.2895e-03 3.5135e-02 -1.3494e+00
## RIDOUT 1.9106e-01 -3.2895e-03 3.5135e-02 1.0368e+00
## RIVERVALE 1.7558e-01 -3.2895e-03 3.5135e-02 9.5428e-01
## ROBERTSON QUAY 1.4402e-01 -3.2895e-03 3.5135e-02 7.8587e-01
## ROCHOR CANAL 2.1556e-01 -3.2895e-03 3.5135e-02 1.1676e+00
## SAFTI 2.8458e-02 -3.2895e-03 3.5135e-02 1.6937e-01
## SAMULUN -9.2070e-02 -3.2895e-03 3.5135e-02 -4.7364e-01
## SAUJANA 4.0771e-03 -3.2895e-03 3.5135e-02 3.9300e-02
## SELEGIE 2.5543e-01 -3.2895e-03 3.5135e-02 1.3802e+00
## SELETAR -1.0592e-01 -3.2895e-03 3.5135e-02 -5.4754e-01
## SELETAR AEROSPACE PARK -2.4430e-01 -3.2895e-03 3.5135e-02 -1.2858e+00
## SELETAR HILLS -1.1014e-01 -3.2895e-03 3.5135e-02 -5.7004e-01
## SEMBAWANG CENTRAL 2.8779e-01 -3.2895e-03 3.5135e-02 1.5529e+00
## SEMBAWANG EAST -9.5763e-02 -3.2895e-03 3.5135e-02 -4.9334e-01
## SEMBAWANG HILLS -6.0799e-03 -3.2895e-03 3.5135e-02 -1.4887e-02
## SEMBAWANG NORTH 3.4822e-02 -3.2895e-03 3.5135e-02 2.0332e-01
## SEMBAWANG SPRINGS -1.2366e-01 -3.2895e-03 3.5135e-02 -6.4219e-01
## SEMBAWANG STRAITS -2.2092e-01 -3.2895e-03 3.5135e-02 -1.1611e+00
## SENGKANG TOWN CENTRE 1.5057e-01 -3.2895e-03 3.5135e-02 8.2086e-01
## SENGKANG WEST -2.1003e-01 -3.2895e-03 3.5135e-02 -1.1030e+00
## SENJA -1.1620e-03 -3.2895e-03 3.5135e-02 1.1350e-02
## SENNETT -5.1194e-02 -3.2895e-03 3.5135e-02 -2.5557e-01
## SENOKO NORTH -1.7699e-01 -3.2895e-03 3.5135e-02 -9.2670e-01
## SENOKO SOUTH -1.9371e-01 -3.2895e-03 3.5135e-02 -1.0159e+00
## SENOKO WEST -1.3234e-01 -3.2895e-03 3.5135e-02 -6.8846e-01
## SENTOSA 2.1255e-01 -3.2895e-03 3.5135e-02 1.1515e+00
## SERANGOON CENTRAL 1.5141e-01 -3.2895e-03 3.5135e-02 8.2533e-01
## SERANGOON GARDEN 2.0765e-01 -3.2895e-03 3.5135e-02 1.1254e+00
## SERANGOON NORTH 8.3950e-02 -3.2895e-03 3.5135e-02 4.6542e-01
## SERANGOON NORTH IND ESTATE -2.3413e-01 -3.2895e-03 3.5135e-02 -1.2315e+00
## SHANGRI-LA 2.9334e-03 -3.2895e-03 3.5135e-02 3.3199e-02
## SHIPYARD 3.1057e-02 -3.2895e-03 3.5135e-02 1.8324e-01
## SIGLAP -5.8302e-01 -3.2895e-03 3.5135e-02 -3.0929e+00
## SIMEI 6.9193e-01 -3.2895e-03 3.5135e-02 3.7089e+00
## SINGAPORE GENERAL HOSPITAL 1.5536e-01 -3.2895e-03 3.5135e-02 8.4641e-01
## SINGAPORE POLYTECHNIC 6.4387e-02 -3.2895e-03 3.5135e-02 3.6105e-01
## SOMERSET -5.2027e-02 -3.2895e-03 3.5135e-02 -2.6001e-01
## SPRINGLEAF -7.5811e-02 -3.2895e-03 3.5135e-02 -3.8690e-01
## STRAITS VIEW 3.6763e-01 -3.2895e-03 3.5135e-02 1.9788e+00
## SUNGEI ROAD 1.6073e-01 -3.2895e-03 3.5135e-02 8.7503e-01
## SUNSET WAY -4.5548e-03 -3.2895e-03 3.5135e-02 -6.7503e-03
## SWISS CLUB 8.4766e-02 -3.2895e-03 3.5135e-02 4.6977e-01
## TAGORE -3.3839e-02 -3.2895e-03 3.5135e-02 -1.6298e-01
## TAI SENG -4.3260e-02 -3.2895e-03 3.5135e-02 -2.1324e-01
## TAMAN JURONG 2.8748e-01 -3.2895e-03 3.5135e-02 1.5512e+00
## TAMPINES EAST 2.0744e+00 -3.2895e-03 3.5135e-02 1.1084e+01
## TAMPINES NORTH -3.0958e-01 -3.2895e-03 3.5135e-02 -1.6341e+00
## TAMPINES WEST 1.4984e+00 -3.2895e-03 3.5135e-02 8.0112e+00
## TANGLIN 3.0768e-01 -3.2895e-03 3.5135e-02 1.6590e+00
## TANGLIN HALT 4.8761e-02 -3.2895e-03 3.5135e-02 2.7769e-01
## TANJONG PAGAR 4.0191e-01 -3.2895e-03 3.5135e-02 2.1617e+00
## TANJONG RHU 8.2306e-02 -3.2895e-03 3.5135e-02 4.5665e-01
## TEBAN GARDENS -4.6511e-03 -3.2895e-03 3.5135e-02 -7.2642e-03
## TECK WHYE 1.2530e-03 -3.2895e-03 3.5135e-02 2.4234e-02
## TELOK BLANGAH DRIVE -4.3171e-02 -3.2895e-03 3.5135e-02 -2.1277e-01
## TELOK BLANGAH RISE 4.7726e-02 -3.2895e-03 3.5135e-02 2.7216e-01
## TELOK BLANGAH WAY 7.9882e-02 -3.2895e-03 3.5135e-02 4.4372e-01
## TENGAH -3.2328e-01 -3.2895e-03 3.5135e-02 -1.7072e+00
## TENGEH 3.4907e-02 -3.2895e-03 3.5135e-02 2.0378e-01
## THE WHARVES -3.8811e-01 -3.2895e-03 3.5135e-02 -2.0530e+00
## TIONG BAHRU 1.1736e-01 -3.2895e-03 3.5135e-02 6.4364e-01
## TIONG BAHRU STATION -2.2719e-01 -3.2895e-03 3.5135e-02 -1.1945e+00
## TOA PAYOH CENTRAL -2.9261e-01 -3.2895e-03 3.5135e-02 -1.5435e+00
## TOA PAYOH WEST -1.9386e-02 -3.2895e-03 3.5135e-02 -8.5875e-02
## TOH GUAN 4.7986e-03 -3.2895e-03 3.5135e-02 4.3150e-02
## TOH TUCK -1.4962e-02 -3.2895e-03 3.5135e-02 -6.2274e-02
## TOWNSVILLE -1.7157e-02 -3.2895e-03 3.5135e-02 -7.3981e-02
## TRAFALGAR 3.8735e-01 -3.2895e-03 3.5135e-02 2.0841e+00
## TUAS BAY 3.1755e-02 -3.2895e-03 3.5135e-02 1.8696e-01
## TUAS NORTH 3.3950e-02 -3.2895e-03 3.5135e-02 1.9867e-01
## TUAS PROMENADE 3.4058e-02 -3.2895e-03 3.5135e-02 1.9925e-01
## TUAS VIEW 8.7543e-02 -3.2895e-03 3.5135e-02 4.8459e-01
## TUAS VIEW EXTENSION 1.4072e-01 -3.2895e-03 3.5135e-02 7.6829e-01
## TUKANG -1.2021e-01 -3.2895e-03 3.5135e-02 -6.2379e-01
## TURF CLUB -5.9972e-02 -3.2895e-03 3.5135e-02 -3.0240e-01
## TYERSALL 2.1779e-01 -3.2895e-03 3.5135e-02 1.1794e+00
## ULU PANDAN 8.4328e-02 -3.2895e-03 3.5135e-02 4.6744e-01
## UPPER PAYA LEBAR -9.9034e-03 -3.2895e-03 3.5135e-02 -3.5285e-02
## UPPER THOMSON 1.2413e-01 -3.2895e-03 3.5135e-02 6.7977e-01
## VICTORIA -3.6845e-02 -3.2895e-03 3.5135e-02 -1.7902e-01
## WATERWAY EAST -4.2655e-02 -3.2895e-03 3.5135e-02 -2.1001e-01
## WENYA -1.4701e-01 -3.2895e-03 3.5135e-02 -7.6676e-01
## WEST COAST -1.0187e-02 -3.2895e-03 3.5135e-02 -3.6800e-02
## WESTERN WATER CATCHMENT 7.2711e-02 -3.2895e-03 3.5135e-02 4.0546e-01
## WOODGROVE -2.8072e-03 -3.2895e-03 3.5135e-02 2.5730e-03
## WOODLANDS EAST 6.2269e-01 -3.2895e-03 3.5135e-02 3.3396e+00
## WOODLANDS REGIONAL CENTRE 2.3189e-02 -3.2895e-03 3.5135e-02 1.4126e-01
## WOODLANDS SOUTH 4.6003e-02 -3.2895e-03 3.5135e-02 2.6297e-01
## WOODLANDS WEST 4.0117e-02 -3.2895e-03 3.5135e-02 2.3157e-01
## WOODLEIGH -1.1495e-01 -3.2895e-03 3.5135e-02 -5.9569e-01
## XILIN -3.0509e-01 -3.2895e-03 3.5135e-02 -1.6101e+00
## YEW TEE -2.4775e-02 -3.2895e-03 3.5135e-02 -1.1462e-01
## YIO CHU KANG 3.7322e-02 -3.2895e-03 3.5135e-02 2.1666e-01
## YIO CHU KANG EAST -9.9311e-02 -3.2895e-03 3.5135e-02 -5.1227e-01
## YIO CHU KANG NORTH -8.9809e-02 -3.2895e-03 3.5135e-02 -4.6158e-01
## YIO CHU KANG WEST -9.1861e-03 -3.2895e-03 3.5135e-02 -3.1458e-02
## YISHUN CENTRAL -4.0080e-02 -3.2895e-03 3.5135e-02 -1.9628e-01
## YISHUN EAST -8.1168e-02 -3.2895e-03 3.5135e-02 -4.1548e-01
## YISHUN SOUTH 3.3359e-02 -3.2895e-03 3.5135e-02 1.9552e-01
## YISHUN WEST 3.7468e-02 -3.2895e-03 3.5135e-02 2.1744e-01
## YUHUA EAST 2.4898e-02 -3.2895e-03 3.5135e-02 1.5038e-01
## YUHUA WEST 8.6845e-02 -3.2895e-03 3.5135e-02 4.8087e-01
## YUNNAN -1.0089e-01 -3.2895e-03 3.5135e-02 -5.2071e-01
## Pr.z...0.
## ADMIRALTY 0.7320
## AIRPORT ROAD 0.7988
## ALEXANDRA HILL 0.7483
## ALEXANDRA NORTH 0.1611
## ALJUNIED 0.9304
## ANAK BUKIT 0.6114
## ANCHORVALE 0.4204
## ANG MO KIO TOWN CENTRE 0.1893
## ANSON 0.0440
## BALESTIER 0.9464
## BANGKIT 0.4755
## BAYFRONT SUBZONE 0.0444
## BAYSHORE 0.9994
## BEDOK NORTH 0.0000
## BEDOK RESERVOIR 0.0755
## BEDOK SOUTH 0.0000
## BENCOOLEN 0.0903
## BENDEMEER 0.6432
## BENOI SECTOR 0.4346
## BIDADARI 0.6038
## BISHAN EAST 0.0112
## BOAT QUAY 0.0788
## BOON KENG 0.4853
## BOON LAY PLACE 0.2466
## BOON TECK 0.5376
## BOULEVARD 0.9971
## BRADDELL 0.6240
## BRAS BASAH 0.2916
## BRICKWORKS 0.5821
## BUGIS 0.6308
## BUKIT BATOK CENTRAL 0.4534
## BUKIT BATOK EAST 0.5251
## BUKIT BATOK SOUTH 0.4994
## BUKIT BATOK WEST 0.5548
## BUKIT HO SWEE 0.2476
## BUKIT MERAH 0.5201
## CECIL 0.0794
## CENTRAL SUBZONE 0.0907
## CENTRAL WATER CATCHMENT 0.4117
## CHANGI AIRPORT 0.0009
## CHANGI POINT 0.9723
## CHANGI WEST 0.9408
## CHATSWORTH 0.2699
## CHENG SAN 0.1740
## CHIN BEE 0.7351
## CHINA SQUARE 0.1134
## CHINATOWN 0.5343
## CHOA CHU KANG CENTRAL 0.6037
## CHOA CHU KANG NORTH 0.4931
## CHONG BOON 0.1689
## CITY HALL 0.4998
## CITY TERMINALS 0.1012
## CLARKE QUAY 0.1159
## CLEMENTI CENTRAL 0.9249
## CLEMENTI NORTH 0.6676
## CLEMENTI WEST 0.4866
## CLEMENTI WOODS 0.4989
## CLIFFORD PIER 0.0607
## COMMONWEALTH 0.2193
## COMPASSVALE 0.5557
## CORONATION ROAD 0.2129
## CRAWFORD 0.3447
## DAIRY FARM 0.5990
## DEFU INDUSTRIAL PARK 0.6211
## DEPOT ROAD 0.2648
## DHOBY GHAUT 0.4516
## DOVER 0.4050
## DUNEARN 0.2098
## EAST COAST 0.9874
## EVERTON PARK 0.2258
## FABER 0.5166
## FAJAR 0.4998
## FARRER COURT 0.0854
## FARRER PARK 0.5673
## FERNVALE 0.4210
## FLORA DRIVE 0.9042
## FORT CANNING 0.0727
## FRANKEL 0.0000
## GALI BATU 0.5958
## GEYLANG BAHRU 0.4786
## GEYLANG EAST 0.1451
## GHIM MOH 0.3064
## GOMBAK 0.5694
## GOODWOOD PARK 0.0774
## GREENWOOD PARK 0.6998
## GUILIN 0.5186
## GUL BASIN 0.3840
## GUL CIRCLE 0.3866
## HENDERSON HILL 0.4359
## HILLCREST 0.1349
## HILLVIEW 0.5146
## HOLLAND DRIVE 0.2857
## HOLLAND ROAD 0.5344
## HONG KAH 0.0037
## HONG KAH NORTH 0.4928
## HOUGANG CENTRAL 0.0491
## HOUGANG EAST 0.4854
## HOUGANG WEST 0.0547
## INSTITUTION HILL 0.0834
## INTERNATIONAL BUSINESS PARK 0.6860
## ISTANA NEGARA 0.0514
## JELEBU 0.4833
## JOO KOON 0.4902
## JOO SENG 0.6622
## JURONG GATEWAY 0.2163
## JURONG PORT 0.7142
## JURONG RIVER 0.7963
## JURONG WEST CENTRAL 0.8942
## KAKI BUKIT 0.0000
## KALLANG BAHRU 0.4951
## KALLANG WAY 0.6844
## KAMPONG BUGIS 0.3615
## KAMPONG GLAM 0.1039
## KAMPONG JAVA 0.3310
## KAMPONG TIONG BAHRU 0.3466
## KAMPONG UBI 0.1633
## KANGKAR 0.4012
## KATONG 0.6558
## KEAT HONG 0.4041
## KEBUN BAHRU 0.4996
## KEMBANGAN 0.0032
## KENT RIDGE 0.2225
## KHATIB 0.3434
## KIAN TECK 0.5768
## KIM KEAT 0.7122
## KOVAN 0.4197
## KRANJI 0.6442
## LAKESIDE 0.6533
## LAVENDER 0.6788
## LEEDON PARK 0.1573
## LEONIE HILL 0.0531
## LIM CHU KANG 0.8097
## LITTLE INDIA 0.0982
## LIU FANG 0.6671
## LORONG 8 TOA PAYOH 0.5758
## LORONG AH SOO 0.3920
## LORONG CHUAN 0.8479
## LORONG HALUS 0.8750
## LOWER SELETAR 0.5642
## LOYANG EAST 0.9896
## LOYANG WEST 0.9462
## MACKENZIE 0.1428
## MACPHERSON 0.3797
## MALCOLM 0.3154
## MANDAI EAST 0.8687
## MANDAI ESTATE 0.6981
## MANDAI WEST 0.7152
## MARGARET DRIVE 0.2752
## MARINA CENTRE 0.1782
## MARINA EAST (MP) 0.3407
## MARINA SOUTH 0.0162
## MARINE PARADE 0.0202
## MARITIME SQUARE 0.9304
## MARYMOUNT 0.2404
## MATILDA 0.4000
## MAXWELL 0.0167
## MEI CHIN 0.4264
## MIDVIEW 0.3910
## MONK'S HILL 0.0292
## MOULMEIN 0.5589
## MOUNT PLEASANT 0.4603
## MOUNTBATTEN 0.6506
## NASSIM 0.1830
## NATIONAL UNIVERSITY OF S'PORE 0.3343
## NATURE RESERVE 0.4441
## NEE SOON 0.7843
## NEWTON CIRCUS 0.1936
## NORTH COAST 0.2349
## NORTHLAND 0.4366
## NORTHSHORE 0.6884
## ONE NORTH 0.4810
## ONE TREE HILL 0.0762
## ORANGE GROVE 0.0268
## OXLEY 0.0438
## PANDAN 0.4324
## PANG SUA 0.8325
## PASIR PANJANG 1 0.4530
## PASIR PANJANG 2 0.3074
## PASIR RIS CENTRAL 0.0001
## PASIR RIS DRIVE 0.0006
## PASIR RIS PARK 0.9147
## PASIR RIS WAFER FAB PARK 0.9688
## PASIR RIS WEST 0.1931
## PATERSON 0.0638
## PAYA LEBAR EAST 0.9999
## PAYA LEBAR NORTH 0.9681
## PAYA LEBAR WEST 0.9241
## PEARL'S HILL 0.1861
## PEI CHUN 0.5843
## PENG SIANG 0.4468
## PENJURU CRESCENT 0.3761
## PEOPLE'S PARK 0.3782
## PHILLIP 0.0316
## PIONEER SECTOR 0.3543
## PLAB 0.8422
## PORT 0.3772
## POTONG PASIR 0.5628
## PUNGGOL FIELD 0.3421
## PUNGGOL TOWN CENTRE 0.6412
## QUEENSWAY 0.2649
## RAFFLES PLACE 0.0381
## REDHILL 0.4262
## RESERVOIR VIEW 0.9114
## RIDOUT 0.1499
## RIVERVALE 0.1700
## ROBERTSON QUAY 0.2160
## ROCHOR CANAL 0.1215
## SAFTI 0.4328
## SAMULUN 0.6821
## SAUJANA 0.4843
## SELEGIE 0.0838
## SELETAR 0.7080
## SELETAR AEROSPACE PARK 0.9007
## SELETAR HILLS 0.7157
## SEMBAWANG CENTRAL 0.0602
## SEMBAWANG EAST 0.6891
## SEMBAWANG HILLS 0.5059
## SEMBAWANG NORTH 0.4194
## SEMBAWANG SPRINGS 0.7396
## SEMBAWANG STRAITS 0.8772
## SENGKANG TOWN CENTRE 0.2059
## SENGKANG WEST 0.8650
## SENJA 0.4955
## SENNETT 0.6009
## SENOKO NORTH 0.8230
## SENOKO SOUTH 0.8452
## SENOKO WEST 0.7544
## SENTOSA 0.1248
## SERANGOON CENTRAL 0.2046
## SERANGOON GARDEN 0.1302
## SERANGOON NORTH 0.3208
## SERANGOON NORTH IND ESTATE 0.8909
## SHANGRI-LA 0.4868
## SHIPYARD 0.4273
## SIGLAP 0.9990
## SIMEI 0.0001
## SINGAPORE GENERAL HOSPITAL 0.1987
## SINGAPORE POLYTECHNIC 0.3590
## SOMERSET 0.6026
## SPRINGLEAF 0.6506
## STRAITS VIEW 0.0239
## SUNGEI ROAD 0.1908
## SUNSET WAY 0.5027
## SWISS CLUB 0.3193
## TAGORE 0.5647
## TAI SENG 0.5844
## TAMAN JURONG 0.0604
## TAMPINES EAST 0.0000
## TAMPINES NORTH 0.9489
## TAMPINES WEST 0.0000
## TANGLIN 0.0486
## TANGLIN HALT 0.3906
## TANJONG PAGAR 0.0153
## TANJONG RHU 0.3240
## TEBAN GARDENS 0.5029
## TECK WHYE 0.4903
## TELOK BLANGAH DRIVE 0.5842
## TELOK BLANGAH RISE 0.3927
## TELOK BLANGAH WAY 0.3286
## TENGAH 0.9561
## TENGEH 0.4193
## THE WHARVES 0.9800
## TIONG BAHRU 0.2599
## TIONG BAHRU STATION 0.8839
## TOA PAYOH CENTRAL 0.9386
## TOA PAYOH WEST 0.5342
## TOH GUAN 0.4828
## TOH TUCK 0.5248
## TOWNSVILLE 0.5295
## TRAFALGAR 0.0186
## TUAS BAY 0.4258
## TUAS NORTH 0.4213
## TUAS PROMENADE 0.4210
## TUAS VIEW 0.3140
## TUAS VIEW EXTENSION 0.2212
## TUKANG 0.7336
## TURF CLUB 0.6188
## TYERSALL 0.1191
## ULU PANDAN 0.3201
## UPPER PAYA LEBAR 0.5141
## UPPER THOMSON 0.2483
## VICTORIA 0.5710
## WATERWAY EAST 0.5832
## WENYA 0.7784
## WEST COAST 0.5147
## WESTERN WATER CATCHMENT 0.3426
## WOODGROVE 0.4990
## WOODLANDS EAST 0.0004
## WOODLANDS REGIONAL CENTRE 0.4438
## WOODLANDS SOUTH 0.3963
## WOODLANDS WEST 0.4084
## WOODLEIGH 0.7243
## XILIN 0.9463
## YEW TEE 0.5456
## YIO CHU KANG 0.4142
## YIO CHU KANG EAST 0.6958
## YIO CHU KANG NORTH 0.6778
## YIO CHU KANG WEST 0.5125
## YISHUN CENTRAL 0.5778
## YISHUN EAST 0.6611
## YISHUN SOUTH 0.4225
## YISHUN WEST 0.4139
## YUHUA EAST 0.4402
## YUHUA WEST 0.3153
## YUNNAN 0.6987Mapping the local Moran’s I
final_q2.localMI_tapout <- cbind(final_q2,localMI_tapout)Mapping both local Moran’s I values and p-values (tapout)
localMI_tapout.map <- tm_shape(final_q2.localMI_tapout) +
tm_fill(col = "Ii",
style = "pretty",
title = "local moran statistics") +
tm_borders(alpha = 0.5)
P_value_tapout.map <- tm_shape(final_q2.localMI_tapout) +
tm_fill(col = "Pr.z...0.",
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_tapout.map, P_value_tapout.map, asp=1, ncol=2)## Warning: The shape final_q2.localMI_tapout is invalid. See sf::st_is_valid## Variable "Ii" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.## Warning: The shape final_q2.localMI_tapout is invalid. See sf::st_is_valid
Creating a LISA Cluster Map
nci <- moran.plot(final_q2$TOTAL_TAP_OUT_VOLUME, rswm_knn25, labels=as.character(final_q2$SUBZONE_N), xlab="TOTAL_TAP_OUT_VOLUME", ylab="Spatially Lag TOTAL_TAP_OUT_VOLUME")
Plotting Moran scatterplot with standardised variable
final_q2$Z.TOTAL_TAP_OUT_VOLUME <- scale(final_q2$TOTAL_TAP_OUT_VOLUME) %>% as.vectorPlot Moran scatterplot again
as.vector() is added to the end ensuring data type obtained in out of the vector
nci2 <- moran.plot(final_q2$Z.TOTAL_TAP_OUT_VOLUME, rswm_knn25, labels=as.character(final_q2$SUBZONE_N), xlab="z-TOTAL_TAP_OUT_VOLUME", ylab="Spatially Lag z-TOTAL_TAP_OUT_VOLUME")
Steps to prepare a LISA cluster map
quadrant <- vector(mode="numeric",length=nrow(localMI_tapout))Center the variable of interest around its mean
DV <- final_q2$TOTAL_TAP_OUT_VOLUME - mean(final_q2$TOTAL_TAP_OUT_VOLUME) Center the local Moran’s around the mean
C_mI <- localMI_tapout[,1] - mean(localMI_tapout[,1]) Setting satistical significance level for the local Moran
signif <- 0.054 types of commands defining ; High-high, low-low, low-high, high-low categories
quadrant[DV >0 & C_mI>0] <- 4
quadrant[DV <0 & C_mI<0] <- 1
quadrant[DV <0 & C_mI>0] <- 2
quadrant[DV >0 & C_mI<0] <- 3Placing non-significant Moran in the category 0
quadrant[localMI_tapout[,5]>signif] <- 0Combining all the above steps into one single code chunk
quadrant <- vector(mode="numeric",length=nrow(localMI_tapout))
DV <- final_q2$TOTAL_TAP_OUT_VOLUME - mean(final_q2$TOTAL_TAP_OUT_VOLUME)
C_mI <- localMI_tapout[,1] - mean(localMI_tapout[,1])
signif <- 0.05
quadrant[DV >0 & C_mI>0] <- 4
quadrant[DV <0 & C_mI<0] <- 1
quadrant[DV <0 & C_mI>0] <- 2
quadrant[DV >0 & C_mI<0] <- 3
quadrant[localMI_tapout[,5]>signif] <- 0Building the LISA map (tapout)
Based on the LISA map, we can see several clusters which primarily align with the initial observation of Local Moran’s I scores. However, it is also evident that we see certain subzones in the north-east and west that fall within the High-High quadrants which indicates a positive auto-correlation with neighbouring and a small portion in the central region falling into the low-high quadrant also indicating a positive auto-correlation but is relatively weaker as compared to the regions in the high-high quadrants.
final_q2.localMI_tapout$quadrant <- quadrant
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high")
tm_shape(final_q2.localMI_tapout) +
tm_fill(col = "quadrant", style = "cat", palette = colors[c(sort(unique(quadrant)))+1], labels = clusters[c(sort(unique(quadrant)))+1], popup.vars = c("Postal.Code")) +
tm_view(set.zoom.limits = c(11,17)) +
tm_borders(alpha=0.5)## Warning: The shape final_q2.localMI_tapout is invalid. See sf::st_is_valid
Creating adaptive proximity matrix
wm_knn25_lw <- nb2listw(wm_knn25, style = "B")
summary(wm_knn25_lw)## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 305
## Number of nonzero links: 7625
## Percentage nonzero weights: 8.196721
## Average number of links: 25
## Non-symmetric neighbours list
## Link number distribution:
##
## 25
## 305
## 305 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 with 25 links
## 305 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 with 25 links
##
## Weights style: B
## Weights constants summary:
## n nn S0 S1 S2
## B 305 93025 7625 13759 777568Gi statistics using adaptive distance
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.
gi.adaptive_tapin <- localG(final_q2$TOTAL_TAP_IN_VOLUME, wm_knn25_lw)
tapin_output.gi <- cbind(final_q2, as.matrix(gi.adaptive_tapin))
names(tapin_output.gi)[11] <- "gstat_adaptive"Mapping Gi values with adaptive distance weights (tapin)
tm_shape(tapin_output.gi) +
tm_fill(col = "gstat_adaptive",
style = "pretty",
palette = "-RdBu",
title = "local Gi") +
tm_borders(alpha = 0.5)## Warning: The shape tapin_output.gi is invalid. See sf::st_is_valid## Variable "gstat_adaptive" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
Gi statistics using adaptive distance (tapout)
gi.adaptive_tapout <- localG(final_q2$TOTAL_TAP_OUT_VOLUME, wm_knn25_lw)
tapout_output.gi <- cbind(final_q2, as.matrix(gi.adaptive_tapout))
names(tapout_output.gi)[11] <- "gstat_adaptive"Mapping Gi values with adaptive distance weights
tm_shape(tapout_output.gi) +
tm_fill(col = "gstat_adaptive",
style = "pretty",
palette = "-RdBu",
title = "local Gi") +
tm_borders(alpha = 0.5)## Warning: The shape tapout_output.gi is invalid. See sf::st_is_valid## Variable "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.
Overall Conclusion
In the choropleth map above, there are signs of clustering for both tapin and tapout around the East side of Singapore which can be deemed as hot spots (indicated in red). Other regions, mainly towards the west side of Singaore and even the central part of Singapore can be said to have a cold spot (indicated in blue). The gradient of the colors represents the intensity of the Gi values. The choropleth above shows clear sign of East-West divide.