Take Home Assignment 1
Jazreel Tho
Overview
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:
1. 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.
2. Performing spatial autocorrelation analysis on the residual of the regression model to test if the model conforms to the randomization assumption.
3. Performing localized geospatial statistics analysis by using commuters’ tap-in and tap-out data to identify geographical clustering.
The first null hypothesis is that the Tap In vs Population regression model conforms to the randomization assumption
The alternate hypothesis is that the Tap In vs Population regression model does not conform to the randomization assumption
The second null hypothesis is that the Tap Out vs Population regression model conforms to the randomization assumption
The alternate hypothesis is that the Tap In vs Population regression model does not conform to the randomization assumption
Confidence interval: 95%
Setting up: Installing and Launching R packages
packages = c('rgdal', 'sf', 'spdep', 'tmap', 'tidyverse','dplyr','gridExtra','ggfortify')
for (p in packages){
if(!require(p, character.only = T)){
install.packages(p)
}
library(p,character.only = T)
}Importing data
passenger_vol <- read_csv("data/aspatial/passenger volume by busstop.csv")The busstop shapefile is downloaded from the LTA datamall which can be downloaded via https://www.mytransport.sg/content/dam/datamall/datasets/Geospatial/BusStopLocation.zip This dataset consist of the bus stop numbers in Singapore and its respective point coordinate.
busstop <- st_read(dsn = "data/geospatial/BusStopLocation/BusStopLocation_Jan2020", layer = "BusStop")## Reading layer `BusStop' from data source `C:\Year 3\term 3\gis\Take hom assignments\Take-home_Ex01\data\geospatial\BusStopLocation\BusStopLocation_Jan2020' 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_defs
The residential population data is obtained from singstat and can be downloaded via https://www.singstat.gov.sg/find-data/search-by-theme/population/geographic-distribution/latest-data This dataset consists of the residential population by subzone from 2011 to 2019, with 2019 being the most updated data.
residents <- read_csv("data/aspatial/Singapore Residents by Planning AreaSubzone Age Group Sex and Type of Dwelling June 20112019/respopagesextod2011to2019.csv")
The subzone dataset is obtained frmo datagov.sg and can be downloaded via https://data.gov.sg/dataset/subzone-census-2010 This dataset consists of the subzones in Singapore with its respective polygon geometry.
subzone <- st_read(dsn = "data/geospatial/master-plan-2014-subzone-boundary-web/master-plan-2014-subzone-boundary-web-shp", layer = "MP14_SUBZONE_WEB_PL")## Reading layer `MP14_SUBZONE_WEB_PL' from data source `C:\Year 3\term 3\gis\Take hom assignments\Take-home_Ex01\data\geospatial\master-plan-2014-subzone-boundary-web\master-plan-2014-subzone-boundary-web-shp' 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_defsData Manipulation
Check crs and input for the 2 spatial maps
st_crs(subzone)## Coordinate Reference System:
## No EPSG code
## 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_defs"
As seen from the Coordinate Reference System, there is no epsg code. Hence, we set the crs to Singapore’s EPSG code which is 3414.
subzone3414 <- st_transform(subzone,3414)st_crs(busstop)## Coordinate Reference System:
## No EPSG code
## 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_defs"
Similar to the subzoone data, there is no epsg code for the busstop data. Hence, we set the crs 3414 as well.
busstop3414 <- st_set_crs(busstop,3414)Check for unique busstop codes to ensure there are no multi joining of passenger data to the busstop point coordinate data
Count number of rows for each BUS_STOP_N
count_busstop <- busstop3414 %>%
group_by(BUS_STOP_N)%>%
tally()
count_busstop## Simple feature collection with 5034 features and 2 fields
## geometry type: GEOMETRY
## dimension: XY
## bbox: xmin: 4427.938 ymin: 26482.1 xmax: 48282.5 ymax: 52983.82
## epsg (SRID): 3414
## proj4string: +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +units=m +no_defs
## # A tibble: 5,034 x 3
## BUS_STOP_N n geometry
## * <fct> <int> <POINT [m]>
## 1 01012 1 (30140.8 31031.95)
## 2 01013 1 (30218.75 31126.49)
## 3 01019 1 (30187.77 31034.55)
## 4 01029 1 (30345.83 31007.64)
## 5 01039 1 (30471.08 31175.63)
## 6 01059 1 (30570.37 31494.55)
## 7 01109 1 (30603.56 31759.58)
## 8 01112 1 (30434.46 31386.45)
## 9 01113 1 (30542.33 31509.91)
## 10 01119 1 (30422.02 31320.02)
## # ... with 5,024 more rowsFilter to those with more than 1
count_morethan1_busstop <- count_busstop %>%
filter(n>1)
count_morethan1_busstop## Simple feature collection with 6 features and 2 fields
## geometry type: MULTIPOINT
## dimension: XY
## bbox: xmin: 28300.11 ymin: 34460.06 xmax: 35245.61 ymax: 43320.34
## epsg (SRID): 3414
## proj4string: +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +units=m +no_defs
## # A tibble: 6 x 3
## BUS_STOP_N n geometry
## * <fct> <int> <MULTIPOINT [m]>
## 1 51071 2 (28300.11 36045.9, 28305.37 36036.67)
## 2 52059 2 (30566.62 36131.26, 30770.3 34460.06)
## 3 65331 2 (34709.62 42698.59, 35245.61 42735.63)
## 4 65339 2 (34708.61 42675.41, 35206.23 42785.7)
## 5 68091 2 (32038.84 43298.68, 32164.11 42695.98)
## 6 68099 2 (32004.05 43320.34, 32154.9 42742.82)Join back to busstop to obtain the other fields
morethan1 <- st_join(count_morethan1_busstop,busstop3414)
view(morethan1)
As seen from above, the data of the geometry is the same for the duplicate BUS_STOP_N codes despite the different namings of the LOC_DESC. Hence, we obtain the distinct busstop code and geometry before proceeding to join the data.
busstop_distinct <- count_busstop [1]
busstop_distinct## Simple feature collection with 5034 features and 1 field
## geometry type: GEOMETRY
## dimension: XY
## bbox: xmin: 4427.938 ymin: 26482.1 xmax: 48282.5 ymax: 52983.82
## epsg (SRID): 3414
## proj4string: +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +units=m +no_defs
## # A tibble: 5,034 x 2
## BUS_STOP_N geometry
## <fct> <POINT [m]>
## 1 01012 (30140.8 31031.95)
## 2 01013 (30218.75 31126.49)
## 3 01019 (30187.77 31034.55)
## 4 01029 (30345.83 31007.64)
## 5 01039 (30471.08 31175.63)
## 6 01059 (30570.37 31494.55)
## 7 01109 (30603.56 31759.58)
## 8 01112 (30434.46 31386.45)
## 9 01113 (30542.33 31509.91)
## 10 01119 (30422.02 31320.02)
## # ... with 5,024 more rowsSum all tap in and tap out data by PT_Code
passenger_vol_sum <- passenger_vol %>%
group_by(PT_CODE)%>%
summarise(TOTAL_TAP_IN_VOLUME=sum(TOTAL_TAP_IN_VOLUME), TOTAL_TAP_OUT_VOLUME=sum(TOTAL_TAP_OUT_VOLUME))Obtain sum of population by subzone in 2019
Sum all residents by area and filter by year first
residents_2019 <- residents %>%
filter(Time == 2019) %>%
group_by(PA, SZ)%>%
summarise(Pop=sum(Pop))Join busstop tap in data to busstop to get busstop point coordinates
We perform a left join as we would only like to include busstops with point coordinates within Singapore.
busstop_passenger<- left_join(busstop_distinct, passenger_vol_sum, by = c("BUS_STOP_N" = "PT_CODE"))
In the case that there are busstops with no tap in and tap out data, we treat the NA values as 0 as this indicates that there are no passengers activity (tap in/tap out) at that paticular busstop. Thus, we replace all NA values with 0.
busstop_passenger[is.na(busstop_passenger)] = 0Join busstop_passenger to obtain subzone by checking which polygon contains the point
bustop_passenger_subzone <- st_join(subzone3414, busstop_passenger, join = st_contains)As some busstops may not be within the subzone are (out of singapore boundaries such as jb busstop), we exclude those with NA. Also, those subzones with no busstops, we omit those from the analysis as well as it is not relevant in analsying commuters’ flow when there is no busstop.
bustop_passenger_subzone_o<- na.omit(bustop_passenger_subzone)Change the subzone to uppercase to join to subzone
residents2 <- mutate_all(residents, funs(toupper))
residents2 <-residents_2019%>%mutate(SZ = toupper(SZ))view(residents2)Join residents population data to subzone to get geometry polygon
resident_subzone<- full_join(subzone3414, residents2, by = c("SUBZONE_N"="SZ"))tmap_mode("view")Remove point from bustop_passenger_subzone. Join by subzone name to resident data
bustop_passenger_subzone_n <- subset(as.data.frame(bustop_passenger_subzone_o),select=-c(geometry))Join data: bustop_passenger_subzone_polygon and resident_subzone
Sum up tap in bustop_passenger_subzone_polygon
bustop_passenger_subzone_n_tap <- bustop_passenger_subzone_n %>%
group_by(SUBZONE_N,SUBZONE_C)%>%
summarise(TOTAL_TAP_IN_VOLUME=sum(TOTAL_TAP_IN_VOLUME),TOTAL_TAP_OUT_VOLUME=sum(TOTAL_TAP_OUT_VOLUME))
bustop_passenger_subzone_n_tap## # A tibble: 305 x 4
## # Groups: SUBZONE_N [305]
## SUBZONE_N SUBZONE_C TOTAL_TAP_IN_VOLUME TOTAL_TAP_OUT_VOLU~
## <fct> <fct> <dbl> <dbl>
## 1 ADMIRALTY SBSZ05 178509 228889
## 2 AIRPORT ROAD PLSZ04 22692 24524
## 3 ALEXANDRA HILL BMSZ07 497549 603813
## 4 ALEXANDRA NORTH BMSZ06 59359 41292
## 5 ALJUNIED GLSZ04 1613882 1704099
## 6 ANAK BUKIT BTSZ01 799579 745657
## 7 ANCHORVALE SESZ04 472053 474260
## 8 ANG MO KIO TOWN CENTRE AMSZ01 1100348 1052820
## 9 ANSON DTSZ10 73701 59522
## 10 BALESTIER NVSZ01 979175 979036
## # ... with 295 more rowsJoin bustop_passenger_subzone_polygon_tapin and resident_subzone
We perform an inner join as previously we have already omitted the polygons that have do not contain any busstop point coordinate. Hence, we perform an inner join to analyse the subzones with busstop point coordinates and whereby these coordinates lie within the singapore subzone.
passenger_resident_tap <- inner_join(resident_subzone,bustop_passenger_subzone_n_tap, by = c("SUBZONE_N"="SUBZONE_N"))The 3 choropleth graphs below shows:
1. Population by Subzone
2. Tap in by Subzone
3. Tap Out by Subzone
res.map <- tm_shape(passenger_resident_tap) +
tm_polygons("Pop",palette = "Blues" ,id="SZ", title = "Population by Subzone", border.col = "grey", id=subzone, auto.palette.mapping = FALSE, n=8, style="jenks" , alpha = 0.9)
in.map<- tm_shape(passenger_resident_tap) +
tm_polygons("TOTAL_TAP_IN_VOLUME",palette = "Reds" ,id="SZ", title = "Tap In by Subzone", border.col = "grey", auto.palette.mapping = FALSE, style="quantile" , alpha = 0.9)
out.map<- tm_shape(passenger_resident_tap) +
tm_polygons("TOTAL_TAP_OUT_VOLUME",palette = "Greens" ,id="SZ", title = "Tap Out by Subzone", border.col = "grey", auto.palette.mapping = FALSE, style="quantile" , alpha = 0.9)
tmap_arrange(res.map, in.map, out.map, asp=1, ncol=3, sync = TRUE)As there are some subzones with a recorded value of 0 residents, Hence, let’s plot a scatterplot to see the distribution of those subzones with 0. Those with a population of 0 are marked in red. The sctterplot below displays the Tap In vs population
plot(passenger_resident_tap$Pop, passenger_resident_tap$TOTAL_TAP_IN_VOLUME, col= ifelse(passenger_resident_tap$Pop ==0, "red", "black"))
The sctterplot below displays the Tap Out vs population
plot(passenger_resident_tap$Pop, passenger_resident_tap$TOTAL_TAP_OUT_VOLUME, col= ifelse(passenger_resident_tap$Pop ==0, "red", "black"))
passenger_resident_tap.s1 <- passenger_resident_tap[passenger_resident_tap$Pop ==0,]
view(passenger_resident_tap.s1)
Lets compare on the map to see how the data is affected when we remove those wth 0 population.
passenger_resident_tap_o <- passenger_resident_tap[passenger_resident_tap$Pop != 0, ]omitted.map <- tm_shape(passenger_resident_tap_o) +
tm_fill(col = "Pop",
palette="-Blues",
id = "SUBZONE_N",
title = "Residual Values") +
tm_borders(alpha = 0.5)
notomit.map <- tm_shape(passenger_resident_tap) +
tm_fill(col = "Pop",
palette="-Blues",
id = "SUBZONE_N",
title = "Residual Values") +
tm_borders(alpha = 0.5)
tmap_arrange(notomit.map, omitted.map, asp=1, ncol=2, sync = TRUE)As seen above, most of the subzone areas are non-residential. There are also some which are such as paya lebar. As we are anlsysing the relationship between the residential population and the commuters’ flow, the subzones with 0 population will not be relevant as no matter how many commuters there are, the population remains 0, which there are no relationnship. If the government/LTA would simply like to analyse which areas have a volume, they can simply use look at the commuters’ flow data. However, if we simply use those with population 0 in the analysis, it shows 0 reationship. Hence, we remove those with 0 population.
Linear Regression Modelling
The scatterplot on the left below shows the relatioship and correlation between Total tap in volume and population, and the scatterplot on the right shows the relationship between total tap out volume and population.
pop_tapin_corr <- round(cor(passenger_resident_tap_o$Pop, passenger_resident_tap_o$TOTAL_TAP_IN_VOLUME),digits=4)
pop_tapout_corr <- round(cor(passenger_resident_tap_o$Pop, passenger_resident_tap_o$TOTAL_TAP_OUT_VOLUME),digits=4)
tapin_scatter <- ggplot(passenger_resident_tap_o, aes(x = Pop, y = TOTAL_TAP_IN_VOLUME)) +
geom_point() +
labs(x="Poplation", y= "Total Tap In Volume",
title="Tap in volume vs population by Subzone", subtitle=paste("Correlation: ", pop_tapin_corr))+
stat_smooth()
tapout_scatter <- ggplot(passenger_resident_tap_o, aes(x = Pop, y = TOTAL_TAP_OUT_VOLUME)) +
geom_point() +
labs(x="Poplation", y= "Total Tap Out Volume",
title="Tap in volume vs population by Subzone", subtitle= paste("Correlation: ", pop_tapout_corr))+
stat_smooth()
grid.arrange(tapin_scatter, tapout_scatter, ncol=2)
LM model for Tap in vs Population
model <- lm(Pop ~ TOTAL_TAP_IN_VOLUME, data = passenger_resident_tap_o)
model##
## Call:
## lm(formula = Pop ~ TOTAL_TAP_IN_VOLUME, data = passenger_resident_tap_o)
##
## Coefficients:
## (Intercept) TOTAL_TAP_IN_VOLUME
## 3.471e+03 3.053e-02summary(model)##
## Call:
## lm(formula = Pop ~ TOTAL_TAP_IN_VOLUME, data = passenger_resident_tap_o)
##
## Residuals:
## Min 1Q Median 3Q Max
## -45970 -5632 -902 5229 48953
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.471e+03 1.107e+03 3.134 0.00195 **
## TOTAL_TAP_IN_VOLUME 3.053e-02 1.675e-03 18.229 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12240 on 230 degrees of freedom
## Multiple R-squared: 0.591, Adjusted R-squared: 0.5892
## F-statistic: 332.3 on 1 and 230 DF, p-value: < 2.2e-16ggplot(passenger_resident_tap_o, aes(Pop, TOTAL_TAP_IN_VOLUME)) +
geom_point() +
stat_smooth(method = lm)
In a lineaer model, there are we need to check if the assumptions are true:
1. Linearity: The relationship between X and the mean of Y is linear.
2. Homoscedasticity: The variance of residual is the same for any value of X.
3. Independence: Observations are independent of each other.
4. Normality: For any fixed value of X, Y is normally distributed.
lm_model <- autoplot(lm(Pop ~ TOTAL_TAP_IN_VOLUME, data = passenger_resident_tap_o), label.size = 3)
lm_model
The above shows 4 charts:
1. Residuals vs Fitted. Used to check the linear relationship assumptions. The blue line for this graph deos not show any distinct patterns. Hence, there is an indication for a possible linear relationship.
2. Normal Q-Q. Used to examine whether the residuals are normally distributed. It’s good if residuals points follow the straight dashed line. As seen from the Normal Q-Q graph, the datapoints do follow the direction of the dotted line, however not all datapoints fall on the line.
3. Scale-Location (or Spread-Location). Used to check the homogeneity of variance of the residuals (homoscedasticity). Horizontal line with equally spread points is a good indication of homoscedasticity. This is not the case in our example, where we have a heteroscedasticity problem. It can be seen that the variability (variances) of the residual points increases with the value of the fitted outcome variable, suggesting non-constant variances in the residuals errors (or heteroscedasticity).A way to solve it is to reduce the heteroscedasticity problem is to use a log or square root transformation of the outcome variable (y).
4. Residuals vs Leverage. Used to identify influential cases, that is extreme values that might influence the regression results when included or excluded from the analysis. This plot will be described further in the next sections.
To further analyse on the Residuals vs Leverage
# Cook's distance
plot(model, 4, id.n = 5)
# Residuals vs Leverage
plot(model, 5)
As seen from above, the extreme values do not present any influential points. Cook’s distance lines (a red dashed line) are not shown on the Residuals vs Leverage plot because all points are well inside of the Cook’s distance lines.
LM model for Tap out vs Population
model_out <- lm(Pop ~ TOTAL_TAP_OUT_VOLUME, data = passenger_resident_tap_o)
model_out##
## Call:
## lm(formula = Pop ~ TOTAL_TAP_OUT_VOLUME, data = passenger_resident_tap_o)
##
## Coefficients:
## (Intercept) TOTAL_TAP_OUT_VOLUME
## 3.298e+03 3.094e-02summary(model_out)##
## Call:
## lm(formula = Pop ~ TOTAL_TAP_OUT_VOLUME, data = passenger_resident_tap_o)
##
## Residuals:
## Min 1Q Median 3Q Max
## -49412 -5659 -866 4951 44585
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.298e+03 1.106e+03 2.983 0.00316 **
## TOTAL_TAP_OUT_VOLUME 3.095e-02 1.682e-03 18.403 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12170 on 230 degrees of freedom
## Multiple R-squared: 0.5956, Adjusted R-squared: 0.5938
## F-statistic: 338.7 on 1 and 230 DF, p-value: < 2.2e-16ggplot(passenger_resident_tap_o, aes(Pop, TOTAL_TAP_OUT_VOLUME)) +
geom_point() +
stat_smooth(method = lm)
lm_model_out <- autoplot(lm(Pop ~ TOTAL_TAP_OUT_VOLUME, data = passenger_resident_tap_o), label.size = 3)
lm_model_out
As seen from the above, the results are similar to tap in.
Spatial Autocorrelation Analysis
Before proceeding with the analysis, we join residual data for both tap in and tap out data to the dataset
passenger_resident_tap_o$residuals <- residuals(model)
passenger_resident_tap_o$residuals_out <- residuals(model_out)Modelling Spatial Neighbours
To proceed with the analysis, we convert the data to a SpatialPolygonDataframe
passenger_resident_tap_sp <- as_Spatial(passenger_resident_tap_o)Modelling using fixed distance
Determine the cut-off distance
To choose a distance for the fixed distance method to define the neighbours, we have to determine the cut off by obtaining the furthest distance among all the distances between each subzone and its nearest neighbour.
coords <- coordinates(passenger_resident_tap_sp)
k1 <- knn2nb(knearneigh(coords,k=1))
k1dists <- unlist(nbdists(k1, coords, longlat = FALSE))
summary(k1dists)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 182.5 616.6 879.3 914.3 1096.8 4597.9The summary report shows that the largest first nearest neighbour distance is 4597.9 , so using this as the upper threshold gives certainty that all units will have at least one neighbour. #### Computing fixed distance weight matrix
passenger_resident_tapin_q_4598 <- dnearneigh(coords, 0, 4598, longlat = FALSE)
passenger_resident_tapin_q_4598## Neighbour list object:
## Number of regions: 232
## Number of nonzero links: 8736
## Percentage nonzero weights: 16.23068
## Average number of links: 37.65517As seen from the data above, the average number of links per subzone is about 38. #### Plotting fixed distance weight matrix
par(mfrow=c(1,2))
plot(passenger_resident_tap_sp, border="lightgrey")
plot(k1, coords, add=TRUE, col="red", length=0.08, main="1st nearest neighbours")
plot(passenger_resident_tap_sp, border="lightgrey")
plot(passenger_resident_tapin_q_4598, coords, add=TRUE, pch = 19, cex = 0.6, main="Distance link")
Modelling Spatial Neighbours using Queens
passenger_resident_tap_sp_q <- poly2nb(passenger_resident_tap_sp, queen=TRUE)
summary(passenger_resident_tap_sp_q)## Neighbour list object:
## Number of regions: 232
## Number of nonzero links: 1182
## Percentage nonzero weights: 2.196046
## Average number of links: 5.094828
## Link number distribution:
##
## 1 2 3 4 5 6 7 8 9
## 4 10 26 35 69 41 31 12 4
## 4 least connected regions:
## 15 263 285 302 with 1 link
## 4 most connected regions:
## 89 94 162 174 with 9 linksplot(passenger_resident_tap_sp, border="lightgrey")
plot(passenger_resident_tap_sp_q, coordinates(passenger_resident_tap_sp), pch = 19, cex = 0.6, add = TRUE, col= "red")
Modelling Spatial Neighbours using ROOK
passenger_resident_tap_sp_r <- poly2nb(passenger_resident_tap_sp, queen=FALSE)
summary(passenger_resident_tap_sp_r)## Neighbour list object:
## Number of regions: 232
## Number of nonzero links: 1014
## Percentage nonzero weights: 1.883918
## Average number of links: 4.37069
## Link number distribution:
##
## 1 2 3 4 5 6 7 8
## 7 17 39 66 50 33 16 4
## 7 least connected regions:
## 15 263 268 271 285 295 302 with 1 link
## 4 most connected regions:
## 84 89 160 162 with 8 linksplot(passenger_resident_tap_sp, border="lightgrey")
plot(passenger_resident_tap_sp_r, coordinates(passenger_resident_tap_sp), pch = 19, cex = 0.6, add = TRUE, col= "red")
Modelling Spatial Neighbours using k=8
We use the number 8 as for for values that are not normally distributed,it is important to evaluate each feature within the cnotext of at least 8 neighbours as a rule of thumb.
passenger_resident_tap_sp_knn8 <- knn2nb(knearneigh(coords, k=8))
passenger_resident_tap_sp_knn8## Neighbour list object:
## Number of regions: 232
## Number of nonzero links: 1856
## Percentage nonzero weights: 3.448276
## Average number of links: 8
## Non-symmetric neighbours listPlotting distance based neighbours
plot(passenger_resident_tap_sp, border="lightgrey")
plot(passenger_resident_tap_sp_knn8, coords, pch = 19, cex = 0.6, add = TRUE, col = "red")
Based on the above, I decided to use Queens method. The fixed distance is not suitable as the average links is 37.6, which is too many neighbours.
Row-standardised weights matrix
Next, we need to assign weights to each neighboring polygon. In our case, each neighboring polygon will be assigned equal weight (style=“W”)
rpassenger_resident_tap_sp_q<- nb2listw(passenger_resident_tap_sp_q, style="W", zero.policy = TRUE)
rpassenger_resident_tap_sp_q## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 232
## Number of nonzero links: 1182
## Percentage nonzero weights: 2.196046
## Average number of links: 5.094828
##
## Weights style: W
## Weights constants summary:
## n nn S0 S1 S2
## W 232 53824 232 99.897 957.3532Compute lag residuals for Tap In vs Population
Calculate the spatially lag residual values for Tap In vs Population
residuals.lag <- lag.listw(rpassenger_resident_tap_sp_q, passenger_resident_tap_sp$residuals)
residuals.lag## [1] -4786.59127 -7367.99684 -4179.85792 -3950.13670 -2694.86431
## [6] -3980.25707 -5544.10238 -4321.66777 -3332.63470 -785.98129
## [11] -4136.98519 -3263.39362 -24879.71489 -2096.20443 -5791.74296
## [16] -5769.44877 -3561.89294 -8141.61359 -9171.39910 -5975.11903
## [21] -4379.99506 -6357.35819 -3156.87489 -5953.04402 -7142.72489
## [26] -2724.66855 -1360.66664 -8122.63401 -4214.45665 -5338.12299
## [31] -8915.54594 -9293.57137 -9612.48017 -9023.69795 -9452.14412
## [36] -7656.77812 -8583.77321 -6791.40206 -10793.64396 -6903.61284
## [41] -7008.24848 -2686.13989 -1398.42921 -6620.75565 -8957.54359
## [46] -964.45896 -5041.42009 -6832.17343 1553.80897 -5915.84224
## [51] -1920.47010 -8828.34961 -9557.03072 -292.40769 -8039.10987
## [56] -10188.84557 -5574.97848 -5564.47255 -10146.26409 -6910.25341
## [61] -4090.38684 -6947.14404 -6641.77212 2114.26069 -2651.42858
## [66] -9192.53503 -8502.31618 -7611.24631 -2433.88015 -7874.68637
## [71] -382.29046 -1320.45548 -8312.26126 -6560.87624 -1029.07614
## [76] -2849.25218 -3650.45246 -2574.55365 -5011.26668 -4546.97998
## [81] -1430.02280 -5117.08703 -5177.46760 -3579.99034 -2207.49716
## [86] -9220.97377 2403.62109 1405.81839 -4861.06001 -6894.29470
## [91] -1891.78166 -486.10613 -1390.19550 -1533.82112 2590.64339
## [96] 145.38649 -29.96132 -4930.52325 -434.10293 3655.56022
## [101] -2104.37239 -4340.51721 -5219.10323 -8671.94395 -37.45432
## [106] 11760.64423 9733.26428 -5547.89157 -4433.29057 -1601.71975
## [111] -107.18841 -6822.19637 -4320.50628 -3918.83843 -2047.09172
## [116] -3595.38268 -1065.35248 -8499.42815 -1744.29630 -214.33022
## [121] -3013.54301 5505.14907 909.29954 677.41726 1811.89519
## [126] -3956.69282 567.54112 5693.78242 2734.34149 2580.40681
## [131] 2338.59701 1743.41876 1572.94173 2532.42754 -400.47280
## [136] 5696.50497 -379.78281 3653.62027 -7425.44333 -1289.34016
## [141] -3273.82101 -2504.05167 -8937.01111 -477.45919 9131.99722
## [146] -1041.31411 7662.75050 3971.87599 4137.90975 7089.11564
## [151] 2317.37052 3903.94464 3667.36313 -710.78003 -3536.39895
## [156] 3766.80159 8170.67691 1748.71118 -3056.57445 -6192.39578
## [161] 13122.82801 3820.75517 8889.80905 -397.55803 4585.70925
## [166] 3413.28374 5948.39763 9481.36407 20886.72008 -9592.52066
## [171] 3186.82176 2861.99451 -3593.39332 3892.38363 -1044.02051
## [176] 2905.84689 6029.48995 -3085.41098 -1090.90621 -2019.00629
## [181] -2413.72799 -418.60193 8940.27404 -2994.91464 -207.03451
## [186] 931.29099 16308.60076 -1388.01507 2893.76473 -2809.18446
## [191] 11323.38492 8861.56324 5922.52408 7482.74542 1681.40162
## [196] 14972.17281 12412.46219 22941.94466 748.87046 22195.56430
## [201] 14017.15251 -8944.09344 22551.44136 19649.16636 -823.20451
## [206] 7639.74021 26340.48577 1585.45514 11145.66621 11942.85400
## [211] 27040.95172 9001.94087 -3761.61344 8862.20227 -4126.52755
## [216] 14559.69993 16343.59660 3946.09321 3291.08657 -17039.24821
## [221] 5056.66709 -995.24661 28972.93170 -8385.12518 6101.21397
## [226] 2604.44469 15083.69889 -1841.24319 24148.90535 -3105.19300
## [231] 8194.62478 4010.12128
We can append the spatially lag residual values onto passenger_resident_tap_sp SpatialPolygonDataFrame
lag.list <- list(passenger_resident_tap_sp$SUBZONE_N, lag.listw(rpassenger_resident_tap_sp_q, passenger_resident_tap_sp$residuals))
lag.res <- as.data.frame(lag.list)
The table show the lag residuals of tap in vs Population for the respective subzones
colnames(lag.res) <- c("SUBZONE_N", "lag residuals")
print(lag.res)## SUBZONE_N lag residuals
## 1 PEARL'S HILL -4786.59127
## 2 BOAT QUAY -7367.99684
## 3 HENDERSON HILL -4179.85792
## 4 REDHILL -3950.13670
## 5 ALEXANDRA HILL -2694.86431
## 6 BUKIT HO SWEE -3980.25707
## 7 CLARKE QUAY -5544.10238
## 8 PASIR PANJANG 1 -4321.66777
## 9 QUEENSWAY -3332.63470
## 10 ALEXANDRA NORTH -785.98129
## 11 INSTITUTION HILL -4136.98519
## 12 ROBERTSON QUAY -3263.39362
## 13 SENTOSA -24879.71489
## 14 MARITIME SQUARE -2096.20443
## 15 TELOK BLANGAH WAY -5791.74296
## 16 CECIL -5769.44877
## 17 KAMPONG TIONG BAHRU -3561.89294
## 18 TELOK BLANGAH DRIVE -8141.61359
## 19 PASIR PANJANG 2 -9171.39910
## 20 CENTRAL SUBZONE -5975.11903
## 21 DEPOT ROAD -4379.99506
## 22 PEOPLE'S PARK -6357.35819
## 23 BUKIT MERAH -3156.87489
## 24 CHINATOWN -5953.04402
## 25 CHINA SQUARE -7142.72489
## 26 TIONG BAHRU -2724.66855
## 27 TIONG BAHRU STATION -1360.66664
## 28 OXLEY -8122.63401
## 29 MEI CHIN -4214.45665
## 30 NATIONAL UNIVERSITY OF S'PORE -5338.12299
## 31 ONE TREE HILL -8915.54594
## 32 SOMERSET -9293.57137
## 33 BENCOOLEN -9612.48017
## 34 LEONIE HILL -9023.69795
## 35 PORT -9452.14412
## 36 DHOBY GHAUT -7656.77812
## 37 BUGIS -8583.77321
## 38 VICTORIA -6791.40206
## 39 PATERSON -10793.64396
## 40 TELOK BLANGAH RISE -6903.61284
## 41 TANJONG PAGAR -7008.24848
## 42 EVERTON PARK -2686.13989
## 43 TANGLIN HALT -1398.42921
## 44 MACKENZIE -6620.75565
## 45 SUNGEI ROAD -8957.54359
## 46 ONE NORTH -964.45896
## 47 TANJONG RHU -5041.42009
## 48 MOUNTBATTEN -6832.17343
## 49 COMMONWEALTH 1553.80897
## 50 DOVER -5915.84224
## 51 RIDOUT -1920.47010
## 52 CLEMENTI WEST -8828.34961
## 53 MONK'S HILL -9557.03072
## 54 SIGLAP -292.40769
## 55 CLEMENTI WOODS -8039.10987
## 56 ORANGE GROVE -10188.84557
## 57 KAMPONG BUGIS -5574.97848
## 58 BOULEVARD -5564.47255
## 59 LITTLE INDIA -10146.26409
## 60 FORT CANNING -6910.25341
## 61 FARRER COURT -4090.38684
## 62 NASSIM -6947.14404
## 63 WEST COAST -6641.77212
## 64 BAYSHORE 2114.26069
## 65 CHATSWORTH -2651.42858
## 66 KAMPONG GLAM -9192.53503
## 67 SELEGIE -8502.31618
## 68 CRAWFORD -7611.24631
## 69 MARGARET DRIVE -2433.88015
## 70 TANGLIN -7874.68637
## 71 MARINE PARADE -382.29046
## 72 GEYLANG BAHRU -1320.45548
## 73 FABER -8312.26126
## 74 MALCOLM -6560.87624
## 75 BEDOK SOUTH -1029.07614
## 76 BENDEMEER -2849.25218
## 77 BALESTIER -3650.45246
## 78 CORONATION ROAD -2574.55365
## 79 KEMBANGAN -5011.26668
## 80 KATONG -4546.97998
## 81 HOLLAND DRIVE -1430.02280
## 82 FARRER PARK -5117.08703
## 83 NEWTON CIRCUS -5177.46760
## 84 GHIM MOH -3579.99034
## 85 LAVENDER -2207.49716
## 86 GOODWOOD PARK -9220.97377
## 87 SINGAPORE POLYTECHNIC 2403.62109
## 88 CLEMENTI CENTRAL 1405.81839
## 89 KAMPONG JAVA -4861.06001
## 90 BOON KENG -6894.29470
## 91 ULU PANDAN -1891.78166
## 92 JURONG GATEWAY -486.10613
## 93 HOLLAND ROAD -1390.19550
## 94 KAMPONG UBI -1533.82112
## 95 SENNETT 2590.64339
## 96 POTONG PASIR 145.38649
## 97 PEI CHUN -29.96132
## 98 BOON TECK -4930.52325
## 99 WOODLEIGH -434.10293
## 100 TAMAN JURONG 3655.56022
## 101 LAKESIDE -2104.37239
## 102 TOA PAYOH WEST -4340.51721
## 103 KAKI BUKIT -5219.10323
## 104 YUHUA EAST -8671.94395
## 105 BUKIT BATOK SOUTH -37.45432
## 106 JURONG WEST CENTRAL 11760.64423
## 107 BEDOK RESERVOIR 9733.26428
## 108 MOUNT PLEASANT -5547.89157
## 109 HILLCREST -4433.29057
## 110 JOO SENG -1601.71975
## 111 LORONG 8 TOA PAYOH -107.18841
## 112 TOH GUAN -6822.19637
## 113 BRADDELL -4320.50628
## 114 ALJUNIED -3918.83843
## 115 TYERSALL -2047.09172
## 116 MOULMEIN -3595.38268
## 117 FRANKEL -1065.35248
## 118 CLEMENTI NORTH -8499.42815
## 119 LEEDON PARK -1744.29630
## 120 GEYLANG EAST -214.33022
## 121 TEBAN GARDENS -3013.54301
## 122 BOON LAY PLACE 5505.14907
## 123 BUKIT BATOK EAST 909.29954
## 124 BUKIT BATOK WEST 677.41726
## 125 BUKIT BATOK CENTRAL 1811.89519
## 126 UPPER PAYA LEBAR -3956.69282
## 127 HONG KAH 567.54112
## 128 SERANGOON CENTRAL 5693.78242
## 129 BISHAN EAST 2734.34149
## 130 TAMPINES WEST 2580.40681
## 131 BRICKWORKS 2338.59701
## 132 GUILIN 1743.41876
## 133 MARYMOUNT 1572.94173
## 134 WENYA 2532.42754
## 135 NATURE RESERVE -400.47280
## 136 TAMPINES EAST 5696.50497
## 137 TAI SENG -379.78281
## 138 YUHUA WEST 3653.62027
## 139 YUNNAN -7425.44333
## 140 LORONG CHUAN -1289.34016
## 141 DUNEARN -3273.82101
## 142 SUNSET WAY -2504.05167
## 143 MACPHERSON -8937.01111
## 144 KIM KEAT -477.45919
## 145 BEDOK NORTH 9131.99722
## 146 TOA PAYOH CENTRAL -1041.31411
## 147 HOUGANG EAST 7662.75050
## 148 KANGKAR 3971.87599
## 149 SEMBAWANG HILLS 4137.90975
## 150 JELEBU 7089.11564
## 151 KEAT HONG 2317.37052
## 152 HOUGANG WEST 3903.94464
## 153 BANGKIT 3667.36313
## 154 ANAK BUKIT -710.78003
## 155 SWISS CLUB -3536.39895
## 156 XILIN 3766.80159
## 157 SIMEI 8170.67691
## 158 PENG SIANG 1748.71118
## 159 PASIR RIS WEST -3056.57445
## 160 YIO CHU KANG WEST -6192.39578
## 161 TRAFALGAR 13122.82801
## 162 TECK WHYE 3820.75517
## 163 CHOA CHU KANG CENTRAL 8889.80905
## 164 CHANGI WEST -397.55803
## 165 FAJAR 4585.70925
## 166 SENJA 3413.28374
## 167 SAUJANA 5948.39763
## 168 SELETAR HILLS 9481.36407
## 169 COMPASSVALE 20886.72008
## 170 YIO CHU KANG EAST -9592.52066
## 171 LOYANG WEST 3186.82176
## 172 TAGORE 2861.99451
## 173 LORONG AH SOO -3593.39332
## 174 FLORA DRIVE 3892.38363
## 175 HILLVIEW -1044.02051
## 176 UPPER THOMSON 2905.84689
## 177 HONG KAH NORTH 6029.48995
## 178 TOWNSVILLE -3085.41098
## 179 KOVAN -1090.90621
## 180 CHONG BOON -2019.00629
## 181 SHANGRI-LA -2413.72799
## 182 SERANGOON GARDEN -418.60193
## 183 HOUGANG CENTRAL 8940.27404
## 184 LOYANG EAST -2994.91464
## 185 DAIRY FARM -207.03451
## 186 PASIR RIS DRIVE 931.29099
## 187 TAMPINES NORTH 16308.60076
## 188 CHENG SAN -1388.01507
## 189 ANG MO KIO TOWN CENTRE 2893.76473
## 190 KEBUN BAHRU -2809.18446
## 191 SERANGOON NORTH 11323.38492
## 192 PASIR RIS CENTRAL 8861.56324
## 193 GOMBAK 5922.52408
## 194 PASIR RIS PARK 7482.74542
## 195 CHOA CHU KANG NORTH 1681.40162
## 196 RIVERVALE 14972.17281
## 197 FERNVALE 12412.46219
## 198 PUNGGOL FIELD 22941.94466
## 199 YEW TEE 748.87046
## 200 MATILDA 22195.56430
## 201 WATERWAY EAST 14017.15251
## 202 CHANGI POINT -8944.09344
## 203 SENGKANG TOWN CENTRE 22551.44136
## 204 ANCHORVALE 19649.16636
## 205 YISHUN SOUTH -823.20451
## 206 LOWER SELETAR 7639.74021
## 207 NORTHSHORE 26340.48577
## 208 MANDAI ESTATE 1585.45514
## 209 YISHUN CENTRAL 11145.66621
## 210 TURF CLUB 11942.85400
## 211 WOODLANDS SOUTH 27040.95172
## 212 WOODGROVE 9001.94087
## 213 YISHUN EAST -3761.61344
## 214 WESTERN WATER CATCHMENT 8862.20227
## 215 YISHUN WEST -4126.52755
## 216 WOODLANDS EAST 14559.69993
## 217 SEMBAWANG CENTRAL 16343.59660
## 218 SEMBAWANG EAST 3946.09321
## 219 ADMIRALTY 3291.08657
## 220 LIM CHU KANG -17039.24821
## 221 SEMBAWANG NORTH 5056.66709
## 222 NORTHLAND -995.24661
## 223 MIDVIEW 28972.93170
## 224 WOODLANDS WEST -8385.12518
## 225 SEMBAWANG SPRINGS 6101.21397
## 226 SPRINGLEAF 2604.44469
## 227 PUNGGOL TOWN CENTRE 15083.69889
## 228 NEE SOON -1841.24319
## 229 SELETAR 24148.90535
## 230 KHATIB -3105.19300
## 231 NORTH COAST 8194.62478
## 232 SEMBAWANG STRAITS 4010.12128Compute lag residuals for Tap out vs population
Calculate the spatially lag residual values
residualsout.lag <- lag.listw(rpassenger_resident_tap_sp_q, passenger_resident_tap_sp$residuals_out)
residualsout.lag## [1] -4758.84448 -6128.26706 -4141.81335 -4044.33734 -2691.24482
## [6] -3221.14746 -5882.74453 -3973.85321 -5184.95708 -606.18647
## [11] -4212.24320 -2640.86214 -25061.04737 -1964.10767 -6706.22101
## [16] -5162.90681 -3348.88337 -7465.17264 -9848.50328 -5450.22844
## [21] -5440.03827 -4013.17529 -3135.95587 -6065.09311 -5704.80682
## [26] -2080.24111 -1759.61156 -7972.41755 -4466.04336 -6035.33588
## [31] -8455.11846 -9131.78063 -9101.24559 -8439.37216 -9517.19694
## [36] -7044.64071 -7785.16747 -6775.12493 -10661.28005 -7116.19215
## [41] -6551.09878 -2080.89388 -1246.06478 -6434.64264 -7869.69845
## [46] -1372.12796 -6170.52830 -6092.25771 1552.12907 -5740.57107
## [51] -1081.76179 -8187.44241 -8221.55845 -1046.13902 -7469.61904
## [56] -10880.03274 -6012.42678 -4610.28595 -9229.43590 -6566.41881
## [61] -3459.55190 -7108.28710 -6434.22094 625.27522 -1915.13122
## [66] -9764.01469 -8037.13624 -7520.41619 -2793.21868 -8259.15139
## [71] -1702.37713 -2048.55858 -7291.19423 -5927.67122 -2368.91606
## [76] -2454.73748 -3303.11635 -2465.07232 -6049.43742 -4427.96684
## [81] -1617.53342 -4635.16143 -4975.22264 -3780.36449 -2466.48051
## [86] -9118.60532 2196.63027 1013.77011 -4351.04693 -8209.95357
## [91] -1285.16377 -1325.48919 -1458.35637 -1443.27426 1951.17084
## [96] 81.54298 -592.60513 -4512.82332 -1924.41623 2996.86718
## [101] -2471.55048 -4433.60685 -4635.60829 -8611.77171 304.42788
## [106] 11925.26177 8159.05931 -5002.11456 -4089.96134 -1954.89881
## [111] -1700.20152 -6664.39359 -5683.61725 -3501.68882 -1481.69413
## [116] -3574.08562 -25.86989 -7135.94075 -987.47353 -1996.47160
## [121] -4443.01239 5338.64808 398.29508 704.06464 1294.34411
## [126] -3430.27180 26.04693 4903.69999 2663.55500 3208.21202
## [131] 2298.14264 2945.72121 -56.80216 2446.28361 -1001.70309
## [136] 5429.18974 -1564.12971 2766.10555 -7421.06791 -2947.34743
## [141] -2805.07350 -1847.70707 -8508.44004 -1261.68195 7580.37474
## [146] -985.97546 7139.94890 3024.48358 4295.27947 7433.34394
## [151] 4418.56569 3615.36844 3596.27232 -1154.00965 -2694.20595
## [156] 4402.49531 7533.25442 1444.34251 -3503.84619 -5551.61836
## [161] 12819.72349 3935.63886 8746.08785 -557.53420 4996.18839
## [166] 4499.97960 5117.92749 10378.59906 21515.32722 -8214.53534
## [171] 3654.56506 2946.44885 -3437.38539 4670.57775 -589.30186
## [176] 2901.26306 5215.38549 -3306.99831 -1000.07138 -1016.55996
## [181] -862.77430 -587.81016 9224.98526 -3062.37202 576.98000
## [186] 537.27013 15805.99655 -2011.50805 3255.07157 -2457.44666
## [191] 11685.53398 9706.56947 5135.47208 7008.73012 2184.95331
## [196] 15334.68377 11981.65320 22568.76361 737.92414 22616.79847
## [201] 14230.83440 -6588.38148 22175.62052 19548.53235 -2424.67391
## [206] 6883.07357 26406.23518 -2511.72706 11169.05828 8490.67383
## [211] 27015.42877 6379.64429 -2663.04663 9592.83654 -5255.47697
## [216] 15602.48635 14498.19335 4466.02760 3221.70784 -18354.33504
## [221] 5369.71848 -946.48575 29042.43801 -6097.11313 6692.68639
## [226] 1849.16934 14828.99922 -5714.10221 23798.35672 -2082.44827
## [231] -2622.27984 2729.81062lagout.list <- list(passenger_resident_tap_sp$SUBZONE_N, lag.listw(rpassenger_resident_tap_sp_q, passenger_resident_tap_sp$residuals_out))
lagout.res <- as.data.frame(lagout.list)
The table show the lag residuals Tap Out vs Populationfor the respective subzones
colnames(lagout.res) <- c("SUBZONE_N", "lag residuals")
print(lagout.res)## SUBZONE_N lag residuals
## 1 PEARL'S HILL -4758.84448
## 2 BOAT QUAY -6128.26706
## 3 HENDERSON HILL -4141.81335
## 4 REDHILL -4044.33734
## 5 ALEXANDRA HILL -2691.24482
## 6 BUKIT HO SWEE -3221.14746
## 7 CLARKE QUAY -5882.74453
## 8 PASIR PANJANG 1 -3973.85321
## 9 QUEENSWAY -5184.95708
## 10 ALEXANDRA NORTH -606.18647
## 11 INSTITUTION HILL -4212.24320
## 12 ROBERTSON QUAY -2640.86214
## 13 SENTOSA -25061.04737
## 14 MARITIME SQUARE -1964.10767
## 15 TELOK BLANGAH WAY -6706.22101
## 16 CECIL -5162.90681
## 17 KAMPONG TIONG BAHRU -3348.88337
## 18 TELOK BLANGAH DRIVE -7465.17264
## 19 PASIR PANJANG 2 -9848.50328
## 20 CENTRAL SUBZONE -5450.22844
## 21 DEPOT ROAD -5440.03827
## 22 PEOPLE'S PARK -4013.17529
## 23 BUKIT MERAH -3135.95587
## 24 CHINATOWN -6065.09311
## 25 CHINA SQUARE -5704.80682
## 26 TIONG BAHRU -2080.24111
## 27 TIONG BAHRU STATION -1759.61156
## 28 OXLEY -7972.41755
## 29 MEI CHIN -4466.04336
## 30 NATIONAL UNIVERSITY OF S'PORE -6035.33588
## 31 ONE TREE HILL -8455.11846
## 32 SOMERSET -9131.78063
## 33 BENCOOLEN -9101.24559
## 34 LEONIE HILL -8439.37216
## 35 PORT -9517.19694
## 36 DHOBY GHAUT -7044.64071
## 37 BUGIS -7785.16747
## 38 VICTORIA -6775.12493
## 39 PATERSON -10661.28005
## 40 TELOK BLANGAH RISE -7116.19215
## 41 TANJONG PAGAR -6551.09878
## 42 EVERTON PARK -2080.89388
## 43 TANGLIN HALT -1246.06478
## 44 MACKENZIE -6434.64264
## 45 SUNGEI ROAD -7869.69845
## 46 ONE NORTH -1372.12796
## 47 TANJONG RHU -6170.52830
## 48 MOUNTBATTEN -6092.25771
## 49 COMMONWEALTH 1552.12907
## 50 DOVER -5740.57107
## 51 RIDOUT -1081.76179
## 52 CLEMENTI WEST -8187.44241
## 53 MONK'S HILL -8221.55845
## 54 SIGLAP -1046.13902
## 55 CLEMENTI WOODS -7469.61904
## 56 ORANGE GROVE -10880.03274
## 57 KAMPONG BUGIS -6012.42678
## 58 BOULEVARD -4610.28595
## 59 LITTLE INDIA -9229.43590
## 60 FORT CANNING -6566.41881
## 61 FARRER COURT -3459.55190
## 62 NASSIM -7108.28710
## 63 WEST COAST -6434.22094
## 64 BAYSHORE 625.27522
## 65 CHATSWORTH -1915.13122
## 66 KAMPONG GLAM -9764.01469
## 67 SELEGIE -8037.13624
## 68 CRAWFORD -7520.41619
## 69 MARGARET DRIVE -2793.21868
## 70 TANGLIN -8259.15139
## 71 MARINE PARADE -1702.37713
## 72 GEYLANG BAHRU -2048.55858
## 73 FABER -7291.19423
## 74 MALCOLM -5927.67122
## 75 BEDOK SOUTH -2368.91606
## 76 BENDEMEER -2454.73748
## 77 BALESTIER -3303.11635
## 78 CORONATION ROAD -2465.07232
## 79 KEMBANGAN -6049.43742
## 80 KATONG -4427.96684
## 81 HOLLAND DRIVE -1617.53342
## 82 FARRER PARK -4635.16143
## 83 NEWTON CIRCUS -4975.22264
## 84 GHIM MOH -3780.36449
## 85 LAVENDER -2466.48051
## 86 GOODWOOD PARK -9118.60532
## 87 SINGAPORE POLYTECHNIC 2196.63027
## 88 CLEMENTI CENTRAL 1013.77011
## 89 KAMPONG JAVA -4351.04693
## 90 BOON KENG -8209.95357
## 91 ULU PANDAN -1285.16377
## 92 JURONG GATEWAY -1325.48919
## 93 HOLLAND ROAD -1458.35637
## 94 KAMPONG UBI -1443.27426
## 95 SENNETT 1951.17084
## 96 POTONG PASIR 81.54298
## 97 PEI CHUN -592.60513
## 98 BOON TECK -4512.82332
## 99 WOODLEIGH -1924.41623
## 100 TAMAN JURONG 2996.86718
## 101 LAKESIDE -2471.55048
## 102 TOA PAYOH WEST -4433.60685
## 103 KAKI BUKIT -4635.60829
## 104 YUHUA EAST -8611.77171
## 105 BUKIT BATOK SOUTH 304.42788
## 106 JURONG WEST CENTRAL 11925.26177
## 107 BEDOK RESERVOIR 8159.05931
## 108 MOUNT PLEASANT -5002.11456
## 109 HILLCREST -4089.96134
## 110 JOO SENG -1954.89881
## 111 LORONG 8 TOA PAYOH -1700.20152
## 112 TOH GUAN -6664.39359
## 113 BRADDELL -5683.61725
## 114 ALJUNIED -3501.68882
## 115 TYERSALL -1481.69413
## 116 MOULMEIN -3574.08562
## 117 FRANKEL -25.86989
## 118 CLEMENTI NORTH -7135.94075
## 119 LEEDON PARK -987.47353
## 120 GEYLANG EAST -1996.47160
## 121 TEBAN GARDENS -4443.01239
## 122 BOON LAY PLACE 5338.64808
## 123 BUKIT BATOK EAST 398.29508
## 124 BUKIT BATOK WEST 704.06464
## 125 BUKIT BATOK CENTRAL 1294.34411
## 126 UPPER PAYA LEBAR -3430.27180
## 127 HONG KAH 26.04693
## 128 SERANGOON CENTRAL 4903.69999
## 129 BISHAN EAST 2663.55500
## 130 TAMPINES WEST 3208.21202
## 131 BRICKWORKS 2298.14264
## 132 GUILIN 2945.72121
## 133 MARYMOUNT -56.80216
## 134 WENYA 2446.28361
## 135 NATURE RESERVE -1001.70309
## 136 TAMPINES EAST 5429.18974
## 137 TAI SENG -1564.12971
## 138 YUHUA WEST 2766.10555
## 139 YUNNAN -7421.06791
## 140 LORONG CHUAN -2947.34743
## 141 DUNEARN -2805.07350
## 142 SUNSET WAY -1847.70707
## 143 MACPHERSON -8508.44004
## 144 KIM KEAT -1261.68195
## 145 BEDOK NORTH 7580.37474
## 146 TOA PAYOH CENTRAL -985.97546
## 147 HOUGANG EAST 7139.94890
## 148 KANGKAR 3024.48358
## 149 SEMBAWANG HILLS 4295.27947
## 150 JELEBU 7433.34394
## 151 KEAT HONG 4418.56569
## 152 HOUGANG WEST 3615.36844
## 153 BANGKIT 3596.27232
## 154 ANAK BUKIT -1154.00965
## 155 SWISS CLUB -2694.20595
## 156 XILIN 4402.49531
## 157 SIMEI 7533.25442
## 158 PENG SIANG 1444.34251
## 159 PASIR RIS WEST -3503.84619
## 160 YIO CHU KANG WEST -5551.61836
## 161 TRAFALGAR 12819.72349
## 162 TECK WHYE 3935.63886
## 163 CHOA CHU KANG CENTRAL 8746.08785
## 164 CHANGI WEST -557.53420
## 165 FAJAR 4996.18839
## 166 SENJA 4499.97960
## 167 SAUJANA 5117.92749
## 168 SELETAR HILLS 10378.59906
## 169 COMPASSVALE 21515.32722
## 170 YIO CHU KANG EAST -8214.53534
## 171 LOYANG WEST 3654.56506
## 172 TAGORE 2946.44885
## 173 LORONG AH SOO -3437.38539
## 174 FLORA DRIVE 4670.57775
## 175 HILLVIEW -589.30186
## 176 UPPER THOMSON 2901.26306
## 177 HONG KAH NORTH 5215.38549
## 178 TOWNSVILLE -3306.99831
## 179 KOVAN -1000.07138
## 180 CHONG BOON -1016.55996
## 181 SHANGRI-LA -862.77430
## 182 SERANGOON GARDEN -587.81016
## 183 HOUGANG CENTRAL 9224.98526
## 184 LOYANG EAST -3062.37202
## 185 DAIRY FARM 576.98000
## 186 PASIR RIS DRIVE 537.27013
## 187 TAMPINES NORTH 15805.99655
## 188 CHENG SAN -2011.50805
## 189 ANG MO KIO TOWN CENTRE 3255.07157
## 190 KEBUN BAHRU -2457.44666
## 191 SERANGOON NORTH 11685.53398
## 192 PASIR RIS CENTRAL 9706.56947
## 193 GOMBAK 5135.47208
## 194 PASIR RIS PARK 7008.73012
## 195 CHOA CHU KANG NORTH 2184.95331
## 196 RIVERVALE 15334.68377
## 197 FERNVALE 11981.65320
## 198 PUNGGOL FIELD 22568.76361
## 199 YEW TEE 737.92414
## 200 MATILDA 22616.79847
## 201 WATERWAY EAST 14230.83440
## 202 CHANGI POINT -6588.38148
## 203 SENGKANG TOWN CENTRE 22175.62052
## 204 ANCHORVALE 19548.53235
## 205 YISHUN SOUTH -2424.67391
## 206 LOWER SELETAR 6883.07357
## 207 NORTHSHORE 26406.23518
## 208 MANDAI ESTATE -2511.72706
## 209 YISHUN CENTRAL 11169.05828
## 210 TURF CLUB 8490.67383
## 211 WOODLANDS SOUTH 27015.42877
## 212 WOODGROVE 6379.64429
## 213 YISHUN EAST -2663.04663
## 214 WESTERN WATER CATCHMENT 9592.83654
## 215 YISHUN WEST -5255.47697
## 216 WOODLANDS EAST 15602.48635
## 217 SEMBAWANG CENTRAL 14498.19335
## 218 SEMBAWANG EAST 4466.02760
## 219 ADMIRALTY 3221.70784
## 220 LIM CHU KANG -18354.33504
## 221 SEMBAWANG NORTH 5369.71848
## 222 NORTHLAND -946.48575
## 223 MIDVIEW 29042.43801
## 224 WOODLANDS WEST -6097.11313
## 225 SEMBAWANG SPRINGS 6692.68639
## 226 SPRINGLEAF 1849.16934
## 227 PUNGGOL TOWN CENTRE 14828.99922
## 228 NEE SOON -5714.10221
## 229 SELETAR 23798.35672
## 230 KHATIB -2082.44827
## 231 NORTH COAST -2622.27984
## 232 SEMBAWANG STRAITS 2729.81062Measure of Global Spatial Autocorrelation for TOTAL_TAP_IN vs Population
Computing Moran’s I
moran.test(passenger_resident_tap_sp$residuals, listw=rpassenger_resident_tap_sp_q, zero.policy = TRUE, na.action=na.omit)##
## Moran I test under randomisation
##
## data: passenger_resident_tap_sp$residuals
## weights: rpassenger_resident_tap_sp_q
##
## Moran I statistic standard deviate = 4.4376, p-value = 4.548e-06
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## 0.183667846 -0.004329004 0.001794758
As the p-value is smaller than the alpha value, we reject the first null hypothesis at the 95% confidence interval whereby the Tap In vs Population regression model does not conform to the randomization assumption.
Visualising spatial lag value using Moran Scatterplot
MS <- moran.plot(passenger_resident_tap_sp$residuals, rpassenger_resident_tap_sp_q, zero.policy = TRUE, spChk=FALSE, labels=as.character(passenger_resident_tap_sp$SUBZONE_N), xlab="Residuals", ylab="Spatially Lag Residuals")
The Moran’s scatterplot is split into 4 quadrants:
1. Top left: Low-High Outliers
2. Top Right: High-High (above average)
3. Bottom left: Low-Low (below average)
4. Bottom right: High-Low Outliers
en from the scatterplot, there is a relationship between the spatially lagged residuals and residuals. The slope of the linear regression line is positive, with alot of observations in the high-high quadrant and low=low quadrant.
Spatial Correlogram
Compute Moran’s I correlogram and plot
MI_corr <- sp.correlogram(passenger_resident_tap_sp_q, passenger_resident_tap_sp$residuals, order=6, method="I", style="B")
plot(MI_corr)
The correlogram shows that with more neighbours of higher degree is added to the analysis, moran I become ssmaller. This shows that the residuals per subzone gradually decreases as more lags are added, showing a trickling effect.
Measure of Global Spatial Autocorrelation for TOTAL_TAP_OUT vs Population
Computing Moran’s I
moran.test(passenger_resident_tap_sp$residuals_out, listw=rpassenger_resident_tap_sp_q, zero.policy = TRUE, na.action=na.omit)##
## Moran I test under randomisation
##
## data: passenger_resident_tap_sp$residuals_out
## weights: rpassenger_resident_tap_sp_q
##
## Moran I statistic standard deviate = 4.7195, p-value = 1.182e-06
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## 0.195690804 -0.004329004 0.001796160
As the p-value is smaller than the alpha value, we reject the second null hypothesis at the 95% confidence interval whereby the Tap Out vs Population regression model does not conform to the randomization assumption.
Visualising spatial lag value using Moran Scatterplot
MS_OUT <- moran.plot(passenger_resident_tap_sp$residuals_out, rpassenger_resident_tap_sp_q, zero.policy = TRUE, spChk=FALSE, labels=as.character(passenger_resident_tap_sp$SUBZONE_N), xlab="Residuals", ylab="Spatially Lag Residuals")
As seen from the scatterplot, there is a relationship between the spatially lagged residuals and residuals. The slope of the linear regression line is positive, with alot of observations in the high-high quadrant and low=low quadrant.
Spatial Correlogram
Compute Moran’s I correlogram and plot
MI_corr_OUT <- sp.correlogram(passenger_resident_tap_sp_q, passenger_resident_tap_sp$residuals_out, order=6, method="I", style="B")
plot(MI_corr_OUT)
Similar to the tap in, the correlogram shows a trickling effect.
Localized Geospatial Statistics Analysis
Computing local Moran’s I for TOTAL_TAP_IN_VOLUME VS Population
Next, we compute local Moran’s I of the Tap In vs Population residuals at subzone level with given a set of zi values and a listw object providing neighbour weighting information for the polygon associated with the zi values.
fips <- order(passenger_resident_tap_sp$SUBZONE_N)
localMI <- localmoran(passenger_resident_tap_sp$residuals, rpassenger_resident_tap_sp_q)
head(localMI)## Ii E.Ii Var.Ii Z.Ii Pr(z > 0)
## 2 0.16637276 -0.004329004 0.1188163 0.4952221 0.3102217
## 3 0.24664660 -0.004329004 0.3237963 0.4410579 0.3295855
## 4 0.05249309 -0.004329004 0.1598123 0.1421386 0.4434853
## 5 0.08105888 -0.004329004 0.1926091 0.1945619 0.4228680
## 6 0.08858649 -0.004329004 0.1363860 0.2515957 0.4006768
## 7 -0.14914057 -0.004329004 0.1363860 -0.3921194 0.6525150The code chunk below list the content of the local Moran matrix derived by using printCoefmat() for each subzone.
printCoefmat(data.frame(localMI[fips,], row.names=passenger_resident_tap_sp$SUBZONE_N[fips]), check.names=FALSE)## Ii E.Ii Var.Ii
## ADMIRALTY 0.11495082 -0.00432900 0.19260909
## ALEXANDRA HILL 0.08858649 -0.00432900 0.13638602
## ALEXANDRA NORTH 0.01674034 -0.00432900 0.15981230
## ALJUNIED 0.33129812 -0.00432900 0.11881631
## ANAK BUKIT 0.02696254 -0.00432900 0.15981230
## ANCHORVALE 3.79981737 -0.00432900 0.24180428
## ANG MO KIO TOWN CENTRE -0.62686473 -0.00432900 0.13638602
## BALESTIER 0.01494986 -0.00432900 0.15981230
## BANGKIT 0.10865735 -0.00432900 0.32379627
## BAYSHORE -0.00274148 -0.00432900 0.24180428
## BEDOK NORTH -0.62074045 -0.00432900 0.11881631
## BEDOK RESERVOIR 0.29572545 -0.00432900 0.19260909
## BEDOK SOUTH -0.10970803 -0.00432900 0.19260909
## BENCOOLEN 0.33394814 -0.00432900 0.15981230
## BENDEMEER -0.27396867 -0.00432900 0.13638602
## BISHAN EAST -0.07568480 -0.00432900 0.10515098
## BOAT QUAY 0.24664660 -0.00432900 0.32379627
## BOON KENG 0.10163501 -0.00432900 0.32379627
## BOON LAY PLACE 0.24532852 -0.00432900 0.19260909
## BOON TECK -0.11405578 -0.00432900 0.19260909
## BOULEVARD 0.96276092 -0.00432900 0.11881631
## BRADDELL 0.04937863 -0.00432900 0.19260909
## BRICKWORKS 0.04003661 -0.00432900 0.24180428
## BUGIS 0.90185664 -0.00432900 0.32379627
## BUKIT BATOK CENTRAL -0.06577114 -0.00432900 0.19260909
## BUKIT BATOK EAST -0.00029696 -0.00432900 0.24180428
## BUKIT BATOK SOUTH -0.00027776 -0.00432900 0.13638602
## BUKIT BATOK WEST 0.01710493 -0.00432900 0.15981230
## BUKIT HO SWEE -0.14914057 -0.00432900 0.13638602
## BUKIT MERAH 0.27907800 -0.00432900 0.13638602
## CECIL 0.30424996 -0.00432900 0.32379627
## CENTRAL SUBZONE 0.22685943 -0.00432900 0.48778023
## CHANGI POINT 0.40303145 -0.00432900 0.97973213
## CHANGI WEST 0.02393797 -0.00432900 0.15981230
## CHATSWORTH 0.06744104 -0.00432900 0.10515098
## CHENG SAN 0.03268992 -0.00432900 0.15981230
## CHINA SQUARE 0.29126716 -0.00432900 0.24180428
## CHINATOWN 0.30264458 -0.00432900 0.15981230
## CHOA CHU KANG CENTRAL -0.98778714 -0.00432900 0.19260909
## CHOA CHU KANG NORTH 0.20982685 -0.00432900 0.19260909
## CHONG BOON -0.03780801 -0.00432900 0.13638602
## CLARKE QUAY 0.40621627 -0.00432900 0.19260909
## CLEMENTI CENTRAL -0.28857249 -0.00432900 0.19260909
## CLEMENTI NORTH -0.21935264 -0.00432900 0.19260909
## CLEMENTI WEST -0.14755721 -0.00432900 0.19260909
## CLEMENTI WOODS -0.01086948 -0.00432900 0.13638602
## COMMONWEALTH -0.04513220 -0.00432900 0.19260909
## COMPASSVALE 1.13333343 -0.00432900 0.13638602
## CORONATION ROAD 0.06986074 -0.00432900 0.15981230
## CRAWFORD 0.14236682 -0.00432900 0.19260909
## DAIRY FARM -0.00097525 -0.00432900 0.19260909
## DEPOT ROAD -0.00003676 -0.00432900 0.19260909
## DHOBY GHAUT 0.66889573 -0.00432900 0.19260909
## DOVER 0.02166199 -0.00432900 0.19260909
## DUNEARN 0.09645287 -0.00432900 0.19260909
## EVERTON PARK 0.02240004 -0.00432900 0.32379627
## FABER 0.06765185 -0.00432900 0.32379627
## FAJAR 0.51909535 -0.00432900 0.32379627
## FARRER COURT -0.00187512 -0.00432900 0.24180428
## FARRER PARK 0.53290945 -0.00432900 0.15981230
## FERNVALE 3.16400340 -0.00432900 0.15981230
## FLORA DRIVE 0.14905969 -0.00432900 0.19260909
## FORT CANNING 0.24751729 -0.00432900 0.19260909
## FRANKEL -0.00756253 -0.00432900 0.11881631
## GEYLANG BAHRU 0.01598340 -0.00432900 0.19260909
## GEYLANG EAST 0.02741630 -0.00432900 0.11881631
## GHIM MOH -0.12856532 -0.00432900 0.19260909
## GOMBAK -0.08532447 -0.00432900 0.11881631
## GOODWOOD PARK 0.20010731 -0.00432900 0.15981230
## GUILIN 0.02010113 -0.00432900 0.15981230
## HENDERSON HILL 0.05249309 -0.00432900 0.15981230
## HILLCREST -0.05244571 -0.00432900 0.19260909
## HILLVIEW -0.04368171 -0.00432900 0.13638602
## HOLLAND DRIVE -0.02385796 -0.00432900 0.15981230
## HOLLAND ROAD 0.06340648 -0.00432900 0.15981230
## HONG KAH 0.04621235 -0.00432900 0.19260909
## HONG KAH NORTH 0.37680913 -0.00432900 0.24180428
## HOUGANG CENTRAL -1.60400490 -0.00432900 0.19260909
## HOUGANG EAST 0.49305508 -0.00432900 0.19260909
## HOUGANG WEST 0.34361840 -0.00432900 0.13638602
## INSTITUTION HILL 0.03798351 -0.00432900 0.24180428
## JELEBU -0.31080021 -0.00432900 0.13638602
## JOO SENG 0.02153822 -0.00432900 0.19260909
## JURONG GATEWAY 0.12650795 -0.00432900 0.32379627
## JURONG WEST CENTRAL -1.46304269 -0.00432900 0.32379627
## KAKI BUKIT -0.20117577 -0.00432900 0.19260909
## KAMPONG BUGIS 0.23746540 -0.00432900 0.19260909
## KAMPONG GLAM 0.35729727 -0.00432900 0.48778023
## KAMPONG JAVA -0.04052045 -0.00432900 0.13638602
## KAMPONG TIONG BAHRU 0.01186342 -0.00432900 0.13638602
## KAMPONG UBI 0.12662500 -0.00432900 0.13638602
## KANGKAR 0.38700602 -0.00432900 0.19260909
## KATONG 0.08444909 -0.00432900 0.24180428
## KEAT HONG 0.34325261 -0.00432900 0.19260909
## KEBUN BAHRU -0.12340584 -0.00432900 0.19260909
## KEMBANGAN -0.36274112 -0.00432900 0.15981230
## KHATIB 0.11612137 -0.00432900 0.13638602
## KIM KEAT 0.00126732 -0.00432900 0.15981230
## KOVAN -0.05354995 -0.00432900 0.13638602
## LAKESIDE 0.10976458 -0.00432900 0.15981230
## LAVENDER 0.18196784 -0.00432900 0.13638602
## LEEDON PARK 0.01633000 -0.00432900 0.10515098
## LEONIE HILL 0.11543457 -0.00432900 0.11881631
## LIM CHU KANG 0.47870228 -0.00432900 0.97973213
## LITTLE INDIA 0.08372681 -0.00432900 0.15981230
## LORONG 8 TOA PAYOH 0.00101977 -0.00432900 0.13638602
## LORONG AH SOO -0.00735629 -0.00432900 0.15981230
## LORONG CHUAN -0.02431289 -0.00432900 0.13638602
## LOWER SELETAR 0.42615083 -0.00432900 0.19260909
## LOYANG EAST 0.06731192 -0.00432900 0.32379627
## LOYANG WEST -0.12291216 -0.00432900 0.19260909
## MACKENZIE 0.34226629 -0.00432900 0.32379627
## MACPHERSON -0.41121506 -0.00432900 0.15981230
## MALCOLM 0.24762763 -0.00432900 0.13638602
## MANDAI ESTATE -0.02505051 -0.00432900 0.48778023
## MARGARET DRIVE -0.05395738 -0.00432900 0.10515098
## MARINE PARADE 0.00447567 -0.00432900 0.24180428
## MARITIME SQUARE 0.35109888 -0.00432900 0.15981230
## MARYMOUNT 0.05831032 -0.00432900 0.15981230
## MATILDA 3.21947041 -0.00432900 0.11881631
## MEI CHIN -0.10882592 -0.00432900 0.15981230
## MIDVIEW 3.21421511 -0.00432900 0.32379627
## MONK'S HILL 0.16942299 -0.00432900 0.24180428
## MOULMEIN 0.23419156 -0.00432900 0.15981230
## MOUNT PLEASANT 0.17376108 -0.00432900 0.19260909
## MOUNTBATTEN -0.06888334 -0.00432900 0.19260909
## NASSIM 0.07680993 -0.00432900 0.11881631
## NATIONAL UNIVERSITY OF S'PORE 0.38660299 -0.00432900 0.24180428
## NATURE RESERVE 0.00808487 -0.00432900 0.24180428
## NEE SOON 0.04819548 -0.00432900 0.32379627
## NEWTON CIRCUS 0.37430613 -0.00432900 0.32379627
## NORTH COAST -1.64980071 -0.00432900 0.97973213
## NORTHLAND -0.05919530 -0.00432900 0.19260909
## NORTHSHORE -0.63539517 -0.00432900 0.48778023
## ONE NORTH 0.07976133 -0.00432900 0.13638602
## ONE TREE HILL 0.21230358 -0.00432900 0.19260909
## ORANGE GROVE 0.13457779 -0.00432900 0.32379627
## OXLEY 0.17061121 -0.00432900 0.19260909
## PASIR PANJANG 1 0.25384115 -0.00432900 0.19260909
## PASIR PANJANG 2 0.41285540 -0.00432900 0.24180428
## PASIR RIS CENTRAL -0.09006209 -0.00432900 0.19260909
## PASIR RIS DRIVE 0.14216525 -0.00432900 0.15981230
## PASIR RIS PARK -0.00741744 -0.00432900 0.24180428
## PASIR RIS WEST -0.29824971 -0.00432900 0.32379627
## PATERSON 0.68526473 -0.00432900 0.19260909
## PEARL'S HILL 0.16637276 -0.00432900 0.11881631
## PEI CHUN -0.00012106 -0.00432900 0.19260909
## PENG SIANG 0.17084192 -0.00432900 0.24180428
## PEOPLE'S PARK 0.48400672 -0.00432900 0.48778023
## PORT 0.43571543 -0.00432900 0.24180428
## POTONG PASIR 0.00114698 -0.00432900 0.13638602
## PUNGGOL FIELD 3.87188331 -0.00432900 0.19260909
## PUNGGOL TOWN CENTRE 1.32378796 -0.00432900 0.19260909
## QUEENSWAY 0.14920851 -0.00432900 0.24180428
## REDHILL 0.08105888 -0.00432900 0.19260909
## RIDOUT 0.06095903 -0.00432900 0.13638602
## RIVERVALE 2.95894339 -0.00432900 0.15981230
## ROBERTSON QUAY 0.13636649 -0.00432900 0.13638602
## SAUJANA 0.63545554 -0.00432900 0.32379627
## SELEGIE 0.32230000 -0.00432900 0.19260909
## SELETAR -1.17997578 -0.00432900 0.32379627
## SELETAR HILLS 0.44035451 -0.00432900 0.19260909
## SEMBAWANG CENTRAL 0.54188877 -0.00432900 0.24180428
## SEMBAWANG EAST 0.07523279 -0.00432900 0.19260909
## SEMBAWANG HILLS 0.01410910 -0.00432900 0.19260909
## SEMBAWANG NORTH 0.39886827 -0.00432900 0.48778023
## SEMBAWANG SPRINGS -0.01986174 -0.00432900 0.19260909
## SEMBAWANG STRAITS -0.06843625 -0.00432900 0.48778023
## SENGKANG TOWN CENTRE 1.68919143 -0.00432900 0.19260909
## SENJA 0.17332308 -0.00432900 0.24180428
## SENNETT -0.12748336 -0.00432900 0.15981230
## SENTOSA 0.30085926 -0.00432900 0.97973213
## SERANGOON CENTRAL -0.82044198 -0.00432900 0.19260909
## SERANGOON GARDEN -0.03621122 -0.00432900 0.11881631
## SERANGOON NORTH -0.02160508 -0.00432900 0.19260909
## SHANGRI-LA -0.05486783 -0.00432900 0.15981230
## SIGLAP 0.00260322 -0.00432900 0.32379627
## SIMEI 0.61609844 -0.00432900 0.15981230
## SINGAPORE POLYTECHNIC -0.19534420 -0.00432900 0.15981230
## SOMERSET 1.19198614 -0.00432900 0.15981230
## SPRINGLEAF -0.00605808 -0.00432900 0.19260909
## SUNGEI ROAD 0.31192990 -0.00432900 0.24180428
## SUNSET WAY -0.01811112 -0.00432900 0.15981230
## SWISS CLUB 0.06860893 -0.00432900 0.19260909
## TAGORE 0.00725696 -0.00432900 0.19260909
## TAI SENG 0.00126149 -0.00432900 0.19260909
## TAMAN JURONG 0.12912933 -0.00432900 0.32379627
## TAMPINES EAST 0.56749943 -0.00432900 0.11881631
## TAMPINES NORTH -0.82483966 -0.00432900 0.19260909
## TAMPINES WEST 0.53999117 -0.00432900 0.19260909
## TANGLIN 0.19975286 -0.00432900 0.19260909
## TANGLIN HALT 0.00421073 -0.00432900 0.19260909
## TANJONG PAGAR 0.19423714 -0.00432900 0.32379627
## TANJONG RHU -0.06433769 -0.00432900 0.24180428
## TEBAN GARDENS -0.05376961 -0.00432900 0.48778023
## TECK WHYE 0.16557197 -0.00432900 0.15981230
## TELOK BLANGAH DRIVE -0.20643464 -0.00432900 0.24180428
## TELOK BLANGAH RISE 0.00055776 -0.00432900 0.24180428
## TELOK BLANGAH WAY 0.03904065 -0.00432900 0.15981230
## TIONG BAHRU -0.05727715 -0.00432900 0.24180428
## TIONG BAHRU STATION 0.09899161 -0.00432900 0.19260909
## TOA PAYOH CENTRAL 0.15245609 -0.00432900 0.13638602
## TOA PAYOH WEST -0.06527106 -0.00432900 0.15981230
## TOH GUAN 0.01042365 -0.00432900 0.24180428
## TOWNSVILLE -0.09342325 -0.00432900 0.13638602
## TRAFALGAR 1.45788673 -0.00432900 0.19260909
## TURF CLUB -0.87965296 -0.00432900 0.48778023
## TYERSALL 0.08579113 -0.00432900 0.13638602
## ULU PANDAN -0.05759574 -0.00432900 0.15981230
## UPPER PAYA LEBAR -0.13911238 -0.00432900 0.15981230
## UPPER THOMSON 0.01290273 -0.00432900 0.24180428
## VICTORIA 0.78635883 -0.00432900 0.24180428
## WATERWAY EAST 3.74104665 -0.00432900 0.24180428
## WENYA -0.01369346 -0.00432900 0.19260909
## WEST COAST -0.07694700 -0.00432900 0.24180428
## WESTERN WATER CATCHMENT -1.01658220 -0.00432900 0.13638602
## WOODGROVE 0.95091017 -0.00432900 0.24180428
## WOODLANDS EAST 4.79821508 -0.00432900 0.32379627
## WOODLANDS SOUTH 4.05499046 -0.00432900 0.32379627
## WOODLANDS WEST -0.46258233 -0.00432900 0.32379627
## WOODLEIGH 0.00862222 -0.00432900 0.13638602
## XILIN -0.18031880 -0.00432900 0.15981230
## YEW TEE 0.10588313 -0.00432900 0.48778023
## YIO CHU KANG EAST 0.20522180 -0.00432900 0.32379627
## YIO CHU KANG WEST -0.40651332 -0.00432900 0.24180428
## YISHUN CENTRAL -3.44930324 -0.00432900 0.19260909
## YISHUN EAST -0.75767115 -0.00432900 0.24180428
## YISHUN SOUTH -0.07649366 -0.00432900 0.15981230
## YISHUN WEST -0.24240354 -0.00432900 0.13638602
## YUHUA EAST -0.38044343 -0.00432900 0.19260909
## YUHUA WEST -0.01175133 -0.00432900 0.24180428
## YUNNAN -1.47294954 -0.00432900 0.24180428
## Z.Ii Pr.z...0.
## ADMIRALTY 0.27178696 0.3929
## ALEXANDRA HILL 0.25159570 0.4007
## ALEXANDRA NORTH 0.05270428 0.4790
## ALJUNIED 0.97368623 0.1651
## ANAK BUKIT 0.07827479 0.4688
## ANCHORVALE 7.73615610 0.0000
## ANG MO KIO TOWN CENTRE -1.68569637 0.9541
## BALESTIER 0.04822546 0.4808
## BANGKIT 0.19855924 0.4213
## BAYSHORE 0.00322841 0.4987
## BEDOK NORTH -1.78826827 0.9631
## BEDOK RESERVOIR 0.68369387 0.2471
## BEDOK SOUTH -0.24011306 0.5949
## BENCOOLEN 0.84618936 0.1987
## BENDEMEER -0.73012774 0.7673
## BISHAN EAST -0.22005061 0.5871
## BOAT QUAY 0.44105789 0.3296
## BOON KENG 0.18621835 0.4261
## BOON LAY PLACE 0.56886115 0.2847
## BOON TECK -0.25001970 0.5987
## BOULEVARD 2.80561989 0.0025
## BRADDELL 0.12237639 0.4513
## BRICKWORKS 0.09022242 0.4641
## BUGIS 1.59250667 0.0556
## BUKIT BATOK CENTRAL -0.13999996 0.5557
## BUKIT BATOK EAST 0.00819962 0.4967
## BUKIT BATOK SOUTH 0.01096992 0.4956
## BUKIT BATOK WEST 0.05361629 0.4786
## BUKIT HO SWEE -0.39211938 0.6525
## BUKIT MERAH 0.76740681 0.2214
## CECIL 0.54228850 0.2938
## CENTRAL SUBZONE 0.33101983 0.3703
## CHANGI POINT 0.41155245 0.3403
## CHANGI WEST 0.07070892 0.4718
## CHATSWORTH 0.22132811 0.4124
## CHENG SAN 0.09260164 0.4631
## CHINA SQUARE 0.60112778 0.2739
## CHINATOWN 0.76788450 0.2213
## CHOA CHU KANG CENTRAL -2.24087424 0.9875
## CHOA CHU KANG NORTH 0.48796825 0.3128
## CHONG BOON -0.09065413 0.5361
## CLARKE QUAY 0.93545449 0.1748
## CLEMENTI CENTRAL -0.64766754 0.7414
## CLEMENTI NORTH -0.48994554 0.6879
## CLEMENTI WEST -0.32635491 0.6279
## CLEMENTI WOODS -0.01771025 0.5071
## COMMONWEALTH -0.09297277 0.5370
## COMPASSVALE 3.08055161 0.0010
## CORONATION ROAD 0.18558325 0.4264
## CRAWFORD 0.33425610 0.3691
## DAIRY FARM 0.00764176 0.4970
## DEPOT ROAD 0.00978016 0.4961
## DHOBY GHAUT 1.53398698 0.0625
## DOVER 0.05922219 0.4764
## DUNEARN 0.22963815 0.4092
## EVERTON PARK 0.04697292 0.4813
## FABER 0.12649726 0.4497
## FAJAR 0.91985211 0.1788
## FARRER COURT 0.00499025 0.4980
## FARRER PARK 1.34388464 0.0895
## FERNVALE 7.92548117 0.0000
## FLORA DRIVE 0.34950626 0.3634
## FORT CANNING 0.57384839 0.2830
## FRANKEL -0.00938076 0.5037
## GEYLANG BAHRU 0.04628316 0.4815
## GEYLANG EAST 0.09209615 0.4633
## GHIM MOH -0.28308063 0.6114
## GOMBAK -0.23497556 0.5929
## GOODWOOD PARK 0.51139084 0.3045
## GUILIN 0.06111120 0.4756
## HENDERSON HILL 0.14213863 0.4435
## HILLCREST -0.10963710 0.5437
## HILLVIEW -0.10655888 0.5424
## HOLLAND DRIVE -0.04885105 0.5195
## HOLLAND ROAD 0.16943813 0.4327
## HONG KAH 0.11516180 0.4542
## HONG KAH NORTH 0.77508692 0.2191
## HOUGANG CENTRAL -3.64496706 0.9999
## HOUGANG EAST 1.13332245 0.1285
## HOUGANG WEST 0.94216869 0.1731
## INSTITUTION HILL 0.08604723 0.4657
## JELEBU -0.82985985 0.7967
## JOO SENG 0.05894018 0.4765
## JURONG GATEWAY 0.22992940 0.4091
## JURONG WEST CENTRAL -2.56350482 0.9948
## KAKI BUKIT -0.44852834 0.6731
## KAMPONG BUGIS 0.55094451 0.2908
## KAMPONG GLAM 0.51778311 0.3023
## KAMPONG JAVA -0.09799886 0.5390
## KAMPONG TIONG BAHRU 0.04384569 0.4825
## KAMPONG UBI 0.35459601 0.3614
## KANGKAR 0.89168267 0.1863
## KATONG 0.18054016 0.4284
## KEAT HONG 0.79198763 0.2142
## KEBUN BAHRU -0.27132442 0.6069
## KEMBANGAN -0.89655632 0.8150
## KHATIB 0.32615439 0.3722
## KIM KEAT 0.01399902 0.4944
## KOVAN -0.13328001 0.5530
## LAKESIDE 0.28540141 0.3877
## LAVENDER 0.50445284 0.3070
## LEEDON PARK 0.06370929 0.4746
## LEONIE HILL 0.34744552 0.3641
## LIM CHU KANG 0.48800198 0.3128
## LITTLE INDIA 0.22026878 0.4128
## LORONG 8 TOA PAYOH 0.01448336 0.4942
## LORONG AH SOO -0.00757267 0.5030
## LORONG CHUAN -0.05411217 0.5216
## LOWER SELETAR 0.98087669 0.1633
## LOYANG EAST 0.12589987 0.4499
## LOYANG WEST -0.27019954 0.6065
## MACKENZIE 0.60909741 0.2712
## MACPHERSON -1.01781231 0.8456
## MALCOLM 0.68224579 0.2475
## MANDAI ESTATE -0.02966944 0.5118
## MARGARET DRIVE -0.15304649 0.5608
## MARINE PARADE 0.01790528 0.4929
## MARITIME SQUARE 0.88909138 0.1870
## MARYMOUNT 0.15669025 0.4377
## MATILDA 9.35254883 0.0000
## MEI CHIN -0.26139566 0.6031
## MIDVIEW 5.65618425 0.0000
## MONK'S HILL 0.35334407 0.3619
## MOULMEIN 0.59665150 0.2754
## MOUNT PLEASANT 0.40579000 0.3424
## MOUNTBATTEN -0.14709131 0.5585
## NASSIM 0.23539176 0.4070
## NATIONAL UNIVERSITY OF S'PORE 0.79500383 0.2133
## NATURE RESERVE 0.02524500 0.4899
## NEE SOON 0.09230513 0.4632
## NEWTON CIRCUS 0.66540337 0.2529
## NORTH COAST -1.66240464 0.9518
## NORTHLAND -0.12501646 0.5497
## NORTHSHORE -0.90357207 0.8169
## ONE NORTH 0.22769902 0.4099
## ONE TREE HILL 0.49361164 0.3108
## ORANGE GROVE 0.24411112 0.4036
## OXLEY 0.39861282 0.3451
## PASIR PANJANG 1 0.58825772 0.2782
## PASIR PANJANG 2 0.84839103 0.1981
## PASIR RIS CENTRAL -0.19534849 0.5774
## PASIR RIS DRIVE 0.36645063 0.3570
## PASIR RIS PARK -0.00628068 0.5025
## PASIR RIS WEST -0.51652847 0.6973
## PATERSON 1.57128482 0.0581
## PEARL'S HILL 0.49522206 0.3102
## PEI CHUN 0.00958808 0.4962
## PENG SIANG 0.35622963 0.3608
## PEOPLE'S PARK 0.69920802 0.2422
## PORT 0.89487945 0.1854
## POTONG PASIR 0.01482781 0.4941
## PUNGGOL FIELD 8.83220546 0.0000
## PUNGGOL TOWN CENTRE 3.02620210 0.0012
## QUEENSWAY 0.31223567 0.3774
## REDHILL 0.19456193 0.4229
## RIDOUT 0.17678631 0.4298
## RIVERVALE 7.41253017 0.0000
## ROBERTSON QUAY 0.38097393 0.3516
## SAUJANA 1.12434043 0.1304
## SELEGIE 0.74424573 0.2284
## SELETAR -2.06605053 0.9806
## SELETAR HILLS 1.01324073 0.1555
## SEMBAWANG CENTRAL 1.11079478 0.1333
## SEMBAWANG EAST 0.18128679 0.4281
## SEMBAWANG HILLS 0.04201243 0.4832
## SEMBAWANG NORTH 0.57730523 0.2819
## SEMBAWANG SPRINGS -0.03539237 0.5141
## SEMBAWANG STRAITS -0.09178993 0.5366
## SENGKANG TOWN CENTRE 3.85879803 0.0001
## SENJA 0.36127533 0.3589
## SENNETT -0.30806665 0.6210
## SENTOSA 0.30832884 0.3789
## SERANGOON CENTRAL -1.85956726 0.9685
## SERANGOON GARDEN -0.09249335 0.5368
## SERANGOON NORTH -0.03936468 0.5157
## SHANGRI-LA -0.12642124 0.5503
## SIGLAP 0.01218251 0.4951
## SIMEI 1.55197921 0.0603
## SINGAPORE POLYTECHNIC -0.47781833 0.6836
## SOMERSET 2.99254368 0.0014
## SPRINGLEAF -0.00393981 0.5016
## SUNGEI ROAD 0.64314778 0.2601
## SUNSET WAY -0.03447550 0.5138
## SWISS CLUB 0.16619390 0.4340
## TAGORE 0.02639938 0.4895
## TAI SENG 0.01273831 0.4949
## TAMAN JURONG 0.23453614 0.4073
## TAMPINES EAST 1.65892870 0.0486
## TAMPINES NORTH -1.86958765 0.9692
## TAMPINES WEST 1.24026942 0.1074
## TANGLIN 0.46501400 0.3210
## TANGLIN HALT 0.01945836 0.4922
## TANJONG PAGAR 0.34895489 0.3636
## TANJONG RHU -0.12203436 0.5486
## TEBAN GARDENS -0.07078996 0.5282
## TECK WHYE 0.42500180 0.3354
## TELOK BLANGAH DRIVE -0.41100435 0.6595
## TELOK BLANGAH RISE 0.00993779 0.4960
## TELOK BLANGAH WAY 0.10848780 0.4568
## TIONG BAHRU -0.10767596 0.5429
## TIONG BAHRU STATION 0.23542283 0.4069
## TOA PAYOH CENTRAL 0.42454121 0.3356
## TOA PAYOH WEST -0.15244459 0.5606
## TOH GUAN 0.03000117 0.4880
## TOWNSVILLE -0.24124856 0.5953
## TRAFALGAR 3.33175502 0.0004
## TURF CLUB -1.25330484 0.8950
## TYERSALL 0.24402644 0.4036
## ULU PANDAN -0.13324503 0.5530
## UPPER PAYA LEBAR -0.33715627 0.6320
## UPPER THOMSON 0.03504266 0.4860
## VICTORIA 1.60795193 0.0539
## WATERWAY EAST 7.61663929 0.0000
## WENYA -0.02133753 0.5085
## WEST COAST -0.14767681 0.5587
## WESTERN WATER CATCHMENT -2.74096966 0.9969
## WOODGROVE 1.94258545 0.0260
## WOODLANDS EAST 8.43986388 0.0000
## WOODLANDS SOUTH 7.13374060 0.0000
## WOODLANDS WEST -0.80532226 0.7897
## WOODLEIGH 0.03506921 0.4860
## XILIN -0.44023278 0.6701
## YEW TEE 0.15780375 0.4373
## YIO CHU KANG EAST 0.36825905 0.3563
## YIO CHU KANG WEST -0.81788668 0.7933
## YISHUN CENTRAL -7.84960106 1.0000
## YISHUN EAST -1.53200531 0.9372
## YISHUN SOUTH -0.18051756 0.5716
## YISHUN WEST -0.64465598 0.7404
## YUHUA EAST -0.85700152 0.8043
## YUHUA WEST -0.01509412 0.5060
## YUNNAN -2.98660373 0.9986Computing local Moran’s I for TOTAL_TAP_OUT_VOLUME VS Population
Next, we compute local Moran’s I of the Tap Out vs Population residuals at subzone level with given a set of zi values and a listw object providing neighbour weighting information for the polygon associated with the zi values.
localMI_OUT <- localmoran(passenger_resident_tap_sp$residuals_out, rpassenger_resident_tap_sp_q)
head(localMI_OUT)## Ii E.Ii Var.Ii Z.Ii Pr(z > 0)
## 2 0.10538999 -0.004329004 0.1189055 0.31818588 0.3751720
## 3 0.28072819 -0.004329004 0.3240451 0.50075962 0.3082702
## 4 0.01285641 -0.004329004 0.1599334 0.04297248 0.4828617
## 5 0.07406694 -0.004329004 0.1927557 0.17856238 0.4291407
## 6 0.15030793 -0.004329004 0.1364889 0.41856665 0.3377664
## 7 -0.12149467 -0.004329004 0.1364889 -0.31714054 0.6244315printCoefmat(data.frame(localMI_OUT[fips,], row.names=passenger_resident_tap_sp$SUBZONE_N[fips]), check.names=FALSE)## Ii E.Ii Var.Ii
## ADMIRALTY 8.1788e-02 -4.3290e-03 1.9276e-01
## ALEXANDRA HILL 1.5031e-01 -4.3290e-03 1.3649e-01
## ALEXANDRA NORTH 1.0137e-02 -4.3290e-03 1.5993e-01
## ALJUNIED 3.7768e-01 -4.3290e-03 1.1891e-01
## ANAK BUKIT 3.2391e-02 -4.3290e-03 1.5993e-01
## ANCHORVALE 3.8112e+00 -4.3290e-03 2.4199e-01
## ANG MO KIO TOWN CENTRE -6.8674e-01 -4.3290e-03 1.3649e-01
## BALESTIER 1.8768e-02 -4.3290e-03 1.5993e-01
## BANGKIT 1.3505e-01 -4.3290e-03 3.2405e-01
## BAYSHORE 7.8810e-03 -4.3290e-03 2.4199e-01
## BEDOK NORTH -6.1078e-01 -4.3290e-03 1.1891e-01
## BEDOK RESERVOIR 3.3044e-01 -4.3290e-03 1.9276e-01
## BEDOK SOUTH -2.4659e-01 -4.3290e-03 1.9276e-01
## BENCOOLEN 2.8960e-01 -4.3290e-03 1.5993e-01
## BENDEMEER -2.2209e-01 -4.3290e-03 1.3649e-01
## BISHAN EAST -1.7167e-01 -4.3290e-03 1.0523e-01
## BOAT QUAY 2.8073e-01 -4.3290e-03 3.2405e-01
## BOON KENG 9.4373e-02 -4.3290e-03 3.2405e-01
## BOON LAY PLACE 2.3817e-01 -4.3290e-03 1.9276e-01
## BOON TECK -4.3701e-02 -4.3290e-03 1.9276e-01
## BOULEVARD 8.8972e-01 -4.3290e-03 1.1891e-01
## BRADDELL 5.2802e-02 -4.3290e-03 1.9276e-01
## BRICKWORKS 3.2846e-02 -4.3290e-03 2.4199e-01
## BUGIS 8.5348e-01 -4.3290e-03 3.2405e-01
## BUKIT BATOK CENTRAL -3.7156e-02 -4.3290e-03 1.9276e-01
## BUKIT BATOK EAST 4.2312e-03 -4.3290e-03 2.4199e-01
## BUKIT BATOK SOUTH 1.7505e-03 -4.3290e-03 1.3649e-01
## BUKIT BATOK WEST 1.3127e-02 -4.3290e-03 1.5993e-01
## BUKIT HO SWEE -1.2149e-01 -4.3290e-03 1.3649e-01
## BUKIT MERAH 3.1250e-01 -4.3290e-03 1.3649e-01
## CECIL 2.6477e-01 -4.3290e-03 3.2405e-01
## CENTRAL SUBZONE 2.7263e-01 -4.3290e-03 4.8816e-01
## CHANGI POINT 3.0727e-01 -4.3290e-03 9.8049e-01
## CHANGI WEST 2.5009e-02 -4.3290e-03 1.5993e-01
## CHATSWORTH 4.3788e-02 -4.3290e-03 1.0523e-01
## CHENG SAN -1.6077e-02 -4.3290e-03 1.5993e-01
## CHINA SQUARE 2.7450e-01 -4.3290e-03 2.4199e-01
## CHINATOWN 1.9712e-01 -4.3290e-03 1.5993e-01
## CHOA CHU KANG CENTRAL -8.4423e-01 -4.3290e-03 1.9276e-01
## CHOA CHU KANG NORTH 2.9499e-01 -4.3290e-03 1.9276e-01
## CHONG BOON 1.9054e-02 -4.3290e-03 1.3649e-01
## CLARKE QUAY 3.2300e-01 -4.3290e-03 1.9276e-01
## CLEMENTI CENTRAL -1.8108e-01 -4.3290e-03 1.9276e-01
## CLEMENTI NORTH -1.9291e-01 -4.3290e-03 1.9276e-01
## CLEMENTI WEST -5.4602e-02 -4.3290e-03 1.9276e-01
## CLEMENTI WOODS -2.8413e-02 -4.3290e-03 1.3649e-01
## COMMONWEALTH -2.5212e-02 -4.3290e-03 1.9276e-01
## COMPASSVALE 1.1733e+00 -4.3290e-03 1.3649e-01
## CORONATION ROAD 5.0183e-02 -4.3290e-03 1.5993e-01
## CRAWFORD 1.7541e-01 -4.3290e-03 1.9276e-01
## DAIRY FARM 1.1658e-03 -4.3290e-03 1.9276e-01
## DEPOT ROAD 1.4410e-02 -4.3290e-03 1.9276e-01
## DHOBY GHAUT 6.7485e-01 -4.3290e-03 1.9276e-01
## DOVER 5.8402e-02 -4.3290e-03 1.9276e-01
## DUNEARN 4.8139e-02 -4.3290e-03 1.9276e-01
## EVERTON PARK 3.1227e-02 -4.3290e-03 3.2405e-01
## FABER 4.1297e-02 -4.3290e-03 3.2405e-01
## FAJAR 5.7574e-01 -4.3290e-03 3.2405e-01
## FARRER COURT 3.7138e-03 -4.3290e-03 2.4199e-01
## FARRER PARK 4.5590e-01 -4.3290e-03 1.5993e-01
## FERNVALE 3.1225e+00 -4.3290e-03 1.5993e-01
## FLORA DRIVE 1.5598e-01 -4.3290e-03 1.9276e-01
## FORT CANNING 2.6847e-01 -4.3290e-03 1.9276e-01
## FRANKEL 9.7398e-04 -4.3290e-03 1.1891e-01
## GEYLANG BAHRU 2.6827e-02 -4.3290e-03 1.9276e-01
## GEYLANG EAST 1.9264e-01 -4.3290e-03 1.1891e-01
## GHIM MOH -1.3093e-01 -4.3290e-03 1.9276e-01
## GOMBAK 3.6850e-02 -4.3290e-03 1.1891e-01
## GOODWOOD PARK 2.2482e-01 -4.3290e-03 1.5993e-01
## GUILIN -1.5461e-02 -4.3290e-03 1.5993e-01
## HENDERSON HILL 1.2856e-02 -4.3290e-03 1.5993e-01
## HILLCREST -6.2686e-02 -4.3290e-03 1.9276e-01
## HILLVIEW -2.3013e-02 -4.3290e-03 1.3649e-01
## HOLLAND DRIVE -3.0535e-02 -4.3290e-03 1.5993e-01
## HOLLAND ROAD 5.5824e-02 -4.3290e-03 1.5993e-01
## HONG KAH 2.0777e-03 -4.3290e-03 1.9276e-01
## HONG KAH NORTH 4.0626e-01 -4.3290e-03 2.4199e-01
## HOUGANG CENTRAL -1.8704e+00 -4.3290e-03 1.9276e-01
## HOUGANG EAST 4.8037e-01 -4.3290e-03 1.9276e-01
## HOUGANG WEST 3.5324e-01 -4.3290e-03 1.3649e-01
## INSTITUTION HILL 4.5863e-02 -4.3290e-03 2.4199e-01
## JELEBU -3.2559e-01 -4.3290e-03 1.3649e-01
## JOO SENG 2.8060e-02 -4.3290e-03 1.9276e-01
## JURONG GATEWAY 3.2604e-01 -4.3290e-03 3.2405e-01
## JURONG WEST CENTRAL -1.4123e+00 -4.3290e-03 3.2405e-01
## KAKI BUKIT -1.0290e-01 -4.3290e-03 1.9276e-01
## KAMPONG BUGIS 2.8101e-01 -4.3290e-03 1.9276e-01
## KAMPONG GLAM 3.6754e-01 -4.3290e-03 4.8816e-01
## KAMPONG JAVA -1.5040e-02 -4.3290e-03 1.3649e-01
## KAMPONG TIONG BAHRU 3.6348e-02 -4.3290e-03 1.3649e-01
## KAMPONG UBI 1.3726e-01 -4.3290e-03 1.3649e-01
## KANGKAR 3.0878e-01 -4.3290e-03 1.9276e-01
## KATONG 9.5455e-02 -4.3290e-03 2.4199e-01
## KEAT HONG 5.5591e-01 -4.3290e-03 1.9276e-01
## KEBUN BAHRU -1.5359e-01 -4.3290e-03 1.9276e-01
## KEMBANGAN -4.4683e-01 -4.3290e-03 1.5993e-01
## KHATIB 2.3685e-01 -4.3290e-03 1.3649e-01
## KIM KEAT -2.0221e-02 -4.3290e-03 1.5993e-01
## KOVAN -5.3071e-02 -4.3290e-03 1.3649e-01
## LAKESIDE 1.5612e-01 -4.3290e-03 1.5993e-01
## LAVENDER 1.8951e-01 -4.3290e-03 1.3649e-01
## LEEDON PARK 5.2314e-03 -4.3290e-03 1.0523e-01
## LEONIE HILL 1.0031e-01 -4.3290e-03 1.1891e-01
## LIM CHU KANG 4.6354e-01 -4.3290e-03 9.8049e-01
## LITTLE INDIA 7.0329e-02 -4.3290e-03 1.5993e-01
## LORONG 8 TOA PAYOH 2.5628e-02 -4.3290e-03 1.3649e-01
## LORONG AH SOO 2.1006e-02 -4.3290e-03 1.5993e-01
## LORONG CHUAN -5.3267e-02 -4.3290e-03 1.3649e-01
## LOWER SELETAR 4.3284e-01 -4.3290e-03 1.9276e-01
## LOYANG EAST 5.2864e-02 -4.3290e-03 3.2405e-01
## LOYANG WEST -1.8671e-01 -4.3290e-03 1.9276e-01
## MACKENZIE 2.5741e-01 -4.3290e-03 3.2405e-01
## MACPHERSON -4.0406e-01 -4.3290e-03 1.5993e-01
## MALCOLM 2.6559e-01 -4.3290e-03 1.3649e-01
## MANDAI ESTATE 3.1563e-02 -4.3290e-03 4.8816e-01
## MARGARET DRIVE -1.0517e-01 -4.3290e-03 1.0523e-01
## MARINE PARADE -6.2610e-03 -4.3290e-03 2.4199e-01
## MARITIME SQUARE 3.3512e-01 -4.3290e-03 1.5993e-01
## MARYMOUNT -3.4170e-03 -4.3290e-03 1.5993e-01
## MATILDA 2.9093e+00 -4.3290e-03 1.1891e-01
## MEI CHIN -5.7048e-02 -4.3290e-03 1.5993e-01
## MIDVIEW 3.3333e+00 -4.3290e-03 3.2405e-01
## MONK'S HILL 1.4741e-01 -4.3290e-03 2.4199e-01
## MOULMEIN 2.1099e-01 -4.3290e-03 1.5993e-01
## MOUNT PLEASANT 1.5174e-01 -4.3290e-03 1.9276e-01
## MOUNTBATTEN -6.0152e-02 -4.3290e-03 1.9276e-01
## NASSIM 3.2582e-02 -4.3290e-03 1.1891e-01
## NATIONAL UNIVERSITY OF S'PORE 4.1637e-01 -4.3290e-03 2.4199e-01
## NATURE RESERVE 2.0373e-02 -4.3290e-03 2.4199e-01
## NEE SOON 1.4609e-01 -4.3290e-03 3.2405e-01
## NEWTON CIRCUS 2.8053e-01 -4.3290e-03 3.2405e-01
## NORTH COAST 4.6846e-01 -4.3290e-03 9.8049e-01
## NORTHLAND -6.0001e-02 -4.3290e-03 1.9276e-01
## NORTHSHORE -6.1278e-01 -4.3290e-03 4.8816e-01
## ONE NORTH 1.3101e-01 -4.3290e-03 1.3649e-01
## ONE TREE HILL 1.9661e-01 -4.3290e-03 1.9276e-01
## ORANGE GROVE 1.5995e-01 -4.3290e-03 3.2405e-01
## OXLEY 1.4861e-01 -4.3290e-03 1.9276e-01
## PASIR PANJANG 1 2.4843e-01 -4.3290e-03 1.9276e-01
## PASIR PANJANG 2 3.2219e-01 -4.3290e-03 2.4199e-01
## PASIR RIS CENTRAL -2.3697e-01 -4.3290e-03 1.9276e-01
## PASIR RIS DRIVE 8.6499e-02 -4.3290e-03 1.5993e-01
## PASIR RIS PARK -5.5140e-02 -4.3290e-03 2.4199e-01
## PASIR RIS WEST -3.6923e-01 -4.3290e-03 3.2405e-01
## PATERSON 3.8161e-01 -4.3290e-03 1.9276e-01
## PEARL'S HILL 1.0539e-01 -4.3290e-03 1.1891e-01
## PEI CHUN 2.5097e-03 -4.3290e-03 1.9276e-01
## PENG SIANG 1.6031e-01 -4.3290e-03 2.4199e-01
## PEOPLE'S PARK 3.5426e-01 -4.3290e-03 4.8816e-01
## PORT 4.1920e-01 -4.3290e-03 2.4199e-01
## POTONG PASIR -5.9535e-05 -4.3290e-03 1.3649e-01
## PUNGGOL FIELD 4.1816e+00 -4.3290e-03 1.9276e-01
## PUNGGOL TOWN CENTRE 1.4360e+00 -4.3290e-03 1.9276e-01
## QUEENSWAY 2.1440e-01 -4.3290e-03 2.4199e-01
## REDHILL 7.4067e-02 -4.3290e-03 1.9276e-01
## RIDOUT 4.0532e-02 -4.3290e-03 1.3649e-01
## RIVERVALE 2.9363e+00 -4.3290e-03 1.5993e-01
## ROBERTSON QUAY 1.1435e-01 -4.3290e-03 1.3649e-01
## SAUJANA 5.5425e-01 -4.3290e-03 3.2405e-01
## SELEGIE 2.9357e-01 -4.3290e-03 1.9276e-01
## SELETAR -1.1574e+00 -4.3290e-03 3.2405e-01
## SELETAR HILLS 3.6534e-01 -4.3290e-03 1.9276e-01
## SEMBAWANG CENTRAL 6.9202e-01 -4.3290e-03 2.4199e-01
## SEMBAWANG EAST 5.2629e-02 -4.3290e-03 1.9276e-01
## SEMBAWANG HILLS -1.9207e-02 -4.3290e-03 1.9276e-01
## SEMBAWANG NORTH 3.5677e-01 -4.3290e-03 4.8816e-01
## SEMBAWANG SPRINGS -3.6212e-03 -4.3290e-03 1.9276e-01
## SEMBAWANG STRAITS -4.2975e-02 -4.3290e-03 4.8816e-01
## SENGKANG TOWN CENTRE 1.9647e+00 -4.3290e-03 1.9276e-01
## SENJA 1.4895e-01 -4.3290e-03 2.4199e-01
## SENNETT -7.8305e-02 -4.3290e-03 1.5993e-01
## SENTOSA 4.0068e-01 -4.3290e-03 9.8049e-01
## SERANGOON CENTRAL -5.5912e-01 -4.3290e-03 1.9276e-01
## SERANGOON GARDEN -5.1179e-02 -4.3290e-03 1.1891e-01
## SERANGOON NORTH -1.3603e-01 -4.3290e-03 1.9276e-01
## SHANGRI-LA -5.1029e-03 -4.3290e-03 1.5993e-01
## SIGLAP -3.1087e-03 -4.3290e-03 3.2405e-01
## SIMEI 5.8282e-01 -4.3290e-03 1.5993e-01
## SINGAPORE POLYTECHNIC -1.5243e-01 -4.3290e-03 1.5993e-01
## SOMERSET 1.0222e+00 -4.3290e-03 1.5993e-01
## SPRINGLEAF -8.7502e-03 -4.3290e-03 1.9276e-01
## SUNGEI ROAD 2.7890e-01 -4.3290e-03 2.4199e-01
## SUNSET WAY -1.2854e-02 -4.3290e-03 1.5993e-01
## SWISS CLUB 1.0853e-01 -4.3290e-03 1.9276e-01
## TAGORE 5.1800e-03 -4.3290e-03 1.9276e-01
## TAI SENG -9.9555e-03 -4.3290e-03 1.9276e-01
## TAMAN JURONG 6.4237e-02 -4.3290e-03 3.2405e-01
## TAMPINES EAST 6.0376e-01 -4.3290e-03 1.1891e-01
## TAMPINES NORTH -6.2095e-01 -4.3290e-03 1.9276e-01
## TAMPINES WEST 5.9318e-01 -4.3290e-03 1.9276e-01
## TANGLIN 2.0067e-01 -4.3290e-03 1.9276e-01
## TANGLIN HALT 1.3917e-02 -4.3290e-03 1.9276e-01
## TANJONG PAGAR 1.5022e-01 -4.3290e-03 3.2405e-01
## TANJONG RHU -9.1535e-02 -4.3290e-03 2.4199e-01
## TEBAN GARDENS -1.0636e-02 -4.3290e-03 4.8816e-01
## TECK WHYE 2.0025e-01 -4.3290e-03 1.5993e-01
## TELOK BLANGAH DRIVE -6.7022e-02 -4.3290e-03 2.4199e-01
## TELOK BLANGAH RISE -6.0596e-03 -4.3290e-03 2.4199e-01
## TELOK BLANGAH WAY -1.8016e-02 -4.3290e-03 1.5993e-01
## TIONG BAHRU -3.3267e-02 -4.3290e-03 2.4199e-01
## TIONG BAHRU STATION 1.0799e-01 -4.3290e-03 1.9276e-01
## TOA PAYOH CENTRAL 1.3907e-01 -4.3290e-03 1.3649e-01
## TOA PAYOH WEST -7.7198e-02 -4.3290e-03 1.5993e-01
## TOH GUAN 2.6612e-02 -4.3290e-03 2.4199e-01
## TOWNSVILLE -1.7755e-01 -4.3290e-03 1.3649e-01
## TRAFALGAR 1.5993e+00 -4.3290e-03 1.9276e-01
## TURF CLUB -6.7380e-01 -4.3290e-03 4.8816e-01
## TYERSALL 4.6069e-02 -4.3290e-03 1.3649e-01
## ULU PANDAN -3.5311e-02 -4.3290e-03 1.5993e-01
## UPPER PAYA LEBAR -5.0883e-02 -4.3290e-03 1.5993e-01
## UPPER THOMSON 1.1194e-02 -4.3290e-03 2.4199e-01
## VICTORIA 6.6427e-01 -4.3290e-03 2.4199e-01
## WATERWAY EAST 3.7388e+00 -4.3290e-03 2.4199e-01
## WENYA -8.1321e-03 -4.3290e-03 1.9276e-01
## WEST COAST -1.7164e-02 -4.3290e-03 2.4199e-01
## WESTERN WATER CATCHMENT -1.1987e+00 -4.3290e-03 1.3649e-01
## WOODGROVE 8.5148e-01 -4.3290e-03 2.4199e-01
## WOODLANDS EAST 4.7361e+00 -4.3290e-03 3.2405e-01
## WOODLANDS SOUTH 4.2192e+00 -4.3290e-03 3.2405e-01
## WOODLANDS WEST 1.0885e-01 -4.3290e-03 3.2405e-01
## WOODLEIGH 5.7887e-02 -4.3290e-03 1.3649e-01
## XILIN -2.3064e-01 -4.3290e-03 1.5993e-01
## YEW TEE 9.8881e-02 -4.3290e-03 4.8816e-01
## YIO CHU KANG EAST 2.3336e-01 -4.3290e-03 3.2405e-01
## YIO CHU KANG WEST -4.0076e-01 -4.3290e-03 2.4199e-01
## YISHUN CENTRAL -3.7574e+00 -4.3290e-03 1.9276e-01
## YISHUN EAST -5.6833e-01 -4.3290e-03 2.4199e-01
## YISHUN SOUTH -3.3366e-01 -4.3290e-03 1.5993e-01
## YISHUN WEST -4.1800e-01 -4.3290e-03 1.3649e-01
## YUHUA EAST -3.4522e-01 -4.3290e-03 1.9276e-01
## YUHUA WEST 3.6823e-03 -4.3290e-03 2.4199e-01
## YUNNAN -1.5012e+00 -4.3290e-03 2.4199e-01
## Z.Ii Pr.z...0.
## ADMIRALTY 1.9615e-01 0.4222
## ALEXANDRA HILL 4.1857e-01 0.3378
## ALEXANDRA NORTH 3.6171e-02 0.4856
## ALJUNIED 1.1078e+00 0.1340
## ANAK BUKIT 9.1819e-02 0.4634
## ANCHORVALE 7.7564e+00 0.0000
## ANG MO KIO TOWN CENTRE -1.8471e+00 0.9676
## BALESTIER 5.7754e-02 0.4770
## BANGKIT 2.4485e-01 0.4033
## BAYSHORE 2.4821e-02 0.4901
## BEDOK NORTH -1.7587e+00 0.9607
## BEDOK RESERVOIR 7.6250e-01 0.2229
## BEDOK SOUTH -5.5180e-01 0.7095
## BENCOOLEN 7.3499e-01 0.2312
## BENDEMEER -5.8944e-01 0.7222
## BISHAN EAST -5.1585e-01 0.6970
## BOAT QUAY 5.0076e-01 0.3083
## BOON KENG 1.7339e-01 0.4312
## BOON LAY PLACE 5.5233e-01 0.2904
## BOON TECK -8.9678e-02 0.5357
## BOULEVARD 2.5928e+00 0.0048
## BRADDELL 1.3013e-01 0.4482
## BRICKWORKS 7.5570e-02 0.4699
## BUGIS 1.5069e+00 0.0659
## BUKIT BATOK CENTRAL -7.4769e-02 0.5298
## BUKIT BATOK EAST 1.7402e-02 0.4931
## BUKIT BATOK SOUTH 1.6456e-02 0.4934
## BUKIT BATOK WEST 4.3649e-02 0.4826
## BUKIT HO SWEE -3.1714e-01 0.6244
## BUKIT MERAH 8.5760e-01 0.1956
## CECIL 4.7273e-01 0.3182
## CENTRAL SUBZONE 3.9641e-01 0.3459
## CHANGI POINT 3.1468e-01 0.3765
## CHANGI WEST 7.3360e-02 0.4708
## CHATSWORTH 1.4833e-01 0.4410
## CHENG SAN -2.9376e-02 0.5117
## CHINA SQUARE 5.6682e-01 0.2854
## CHINATOWN 5.0372e-01 0.3072
## CHOA CHU KANG CENTRAL -1.9131e+00 0.9721
## CHOA CHU KANG NORTH 6.8176e-01 0.2477
## CHONG BOON 6.3293e-02 0.4748
## CLARKE QUAY 7.4556e-01 0.2280
## CLEMENTI CENTRAL -4.0260e-01 0.6564
## CLEMENTI NORTH -4.2954e-01 0.6662
## CLEMENTI WEST -1.1451e-01 0.5456
## CLEMENTI WOODS -6.5191e-02 0.5260
## COMMONWEALTH -4.7565e-02 0.5190
## COMPASSVALE 3.1876e+00 0.0007
## CORONATION ROAD 1.3631e-01 0.4458
## CRAWFORD 4.0939e-01 0.3411
## DAIRY FARM 1.2515e-02 0.4950
## DEPOT ROAD 4.2683e-02 0.4830
## DHOBY GHAUT 1.5470e+00 0.0609
## DOVER 1.4288e-01 0.4432
## DUNEARN 1.1951e-01 0.4524
## EVERTON PARK 6.2460e-02 0.4751
## FABER 8.0150e-02 0.4681
## FAJAR 1.0190e+00 0.1541
## FARRER COURT 1.6350e-02 0.4935
## FARRER PARK 1.1508e+00 0.1249
## FERNVALE 7.8187e+00 0.0000
## FLORA DRIVE 3.6514e-01 0.3575
## FORT CANNING 6.2136e-01 0.2672
## FRANKEL 1.5379e-02 0.4939
## GEYLANG BAHRU 7.0964e-02 0.4717
## GEYLANG EAST 5.7121e-01 0.2839
## GHIM MOH -2.8837e-01 0.6135
## GOMBAK 1.1942e-01 0.4525
## GOODWOOD PARK 5.7299e-01 0.2833
## GUILIN -2.7835e-02 0.5111
## HENDERSON HILL 4.2972e-02 0.4829
## HILLCREST -1.3292e-01 0.5529
## HILLVIEW -5.0574e-02 0.5202
## HOLLAND DRIVE -6.5528e-02 0.5261
## HOLLAND ROAD 1.5041e-01 0.4402
## HONG KAH 1.4592e-02 0.4942
## HONG KAH NORTH 8.3466e-01 0.2020
## HOUGANG CENTRAL -4.2504e+00 1.0000
## HOUGANG EAST 1.1040e+00 0.1348
## HOUGANG WEST 9.6786e-01 0.1666
## INSTITUTION HILL 1.0203e-01 0.4594
## JELEBU -8.6959e-01 0.8077
## JOO SENG 7.3773e-02 0.4706
## JURONG GATEWAY 5.8035e-01 0.2808
## JURONG WEST CENTRAL -2.4733e+00 0.9933
## KAKI BUKIT -2.2451e-01 0.5888
## KAMPONG BUGIS 6.4992e-01 0.2579
## KAMPONG GLAM 5.3224e-01 0.2973
## KAMPONG JAVA -2.8991e-02 0.5116
## KAMPONG TIONG BAHRU 1.1010e-01 0.4562
## KAMPONG UBI 3.8325e-01 0.3508
## KANGKAR 7.1317e-01 0.2379
## KATONG 2.0284e-01 0.4196
## KEAT HONG 1.2761e+00 0.1010
## KEBUN BAHRU -3.3997e-01 0.6331
## KEMBANGAN -1.1065e+00 0.8657
## KHATIB 6.5282e-01 0.2569
## KIM KEAT -3.9738e-02 0.5158
## KOVAN -1.3193e-01 0.5525
## LAKESIDE 4.0121e-01 0.3441
## LAVENDER 5.2467e-01 0.2999
## LEEDON PARK 2.9472e-02 0.4882
## LEONIE HILL 3.0346e-01 0.3808
## LIM CHU KANG 4.7250e-01 0.3183
## LITTLE INDIA 1.8668e-01 0.4260
## LORONG 8 TOA PAYOH 8.1087e-02 0.4677
## LORONG AH SOO 6.3350e-02 0.4747
## LORONG CHUAN -1.3246e-01 0.5527
## LOWER SELETAR 9.9573e-01 0.1597
## LOYANG EAST 1.0047e-01 0.4600
## LOYANG WEST -4.1541e-01 0.6611
## MACKENZIE 4.5979e-01 0.3228
## MACPHERSON -9.9954e-01 0.8412
## MALCOLM 7.3062e-01 0.2325
## MANDAI ESTATE 5.1372e-02 0.4795
## MARGARET DRIVE -3.1087e-01 0.6220
## MARINE PARADE -3.9275e-03 0.5016
## MARITIME SQUARE 8.4881e-01 0.1980
## MARYMOUNT 2.2805e-03 0.4991
## MATILDA 8.4496e+00 0.0000
## MEI CHIN -1.3182e-01 0.5524
## MIDVIEW 5.8633e+00 0.0000
## MONK'S HILL 3.0847e-01 0.3789
## MOULMEIN 5.3841e-01 0.2951
## MOUNT PLEASANT 3.5548e-01 0.3611
## MOUNTBATTEN -1.2715e-01 0.5506
## NASSIM 1.0704e-01 0.4574
## NATIONAL UNIVERSITY OF S'PORE 8.5520e-01 0.1962
## NATURE RESERVE 5.0214e-02 0.4800
## NEE SOON 2.6424e-01 0.3958
## NEWTON CIRCUS 5.0041e-01 0.3084
## NORTH COAST 4.7747e-01 0.3165
## NORTHLAND -1.2680e-01 0.5505
## NORTHSHORE -8.7086e-01 0.8081
## ONE NORTH 3.6633e-01 0.3571
## ONE TREE HILL 4.5768e-01 0.3236
## ORANGE GROVE 2.8858e-01 0.3865
## OXLEY 3.4836e-01 0.3638
## PASIR PANJANG 1 5.7570e-01 0.2824
## PASIR PANJANG 2 6.6377e-01 0.2534
## PASIR RIS CENTRAL -5.2988e-01 0.7019
## PASIR RIS DRIVE 2.2712e-01 0.4102
## PASIR RIS PARK -1.0329e-01 0.5411
## PASIR RIS WEST -6.4102e-01 0.7392
## PATERSON 8.7905e-01 0.1897
## PEARL'S HILL 3.1819e-01 0.3752
## PEI CHUN 1.5577e-02 0.4938
## PENG SIANG 3.3468e-01 0.3689
## PEOPLE'S PARK 5.1324e-01 0.3039
## PORT 8.6097e-01 0.1946
## POTONG PASIR 1.1556e-02 0.4954
## PUNGGOL FIELD 9.5344e+00 0.0000
## PUNGGOL TOWN CENTRE 3.2807e+00 0.0005
## QUEENSWAY 4.4464e-01 0.3283
## REDHILL 1.7856e-01 0.4291
## RIDOUT 1.2143e-01 0.4517
## RIVERVALE 7.3531e+00 0.0000
## ROBERTSON QUAY 3.2124e-01 0.3740
## SAUJANA 9.8125e-01 0.1632
## SELEGIE 6.7852e-01 0.2487
## SELETAR -2.0256e+00 0.9786
## SELETAR HILLS 8.4199e-01 0.1999
## SEMBAWANG CENTRAL 1.4156e+00 0.0785
## SEMBAWANG EAST 1.2973e-01 0.4484
## SEMBAWANG HILLS -3.3887e-02 0.5135
## SEMBAWANG NORTH 5.1683e-01 0.3026
## SEMBAWANG SPRINGS 1.6122e-03 0.4994
## SEMBAWANG STRAITS -5.5312e-02 0.5221
## SENGKANG TOWN CENTRE 4.4849e+00 0.0000
## SENJA 3.1159e-01 0.3777
## SENNETT -1.8498e-01 0.5734
## SENTOSA 4.0902e-01 0.3413
## SERANGOON CENTRAL -1.2636e+00 0.8968
## SERANGOON GARDEN -1.3587e-01 0.5540
## SERANGOON NORTH -2.9997e-01 0.6179
## SHANGRI-LA -1.9352e-03 0.5008
## SIGLAP 2.1436e-03 0.4991
## SIMEI 1.4682e+00 0.0710
## SINGAPORE POLYTECHNIC -3.7033e-01 0.6444
## SOMERSET 2.5668e+00 0.0051
## SPRINGLEAF -1.0070e-02 0.5040
## SUNGEI ROAD 5.7577e-01 0.2824
## SUNSET WAY -2.1318e-02 0.5085
## SWISS CLUB 2.5706e-01 0.3986
## TAGORE 2.1659e-02 0.4914
## TAI SENG -1.2816e-02 0.5051
## TAMAN JURONG 1.2045e-01 0.4521
## TAMPINES EAST 1.7635e+00 0.0389
## TAMPINES NORTH -1.4045e+00 0.9199
## TAMPINES WEST 1.3610e+00 0.0868
## TANGLIN 4.6691e-01 0.3203
## TANGLIN HALT 4.1558e-02 0.4834
## TANJONG PAGAR 2.7149e-01 0.3930
## TANJONG RHU -1.7727e-01 0.5704
## TEBAN GARDENS -9.0265e-03 0.5036
## TECK WHYE 5.1155e-01 0.3045
## TELOK BLANGAH DRIVE -1.2744e-01 0.5507
## TELOK BLANGAH RISE -3.5180e-03 0.5014
## TELOK BLANGAH WAY -3.4224e-02 0.5137
## TIONG BAHRU -5.8826e-02 0.5235
## TIONG BAHRU STATION 2.5582e-01 0.3990
## TOA PAYOH CENTRAL 3.8816e-01 0.3489
## TOA PAYOH WEST -1.8221e-01 0.5723
## TOH GUAN 6.2898e-02 0.4749
## TOWNSVILLE -4.6886e-01 0.6804
## TRAFALGAR 3.6526e+00 0.0001
## TURF CLUB -9.5819e-01 0.8310
## TYERSALL 1.3642e-01 0.4457
## ULU PANDAN -7.7472e-02 0.5309
## UPPER PAYA LEBAR -1.1641e-01 0.5463
## UPPER THOMSON 3.1555e-02 0.4874
## VICTORIA 1.3592e+00 0.0870
## WATERWAY EAST 7.6092e+00 0.0000
## WENYA -8.6622e-03 0.5035
## WEST COAST -2.6092e-02 0.5104
## WESTERN WATER CATCHMENT -3.2330e+00 0.9994
## WOODGROVE 1.7397e+00 0.0410
## WOODLANDS EAST 8.3275e+00 0.0000
## WOODLANDS SOUTH 7.4194e+00 0.0000
## WOODLANDS WEST 1.9883e-01 0.4212
## WOODLEIGH 1.6840e-01 0.4331
## XILIN -5.6590e-01 0.7143
## YEW TEE 1.4772e-01 0.4413
## YIO CHU KANG EAST 4.1755e-01 0.3381
## YIO CHU KANG WEST -8.0588e-01 0.7898
## YISHUN CENTRAL -8.5484e+00 1.0000
## YISHUN EAST -1.1465e+00 0.8742
## YISHUN SOUTH -8.2350e-01 0.7949
## YISHUN WEST -1.1197e+00 0.8686
## YUHUA EAST -7.7644e-01 0.7813
## YUHUA WEST 1.6286e-02 0.4935
## YUNNAN -3.0429e+00 0.9988Mapping the local Moran’s I for TOTAL_TAP_IN_VOLUME VS Population
Before mapping the local Moran’s I map, it is wise to append the local Moran’s I dataframe (i.e. localMI) onto passenger_resident_tap_sp SpatialPolygonDataFrame.
passenger_resident_tap_sp.localMI <- cbind(passenger_resident_tap_sp,localMI)Mapping both local Moran’s I values and p-values
Using choropleth mapping functions of tmap package, we can plot both the local Moran’s I values map and its correpence p-values map next to each other for Tap In vs Population.
localMI.map <- tm_shape(passenger_resident_tap_sp.localMI) +
tm_fill(col = "Ii",
style = "pretty",
title = "local moran statistics") +
tm_borders(alpha = 0.5)
pvalue.map <- tm_shape(passenger_resident_tap_sp.localMI) +
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.map, pvalue.map, asp=1, ncol=2, sync = TRUE)Mapping the local Moran’s I for Tap In VS Population
passenger_resident_tap_sp.localMI_OUT <- cbind(passenger_resident_tap_sp,localMI_OUT)Mapping both local Moran’s I values and p-values
Using choropleth mapping functions of tmap package, we can plot both the local Moran’s I values map and its correpence p-values map next to each other for Tap Out vs Population.
localMI_OUT.map <- tm_shape(passenger_resident_tap_sp.localMI_OUT) +
tm_fill(col = "Ii",
style = "pretty",
title = "local moran statistics") +
tm_borders(alpha = 0.5)
pvalue_OUT.map <- tm_shape(passenger_resident_tap_sp.localMI_OUT) +
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_OUT.map, pvalue_OUT.map, asp=1, ncol=2, sync = TRUE)Creating a LISA Cluster Map for Tap out VS Population
The LISA Cluster Map shows the significant locations color coded by type of spatial autocorrelation. The first step before we can generate the LISA cluster map is to plot the Moran scatterplot.
Plotting Moran scatterplot
The code chunk below plots the Moran scatterplot of Tap in vs Population residuals to illustrate the relationship between the values of the chosen attribute at each location and the average value of the same attribute at neighboring locations
nci <- moran.plot(passenger_resident_tap_sp$TOTAL_TAP_IN_VOLUME, rpassenger_resident_tap_sp_q, labels=as.character(passenger_resident_tap_sp$SUBZONE_N), xlab="Residuals", ylab="Spatially Lag Residuals")
### Plotting Moran scatterplot with standardised variable Scaling the variable of interest by dividing the (centered) variable by their standard deviations.
passenger_resident_tap_sp$Z.TOTAL_TAP_IN_VOLUME <- scale(passenger_resident_tap_sp$TOTAL_TAP_IN_VOLUME) %>% as.vector
We then plot the Moran scatterplot again with the scaled data.
nci2 <- moran.plot(passenger_resident_tap_sp$Z.TOTAL_TAP_IN_VOLUME, rpassenger_resident_tap_sp_q, labels=as.character(passenger_resident_tap_sp$SUBZONE_N), xlab="z-Residuals", ylab="Spatially Lag Residuals")
With the local Moran I values, we plot a LISA cluster map. But to do so, we have to create the quadrants such that we can view the clusters and outliers.As we are testing at the confidence interval oof 95%, we set the significance level to 0.05.
quadrant <- vector(mode="numeric",length=nrow(localMI))
DV <- passenger_resident_tap_sp$residuals - mean(passenger_resident_tap_sp$residuals)
C_mI <- localMI[,1] - mean(localMI[,1])
signif <- 0.05
quadrant[DV >0 & C_mI>0] <- 4
quadrant[DV <0 & C_mI<0] <- 1
quadrant[DV <0 & C_mI>0] <- 2
quadrant[DV >0 & C_mI<0] <- 3
quadrant[localMI[,5]>signif] <- 0Creating a LISA Cluster Map for Tap Out VS Population
The LISA Cluster Map shows the significant locations color coded by type of spatial autocorrelation. The first step before we can generate the LISA cluster map is to plot the Moran scatterplot.
Plotting Moran scatterplot
The Moran scatterplot is an illustration of the relationship between the values of the chosen attribute at each location and the average value of the same attribute at neighboring locations.
The code chunk below plots the Moran scatterplot of GDPPC 2012 by using moran.plot() of spdep.
nci_OUT <- moran.plot(passenger_resident_tap_sp$TOTAL_TAP_OUT_VOLUME, rpassenger_resident_tap_sp_q, labels=as.character(passenger_resident_tap_sp$SUBZONE_N), xlab="Residuals", ylab="Spatially Lag Residuals")
Plotting Moran scatterplot with standardised variable
First we will use scale() to centers and scales the variable. here centering is done by subtracting the mean (omitting NAs) the corresponding columns, and scaling is done by dividing the (centered) variable by their standard deviations.
passenger_resident_tap_sp$Z.TOTAL_TAP_OUT_VOLUME <- scale(passenger_resident_tap_sp$TOTAL_TAP_OUT_VOLUME) %>% as.vector
The as.vector() added to the end is to make sure that the data type we get out of this is a vector, that map neatly into out dataframe.
Now, we are ready to plot the Moran scatterplot again by using the code chunk below.
nci2_OUT <- moran.plot(passenger_resident_tap_sp$Z.TOTAL_TAP_OUT_VOLUME, rpassenger_resident_tap_sp_q, labels=as.character(passenger_resident_tap_sp$SUBZONE_N), xlab="z-Residuals", ylab="Spatially Lag Residuals")
quadrant_OUT <- vector(mode="numeric",length=nrow(localMI_OUT))
DV_OUT <- passenger_resident_tap_sp$residuals_out - mean(passenger_resident_tap_sp$residuals_out)
C_mI_OUT <- localMI_OUT[,1] - mean(localMI_OUT[,1])
signif <- 0.05
quadrant_OUT[DV_OUT >0 & C_mI_OUT>0] <- 4
quadrant_OUT[DV_OUT <0 & C_mI_OUT<0] <- 1
quadrant_OUT[DV_OUT <0 & C_mI_OUT>0] <- 2
quadrant_OUT[DV_OUT >0 & C_mI_OUT<0] <- 3
quadrant_OUT[localMI_OUT[,5]>signif] <- 0Plotting LISA map for bot Tap in vs Population residuals and Tap Out vs Population residuals
Now, we can build the LISA map by using the code chunks below.
passenger_resident_tap_sp.localMI$quadrant <- quadrant
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high")
lisa_in <- tm_shape(passenger_resident_tap_sp.localMI) +
tm_fill(col = "quadrant", style = "cat", palette = colors[c(sort(unique(quadrant)))+1], labels = clusters[c(sort(unique(quadrant)))+1], popup.vars = c("SUBZONE_N")) +
tm_view(set.zoom.limits = c(11,17)) +
tm_borders(alpha=0.5)
passenger_resident_tap_sp.localMI_OUT$quadrant_OUT <- quadrant_OUT
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high")
lisa_out <- tm_shape(passenger_resident_tap_sp.localMI_OUT) +
tm_fill(col = "quadrant_OUT", style = "cat", palette = colors[c(sort(unique(quadrant_OUT)))+1], labels = clusters[c(sort(unique(quadrant_OUT)))+1], popup.vars = c("SUBZONE_N")) +
tm_view(set.zoom.limits = c(11,17)) +
tm_borders(alpha=0.5)
tmap_arrange(lisa_in,lisa_out, sync = TRUE, asp=1, ncol=2)The above map shows the lisa map. The high-high indicates a cluster with subzones that are of high value and so are their neighbours, and low-high indicates outliers which the subzones are of low value but the neighbours are of high value.
As seen from both graphs:
1. Woodlands east, Midview, Woodlands South, Woord Groove and their resepctive neighbours belong to one cluster
2. Fernvale, Trafalgar, Compassvale, Rivervale, Sengkang Town Centre, Punggol field, Waterway East, Punggol Town Centre, Matilda, Anchorvale and their respective neighbours belong to one cluster
3. Tampines East and its neighbours belong to one cluster
4. Boulevard and Somerset are low outliers among high neighbours
Getis and Ord’s G-Statistics for Tap In VS Population
Beside detecting cluster and outliers, localised spatial statistics can be also used to detect hot spot and/or cold spot areas - Getis and Ord’s G-statistics. Here, statistically significant hot-spots are recognised as areas of high values where other areas within a neighbourhood range also share high values too.
The analysis consists of 2 steps using the queens weight matrix:
1. Computing Gi statistics
2. Mapping Gi statistics
Computing Gi statistics using queens contiguity
Here, we compute the Gi values for Tap in vs Population residuals by using queens contiguity. 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. Next, we will join the Gi values to their correponding hunan SpatialPolygonDataFrame using the code chunk below.
fips <- order(passenger_resident_tap_sp$SUBZONE_N)
gi.queen <- localG(passenger_resident_tap_sp$residuals, rpassenger_resident_tap_sp_q)
gi.queen## [1] -1.131389104 -1.052851820 -0.849194744 -0.732067603 -0.596358263
## [6] -0.868753109 -1.034401737 -0.806017875 -0.554398023 -0.162167392
## [11] -0.682862528 -0.722604815 -2.037692923 -0.450953899 -1.175238522
## [16] -0.827298893 -0.782293285 -1.339515873 -1.517418874 -0.696493779
## [21] -0.808918913 -0.744762040 -0.707177452 -1.214686450 -1.182240589
## [26] -0.446923893 -0.260378410 -1.502837304 -0.851345298 -0.889022673
## [31] -1.649697458 -1.911237009 -1.954329071 -2.124206863 -1.563886636
## [36] -1.427976055 -1.236585930 -1.136562061 -2.003563424 -1.137883724
## [41] -1.000954011 -0.383352931 -0.258627410 -0.948528738 -1.480678723
## [46] -0.223860190 -0.829633546 -1.260644606 0.283592816 -1.093007603
## [51] -0.426153279 -1.628626136 -1.577258117 -0.042463393 -1.764360717
## [56] -1.452464569 -1.035278219 -1.347833570 -2.058392681 -1.281003347
## [61] -0.674141870 -1.635540429 -1.093537040 0.348341848 -0.667094002
## [66] -1.070098944 -1.575481204 -1.408063713 -0.605009909 -1.457651504
## [71] -0.064254000 -0.245317558 -1.184666519 -1.446074211 -0.178046076
## [76] -0.613653998 -0.740709163 -0.525682787 -1.008354240 -0.751499341
## [81] -0.287804050 -1.054811490 -0.745289323 -0.657178580 -0.497258607
## [86] -1.872771533 0.477781133 0.238509291 -1.065829326 -0.983357104
## [91] -0.379724102 -0.095165556 -0.288017589 -0.349085227 0.519271110
## [96] 0.033025891 -0.005053576 -0.908003288 -0.098099629 0.524098390
## [101] -0.433866230 -0.878192957 -0.959771587 -1.597357699 -0.007174465
## [106] 1.671987678 1.801732189 -1.028657083 -0.817394653 -0.297428050
## [111] -0.024870947 -1.124618624 -0.799324081 -0.936557562 -0.455500434
## [116] -0.738506055 -0.249476264 -1.566988561 -0.437597356 -0.070119734
## [121] -0.348388312 1.022664649 0.149838998 0.140675192 0.330459172
## [126] -0.797998053 0.114731318 1.041419912 0.679312197 0.508627770
## [131] 0.387305909 0.355016657 0.323908605 0.467063910 -0.068155830
## [136] 1.359092780 -0.070534957 0.601862281 -1.218373501 -0.280375214
## [141] -0.608294695 -0.506790759 -1.807313130 -0.097156638 2.140532675
## [146] -0.250964221 1.424735329 0.747402860 0.764618151 1.550801463
## [151] 0.448751547 0.871496080 0.525195730 -0.149133775 -0.655503628
## [156] 0.758079545 1.669584978 0.299503156 -0.427715388 -1.015099834
## [161] 2.446512475 0.780823788 1.635123262 -0.088563486 0.666249856
## [166] 0.568441558 0.860162311 1.757802089 4.596558424 -1.368401014
## [171] 0.584257628 0.528870022 -0.728335870 0.723754611 -0.223378368
## [176] 0.479424467 1.001681730 -0.673159368 -0.232701197 -0.440569915
## [181] -0.486528111 -0.085569437 1.646962767 -0.428686748 -0.037677039
## [186] 0.210315256 3.008424684 -0.284557503 0.613927358 -0.513916484
## [191] 2.091036547 1.635446195 1.390751826 1.233224937 0.326991633
## [196] 3.100733614 2.605007582 4.296608095 0.098079600 5.277630656
## [201] 2.394110965 -0.735126286 4.181360860 3.299042278 -0.155230235
## [206] 1.418991130 3.055255947 0.182807973 2.086971738 1.382737039
## [211] 3.893365305 1.500316434 -0.606617890 1.937238377 -0.898461455
## [216] 2.181438969 2.698270960 0.731134316 0.612202928 -1.396876726
## [221] 0.593837929 -0.176945016 4.153174225 -1.190386541 1.126420660
## [226] 0.480726773 2.803107786 -0.264699595 3.437636712 -0.687163949
## [231] 0.669090997 0.464094524
## attr(,"gstari")
## [1] FALSE
## attr(,"call")
## localG(x = passenger_resident_tap_sp$residuals, listw = rpassenger_resident_tap_sp_q)
## attr(,"class")
## [1] "localG"
Next, we bind the gi data into passenger_resident_tap_sp.gi. To change the data name, we have to count the number of data there are and changed the last index.
passenger_resident_tap_sp.gi<- cbind(passenger_resident_tap_sp, as.matrix(gi.queen))
a= names(passenger_resident_tap_sp.gi)
length(a)## [1] 25names(passenger_resident_tap_sp.gi)[25]="gstat"Getis and Ord’s G-Statistics for Tap Out VS Population
Computing Gi statistics using queens contiguity
fips <- order(passenger_resident_tap_sp$SUBZONE_N)
gi.queen_out <- localG(passenger_resident_tap_sp$residuals_out, rpassenger_resident_tap_sp_q)
gi.queen_out## [1] -1.128994409 -0.882524742 -0.844947917 -0.753390121 -0.602489307
## [6] -0.706046651 -1.100129877 -0.746366685 -0.864255012 -0.125784577
## [11] -0.699369831 -0.589360258 -2.064398550 -0.426582785 -1.367097249
## [16] -0.744786968 -0.740767935 -1.236467325 -1.636433150 -0.640223492
## [21] -1.010683013 -0.476039305 -0.708442736 -1.241342828 -0.951366048
## [26] -0.343150656 -0.334457359 -1.483067120 -0.909046543 -1.009179709
## [31] -1.573369571 -1.884063170 -1.860528167 -1.997826557 -1.583131939
## [36] -1.323567767 -1.129392757 -1.136816541 -1.985134951 -1.179447480
## [41] -0.940572440 -0.299438667 -0.232757371 -0.925760976 -1.308691427
## [46] -0.317198237 -1.021297471 -1.130372452 0.286379745 -1.067421856
## [51] -0.244150755 -1.519871998 -1.364784987 -0.149570358 -1.648282445
## [56] -1.559814735 -1.122976154 -1.132868347 -1.882965178 -1.225047996
## [61] -0.573547737 -1.681842300 -1.066218793 0.104975510 -0.485228894
## [66] -1.142698094 -1.497670918 -1.399749162 -0.696552669 -1.537114129
## [71] -0.281789330 -0.382042188 -1.044858728 -1.315574870 -0.429162343
## [76] -0.530531286 -0.674270645 -0.505350362 -1.226071872 -0.736333773
## [81] -0.327415280 -0.960851808 -0.718472765 -0.698296075 -0.556267964
## [86] -1.862900005 0.439583966 0.168913492 -0.959948241 -1.177024295
## [91] -0.258553067 -0.216458485 -0.302472240 -0.332888168 0.392854533
## [96] 0.017896947 -0.110564184 -0.837039441 -0.429131913 0.431262340
## [101] -0.512805920 -0.901870928 -0.858475834 -1.595529305 0.068005747
## [106] 1.704912375 1.520942579 -0.932888523 -0.757867330 -0.364798620
## [111] -0.377437398 -1.105076006 -1.056733489 -0.847524378 -0.331527940
## [116] -0.737250590 -0.011785297 -1.322459455 -0.249115006 -0.488131586
## [121] -0.518290903 0.997436586 0.067141010 0.145996809 0.237068177
## [126] -0.697580524 0.014286377 0.901021680 0.660227828 0.624514694
## [131] 0.382457360 0.599976634 -0.003787346 0.453952613 -0.168201826
## [136] 1.305895341 -0.289754912 0.458633478 -1.224790339 -0.648114423
## [141] -0.523056575 -0.375863385 -1.730010448 -0.255208146 1.784362750
## [146] -0.238952826 1.335958080 0.575699094 0.797231070 1.635651871
## [151] 0.839746010 0.814227495 0.518754005 -0.239009095 -0.505407734
## [156] 0.891683710 1.549061063 0.252092211 -0.494012940 -0.914110240
## [161] 2.407658180 0.809766072 1.617794407 -0.119577038 0.729193703
## [166] 0.749639083 0.745699157 1.932515827 4.761350154 -1.179474083
## [171] 0.673280952 0.547446477 -0.701706026 0.871710622 -0.124659239
## [176] 0.481304712 0.874368824 -0.723098976 -0.213494199 -0.227046773
## [181] -0.175160451 -0.126231216 1.711917396 -0.440243474 0.107400137
## [186] 0.131514557 2.932417419 -0.409131751 0.698858834 -0.449594787
## [191] 2.169050712 1.800240764 1.215661121 1.160918383 0.424216529
## [196] 3.189061162 2.532203961 4.260288742 0.096605883 5.396783642
## [201] 2.440665870 -0.545271126 4.139441347 3.300926940 -0.479460762
## [206] 1.287425831 3.080223179 -0.294047634 2.112091041 0.986890254
## [211] 3.914167281 1.077638222 -0.425119174 2.110442556 -1.151224017
## [216] 2.331756532 2.409909460 0.830895127 0.601482885 -1.512827555
## [221] 0.632425424 -0.168518166 4.187834374 -0.875016261 1.242956101
## [226] 0.342886328 2.773880413 -0.820941239 3.406819515 -0.477601315
## [231] -0.227577779 0.317406194
## attr(,"gstari")
## [1] FALSE
## attr(,"call")
## localG(x = passenger_resident_tap_sp$residuals_out, listw = rpassenger_resident_tap_sp_q)
## attr(,"class")
## [1] "localG"
Next, we bind the gi data into passenger_resident_tap_sp.gi. To change the data name, we have to count the number of data there are and changed the last index.
passenger_resident_tap_sp.gi<- cbind(passenger_resident_tap_sp.gi, as.matrix(gi.queen_out))
b = names(passenger_resident_tap_sp.gi)
length(b)## [1] 26names(passenger_resident_tap_sp.gi)[26]="gstat_out"Visualising Hotspot and Cold spot areas for both tap in and tap out
We use choropleth map to discover hot spots and cold spots among the subzones.
Mapping Gi values with queens weights
The code chunk below shows the functions used to map the Gi values derived using fixed distance weight matrix.
hotcold_in <- tm_shape(passenger_resident_tap_sp.gi) +
tm_fill(col = "gstat",
id = "SUBZONE_N",
style = "pretty",
palette="-RdBu",
title = "Tap In vs Population residuals local Gi") +
tm_borders(alpha = 0.5)
hotcold_out <- tm_shape(passenger_resident_tap_sp.gi) +
tm_fill(col = "gstat_out",
id = "SUBZONE_N",
style = "pretty",
palette="-RdBu",
title = "Tap Out vs Population residuals local Gi") +
tm_borders(alpha = 0.5)
tmap_arrange(hotcold_in, hotcold_out, asp=1, ncol=2, sync = TRUE)In the choropleth map above, counties shaded in red are to hot spot areas and counties shaded in blue are the cold spot areas. The darkness of the colours representing the intensity of the Gi values.
In conclusion, the choropleth above shows clear sign of divide among the top and bottom of the map (North and South divide) in both the Tap In vs Population and Tap Out vs Population by subzone of Singapore in 2020.
For Tap In vs Population residuals, the hot spot areas mainly consist of the North and North-East of Singapore: Compassvale,Seng Kang Town Centre, Punggol Field, Matilda and Midview. The cold spots mainly compromise of the Central and South of Singapore: Sentosa, Leonie Hill and Lavender.
For Tap-Out vs Population residuals, the areas also mainly consist of the North and East of Singapore: Compassvale,Seng Kang Town Centre, Punggol Field, Matilda and Midview. The cold spots mainly compromise of the south of Singapore: Sentosa.