Overview

In this exercise, we will analyse the distribution of Airbnb listings by using appropriate spatial point patterns analysis techniques. The specific tasks are as follow:

Section A: Nation-wide analysis

  1. Exploratory Spatial Data Analysis:

–> Using appropriate tmap function, display the locations of the Airbnb listing by room type with Openstreetmap of Singapore as the background. Describe the spatial patterns observed.

  1. With reference to the spatial point patterns observed in (2):

–> Formulate the null hypothesis and alternative hypothesis and select the confidence level.

–> Perform the test by using appropriate 1nd order spatial point patterns analysis technique.

–> With reference to the analysis results, draw statistical conclusions.

  1. With reference to the results derived in (1) and (2)

–> Derive kernel density maps of Airbnb listing by room type.

–> Using appropriate tmap functions, display the kernel density maps on openstreetmap of Singapore. Describe the spatial patterns revealed by the kernel density maps. Highlight the advantage of kernel density map over point map.

Section B: By planning subzones

  1. Exploratory Spatial Data Analysis:

–> Extract Airbnb listing by room type within Aljunied, Balestier, Lavender and Tanjong Pagar planning subzones.

–> Display their distribution as point maps. Describe the spatial patterns reveal by their respective distribution.

  1. With reference to the spatial point patterns observed in (4):

–> Formulate the null hypothesis and alternative hypothesis and select the confidence level.

–> Perform the test by using appropriate 2nd order spatial point patterns analysis technique.

–> With reference to the analysis results, draw statistical conclusions.

  1. With reference to the results derived in (4) and (5):

–> Derive kernel density maps of Airbnb listing by room type.

–> Using appropriate tmap functions, display the kernel density maps on openstreetmap of Singapore. Deduce what are the possible factors determine the spatial patterns observed.

The data used in this assignment are as follow:

  1. AirBnb Listings (taken from Inside AirBnb and converted to ESRI shapefile format)

  2. Planning Subzone Levels (taken from URA)

  3. Singapore Coastal Boundary Outline (taken from SLA)

The data is in ESRI shapefile format.

Section A: Nation-Wide Analysis

1 Exploratory Spatial Data Analysis

1.1 Installing and Loading Packages

packages = c('rgdal', 'maptools', 'raster','spatstat', 'tmap', 'sf', 'spdep', 'tidyverse', 'rgeos', 'sp', 'markdown')
for (p in packages){
if(!require(p, character.only = T)){
install.packages(p)
}
library(p,character.only = T)
}

1.2 Importing Data

listings <- read_csv("data/aspatial/listings.csv")
## Parsed with column specification:
## cols(
##   id = col_double(),
##   name = col_character(),
##   host_id = col_double(),
##   host_name = col_character(),
##   neighbourhood_group = col_character(),
##   neighbourhood = col_character(),
##   latitude = col_double(),
##   longitude = col_double(),
##   room_type = col_character(),
##   price = col_double(),
##   minimum_nights = col_double(),
##   number_of_reviews = col_double(),
##   last_review = col_date(format = ""),
##   reviews_per_month = col_double(),
##   calculated_host_listings_count = col_double(),
##   availability_365 = col_double()
## )
subzones <- readOGR(dsn = "data/geospatial", 
                layer = "MP14_SUBZONE_WEB_PL")
## OGR data source with driver: ESRI Shapefile 
## Source: "F:\IS415\Assignments\IS415_Take-Home_Ex02\data\geospatial", layer: "MP14_SUBZONE_WEB_PL"
## with 323 features
## It has 15 fields
sg <- readOGR(dsn = "data/geospatial",
              layer="CostalOutline")
## OGR data source with driver: ESRI Shapefile 
## Source: "F:\IS415\Assignments\IS415_Take-Home_Ex02\data\geospatial", layer: "CostalOutline"
## with 60 features
## It has 4 fields

–> Converting into SFDF

listings_sf <- st_as_sf(listings, 
                       coords = c("longitude", "latitude"),
                       crs= 4326)

1.3 Checking Projection of Data and Standardising Projection

Before we analyse the data, we need to ensure that they are in the same projected system.

crs(listings_sf)
## [1] "+proj=longlat +datum=WGS84 +no_defs "
crs(subzones)
## CRS arguments:
##  +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
## +ellps=WGS84 +towgs84=0,0,0
crs(sg)
## CRS arguments:
##  +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
## +ellps=WGS84 +towgs84=0,0,0

Since the crs are not the same, we need to standardise them.

listings_sf_crs <- st_transform(listings_sf, crs = "+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
+ellps=WGS84 +towgs84=0,0,0 ")

We will recheck the crs to confirm that they are the same.

crs(listings_sf_crs)
## [1] "+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 "
crs(subzones)
## CRS arguments:
##  +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
## +ellps=WGS84 +towgs84=0,0,0
crs(sg)
## CRS arguments:
##  +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
## +ellps=WGS84 +towgs84=0,0,0

1.4 Filtering Data by Rooms

listings_private <- listings_sf_crs %>%
  filter(room_type == 'Private room') 

listings_home <- listings_sf_crs %>%
  filter(room_type == 'Entire home/apt') 

listings_hotel <- listings_sf_crs %>%
  filter(room_type == 'Hotel room') 

listings_shared <- listings_sf_crs %>%
  filter(room_type == 'Shared room')

1.5 Mapping the Geospatial Layer

1.5.1 All Types of Rooms

We will be taking a look at the distribution of all airbnbs by room type in Singapore.

tmap_mode('view')


tm_basemap(leaflet::providers$OpenStreetMap)+
tm_shape(sg) +
  tm_borders(alpha = 0.5) +
tm_shape(listings_sf_crs) +
  tm_dots(col = 'room_type', size = 0.02)

1.5.2 Separating By Room Type

tm_basemap(leaflet::providers$OpenStreetMap)+
tm_shape(sg) +
  tm_borders(alpha = 0.5) +
tm_shape(listings_sf_crs) +
  tm_dots(col = 'room_type', 
          size = 0.5) +
tm_facets(by="room_type")

From the maps:

–> The number of AirBnb listings for each room type are in the following descending order (Private room, Entire home/apt, Shared room, Hotel room)

–> The number of AirBnb listings for private rooms are the highest while the number of listings for hotel room are the lowest.

–> There are very few AirBnb listings in the west region of Singapore.

–> Majority of the AirBnb listings for hotel rooms are towards the south of Singapore.

tmap_mode('plot')
## tmap mode set to plotting

2 First Order Spatial Point Patterns Analysis

2.1 Spatial Data Wrangling

2.1.1 Converting Spatial Point Data into Generic ‘sp’ Format

listings_home_sp <- as_Spatial(listings_home)
listings_home_point <- as(listings_home_sp, "SpatialPoints")

listings_hotel_sp <- as_Spatial(listings_hotel)
listings_hotel_point <- as(listings_hotel_sp, "SpatialPoints")

listings_shared_sp <- as_Spatial(listings_shared)
listings_shared_point <- as(listings_shared_sp, "SpatialPoints")

listings_private_sp <- as_Spatial(listings_private)
listings_private_point <- as(listings_private_sp, "SpatialPoints")

sg_sp <- as(sg, "SpatialPolygons")

Checking Class of Generic Spatial Objects

class(listings_home_point)
## [1] "SpatialPoints"
## attr(,"package")
## [1] "sp"
class(listings_hotel_point)
## [1] "SpatialPoints"
## attr(,"package")
## [1] "sp"
class(listings_shared_point)
## [1] "SpatialPoints"
## attr(,"package")
## [1] "sp"
class(listings_private_point)
## [1] "SpatialPoints"
## attr(,"package")
## [1] "sp"
class(sg_sp)
## [1] "SpatialPolygons"
## attr(,"package")
## [1] "sp"

2.1.2 Converting Generic ‘sp’ Format into ‘ppp’ Format

listings_home_ppp <- as(listings_home_point, "ppp")
listings_hotel_ppp <- as(listings_hotel_point, "ppp")
listings_shared_ppp <- as(listings_shared_point, "ppp")
listings_private_ppp <- as(listings_private_point, "ppp")

Checking Class of ppp Objects

class(listings_home_ppp)
## [1] "ppp"
class(listings_hotel_ppp)
## [1] "ppp"
class(listings_shared_ppp)
## [1] "ppp"
class(listings_private_ppp)
## [1] "ppp"

2.1.3 Handling Duplicate Points

–> Checking for Duplication

any(duplicated(listings_home_ppp))
## [1] TRUE
any(duplicated(listings_hotel_ppp))
## [1] TRUE
any(duplicated(listings_shared_ppp))
## [1] TRUE
any(duplicated(listings_private_ppp))
## [1] TRUE

–> Overcoming Duplication with Jittering Approach (adding a small perturbation to the duplicate points so that they do not occupy the exact same space.)

listings_home_jit <- rjitter(listings_home_ppp, retry=TRUE, nsim=1, drop=TRUE)
listings_hotel_jit <- rjitter(listings_hotel_ppp, retry=TRUE, nsim=1, drop=TRUE)
listings_shared_jit <- rjitter(listings_shared_ppp, retry=TRUE, nsim=1, drop=TRUE)
listings_private_jit <- rjitter(listings_private_ppp, retry=TRUE, nsim=1, drop=TRUE)

–> Rechecking for Duplication

any(duplicated(listings_home_jit))
## [1] FALSE
any(duplicated(listings_hotel_jit))
## [1] FALSE
any(duplicated(listings_shared_jit))
## [1] FALSE
any(duplicated(listings_private_jit))
## [1] FALSE

2.1.4 Creating Owin

sg_owin <- as(sg_sp, "owin")

2.1.5 Combining PPP variables with Owin

SG_listings_home <- listings_home_jit[sg_owin]
SG_listings_hotel <- listings_hotel_jit[sg_owin]
SG_listings_shared <- listings_shared_jit[sg_owin]
SG_listings_private <- listings_private_jit[sg_owin]

–> Plotting Combined Points

plot(SG_listings_home)

plot(SG_listings_hotel)

plot(SG_listings_shared)

plot(SG_listings_private)

2.2 Quadrat Analysis (Room Type: Entire Home/ Apartment)

We will perform a test of Complete Spatial Randomness for a given point pattern, based on quadrat counts by using quadrat.test() of statspat.

The test hypotheses are:

Ho = AirBnb listings that are entire homes/ apartments are randomly distributed.

H1 = AirBnb listings that are entire homes/ apartments are not randomly distributed.

The 95% confidence interval will be used.

2.2.1 Chi-squared test of CSR using Quadrat Counts

–> The nx and ny values are chosen as such since SG has more of a rectangle shape to reduce the no of rectangles with 0 value

qt_home <- quadrat.test(SG_listings_home, 
                   nx = 20, ny = 15)
## Warning: Some expected counts are small; chi^2 approximation may be inaccurate
qt_home
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  SG_listings_home
## X2 = 43765, df = 184, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)
plot(SG_listings_home)
plot(qt_home, add = TRUE, cex =.1)

Conclusion:

–> The p value is smaller than 2.2e-16, which is also smaller than 0.05.

–> Therefore, we reject the null hypothesis.

–> AirBnb listings that are entire homes/ apartments are not randomly distributed

–> The x2 square value is greater than 1, therefore there is clustering.

2.2.2 Conditional Monte Carlo Test of CSR using Quadrat Counts

quadrat.test(SG_listings_home, 
             nx = 20, ny = 15,
             method="M",
             nsim=999)
## 
##  Conditional Monte Carlo test of CSR using quadrat counts
##  Test statistic: Pearson X2 statistic
## 
## data:  SG_listings_home
## X2 = 43765, p-value = 0.002
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)

Conclusion:

–> The p value is 0.002 which is smaller than 0.05.

–> Therefore, we reject the null hypothesis.

–> AirBnb listings that are entire homes/ apartments are not randomly distributed.

–> The x2 square value is greater than 1, therefore there is clustering.

2.2.3 Overall Conclusion of Quadrat Analysis

  1. AirBnb listings that are entire homes/ apartments are not randomly distributed.

  2. There is presence of clustering.

2.3 Quadrat Analysis (Room Type: Hotel Room)

The test hypotheses are:

Ho = AirBnb listings that are hotel rooms are randomly distributed.

H1 = AirBnb listings that are hotel rooms are not randomly distributed.

The 95% confidence interval will be used.

2.3.1 Chi-squared test of CSR using Quadrat Counts

–> The nx and ny values are chosen as such since SG has more of a rectangle shape to reduce the no of rectangles with 0 value

qt_hotel <- quadrat.test(SG_listings_hotel, 
                   nx = 20, ny = 15)
## Warning: Some expected counts are small; chi^2 approximation may be inaccurate
qt_hotel
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  SG_listings_hotel
## X2 = 9226.9, df = 184, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)
plot(SG_listings_hotel)
plot(qt_hotel, add = TRUE, cex =.1)

Conclusion:

–> The p value is smaller than 2.2e-16, which is also smaller than 0.05.

–> Therefore, we reject the null hypothesis.

–> AirBnb listings that are hotel rooms are not randomly distributed.

–> The x2 square value is greater than 1, therefore there is clustering.

2.3.2 Conditional Monte Carlo Test of CSR using Quadrat Counts

quadrat.test(SG_listings_hotel, 
             nx = 20, ny = 15,
             method="M",
             nsim=999)
## 
##  Conditional Monte Carlo test of CSR using quadrat counts
##  Test statistic: Pearson X2 statistic
## 
## data:  SG_listings_hotel
## X2 = 9226.9, p-value = 0.002
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)

Conclusion:

–> The p value is 0.002 which is smaller than 0.05.

–> Therefore, we reject the null hypothesis.

–> AirBnb listings that are hotel rooms are not randomly distributed.

–> The x2 square value is greater than 1, therefore there is clustering.

2.3.3 Overall Conclusion of Quadrat Analysis

  1. AirBnb listings that are hotel rooms are not randomly distributed.

  2. There is presence of clustering.

2.3 Quadrat Analysis (Room Type: Shared Room)

The test hypotheses are:

Ho = AirBnb listings that are shared rooms are randomly distributed.

H1 = AirBnb listings that are shared rooms are not randomly distributed.

The 95% confidence interval will be used.

2.4.1 Chi-squared test of CSR using Quadrat Counts

–> The nx and ny values are chosen as such since SG has more of a rectangle shape to reduce the no of rectangles with 0 value

qt_shared <- quadrat.test(SG_listings_shared, 
                   nx = 20, ny = 15)
## Warning: Some expected counts are small; chi^2 approximation may be inaccurate
qt_shared
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  SG_listings_shared
## X2 = 4495.8, df = 184, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)
plot(SG_listings_shared)
plot(qt_shared, add = TRUE, cex =.1)

Conclusion:

–> The p value is smaller than 2.2e-16, which is also smaller than 0.05.

–> Therefore, we reject the null hypothesis.

–> AirBnb listings that are shared rooms are not randomly distributed.

–> The x2 square value is greater than 1, therefore there is clustering.

2.4.2 Conditional Monte Carlo Test of CSR using Quadrat Counts

quadrat.test(SG_listings_shared, 
             nx = 20, ny = 15,
             method="M",
             nsim=999)
## 
##  Conditional Monte Carlo test of CSR using quadrat counts
##  Test statistic: Pearson X2 statistic
## 
## data:  SG_listings_shared
## X2 = 4495.8, p-value = 0.002
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)

Conclusion:

–> The p value is 0.002 which is smaller than 0.05.

–> Therefore, we reject the null hypothesis.

–> AirBnb listings that are shared rooms are not randomly distributed.

–> The x2 square value is greater than 1, therefore there is clustering.

2.4.3 Overall Conclusion of Quadrat Analysis

  1. AirBnb listings that are shared rooms are not randomly distributed.

  2. There is presence of clustering.

2.5 Quadrat Analysis (Room Type: Private Room)

The test hypotheses are:

Ho = AirBnb listings that are private rooms are randomly distributed.

H1 = AirBnb listings that are private rooms are not randomly distributed.

The 95% confidence interval will be used.

2.5.1 Chi-squared test of CSR using Quadrat Counts

–> The nx and ny values are chosen as such since SG has more of a rectangle shape to reduce the no of rectangles with 0 value

qt_private <- quadrat.test(SG_listings_private, 
                   nx = 20, ny = 15)
## Warning: Some expected counts are small; chi^2 approximation may be inaccurate
qt_private
## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  SG_listings_private
## X2 = 22002, df = 184, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)
plot(SG_listings_private)
plot(qt_shared, add = TRUE, cex =.1)

Conclusion:

–> The p value is smaller than 2.2e-16, which is also smaller than 0.05.

–> Therefore, we reject the null hypothesis.

–> AirBnb listings that are private rooms are not randomly distributed.

–> The x2 square value is greater than 1, therefore there is clustering.

2.5.2 Conditional Monte Carlo Test of CSR using Quadrat Counts

quadrat.test(SG_listings_private, 
             nx = 20, ny = 15,
             method="M",
             nsim=999)
## 
##  Conditional Monte Carlo test of CSR using quadrat counts
##  Test statistic: Pearson X2 statistic
## 
## data:  SG_listings_private
## X2 = 22002, p-value = 0.002
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)

Conclusion:

–> The p value is 0.002 which is smaller than 0.05.

–> Therefore, we reject the null hypothesis.

–> AirBnb listings that are private rooms are not randomly distributed.

–> The x2 square value is greater than 1, therefore there is clustering.

2.5.3 Overall Conclusion of Quadrat Analysis

  1. AirBnb listings that are private rooms are not randomly distributed.

  2. There is presence of clustering.

2.6 Nearest Neighbour Analysis (Room Type: Entire Home/ Apartment)

The nearest neighbour analysis will be done as the quadrat analysis may be too sensitive to quadrat size and is a measure of dispersion rather than pattern.

We will perform the Clark-Evans test of aggregation for a spatial point pattern by using clarkevans.test() of statspat.

The test hypotheses are:

Ho = AirBnb listings that are entire homes/ apartments are randomly distributed.

H1 = AirBnb listings that are entire homes/ apartments are not randomly distributed.

The 95% confidence interval will be used.

2.6.1 Testing spatial point patterns using Clark and Evans Test

clarkevans.test(SG_listings_home,
                correction="none",
                clipregion="sg_owin",
                alternative=c("two.sided"),
                nsim=999)
## 
##  Clark-Evans test
##  No edge correction
##  Monte Carlo test based on 999 simulations of CSR with fixed n
## 
## data:  SG_listings_home
## R = 0.26394, p-value = 0.002
## alternative hypothesis: two-sided

Conclusion:

–> The p value is 0.002 which is smaller than 0.05.

–> Therefore, we reject the null hypothesis.

–> AirBnb listings that are entire homes/ apartments are not randomly distributed.

–> The R value is smaller than 1, therefore there is clustering.

2.7 Nearest Neighbour Analysis (Room Type: Hotel Room)

The test hypotheses are:

Ho = AirBnb listings that are hotel rooms are randomly distributed.

H1 = AirBnb listings that are hotel rooms are not randomly distributed.

The 95% confidence interval will be used.

2.7.1 Testing spatial point patterns using Clark and Evans Test

clarkevans.test(SG_listings_hotel,
                correction="none",
                clipregion="sg_owin",
                alternative=c("two.sided"),
                nsim=999)
## 
##  Clark-Evans test
##  No edge correction
##  Monte Carlo test based on 999 simulations of CSR with fixed n
## 
## data:  SG_listings_hotel
## R = 0.10366, p-value = 0.002
## alternative hypothesis: two-sided

Conclusion:

–> The p value is 0.002 which is smaller than 0.05.

–> Therefore, we reject the null hypothesis.

–> AirBnb listings that are hotel rooms rooms are not randomly distributed.

–> The R value is smaller than 1, therefore there is clustering.

2.8 Nearest Neighbour Analysis (Room Type: Shared Room)

The test hypotheses are:

Ho = AirBnb listings that are shared rooms are randomly distributed.

H1 = AirBnb listings that are shared rooms are not randomly distributed.

The 95% confidence interval will be used.

2.8.1 Testing spatial point patterns using Clark and Evans Test

clarkevans.test(SG_listings_shared,
                correction="none",
                clipregion="sg_owin",
                alternative=c("two.sided"),
                nsim=999)
## 
##  Clark-Evans test
##  No edge correction
##  Monte Carlo test based on 999 simulations of CSR with fixed n
## 
## data:  SG_listings_shared
## R = 0.35551, p-value = 0.002
## alternative hypothesis: two-sided

Conclusion:

–> The p value is 0.002 which is smaller than 0.05.

–> Therefore, we reject the null hypothesis.

–> AirBnb listings that are shared rooms are not randomly distributed.

–> The R value is smaller than 1, therefore there is clustering.

2.9 Nearest Neighbour Analysis (Room Type: Private Room)

The test hypotheses are:

Ho = AirBnb listings that are private rooms are randomly distributed.

H1 = AirBnb listings that are private rooms are not randomly distributed.

The 95% confidence interval will be used.

2.9.1 Testing spatial point patterns using Clark and Evans Test

clarkevans.test(SG_listings_private,
                correction="none",
                clipregion="sg_owin",
                alternative=c("two.sided"),
                nsim=999)
## 
##  Clark-Evans test
##  No edge correction
##  Monte Carlo test based on 999 simulations of CSR with fixed n
## 
## data:  SG_listings_private
## R = 0.37669, p-value = 0.002
## alternative hypothesis: two-sided

Conclusion:

–> The p value is 0.002 which is smaller than 0.05.

–> Therefore, we reject the null hypothesis.

–> AirBnb listings that are private rooms are not randomly distributed.

–> The R value is smaller than 1, therefore there is clustering.

3 Kernel Density Estimation (By Room Type)

3.1 Kernel Density Estimation (Room Type: Entire Home/ Apartment)

3.1.1 Computing Kernel Density Estimation using Fixed Bandwidth

The bandwidths are derived by bw.diggle method.

SG_listings_home.km <- rescale(SG_listings_home, 1000, "km")

kde_home <-  density(SG_listings_home.km, sigma=0.6, edge=TRUE, kernel="gaussian")
## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)
gridded_kde_home <- as.SpatialGridDataFrame.im(kde_home)

spplot(gridded_kde_home)

3.1.2 Converting Gridded Output into Raster and Assigning Projection

kde_home_raster <- raster(gridded_kde_home)
projection(kde_home_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_home_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.4170614, 0.2647348  (x, y)
## extent     : 2.663926, 56.04779, 16.35798, 50.24403  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : -6.096084e-15, 172.7349  (min, max)

3.2 Kernel Density Estimation (Room Type: Hotel Room)

3.2.1 Computing Kernel Density Estimation using Fixed Bandwidth

SG_listings_hotel.km <- rescale(SG_listings_hotel, 1000, "km")

kde_hotel <-  density(SG_listings_hotel.km, sigma=0.6, edge=TRUE, kernel="gaussian")
## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)
gridded_kde_hotel <- as.SpatialGridDataFrame.im(kde_hotel)

spplot(gridded_kde_hotel)

3.2.2 Converting Gridded Output into Raster and Assigning Projection

kde_hotel_raster <- raster(gridded_kde_hotel)
projection(kde_hotel_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_hotel_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.4170614, 0.2647348  (x, y)
## extent     : 2.663926, 56.04779, 16.35798, 50.24403  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : -2.388157e-15, 67.80641  (min, max)

3.3 Kernel Density Estimation (Room Type: Shared Room)

3.3.1 Computing Kernel Density Estimation using Fixed Bandwidth

SG_listings_shared.km <- rescale(SG_listings_shared, 1000, "km")

kde_shared <-  density(SG_listings_shared.km, sigma=0.6, edge=TRUE, kernel="gaussian")
## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)
gridded_kde_shared <- as.SpatialGridDataFrame.im(kde_shared)

spplot(gridded_kde_shared)

3.3.2 Converting Gridded Output into Raster and Assigning Projection

kde_shared_raster <- raster(gridded_kde_shared)
projection(kde_shared_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_shared_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.4170614, 0.2647348  (x, y)
## extent     : 2.663926, 56.04779, 16.35798, 50.24403  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : -6.740139e-16, 26.14346  (min, max)

3.4 Kernel Density Estimation (Room Type: Private Room)

3.4.1 Computing Kernel Density Estimation using Fixed Bandwidth

SG_listings_private.km <- rescale(SG_listings_private, 1000, "km")

kde_private <-  density(SG_listings_private.km, sigma=0.6, edge=TRUE, kernel="gaussian")
## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)
gridded_kde_private <- as.SpatialGridDataFrame.im(kde_private)

spplot(gridded_kde_private)

3.4.2 Converting Gridded Output into Raster and Assigning Projection

kde_private_raster <- raster(gridded_kde_private)
projection(kde_private_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_private_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.4170614, 0.2647348  (x, y)
## extent     : 2.663926, 56.04779, 16.35798, 50.24403  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : -6.15893e-15, 155.1096  (min, max)

3.5 Plotting Kernel Density Maps on Openstreetmap of SG by Room Type

3.5.1 Mapping Kernel Density (Room Type: Entire Home/ Apartment)

tmap_mode('view')

tm_basemap(leaflet::providers$OpenStreetMap)+

  tm_shape(sg)+
  tm_borders(alpha = 0.5) +
  tm_shape(kde_home_raster) + 
    tm_raster("v", alpha=0.5,  
          palette = "YlOrRd")

3.5.2 Mapping Kernel Density (Room Type: Hotel Room)

tmap_mode('view')

tm_basemap(leaflet::providers$OpenStreetMap)+

  tm_shape(sg)+
  tm_borders(alpha = 0.5) +
  tm_shape(kde_hotel_raster) + 
    tm_raster("v", alpha=0.5,  
          palette = "YlOrRd")

3.5.3 Mapping Kernel Density (Room Type: Shared Room)

tmap_mode('view')

tm_basemap(leaflet::providers$OpenStreetMap)+

  tm_shape(sg)+
  tm_borders(alpha = 0.5) +
  tm_shape(kde_shared_raster) + 
    tm_raster("v", alpha=0.5,  
          palette = "YlOrRd")

#### 3.5.4 Mapping Kernel Density (Room Type: Private Room)

tmap_mode('view')

tm_basemap(leaflet::providers$OpenStreetMap)+

  tm_shape(sg)+
  tm_borders(alpha = 0.5) +
  tm_shape(kde_private_raster) + 
    tm_raster("v", alpha=0.5,  
          palette = "YlOrRd")

tmap_mode('plot')
## tmap mode set to plotting

3.6 Observations from Kernel Density Maps

  1. For all 4 room types, there are hot spots towards the South of Singapore. near Clarke Quay, Geylang and Marina.

  2. Kernel density maps are better than point maps as they enable you to analyse and understand the concentration of AirBnb listings.

Section B: By Planning Subzones

4 Exploratory Spatial Data Analysis

4.1 Extracting Specific Subzones

ALJ <- subzones[subzones@data$SUBZONE_N == "ALJUNIED",]


BAL <- subzones[subzones@data$SUBZONE_N == "BALESTIER",]


LAV <- subzones[subzones@data$SUBZONE_N == "LAVENDER",]


TP <-  subzones[subzones@data$SUBZONE_N == "TANJONG PAGAR",]

The four subzones are plotted below.

par(mfrow=c(2,2))
plot(ALJ, main = "ALJUNIED")
plot(BAL, main = "BALESTIER")
plot(LAV, main = "LAVENDER")
plot(TP, main = "TANJONG PAGAR")

4.2 Converting Spatial Point Data into Generic ‘sp’ Format

ALJ_sp = as(ALJ, "SpatialPolygons")
BAL_sp = as(BAL, "SpatialPolygons")
LAV_sp = as(LAV, "SpatialPolygons")
TP_sp = as(TP, "SpatialPolygons")

4.3 Creating Owin Objects for the Subzones

ALJ_owin = as(ALJ_sp, "owin")

BAL_owin = as(BAL_sp, "owin")

LAV_owin = as(LAV_sp, "owin")

TP_owin = as(TP_sp, "owin")

4.4 Combining Room PPP Variables with Subzone Owins

#ALJUNIED

ALJ_listings_home <- listings_home_jit[ALJ_owin]
ALJ_listings_hotel <- listings_hotel_jit[ALJ_owin]
ALJ_listings_shared <- listings_shared_jit[ALJ_owin]
ALJ_listings_private <- listings_private_jit[ALJ_owin]

# BALESTIER

BAL_listings_home <- listings_home_jit[BAL_owin]
BAL_listings_hotel <- listings_hotel_jit[BAL_owin]
BAL_listings_shared <- listings_shared_jit[BAL_owin]
BAL_listings_private <- listings_private_jit[BAL_owin] 

# LAVENDER 

LAV_listings_home <- listings_home_jit[LAV_owin]
LAV_listings_hotel <- listings_hotel_jit[LAV_owin]
LAV_listings_shared <- listings_shared_jit[LAV_owin]
LAV_listings_private <- listings_private_jit[LAV_owin]

#TANJONG PAGAR

TP_listings_home <- listings_home_jit[TP_owin]
TP_listings_hotel <- listings_hotel_jit[TP_owin]
TP_listings_shared <- listings_shared_jit[TP_owin]
TP_listings_private <- listings_private_jit[TP_owin]

4.5 Visualisation of the Joint PPP Variables (Aljunied)

par(mfrow=c(2,2))
plot(ALJ_listings_home, main="Entire Home/ Apartment")
plot(ALJ_listings_hotel, main="Hotel Room")
plot(ALJ_listings_shared, main="Shared Room")
plot(ALJ_listings_private, main="Private Room")

From the maps:

–> The number of AirBnb listings for each room type in Aljunied are in the following descending order (Entire Home/ Apartment, Private Room, Hotel ROom, Shared Room)

–> The number of AirBnb listings for entire homes/apartments are the highest while the number of listings for shared room are the lowest.

–> There seems to be clustering towards the centre of Aljunied.

4.6 Visualisation of the Joint PPP Variables (Balestier)

par(mfrow=c(2,2))
plot(BAL_listings_home, main="Entire Home/ Apartment")
plot(BAL_listings_hotel, main="Hotel Room")
plot(BAL_listings_shared, main="Shared Room")
plot(BAL_listings_private, main="Private Room")

From the maps:

–> The number of AirBnb listings for each room type in Balestier are in the following descending order (Entire Home/ Apartment, Private Room, Hotel ROom, Shared Room)

–> The number of AirBnb listings for entire homes/apartments are the highest while the number of listings for shared room are the lowest in Balestier.

–> There seems to be clustering towards the east and centre of Balestier.

4.7 Visualisation of the Joint PPP Variables (Lavender)

par(mfrow=c(2,2))
plot(LAV_listings_home, main="Entire Home/ Apartment")
plot(LAV_listings_hotel, main="Hotel Room")
plot(LAV_listings_shared, main="Shared Room")
plot(LAV_listings_private, main="Private Room")

From the maps:

–> The number of AirBnb listings for each room type in Lavender are in the following descending order (Private Room, Entire Home/ Apartment, Shared ROom, Hotel Room)

–> The number of AirBnb listings for private rooms are the highest while the number of listings for hotel rooms are the lowest in Lavender.

4.8 Visualisation of the Joint PPP Variables (Tanjong Pagar)

par(mfrow=c(2,2))
plot(TP_listings_home, main="Entire Home/ Apartment")
plot(TP_listings_hotel, main="Hotel Room")
plot(TP_listings_shared, main="Shared Room")
plot(TP_listings_private, main="Private Room")

From the maps:

–> The number of AirBnb listings for each room type in Tanjong Pagar are in the following descending order (Entire Home/ Apartment, Private Room, Hotel ROom, Shared Room)

–> The number of AirBnb listings for entire homes/apartments are the highest while the number of listings for shared room are the lowest in Tanjong Pagar.

–> There seem to be no shared rooms as AirBnb listings in Tanjong Pagar.

5 Second Order Spatial Point Patterns Analysis

5.1 Analysing Spatial Point Process Using K-Function (Subzone: Aljunied)

K-function measures the number of events found up to a given distance of any particular event. It will be the preferred method of analysis as it assumes isotropy over the regions analysed and provides an estimate of spatial dependence over a wider range of scales.

5.1.1 Room Type: Entire Home/ Apartment

To confirm the observed spatial patterns, a hypothesis test will be conducted.

Ho = The distribution of AirBnb listings that are of entire homes/apartments at Aljunied are randomly distributed.

H1= The distribution of AirBnb listings that are of entire homes/apartments at Aljunied are not randomly distributed.

The 99% confidence interval will be used.

5.1.1.1 Computing K-function estimate
K_ALJ_home = Kest(ALJ_listings_home, correction = "Ripley")
plot(K_ALJ_home, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.1.1.2 Performing Complete Spatial Randomness Test
K_ALJ_home.csr <- envelope(ALJ_listings_home, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10 [etd 10:41] .........20 [etd 10:09] .........
## 30 [etd 10:29] .........40 [etd 10:20] .........50 [etd 10:31] ........
## .60 [etd 10:18] .........70 [etd 10:12] .........80 [etd 10:05] .......
## ..90 [etd 9:58] .........100 [etd 9:51] .........110 [etd 9:43] ......
## ...120 [etd 9:39] .........130 [etd 9:31] .........140 [etd 9:24] .....
## ....150 [etd 9:17] .........160 [etd 9:09] .........170 [etd 9:05] ....
## .....180 [etd 8:57] .........190 [etd 8:48] .........200 [etd 8:43] ...
## ......210 [etd 8:36] .........220 [etd 8:29] .........230 [etd 8:23] ..
## .......240 [etd 8:16] .........250 [etd 8:09] .........260 [etd 8:03] .
## ........270 [etd 7:56] .........280 [etd 7:48] .........290
##  [etd 7:40] .........300 [etd 7:34] .........310 [etd 7:28] .........
## 320 [etd 7:21] .........330 [etd 7:14] .........340 [etd 7:07] ........
## .350 [etd 7:00] .........360 [etd 6:54] .........370 [etd 6:47] .......
## ..380 [etd 6:40] .........390 [etd 6:34] .........400 [etd 6:28] ......
## ...410 [etd 6:21] .........420 [etd 6:14] .........430 [etd 6:08] .....
## ....440 [etd 6:01] .........450 [etd 5:54] .........460 [etd 5:48] ....
## .....470 [etd 5:41] .........480 [etd 5:35] .........490 [etd 5:28] ...
## ......500 [etd 5:22] .........510 [etd 5:15] .........520 [etd 5:09] ..
## .......530 [etd 5:02] .........540 [etd 4:56] .........550 [etd 4:50] .
## ........560 [etd 4:43] .........570 [etd 4:37] .........580
##  [etd 4:31] .........590 [etd 4:24] .........600 [etd 4:17] .........
## 610 [etd 4:11] .........620 [etd 4:04] .........630 [etd 3:58] ........
## .640 [etd 3:52] .........650 [etd 3:45] .........660 [etd 3:39] .......
## ..670 [etd 3:32] .........680 [etd 3:26] .........690 [etd 3:19] ......
## ...700 [etd 3:13] .........710 [etd 3:06] .........720 [etd 3:00] .....
## ....730 [etd 2:53] .........740 [etd 2:47] .........750 [etd 2:40] ....
## .....760 [etd 2:34] .........770 [etd 2:27] .........780 [etd 2:21] ...
## ......790 [etd 2:14] .........800 [etd 2:08] .........810 [etd 2:01] ..
## .......820 [etd 1:55] .........830 [etd 1:48] .........840 [etd 1:42] .
## ........850 [etd 1:36] .........860 [etd 1:29] .........870
##  [etd 1:23] .........880 [etd 1:16] .........890 [etd 1:10] .........
## 900 [etd 1:03] .........910 [etd 57 sec] .........920 [etd 51 sec] ........
## .930 [etd 44 sec] .........940 [etd 38 sec] .........950 [etd 31 sec] .......
## ..960 [etd 25 sec] .........970 [etd 19 sec] .........980 [etd 12 sec] ......
## ...990 [etd 6 sec] ........ 999.
## 
## Done.
plot(K_ALJ_home.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is above the envelope, hence we reject the null hypothesis.

–> The distribution of AirBnb listings that are of entire homes/apartments at Aljunied are not randomly distributed.

–> The observed pattern resembles significant clustered pattern.

5.1.2 Room Type: Hotel Room

Ho = The distribution of AirBnb listings that are of hotel rooms at Aljunied are randomly distributed.

H1= The distribution of AirBnb listings that are of hotel rooms at Aljunied are not randomly distributed.

The 99% confidence interval will be used.

5.1.2.1 Computing K-function estimate
K_ALJ_hotel = Kest(ALJ_listings_hotel, correction = "Ripley")
plot(K_ALJ_hotel, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.1.2.2 Performing Complete Spatial Randomness Test
K_ALJ_hotel.csr <- envelope(ALJ_listings_hotel, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10.........20.........30.........40.........50.........60........
## .70.........80.........90.........100.........110.........120.........130......
## ...140.........150.........160.........170.........180.........190.........200....
## .....210.........220.........230.........240.........250.........260.........270..
## .......280.........290.........300.........310.........320.........330.........340
## .........350.........360.........370.........380.........390.........400........
## .410.........420.........430.........440.........450.........460.........470......
## ...480.........490.........500.........510.........520.........530.........540....
## .....550.........560.........570.........580.........590.........600.........610..
## .......620.........630.........640.........650.........660.........670.........680
## .........690.........700.........710.........720.........730.........740........
## .750.........760.........770.........780.........790.........800.........810......
## ...820.........830.........840.........850.........860.........870.........880....
## .....890.........900.........910.........920.........930.........940.........950..
## .......960.........970.........980.........990........ 999.
## 
## Done.
plot(K_ALJ_hotel.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is above the envelope from d=0 to d=275. From 275 onwards, the black line is within the envelope.

–> It can be observed that below the distance of ~275m, there is significant clustering pattern. Above 275, the observed pattern resembles CSR pattern.

5.1.3 Room Type: Shared Room

To confirm the observed spatial patterns, a hypothesis test will be conducted.

Ho = The distribution of AirBnb listings that are of shared rooms at Aljunied are randomly distributed.

H1= The distribution of AirBnb listings that are of shared rooms at Aljunied are not randomly distributed.

The 99% confidence interval will be used.

5.1.3.1 Computing K-function estimate
K_ALJ_shared = Kest(ALJ_listings_shared, correction = "Ripley")
plot(K_ALJ_shared, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.1.3.2 Performing Complete Spatial Randomness Test
K_ALJ_shared.csr <- envelope(ALJ_listings_shared, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10.........20.........30.........40.........50.........60........
## .70.........80.........90.........100.........110.........120.........130......
## ...140.........150.........160.........170.........180.........190.........200....
## .....210.........220.........230.........240.........250.........260.........270..
## .......280.........290.........300.........310.........320.........330.........340
## .........350.........360.........370.........380.........390.........400........
## .410.........420.........430.........440.........450.........460.........470......
## ...480.........490.........500.........510.........520.........530.........540....
## .....550.........560.........570.........580.........590.........600.........610..
## .......620.........630.........640.........650.........660.........670.........680
## .........690.........700.........710.........720.........730.........740........
## .750.........760.........770.........780.........790.........800.........810......
## ...820.........830.........840.........850.........860.........870.........880....
## .....890.........900.........910.........920.........930.........940.........950..
## .......960.........970.........980.........990........ 999.
## 
## Done.
plot(K_ALJ_shared.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is within the envelope, hence we do not reject the null hypothesis.

–> The distribution of AirBnb listings that are of shared rooms at Aljunied are not randomly distributed.

–> The observed pattern resembles CSR pattern .

5.1.4 Room Type: Private Room

To confirm the observed spatial patterns, a hypothesis test will be conducted.

Ho = The distribution of AirBnb listings that are of private rooms at Aljunied are randomly distributed.

H1= The distribution of AirBnb listings that are of private rooms at Aljunied are not randomly distributed.

The 99% confidence interval will be used.

5.1.4.1 Computing K-function estimate
K_ALJ_private = Kest(ALJ_listings_private, correction = "Ripley")
plot(K_ALJ_private, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.1.4.2 Performing Complete Spatial Randomness Test
K_ALJ_private.csr <- envelope(ALJ_listings_private, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10.........20.........30.........40.........50.........60........
## .70.........80.........90.........100.........110.........120.........130......
## ...140.........150.........160.........170.........180.........190.........200....
## .....210.........220.........230.........240.........250.........260.........270..
## .......280.........290.........300.........310.........320.........330.........340
## .........350.........360.........370.........380.........390.........400........
## .410.........420.........430.........440.........450.........460.........470......
## ...480.........490.........500.........510.........520.........530.........540....
## .....550.........560.........570.........580.........590.........600.........610..
## .......620.........630.........640.........650.........660.........670.........680
## .........690.........700.........710.........720.........730.........740........
## .750.........760.........770.........780.........790.........800.........810......
## ...820.........830.........840.........850.........860.........870.........880....
## .....890.........900.........910.........920.........930.........940.........950..
## .......960.........970.........980.........990........ 999.
## 
## Done.
plot(K_ALJ_private.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is above the envelope, hence we reject the null hypothesis.

–> The distribution of AirBnb listings that are of private rooms at Aljunied are not randomly distributed.

–> The observed pattern resembles significant clustered pattern.

5.2 Analysing Spatial Point Process Using K-Function (Subzone: Balestier)

5.2.1 Room Type: Entire Home/ Apartment

To confirm the observed spatial patterns, a hypothesis test will be conducted.

Ho = The distribution of AirBnb listings that are of entire homes/apartments at Balestier are randomly distributed.

H1= The distribution of AirBnb listings that are of entire homes/apartments at Balestier are not randomly distributed.

The 99% confidence interval will be used.

5.2.1.1 Computing K-function estimate
K_BAL_home = Kest(BAL_listings_home, correction = "Ripley")
plot(K_BAL_home, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.2.1.2 Performing Complete Spatial Randomness Test
K_BAL_home.csr <- envelope(BAL_listings_home, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10 [etd 2:39] .........20 [etd 2:43] .........
## 30 [etd 2:41] .........40 [etd 2:40] .........50 [etd 2:42] ........
## .60 [etd 2:41] .........70 [etd 2:39] .........80 [etd 2:37] .......
## ..90 [etd 2:35] .........100 [etd 2:33] .........110 [etd 2:31] ......
## ...120 [etd 2:29] .........130 [etd 2:27] .........140 [etd 2:25] .....
## ....150 [etd 2:23] .........160 [etd 2:23] .........170 [etd 2:21] ....
## .....180 [etd 2:19] .........190 [etd 2:17] .........200 [etd 2:17] ...
## ......210 [etd 2:15] .........220 [etd 2:13] .........230 [etd 2:11] ..
## .......240 [etd 2:09] .........250 [etd 2:08] .........260 [etd 2:06] .
## ........270 [etd 2:04] .........280 [etd 2:02] .........290
##  [etd 2:00] .........300 [etd 1:59] .........310 [etd 1:57] .........
## 320 [etd 1:56] .........330 [etd 1:54] .........340 [etd 1:52] ........
## .350 [etd 1:51] .........360 [etd 1:49] .........370 [etd 1:47] .......
## ..380 [etd 1:46] .........390 [etd 1:44] .........400 [etd 1:42] ......
## ...410 [etd 1:40] .........420 [etd 1:39] .........430 [etd 1:37] .....
## ....440 [etd 1:36] .........450 [etd 1:34] .........460 [etd 1:32] ....
## .....470 [etd 1:30] .........480 [etd 1:28] .........490 [etd 1:27] ...
## ......500 [etd 1:25] .........510 [etd 1:23] .........520 [etd 1:22] ..
## .......530 [etd 1:20] .........540 [etd 1:19] .........550 [etd 1:17] .
## ........560 [etd 1:15] .........570 [etd 1:14] .........580
##  [etd 1:12] .........590 [etd 1:10] .........600 [etd 1:08] .........
## 610 [etd 1:06] .........620 [etd 1:05] .........630 [etd 1:03] ........
## .640 [etd 1:01] .........650 [etd 1:00] .........660 [etd 58 sec] .......
## ..670 [etd 56 sec] .........680 [etd 55 sec] .........690 [etd 53 sec] ......
## ...700 [etd 51 sec] .........710 [etd 49 sec] .........720 [etd 48 sec] .....
## ....730 [etd 46 sec] .........740 [etd 44 sec] .........750 [etd 42 sec] ....
## .....760 [etd 41 sec] .........770 [etd 39 sec] .........780 [etd 37 sec] ...
## ......790 [etd 36 sec] .........800 [etd 34 sec] .........810 [etd 32 sec] ..
## .......820 [etd 31 sec] .........830 [etd 29 sec] .........840 [etd 27 sec] .
## ........850 [etd 25 sec] .........860 [etd 24 sec] .........870
##  [etd 22 sec] .........880 [etd 20 sec] .........890 [etd 19 sec] .........
## 900 [etd 17 sec] .........910 [etd 15 sec] .........920 [etd 13 sec] ........
## .930 [etd 12 sec] .........940 [etd 10 sec] .........950 [etd 8 sec] .......
## ..960 [etd 7 sec] .........970 [etd 5 sec] .........980 [etd 3 sec] ......
## ...990 [etd 2 sec] ........ 999.
## 
## Done.
plot(K_BAL_home.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is above the envelope, hence we reject the null hypothesis.

–> The distribution of AirBnb listings that are of entire homes/apartments at Balestier are not randomly distributed.

–> The observed pattern resembles significant clustered pattern.

5.2.2 Room Type: Hotel Room

Ho = The distribution of AirBnb listings that are of hotel rooms at Balestier are randomly distributed.

H1= The distribution of AirBnb listings that are of hotel rooms at Balestier are not randomly distributed.

The 99% confidence interval will be used.

5.2.2.1 Computing K-function estimate
K_BAL_hotel = Kest(BAL_listings_hotel, correction = "Ripley")
plot(K_BAL_hotel, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.2.2.2 Performing Complete Spatial Randomness Test
K_BAL_hotel.csr <- envelope(BAL_listings_hotel, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10.........20.........30.........40.........50.........60........
## .70.........80.........90.........100.........110.........120.........130......
## ...140.........150.........160.........170.........180.........190.........200....
## .....210.........220.........230.........240.........250.........260.........270..
## .......280.........290.........300.........310.........320.........330.........340
## .........350.........360.........370.........380.........390.........400........
## .410.........420.........430.........440.........450.........460.........470......
## ...480.........490.........500.........510.........520.........530.........540....
## .....550.........560.........570.........580.........590.........600.........610..
## .......620.........630.........640.........650.........660.........670.........680
## .........690.........700.........710.........720.........730.........740........
## .750.........760.........770.........780.........790.........800.........810......
## ...820.........830.........840.........850.........860.........870.........880....
## .....890.........900.........910.........920.........930.........940.........950..
## .......960.........970.........980.........990........ 999.
## 
## Done.
plot(K_BAL_hotel.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is above the envelope, hence we reject the null hypothesis.

–> The distribution of AirBnb listings that are of hotel rooms at Balestier are not randomly distributed.

–> The observed pattern resembles significant clustered pattern.

5.2.3 Room Type: Shared Room

To confirm the observed spatial patterns, a hypothesis test will be conducted.

Ho = The distribution of AirBnb listings that are of shared rooms at Balestier are randomly distributed.

H1= The distribution of AirBnb listings that are of shared rooms at Balestier are not randomly distributed.

The 99% confidence interval will be used.

5.2.3.1 Computing K-function estimate
K_BAL_shared = Kest(BAL_listings_shared, correction = "Ripley")
plot(K_BAL_shared, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

There is only one observation for shared rooms AirBnb listings at Balestier.

5.2.4 Room Type: Private Room

To confirm the observed spatial patterns, a hypothesis test will be conducted.

Ho = The distribution of AirBnb listings that are of private rooms at Balestier are randomly distributed.

H1= The distribution of AirBnb listings that are of private rooms at Balestier are not randomly distributed.

The 99% confidence interval will be used.

5.2.4.1 Computing K-function estimate
K_BAL_private = Kest(BAL_listings_private, correction = "Ripley")
plot(K_BAL_private, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.2.4.2 Performing Complete Spatial Randomness Test
K_BAL_private.csr <- envelope(BAL_listings_private, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10.........20.........30.........40.........50.........60........
## .70.........80.........90.........100.........110.........120.........130......
## ...140.........150.........160.........170.........180.........190.........200....
## .....210.........220.........230.........240.........250.........260.........270..
## .......280.........290.........300.........310.........320.........330.........340
## .........350.........360.........370.........380.........390.........400........
## .410.........420.........430.........440.........450.........460.........470......
## ...480.........490.........500.........510.........520.........530.........540....
## .....550.........560.........570.........580.........590.........600.........610..
## .......620.........630.........640.........650.........660.........670.........680
## .........690.........700.........710.........720.........730.........740........
## .750.........760.........770.........780.........790.........800.........810......
## ...820.........830.........840.........850.........860.........870.........880....
## .....890.........900.........910.........920.........930.........940.........950..
## .......960.........970.........980.........990........ 999.
## 
## Done.
plot(K_BAL_private.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is above the envelope, hence we reject the null hypothesis.

–> The distribution of AirBnb listings that are of private rooms at Balestier are not randomly distributed.

–> The observed pattern resembles significant clustered pattern.

5.3 Analysing Spatial Point Process Using K-Function (Subzone: Lavender)

5.3.1 Room Type: Entire Home/ Apartment

To confirm the observed spatial patterns, a hypothesis test will be conducted.

Ho = The distribution of AirBnb listings that are of entire homes/apartments at Lavender are randomly distributed.

H1= The distribution of AirBnb listings that are of entire homes/apartments at Lavender are not randomly distributed.

The 99% confidence interval will be used.

5.3.1.1 Computing K-function estimate
K_LAV_home = Kest(LAV_listings_home, correction = "Ripley")
plot(K_LAV_home, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.3.1.2 Performing Complete Spatial Randomness Test
K_LAV_home.csr <- envelope(LAV_listings_home, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10.........20.........30.........40.........50.........60........
## .70.........80.........90.........100.........110.........120.........130......
## ...140.........150.........160.........170.........180.........190.........200....
## .....210.........220.........230.........240.........250.........260.........270..
## .......280.........290.........300.........310.........320.........330.........340
## .........350.........360.........370.........380.........390.........400........
## .410.........420.........430.........440.........450.........460.........470......
## ...480.........490.........500.........510.........520.........530.........540....
## .....550.........560.........570.........580.........590.........600.........610..
## .......620.........630.........640.........650.........660.........670.........680
## .........690.........700.........710.........720.........730.........740........
## .750.........760.........770.........780.........790.........800.........810......
## ...820.........830.........840.........850.........860.........870.........880....
## .....890.........900.........910.........920.........930.........940.........950..
## .......960.........970.........980.........990........ 999.
## 
## Done.
plot(K_LAV_home.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is above the envelope, hence we reject the null hypothesis.

–> The distribution of AirBnb listings that are of entire homes/apartments at Lavender are not randomly distributed.

–> The observed pattern resembles significant clustered pattern.

5.3.2 Room Type: Hotel Room

Ho = The distribution of AirBnb listings that are of hotel rooms at Lavender are randomly distributed.

H1= The distribution of AirBnb listings that are of hotel rooms at Lavender are not randomly distributed.

The 99% confidence interval will be used.

5.3.2.1 Computing K-function estimate
K_LAV_hotel = Kest(LAV_listings_hotel, correction = "Ripley")
plot(K_LAV_hotel, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.3.2.2 Performing Complete Spatial Randomness Test
K_LAV_hotel.csr <- envelope(LAV_listings_hotel, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10.........20.........30.........40.........50.........60........
## .70.........80.........90.........100.........110.........120.........130......
## ...140.........150.........160.........170.........180.........190.........200....
## .....210.........220.........230.........240.........250.........260.........270..
## .......280.........290.........300.........310.........320.........330.........340
## .........350.........360.........370.........380.........390.........400........
## .410.........420.........430.........440.........450.........460.........470......
## ...480.........490.........500.........510.........520.........530.........540....
## .....550.........560.........570.........580.........590.........600.........610..
## .......620.........630.........640.........650.........660.........670.........680
## .........690.........700.........710.........720.........730.........740........
## .750.........760.........770.........780.........790.........800.........810......
## ...820.........830.........840.........850.........860.........870.........880....
## .....890.........900.........910.........920.........930.........940.........950..
## .......960.........970.........980.........990........ 999.
## 
## Done.
plot(K_LAV_hotel.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is above the envelope, hence we reject the null hypothesis.

–> The distribution of AirBnb listings that are of hotel rooms at Lavender are not randomly distributed.

–> The observed pattern resembles significant clustered pattern.

5.3.3 Room Type: Shared Room

To confirm the observed spatial patterns, a hypothesis test will be conducted.

Ho = The distribution of AirBnb listings that are of shared rooms at Lavender are randomly distributed.

H1= The distribution of AirBnb listings that are of shared rooms at Lavender are not randomly distributed.

The 99% confidence interval will be used.

5.3.3.1 Computing K-function estimate
K_LAV_shared = Kest(LAV_listings_shared, correction = "Ripley")
plot(K_LAV_shared, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.3.3.2 Performing Complete Spatial Randomness Test
K_LAV_shared.csr <- envelope(LAV_listings_shared, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10.........20.........30.........40.........50.........60........
## .70.........80.........90.........100.........110.........120.........130......
## ...140.........150.........160.........170.........180.........190.........200....
## .....210.........220.........230.........240.........250.........260.........270..
## .......280.........290.........300.........310.........320.........330.........340
## .........350.........360.........370.........380.........390.........400........
## .410.........420.........430.........440.........450.........460.........470......
## ...480.........490.........500.........510.........520.........530.........540....
## .....550.........560.........570.........580.........590.........600.........610..
## .......620.........630.........640.........650.........660.........670.........680
## .........690.........700.........710.........720.........730.........740........
## .750.........760.........770.........780.........790.........800.........810......
## ...820.........830.........840.........850.........860.........870.........880....
## .....890.........900.........910.........920.........930.........940.........950..
## .......960.........970.........980.........990........ 999.
## 
## Done.
plot(K_LAV_shared.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is above the envelope, hence we reject the null hypothesis.

–> The distribution of AirBnb listings that are of shared rooms at Lavender are not randomly distributed.

–> The observed pattern resembles significant clustered pattern.

5.3.4 Room Type: Private Room

To confirm the observed spatial patterns, a hypothesis test will be conducted.

Ho = The distribution of AirBnb listings that are of private rooms at Lavender are randomly distributed.

H1= The distribution of AirBnb listings that are of private rooms at Lavender are not randomly distributed.

The 99% confidence interval will be used.

5.3.4.1 Computing K-function estimate
K_LAV_private = Kest(LAV_listings_private, correction = "Ripley")
plot(K_LAV_private, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.3.4.2 Performing Complete Spatial Randomness Test
K_LAV_private.csr <- envelope(LAV_listings_private, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10 [etd 3:32] .........20 [etd 3:13] .........
## 30 [etd 3:02] .........40 [etd 2:58] .........50 [etd 3:01] ........
## .60 [etd 2:58] .........70 [etd 2:56] .........80 [etd 2:53] .......
## ..90 [etd 2:50] .........100 [etd 2:47] .........110 [etd 2:46] ......
## ...120 [etd 2:43] .........130 [etd 2:42] .........140 [etd 2:39] .....
## ....150 [etd 2:39] .........160 [etd 2:37] .........170 [etd 2:35] ....
## .....180 [etd 2:33] .........190 [etd 2:30] .........200 [etd 2:28] ...
## ......210 [etd 2:27] .........220 [etd 2:25] .........230 [etd 2:23] ..
## .......240 [etd 2:21] .........250 [etd 2:19] .........260 [etd 2:17] .
## ........270 [etd 2:15] .........280 [etd 2:13] .........290
##  [etd 2:11] .........300 [etd 2:09] .........310 [etd 2:07] .........
## 320 [etd 2:05] .........330 [etd 2:04] .........340 [etd 2:02] ........
## .350 [etd 2:00] .........360 [etd 1:58] .........370 [etd 1:56] .......
## ..380 [etd 1:54] .........390 [etd 1:53] .........400 [etd 1:51] ......
## ...410 [etd 1:49] .........420 [etd 1:47] .........430 [etd 1:45] .....
## ....440 [etd 1:43] .........450 [etd 1:42] .........460 [etd 1:40] ....
## .....470 [etd 1:38] .........480 [etd 1:36] .........490 [etd 1:34] ...
## ......500 [etd 1:32] .........510 [etd 1:30] .........520 [etd 1:28] ..
## .......530 [etd 1:27] .........540 [etd 1:25] .........550 [etd 1:23] .
## ........560 [etd 1:21] .........570 [etd 1:19] .........580
##  [etd 1:18] .........590 [etd 1:16] .........600 [etd 1:14] .........
## 610 [etd 1:12] .........620 [etd 1:10] .........630 [etd 1:08] ........
## .640 [etd 1:06] .........650 [etd 1:05] .........660 [etd 1:03] .......
## ..670 [etd 1:01] .........680 [etd 59 sec] .........690 [etd 57 sec] ......
## ...700 [etd 55 sec] .........710 [etd 53 sec] .........720 [etd 51 sec] .....
## ....730 [etd 49 sec] .........740 [etd 48 sec] .........750 [etd 46 sec] ....
## .....760 [etd 44 sec] .........770 [etd 42 sec] .........780 [etd 40 sec] ...
## ......790 [etd 38 sec] .........800 [etd 37 sec] .........810 [etd 35 sec] ..
## .......820 [etd 33 sec] .........830 [etd 31 sec] .........840 [etd 29 sec] .
## ........850 [etd 27 sec] .........860 [etd 25 sec] .........870
##  [etd 24 sec] .........880 [etd 22 sec] .........890 [etd 20 sec] .........
## 900 [etd 18 sec] .........910 [etd 16 sec] .........920 [etd 14 sec] ........
## .930 [etd 13 sec] .........940 [etd 11 sec] .........950 [etd 9 sec] .......
## ..960 [etd 7 sec] .........970 [etd 5 sec] .........980 [etd 3 sec] ......
## ...990 [etd 2 sec] ........ 999.
## 
## Done.
plot(K_LAV_private.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is above the envelope, hence we reject the null hypothesis.

–> The distribution of AirBnb listings that are of private rooms at Lavender are not randomly distributed.

–> The observed pattern resembles significant clustered pattern.

5.4 Analysing Spatial Point Process Using K-Function (Subzone: Tanjong Pagar)

5.4.1 Room Type: Entire Home/ Apartment

To confirm the observed spatial patterns, a hypothesis test will be conducted.

Ho = The distribution of AirBnb listings that are of entire homes/apartments at Tanjong Pagar are randomly distributed.

H1= The distribution of AirBnb listings that are of entire homes/apartments at Tanjong Pagar are not randomly distributed.

The 99% confidence interval will be used.

5.4.1.1 Computing K-function estimate
K_TP_home = Kest(TP_listings_home, correction = "Ripley")
plot(K_TP_home, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.4.1.2 Performing Complete Spatial Randomness Test
K_TP_home.csr <- envelope(TP_listings_home, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10.........20.........30.........40.........50.........60........
## .70.........80.........90.........100.........110.........120.........130......
## ...140.........150.........160.........170.........180.........190.........200....
## .....210.........220.........230.........240.........250.........260.........270..
## .......280.........290.........300.........310.........320.........330.........340
## .........350.........360.........370.........380.........390.........400........
## .410.........420.........430.........440.........450.........460.........470......
## ...480.........490.........500.........510.........520.........530.........540....
## .....550.........560.........570.........580.........590.........600.........610..
## .......620.........630.........640.........650.........660.........670.........680
## .........690.........700.........710.........720.........730.........740........
## .750.........760.........770.........780.........790.........800.........810......
## ...820.........830.........840.........850.........860.........870.........880....
## .....890.........900.........910.........920.........930.........940.........950..
## .......960.........970.........980.........990........ 999.
## 
## Done.
plot(K_TP_home.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is above the envelope, hence we reject the null hypothesis.

–> The distribution of AirBnb listings that are of entire homes/ apartments at Tanjong Pagar are not randomly distributed.

–> The observed pattern resembles significant clustered pattern.

5.4.2 Room Type: Hotel Room

Ho = The distribution of AirBnb listings that are of hotel rooms at Tanjong Pagar are randomly distributed.

H1= The distribution of AirBnb listings that are of hotel rooms at Tanjong Pagar are not randomly distributed.

The 99% confidence interval will be used.

5.4.2.1 Computing K-function estimate
K_TP_hotel = Kest(TP_listings_hotel, correction = "Ripley")
plot(K_TP_hotel, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

There are only 2 observations of hotel rooms as AirBnb listings at Tanjong Pagar.

5.4.3 Room Type: Shared Room

To confirm the observed spatial patterns, a hypothesis test will be conducted.

Ho = The distribution of AirBnb listings that are of shared rooms at Tanjong Pagar are randomly distributed.

H1= The distribution of AirBnb listings that are of shared rooms at Tanjong Pagar are not randomly distributed.

The 99% confidence interval will be used.

5.4.3.1 Computing K-function estimate
K_TP_shared = Kest(TP_listings_shared, correction = "Ripley")
plot(K_TP_shared, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

There are no observations of shared rooms as AirBnb listings at Tanjong Pagar.

5.4.4 Room Type: Private Room

To confirm the observed spatial patterns, a hypothesis test will be conducted.

Ho = The distribution of AirBnb listings that are of private rooms at Tanjong Pagar are randomly distributed.

H1= The distribution of AirBnb listings that are of private rooms at Tanjong Pagar are not randomly distributed.

The 99% confidence interval will be used.

5.4.4.1 Computing K-function estimate
K_TP_private = Kest(TP_listings_private, correction = "Ripley")
plot(K_TP_private, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.4.4.2 Performing Complete Spatial Randomness Test
K_TP_private.csr <- envelope(TP_listings_private, Kest, nsim = 999, rank = 1, glocal=TRUE)
## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10.........20.........30.........40.........50.........60........
## .70.........80.........90.........100.........110.........120.........130......
## ...140.........150.........160.........170.........180.........190.........200....
## .....210.........220.........230.........240.........250.........260.........270..
## .......280.........290.........300.........310.........320.........330.........340
## .........350.........360.........370.........380.........390.........400........
## .410.........420.........430.........440.........450.........460.........470......
## ...480.........490.........500.........510.........520.........530.........540....
## .....550.........560.........570.........580.........590.........600.........610..
## .......620.........630.........640.........650.........660.........670.........680
## .........690.........700.........710.........720.........730.........740........
## .750.........760.........770.........780.........790.........800.........810......
## ...820.........830.........840.........850.........860.........870.........880....
## .....890.........900.........910.........920.........930.........940.........950..
## .......960.........970.........980.........990........ 999.
## 
## Done.
plot(K_TP_private.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

Conclusion:

–> The observed line in black is within the envelope, hence we do not reject the null hypothesis.

–> The distribution of AirBnb listings that are of private rooms at Tanjong Pagar are randomly distributed.

–> The observed pattern resembles CSR pattern.

6 Kernel Density Estimation (By Room Type in each Subzone)

6.1 Kernel Density Estimation (Subzone: Aljunied)

6.1.1 Fixed Bandwidth Kernel Density Estimation (Room Type: Entire Home/ Apartment)

ALJ_listings_home.km <- rescale(ALJ_listings_home, 1000, "km")

kde_ALJ_home <- density(ALJ_listings_home.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_ALJ_home <- as.SpatialGridDataFrame.im(kde_ALJ_home)

spplot(gridded_kde_ALJ_home) 

kde_ALJ_home_raster <- raster(gridded_kde_ALJ_home)
projection(kde_ALJ_home_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_ALJ_home_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.01534011, 0.01585319  (x, y)
## extent     : 32.60574, 34.56928, 31.88027, 33.90948  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : 2.004246e-07, 1444.006  (min, max)

6.1.2 Fixed Bandwidth Kernel Density Estimation (Room Type: Hotel Room)

ALJ_listings_hotel.km <- rescale(ALJ_listings_hotel, 1000, "km")

kde_ALJ_hotel <- density(ALJ_listings_hotel.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_ALJ_hotel <- as.SpatialGridDataFrame.im(kde_ALJ_hotel)

spplot(gridded_kde_ALJ_hotel) 

kde_ALJ_hotel_raster <- raster(gridded_kde_ALJ_hotel)
projection(kde_ALJ_hotel_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_ALJ_hotel_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.01534011, 0.01585319  (x, y)
## extent     : 32.60574, 34.56928, 31.88027, 33.90948  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : -5.075579e-15, 79.3737  (min, max)

6.1.3 Fixed Bandwidth Kernel Density Estimation (Room Type: Shared Room)

ALJ_listings_shared.km <- rescale(ALJ_listings_shared, 1000, "km")

kde_ALJ_shared <- density(ALJ_listings_shared.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_ALJ_shared <- as.SpatialGridDataFrame.im(kde_ALJ_shared)

spplot(gridded_kde_ALJ_shared) 

kde_ALJ_shared_raster <- raster(gridded_kde_ALJ_shared)
projection(kde_ALJ_shared_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_ALJ_shared_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.01534011, 0.01585319  (x, y)
## extent     : 32.60574, 34.56928, 31.88027, 33.90948  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : -1.010673e-15, 21.68527  (min, max)

6.1.4 Fixed Bandwidth Kernel Density Estimation (Room Type: Private Room)

ALJ_listings_private.km <- rescale(ALJ_listings_private, 1000, "km")

kde_ALJ_private <- density(ALJ_listings_private.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_ALJ_private <- as.SpatialGridDataFrame.im(kde_ALJ_private)

spplot(gridded_kde_ALJ_private)

kde_ALJ_private_raster <- raster(gridded_kde_ALJ_private)
projection(kde_ALJ_private_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_ALJ_private_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.01534011, 0.01585319  (x, y)
## extent     : 32.60574, 34.56928, 31.88027, 33.90948  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : 2.354563e-06, 584.4013  (min, max)

6.2 Kernel Density Estimation (Subzone: Balestier)

6.2.1 Fixed Bandwidth Kernel Density Estimation (Room Type: Entire Home/ Apartment)

BAL_listings_home.km <- rescale(BAL_listings_home, 1000, "km")

kde_BAL_home <- density(BAL_listings_home.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_BAL_home <- as.SpatialGridDataFrame.im(kde_BAL_home)

spplot(gridded_kde_BAL_home) 

kde_BAL_home_raster <- raster(gridded_kde_BAL_home)
projection(kde_BAL_home_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_BAL_home_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.01893197, 0.01039581  (x, y)
## extent     : 28.80786, 31.23115, 33.41793, 34.74859  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : -4.398289e-14, 1002.327  (min, max)

6.2.2 Fixed Bandwidth Kernel Density Estimation (Room Type: Hotel Room)

BAL_listings_hotel.km <- rescale(BAL_listings_hotel, 1000, "km")

kde_BAL_hotel <- density(BAL_listings_hotel.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_BAL_hotel <- as.SpatialGridDataFrame.im(kde_BAL_hotel)

spplot(gridded_kde_BAL_hotel) 

kde_BAL_hotel_raster <- raster(gridded_kde_BAL_hotel)
projection(kde_BAL_hotel_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_BAL_hotel_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.01893197, 0.01039581  (x, y)
## extent     : 28.80786, 31.23115, 33.41793, 34.74859  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : 5.518547e-07, 151.9367  (min, max)

6.2.3 Fixed Bandwidth Kernel Density Estimation (Room Type: Shared Room)

BAL_listings_shared.km <- rescale(BAL_listings_shared, 1000, "km")

kde_BAL_shared <- density(BAL_listings_shared.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_BAL_shared <- as.SpatialGridDataFrame.im(kde_BAL_shared)

spplot(gridded_kde_BAL_shared) 

kde_BAL_shared_raster <- raster(gridded_kde_BAL_shared)
projection(kde_BAL_shared_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_BAL_shared_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.01893197, 0.01039581  (x, y)
## extent     : 28.80786, 31.23115, 33.41793, 34.74859  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : -1.858529e-15, 15.91549  (min, max)

6.2.4 Fixed Bandwidth Kernel Density Estimation (Room Type: Private Room)

BAL_listings_private.km <- rescale(BAL_listings_private, 1000, "km")

kde_BAL_private <- density(BAL_listings_private.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_BAL_private <- as.SpatialGridDataFrame.im(kde_BAL_private)

spplot(gridded_kde_BAL_private) 

kde_BAL_private_raster <- raster(gridded_kde_BAL_private)
projection(kde_BAL_private_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_BAL_private_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.01893197, 0.01039581  (x, y)
## extent     : 28.80786, 31.23115, 33.41793, 34.74859  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : 0.02583227, 163.5153  (min, max)

6.3 Kernel Density Estimation (Subzone: Lavender)

6.3.1 Fixed Bandwidth Kernel Density Estimation (Room Type: Entire Home/ Apartment)

LAV_listings_home.km <- rescale(LAV_listings_home, 1000, "km")

kde_LAV_home <- density(LAV_listings_home.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_LAV_home <- as.SpatialGridDataFrame.im(kde_LAV_home)

spplot(gridded_kde_LAV_home) 

kde_LAV_home_raster <- raster(gridded_kde_LAV_home)
projection(kde_LAV_home_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_LAV_home_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.008682154, 0.009355564  (x, y)
## extent     : 30.34265, 31.45396, 32.0356, 33.23311  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : 0.2245951, 426.8348  (min, max)

6.3.2 Fixed Bandwidth Kernel Density Estimation (Room Type: Hotel Room)

LAV_listings_hotel.km <- rescale(LAV_listings_hotel, 1000, "km")

kde_LAV_hotel <- density(LAV_listings_hotel.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_LAV_hotel <- as.SpatialGridDataFrame.im(kde_LAV_hotel)

spplot(gridded_kde_LAV_hotel) 

kde_LAV_hotel_raster <- raster(gridded_kde_LAV_hotel)
projection(kde_LAV_hotel_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_LAV_hotel_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.008682154, 0.009355564  (x, y)
## extent     : 30.34265, 31.45396, 32.0356, 33.23311  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : 0.01563053, 191.7775  (min, max)

6.3.3 Fixed Bandwidth Kernel Density Estimation (Room Type: Shared Room)

LAV_listings_shared.km <- rescale(LAV_listings_shared, 1000, "km")

kde_LAV_shared <- density(LAV_listings_shared.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_LAV_shared <- as.SpatialGridDataFrame.im(kde_LAV_shared)

spplot(gridded_kde_LAV_shared) 

kde_LAV_shared_raster <- raster(gridded_kde_LAV_shared)
projection(kde_LAV_shared_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_LAV_shared_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.008682154, 0.009355564  (x, y)
## extent     : 30.34265, 31.45396, 32.0356, 33.23311  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : 0.0610804, 147.3463  (min, max)

6.3.4 Fixed Bandwidth Kernel Density Estimation (Room Type: Private Room)

LAV_listings_private.km <- rescale(LAV_listings_private, 1000, "km")

kde_LAV_private <- density(LAV_listings_private.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_LAV_private <- as.SpatialGridDataFrame.im(kde_LAV_private)

spplot(gridded_kde_LAV_private) 

kde_LAV_private_raster <- raster(gridded_kde_LAV_private)
projection(kde_LAV_private_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_LAV_private_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.008682154, 0.009355564  (x, y)
## extent     : 30.34265, 31.45396, 32.0356, 33.23311  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : 5.711151, 1055.866  (min, max)

6.4 Kernel Density Estimation (Subzone: Tanjong Pagar)

6.4.1 Fixed Bandwidth Kernel Density Estimation (Room Type: Entire Home/ Apartment)

TP_listings_home.km <- rescale(TP_listings_home, 1000, "km")

kde_TP_home <- density(TP_listings_home.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_TP_home <- as.SpatialGridDataFrame.im(kde_TP_home)

spplot(gridded_kde_TP_home) 

kde_TP_home_raster <- raster(gridded_kde_TP_home)
projection(kde_TP_home_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_TP_home_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.003758669, 0.004986962  (x, y)
## extent     : 29.16913, 29.65024, 28.43025, 29.06858  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : 12.33845, 1615.645  (min, max)

6.4.2 Fixed Bandwidth Kernel Density Estimation (Room Type: Hotel Room)

TP_listings_hotel.km <- rescale(TP_listings_hotel, 1000, "km")

kde_TP_hotel <- density(TP_listings_hotel.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_TP_hotel <- as.SpatialGridDataFrame.im(kde_TP_hotel)

spplot(gridded_kde_TP_hotel) 

kde_TP_hotel_raster <- raster(gridded_kde_TP_hotel)
projection(kde_TP_hotel_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_TP_hotel_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.003758669, 0.004986962  (x, y)
## extent     : 29.16913, 29.65024, 28.43025, 29.06858  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : 0.0008411488, 27.33706  (min, max)

6.4.3 Fixed Bandwidth Kernel Density Estimation (Room Type: Shared Room)

TP_listings_shared.km <- rescale(TP_listings_shared, 1000, "km")

kde_TP_shared <- density(TP_listings_shared.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_TP_shared <- as.SpatialGridDataFrame.im(kde_TP_shared)

spplot(gridded_kde_TP_shared) 

kde_TP_shared_raster <- raster(gridded_kde_TP_shared)
projection(kde_TP_shared_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_TP_shared_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.003758669, 0.004986962  (x, y)
## extent     : 29.16913, 29.65024, 28.43025, 29.06858  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : 0, 0  (min, max)

6.4.4 Fixed Bandwidth Kernel Density Estimation (Room Type: Private Room)

TP_listings_private.km <- rescale(TP_listings_private, 1000, "km")

kde_TP_private <- density(TP_listings_private.km, sigma=0.1, edge=TRUE, kernel="gaussian")

gridded_kde_TP_private <- as.SpatialGridDataFrame.im(kde_TP_private)

spplot(gridded_kde_TP_private) 

kde_TP_private_raster <- raster(gridded_kde_TP_private)
projection(kde_TP_private_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_TP_private_raster
## class      : RasterLayer 
## dimensions : 128, 128, 16384  (nrow, ncol, ncell)
## resolution : 0.003758669, 0.004986962  (x, y)
## extent     : 29.16913, 29.65024, 28.43025, 29.06858  (xmin, xmax, ymin, ymax)
## crs        : +init=EPSG:3414 +datum=WGS84 +units=km +proj=tmerc +lat_0=1.366666666666667 +lon_0=103.8333333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +no_defs +ellps=WGS84 +towgs84=0,0,0 
## source     : memory
## names      : v 
## values     : 20.49776, 193.2663  (min, max)

6.5 Plotting Kernel Density Maps on Openstreetmap of SG by Room Type

6.5.1 Mapping Kernel Density by Subzones (Room Type: Entire Home/ Apartment)

tm_shape(sg)+
  tm_borders(alpha = 0.5) +
tm_shape(kde_ALJ_home_raster) + 
    tm_raster("v", alpha=0.6,  
          palette = "YlOrRd") +
tm_shape(kde_BAL_home_raster) + 
    tm_raster("v", alpha=0.6,  
          palette = "YlOrRd") +
tm_shape(kde_LAV_home_raster) + 
    tm_raster("v", alpha=0.6,  
          palette = "YlOrRd") +
tm_shape(kde_TP_home_raster) + 
    tm_raster("v", alpha=0.6,  
          palette = "YlOrRd")
## Warning: The shape sg is invalid. See sf::st_is_valid

From the map:

–> Tanjong Pagar is very dense with AirBnb listings of entire homes/ apartments as compared to other subzones. One reason for such a pattern to be observed is that tourists on long business trips may want to look for Airbnb listings near the Central Business District for ease of accessibility and have the convenience of having an entire home to themselves for their stay.

6.5.2 Mapping Kernel Density by Subzones (Room Type: Hotel Room)

tm_shape(sg)+
  tm_borders(alpha = 0.5) +
tm_shape(kde_ALJ_hotel_raster) + 
    tm_raster("v", alpha=0.8,  
          palette = "YlOrRd") +
tm_shape(kde_BAL_hotel_raster) + 
    tm_raster("v", alpha=0.8,  
          palette = "YlOrRd") +
tm_shape(kde_LAV_hotel_raster) + 
    tm_raster("v", alpha=0.8,  
          palette = "YlOrRd") +
tm_shape(kde_TP_hotel_raster) + 
    tm_raster("v", alpha=0.8,  
          palette = "YlOrRd")
## Warning: The shape sg is invalid. See sf::st_is_valid

From the map:

–> AirBnb listings of hotel rooms are most dense in Lavender. This can be due to Lavender being a residential area in the city, hence offering more hotel rooms as compared to the other subzones.

6.5.3 Mapping Kernel Density by Subzones (Room Type: Shared Room)

tm_shape(sg)+
  tm_borders(alpha = 0.5) +
tm_shape(kde_ALJ_shared_raster) + 
    tm_raster("v", alpha=0.8,  
          palette = "YlOrRd") +
tm_shape(kde_BAL_shared_raster) + 
    tm_raster("v", alpha=0.8,  
          palette = "YlOrRd") +
tm_shape(kde_LAV_shared_raster) + 
    tm_raster("v", alpha=0.8,  
          palette = "YlOrRd") +
tm_shape(kde_TP_shared_raster) + 
    tm_raster("v", alpha=0.8,  
          palette = "YlOrRd")
## Warning: The shape sg is invalid. See sf::st_is_valid

From the map:

–> Tanjong Pagar has no AirBnb listings of private rooms while Lavender has the highest density. This can be due to Lavender being a residential area in the city while Tanjong Pagar is in the work district.

6.5.4 Mapping Kernel Density by Subzones (Room Type: Private Room)

tm_shape(sg)+
  tm_borders(alpha = 0.5) +
tm_shape(kde_ALJ_home_raster) + 
    tm_raster("v", alpha=0.8,  
          palette = "YlOrRd") +
tm_shape(kde_BAL_home_raster) + 
    tm_raster("v", alpha=0.8,  
          palette = "YlOrRd") +
tm_shape(kde_LAV_home_raster) + 
    tm_raster("v", alpha=0.8,  
          palette = "YlOrRd") +
tm_shape(kde_TP_home_raster) + 
    tm_raster("v", alpha=0.8,  
          palette = "YlOrRd")
## Warning: The shape sg is invalid. See sf::st_is_valid

From the map:

–> AirBnb listings of private rooms are most dense in Lavender. This can be due to Lavender being a residential area in the city, hence offering more private rooms as compared to the other subzones.

tmap_mode('plot')
## tmap mode set to plotting

6.5.5 Overall Conclusion from Kernel Density Maps of Subzones for each Room Type

  1. Aljunied, Lavender and Balestier have are more dense in terms of listings by room type as compared to Tanjong Pagar.

  2. This may be because Tanjong Pagar is significantly smaller in size as compared to the other subzones.

  3. This may also be because Aljunied, Balestier and Lavender are closer to popular tourists spots towards the South of Singapore as compared to Tanjong Pagar. Tanjong Pagar is located in the Central Business District where most of the offices are. Therefore, there are more AirBnb listings for each room type in Aljunied, Balestier and Lavender as compared to Tanjong Pagar due to the increased ease of accessibility.