TakeHome_Ex02

Objective

In this report, we will analyse the distribution of Airbnb listing, by using appropriate spatial point patterns analysis techniques. Our main focus for this report will be on the locations of Airbnb listing by room type. There are 4 different room types in the listings, namely, Private, Shared, Entire home / Apartment, and Hotel.

There will be two sections to this report, the first section is on a nation-wide analysis, while the second section will be on the analysis of 4 planning subzones.

To begin,

Import packages

packages = c('rgdal', 'maptools', 'raster','spatstat', 'tmap', 'dplyr', 'leaflet', 'sf', 'ggplot2', 'ggmap','readr')
for (p in packages){
if(!require(p, character.only = T)){
install.packages(p)
}
library(p,character.only = T)
}

## Loading required package: rgdal

## Loading required package: sp

## rgdal: version: 1.4-8, (SVN revision 845)
##  Geospatial Data Abstraction Library extensions to R successfully loaded
##  Loaded GDAL runtime: GDAL 2.2.3, released 2017/11/20
##  Path to GDAL shared files: C:/R/R-4.0.0/library/rgdal/gdal
##  GDAL binary built with GEOS: TRUE 
##  Loaded PROJ.4 runtime: Rel. 4.9.3, 15 August 2016, [PJ_VERSION: 493]
##  Path to PROJ.4 shared files: C:/R/R-4.0.0/library/rgdal/proj
##  Linking to sp version: 1.4-1

## Loading required package: maptools

## Checking rgeos availability: FALSE
##      Note: when rgeos is not available, polygon geometry     computations in maptools depend on gpclib,
##      which has a restricted licence. It is disabled by default;
##      to enable gpclib, type gpclibPermit()

## Loading required package: raster

## Loading required package: spatstat

## Loading required package: spatstat.data

## Loading required package: nlme

## 
## Attaching package: 'nlme'

## The following object is masked from 'package:raster':
## 
##     getData

## Loading required package: rpart

## 
## spatstat 1.64-1       (nickname: 'Help you I can, yes!') 
## For an introduction to spatstat, type 'beginner'

## 
## Attaching package: 'spatstat'

## The following objects are masked from 'package:raster':
## 
##     area, rotate, shift

## Loading required package: tmap

## Loading required package: dplyr

## 
## Attaching package: 'dplyr'

## The following object is masked from 'package:nlme':
## 
##     collapse

## The following objects are masked from 'package:raster':
## 
##     intersect, select, union

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

## Loading required package: leaflet

## Loading required package: sf

## Linking to GEOS 3.8.0, GDAL 3.0.4, PROJ 6.3.1

## Loading required package: ggplot2

## Loading required package: ggmap

## Google's Terms of Service: https://cloud.google.com/maps-platform/terms/.

## Please cite ggmap if you use it! See citation("ggmap") for details.

## Loading required package: readr

Import listings data

listings <- read.csv("data/aspatial/listings.csv")

Section A: Nation-wide analysis

Part 1: Exploratory Spatial Data Analysis

In this section, we will use appropriate tmap function to display the locations of the Airbnb listing by room type, and describe the spatial patterns observed.

Plotting an interactive map to depict the locations of Airbnb listing by room type, with Openstreetmap of Singapore as background. Setting the 4 different room types as different coloured b ubbble, we plot an interactive map to clearly identify which area has the most rooms, and which room type is the most popular.

tmap_mode("view")

## tmap mode set to interactive viewing

 pal <- colorFactor(palette = c("#FF5A5F", "#00A699", "#767676", "#FC642D"), domain = listings$toom_type)
 
 leaflet(data = listings) %>% addProviderTiles(providers$CartoDB.Positron) %>%  addCircleMarkers(~longitude, ~latitude, color = ~pal(room_type), weight = 2, radius=2, fillOpacity = 0.2, opacity = 0.2,
                                                                                                        label = paste("Name:", listings$name)) %>% 
     addLegend("bottomright", pal = pal, values = ~room_type,
     title = "Room Types",
     opacity = 1
   )

tmap_mode("plot")

## tmap mode set to plotting

At first glance, it is very clear that the Central Region has the highest demand and that “entire apartment” is the most frequent room rented out in the Central Region. However, if we take a look at the whole map, it is interesting to note that private rooms are significantly more popular in other areas of Singapore.

We would like to analyse each of the 4 individual room types, to analyse whether they are random or clustered, and if clustered, which are the clustered locations. This will help us in understanding the relationship between location and room type in Singapore.

Import data

sg <- readOGR(dsn = "data/geospatial", layer="CostalOutline")

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\amoss\OneDrive\Documents\A2\data\geospatial", layer: "CostalOutline"
## with 60 features
## It has 4 fields

mpsz <- readOGR(dsn = "data/geospatial", layer="MP14_SUBZONE_WEB_PL")

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\amoss\OneDrive\Documents\A2\data\geospatial", layer: "MP14_SUBZONE_WEB_PL"
## with 323 features
## It has 15 fields

There are 4 different room types - private, shared, entire apartment, and hotel. We will be splitting the analysis for the 4 different room types.

DO PRIVATE FIRST

private <- listings %>%
   filter(room_type == 'Private room')

Check projection

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

crs(mpsz)

## 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

coordinates(private)=c("longitude","latitude")
proj4string(private) <- CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs")

private <- spTransform(private,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 "))

The graph below shows the distribution of Airbnb private room types across the Singapore map, and we can see significant clustering at the Central area, as well as the East and West regions.

plot(sg, border="lightgrey")
plot(sg, add=TRUE)
plot(private, add=TRUE )

tmap_mode('view')

## tmap mode set to interactive viewing

This graph shows the location of the different private room types across Singapore, with openstreetmap of Singapore as background. It gives the same results as the above graph, with clustering mainly in the Central area.

tm_shape(private)+
  tm_dots()

Plotting an interactive map to show the various Private Airbnb room types across Singapore

 privroom <- listings %>% 
               filter(room_type == "Private room" )

Pic <- makeIcon(iconUrl = "images (1).png", 
                 iconWidth = 100*0.35,
                 iconHeight = 100*0.35) 

 map <- leaflet()
      map <- addTiles(map) 
      
      map <- addMarkers(map,
                        lng = privroom$longitude,
                        lat = privroom$latitude,
                        popup = privroom$name,
                        clusterOptions = markerClusterOptions(), 
                        icon = Pic)
map

tmap_mode('plot')

## tmap mode set to plotting

Examine SpatialPointsDataFrame

private

## class       : SpatialPointsDataFrame 
## features    : 3206 
## extent      : 10737.87, 43386.87, 26334.02, 48466.72  (xmin, xmax, ymin, ymax)
## 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 
## variables   : 14
## names       :       id,                                     name,   host_id, host_name, neighbourhood_group, neighbourhood,    room_type, price, minimum_nights, number_of_reviews, last_review, reviews_per_month, calculated_host_listings_count, availability_365 
## min values  :    49091,                                         ,    227796,   ~小秦,      Central Region,    Ang Mo Kio, Private room,    14,              1,                 0,            ,              0.01,                              1,                0 
## max values  : 42970150, Yunnan Garden Corner Terrace ( Near NTU), 341869568,   Zulaiha,         West Region,        Yishun, Private room,  9999,           1000,               352,  2020-03-20,             29.17,                            151,              365

Converting the spatial point data frame into generic sp format (so as to be able to convert into ppp)

private_sp <- as(private, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")

The plotting of sp format of private Airbnb room types give the same readings as above

plot(private_sp)

tmap_mode("view")

## tmap mode set to interactive viewing

This graph shows the location of the different private room types across Singapore, using the sp format of data, with openstreetmap of Singapore as background. It gives the same results as the above graph, with clustering mainly in the Central area.

tm_shape(private_sp)+
tm_bubbles(col = "blue",
           size = 1,
           border.col = "black",
           border.lwd = 1)

tmap_mode("plot")

## tmap mode set to plotting

private_sp

## class       : SpatialPoints 
## features    : 3206 
## extent      : 10737.87, 43386.87, 26334.02, 48466.72  (xmin, xmax, ymin, ymax)
## 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

Converting the generic sp format into spatstat’s ppp format

private_ppp <- as(private_sp, "ppp")
private_ppp

## Planar point pattern: 3206 points
## window: rectangle = [10737.87, 43386.87] x [26334.02, 48466.72] units

This ppp plot of private Airbnb room types in Singapore shows significant clustering in the central-south area

plot(private_ppp)

summary(private_ppp)

## Planar point pattern:  3206 points
## Average intensity 4.436692e-06 points per square unit
## 
## *Pattern contains duplicated points*
## 
## Coordinates are given to 3 decimal places
## i.e. rounded to the nearest multiple of 0.001 units
## 
## Window: rectangle = [10737.87, 43386.87] x [26334.02, 48466.72] units
##                     (32650 x 22130 units)
## Window area = 722610000 square units

Handling duplicated points

any(duplicated(private_ppp))

## [1] TRUE

Count number of coincidence point

multiplicity(private_ppp) 

##    1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16 
##    1    1    1    1    1    1    1    1    3    3    3    1    1    1    1    1 
##   17   18   19   20   21   22   23   24   25   26   27   28   29   30   31   32 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1   17 
##   33   34   35   36   37   38   39   40   41   42   43   44   45   46   47   48 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   49   50   51   52   53   54   55   56   57   58   59   60   61   62   63   64 
##    1    1    1    1    1    1    1    1    1    1    1    1   17    1    1    1 
##   65   66   67   68   69   70   71   72   73   74   75   76   77   78   79   80 
##    1    1    1   17    1    1    1    1    1    1    1    1    1    1    1    1 
##   81   82   83   84   85   86   87   88   89   90   91   92   93   94   95   96 
##    1    1    1    1    1    1    1    1    1    1    1    1    1   11    1   11 
##   97   98   99  100  101  102  103  104  105  106  107  108  109  110  111  112 
##   11   11   11   11   11    1    1    1    1    4    1    1    1    1    1    1 
##  113  114  115  116  117  118  119  120  121  122  123  124  125  126  127  128 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  129  130  131  132  133  134  135  136  137  138  139  140  141  142  143  144 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  145  146  147  148  149  150  151  152  153  154  155  156  157  158  159  160 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  161  162  163  164  165  166  167  168  169  170  171  172  173  174  175  176 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  177  178  179  180  181  182  183  184  185  186  187  188  189  190  191  192 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  193  194  195  196  197  198  199  200  201  202  203  204  205  206  207  208 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  209  210  211  212  213  214  215  216  217  218  219  220  221  222  223  224 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  225  226  227  228  229  230  231  232  233  234  235  236  237  238  239  240 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  241  242  243  244  245  246  247  248  249  250  251  252  253  254  255  256 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  257  258  259  260  261  262  263  264  265  266  267  268  269  270  271  272 
##    1    1    1    1   17    1    1    1    1    1    1    1    1    1    1    1 
##  273  274  275  276  277  278  279  280  281  282  283  284  285  286  287  288 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  289  290  291  292  293  294  295  296  297  298  299  300  301  302  303  304 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  305  306  307  308  309  310  311  312  313  314  315  316  317  318  319  320 
##    1    1    1    1    1    4    1    1    1    1    1    1    1    1    1    1 
##  321  322  323  324  325  326  327  328  329  330  331  332  333  334  335  336 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  337  338  339  340  341  342  343  344  345  346  347  348  349  350  351  352 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  353  354  355  356  357  358  359  360  361  362  363  364  365  366  367  368 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  369  370  371  372  373  374  375  376  377  378  379  380  381  382  383  384 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  385  386  387  388  389  390  391  392  393  394  395  396  397  398  399  400 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  401  402  403  404  405  406  407  408  409  410  411  412  413  414  415  416 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  417  418  419  420  421  422  423  424  425  426  427  428  429  430  431  432 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  433  434  435  436  437  438  439  440  441  442  443  444  445  446  447  448 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  449  450  451  452  453  454  455  456  457  458  459  460  461  462  463  464 
##    1    1    1    1    1   11    1    1    1    1    1    1    1    1    1    1 
##  465  466  467  468  469  470  471  472  473  474  475  476  477  478  479  480 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  481  482  483  484  485  486  487  488  489  490  491  492  493  494  495  496 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  497  498  499  500  501  502  503  504  505  506  507  508  509  510  511  512 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  513  514  515  516  517  518  519  520  521  522  523  524  525  526  527  528 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  529  530  531  532  533  534  535  536  537  538  539  540  541  542  543  544 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  545  546  547  548  549  550  551  552  553  554  555  556  557  558  559  560 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  561  562  563  564  565  566  567  568  569  570  571  572  573  574  575  576 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  577  578  579  580  581  582  583  584  585  586  587  588  589  590  591  592 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  593  594  595  596  597  598  599  600  601  602  603  604  605  606  607  608 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  609  610  611  612  613  614  615  616  617  618  619  620  621  622  623  624 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  625  626  627  628  629  630  631  632  633  634  635  636  637  638  639  640 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  641  642  643  644  645  646  647  648  649  650  651  652  653  654  655  656 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  657  658  659  660  661  662  663  664  665  666  667  668  669  670  671  672 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  673  674  675  676  677  678  679  680  681  682  683  684  685  686  687  688 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  689  690  691  692  693  694  695  696  697  698  699  700  701  702  703  704 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  705  706  707  708  709  710  711  712  713  714  715  716  717  718  719  720 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  721  722  723  724  725  726  727  728  729  730  731  732  733  734  735  736 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1   17 
##  737  738  739  740  741  742  743  744  745  746  747  748  749  750  751  752 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  753  754  755  756  757  758  759  760  761  762  763  764  765  766  767  768 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  769  770  771  772  773  774  775  776  777  778  779  780  781  782  783  784 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  785  786  787  788  789  790  791  792  793  794  795  796  797  798  799  800 
##    1    1    1    1    1    1    1    1    1    1   17    1    1    1    1    1 
##  801  802  803  804  805  806  807  808  809  810  811  812  813  814  815  816 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  817  818  819  820  821  822  823  824  825  826  827  828  829  830  831  832 
##    1    1    1    1    1    1    1   17    1    1    1    1    1    1    1    1 
##  833  834  835  836  837  838  839  840  841  842  843  844  845  846  847  848 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  849  850  851  852  853  854  855  856  857  858  859  860  861  862  863  864 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  865  866  867  868  869  870  871  872  873  874  875  876  877  878  879  880 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  881  882  883  884  885  886  887  888  889  890  891  892  893  894  895  896 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  897  898  899  900  901  902  903  904  905  906  907  908  909  910  911  912 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  913  914  915  916  917  918  919  920  921  922  923  924  925  926  927  928 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  929  930  931  932  933  934  935  936  937  938  939  940  941  942  943  944 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    3    3    1 
##  945  946  947  948  949  950  951  952  953  954  955  956  957  958  959  960 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  961  962  963  964  965  966  967  968  969  970  971  972  973  974  975  976 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  977  978  979  980  981  982  983  984  985  986  987  988  989  990  991  992 
##    1    1    1    1    1    1    1    1    1    1   11   11   11    1    1    1 
##  993  994  995  996  997  998  999 1000 1001 1002 1003 1004 1005 1006 1007 1008 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 
##    1    1    1    1    1    1    3    1    1    1    1    1    1    1    1    1 
## 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 
##    1    1    1    1    3    1    1    1    1    1    3    1    1    3    1    1 
## 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 
##    1    1    1    1    6    1    1    1    1    1    1    1    1    6    6    1 
## 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 
##    1    1    1    1    1    1    1    6    1    1    1    1    1    1    1    1 
## 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    4    4    4 
## 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 
##    1    4    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 
##   16    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 
##    1    1    1    1    1    1    1    1    1    1    6    1    1    1    1    1 
## 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 
##    1    1    1    1    1    1    1    1    1    1    1    1    3    1    1    1 
## 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 
##    3    1    1    1    1    1    1    1    1    1    1    1    6    1    1    1 
## 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 
##    1    1    1    1    3    1    1    1    1    1    1    1    1    1    1    1 
## 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1   16    1 
## 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 
##    1    1    1    1    1    1    1    1    1   11    1    1    1    1    1    1 
## 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1   11 
## 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 
##    1    1   11    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 
##    1    1    1    1    1    1    1    1    1    1    1   11    1   16    1    1 
## 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 
##    1    1    1    1    1    1    1    1    1    1    1   11    1    1    1    1 
## 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 
##    1    1    1    1    1   11    1    1    1    1    1   11    1    1    1    1 
## 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 
##    1   11    1    1    1   11    1    1    1    1    1    1    1    1    1    1 
## 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 
##    1    1    1    1    1    1   11    1   16    1   11    1    1    1    1    1 
## 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 
##    1    1   14    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 
##    1    1    1    1    1    1   16    1    1    1    1    1    1    1    1    1 
## 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1   14 
## 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 
##    1    1    1    1    1    1    1   14    1    1    1    1    1    1    1    1 
## 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 
##    1    1   14    1   16    1    1    1    1    1    1    1    1    1    1    1 
## 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 
##    1    1    1    1    1    1    1    1    1    1   16    1    1    1    1    1 
## 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 
##    1    1    4    1    1    1    1    1    1    1    1    3    3    3    1    1 
## 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 
##    1    1    1    1    1    1    1    1    1    1    1   14    1    1    1    1 
## 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 
##    1    1    4    1    1   16    1    1    1    1    1    1    1    1    1    1 
## 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1   14 
## 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 
##    1    4    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 
##    4    1    1    1    1    1    1    1    1    1    1    1   14    1    1    3 
## 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 
##    1    1   14    1    1   16    1    1    1    1   14    1    1    1    1    1 
## 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 
##   14    1    1    1    1    1    4    1    1    1    1    1   16    1    1    1 
## 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2177 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 
##    1    1    1   14    1    1    1    1    1    1    1    1    1    1    1    1 
## 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204 2205 2206 2207 2208 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2225 2226 2227 2228 2229 2230 2231 2232 2233 2234 2235 2236 2237 2238 2239 2240 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2241 2242 2243 2244 2245 2246 2247 2248 2249 2250 2251 2252 2253 2254 2255 2256 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2268 2269 2270 2271 2272 
##    1    1    1    1    1    4    1    1    1    1    1    1    1    1    1    1 
## 2273 2274 2275 2276 2277 2278 2279 2280 2281 2282 2283 2284 2285 2286 2287 2288 
##    4    1   14    4    1    1    1    3    1    1    1    4    1    1    1    1 
## 2289 2290 2291 2292 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 
##    1    1    1    1    1    1   14    1    1    1    1    1    1    1    1    1 
## 2305 2306 2307 2308 2309 2310 2311 2312 2313 2314 2315 2316 2317 2318 2319 2320 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2321 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351 2352 
##    1    1    1    1    1    1    1    1    1    1    1    1    1   17    1    1 
## 2353 2354 2355 2356 2357 2358 2359 2360 2361 2362 2363 2364 2365 2366 2367 2368 
##    1    1    1   17    1    1    1    1   17    1    1    1    1    1    1    1 
## 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 2379 2380 2381 2382 2383 2384 
##    1    1    1    1    1    1    4   16    1    1    1    1    1    1    1    1 
## 2385 2386 2387 2388 2389 2390 2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2401 2402 2403 2404 2405 2406 2407 2408 2409 2410 2411 2412 2413 2414 2415 2416 
##   16    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2417 2418 2419 2420 2421 2422 2423 2424 2425 2426 2427 2428 2429 2430 2431 2432 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443 2444 2445 2446 2447 2448 
##    1    3    1    1    1    1   16   16    1    1    1   16    1    1    1    1 
## 2449 2450 2451 2452 2453 2454 2455 2456 2457 2458 2459 2460 2461 2462 2463 2464 
##    1   17    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2465 2466 2467 2468 2469 2470 2471 2472 2473 2474 2475 2476 2477 2478 2479 2480 
##    1    1    1    1   17    1    1    1    1    1    1    1    1    1    1    1 
## 2481 2482 2483 2484 2485 2486 2487 2488 2489 2490 2491 2492 2493 2494 2495 2496 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2497 2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 
##    1    1    1    1    1    1    1    1    1    1    1   17    1    1    1    1 
## 2513 2514 2515 2516 2517 2518 2519 2520 2521 2522 2523 2524 2525 2526 2527 2528 
##    1   17    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 2539 2540 2541 2542 2543 2544 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2545 2546 2547 2548 2549 2550 2551 2552 2553 2554 2555 2556 2557 2558 2559 2560 
##    1    1    4    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2561 2562 2563 2564 2565 2566 2567 2568 2569 2570 2571 2572 2573 2574 2575 2576 
##    1    1    1    1    1    1    1   17    1    1    1    3    3    1    3    1 
## 2577 2578 2579 2580 2581 2582 2583 2584 2585 2586 2587 2588 2589 2590 2591 2592 
##    1    1    1    1    1    1    1    1    1    1   17    1    1    1    1    1 
## 2593 2594 2595 2596 2597 2598 2599 2600 2601 2602 2603 2604 2605 2606 2607 2608 
##    1    1    1    1    1    1    1    4    1    1    1    1    1    1    1    1 
## 2609 2610 2611 2612 2613 2614 2615 2616 2617 2618 2619 2620 2621 2622 2623 2624 
##    1    1    1    1    1    1   14    1    1    1    1    1    1    1    1    1 
## 2625 2626 2627 2628 2629 2630 2631 2632 2633 2634 2635 2636 2637 2638 2639 2640 
##    1    1    1    1    1    1    1    1   16    1    1    4    1    1    1    1 
## 2641 2642 2643 2644 2645 2646 2647 2648 2649 2650 2651 2652 2653 2654 2655 2656 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2657 2658 2659 2660 2661 2662 2663 2664 2665 2666 2667 2668 2669 2670 2671 2672 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2673 2674 2675 2676 2677 2678 2679 2680 2681 2682 2683 2684 2685 2686 2687 2688 
##    1    1    1    1    1    1    1    1    1    1    1    1    4    1    1    1 
## 2689 2690 2691 2692 2693 2694 2695 2696 2697 2698 2699 2700 2701 2702 2703 2704 
##    1    1    1    1    1    1    1    1    1    1    1    1   17    1    1    1 
## 2705 2706 2707 2708 2709 2710 2711 2712 2713 2714 2715 2716 2717 2718 2719 2720 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2721 2722 2723 2724 2725 2726 2727 2728 2729 2730 2731 2732 2733 2734 2735 2736 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2737 2738 2739 2740 2741 2742 2743 2744 2745 2746 2747 2748 2749 2750 2751 2752 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2753 2754 2755 2756 2757 2758 2759 2760 2761 2762 2763 2764 2765 2766 2767 2768 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2769 2770 2771 2772 2773 2774 2775 2776 2777 2778 2779 2780 2781 2782 2783 2784 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2785 2786 2787 2788 2789 2790 2791 2792 2793 2794 2795 2796 2797 2798 2799 2800 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2801 2802 2803 2804 2805 2806 2807 2808 2809 2810 2811 2812 2813 2814 2815 2816 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2817 2818 2819 2820 2821 2822 2823 2824 2825 2826 2827 2828 2829 2830 2831 2832 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2833 2834 2835 2836 2837 2838 2839 2840 2841 2842 2843 2844 2845 2846 2847 2848 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2849 2850 2851 2852 2853 2854 2855 2856 2857 2858 2859 2860 2861 2862 2863 2864 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2865 2866 2867 2868 2869 2870 2871 2872 2873 2874 2875 2876 2877 2878 2879 2880 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2881 2882 2883 2884 2885 2886 2887 2888 2889 2890 2891 2892 2893 2894 2895 2896 
##    1    1    1    1    1    1    1    1    1    1    1    1    2    1    1    1 
## 2897 2898 2899 2900 2901 2902 2903 2904 2905 2906 2907 2908 2909 2910 2911 2912 
##    1    1    1    1    1    2    1    1    1    1    1    1    1    1    1    1 
## 2913 2914 2915 2916 2917 2918 2919 2920 2921 2922 2923 2924 2925 2926 2927 2928 
##    1    1    1    1    2    2    1    1    1    1    1    1    1    1    1    1 
## 2929 2930 2931 2932 2933 2934 2935 2936 2937 2938 2939 2940 2941 2942 2943 2944 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2945 2946 2947 2948 2949 2950 2951 2952 2953 2954 2955 2956 2957 2958 2959 2960 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2961 2962 2963 2964 2965 2966 2967 2968 2969 2970 2971 2972 2973 2974 2975 2976 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2977 2978 2979 2980 2981 2982 2983 2984 2985 2986 2987 2988 2989 2990 2991 2992 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2993 2994 2995 2996 2997 2998 2999 3000 3001 3002 3003 3004 3005 3006 3007 3008 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3009 3010 3011 3012 3013 3014 3015 3016 3017 3018 3019 3020 3021 3022 3023 3024 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3025 3026 3027 3028 3029 3030 3031 3032 3033 3034 3035 3036 3037 3038 3039 3040 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3041 3042 3043 3044 3045 3046 3047 3048 3049 3050 3051 3052 3053 3054 3055 3056 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3057 3058 3059 3060 3061 3062 3063 3064 3065 3066 3067 3068 3069 3070 3071 3072 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3073 3074 3075 3076 3077 3078 3079 3080 3081 3082 3083 3084 3085 3086 3087 3088 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3089 3090 3091 3092 3093 3094 3095 3096 3097 3098 3099 3100 3101 3102 3103 3104 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3105 3106 3107 3108 3109 3110 3111 3112 3113 3114 3115 3116 3117 3118 3119 3120 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3121 3122 3123 3124 3125 3126 3127 3128 3129 3130 3131 3132 3133 3134 3135 3136 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3137 3138 3139 3140 3141 3142 3143 3144 3145 3146 3147 3148 3149 3150 3151 3152 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3153 3154 3155 3156 3157 3158 3159 3160 3161 3162 3163 3164 3165 3166 3167 3168 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3169 3170 3171 3172 3173 3174 3175 3176 3177 3178 3179 3180 3181 3182 3183 3184 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3185 3186 3187 3188 3189 3190 3191 3192 3193 3194 3195 3196 3197 3198 3199 3200 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3201 3202 3203 3204 3205 3206 
##    1    1    1    1    1    1

Total number of duplicates

sum(multiplicity(private_ppp) >1)

## [1] 120

tmap_mode("plot")

## tmap mode set to plotting

To view locations of duplicate points

tm_shape(private) +
  tm_dots(alpha=0.4, size=0.05)

tmap_mode("plot")

## tmap mode set to plotting

###To solve this problem, use jittering #### There are no more overlapping of circumference

private_ppp_jit <- rjitter(private_ppp, retry=TRUE, nsim=1, drop=TRUE)
plot(private_ppp_jit)

Creating owin

sg_owin <- as(sg_sp, "owin")

plot(sg_owin)

summary(sg_owin)

## Window: polygonal boundary
## 60 separate polygons (no holes)
##             vertices        area relative.area
## polygon 1         38 1.56140e+04      2.09e-05
## polygon 2        735 4.69093e+06      6.27e-03
## polygon 3         49 1.66986e+04      2.23e-05
## polygon 4         76 3.12332e+05      4.17e-04
## polygon 5       5141 6.36179e+08      8.50e-01
## polygon 6         42 5.58317e+04      7.46e-05
## polygon 7         67 1.31354e+06      1.75e-03
## polygon 8         15 4.46420e+03      5.96e-06
## polygon 9         14 5.46674e+03      7.30e-06
## polygon 10        37 5.26194e+03      7.03e-06
## polygon 11        53 3.44003e+04      4.59e-05
## polygon 12        74 5.82234e+04      7.78e-05
## polygon 13        69 5.63134e+04      7.52e-05
## polygon 14       143 1.45139e+05      1.94e-04
## polygon 15       165 3.38736e+05      4.52e-04
## polygon 16       130 9.40465e+04      1.26e-04
## polygon 17        19 1.80977e+03      2.42e-06
## polygon 18        16 2.01046e+03      2.69e-06
## polygon 19        93 4.30642e+05      5.75e-04
## polygon 20        90 4.15092e+05      5.54e-04
## polygon 21       721 1.92795e+06      2.57e-03
## polygon 22       330 1.11896e+06      1.49e-03
## polygon 23       115 9.28394e+05      1.24e-03
## polygon 24        37 1.01705e+04      1.36e-05
## polygon 25        25 1.66227e+04      2.22e-05
## polygon 26        10 2.14507e+03      2.86e-06
## polygon 27       190 2.02489e+05      2.70e-04
## polygon 28       175 9.25904e+05      1.24e-03
## polygon 29      1993 9.99217e+06      1.33e-02
## polygon 30        38 2.42492e+04      3.24e-05
## polygon 31        24 6.35239e+03      8.48e-06
## polygon 32        53 6.35791e+05      8.49e-04
## polygon 33        41 1.60161e+04      2.14e-05
## polygon 34        22 2.54368e+03      3.40e-06
## polygon 35        30 1.08382e+04      1.45e-05
## polygon 36       327 2.16921e+06      2.90e-03
## polygon 37       111 6.62927e+05      8.85e-04
## polygon 38        90 1.15991e+05      1.55e-04
## polygon 39        98 6.26829e+04      8.37e-05
## polygon 40       415 3.25384e+06      4.35e-03
## polygon 41       222 1.51142e+06      2.02e-03
## polygon 42       107 6.33039e+05      8.45e-04
## polygon 43         7 2.48299e+03      3.32e-06
## polygon 44        17 3.28303e+04      4.38e-05
## polygon 45        26 8.34758e+03      1.11e-05
## polygon 46       177 4.67446e+05      6.24e-04
## polygon 47        16 3.19460e+03      4.27e-06
## polygon 48        15 4.87296e+03      6.51e-06
## polygon 49        66 1.61841e+04      2.16e-05
## polygon 50       149 5.63430e+06      7.53e-03
## polygon 51       609 2.62570e+07      3.51e-02
## polygon 52         8 7.82256e+03      1.04e-05
## polygon 53       976 2.33447e+07      3.12e-02
## polygon 54        55 8.25379e+04      1.10e-04
## polygon 55       976 2.33447e+07      3.12e-02
## polygon 56        61 3.33449e+05      4.45e-04
## polygon 57         6 1.68410e+04      2.25e-05
## polygon 58         4 9.45963e+03      1.26e-05
## polygon 59        46 6.99702e+05      9.35e-04
## polygon 60        13 7.00873e+04      9.36e-05
## enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
##                      (53380 x 33890 units)
## Window area = 748741000 square units
## Fraction of frame area: 0.414

Combining private points and study area

privateSG_ppp = private_ppp_jit[sg_owin]

Plot

plot(privateSG_ppp)

summary(privateSG_ppp)

## Planar point pattern:  3206 points
## Average intensity 4.281853e-06 points per square unit
## 
## Coordinates are given to 3 decimal places
## i.e. rounded to the nearest multiple of 0.001 units
## 
## Window: polygonal boundary
## 60 separate polygons (no holes)
##             vertices        area relative.area
## polygon 1         38 1.56140e+04      2.09e-05
## polygon 2        735 4.69093e+06      6.27e-03
## polygon 3         49 1.66986e+04      2.23e-05
## polygon 4         76 3.12332e+05      4.17e-04
## polygon 5       5141 6.36179e+08      8.50e-01
## polygon 6         42 5.58317e+04      7.46e-05
## polygon 7         67 1.31354e+06      1.75e-03
## polygon 8         15 4.46420e+03      5.96e-06
## polygon 9         14 5.46674e+03      7.30e-06
## polygon 10        37 5.26194e+03      7.03e-06
## polygon 11        53 3.44003e+04      4.59e-05
## polygon 12        74 5.82234e+04      7.78e-05
## polygon 13        69 5.63134e+04      7.52e-05
## polygon 14       143 1.45139e+05      1.94e-04
## polygon 15       165 3.38736e+05      4.52e-04
## polygon 16       130 9.40465e+04      1.26e-04
## polygon 17        19 1.80977e+03      2.42e-06
## polygon 18        16 2.01046e+03      2.69e-06
## polygon 19        93 4.30642e+05      5.75e-04
## polygon 20        90 4.15092e+05      5.54e-04
## polygon 21       721 1.92795e+06      2.57e-03
## polygon 22       330 1.11896e+06      1.49e-03
## polygon 23       115 9.28394e+05      1.24e-03
## polygon 24        37 1.01705e+04      1.36e-05
## polygon 25        25 1.66227e+04      2.22e-05
## polygon 26        10 2.14507e+03      2.86e-06
## polygon 27       190 2.02489e+05      2.70e-04
## polygon 28       175 9.25904e+05      1.24e-03
## polygon 29      1993 9.99217e+06      1.33e-02
## polygon 30        38 2.42492e+04      3.24e-05
## polygon 31        24 6.35239e+03      8.48e-06
## polygon 32        53 6.35791e+05      8.49e-04
## polygon 33        41 1.60161e+04      2.14e-05
## polygon 34        22 2.54368e+03      3.40e-06
## polygon 35        30 1.08382e+04      1.45e-05
## polygon 36       327 2.16921e+06      2.90e-03
## polygon 37       111 6.62927e+05      8.85e-04
## polygon 38        90 1.15991e+05      1.55e-04
## polygon 39        98 6.26829e+04      8.37e-05
## polygon 40       415 3.25384e+06      4.35e-03
## polygon 41       222 1.51142e+06      2.02e-03
## polygon 42       107 6.33039e+05      8.45e-04
## polygon 43         7 2.48299e+03      3.32e-06
## polygon 44        17 3.28303e+04      4.38e-05
## polygon 45        26 8.34758e+03      1.11e-05
## polygon 46       177 4.67446e+05      6.24e-04
## polygon 47        16 3.19460e+03      4.27e-06
## polygon 48        15 4.87296e+03      6.51e-06
## polygon 49        66 1.61841e+04      2.16e-05
## polygon 50       149 5.63430e+06      7.53e-03
## polygon 51       609 2.62570e+07      3.51e-02
## polygon 52         8 7.82256e+03      1.04e-05
## polygon 53       976 2.33447e+07      3.12e-02
## polygon 54        55 8.25379e+04      1.10e-04
## polygon 55       976 2.33447e+07      3.12e-02
## polygon 56        61 3.33449e+05      4.45e-04
## polygon 57         6 1.68410e+04      2.25e-05
## polygon 58         4 9.45963e+03      1.26e-05
## polygon 59        46 6.99702e+05      9.35e-04
## polygon 60        13 7.00873e+04      9.36e-05
## enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
##                      (53380 x 33890 units)
## Window area = 748741000 square units
## Fraction of frame area: 0.414

Visualise ppp object by the density of points using a gaussian

(normal) kernel with a 1000m standard deviation (sigma)

plot(density(private_ppp, sigma=1000))

Visualising ppp object by contour of point density

contour(density(private_ppp,1000), axes=F)

The two graphs above show the density of the private_ppp list, which focus mainly on the central South region, which is mainly where the significant clustering of private Airbnb room types are.

SHARED

shared <- listings %>% 
                filter(room_type == 'Shared room')

Check projection

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

crs(mpsz)

## 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

coordinates(shared)=c("longitude","latitude")
proj4string(shared) <- CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs")

shared <- spTransform(shared,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 "))

The graph below shows the distribution of Airbnb shared room types across the Singapore map, and we can see significant clustering mainly at the Central area.

plot(sg, border="lightgrey")
plot(sg, add=TRUE)
plot(shared, add=TRUE )

tmap_mode('view')

## tmap mode set to interactive viewing

This graph shows the location of the different private room types across Singapore, with openstreetmap of Singapore as background. It gives the same results as the above graph, with clustering mainly in the Central area. (such as BoonKeng, Bendemeer, Little India, Beach Road)

tm_shape(shared)+
  tm_dots()

Plotting an interactive map to show the various Shared Airbnb room types across Singapore

sharedroom <- listings %>% 
               filter(room_type == "Shared room" )

Pic <- makeIcon(iconUrl = "images (1).png", 
                 iconWidth = 100*0.35,
                 iconHeight = 100*0.35) 

 map <- leaflet()
      map <- addTiles(map) 
      
      map <- addMarkers(map,
                        lng = sharedroom$longitude,
                        lat = sharedroom$latitude,
                        popup = sharedroom$name,
                        clusterOptions = markerClusterOptions(), 
                        icon = Pic)
map

tmap_mode('plot')

## tmap mode set to plotting

Examine SpatialPointsDataFrame

shared

## class       : SpatialPointsDataFrame 
## features    : 272 
## extent      : 13607.1, 43401.32, 28185.04, 48252.18  (xmin, xmax, ymin, ymax)
## 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 
## variables   : 14
## names       :       id,                                               name,   host_id, host_name, neighbourhood_group, neighbourhood,   room_type, price, minimum_nights, number_of_reviews, last_review, reviews_per_month, calculated_host_listings_count, availability_365 
## min values  :   719944, (2 mins to MRT) Single Mixed Dorm A with Breakfast,    581033,    天一,      Central Region,    Ang Mo Kio, Shared room,    14,              1,                 0,            ,              0.01,                              1,                0 
## max values  : 42636866,              Your Private Pod Outside The City (2), 339664848,   Zi Ying,         West Region,     Woodlands, Shared room,  3770,            240,               150,  2020-03-18,                 4,                            116,              365

Converting the spatial point data frame into generic sp format (so as to be able to convert into ppp)

shared_sp <- as(shared, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")

The plotting of sp format of private Airbnb room types give the same readings as above

plot(shared_sp)

tmap_mode("view")

## tmap mode set to interactive viewing

This graph shows the location of the different shared room types across Singapore, using the sp format of data, with openstreetmap of Singapore as background. It gives the same results as the above graph, with clustering mainly in the Central area.

tm_shape(shared)+
tm_bubbles(col = "blue",
           size = 1,
           border.col = "black",
           border.lwd = 1)

tmap_mode("plot")

## tmap mode set to plotting

shared_sp

## class       : SpatialPoints 
## features    : 272 
## extent      : 13607.1, 43401.32, 28185.04, 48252.18  (xmin, xmax, ymin, ymax)
## 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

Converting the generic sp format into spatstat’s ppp format

shared_ppp <- as(shared_sp, "ppp")
shared_ppp

## Planar point pattern: 272 points
## window: rectangle = [13607.1, 43401.32] x [28185.04, 48252.18] units

This ppp plot of shared Airbnb room types in Singapore shows significant clustering in the central-south area

plot(shared_ppp)

summary(shared_ppp)

## Planar point pattern:  272 points
## Average intensity 4.549374e-07 points per square unit
## 
## *Pattern contains duplicated points*
## 
## Coordinates are given to 3 decimal places
## i.e. rounded to the nearest multiple of 0.001 units
## 
## Window: rectangle = [13607.1, 43401.32] x [28185.04, 48252.18] units
##                     (29790 x 20070 units)
## Window area = 597885000 square units

Handling duplicated points

any(duplicated(shared_ppp))

## [1] TRUE

Count number of coincidence point

multiplicity(shared_ppp)

##   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20 
##   1   3   1   1   1   1   1   1   1   1   1   1   1   1   1   1   3   1   1   1 
##  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   3   1   1   1 
##  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
##  61  62  63  64  65  66  67  68  69  70  71  72  73  74  75  76  77  78  79  80 
##   3   1   1   1   1   1   1  10  10  10  10  10  10  10  10  10  10   1   1   1 
##  81  82  83  84  85  86  87  88  89  90  91  92  93  94  95  96  97  98  99 100 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   3   1   1   1   1   1   1 
## 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 
##   1   3   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 261 262 263 264 265 266 267 268 269 270 271 272 
##   1   1   1   1   1   1   1   1   1   1   1   1

Total number of duplicates

sum(multiplicity(shared_ppp) >1)

## [1] 16

tmap_mode("view")

## tmap mode set to interactive viewing

To view locations of duplicate points

tm_shape(shared) +
  tm_dots(alpha=0.4, size=0.05)

tmap_mode("plot")

## tmap mode set to plotting

To solve this problem, use jittering

There are no more overlapping of circumference

shared_ppp_jit <- rjitter(shared_ppp, retry=TRUE, nsim=1, drop=TRUE)
plot(shared_ppp_jit)

Creating owin

sg_owin <- as(sg_sp, "owin")

plot(sg_owin)

summary(sg_owin)

## Window: polygonal boundary
## 60 separate polygons (no holes)
##             vertices        area relative.area
## polygon 1         38 1.56140e+04      2.09e-05
## polygon 2        735 4.69093e+06      6.27e-03
## polygon 3         49 1.66986e+04      2.23e-05
## polygon 4         76 3.12332e+05      4.17e-04
## polygon 5       5141 6.36179e+08      8.50e-01
## polygon 6         42 5.58317e+04      7.46e-05
## polygon 7         67 1.31354e+06      1.75e-03
## polygon 8         15 4.46420e+03      5.96e-06
## polygon 9         14 5.46674e+03      7.30e-06
## polygon 10        37 5.26194e+03      7.03e-06
## polygon 11        53 3.44003e+04      4.59e-05
## polygon 12        74 5.82234e+04      7.78e-05
## polygon 13        69 5.63134e+04      7.52e-05
## polygon 14       143 1.45139e+05      1.94e-04
## polygon 15       165 3.38736e+05      4.52e-04
## polygon 16       130 9.40465e+04      1.26e-04
## polygon 17        19 1.80977e+03      2.42e-06
## polygon 18        16 2.01046e+03      2.69e-06
## polygon 19        93 4.30642e+05      5.75e-04
## polygon 20        90 4.15092e+05      5.54e-04
## polygon 21       721 1.92795e+06      2.57e-03
## polygon 22       330 1.11896e+06      1.49e-03
## polygon 23       115 9.28394e+05      1.24e-03
## polygon 24        37 1.01705e+04      1.36e-05
## polygon 25        25 1.66227e+04      2.22e-05
## polygon 26        10 2.14507e+03      2.86e-06
## polygon 27       190 2.02489e+05      2.70e-04
## polygon 28       175 9.25904e+05      1.24e-03
## polygon 29      1993 9.99217e+06      1.33e-02
## polygon 30        38 2.42492e+04      3.24e-05
## polygon 31        24 6.35239e+03      8.48e-06
## polygon 32        53 6.35791e+05      8.49e-04
## polygon 33        41 1.60161e+04      2.14e-05
## polygon 34        22 2.54368e+03      3.40e-06
## polygon 35        30 1.08382e+04      1.45e-05
## polygon 36       327 2.16921e+06      2.90e-03
## polygon 37       111 6.62927e+05      8.85e-04
## polygon 38        90 1.15991e+05      1.55e-04
## polygon 39        98 6.26829e+04      8.37e-05
## polygon 40       415 3.25384e+06      4.35e-03
## polygon 41       222 1.51142e+06      2.02e-03
## polygon 42       107 6.33039e+05      8.45e-04
## polygon 43         7 2.48299e+03      3.32e-06
## polygon 44        17 3.28303e+04      4.38e-05
## polygon 45        26 8.34758e+03      1.11e-05
## polygon 46       177 4.67446e+05      6.24e-04
## polygon 47        16 3.19460e+03      4.27e-06
## polygon 48        15 4.87296e+03      6.51e-06
## polygon 49        66 1.61841e+04      2.16e-05
## polygon 50       149 5.63430e+06      7.53e-03
## polygon 51       609 2.62570e+07      3.51e-02
## polygon 52         8 7.82256e+03      1.04e-05
## polygon 53       976 2.33447e+07      3.12e-02
## polygon 54        55 8.25379e+04      1.10e-04
## polygon 55       976 2.33447e+07      3.12e-02
## polygon 56        61 3.33449e+05      4.45e-04
## polygon 57         6 1.68410e+04      2.25e-05
## polygon 58         4 9.45963e+03      1.26e-05
## polygon 59        46 6.99702e+05      9.35e-04
## polygon 60        13 7.00873e+04      9.36e-05
## enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
##                      (53380 x 33890 units)
## Window area = 748741000 square units
## Fraction of frame area: 0.414

Combining shared points and study area

sharedSG_ppp = shared_ppp_jit[sg_owin]

Plot

plot(sharedSG_ppp)

summary(sharedSG_ppp)

## Planar point pattern:  272 points
## Average intensity 3.632764e-07 points per square unit
## 
## Coordinates are given to 3 decimal places
## i.e. rounded to the nearest multiple of 0.001 units
## 
## Window: polygonal boundary
## 60 separate polygons (no holes)
##             vertices        area relative.area
## polygon 1         38 1.56140e+04      2.09e-05
## polygon 2        735 4.69093e+06      6.27e-03
## polygon 3         49 1.66986e+04      2.23e-05
## polygon 4         76 3.12332e+05      4.17e-04
## polygon 5       5141 6.36179e+08      8.50e-01
## polygon 6         42 5.58317e+04      7.46e-05
## polygon 7         67 1.31354e+06      1.75e-03
## polygon 8         15 4.46420e+03      5.96e-06
## polygon 9         14 5.46674e+03      7.30e-06
## polygon 10        37 5.26194e+03      7.03e-06
## polygon 11        53 3.44003e+04      4.59e-05
## polygon 12        74 5.82234e+04      7.78e-05
## polygon 13        69 5.63134e+04      7.52e-05
## polygon 14       143 1.45139e+05      1.94e-04
## polygon 15       165 3.38736e+05      4.52e-04
## polygon 16       130 9.40465e+04      1.26e-04
## polygon 17        19 1.80977e+03      2.42e-06
## polygon 18        16 2.01046e+03      2.69e-06
## polygon 19        93 4.30642e+05      5.75e-04
## polygon 20        90 4.15092e+05      5.54e-04
## polygon 21       721 1.92795e+06      2.57e-03
## polygon 22       330 1.11896e+06      1.49e-03
## polygon 23       115 9.28394e+05      1.24e-03
## polygon 24        37 1.01705e+04      1.36e-05
## polygon 25        25 1.66227e+04      2.22e-05
## polygon 26        10 2.14507e+03      2.86e-06
## polygon 27       190 2.02489e+05      2.70e-04
## polygon 28       175 9.25904e+05      1.24e-03
## polygon 29      1993 9.99217e+06      1.33e-02
## polygon 30        38 2.42492e+04      3.24e-05
## polygon 31        24 6.35239e+03      8.48e-06
## polygon 32        53 6.35791e+05      8.49e-04
## polygon 33        41 1.60161e+04      2.14e-05
## polygon 34        22 2.54368e+03      3.40e-06
## polygon 35        30 1.08382e+04      1.45e-05
## polygon 36       327 2.16921e+06      2.90e-03
## polygon 37       111 6.62927e+05      8.85e-04
## polygon 38        90 1.15991e+05      1.55e-04
## polygon 39        98 6.26829e+04      8.37e-05
## polygon 40       415 3.25384e+06      4.35e-03
## polygon 41       222 1.51142e+06      2.02e-03
## polygon 42       107 6.33039e+05      8.45e-04
## polygon 43         7 2.48299e+03      3.32e-06
## polygon 44        17 3.28303e+04      4.38e-05
## polygon 45        26 8.34758e+03      1.11e-05
## polygon 46       177 4.67446e+05      6.24e-04
## polygon 47        16 3.19460e+03      4.27e-06
## polygon 48        15 4.87296e+03      6.51e-06
## polygon 49        66 1.61841e+04      2.16e-05
## polygon 50       149 5.63430e+06      7.53e-03
## polygon 51       609 2.62570e+07      3.51e-02
## polygon 52         8 7.82256e+03      1.04e-05
## polygon 53       976 2.33447e+07      3.12e-02
## polygon 54        55 8.25379e+04      1.10e-04
## polygon 55       976 2.33447e+07      3.12e-02
## polygon 56        61 3.33449e+05      4.45e-04
## polygon 57         6 1.68410e+04      2.25e-05
## polygon 58         4 9.45963e+03      1.26e-05
## polygon 59        46 6.99702e+05      9.35e-04
## polygon 60        13 7.00873e+04      9.36e-05
## enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
##                      (53380 x 33890 units)
## Window area = 748741000 square units
## Fraction of frame area: 0.414

Visualise ppp object by the density of points using a gaussian

(normal) kernel with a 1000m standard deviation (sigma)

plot(density(shared_ppp, sigma=1000))

Visualising ppp object by contour of point density

contour(density(shared_ppp,1000), axes=F)

The two graphs above show the density of the shared_ppp list, which focus mainly on the central South region, which is mainly where the significant clustering of shared Airbnb room types are.

ENTIRE HOME / APARTMENT

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

Check projection

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

crs(mpsz)

## 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

coordinates(apt)=c("longitude","latitude")
proj4string(apt) <- CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs")

apt <- spTransform(apt,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 "))

The graph below shows the distribution of Airbnb entire home / apartment room types across the Singapore map, and we can see very significant clustering at the Central area, with many plots plotted.

plot(sg, border="lightgrey")
plot(sg, add=TRUE)
plot(apt, add=TRUE )

tmap_mode('view')

## tmap mode set to interactive viewing

This graph shows the location of the different entire home / apartment room types across Singapore, with openstreetmap of Singapore as background. It gives the same results as the above graph, with clustering mainly in the Central area.

tm_shape(apt)+
  tm_dots()

Plotting an interactive map to show the various Entire home / Apartment Airbnb room types across Singapore

aptroom <- listings %>% 
               filter(room_type == "Entire home/apt" )

Pic <- makeIcon(iconUrl = "images (1).png", 
                 iconWidth = 100*0.35,
                 iconHeight = 100*0.35) 

 map <- leaflet()
      map <- addTiles(map) 
      
      map <- addMarkers(map,
                        lng = aptroom$longitude,
                        lat = aptroom$latitude,
                        popup = aptroom$name,
                        clusterOptions = markerClusterOptions(), 
                        icon = Pic)
map

tmap_mode('plot')

## tmap mode set to plotting

Examine SpatialPointsDataFrame

apt

## class       : SpatialPointsDataFrame 
## features    : 3728 
## extent      : 7215.566, 42932.86, 25166.35, 48181.41  (xmin, xmax, ymin, ymax)
## 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 
## variables   : 14
## names       :       id,                    name,   host_id, host_name, neighbourhood_group, neighbourhood,       room_type, price, minimum_nights, number_of_reviews, last_review, reviews_per_month, calculated_host_listings_count, availability_365 
## min values  :   604966,    "Studio" @Marina Bay,     23666,          ,      Central Region,    Ang Mo Kio, Entire home/apt,    14,              1,                 0,            ,              0.01,                              1,                0 
## max values  : 42972584, Your Place at Owen Road, 341361215,     Zsolt,         West Region,     Woodlands, Entire home/apt,  9999,            700,               367,  2020-03-20,              9.57,                            342,              365

Converting the spatial point data frame into generic sp format (so as to be able to convert into ppp)

apt_sp <- as(apt, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")

The plotting of sp format of entire home / apartment Airbnb room types give the same readings as above

plot(apt_sp)

tmap_mode("view")

## tmap mode set to interactive viewing

This graph shows the location of the different entire home / apartment room types across Singapore, using the sp format of data, with openstreetmap of Singapore as background. It gives the same results as the above graph, with clustering mainly in the Central area.

tm_shape(apt)+
tm_bubbles(col = "blue",
           size = 1,
           border.col = "black",
           border.lwd = 1)

tmap_mode("plot")

## tmap mode set to plotting

apt_sp

## class       : SpatialPoints 
## features    : 3728 
## extent      : 7215.566, 42932.86, 25166.35, 48181.41  (xmin, xmax, ymin, ymax)
## 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

Converting the generic sp format into spatstat’s ppp format

apt_ppp <- as(apt_sp, "ppp")
apt_ppp

## Planar point pattern: 3728 points
## window: rectangle = [7215.57, 42932.86] x [25166.35, 48181.41] units

This ppp plot of entire home / apartment room types in Singapore shows significant clustering in the central area

plot(apt_ppp)

summary(apt_ppp)

## Planar point pattern:  3728 points
## Average intensity 4.535082e-06 points per square unit
## 
## *Pattern contains duplicated points*
## 
## Coordinates are given to 3 decimal places
## i.e. rounded to the nearest multiple of 0.001 units
## 
## Window: rectangle = [7215.57, 42932.86] x [25166.35, 48181.41] units
##                     (35720 x 23020 units)
## Window area = 822036000 square units

Handling duplicated points

any(duplicated(apt_ppp))

## [1] TRUE

Count number of coincidence point

multiplicity(apt_ppp)

##    1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16 
##    1    1    1    1    1    1    1    2    1    1    1    1    1    1    1    1 
##   17   18   19   20   21   22   23   24   25   26   27   28   29   30   31   32 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   33   34   35   36   37   38   39   40   41   42   43   44   45   46   47   48 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   49   50   51   52   53   54   55   56   57   58   59   60   61   62   63   64 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   65   66   67   68   69   70   71   72   73   74   75   76   77   78   79   80 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    2    1 
##   81   82   83   84   85   86   87   88   89   90   91   92   93   94   95   96 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##   97   98   99  100  101  102  103  104  105  106  107  108  109  110  111  112 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  113  114  115  116  117  118  119  120  121  122  123  124  125  126  127  128 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  129  130  131  132  133  134  135  136  137  138  139  140  141  142  143  144 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
##  145  146  147  148  149  150  151  152  153  154  155  156  157  158  159  160 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    5    5    1    5    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    5    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
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##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2801 2802 2803 2804 2805 2806 2807 2808 2809 2810 2811 2812 2813 2814 2815 2816 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2817 2818 2819 2820 2821 2822 2823 2824 2825 2826 2827 2828 2829 2830 2831 2832 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2833 2834 2835 2836 2837 2838 2839 2840 2841 2842 2843 2844 2845 2846 2847 2848 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2849 2850 2851 2852 2853 2854 2855 2856 2857 2858 2859 2860 2861 2862 2863 2864 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2865 2866 2867 2868 2869 2870 2871 2872 2873 2874 2875 2876 2877 2878 2879 2880 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2881 2882 2883 2884 2885 2886 2887 2888 2889 2890 2891 2892 2893 2894 2895 2896 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2897 2898 2899 2900 2901 2902 2903 2904 2905 2906 2907 2908 2909 2910 2911 2912 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2913 2914 2915 2916 2917 2918 2919 2920 2921 2922 2923 2924 2925 2926 2927 2928 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2929 2930 2931 2932 2933 2934 2935 2936 2937 2938 2939 2940 2941 2942 2943 2944 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2945 2946 2947 2948 2949 2950 2951 2952 2953 2954 2955 2956 2957 2958 2959 2960 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2961 2962 2963 2964 2965 2966 2967 2968 2969 2970 2971 2972 2973 2974 2975 2976 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2977 2978 2979 2980 2981 2982 2983 2984 2985 2986 2987 2988 2989 2990 2991 2992 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 2993 2994 2995 2996 2997 2998 2999 3000 3001 3002 3003 3004 3005 3006 3007 3008 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3009 3010 3011 3012 3013 3014 3015 3016 3017 3018 3019 3020 3021 3022 3023 3024 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3025 3026 3027 3028 3029 3030 3031 3032 3033 3034 3035 3036 3037 3038 3039 3040 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3041 3042 3043 3044 3045 3046 3047 3048 3049 3050 3051 3052 3053 3054 3055 3056 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3057 3058 3059 3060 3061 3062 3063 3064 3065 3066 3067 3068 3069 3070 3071 3072 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3073 3074 3075 3076 3077 3078 3079 3080 3081 3082 3083 3084 3085 3086 3087 3088 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3089 3090 3091 3092 3093 3094 3095 3096 3097 3098 3099 3100 3101 3102 3103 3104 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3105 3106 3107 3108 3109 3110 3111 3112 3113 3114 3115 3116 3117 3118 3119 3120 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3121 3122 3123 3124 3125 3126 3127 3128 3129 3130 3131 3132 3133 3134 3135 3136 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3137 3138 3139 3140 3141 3142 3143 3144 3145 3146 3147 3148 3149 3150 3151 3152 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3153 3154 3155 3156 3157 3158 3159 3160 3161 3162 3163 3164 3165 3166 3167 3168 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3169 3170 3171 3172 3173 3174 3175 3176 3177 3178 3179 3180 3181 3182 3183 3184 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3185 3186 3187 3188 3189 3190 3191 3192 3193 3194 3195 3196 3197 3198 3199 3200 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 3214 3215 3216 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3217 3218 3219 3220 3221 3222 3223 3224 3225 3226 3227 3228 3229 3230 3231 3232 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3233 3234 3235 3236 3237 3238 3239 3240 3241 3242 3243 3244 3245 3246 3247 3248 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3249 3250 3251 3252 3253 3254 3255 3256 3257 3258 3259 3260 3261 3262 3263 3264 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3265 3266 3267 3268 3269 3270 3271 3272 3273 3274 3275 3276 3277 3278 3279 3280 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3281 3282 3283 3284 3285 3286 3287 3288 3289 3290 3291 3292 3293 3294 3295 3296 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3297 3298 3299 3300 3301 3302 3303 3304 3305 3306 3307 3308 3309 3310 3311 3312 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3313 3314 3315 3316 3317 3318 3319 3320 3321 3322 3323 3324 3325 3326 3327 3328 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3329 3330 3331 3332 3333 3334 3335 3336 3337 3338 3339 3340 3341 3342 3343 3344 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3345 3346 3347 3348 3349 3350 3351 3352 3353 3354 3355 3356 3357 3358 3359 3360 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3361 3362 3363 3364 3365 3366 3367 3368 3369 3370 3371 3372 3373 3374 3375 3376 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3377 3378 3379 3380 3381 3382 3383 3384 3385 3386 3387 3388 3389 3390 3391 3392 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3393 3394 3395 3396 3397 3398 3399 3400 3401 3402 3403 3404 3405 3406 3407 3408 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3409 3410 3411 3412 3413 3414 3415 3416 3417 3418 3419 3420 3421 3422 3423 3424 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3425 3426 3427 3428 3429 3430 3431 3432 3433 3434 3435 3436 3437 3438 3439 3440 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3441 3442 3443 3444 3445 3446 3447 3448 3449 3450 3451 3452 3453 3454 3455 3456 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3457 3458 3459 3460 3461 3462 3463 3464 3465 3466 3467 3468 3469 3470 3471 3472 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3473 3474 3475 3476 3477 3478 3479 3480 3481 3482 3483 3484 3485 3486 3487 3488 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3489 3490 3491 3492 3493 3494 3495 3496 3497 3498 3499 3500 3501 3502 3503 3504 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3505 3506 3507 3508 3509 3510 3511 3512 3513 3514 3515 3516 3517 3518 3519 3520 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3521 3522 3523 3524 3525 3526 3527 3528 3529 3530 3531 3532 3533 3534 3535 3536 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3537 3538 3539 3540 3541 3542 3543 3544 3545 3546 3547 3548 3549 3550 3551 3552 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3553 3554 3555 3556 3557 3558 3559 3560 3561 3562 3563 3564 3565 3566 3567 3568 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3569 3570 3571 3572 3573 3574 3575 3576 3577 3578 3579 3580 3581 3582 3583 3584 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3585 3586 3587 3588 3589 3590 3591 3592 3593 3594 3595 3596 3597 3598 3599 3600 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3601 3602 3603 3604 3605 3606 3607 3608 3609 3610 3611 3612 3613 3614 3615 3616 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3617 3618 3619 3620 3621 3622 3623 3624 3625 3626 3627 3628 3629 3630 3631 3632 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3633 3634 3635 3636 3637 3638 3639 3640 3641 3642 3643 3644 3645 3646 3647 3648 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3649 3650 3651 3652 3653 3654 3655 3656 3657 3658 3659 3660 3661 3662 3663 3664 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3665 3666 3667 3668 3669 3670 3671 3672 3673 3674 3675 3676 3677 3678 3679 3680 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3681 3682 3683 3684 3685 3686 3687 3688 3689 3690 3691 3692 3693 3694 3695 3696 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3697 3698 3699 3700 3701 3702 3703 3704 3705 3706 3707 3708 3709 3710 3711 3712 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
## 3713 3714 3715 3716 3717 3718 3719 3720 3721 3722 3723 3724 3725 3726 3727 3728 
##    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1

Total number of duplicates

sum(multiplicity(apt_ppp) >1)

## [1] 35

tmap_mode("plot")

## tmap mode set to plotting

To view locations of duplicate points

tm_shape(apt) +
  tm_dots(alpha=0.4, size=0.05)

tmap_mode("plot")

## tmap mode set to plotting

To solve this problem, use jittering

There are no more overlapping of circumference

apt_ppp_jit <- rjitter(apt_ppp, retry=TRUE, nsim=1, drop=TRUE)
plot(apt_ppp_jit)

Creating owin

sg_owin <- as(sg_sp, "owin")

plot(sg_owin)

summary(sg_owin)

## Window: polygonal boundary
## 60 separate polygons (no holes)
##             vertices        area relative.area
## polygon 1         38 1.56140e+04      2.09e-05
## polygon 2        735 4.69093e+06      6.27e-03
## polygon 3         49 1.66986e+04      2.23e-05
## polygon 4         76 3.12332e+05      4.17e-04
## polygon 5       5141 6.36179e+08      8.50e-01
## polygon 6         42 5.58317e+04      7.46e-05
## polygon 7         67 1.31354e+06      1.75e-03
## polygon 8         15 4.46420e+03      5.96e-06
## polygon 9         14 5.46674e+03      7.30e-06
## polygon 10        37 5.26194e+03      7.03e-06
## polygon 11        53 3.44003e+04      4.59e-05
## polygon 12        74 5.82234e+04      7.78e-05
## polygon 13        69 5.63134e+04      7.52e-05
## polygon 14       143 1.45139e+05      1.94e-04
## polygon 15       165 3.38736e+05      4.52e-04
## polygon 16       130 9.40465e+04      1.26e-04
## polygon 17        19 1.80977e+03      2.42e-06
## polygon 18        16 2.01046e+03      2.69e-06
## polygon 19        93 4.30642e+05      5.75e-04
## polygon 20        90 4.15092e+05      5.54e-04
## polygon 21       721 1.92795e+06      2.57e-03
## polygon 22       330 1.11896e+06      1.49e-03
## polygon 23       115 9.28394e+05      1.24e-03
## polygon 24        37 1.01705e+04      1.36e-05
## polygon 25        25 1.66227e+04      2.22e-05
## polygon 26        10 2.14507e+03      2.86e-06
## polygon 27       190 2.02489e+05      2.70e-04
## polygon 28       175 9.25904e+05      1.24e-03
## polygon 29      1993 9.99217e+06      1.33e-02
## polygon 30        38 2.42492e+04      3.24e-05
## polygon 31        24 6.35239e+03      8.48e-06
## polygon 32        53 6.35791e+05      8.49e-04
## polygon 33        41 1.60161e+04      2.14e-05
## polygon 34        22 2.54368e+03      3.40e-06
## polygon 35        30 1.08382e+04      1.45e-05
## polygon 36       327 2.16921e+06      2.90e-03
## polygon 37       111 6.62927e+05      8.85e-04
## polygon 38        90 1.15991e+05      1.55e-04
## polygon 39        98 6.26829e+04      8.37e-05
## polygon 40       415 3.25384e+06      4.35e-03
## polygon 41       222 1.51142e+06      2.02e-03
## polygon 42       107 6.33039e+05      8.45e-04
## polygon 43         7 2.48299e+03      3.32e-06
## polygon 44        17 3.28303e+04      4.38e-05
## polygon 45        26 8.34758e+03      1.11e-05
## polygon 46       177 4.67446e+05      6.24e-04
## polygon 47        16 3.19460e+03      4.27e-06
## polygon 48        15 4.87296e+03      6.51e-06
## polygon 49        66 1.61841e+04      2.16e-05
## polygon 50       149 5.63430e+06      7.53e-03
## polygon 51       609 2.62570e+07      3.51e-02
## polygon 52         8 7.82256e+03      1.04e-05
## polygon 53       976 2.33447e+07      3.12e-02
## polygon 54        55 8.25379e+04      1.10e-04
## polygon 55       976 2.33447e+07      3.12e-02
## polygon 56        61 3.33449e+05      4.45e-04
## polygon 57         6 1.68410e+04      2.25e-05
## polygon 58         4 9.45963e+03      1.26e-05
## polygon 59        46 6.99702e+05      9.35e-04
## polygon 60        13 7.00873e+04      9.36e-05
## enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
##                      (53380 x 33890 units)
## Window area = 748741000 square units
## Fraction of frame area: 0.414

Combining entire home / apartment points and study area

aptSG_ppp = apt_ppp_jit[sg_owin]

Plot

plot(aptSG_ppp)

summary(aptSG_ppp)

## Planar point pattern:  3728 points
## Average intensity 4.979023e-06 points per square unit
## 
## Coordinates are given to 3 decimal places
## i.e. rounded to the nearest multiple of 0.001 units
## 
## Window: polygonal boundary
## 60 separate polygons (no holes)
##             vertices        area relative.area
## polygon 1         38 1.56140e+04      2.09e-05
## polygon 2        735 4.69093e+06      6.27e-03
## polygon 3         49 1.66986e+04      2.23e-05
## polygon 4         76 3.12332e+05      4.17e-04
## polygon 5       5141 6.36179e+08      8.50e-01
## polygon 6         42 5.58317e+04      7.46e-05
## polygon 7         67 1.31354e+06      1.75e-03
## polygon 8         15 4.46420e+03      5.96e-06
## polygon 9         14 5.46674e+03      7.30e-06
## polygon 10        37 5.26194e+03      7.03e-06
## polygon 11        53 3.44003e+04      4.59e-05
## polygon 12        74 5.82234e+04      7.78e-05
## polygon 13        69 5.63134e+04      7.52e-05
## polygon 14       143 1.45139e+05      1.94e-04
## polygon 15       165 3.38736e+05      4.52e-04
## polygon 16       130 9.40465e+04      1.26e-04
## polygon 17        19 1.80977e+03      2.42e-06
## polygon 18        16 2.01046e+03      2.69e-06
## polygon 19        93 4.30642e+05      5.75e-04
## polygon 20        90 4.15092e+05      5.54e-04
## polygon 21       721 1.92795e+06      2.57e-03
## polygon 22       330 1.11896e+06      1.49e-03
## polygon 23       115 9.28394e+05      1.24e-03
## polygon 24        37 1.01705e+04      1.36e-05
## polygon 25        25 1.66227e+04      2.22e-05
## polygon 26        10 2.14507e+03      2.86e-06
## polygon 27       190 2.02489e+05      2.70e-04
## polygon 28       175 9.25904e+05      1.24e-03
## polygon 29      1993 9.99217e+06      1.33e-02
## polygon 30        38 2.42492e+04      3.24e-05
## polygon 31        24 6.35239e+03      8.48e-06
## polygon 32        53 6.35791e+05      8.49e-04
## polygon 33        41 1.60161e+04      2.14e-05
## polygon 34        22 2.54368e+03      3.40e-06
## polygon 35        30 1.08382e+04      1.45e-05
## polygon 36       327 2.16921e+06      2.90e-03
## polygon 37       111 6.62927e+05      8.85e-04
## polygon 38        90 1.15991e+05      1.55e-04
## polygon 39        98 6.26829e+04      8.37e-05
## polygon 40       415 3.25384e+06      4.35e-03
## polygon 41       222 1.51142e+06      2.02e-03
## polygon 42       107 6.33039e+05      8.45e-04
## polygon 43         7 2.48299e+03      3.32e-06
## polygon 44        17 3.28303e+04      4.38e-05
## polygon 45        26 8.34758e+03      1.11e-05
## polygon 46       177 4.67446e+05      6.24e-04
## polygon 47        16 3.19460e+03      4.27e-06
## polygon 48        15 4.87296e+03      6.51e-06
## polygon 49        66 1.61841e+04      2.16e-05
## polygon 50       149 5.63430e+06      7.53e-03
## polygon 51       609 2.62570e+07      3.51e-02
## polygon 52         8 7.82256e+03      1.04e-05
## polygon 53       976 2.33447e+07      3.12e-02
## polygon 54        55 8.25379e+04      1.10e-04
## polygon 55       976 2.33447e+07      3.12e-02
## polygon 56        61 3.33449e+05      4.45e-04
## polygon 57         6 1.68410e+04      2.25e-05
## polygon 58         4 9.45963e+03      1.26e-05
## polygon 59        46 6.99702e+05      9.35e-04
## polygon 60        13 7.00873e+04      9.36e-05
## enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
##                      (53380 x 33890 units)
## Window area = 748741000 square units
## Fraction of frame area: 0.414

Visualise ppp object by the density of points using a gaussian

(normal) kernel with a 1000m standard deviation (sigma)

plot(density(apt_ppp, sigma=1000))

Visualising ppp object by contour of point density

contour(density(apt_ppp,1000), axes=F)

The two graphs above show the density of the apt_ppp list, which focus mainly on the central South region, which is mainly where the significant clustering of entire home / apartment Airbnb room types are.

HOTEL

hotel <- listings %>% 
                filter(room_type == 'Hotel room')

Check projection

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

crs(mpsz)

## 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

coordinates(hotel)=c("longitude","latitude")
proj4string(hotel) <- CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs")

hotel <- spTransform(hotel,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 "))

The graph below shows the distribution of Airbnb hotel room types across the Singapore map, and we can see significant clustering at the Central area, with few points in other regions.

plot(sg, border="lightgrey")
plot(sg, add=TRUE)
plot(hotel, add=TRUE )

tmap_mode('view')

## tmap mode set to interactive viewing

This graph shows the location of the different hotel room types across Singapore, with openstreetmap of Singapore as background. It gives the same results as the above graph, with clustering mainly in the Central area.

tm_shape(hotel)+
  tm_dots()

Plotting an interactive map to show the various Hotel Airbnb room types across Singapore

 hotelroom <- listings %>% 
               filter(room_type == "Hotel room" )

Pic <- makeIcon(iconUrl = "images (1).png", 
                 iconWidth = 100*0.35,
                 iconHeight = 100*0.35) 

 map <- leaflet()
      map <- addTiles(map) 
      
      map <- addMarkers(map,
                        lng = hotelroom$longitude,
                        lat = hotelroom$latitude,
                        popup = hotelroom$name,
                        clusterOptions = markerClusterOptions(), 
                        icon = Pic)
map

tmap_mode('plot')

## tmap mode set to plotting

Examine SpatialPointsDataFrame

hotel

## class       : SpatialPointsDataFrame 
## features    : 507 
## extent      : 20126.35, 36915.62, 28442.68, 39865.12  (xmin, xmax, ymin, ymax)
## 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 
## variables   : 14
## names       :       id,                                               name,   host_id,           host_name, neighbourhood_group, neighbourhood,  room_type, price, minimum_nights, number_of_reviews, last_review, reviews_per_month, calculated_host_listings_count, availability_365 
## min values  :  1678754, (3 mins to MRT) Double Capsule + All Day Breakfast,    646629,               Aaron,      Central Region,         Bedok, Hotel room,    20,              1,                 0,            ,              0.03,                              1,                0 
## max values  : 38422421,  Work Out in the comfort of your room in Chinatown, 287240181, Your Community Host,         West Region,       Tanglin, Hotel room,  2500,             90,               206,  2020-03-19,             12.27,                            342,              365

Converting the spatial point data frame into generic sp format (so as to be able to convert into ppp)

hotel_sp <- as(hotel, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")

The plotting of sp format of hotel Airbnb room types gives the same readings as above

plot(hotel_sp)

tmap_mode("view")

## tmap mode set to interactive viewing

This graph shows the location of the different shared room types across Singapore, using the sp format of data, with openstreetmap of Singapore as background. It gives the same results as the above graph, with clustering mainly in the Central area.

tm_shape(hotel)+
tm_bubbles(col = "blue",
           size = 1,
           border.col = "black",
           border.lwd = 1)

tmap_mode("plot")

## tmap mode set to plotting

hotel_sp

## class       : SpatialPoints 
## features    : 507 
## extent      : 20126.35, 36915.62, 28442.68, 39865.12  (xmin, xmax, ymin, ymax)
## 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

Converting the generic sp format into spatstat’s ppp format

hotel_ppp <- as(hotel_sp, "ppp")
hotel_ppp

## Planar point pattern: 507 points
## window: rectangle = [20126.35, 36915.62] x [28442.68, 39865.12] units

This ppp plot of hotel Airbnb room types in Singapore shows significant clustering in the central-south area

plot(hotel_ppp)

summary(hotel_ppp)

## Planar point pattern:  507 points
## Average intensity 2.643733e-06 points per square unit
## 
## *Pattern contains duplicated points*
## 
## Coordinates are given to 3 decimal places
## i.e. rounded to the nearest multiple of 0.001 units
## 
## Window: rectangle = [20126.35, 36915.62] x [28442.68, 39865.12] units
##                     (16790 x 11420 units)
## Window area = 191774000 square units

Handling duplicated points

any(duplicated(hotel_ppp))

## [1] TRUE

Count number of coincidence point

multiplicity(hotel_ppp)

##   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20 
##   2   2   1   9   1   9   9   9   1   1   1   1   1   1   1   1   1   1   1   1 
##  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40 
##   1   1   1   1   1   1   1   1   1   1   1   1   9   9   9   9   1   1   1   1 
##  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60 
##   1   1   1   1   1   1   1   1   2   2   1   2   1   1   2   1   1   1   1   1 
##  61  62  63  64  65  66  67  68  69  70  71  72  73  74  75  76  77  78  79  80 
##   2   2   1   1   1   9   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
##  81  82  83  84  85  86  87  88  89  90  91  92  93  94  95  96  97  98  99 100 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   8   8   8   8   8   8   1 
## 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 
##   7   7   7   7   7   7   7   1   5   1   1   1   1   3   3   3   1   1   1   1 
## 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 
##   1   1   8   8   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 
##   1   1   1   1   1   1   1   5   1   5   1   1   1   1   1   1   1   1   1   1 
## 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 
##   1   1   1   1   1   1   1   1   1   1   1   1   5   1   1   1   1   1   1   1 
## 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 
##   1   1   1   1   1   1   1   5   1   1   1   1   1   1   1   1   1   1   1   1 
## 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 
##   1   1   1   1   1   1   1   1   1   1   1   2   1   1   1   1   1   1   1   2 
## 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 
##   1   1   4   4   4   4   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   3   3   1 
## 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 
##   1   3   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 
##   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1   1 
## 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 
##   1   1   1   1   1   1   7   7   7   7   7   7   1   7   1   1   1   1   1   1 
## 501 502 503 504 505 506 507 
##   1   3   3   1   3   1   1

Total number of duplicates

sum(multiplicity(hotel_ppp) >1)

## [1] 59

tmap_mode("view")

## tmap mode set to interactive viewing

To view locations of duplicate points

tm_shape(hotel) +
  tm_dots(alpha=0.4, size=0.05)

tmap_mode("plot")

## tmap mode set to plotting

To solve this problem, use jittering

There are no more overlapping of circumference

hotel_ppp_jit <- rjitter(hotel_ppp, retry=TRUE, nsim=1, drop=TRUE)
plot(hotel_ppp_jit)

Creating owin

sg_owin <- as(sg_sp, "owin")

plot(sg_owin)

summary(sg_owin)

## Window: polygonal boundary
## 60 separate polygons (no holes)
##             vertices        area relative.area
## polygon 1         38 1.56140e+04      2.09e-05
## polygon 2        735 4.69093e+06      6.27e-03
## polygon 3         49 1.66986e+04      2.23e-05
## polygon 4         76 3.12332e+05      4.17e-04
## polygon 5       5141 6.36179e+08      8.50e-01
## polygon 6         42 5.58317e+04      7.46e-05
## polygon 7         67 1.31354e+06      1.75e-03
## polygon 8         15 4.46420e+03      5.96e-06
## polygon 9         14 5.46674e+03      7.30e-06
## polygon 10        37 5.26194e+03      7.03e-06
## polygon 11        53 3.44003e+04      4.59e-05
## polygon 12        74 5.82234e+04      7.78e-05
## polygon 13        69 5.63134e+04      7.52e-05
## polygon 14       143 1.45139e+05      1.94e-04
## polygon 15       165 3.38736e+05      4.52e-04
## polygon 16       130 9.40465e+04      1.26e-04
## polygon 17        19 1.80977e+03      2.42e-06
## polygon 18        16 2.01046e+03      2.69e-06
## polygon 19        93 4.30642e+05      5.75e-04
## polygon 20        90 4.15092e+05      5.54e-04
## polygon 21       721 1.92795e+06      2.57e-03
## polygon 22       330 1.11896e+06      1.49e-03
## polygon 23       115 9.28394e+05      1.24e-03
## polygon 24        37 1.01705e+04      1.36e-05
## polygon 25        25 1.66227e+04      2.22e-05
## polygon 26        10 2.14507e+03      2.86e-06
## polygon 27       190 2.02489e+05      2.70e-04
## polygon 28       175 9.25904e+05      1.24e-03
## polygon 29      1993 9.99217e+06      1.33e-02
## polygon 30        38 2.42492e+04      3.24e-05
## polygon 31        24 6.35239e+03      8.48e-06
## polygon 32        53 6.35791e+05      8.49e-04
## polygon 33        41 1.60161e+04      2.14e-05
## polygon 34        22 2.54368e+03      3.40e-06
## polygon 35        30 1.08382e+04      1.45e-05
## polygon 36       327 2.16921e+06      2.90e-03
## polygon 37       111 6.62927e+05      8.85e-04
## polygon 38        90 1.15991e+05      1.55e-04
## polygon 39        98 6.26829e+04      8.37e-05
## polygon 40       415 3.25384e+06      4.35e-03
## polygon 41       222 1.51142e+06      2.02e-03
## polygon 42       107 6.33039e+05      8.45e-04
## polygon 43         7 2.48299e+03      3.32e-06
## polygon 44        17 3.28303e+04      4.38e-05
## polygon 45        26 8.34758e+03      1.11e-05
## polygon 46       177 4.67446e+05      6.24e-04
## polygon 47        16 3.19460e+03      4.27e-06
## polygon 48        15 4.87296e+03      6.51e-06
## polygon 49        66 1.61841e+04      2.16e-05
## polygon 50       149 5.63430e+06      7.53e-03
## polygon 51       609 2.62570e+07      3.51e-02
## polygon 52         8 7.82256e+03      1.04e-05
## polygon 53       976 2.33447e+07      3.12e-02
## polygon 54        55 8.25379e+04      1.10e-04
## polygon 55       976 2.33447e+07      3.12e-02
## polygon 56        61 3.33449e+05      4.45e-04
## polygon 57         6 1.68410e+04      2.25e-05
## polygon 58         4 9.45963e+03      1.26e-05
## polygon 59        46 6.99702e+05      9.35e-04
## polygon 60        13 7.00873e+04      9.36e-05
## enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
##                      (53380 x 33890 units)
## Window area = 748741000 square units
## Fraction of frame area: 0.414

Combining hotel points and study area

hotelSG_ppp = hotel_ppp_jit[sg_owin]

Plot

plot(hotelSG_ppp)

summary(hotelSG_ppp)

## Planar point pattern:  507 points
## Average intensity 6.771365e-07 points per square unit
## 
## Coordinates are given to 3 decimal places
## i.e. rounded to the nearest multiple of 0.001 units
## 
## Window: polygonal boundary
## 60 separate polygons (no holes)
##             vertices        area relative.area
## polygon 1         38 1.56140e+04      2.09e-05
## polygon 2        735 4.69093e+06      6.27e-03
## polygon 3         49 1.66986e+04      2.23e-05
## polygon 4         76 3.12332e+05      4.17e-04
## polygon 5       5141 6.36179e+08      8.50e-01
## polygon 6         42 5.58317e+04      7.46e-05
## polygon 7         67 1.31354e+06      1.75e-03
## polygon 8         15 4.46420e+03      5.96e-06
## polygon 9         14 5.46674e+03      7.30e-06
## polygon 10        37 5.26194e+03      7.03e-06
## polygon 11        53 3.44003e+04      4.59e-05
## polygon 12        74 5.82234e+04      7.78e-05
## polygon 13        69 5.63134e+04      7.52e-05
## polygon 14       143 1.45139e+05      1.94e-04
## polygon 15       165 3.38736e+05      4.52e-04
## polygon 16       130 9.40465e+04      1.26e-04
## polygon 17        19 1.80977e+03      2.42e-06
## polygon 18        16 2.01046e+03      2.69e-06
## polygon 19        93 4.30642e+05      5.75e-04
## polygon 20        90 4.15092e+05      5.54e-04
## polygon 21       721 1.92795e+06      2.57e-03
## polygon 22       330 1.11896e+06      1.49e-03
## polygon 23       115 9.28394e+05      1.24e-03
## polygon 24        37 1.01705e+04      1.36e-05
## polygon 25        25 1.66227e+04      2.22e-05
## polygon 26        10 2.14507e+03      2.86e-06
## polygon 27       190 2.02489e+05      2.70e-04
## polygon 28       175 9.25904e+05      1.24e-03
## polygon 29      1993 9.99217e+06      1.33e-02
## polygon 30        38 2.42492e+04      3.24e-05
## polygon 31        24 6.35239e+03      8.48e-06
## polygon 32        53 6.35791e+05      8.49e-04
## polygon 33        41 1.60161e+04      2.14e-05
## polygon 34        22 2.54368e+03      3.40e-06
## polygon 35        30 1.08382e+04      1.45e-05
## polygon 36       327 2.16921e+06      2.90e-03
## polygon 37       111 6.62927e+05      8.85e-04
## polygon 38        90 1.15991e+05      1.55e-04
## polygon 39        98 6.26829e+04      8.37e-05
## polygon 40       415 3.25384e+06      4.35e-03
## polygon 41       222 1.51142e+06      2.02e-03
## polygon 42       107 6.33039e+05      8.45e-04
## polygon 43         7 2.48299e+03      3.32e-06
## polygon 44        17 3.28303e+04      4.38e-05
## polygon 45        26 8.34758e+03      1.11e-05
## polygon 46       177 4.67446e+05      6.24e-04
## polygon 47        16 3.19460e+03      4.27e-06
## polygon 48        15 4.87296e+03      6.51e-06
## polygon 49        66 1.61841e+04      2.16e-05
## polygon 50       149 5.63430e+06      7.53e-03
## polygon 51       609 2.62570e+07      3.51e-02
## polygon 52         8 7.82256e+03      1.04e-05
## polygon 53       976 2.33447e+07      3.12e-02
## polygon 54        55 8.25379e+04      1.10e-04
## polygon 55       976 2.33447e+07      3.12e-02
## polygon 56        61 3.33449e+05      4.45e-04
## polygon 57         6 1.68410e+04      2.25e-05
## polygon 58         4 9.45963e+03      1.26e-05
## polygon 59        46 6.99702e+05      9.35e-04
## polygon 60        13 7.00873e+04      9.36e-05
## enclosing rectangle: [2663.93, 56047.79] x [16357.98, 50244.03] units
##                      (53380 x 33890 units)
## Window area = 748741000 square units
## Fraction of frame area: 0.414

Visualise ppp object by the density of points using a gaussian

(normal) kernel with a 1000m standard deviation (sigma)

plot(density(hotel_ppp, sigma=1000))

Visualising ppp object by contour of point density

contour(density(hotel_ppp,1000), axes=F)

The two graphs above show the density of the hotel_ppp list, which focus mainly on the central South region, which is mainly where the significant clustering of hotel Airbnb room types are.

Part 2

In this section, with reference to the spatial point patterns observed previously, we will attempt to formulate the null hypothesis and select the confidence level. From which, we will perform test using appropriate 1st order spatial point patterns analysis technique, before drawing statistical conclusions.

PRIVATE

Quadrat Analysis

Test hypotheses at the 95% confidence level,

H0: Distribution of private room types are conformed to complete complete spatial randomness (CSR). This means that distribution of private room types are random.

H1: Distribution of private room types are not CSR, hence, distribution are not random.

Chi squared test of CSR using quadrat counts

From the result, we observed that p-value < 2.2e-16 < 0.05, chi-squared statistic = 21954, which is large. Reject null hypothesis that the points are randomly distributed. Hence, we conclude that distribution of private Airbnb room types is not random, but instead, shows signs of clustering. This result is supported by the graphs that were plotted earlier, which showed clustering at different locations in Singapore.

qt <- quadrat.test(privateSG_ppp, 
                   nx = 20, ny = 15)

## Warning: Some expected counts are small; chi^2 approximation may be inaccurate

qt

## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  privateSG_ppp
## X2 = 22001, df = 184, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)

Conclusion

From this plot, we can affirm the conclusion that we previously had. The private room types in Airbnb are not randomly distributed, and there shows signs of clustering, especially in the Central-south region.

plot(privateSG_ppp)
plot(qt, add = TRUE, cex =.1)

Monte Carlo Test of CSR

same readings as before, pvalue = 0.002 < 0.05, chi-squared distribution large, reject null hypothesis. Clustering can be seen.

quadrat.test(privateSG_ppp,
             nx=20, ny=15,
             method="M",
             nsim=999)

## 
##  Conditional Monte Carlo test of CSR using quadrat counts
##  Test statistic: Pearson X2 statistic
## 
## data:  privateSG_ppp
## X2 = 22001, p-value = 0.002
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)

Next, we use the Nearest Neighbour Analysis to identify the direct distance from a point to its nearest neighbour.

The nearest neighbour analysis will also allow us to identify the expected distance, which is the average distance between neighbours in a hypothetical random distribution. (It tells us how dispersed or clustered the points are)

To test aggregation for a spatial point pattern, we have the following test hypothesis at the 95% significance level:

H0: Distribution of private room types are randomly distributed (CSR)

H1: Distribution of private room types are not randomly distributed (not CSR)

Testing spatial point patterns using Clark and Evans Test

Since the p-value = 0.02 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random

Additionally, since R = 0.37962 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(privateSG_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("two.sided"),
                nsim=99)

## Warning: point-in-polygon test had difficulty with 33 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 48 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 48 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 28 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 49 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 48 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 31 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 31 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 54 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 51 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 56 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 50 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 32 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 31 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 56 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 57 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 53 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 49 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 36 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 33 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 30 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 33 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 54 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 50 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 32 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 32 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 49 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 52 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 50 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 48 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 34 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 33 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 49 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 52 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 36 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 34 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 52 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 54 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 33 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 36 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 30 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 33 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 56 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 49 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 60 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 28 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 29 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 52 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 51 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 31 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 34 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 32 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 33 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 49 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 36 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 50 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 60 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 31 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 48 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 30 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 48 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 31 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 48 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 48 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 36 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 52 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 27 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 32 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 56 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 26 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 36 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 48 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 34 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 46 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 33 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 34 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 57 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 33 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 45 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 52 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 52 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 34 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 50 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 50 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 38 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 51 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 36 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 34 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 51 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 43 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 44 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 37 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 35 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 56 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 48 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 39 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 48 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 33 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 40 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 41 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
## or 1)

## 
##  Clark-Evans test
##  No edge correction
##  Monte Carlo test based on 99 simulations of CSR with fixed n
## 
## data:  privateSG_ppp
## R = 0.38083, p-value = 0.02
## alternative hypothesis: two-sided

SHARED

Quadrat Analysis

Test hypotheses at the 95% confidence level,

H0: Distribution of shared room types are conformed to complete complete spatial randomness (CSR). This means that distribution of shared room types are random.

H1: Distribution of shared room types are not CSR, hence, distribution are not random.

Chi squared test of CSR using quadrat counts

From the result, we observed that p-value < 2.2e-16 < 0.05, chi-squared statistic = 4553.9, which is large. Reject null hypothesis that the points are randomly distributed. Hence, we conclude that distribution of shared Airbnb room types is not random, but instead, shows signs of clustering. This result is supported by the graphs that were plotted earlier, which showed clustering at different locations in Singapore

qt <- quadrat.test(sharedSG_ppp, 
                   nx = 20, ny = 15)

## Warning: Some expected counts are small; chi^2 approximation may be inaccurate

qt

## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  sharedSG_ppp
## X2 = 4612.3, df = 184, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)

Conclusion

From this plot, we can affirm the conclusion that we previously had. The shared room types in Airbnb are not randomly distributed, and there shows signs of clustering, especially in the Central-south region.

plot(sharedSG_ppp)
plot(qt, add = TRUE, cex =.1)

Monte Carlo Test of CSR

same readings as before, pvalue = 0.002 < 0.05, chi-squared distribution large, reject null hypothesis. Clustering can be seen.

quadrat.test(sharedSG_ppp,
             nx=20, ny=15,
             method="M",
             nsim=999)

## 
##  Conditional Monte Carlo test of CSR using quadrat counts
##  Test statistic: Pearson X2 statistic
## 
## data:  sharedSG_ppp
## X2 = 4612.3, p-value = 0.002
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)

Next, we use the Nearest Neighbour Analysis to identify the direct distance from a point to its nearest neighbour.

The nearest neighbour analysis will also allow us to identify the expected distance, which is the average distance between neighbours in a hypothetical random distribution. (It tells us how dispersed or clustered the points are)

To test aggregation for a spatial point pattern, we have the following test hypothesis at the 95% significance level:

H0: Distribution of shared room types are randomly distributed (CSR)

H1: Distribution of shared room types are not randomly distributed (not CSR)

Testing spatial point patterns using Clark and Evans Test

p-value = 0.02 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random.

Additionally, since R = 0.35484 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(sharedSG_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("two.sided"),
                nsim=99)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 9 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 9 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 8 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 8 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 8 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 9 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 8 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 8 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 8 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 8 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 7 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 9 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
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## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 2 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 3 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 6 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 1 point (total score not 0 or
## 1)

## Warning: point-in-polygon test had difficulty with 5 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 4 points (total score not 0
## or 1)

## 
##  Clark-Evans test
##  No edge correction
##  Monte Carlo test based on 99 simulations of CSR with fixed n
## 
## data:  sharedSG_ppp
## R = 0.35076, p-value = 0.02
## alternative hypothesis: two-sided

ENTIRE HOME / APARTMENT

Quadrat Analysis

Test hypotheses at the 95% confidence level,

H0: Distribution of entire home / apartment room types are conformed to complete complete spatial randomness (CSR). This means that distribution of entire home / apartment room types are random.

H1: Distribution of entire home / apartment room types are not CSR, hence, distribution are not random.

Chi squared test of CSR using quadrat counts

From the result, we observed that p-value < 2.2e-16 < 0.05, chi-squared statistic = 43936, which is large. Reject null hypothesis that the points are randomly distributed. Hence, we conclude that distribution of entire home / apartment Airbnb room types is not random, but instead, shows signs of clustering. This result is supported by the graphs that were plotted earlier, which showed clustering at different locations in Singapore.

qt <- quadrat.test(aptSG_ppp, 
                   nx = 20, ny = 15)

## Warning: Some expected counts are small; chi^2 approximation may be inaccurate

qt

## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  aptSG_ppp
## X2 = 43735, df = 184, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)

Conclusion

From this plot, we can affirm the conclusion that we previously had. The entire home / apartment room types in Airbnb are not randomly distributed, and there shows signs of clustering, especially in the Central-south region.

plot(aptSG_ppp)
plot(qt, add = TRUE, cex =.1)

Monte Carlo Test of CSR

same readings as before, pvalue = 0.002 < 0.05, chi-squared distribution large, reject null hypothesis. Clustering can be seen.

quadrat.test(aptSG_ppp,
             nx=20, ny=15,
             method="M",
             nsim=999)

## 
##  Conditional Monte Carlo test of CSR using quadrat counts
##  Test statistic: Pearson X2 statistic
## 
## data:  aptSG_ppp
## X2 = 43735, p-value = 0.002
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)

Next, we use the Nearest Neighbour Analysis to identify the direct distance from a point to its nearest neighbour.

The nearest neighbour analysis will also allow us to identify the expected distance, which is the average distance between neighbours in a hypothetical random distribution. (It tells us how dispersed or clustered the points are)

To test aggregation for a spatial point pattern, we have the following test hypothesis at the 95% significance level:

H0: Distribution of entire home / apartment room types are randomly distributed (CSR)

H1: Distribution of entire home / apartment room types are not randomly distributed (not CSR)

Testing spatial point patterns using Clark and Evans Test

Since the p-value = 0.02 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random

Additionally, since R = 0.26256 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(aptSG_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("two.sided"),
                nsim=99)

## Warning: point-in-polygon test had difficulty with 47 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 42 points (total score not 0
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## 
##  Clark-Evans test
##  No edge correction
##  Monte Carlo test based on 99 simulations of CSR with fixed n
## 
## data:  aptSG_ppp
## R = 0.26529, p-value = 0.02
## alternative hypothesis: two-sided

HOTEL

Quadrat Analysis

Test hypotheses at the 95% confidence level,

H0: Distribution of hotel room types are conformed to complete complete spatial randomness (CSR). This means that distribution of hotel room types are random.

H1: Distribution of hotel room types are not CSR, hence, distribution are not random.

Chi squared test of CSR using quadrat counts

From the result, we observed that p-value < 2.2e-16 < 0.05, chi-squared statistic = 21954, which is large. Reject null hypothesis that the points are randomly distributed. Hence, we conclude that distribution of hotel Airbnb room types is not random, but instead, shows signs of clustering. This result is supported by the graphs that were plotted earlier, which showed clustering at different location in Singapore.

qt <- quadrat.test(hotelSG_ppp, 
                   nx = 20, ny = 15)

## Warning: Some expected counts are small; chi^2 approximation may be inaccurate

qt

## 
##  Chi-squared test of CSR using quadrat counts
## 
## data:  hotelSG_ppp
## X2 = 9195.6, df = 184, p-value < 2.2e-16
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)

Conclusion

From this plot, we can affirm the conclusion that we previously had. The hotel room types in Airbnb are not randomly distributed, and there shows signs of clustering, especially in the Central-south region.

plot(hotelSG_ppp)
plot(qt, add = TRUE, cex =.1)

Monte Carlo Test of CSR

same readings as before, pvalue = 0.002 < 0.05, chi-squared distribution large, reject null hypothesis. Clustering can be seen.

quadrat.test(hotelSG_ppp,
             nx=20, ny=15,
             method="M",
             nsim=999)

## 
##  Conditional Monte Carlo test of CSR using quadrat counts
##  Test statistic: Pearson X2 statistic
## 
## data:  hotelSG_ppp
## X2 = 9195.6, p-value = 0.002
## alternative hypothesis: two.sided
## 
## Quadrats: 185 tiles (irregular windows)

Next, we use the Nearest Neighbour Analysis to identify the direct distance from a point to its nearest neighbour.

The nearest neighbour analysis will also allow us to identify the expected distance, which is the average distance between neighbours in a hypothetical random distribution. (It tells us how dispersed or clustered the points are)

To test aggregation for a spatial point pattern, we have the following test hypothesis at the 95% significance level:

H0: Distribution of hotel room types are randomly distributed (CSR)

H1: Distribution of hotel room types are not randomly distributed (not CSR)

Testing spatial point patterns using Clark and Evans Test

Since the p-value = 0.02 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random

Additionally, since R = 0.10325 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(hotelSG_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("two.sided"),
                nsim=99)

## Warning: point-in-polygon test had difficulty with 10 points (total score not 0
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## 
##  Clark-Evans test
##  No edge correction
##  Monte Carlo test based on 99 simulations of CSR with fixed n
## 
## data:  hotelSG_ppp
## R = 0.10003, p-value = 0.02
## alternative hypothesis: two-sided

Part 3:

Having formulated the null and alternate hypothesis and performed 1st order spatial point pattern analysis, we will now derive the kernel density maps of Airbnb listing by room types.

PRIVATE

Kernel Density Estimation

kde_privateSG_bw <- density(privateSG_ppp, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

plot(kde_privateSG_bw)

##### The density values of the output range from 0 to 0.00008 is way too small to comprehend. This is because the default unit of measurement is meter. As a result, the density values computed is in ‘number of points per square meter’.

We need to rescale the unit of measurement from meter to kilometer

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

Now, re-run density() using the rescale data set and plot the output kde map

kde_privateSG.bw <- density(privateSG_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

plot(kde_privateSG.bw)

Computing kernel density estimation using defining bandwidth manually

Setting the bandwidth to 600 (600m = 0.6km, so sigma = 0.6)

kde_privateSG_600 <- density(privateSG_ppp.km, sigma=0.6, edge=TRUE, kernel="gaussian")

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

plot(kde_privateSG_600)

We can see that there is higher density of points in the Central-South region, mainly which is where the clustering of private Airbnb room types are.

Converting KDE output into grid object

Convert into grid so that it is suitable for mapping purposes

gridded_kde_privateSG_bw <- as.SpatialGridDataFrame.im(kde_privateSG.bw)
spplot(gridded_kde_privateSG_bw)

Converting gridded output into raster

kde_privateSG_bw_raster <- raster(gridded_kde_privateSG_bw)

Properties of kde_privateSG_bw_raster

kde_privateSG_bw_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        : NA 
## source     : memory
## names      : v 
## values     : -1.279744e-13, 806.0808  (min, max)

Assigning projection systems

projection(kde_privateSG_bw_raster) <- CRS("+init=EPSG:3414")
kde_privateSG_bw_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 +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 
## source     : memory
## names      : v 
## values     : -1.279744e-13, 806.0808  (min, max)

Visualising the output in tmap

The raster values are encoded explicitly onto the raster pixel using the values in “v” field

tm_shape(kde_privateSG_bw_raster) + 
  tm_raster("v") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)

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

Plotting the kernel density map on openstreetmap of Singapore

wgs84 <- CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs")
priv_wgs84 <- spTransform(private, wgs84)
priv_wgs84@data['lon'] <- priv_wgs84@coords[,1]
priv_wgs84@data['lat'] <- priv_wgs84@coords[,2]
xys <- priv_wgs84@data[c('lon', 'lat')]

osm_ <- c(left = min(xys$lon), bottom = min(xys$lat), 
         right = max(xys$lon), top = max(xys$lat))

basemap <- get_stamenmap(osm_, zoom = 12, 
                         maptype = "toner-lite")

## Source : http://tile.stamen.com/toner-lite/12/3227/2031.png

## Source : http://tile.stamen.com/toner-lite/12/3228/2031.png

## Source : http://tile.stamen.com/toner-lite/12/3229/2031.png

## Source : http://tile.stamen.com/toner-lite/12/3230/2031.png

## Source : http://tile.stamen.com/toner-lite/12/3227/2032.png

## Source : http://tile.stamen.com/toner-lite/12/3228/2032.png

## Source : http://tile.stamen.com/toner-lite/12/3229/2032.png

## Source : http://tile.stamen.com/toner-lite/12/3230/2032.png

## Source : http://tile.stamen.com/toner-lite/12/3227/2033.png

## Source : http://tile.stamen.com/toner-lite/12/3228/2033.png

## Source : http://tile.stamen.com/toner-lite/12/3229/2033.png

## Source : http://tile.stamen.com/toner-lite/12/3230/2033.png

osm <- ggmap(basemap, extent = "device", 
               maprange=FALSE) +
  stat_density2d(data = priv_wgs84@data, 
                aes(x = lon, y = lat, 
                    alpha=..level.., 
                    fill = ..level..), 
                size = 0.01, bins = 16, 
                geom = 'polygon', 
                show.legend = TRUE) +
  scale_fill_gradient2("Transaction\nDensity", 
                       low = "#fffff8", 
                       high = "#8da0cb")
osm

This kernel density estimation on the openstreetmap of Singapore allows us to not only see the distribution of Private room types, but also to relate it to what we know about Singapore, allowing us to establish many more connections than we were previously able.

We are able to see that the area with the highest volume of private room types are in the central region, and clustering is seen mainly in the central-south regions.

SHARED

Kernel Density Estimation

kde_sharedSG_bw <- density(sharedSG_ppp, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

plot(kde_sharedSG_bw)

The density values of the output range from 0 to 0.00008 is way too small to comprehend. This is because the default unit of measurement is meter. As a result, the density values computed is in ‘number of points per square meter’.

We need to rescale the unit of measurement from meter to kilometer

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

Now, re-run density() using the rescale data set and plot the output kde map

kde_sharedSG.bw <- density(sharedSG_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

plot(kde_sharedSG.bw)

Computing kernel density estimation using defining bandwidth manually

Setting the bandwidth to 600 (600m = 0.6km, so sigma = 0.6)

kde_sharedSG_600 <- density(sharedSG_ppp.km, sigma=0.6, edge=TRUE, kernel="gaussian")

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

plot(kde_sharedSG_600)

We can see that there is higher density of points in the Central-South region, mainly which is where the clustering of shared Airbnb room types are.

Converting KDE output into grid object

Convert into grid so that it is suitable for mapping purposes

gridded_kde_sharedSG_bw <- as.SpatialGridDataFrame.im(kde_sharedSG.bw)
spplot(gridded_kde_sharedSG_bw)

Converting gridded output into raster

kde_sharedSG_bw_raster <- raster(gridded_kde_sharedSG_bw)

Properties of kde_sharedSG_bew_raster

kde_sharedSG_bw_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        : NA 
## source     : memory
## names      : v 
## values     : -2.331955e-14, 125.8712  (min, max)

Assigning projection systems

projection(kde_sharedSG_bw_raster) <- CRS("+init=EPSG:3414")
kde_sharedSG_bw_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 +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 
## source     : memory
## names      : v 
## values     : -2.331955e-14, 125.8712  (min, max)

Visualising the output in tmap

The raster values are encoded explicitly onto the raster pixel using the values in “v” field

tm_shape(kde_sharedSG_bw_raster) + 
  tm_raster("v") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)

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

Plotting the kernel density map on openstreetmap of Singapore

wgs84 <- CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs")
shared_wgs84 <- spTransform(shared, wgs84)
shared_wgs84@data['lon'] <- shared_wgs84@coords[,1]
shared_wgs84@data['lat'] <- shared_wgs84@coords[,2]
xys <- shared_wgs84@data[c('lon', 'lat')]

osm_ <- c(left = min(xys$lon), bottom = min(xys$lat), 
         right = max(xys$lon), top = max(xys$lat))

basemap <- get_stamenmap(osm_, zoom = 12, 
                         maptype = "toner-lite")

osm <- ggmap(basemap, extent = "device", 
               maprange=FALSE) +
  stat_density2d(data = shared_wgs84@data, 
                aes(x = lon, y = lat, 
                    alpha=..level.., 
                    fill = ..level..), 
                size = 0.01, bins = 16, 
                geom = 'polygon', 
                show.legend = TRUE) +
  scale_fill_gradient2("Transaction\nDensity", 
                       low = "#fffff8", 
                       high = "#8da0cb")
osm

This kernel density estimation on the openstreetmap of Singapore allows us to not only see the distribution of Shared room types, but also to relate it to what we know about Singapore, allowing us to establish many more connections than we were previously able.

We are able to see that the area with the highest volume of private room types are in the central region, and clustering is seen mainly in the central-south regions.

ENTIRE HOME / APARTMENT

Kernel Density Estimation

kde_aptSG_bw <- density(aptSG_ppp, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

plot(kde_aptSG_bw)

The density values of the output range from 0 to 0.00008 is way too small to comprehend. This is because the default unit of measurement is meter. As a result, the density values computed is in ‘number of points per square meter’.

We need to rescale the unit of measurement from meter to kilometer

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

Now, re-run density() using the rescale data set and plot the output kde map

kde_aptSG.bw <- density(aptSG_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

plot(kde_aptSG.bw)

Computing kernel density estimation using defining bandwidth manually

Setting the bandwidth to 600 (600m = 0.6km, so sigma = 0.6)

kde_aptSG_600 <- density(aptSG_ppp.km, sigma=0.6, edge=TRUE, kernel="gaussian")

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

plot(kde_aptSG_600)

We can see that there is higher density of points in the Central-South region, mainly which is where the clustering of entire home / apartment Airbnb room types are.

Converting KDE output into grid object

Convert into grid so that it is suitable for mapping purposes

gridded_kde_aptSG_bw <- as.SpatialGridDataFrame.im(kde_aptSG.bw)
spplot(gridded_kde_aptSG_bw)

Converting gridded output into raster

kde_aptSG_bw_raster <- raster(gridded_kde_aptSG_bw)

Properties of kde_aptSG_bw_raster

kde_aptSG_bw_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        : NA 
## source     : memory
## names      : v 
## values     : -1.953859e-13, 1213.651  (min, max)

Assigning projection systems

projection(kde_aptSG_bw_raster) <- CRS("+init=EPSG:3414")
kde_aptSG_bw_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 +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 
## source     : memory
## names      : v 
## values     : -1.953859e-13, 1213.651  (min, max)

Visualising the output in tmap

The raster values are encoded explicity onto the raster pixel using the values in “v” field

tm_shape(kde_aptSG_bw_raster) + 
  tm_raster("v") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)

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

Plotting the kernel density map on openstreetmap of Singapore

wgs84 <- CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs")
apt_wgs84 <- spTransform(apt, wgs84)
apt_wgs84@data['lon'] <- apt_wgs84@coords[,1]
apt_wgs84@data['lat'] <- apt_wgs84@coords[,2]
xys <- apt_wgs84@data[c('lon', 'lat')]

osm_ <- c(left = min(xys$lon), bottom = min(xys$lat), 
         right = max(xys$lon), top = max(xys$lat))

basemap <- get_stamenmap(osm_, zoom = 12, 
                         maptype = "toner-lite")

osm <- ggmap(basemap, extent = "device", 
               maprange=FALSE) +
  stat_density2d(data = apt_wgs84@data, 
                aes(x = lon, y = lat, 
                    alpha=..level.., 
                    fill = ..level..), 
                size = 0.01, bins = 16, 
                geom = 'polygon', 
                show.legend = TRUE) +
  scale_fill_gradient2("Transaction\nDensity", 
                       low = "#fffff8", 
                       high = "#8da0cb")
osm

This kernel density estimation on the openstreetmap of Singapore allows us to not only see the distribution of Entire home / Apartment room types, but also to relate it to what we know about Singapore, allowing us to establish many more connections than we were previously able.

We are able to see that the area with the highest volume of private room types are in the central region, and clustering is seen mainly in the central-south regions, with a small part towards the east.

HOTEL

Kernel Density Estimation

kde_hotelSG_bw <- density(hotelSG_ppp, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

plot(kde_hotelSG_bw)

The density values of the output range from 0 to 0.00008 is way too small to comprehend. This is because the default unit of measurement is meter. As a result, the density values computed is in ‘number of points per square meter’.

We need to rescale the unit of measurement from meter to kilometer

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

Now, re-run density() using the rescale data set and plot the output kde map

kde_hotelSG.bw <- density(hotelSG_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

plot(kde_hotelSG.bw)

Computing kernel density estimation using defining bandwidth manually

Setting the bandwidth to 600 (600m = 0.6km, so sigma = 0.6)

kde_hotelSG_600 <- density(hotelSG_ppp.km, sigma=0.6, edge=TRUE, kernel="gaussian")

## Warning: point-in-polygon test had difficulty with 215 points (total score not 0
## or 1)

plot(kde_hotelSG_600)

We can see that there is higher density of points in the Central-South region, mainly which is where the clustering of hotel Airbnb room types are.

Converting KDE output into grid object

Convert into grid so that it is suitable for mapping purposes

gridded_kde_hotelSG_bw <- as.SpatialGridDataFrame.im(kde_hotelSG.bw)
spplot(gridded_kde_hotelSG_bw)

Converting gridded output into raster

kde_hotelSG_bw_raster <- raster(gridded_kde_hotelSG_bw)

Properties of kde_hoteSG_bw_raster

kde_hotelSG_bw_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        : NA 
## source     : memory
## names      : v 
## values     : -7.73794e-14, 541.8622  (min, max)

Assigning projection systems

projection(kde_hotelSG_bw_raster) <- CRS("+init=EPSG:3414")
kde_hotelSG_bw_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 +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 
## source     : memory
## names      : v 
## values     : -7.73794e-14, 541.8622  (min, max)

Visualising the output in tmap

The raster values are encoded explicitly onto the raster pixel using the values in “v” field

tm_shape(kde_hotelSG_bw_raster) + 
  tm_raster("v") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)

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

Plotting the kernel density map on openstreetmap of Singapore

wgs84 <- CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs")
hotel_wgs84 <- spTransform(hotel, wgs84)
hotel_wgs84@data['lon'] <- hotel_wgs84@coords[,1]
hotel_wgs84@data['lat'] <- hotel_wgs84@coords[,2]
xys <- hotel_wgs84@data[c('lon', 'lat')]

osm_ <- c(left = min(xys$lon), bottom = min(xys$lat), 
         right = max(xys$lon), top = max(xys$lat))

basemap <- get_stamenmap(osm_, zoom = 12, 
                         maptype = "toner-lite")

osm <- ggmap(basemap, extent = "device", 
               maprange=FALSE) +
  stat_density2d(data = hotel_wgs84@data, 
                aes(x = lon, y = lat, 
                    alpha=..level.., 
                    fill = ..level..), 
                size = 0.01, bins = 16, 
                geom = 'polygon', 
                show.legend = TRUE) +
  scale_fill_gradient2("Transaction\nDensity", 
                       low = "#fffff8", 
                       high = "#8da0cb")
osm

This kernel density estimation on the openstreetmap of Singapore allows us to not only see the distribution of hotel room types, but also to relate it to what we know about Singapore, allowing us to establish many more connections than we were previously able.

We are able to see that the area with the highest volume of hotel room types are in the central-south region, and this seems to be the only concentrated cluster region.

From the analysis above, we can conclude that,

Kernel density map has more advantages as compared to point map, as kernel density estimation is a method to compute the intensity of a point distribution.

There are weaknesses to the quadrant analysis. For one, it is sensitive to the quadrant size. For example, if the quadrant size is too small, they may contain only a couple of points, and if the quadrant size is too large, they may contain too many points. Hence, quadrant analysis is more of a measure of dispersion rather than a measure of pattern, and variation within region are not easily recognised.

On the other hand, kernel density estimation is a simple computation, and it gives better and more accurate results.

Section B: By planning subzones

PART 4: Exploratory Spatial Data Analysis

In this secion, we will Extract Airbnb listing by room type within Aljunied, Balestier, Lavender, and Tanjong Pagar planning subzones. From there, we will display their distribution as point maps, and describe the spatial patterns revealed by their respective distribution.

As identified above, there are 4 different room types. For a more concise and accurate analysis, we will split the analysis of the 4 different room types.

PRIVATE

Convert spatial point data frame into generic sp format

private_sp <- as(private, "SpatialPoints")

Converting generic sp format into spatspat’s ppp format

private_ppp <- as(private_sp, "ppp")

Check for duplicate spatial point events

duplicated(private_ppp)

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Since there are several duplicates, eliminate duplicate point events

private_ppp_u <- unique(private_ppp)
duplicated(private_ppp_u) 

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## [2917] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2929] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [2965] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2977] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2989] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3001] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3013] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3025] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [3049] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3061] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3073] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3085] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3097] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE

There are no more duplicated point events in private_ppp_u object

Comparing Spatial Point Patterns using KDE

Extracting study area

aj = mpsz[mpsz@data$SUBZONE_N == "ALJUNIED",]
bl = mpsz[mpsz@data$SUBZONE_N == "BALESTIER",]
lv = mpsz[mpsz@data$SUBZONE_N == "LAVENDER",]
tp = mpsz[mpsz@data$SUBZONE_N == "TANJONG PAGAR",]

Plot target planning areas

par(mfrow=c(2,2))
plot(aj, main = "ALJUNIED")
plot(bl, main = "BALESTIER")
plot(lv, main = "LAVENDER")
plot(tp, main = "TANJONG PAGAR")

Converting spatial point data frame into generic sp format

private_sp = as(private,"SpatialPoints")
aj_sp = as(aj, "SpatialPolygons")
bl_sp = as(bl, "SpatialPolygons")
lv_sp = as(lv, "SpatialPolygons")
tp_sp = as(tp, "SpatialPolygons")

Creating owin object

aj_owin = as(aj_sp, "owin")
bl_owin = as(bl_sp, "owin")
lv_owin = as(lv_sp, "owin")
tp_owin = as(tp_sp, "owin")

Combining private points and study area

private_aj_ppp = private_ppp_jit[aj_owin]
private_bl_ppp = private_ppp_jit[bl_owin]
private_lv_ppp = private_ppp_jit[lv_owin]
private_tp_ppp = private_ppp_jit[tp_owin]

Visualising ppp objects

par(mfrow=c(2,2))
plot(private_aj_ppp)
plot(private_bl_ppp)
plot(private_lv_ppp)
plot(private_tp_ppp)

From the above graph, we can see a significant clustering in the Lavender and Aljunied subzones, and a less significant clustering in Balestier. Tanjong Pagar subzone does not seem to have much clustering. We will further our analysis by conducting null and alternative hyothesis test as shown below.

SHARED

Convert spatial point data frame into generic sp format

shared_sp <- as(shared, "SpatialPoints")

Converting generic sp format into spatspat’s ppp format

shared_ppp <- as(shared_sp, "ppp")

Check for duplicate spatial point events

duplicated(shared_ppp)

##   [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [13] FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [61]  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE
##  [73]  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE
##  [97] FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE

Since there are several duplicates, eliminate duplicate point events

shared_ppp_u <- unique(shared_ppp)
duplicated(shared_ppp_u) 

##   [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE

There are no more duplicated point events in shared_ppp_u object

Comparing Spatial Point Patterns using KDE

Extracting study area

aj = mpsz[mpsz@data$SUBZONE_N == "ALJUNIED",]
bl = mpsz[mpsz@data$SUBZONE_N == "BALESTIER",]
lv = mpsz[mpsz@data$SUBZONE_N == "LAVENDER",]
tp = mpsz[mpsz@data$SUBZONE_N == "TANJONG PAGAR",]

Plot target planning areas

par(mfrow=c(2,2))
plot(aj, main = "ALJUNIED")
plot(bl, main = "BALESTIER")
plot(lv, main = "LAVENDER")
plot(tp, main = "TANJONG PAGAR")

Converting spatial point data frame into generic sp format

shared_sp = as(shared,"SpatialPoints")
aj_sp = as(aj, "SpatialPolygons")
bl_sp = as(bl, "SpatialPolygons")
lv_sp = as(lv, "SpatialPolygons")
tp_sp = as(tp, "SpatialPolygons")

Creating owin object

aj_owin = as(aj_sp, "owin")
bl_owin = as(bl_sp, "owin")
lv_owin = as(lv_sp, "owin")
tp_owin = as(tp_sp, "owin")

Combining private points and study area

shared_aj_ppp = shared_ppp_jit[aj_owin]
shared_bl_ppp = shared_ppp_jit[bl_owin]
shared_lv_ppp = shared_ppp_jit[lv_owin]
shared_tp_ppp = shared_ppp_jit[tp_owin]

Visualising ppp objects

par(mfrow=c(2,2))
plot(shared_aj_ppp)
plot(shared_bl_ppp)
plot(shared_lv_ppp)
plot(shared_tp_ppp)

From the above graph, we can see a significant clustering in the Lavender subzone, and a less significant clustering in Aljunied. Balestier subzone only has one point, and Tanjong Pagar subzone does not have any data at all. We will further our analysis by conducting null and alternative hyothesis test as shown below.

ENTIRE HOME / APARTMENT

Convert spatial point data frame into generic sp format

apt_sp <- as(apt, "SpatialPoints")

Converting generic sp format into spatspat’s ppp format

apt_ppp <- as(apt_sp, "ppp")

Check for duplicate spatial point events

duplicated(apt_ppp)

##    [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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##   [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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##  [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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##  [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE
##  [997]  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1009] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1021] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1033] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [1069] FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE  TRUE  TRUE  TRUE
## [1081]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE
## [1093] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1105] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE
## [1117]  TRUE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [1141] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE
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## [1501] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE
## [1513] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1525] FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [1885] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1897] FALSE  TRUE  TRUE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1909] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1921] FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1933] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1945] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1957] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1969] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1981] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1993] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2005] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2017] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2029] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2041] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2053] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2065] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2077] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2089] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2101] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2113] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2125] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2137] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2149] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2161] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2173] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2185] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2197] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2209] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2221] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2233] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2245] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2257] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2269] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2281] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2293] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2305] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2317] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2329] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2341] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2353] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2365] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2377] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2389] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2401] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2413] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2425] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2437] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2449] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2461] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2473] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2485] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2497] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2509] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2521] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2533] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2545] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2557] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2569] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2581] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2593] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2605] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2617] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2629] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2641] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2653] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2665] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2677] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2689] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2701] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2713] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2725] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2737] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2749] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2761] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2773] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2785] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2797] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2809] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2821] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2833] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2845] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2857] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2869] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2881] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2893] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2905] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2917] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2929] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2941] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2953] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2965] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2977] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2989] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3001] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3013] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3025] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3037] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3049] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3061] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3073] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3085] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3097] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3589] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE

Since there are several duplicates, eliminate duplicate point events

apt_ppp_u <- unique(apt_ppp)
duplicated(apt_ppp_u) 

##    [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [589] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [697] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [709] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [721] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [733] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [745] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [757] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [769] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [781] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [793] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [805] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [817] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [829] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [841] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [853] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [865] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [877] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [901] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [913] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [925] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [937] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [949] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [961] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [973] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [985] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [997] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1009] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1021] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1033] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1045] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1057] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1069] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1081] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1093] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1105] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1117] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1129] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1141] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1153] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1165] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1177] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1189] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1201] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1213] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1225] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1237] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1249] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1261] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1273] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1285] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1297] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1309] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1321] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1333] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1345] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1357] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1369] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1381] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1393] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1405] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1417] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1429] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1441] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1453] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1465] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1477] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1489] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1501] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1513] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1525] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1537] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1549] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1561] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1573] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1585] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1597] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1609] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1621] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1633] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1645] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1657] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1669] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1681] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1693] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1705] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1717] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1729] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1741] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1753] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1765] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1777] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1789] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1801] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1813] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1825] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1837] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1849] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1861] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1873] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1885] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1897] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1909] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1921] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1933] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1945] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1957] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1969] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1981] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1993] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2005] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2017] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2029] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2041] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2053] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2065] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2077] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2089] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2101] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2113] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2125] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2137] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2149] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2161] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2173] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2185] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2197] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2209] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2221] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2233] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2245] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2257] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2269] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2281] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2293] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2305] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2317] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2329] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2341] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2353] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2365] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2377] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2389] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2401] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2413] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2425] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2437] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2449] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2461] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2473] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2485] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2497] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2509] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2521] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2533] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2545] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2557] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2569] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2581] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2593] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2605] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2617] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2629] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2641] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2653] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2665] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2677] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2689] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2701] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2713] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2725] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2737] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2749] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2761] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2773] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2785] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2797] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2809] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2821] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2833] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2845] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2857] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2869] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2881] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2893] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2905] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2917] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2929] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2941] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2953] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2965] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2977] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [2989] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3001] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3013] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3025] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3037] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3049] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3061] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3073] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3085] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3097] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3493] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3505] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3517] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3529] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3541] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3589] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3601] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3613] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3625] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3649] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3661] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3673] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3685] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [3697] FALSE FALSE

There are no more duplicated point events in apt_ppp_u object

Comparing Spatial Point Patterns using KDE

Extracting study area

aj = mpsz[mpsz@data$SUBZONE_N == "ALJUNIED",]
bl = mpsz[mpsz@data$SUBZONE_N == "BALESTIER",]
lv = mpsz[mpsz@data$SUBZONE_N == "LAVENDER",]
tp = mpsz[mpsz@data$SUBZONE_N == "TANJONG PAGAR",]

Plot target planning areas

par(mfrow=c(2,2))
plot(aj, main = "ALJUNIED")
plot(bl, main = "BALESTIER")
plot(lv, main = "LAVENDER")
plot(tp, main = "TANJONG PAGAR")

Converting spatial point data frame into generic sp format

apt_sp = as(apt,"SpatialPoints")
aj_sp = as(aj, "SpatialPolygons")
bl_sp = as(bl, "SpatialPolygons")
lv_sp = as(lv, "SpatialPolygons")
tp_sp = as(tp, "SpatialPolygons")

Creating owin object

aj_owin = as(aj_sp, "owin")
bl_owin = as(bl_sp, "owin")
lv_owin = as(lv_sp, "owin")
tp_owin = as(tp_sp, "owin")

Combining private points and study area

apt_aj_ppp = apt_ppp_jit[aj_owin]
apt_bl_ppp = apt_ppp_jit[bl_owin]
apt_lv_ppp = apt_ppp_jit[lv_owin]
apt_tp_ppp = apt_ppp_jit[tp_owin]

Visualising ppp objects

par(mfrow=c(2,2))
plot(apt_aj_ppp)
plot(apt_bl_ppp)
plot(apt_lv_ppp)
plot(apt_tp_ppp)

From the above graph, we can see a significant clustering in all 4 planning subzones, with each of the subzones having different areas clustered. We will further our analysis by conducting null and alternative hyothesis test as shown below.

HOTEL

Convert spatial point data frame into generic sp format

hotel_sp <- as(hotel, "SpatialPoints")

Converting generic sp format into spatspat’s ppp format

hotel_ppp <- as(hotel_sp, "ppp")

Check for duplicate spatial point events

duplicated(hotel_ppp)

##   [1] FALSE  TRUE FALSE FALSE FALSE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE
##  [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE
##  [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [49] FALSE  TRUE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE
##  [61] FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
##  [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE
##  [97]  TRUE  TRUE  TRUE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
## [169] FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193]  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE  TRUE FALSE FALSE FALSE  TRUE  TRUE  TRUE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE
## [361] FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [469] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [481] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE
## [493] FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE
## [505]  TRUE FALSE FALSE

Since there are several duplicates, eliminate duplicate point events

hotel_ppp_u <- unique(hotel_ppp)
duplicated(hotel_ppp_u) 

##   [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [181] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [193] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [205] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [217] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [229] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [241] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [253] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [265] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [277] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [289] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [301] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [313] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [325] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [337] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [349] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [361] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [373] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [385] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [397] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [409] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [421] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [433] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [445] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [457] FALSE FALSE FALSE FALSE FALSE FALSE

There are no more duplicated point events in hotel_ppp_u object

Comparing Spatial Point Patterns using KDE

Extracting study area

aj = mpsz[mpsz@data$SUBZONE_N == "ALJUNIED",]
bl = mpsz[mpsz@data$SUBZONE_N == "BALESTIER",]
lv = mpsz[mpsz@data$SUBZONE_N == "LAVENDER",]
tp = mpsz[mpsz@data$SUBZONE_N == "TANJONG PAGAR",]

Plot target planning areas

par(mfrow=c(2,2))
plot(aj, main = "ALJUNIED")
plot(bl, main = "BALESTIER")
plot(lv, main = "LAVENDER")
plot(tp, main = "TANJONG PAGAR")

Converting spatial point data frame into generic sp format

hotel_sp = as(hotel,"SpatialPoints")
aj_sp = as(aj, "SpatialPolygons")
bl_sp = as(bl, "SpatialPolygons")
lv_sp = as(lv, "SpatialPolygons")
tp_sp = as(tp, "SpatialPolygons")

Creating owin object

aj_owin = as(aj_sp, "owin")
bl_owin = as(bl_sp, "owin")
lv_owin = as(lv_sp, "owin")
tp_owin = as(tp_sp, "owin")

Combining private points and study area

hotel_aj_ppp = hotel_ppp_jit[aj_owin]
hotel_bl_ppp = hotel_ppp_jit[bl_owin]
hotel_lv_ppp = hotel_ppp_jit[lv_owin]
hotel_tp_ppp = hotel_ppp_jit[tp_owin]

Visualising ppp objects

par(mfrow=c(2,2))
plot(hotel_aj_ppp)
plot(hotel_bl_ppp)
plot(hotel_lv_ppp)
plot(hotel_tp_ppp)

From the above graph, we can see a slight clustering in the Lavender and Balestier subzones, and a less significant clustering in Aljunied. There are only two points in the Tanjong Pagar subzone. We will further our analysis by conducting null and alternative hyothesis test as shown below.

PART 5: Analysing Spatial Point Process

With reference to the spatial point patterns observed previously, we will attempt to formulate the null hypothesis and alternative hypothesis, and select the confidence level.

Then, we will perform the test by using appropriate 2nd order spatial point patterns analysis technique, before drawing statistical conclusions.

We will be using G-Function and L-Function to derive our conclusion. This is because the F-Function is based on distance pairs which is not really relevant to us as compared to G-Function which is based on nearest neighbour distances. Since L-Function is the normalised version of K-Function, it will make more sense to use L-Function instead of K-Function.

PRIVATE

Using G Function

Aljunied planning area

G function estimation

private_G_AJ = Gest(private_aj_ppp, correction="border")
plot(private_G_AJ)

Performing Complete Spatial Randomness Test

H0: Distribution of private room types at Aljunied are randomly distributed

H1: Distribution of private room types at Aljunied are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

private_G_AJ.csr <- envelope(private_aj_ppp, Gest, nsim = 999)

## 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(private_G_AJ.csr)

Since the estimated G(r) function lies above the envelope from point 0, the estimated G(r) is statistically significant. Reject null hypothesis that the distribution of room types in Aljunied is randomly distributed.

As the G increases rapidly at the start (short distance), this tells us that the points of private room type in Aljunied are clustered.

This observation is consistent with the ppp graph that we have previously plotted to visualise.

Balestier planning area

Computing G-function estimation

private_G_bl = Gest(private_bl_ppp, correction="best")
plot(private_G_bl)

Performing Complete Spatial Randomness Test

H0: Distribution of private room types at Balestier are randomly distributed

H1: Distribution of private room types at Balestier are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

private_G_bl.csr <- envelope(private_bl_ppp, Gest, correction = "all", nsim = 999)

## 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(private_G_bl.csr)

For r < 60, the black line(observed) is within the envelope. Hence we cannot reject the null hypothesis. Therefore, we conclude that for all the points where r < 60, they exibit complete spatial randomness.

For r > 60, the black line(observed) is outside of the envelope. Hence, we reject the null hypothesis. Since the black line(observed) is above the envelope, it represents clustered distribution of private room types listing in Balestier area.

Hence, we conclude that the Balestier area consists of an area that is random, and another that is clustered.

This is consistent with the ppp graph that we have previously plotted, which shows us one part of the Balestier map being clustered, and the other part, random.

Lavender planning area

G function estimate

private_G_LV = Gest(private_lv_ppp, correction="border")
plot(private_G_LV)

Performing Complete Spatial Randomness Test

H0: Distribution of private room types at Lavender are randomly distributed

H1: Distribution of private room types at Lavender are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

private_G_lv.csr <- envelope(private_lv_ppp, Gest, correction = "all", nsim = 999)

## 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(private_G_lv.csr)

For r < 5, the black line(observed) is within the envelope. Hence we cannot reject the null hypothesis. Therefore, we conclude that for all the points where r < 5, they exibit complete spatial randomness.

For r > 5, the black line(observed) is outside of the envelope. Hence, we reject the null hypothesis. Since the black line(observed) is above the envelope, it represents clustered distribution of private room types listing in Lavender area.

Hence, majority of Lavender area is clustered.

This observation is conssitent with the ppp graph that we have previously plotted to visualise.

Tanjong Pagar planning area

G function estimate

private_G_TP = Gest(private_tp_ppp, correction="border")
plot(private_G_TP)

Performing Complete Spatial Randomness Test

H0: Distribution of private room types at Tanjong Pagar are randomly distributed

H1: Distribution of private room types at Tanjong Pagar are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

private_G_tp.csr <- envelope(private_tp_ppp, Gest, correction = "all", nsim = 999)

## 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(private_G_tp.csr)

From point 0, since the black line is within the envelope, are cannot reject the null hypothesis. Hence, we conclude that the data points are statistically not significant, and they exhibit complete spatial randomness.

There are certain points which has the black line (observed) above the red line, while majority of the black line are below the red line.

Since the G function increases slowly up (in a staircase way), we conclude that there are evenness in the randomness of the events.

This observation is consistent with the ppp graph that we have previously plotted, which showed us that there is not much clustering in Tanjong Pagar planning subzone.

Using L Function

Aljunied planning area

L function estimation

private_L_aj = Lest(private_aj_ppp, correction = "Ripley")
plot(private_L_aj, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of private room types at Aljunied are randomly distributed.

H1= The distribution of private room types at Aljunied are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

private_L_aj.csr <- envelope(private_aj_ppp, Lest, nsim = 999, rank = 1, glocal=TRUE)

## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10 [etd 2:50] .........20 [etd 2:56] .........
## 30 [etd 2:50] .........40 [etd 2:48] .........50 [etd 2:44] ........
## .60 [etd 2:41] .........70 [etd 2:40] .........80 [etd 2:39] .......
## ..90 [etd 2:36] .........100 [etd 2:33] .........110 [etd 2:31] ......
## ...120 [etd 2:29] .........130 [etd 2:27] .........140 [etd 2:26] .....
## ....150 [etd 2:24] .........160 [etd 2:22] .........170 [etd 2:20] ....
## .....180 [etd 2:18] .........190 [etd 2:16] .........200 [etd 2:14] ...
## ......210 [etd 2:12] .........220 [etd 2:11] .........230 [etd 2:09] ..
## .......240 [etd 2:07] .........250 [etd 2:05] .........260 [etd 2:03] .
## ........270 [etd 2:01] .........280 [etd 2:00] .........290
##  [etd 1:58] .........300 [etd 1:56] .........310 [etd 1:55] .........
## 320 [etd 1:53] .........330 [etd 1:52] .........340 [etd 1:50] ........
## .350 [etd 1:49] .........360 [etd 1:47] .........370 [etd 1:45] .......
## ..380 [etd 1:43] .........390 [etd 1:41] .........400 [etd 1:39] ......
## ...410 [etd 1:38] .........420 [etd 1:36] .........430 [etd 1:35] .....
## ....440 [etd 1:33] .........450 [etd 1:31] .........460 [etd 1:30] ....
## .....470 [etd 1:28] .........480 [etd 1:26] .........490 [etd 1:24] ...
## ......500 [etd 1:23] .........510 [etd 1:21] .........520 [etd 1:19] ..
## .......530 [etd 1:18] .........540 [etd 1:16] .........550 [etd 1:15] .
## ........560 [etd 1:13] .........570 [etd 1:11] .........580
##  [etd 1:10] .........590 [etd 1:08] .........600 [etd 1:06] .........
## 610 [etd 1:05] .........620 [etd 1:03] .........630 [etd 1:01] ........
## .640 [etd 1:00] .........650 [etd 58 sec] .........660 [etd 56 sec] .......
## ..670 [etd 55 sec] .........680 [etd 53 sec] .........690 [etd 52 sec] ......
## ...700 [etd 50 sec] .........710 [etd 48 sec] .........720 [etd 47 sec] .....
## ....730 [etd 45 sec] .........740 [etd 43 sec] .........750 [etd 41 sec] ....
## .....760 [etd 40 sec] .........770 [etd 38 sec] .........780 [etd 36 sec] ...
## ......790 [etd 35 sec] .........800 [etd 33 sec] .........810 [etd 31 sec] ..
## .......820 [etd 30 sec] .........830 [etd 28 sec] .........840 [etd 26 sec] .
## ........850 [etd 25 sec] .........860 [etd 23 sec] .........870
##  [etd 22 sec] .........880 [etd 20 sec] .........890 [etd 18 sec] .........
## 900 [etd 16 sec] .........910 [etd 15 sec] .........920 [etd 13 sec] ........
## .930 [etd 11 sec] .........940 [etd 10 sec] .........950 [etd 8 sec] .......
## ..960 [etd 6 sec] .........970 [etd 5 sec] .........980 [etd 3 sec] ......
## ...990 [etd 1 sec] ........ 999.
## 
## Done.

plot(private_L_aj.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

For d > 0, the black line (observed) is greater than the red line (theo), and above the upper confidence envelope, we reject the null hypothesis that private room types in Balestier are randomly distributed. In fact, we conclude that spatial clustering of private room types in Balestier is statistically significant, and clustering can be observed.

This is consistent with the test results from the G-function, as well as the ppp graph that we have previously plotted.

Balestier planning area

L function estimation

private_L_bl = Lest(private_bl_ppp, correction = "Ripley")
plot(private_L_bl, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of private room types at Balestier are randomly distributed.

H1= The distribution of private room types at Balestier are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

private_L_bl.csr <- envelope(private_bl_ppp, Lest, 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(private_L_bl.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

For d < 10, the black line (observed) is greater than the red line (theo), and is within the lower confidence envelope, spatial dispersion for this distance is statistically not significant. Spatial randomness occurs for d < 10 for private room types in Balestier.

For 10 < d < 40, the black line (observed) is greater the red line (theo), and lower the upper confidence envelope. Hence, spatial clustering for this distance is statistically not significant. Spatial randomness occurs for 10 < d < 40 for private room types in Balestier.

For d > 60, the black line (observed) is greater than the red line (theo), and above the upper confidence envelope, we reject the null hypothesis that private room types in Balestier are randomly distributed. In fact, we conclude that spatial clustering of private room types in Balestier is statistically significant, and clustering can be observed.

Hence, there is a part of Balestier that is random, and another part that is clustered.

This is consistent with the test results from the G function, as well as the ppp graph that we have previously plotted.

Lavender planning area

L function estimation

private_L_lv = Lest(private_lv_ppp, correction = "Ripley")
plot(private_L_lv, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of private room types at Lavender are randomly distributed.

H1= The distribution of private room types at Lavender are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

private_L_lv.csr <- envelope(private_lv_ppp, Lest, nsim = 999, rank = 1, glocal=TRUE)

## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10 [etd 3:46] .........20 [etd 3:37] .........
## 30 [etd 3:33] .........40 [etd 3:28] .........50 [etd 3:27] ........
## .60 [etd 3:24] .........70 [etd 3:22] .........80 [etd 3:19] .......
## ..90 [etd 3:17] .........100 [etd 3:17] .........110 [etd 3:14] ......
## ...120 [etd 3:12] .........130 [etd 3:08] .........140 [etd 3:06] .....
## ....150 [etd 3:04] .........160 [etd 3:02] .........170 [etd 3:00] ....
## .....180 [etd 2:58] .........190 [etd 2:56] .........200 [etd 2:54] ...
## ......210 [etd 2:51] .........220 [etd 2:49] .........230 [etd 2:47] ..
## .......240 [etd 2:45] .........250 [etd 2:42] .........260 [etd 2:40] .
## ........270 [etd 2:37] .........280 [etd 2:35] .........290
##  [etd 2:33] .........300 [etd 2:31] .........310 [etd 2:28] .........
## 320 [etd 2:26] .........330 [etd 2:24] .........340 [etd 2:22] ........
## .350 [etd 2:20] .........360 [etd 2:18] .........370 [etd 2:16] .......
## ..380 [etd 2:14] .........390 [etd 2:12] .........400 [etd 2:10] ......
## ...410 [etd 2:08] .........420 [etd 2:06] .........430 [etd 2:04] .....
## ....440 [etd 2:01] .........450 [etd 1:59] .........460 [etd 1:57] ....
## .....470 [etd 1:55] .........480 [etd 1:53] .........490 [etd 1:50] ...
## ......500 [etd 1:48] .........510 [etd 1:46] .........520 [etd 1:44] ..
## .......530 [etd 1:42] .........540 [etd 1:40] .........550 [etd 1:38] .
## ........560 [etd 1:35] .........570 [etd 1:33] .........580
##  [etd 1:31] .........590 [etd 1:29] .........600 [etd 1:27] .........
## 610 [etd 1:24] .........620 [etd 1:22] .........630 [etd 1:20] ........
## .640 [etd 1:18] .........650 [etd 1:16] .........660 [etd 1:13] .......
## ..670 [etd 1:11] .........680 [etd 1:09] .........690 [etd 1:07] ......
## ...700 [etd 1:05] .........710 [etd 1:03] .........720 [etd 1:01] .....
## ....730 [etd 58 sec] .........740 [etd 56 sec] .........750 [etd 54 sec] ....
## .....760 [etd 52 sec] .........770 [etd 50 sec] .........780 [etd 47 sec] ...
## ......790 [etd 45 sec] .........800 [etd 43 sec] .........810 [etd 41 sec] ..
## .......820 [etd 39 sec] .........830 [etd 37 sec] .........840 [etd 34 sec] .
## ........850 [etd 32 sec] .........860 [etd 30 sec] .........870
##  [etd 28 sec] .........880 [etd 26 sec] .........890 [etd 24 sec] .........
## 900 [etd 21 sec] .........910 [etd 19 sec] .........920 [etd 17 sec] ........
## .930 [etd 15 sec] .........940 [etd 13 sec] .........950 [etd 11 sec] .......
## ..960 [etd 8 sec] .........970 [etd 6 sec] .........980 [etd 4 sec] ......
## ...990 [etd 2 sec] ........ 999.
## 
## Done.

plot(private_L_lv.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

For d < 10, the black line (observed) is greater than the red line (theo), and is within the upper confidence envelope. Hence, spatial clustering for this distance is statistically not significant. Spatial randomness occurs for d < 5 for private room types in Lavender.

For d > 10, the black line (observed) is greater than the red line (theo), and above the upper confidence envelope. Hence, we reject null hypothesis that private room types in Lavender are randomly distributed. This means that spatial clustering or private room types in Lavender is statistically significant, and clustering can be observed.

Overall, Lavender is clustered.

This is consistent with the test results from the G function, as well as the ppp graph that we have previously plotted to visualise.

Tanjong Pagar planning area

L function estimation

private_L_tp = Lest(private_tp_ppp, correction = "Ripley")
plot(private_L_tp, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of private room types at Tanjong Pagar are randomly distributed.

H1= The distribution of private room types at Tanjong Pagar are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

private_L_tp.csr <- envelope(private_tp_ppp, Lest, 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(private_L_tp.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

There are certain points which has the black line (observed) above the red line, while majority of the black line are below the red line.

For distances with black line (observed) greater than the red line (theo), they are above the upper confidence envelope, hence spatial clustering for these distance is statistically significant. Spatial randomness occurs for d < 10 for private room types in Balestier.

For distances with black line (observed) less than the red line (theo), they are below the lower confidence envelope, hence, spatial dispersion for these distance is statistically significant.

Overall, spatial dispersion is statistically significant. Hence, reject null hypothesis that the data points of private room types in Tanjong Pagar are randomly distributed.

This is inconsistent with the test results from the G function, and observation of ppp graph.

The L function of Tanjong Pagar concludes that Tanjong Pagar is clustered.

SHARED

Using G Function

Aljunied planning area

G function estimation

shared_G_AJ = Gest(shared_aj_ppp, correction="border")
plot(shared_G_AJ)

Performing Complete Spatial Randomness Test

H0: Distribution of shared room types at Aljunied are randomly distributed

H1: Distribution of shared room types at Aljunied are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

shared_G_AJ.csr <- envelope(shared_aj_ppp, Gest, nsim = 999)

## 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(shared_G_AJ.csr)

Since the estimated G(r) function lies within the envelope, the estimated G(r) is statistically not significant. Do not reject null hypothesis, and therefore, the distribution of shared room types in Aljunied is randomly distributed.

This observation is consistent with the ppp graph that we have previously plotted to visualise.

Balestier planning area

Computing G-function estimation

shared_G_bl = Gest(shared_bl_ppp, correction="best")
plot(shared_G_bl)

Performing Complete Spatial Randomness Test

H0: Distribution of shared room types at Balestier are randomly distributed

H1: Distribution of shared room types at Balestier are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

shared_G_bl.csr <- envelope(shared_bl_ppp, Gest, correction = "all", nsim = 999)

## 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(shared_G_bl.csr)

We are unable to deduce anything from this graph, since the Balestier subzone only has one point. It is impossible to deduce if this one point is random or clustered.

Lavender planning area

G function estimate

shared_G_LV = Gest(shared_lv_ppp, correction="border")
plot(shared_G_LV)

Performing Complete Spatial Randomness Test

H0: Distribution of shared room types at Lavender are randomly distributed

H1: Distribution of shared room types at Lavender are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

shared_G_lv.csr <- envelope(shared_lv_ppp, Gest, correction = "all", nsim = 999)

## 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(shared_G_lv.csr)

For 0< r < 60, the black line(observed) is within the envelope, the estimated G(r) is statistically not significant. Do not reject null hypothesis, and conclude that the distribution of shared room types in Lavender is randomly distributed.

For 60 < r < 65, the black line(observed) is above the envelope. Hence, reject null hypothesis. There is clustered distribution of shared room types listing in Lavender area.

Majority of the Lavender planning subzone area is clustered.

This observation is consistent with the ppp graph that we have previously plotted to visualise.

Tanjong Pagar planning area

G function estimate

shared_G_tp.csr = Gest(shared_tp_ppp, correction="border")
plot(shared_G_tp.csr)

Performing Complete Spatial Randomness Test

H0: Distribution of shared room types at Tanjong Pagar are randomly distributed

H1: Distribution of shared room types at Tanjong Pagar are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

plot(shared_G_tp.csr)

There are no observations of shared room types in Tanjong Pagar. Hence, unable to come up with a conclusion.

Using L Function

Aljunied planning area

L function estimation

shared_L_aj = Lest(shared_aj_ppp, correction = "Ripley")
plot(shared_L_aj, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of shared room types at Aljunied are randomly distributed.

H1= The distribution of shared room types at Aljunied are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

shared_L_aj.csr <- envelope(shared_aj_ppp, Lest, 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(shared_L_aj.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

For 0 < d < 50, the observed L value (black line) is smaller than the corresponding L (theo) value, and within the lower confidence envelope, spartial dispersion for that distance is not statistically significant. Hence, do not reject null hypothesis. We conclude that spatial clustering of shared room types in Aljunied is random.

This is consistent with the test results from the G function, as well as the ppp graph previously plotted.

Balestier planning area

L function estimation

shared_L_bl = Lest(shared_bl_ppp, correction = "Ripley")
plot(shared_L_bl, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of shared room types at Balestier are randomly distributed.

H1= The distribution of shared room types at Balestier are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

shared_L_bl.csr <- envelope(shared_bl_ppp, Lest, 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(shared_L_bl.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

It is impossible to deduce anything from the one point of data in Balestier.

Lavender planning area

L function estimation

shared_L_lv = Lest(shared_lv_ppp, correction = "Ripley")
plot(shared_L_lv, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of shared room types at Lavender are randomly distributed.

H1= The distribution of shared room types at Lavender are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

shared_L_lv.csr <- envelope(shared_lv_ppp, Lest, 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(shared_L_lv.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

For 0 < r < 5, the observed L value (black line) is smaller than the corresponding L (theo) valude, and within the lower confidence envelope, hence, spatial dispersion for this distance is statistically not significant. Do not reject null hypothesis. The distribution of shared room types in Lavender is randomly distributed.

For 10 < d < 50, the observed L value (black line) is greater than the corresponding L (theo) value, and within the upper confidence envelope, hence, spatial clustering for this distance is statistically not significant. Hence, do not reject null hypothesis. The distribution of shared room types in Lavender for this particular distance is randomly distributed.

For d > 50, the observed L value (black line) is greater than the corresponding L (theo) value, and above the upper confidence envelope, hence, spatial clustering for this distance is statistically significant. Reject null hypothesis. The distribution of shared room types in Lavender is clustered.

Hence, a part of Lavender is random, whereas a part of Lavender is clustered.

This is consistent with the test results from the G function, as well as the observations in the ppp graph.

Tanjong Pagar planning area

L function estimation

shared_L_tp = Lest(shared_tp_ppp, correction = "Ripley")
plot(shared_L_tp, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of shared room types at Tanjong Pagar are randomly distributed.

H1= The distribution of shared room types at Tanjong Pagar are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

shared_L_tp.csr <- envelope(shared_tp_ppp, Lest, 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(shared_L_tp.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

There are no points in the Tanjong Pagar planning subzone, hence unable to deduce anything.

ENTIRE HOME / APARTMENT

Using G Function

Aljunied planning area

G function estimation

apt_G_AJ = Gest(apt_aj_ppp, correction="border")
plot(apt_G_AJ)

Performing Complete Spatial Randomness Test

H0: Distribution of entire home / apartment room types at Aljunied are randomly distributed

H1: Distribution of entire home / apartment room types at Aljunied are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

apt_G_AJ.csr <- envelope(apt_aj_ppp, Gest, nsim = 999)

## 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(apt_G_AJ.csr)

From point 0, since the estimated G(r) function lies above the envelope, the estimated G(r) is statistically significant. Reject null hypothesis. The distribution of entire home / apartment room types in Aljunied are not randomly distributed. Hence, there is clustering in the distribution.

This observation is consistent with the ppp graph that we have previously plotted.

Balestier planning area

Computing G-function estimation

apt_G_bl = Gest(apt_bl_ppp, correction="best")
plot(apt_G_bl)

Performing Complete Spatial Randomness Test

H0: Distribution of entire home / apartment room types at Balestier are randomly distributed

H1: Distribution of entire home / apartment room types at Balestier are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

apt_G_bl.csr <- envelope(apt_bl_ppp, Gest, correction = "all", nsim = 999)

## 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(apt_G_bl.csr)

For r < 5, the estimated G(r) function lies within the envelope, hence, the estimated G(r) is statistically not significant. Do not reject null hypothesis. The distribution of entire home / apartment room type in Balestier for this distance is randomly distributed.

For r > 5, since the estimated G(r) function lies above the envelope, the estimated G(r) is statistically significant. Reject null hypothesis. The distribution of entire home / apartment room types in Balestier are not randomly distributed.

Majority of Balestier is clustered.

This observation is consistent with the ppp graph that we have previously plotted to visualise.

Lavender planning area

G function estimate

apt_G_LV = Gest(apt_lv_ppp, correction="border")
plot(apt_G_LV)

Performing Complete Spatial Randomness Test

H0: Distribution of entire home / apartment room types at Lavender are randomly distributed

H1: Distribution of entire home / apartment room types at Lavender are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

apt_G_lv.csr <- envelope(apt_lv_ppp, Gest, correction = "all", nsim = 999)

## 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(apt_G_lv.csr)

For 0 < r < 12, the black line(observed) is within the envelope, the estimated G(r) is statistically not significant. Do not reject null hypothesis, and conclude that the distribution of entire home / apartment room types in Lavender is randomly distributed.

For 12 < r < 45, the black line(observed) is above the envelope. Hence, reject null hypothesis. There is clustered distribution of entire home / apartment room types listing in Lavender area.

For r > 45, the black line (observed) is back to within the envelope, hence, there do not reject null hypothesis, distribution of entire home / apartment for this particular distance of room types in Lavender is randomly distributed.

An area in Lavender is randomly distributed, whereas another area is clustered.

This observation is consistent with the ppp graph that we have previously plotted.

Tanjong Pagar planning area

G function estimate

apt_G_TP = Gest(apt_tp_ppp, correction="border")
plot(apt_G_TP)

Performing Complete Spatial Randomness Test

H0: Distribution of entire home / apartment room types at Tanjong Pagar are randomly distributed

H1: Distribution of entire home / apartment room types at Tanjong Pagar are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

apt_G_tp.csr <- envelope(apt_tp_ppp, Gest, correction = "all", nsim = 999)

## 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(apt_G_tp.csr)

For 0 < r < 5, the black line(observed) is within the envelope, the estimated G(r) is statistically not significant. Do not reject null hypothesis, and conclude that the distribution of entire home / apartment room types in Tanjong Pagar is randomly distributed.

For 5 < r < 17, the black line(observed) is above the envelope. Hence, reject null hypothesis. There is clustered distribution of entire home / apartment room types listing in Tanjong Pagar area.

For r > 17, the black line (observed) is back to within the envelope, hence, therefore do not reject null hypothesis, distribution of entire home / apartment for this particular distance of room types in Tanjong Pagar is randomly distributed.

An area in Tanjong Pagar is randomly distributed, whereas another area is clustered.

This observation is consistent with the ppp graph that we have previously plotted.

Using L Function

Aljunied planning area

L function estimation

apt_L_aj = Lest(apt_aj_ppp, correction = "Ripley")
plot(apt_L_aj, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of entire home / apartment room types at Aljunied are randomly distributed.

H1= The distribution of entire home / apartment room types at Aljunied are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

apt_L_aj.csr <- envelope(apt_aj_ppp, Lest, nsim = 999, rank = 1, glocal=TRUE)

## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10 [etd 12:33] .........20 [etd 12:05] .........
## 30 [etd 11:54] .........40 [etd 11:50] .........50 [etd 11:36] ........
## .60 [etd 11:25] .........70 [etd 11:16] .........80 [etd 11:11] .......
## ..90 [etd 11:04] .........100 [etd 10:56] .........110 [etd 10:47] ......
## ...120 [etd 10:43] .........130 [etd 10:34] .........140 [etd 10:26] .....
## ....150 [etd 10:17] .........160 [etd 10:10] .........170 [etd 10:04] ....
## .....180 [etd 9:57] .........190 [etd 9:47] .........200 [etd 9:38] ...
## ......210 [etd 9:31] .........220 [etd 9:24] .........230 [etd 9:15] ..
## .......240 [etd 9:06] .........250 [etd 8:57] .........260 [etd 8:50] .
## ........270 [etd 8:42] .........280 [etd 8:35] .........290
##  [etd 8:27] .........300 [etd 8:19] .........310 [etd 8:12] .........
## 320 [etd 8:04] .........330 [etd 7:56] .........340 [etd 7:49] ........
## .350 [etd 7:41] .........360 [etd 7:34] .........370 [etd 7:26] .......
## ..380 [etd 7:19] .........390 [etd 7:11] .........400 [etd 7:04] ......
## ...410 [etd 6:57] .........420 [etd 6:49] .........430 [etd 6:42] .....
## ....440 [etd 6:35] .........450 [etd 6:28] .........460 [etd 6:21] ....
## .....470 [etd 6:14] .........480 [etd 6:07] .........490 [etd 6:00] ...
## ......500 [etd 5:52] .........510 [etd 5:46] .........520 [etd 5:38] ..
## .......530 [etd 5:31] .........540 [etd 5:24] .........550 [etd 5:17] .
## ........560 [etd 5:09] .........570 [etd 5:02] .........580
##  [etd 4:55] .........590 [etd 4:48] .........600 [etd 4:41] .........
## 610 [etd 4:34] .........620 [etd 4:27] .........630 [etd 4:20] ........
## .640 [etd 4:12] .........650 [etd 4:05] .........660 [etd 3:58] .......
## ..670 [etd 3:51] .........680 [etd 3:44] .........690 [etd 3:37] ......
## ...700 [etd 3:30] .........710 [etd 3:23] .........720 [etd 3:16] .....
## ....730 [etd 3:09] .........740 [etd 3:02] .........750 [etd 2:55] ....
## .....760 [etd 2:48] .........770 [etd 2:41] .........780 [etd 2:34] ...
## ......790 [etd 2:27] .........800 [etd 2:20] .........810 [etd 2:13] ..
## .......820 [etd 2:06] .........830 [etd 1:59] .........840 [etd 1:52] .
## ........850 [etd 1:44] .........860 [etd 1:37] .........870
##  [etd 1:30] .........880 [etd 1:23] .........890 [etd 1:16] .........
## 900 [etd 1:09] .........910 [etd 1:02] .........920 [etd 55 sec] ........
## .930 [etd 48 sec] .........940 [etd 41 sec] .........950 [etd 34 sec] .......
## ..960 [etd 27 sec] .........970 [etd 20 sec] .........980 [etd 13 sec] ......
## ...990 [etd 6 sec] ........ 999.
## 
## Done.

plot(apt_L_aj.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

From point 0, the observed L value (black line) is greater than the corresponding L (theo) value, and above the confidence envelope, hence, spatial clustering for entire home / apartment room types in Aljunied is statistically significant. We conclude that entire home / aoartment room types in Aljunied is clustered.

This is consistent with the test results from the G function and the ppp graph that was previously plotted.

Balestier planning area

L function estimation

apt_L_bl = Lest(apt_bl_ppp, correction = "Ripley")
plot(apt_L_bl, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of entire home / apartment room types at Balestier are randomly distributed.

H1= The distribution of entire home / apartment room types at Balestier are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

apt_L_bl.csr <- envelope(apt_bl_ppp, Lest, nsim = 999, rank = 1, glocal=TRUE)

## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10 [etd 3:19] .........20 [etd 3:16] .........
## 30 [etd 3:11] .........40 [etd 3:07] .........50 [etd 3:03] ........
## .60 [etd 3:02] .........70 [etd 3:00] .........80 [etd 2:59] .......
## ..90 [etd 2:56] .........100 [etd 2:53] .........110 [etd 2:51] ......
## ...120 [etd 2:49] .........130 [etd 2:46] .........140 [etd 2:44] .....
## ....150 [etd 2:42] .........160 [etd 2:41] .........170 [etd 2:39] ....
## .....180 [etd 2:37] .........190 [etd 2:35] .........200 [etd 2:33] ...
## ......210 [etd 2:31] .........220 [etd 2:30] .........230 [etd 2:28] ..
## .......240 [etd 2:26] .........250 [etd 2:23] .........260 [etd 2:21] .
## ........270 [etd 2:19] .........280 [etd 2:17] .........290
##  [etd 2:15] .........300 [etd 2:13] .........310 [etd 2:11] .........
## 320 [etd 2:09] .........330 [etd 2:07] .........340 [etd 2:05] ........
## .350 [etd 2:03] .........360 [etd 2:01] .........370 [etd 1:59] .......
## ..380 [etd 1:57] .........390 [etd 1:55] .........400 [etd 1:54] ......
## ...410 [etd 1:52] .........420 [etd 1:50] .........430 [etd 1:48] .....
## ....440 [etd 1:46] .........450 [etd 1:44] .........460 [etd 1:42] ....
## .....470 [etd 1:40] .........480 [etd 1:38] .........490 [etd 1:36] ...
## ......500 [etd 1:34] .........510 [etd 1:32] .........520 [etd 1:30] ..
## .......530 [etd 1:28] .........540 [etd 1:27] .........550 [etd 1:25] .
## ........560 [etd 1:23] .........570 [etd 1:21] .........580
##  [etd 1:20] .........590 [etd 1:18] .........600 [etd 1:16] .........
## 610 [etd 1:14] .........620 [etd 1:12] .........630 [etd 1:10] ........
## .640 [etd 1:08] .........650 [etd 1:06] .........660 [etd 1:04] .......
## ..670 [etd 1:03] .........680 [etd 1:01] .........690 [etd 59 sec] ......
## ...700 [etd 57 sec] .........710 [etd 55 sec] .........720 [etd 53 sec] .....
## ....730 [etd 51 sec] .........740 [etd 49 sec] .........750 [etd 47 sec] ....
## .....760 [etd 45 sec] .........770 [etd 44 sec] .........780 [etd 42 sec] ...
## ......790 [etd 40 sec] .........800 [etd 38 sec] .........810 [etd 36 sec] ..
## .......820 [etd 34 sec] .........830 [etd 32 sec] .........840 [etd 30 sec] .
## ........850 [etd 28 sec] .........860 [etd 27 sec] .........870
##  [etd 25 sec] .........880 [etd 23 sec] .........890 [etd 21 sec] .........
## 900 [etd 19 sec] .........910 [etd 17 sec] .........920 [etd 15 sec] ........
## .930 [etd 13 sec] .........940 [etd 11 sec] .........950 [etd 9 sec] .......
## ..960 [etd 7 sec] .........970 [etd 6 sec] .........980 [etd 4 sec] ......
## ...990 [etd 2 sec] ........ 999.
## 
## Done.

plot(apt_L_bl.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

From d < 5, the observed L value (black line) is greater than the corresponding L (theo) value, and lower than the upper confidence envelope, hence, spatial clustering for this particular distance is statistically not significant. Entire home / apartment room types in Balestier for this distance is random.

For d > 5, the observed L value (black line) is greater than the corresponding L (theo) value, and above the confidence envelope, hence, spatial clustering for entire home / apartment room types in Balestier is statistically significant. We conclude that entire home / aoartment room types in Balestier is clustered.

Majority of entire home / apartment room type distribution in Balestier is clustered.

This is consistent with the test results from the G function and the ppp graph that we have previously plotted.

Lavender planning area

L function estimation

apt_L_lv = Lest(apt_lv_ppp, correction = "Ripley")
plot(apt_L_lv, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of entire home / apartment room types at Lavender are randomly distributed.

H1= The distribution of entire home / apartment room types at Lavender are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

apt_L_lv.csr <- envelope(apt_lv_ppp, Lest, 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(apt_L_lv.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

For r < 12, the black line (observed) is smaller than the corresponding L (theo) value, and within the lower confidence envelope, hence, spatial dispersion for this particular distance is statistically not significant. We conclude that the distribution of entire home / apartment room types in Lavender is randomly distributed.

For 12 < r < 20, the black line (observed) is greater than the corresponding L (theo) value, and lower than the upper confidence envelope, hence, spatial clustering is not significant. We conclude that the distribution of entire home / apartment room types in Lavender is randomly distributed.

For r > 20, the black line (observed) is greater than the corresponding L (theo) value, and above the upper confidence envelope, hence, spatial clustering for this distance is statistically significant. Reject null hypothesis. The distribution of entire home / apartment room types in Lavender is clustered.

An area in Lavender is randomly distributed, whereas another area is clustered.

This is consistent with the test results from the G function and the ppp graph that we have previously plotted.

Tanjong Pagar planning area

L function estimation

apt_L_tp = Lest(apt_tp_ppp, correction = "Ripley")
plot(apt_L_tp, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of entire home / apartment room types at Tanjong Pagar are randomly distributed.

H1= The distribution of entire home / apartment room types at Tanjong Pagar are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

apt_L_tp.csr <- envelope(apt_tp_ppp, Lest, 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(apt_L_tp.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

For 0 < r < 5, the observed L value (black line) is smaller than the corresponding L (theo) value, and within the lower confidence envelope, hence spatial dispersion for this particular distance is not statistically significant. We conclude that the distribution of entire home / apartment room types in Tanjong Pagar is randomly distributed.

For 5 < r < 10, the observed L value (black line) is greater than the corresponding L (theo) value, and within the upper confidence envelope, hence, spatial clustering is not significant. Do not reject null hypothesis. The distribution of entire home / apartment in Tanjong Pagar is randomly distributed.

For r > 10, the observed L value (black line) is greater than the corresponding L (theo) value, and above the upper confidence envelope, hence, spatial clustering for this distance is statistically significant. Reject null hypothesis, hence, the distribution of entire home / apartment in Tanjong Pagar is clustered distribution.

Majority of the distribution of entire home / apartment room types in Tanjong Pagar is clustered.

This observation is the same as the G-function, and the ppp graph that we have previously plotted.

HOTEL

Using G function

Aljunied planning area

G function estimation

hotel_G_AJ = Gest(hotel_aj_ppp, correction="border")
plot(hotel_G_AJ)

Performing Complete Spatial Randomness Test

H0: Distribution of hotel room types at Aljunied are randomly distributed

H1: Distribution of hotel room types at Aljunied are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

hotel_G_AJ.csr <- envelope(hotel_aj_ppp, Gest, nsim = 999)

## 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(hotel_G_AJ.csr)

From point 0 < r < 40, the estimated G(r) function lies within the envelope, hence the estimated G(r) is statistically not significant. Do not reject null hypothesis. The distribuion of hotel room types in Aljunied are randomly distributed.

This observation is consistent with the ppp graph that we have previously plotted.

Balestier planning area

Computing G-function estimation

hotel_G_bl = Gest(hotel_bl_ppp, correction="best")
plot(hotel_G_bl)

Performing Complete Spatial Randomness Test

H0: Distribution of hotel room types at Balestier are randomly distributed

H1: Distribution of hotel room types at Balestier are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

hotel_G_bl.csr <- envelope(hotel_bl_ppp, Gest, correction = "all", nsim = 999)

## 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(hotel_G_bl.csr)

For 0 r < 40, the estimated G(r) function lies within the envelope, hence, the estimated G(r) is statistically not significant. Do not reject null hypothesis. The distribution of hotel room type in Balestier for this distance is randomly distributed.

For 40 < r < 60, since the estimated G(r) function lies above the envelope, the estimated G(r) is statistically significant. Reject null hypothesis. The distribution of hotel room types in Balestier are not randomly distributed.

For 60 < r < 65, the estimated G(r) function lies within the envelope, hence, the estimated G(r) is statistically not significant. Do not reject null hypothesis. The distribution of hotel room type in Balestier for this distance is randomly distributed.

For 65 < r < 105, since the estimated G(r) function lies above the envelope, the estimated G(r) is statistically significant. Reject null hypothesis. The distribution of hotel room types in Balestier are not randomly distributed.

For r > 105, the estimated G(r) function lies within the envelope, hence, the estimated G(r) is statistically not significant. Do not reject null hypothesis. The distribution of hotel room type in Balestier for this distance is randomly distributed.

Majority of the distribution of hotel room types in Balestier is clustered.

This observation is consistent with the ppp graph that we have previously plotted.

Lavender planning area

G function estimate

hotel_G_LV = Gest(hotel_lv_ppp, correction="border")
plot(hotel_G_LV)

Performing Complete Spatial Randomness Test

H0: Distribution of hotel room types at Lavender are randomly distributed

H1: Distribution of hotel room types at Lavender are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

hotel_G_lv.csr <- envelope(hotel_lv_ppp, Gest, correction = "all", nsim = 999)

## 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(hotel_G_lv.csr)

For 0 < r < 25, the black line (observed) is within the envelope, the estimated G(r) is statistically not significant. Do not reject null hypothesis, and conclude that the distribution of hotel room types in Lavender is randomly distributed.

For 25 < r < 35, the black line (observed) is above the envelope. Hence, reject null hypothesis. There is clustered distribution of hotel room types listing in Lavender area.

For 35 < r < 60, the black line (observed) is back to within the envelope, hence, there do not reject null hypothesis, distribution of entire home / apartment for this particular distance of room types in Lavender is randomly distributed.

For 60 < r < 65, the black line (observed) is above the envelope. Hence, reject null hypothesis. There is clustered distribution of hotel room types listing in Lavender area.

For 65 < r < 70, the black line (observed) is back to within the envelope, hence, there do not reject null hypothesis, distribution of entire home / apartment for this particular distance of room types in Lavender is randomly distributed.

For 70 < r < 75, the black line (observed) is above the envelope. Hence, reject null hypothesis. There is clustered distribution of hotel room types listing in Lavender area.

For r > 75, the black line (observed) is back to within the envelope, hence, there do not reject null hypothesis, distribution of entire home / apartment for this particular distance of room types in Lavender is randomly distributed.

Majority of the distribution of hotel room types in Lavender is clustered.

This observation is consistent with the ppp graph that we have previously plotted.

Tanjong Pagar planning area

G function estimate

hotel_G_TP = Gest(hotel_tp_ppp, correction="border")
plot(hotel_G_TP)

Performing Complete Spatial Randomness Test

H0: Distribution of hotel room types at Tanjong Pagar are randomly distributed

H1: Distribution of hotel room types at Tanjong Pagar are not randomly distributed

Null hypothesis will be rejected if p values is smaller than alpha value of 0.001

Monte Carlo test with G function (1000 simulations)

hotel_G_tp.csr <- envelope(hotel_tp_ppp, Gest, correction = "all", nsim = 999)

## 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(hotel_G_tp.csr)

There are only two points in the Tanjong Pagar planning subzone. These two points are insufficient for us to be able to draw a conclusion if the distribution is random or clustered.

Using L Function

Aljunied planning area

L function estimation

hotel_L_aj = Lest(hotel_aj_ppp, correction = "Ripley")
plot(hotel_L_aj, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of hotel room types at Aljunied are randomly distributed.

H1= The distribution of hotel room types at Aljunied are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

hotel_L_aj.csr <- envelope(hotel_aj_ppp, Lest, 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(hotel_L_aj.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

For 0 < d < 5, the observed L value (black line) is smaller than the corresponding L (theo) value, and within the lower confidence envelope, hence, spatial dispersion for that distance is statistically not significant. We conclude that the hotel room types in Aljunied for this particular distance is random.

For 5 < d < 100, the observed L value (black line) is greater than the corresponding L (theo) value, and lower than the upper confidence envelope, hence, spatial clustering for these distance is statistically not significant. We conclude that the hotel room types in Aljunied for this particular distance is random.

For 100 < d < 450, the observed L value (black line) is greater than its corresponding L (theo) value, and above the upper confidence envelope, hence, spatial clustering for this distance is statistically significant. We conclude that the hotel room types in Aljunied for this distance is clustered.

For d > 450, the observed L value (black line) is back to being greater than the corresponding L (theo) value, and lower than the upper confidence envelope, hence, spatial clustering for these distance is statistically not significant. We conclude that the hotel room types in Aljunied for this particular distance is random.

Majority of the distribution of hotel room types in Aljunied is random.

This is consistent with the test results from the G function, and the ppp graph that we have previously plotted.

Balestier planning area

L function estimation

hotel_L_bl = Lest(hotel_bl_ppp, correction = "Ripley")
plot(hotel_L_bl, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of hotel room types at Balestier are randomly distributed.

H1= The distribution of hotel room types at Balestier are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

hotel_L_bl.csr <- envelope(hotel_bl_ppp, Lest, 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(hotel_L_bl.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

For 0 < d < 5, the observed L value (black line) is smaller than the corresponding L (theo) value, and within the lower confidence envelope, hence, spatial dispersion for that distance is statistically not significant. We conclude that the hotel room types in Balestier for this particular distance is random.

For 5 < d < 45, the observed L value (black line) is greater than the corresponding L (theo) value, and lower than the upper confidence envelope, hence, spatial clustering for these distance is statistically not significant. We conclude that the hotel room types in Balestier for this particular distance is random.

For 45 < d < 50, he observed L value (black line) is greater than its corresponding L (theo) value, and above the upper confidence envelope, hence, spatial clustering for this distance is statistically significant. We conclude that the hotel room types in Balestier for this distance is clustered.

For 50 < d < 55, the observed L value (black line) is greater than the corresponding L (theo) value, and lower than the upper confidence envelope, hence, spatial clustering for these distance is statistically not significant. We conclude that the hotel room types in Balestier for this particular distance is random

For d > 55, the observed L value (black line) is greater than its corresponding L (theo) value, and above the upper confidence envelope, hence, spatial clustering for this distance is statistically significant. We conclude that the hotel room types in Balestier for this distance is clustered.

Majority of the distribution of hotel room types in Balestier are clustered.

This is consistent with the test results from the G function, and the ppp graph that we have previously plotted.

Lavender planning area

L function estimation

hotel_L_lv = Lest(hotel_lv_ppp, correction = "Ripley")
plot(hotel_L_lv, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of hotel room types at Lavender are randomly distributed.

H1= The distribution of hotel room types at Lavender are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

hotel_L_lv.csr <- envelope(hotel_lv_ppp, Lest, 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(hotel_L_lv.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

For 0 < d < 5, the observed L value (black line) is smaller than the corresponding L (theo) value, and within the lower confidence envelope, hence, spatial dispersion for that distance is statistically not significant. We conclude that the hotel room types in Lavender for this particular distance is random.

For 5 < d < 25, the observed L value (black line) is greater than the corresponding L (theo) value, and lower than the upper confidence envelope, hence, spatial clustering for these distance is statistically not significant. We conclude that the hotel room types in Lavender for this particular distance is random.

For d > 25, the observed L value (black line) is greater than its corresponding L (theo) value, and above the upper confidence envelope, hence, spatial clustering for this distance is statistically significant. We conclude that the hotel room types in Lavender for this distance is clustered.

Majority of the distribution of hotel room types in Lavender is clustered.

This is not consistent with the test results from the G function, and the ppp graph that we have previously plotted.

Tanjong Pagar planning area

L function estimation

hotel_L_tp = Lest(hotel_tp_ppp, correction = "Ripley")
plot(hotel_L_tp, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of hotel room types at Tanjong Pagar are randomly distributed.

H1= The distribution of hotel room types at Tanjong Pagar are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

hotel_L_tp.csr <- envelope(hotel_tp_ppp, Lest, 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(hotel_L_tp.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

It is impossible to deduce a conclusion based on the two points in Tanjong Pagar.

PART 6:

With reference to the results derived previously, we will now derive kernel density maps of Airbnb listing by room type

We will also display the kernel density maps on openstreetmap of Singapore, as well as deduce possible factors that determine the spatial patterns observed.

Kernel Density Estimation

Rescale

private_aj_ppp.km = rescale(private_aj_ppp, 1000, "km")
private_bl_ppp.km = rescale(private_bl_ppp, 1000, "km")
private_lv_ppp.km = rescale(private_lv_ppp, 1000, "km")
private_tp_ppp.km = rescale(private_tp_ppp, 1000, "km")

par(mfrow=c(2,2))
plot(private_aj_ppp.km, main="Aljunied")
plot(private_bl_ppp.km, main="Balestier")
plot(private_lv_ppp.km, main="Lavender")
plot(private_tp_ppp.km, main="Tanjong Pagar")

KDE for the 4 planning subzones

kde_private_aj_bw <- density(private_aj_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_private_aj_bw)

kde_private_bl_bw <- density(private_bl_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 
plot(kde_private_bl_bw)

kde_private_lv_bw <- density(private_lv_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 
plot(kde_private_lv_bw)

kde_private_tp_bw <- density(private_tp_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 
plot(kde_private_tp_bw)

Computing fixed bandwidth KDE - for the 4 planning subzones

kde_private_aj_250 <- density(private_aj_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_private_aj_250)

kde_private_bl_250 <- density(private_bl_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_private_bl_250)

kde_private_lv_250 <- density(private_lv_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_private_lv_250)

kde_private_tp_250 <- density(private_tp_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_private_tp_250)

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

Clark and Evans Test: Aljunied planning area

Since the p-value = 0.002 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random (points are clustered)

Additionally, since R = 0.74182 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(private_aj_ppp,
                correction="none",
                clipregion=NULL,
                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:  private_aj_ppp
## R = 0.7425, p-value = 0.002
## alternative hypothesis: two-sided

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

Clark and Evans Test: Balestier planning area

Since the p-value = 0.004 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random (points are clustered)

Additionally, since R = 0.79266 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(private_bl_ppp,
                correction="none",
                clipregion=NULL,
                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:  private_bl_ppp
## R = 0.8294, p-value = 0.002
## alternative hypothesis: two-sided

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

Clark and Evans Test: Lavender planning area

Since the p-value = 0.002 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random (points are clustered)

Additionally, since R = 0.78692 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(private_lv_ppp,
                correction="none",
                clipregion=NULL,
                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:  private_lv_ppp
## R = 0.77909, p-value = 0.002
## alternative hypothesis: two-sided

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

Clark and Evans Test: Tanjong Pagar planning area

Since the p-value = 0.08 > 0.05, do not reject null hypothesis that the points are randomly distributed. We can conclude that the points are random.

Additionally, since R = 1.3786 > 1, the nearest neighbour index tells us that the pattern exhibit randomness.

These analysis are consistent with our previous analysis.

clarkevans.test(private_tp_ppp,
                correction="none",
                clipregion=NULL,
                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:  private_tp_ppp
## R = 1.0617, p-value = 0.726
## alternative hypothesis: two-sided

SHARED

Kernel Density Estimation

Rescale

shared_aj_ppp.km = rescale(shared_aj_ppp, 1000, "km")
shared_bl_ppp.km = rescale(shared_bl_ppp, 1000, "km")
shared_lv_ppp.km = rescale(shared_lv_ppp, 1000, "km")
shared_tp_ppp.km = rescale(shared_tp_ppp, 1000, "km")

par(mfrow=c(2,2))
plot(shared_aj_ppp.km, main="Aljunied")
plot(shared_bl_ppp.km, main="Balestier")
plot(shared_lv_ppp.km, main="Lavender")
plot(shared_tp_ppp.km, main="Tanjong Pagar")

KDE for 4 different planning subzones

We omit Balestier and Tanjong Pagar since there are insufficient data points to plot a KDE

kde_shared_aj_bw <- density(shared_aj_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_shared_aj_bw)

kde_shared_lv_bw <- density(shared_lv_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 
plot(kde_shared_lv_bw)

Computing fixed bandwidth KDE - for 4 different planning subzones

KDE of Tanjong Pagar is in one solid colour since there are no points in that area.

kde_shared_aj_250 <- density(shared_aj_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_shared_aj_250)

kde_shared_bl_250 <- density(shared_bl_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_shared_bl_250)

kde_shared_lv_250 <- density(shared_lv_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_shared_lv_250)

kde_shared_tp_250 <- density(shared_tp_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_shared_tp_250)

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

We do not conduct for Balestier and Tanjong Pagar due to the lack of data.

Clark and Evans Test: Aljunied planning area

Since the p-value = 0.396 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random (points are clustered)

Additionally, since R = 0.97832 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(shared_aj_ppp,
                correction="none",
                clipregion=NULL,
                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:  shared_aj_ppp
## R = 0.74036, p-value = 0.068
## alternative hypothesis: two-sided

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

Clark and Evans Test: Lavender planning area

Since the p-value = 0.002 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random (points are clustered)

Additionally, since R = 0.68053 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(shared_lv_ppp,
                correction="none",
                clipregion=NULL,
                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:  shared_lv_ppp
## R = 0.82171, p-value = 0.002
## alternative hypothesis: two-sided

ENTIRE HOME / APARTMENT

Kernel Density Estimation

Rescale

apt_aj_ppp.km = rescale(apt_aj_ppp, 1000, "km")
apt_bl_ppp.km = rescale(apt_bl_ppp, 1000, "km")
apt_lv_ppp.km = rescale(apt_lv_ppp, 1000, "km")
apt_tp_ppp.km = rescale(apt_tp_ppp, 1000, "km")

par(mfrow=c(2,2))
plot(apt_aj_ppp.km, main="Aljunied")
plot(apt_bl_ppp.km, main="Balestier")
plot(apt_lv_ppp.km, main="Lavender")
plot(apt_tp_ppp.km, main="Tanjong Pagar")

KDE for 4 different planning subzones

kde_apt_aj_bw <- density(apt_aj_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_apt_aj_bw)

kde_apt_bl_bw <- density(apt_bl_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 
plot(kde_apt_bl_bw)

kde_apt_lv_bw <- density(apt_lv_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 
plot(kde_apt_lv_bw)

kde_apt_tp_bw <- density(apt_tp_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 
plot(kde_apt_tp_bw)

Computing fixed bandwidth KDE - 4 different planning subzones

kde_apt_aj_250 <- density(apt_aj_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_apt_aj_250)

kde_apt_bl_250 <- density(apt_bl_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_apt_bl_250)

kde_apt_lv_250 <- density(apt_lv_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_apt_lv_250)

kde_apt_tp_250 <- density(apt_tp_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_apt_tp_250)

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

Clark and Evans Test: Aljunied planning area

Since the p-value = 0.002 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random (points are clustered)

Additionally, since R = 0.58656 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(apt_aj_ppp,
                correction="none",
                clipregion=NULL,
                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:  apt_aj_ppp
## R = 0.60077, p-value = 0.002
## alternative hypothesis: two-sided

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

Clark and Evans Test: Balestier planning area

Since the p-value = 0.002 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random (points are clustered)

Additionally, since R = 0.69626 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(apt_bl_ppp,
                correction="none",
                clipregion=NULL,
                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:  apt_bl_ppp
## R = 0.73001, p-value = 0.002
## alternative hypothesis: two-sided

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

Clark and Evans Test: Lavender planning area

Since the p-value = 0.002 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random (points are clustered)

Additionally, since R = 0.83369 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(apt_lv_ppp,
                correction="none",
                clipregion=NULL,
                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:  apt_lv_ppp
## R = 0.85448, p-value = 0.002
## alternative hypothesis: two-sided

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

Clark and Evans Test: Tanjong Pagar planning area

Since the p-value = 0.002 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random (points are clustered)

Additionally, since R = 0.87722 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(apt_tp_ppp,
                correction="none",
                clipregion=NULL,
                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:  apt_tp_ppp
## R = 0.91251, p-value = 0.008
## alternative hypothesis: two-sided

HOTEL

Kernel Density Estimation

Rescale

hotel_aj_ppp.km = rescale(hotel_aj_ppp, 1000, "km")
hotel_bl_ppp.km = rescale(hotel_bl_ppp, 1000, "km")
hotel_lv_ppp.km = rescale(hotel_lv_ppp, 1000, "km")
hotel_tp_ppp.km = rescale(hotel_tp_ppp, 1000, "km")

par(mfrow=c(2,2))
plot(hotel_aj_ppp.km, main="Aljunied")
plot(hotel_bl_ppp.km, main="Balestier")
plot(hotel_lv_ppp.km, main="Lavender")
plot(hotel_tp_ppp.km, main="Tanjong Pagar")

KDE for 4 different planning subzones

We do not plot for tanjong pagar since there are only 2 points

kde_hotel_aj_bw <- density(hotel_aj_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_hotel_aj_bw)

kde_hotel_bl_bw <- density(hotel_bl_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 
plot(kde_hotel_bl_bw)

kde_hotel_lv_bw <- density(hotel_lv_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian") 
plot(kde_hotel_lv_bw)

Computing fixed bandwidth KDE - 4 different planning subzones

kde_hotel_aj_250 <- density(hotel_aj_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_hotel_aj_250)

kde_hotel_bl_250 <- density(hotel_bl_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_hotel_bl_250)

kde_hotel_lv_250 <- density(hotel_lv_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_hotel_lv_250)

kde_hotel_tp_250 <- density(hotel_tp_ppp.km, sigma=0.25, edge=TRUE, kernel="gaussian")
plot(kde_hotel_tp_250)

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

We do not conduct on Tanjong Pagar planning area due to the lack of points.

Clark and Evans Test: ALjunied planning area

Since the p-value = 0.002 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random (points are clustered)

Additionally, since R = 0.43705 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(hotel_aj_ppp,
                correction="none",
                clipregion=NULL,
                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:  hotel_aj_ppp
## R = 0.41587, p-value = 0.002
## alternative hypothesis: two-sided

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

Clark and Evans Test: Balestier planning area

Since the p-value = 0.006 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random (points are clustered)

Additionally, since R = 0.8107 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(hotel_bl_ppp,
                correction="none",
                clipregion=NULL,
                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:  hotel_bl_ppp
## R = 0.77209, p-value = 0.002
## alternative hypothesis: two-sided

Analysing Spatial Point Process Using Nearest Neighbour Index (to verify conclusion)

Clark and Evans Test: Lavender planning area

Since the p-value = 0.002 < 0.05, reject null hypothesis that the points are randomly distributed. We can conclude that the points are not random (points are clustered)

Additionally, since R = 0.51442 < 1, the nearest neighbour index tells us that the pattern exhibit clustering.

These analysis are consistent with our previous analysis.

clarkevans.test(hotel_lv_ppp,
                correction="none",
                clipregion=NULL,
                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:  hotel_lv_ppp
## R = 0.5523, p-value = 0.002
## alternative hypothesis: two-sided

Kernel Density Maps on openstreetmap of Singapore

ALJUNIED

Set as sf

aj = st_as_sf(aj)

Check projection

crs(aj)

## [1] "+proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs"

aj <- spTransform(private,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 "))

wgs84 <- CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs")
aj_wgs84 <- spTransform(aj, wgs84)
aj_wgs84@data['lon'] <- aj_wgs84@coords[,1]
aj_wgs84@data['lat'] <- aj_wgs84@coords[,2]
xys <- aj_wgs84@data[c('lon', 'lat')]

osm_aj <- c(left = min(xys$lon), bottom = min(xys$lat), 
         right = max(xys$lon), top = max(xys$lat))

basemap_aj <- get_stamenmap(osm_aj, zoom = 12, 
                         maptype = "toner-lite")

osm_aj <- ggmap(basemap_aj, extent = "device", 
               maprange=FALSE) +
  stat_density2d(data = aj_wgs84@data, 
                aes(x = lon, y = lat, 
                    alpha=..level.., 
                    fill = ..level..), 
                size = 0.01, bins = 16, 
                geom = 'polygon', 
                show.legend = TRUE) +
  scale_fill_gradient2("Transaction\nDensity", 
                       low = "#fffff8", 
                       high = "#8da0cb")
osm_aj

This kernel density map on openstreetmap of Singapore shows us the transaction Density of the Aljunied planning subzone. (Repeat this for the other 3 subzones)

BONUS part

Based on the other variables in the listings, what else can we conclude?

Data Exploratoration

Singapore’s Real Estate Scene

When looking for accommodation, location is usually the first consideration for any traveller. Using the longtitude and latitude variables, plot an interactive map and group the listings using the clustering function.

To view the specific clusters, simply click to zoom.

tmap_mode("view")

## tmap mode set to interactive viewing

listing_distribution <- leaflet(listings) %>%
  addTiles() %>%
  addMarkers(~longitude, ~latitude, labelOptions = labelOptions(noHide = F),
             clusterOptions = markerClusterOptions(),
             popup = paste0("<b> Name: </b>", listings$name, 
                            "<br/><b> Host Name: </b>", listings$host_name, 
                            "<br> <b> Price per Night: </b>", listings$price, 
                            "<br/><b> Room Type: </b>", listings$room_type,
                            "<br/><b> Review Rating: </b>", listings$review_scores_rating,
                            "<br/><b> Neighbourhood: </b>", listings$neighbourhood)) %>%
  addProviderTiles("CartoDB.Positron") 
# To mute the background, and highlight the cluster details.  
print(listing_distribution)
# Unsurprisingly, there are many listings around town but also many around the sengkang area. 

tmap_mode("plot")

## tmap mode set to plotting

Best Location by Average Location Score and Average Price

Importing the basemap (shapefile)

sgmap <- st_read(dsn = "data/geospatial", layer = "MP14_SUBZONE_WEB_PL")

## Reading layer `MP14_SUBZONE_WEB_PL' from data source `C:\Users\amoss\OneDrive\Documents\A2\data\geospatial' using driver `ESRI Shapefile'
## Simple feature collection with 323 features and 15 fields
## geometry type:  MULTIPOLYGON
## dimension:      XY
## bbox:           xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
## projected CRS:  SVY21

Clean out the review data and get the average location score

Mutate the format to a factor (so the data can be merged with the shapefile)

avg_location_reviews <- listings %>%
  filter(!(is.na(number_of_reviews))) %>%
  group_by(neighbourhood) %>%
  count(number_of_reviews) %>% 
  filter(n>"1") %>%
  summarise(avg_loc_review = mean(number_of_reviews), na.rm=TRUE) %>%
  mutate(neighbourhood = toupper(neighbourhood)) %>% 
  mutate(neighbourhood = factor(neighbourhood, level=levels(sgmap$PLN_AREA_N)))

Get average price before mutating the data to factor format to ensure that it can be merged.

avg_price <- listings %>%
  filter(!(is.na(price))) %>%
  group_by(neighbourhood) %>%
  count(price) %>% # remove this for the skewed vers
  filter(n>"1") %>% # remove this for the skewed vers
  mutate(price_int = as.numeric(price)) %>%
  summarise(avg_price = mean(price_int), na.rm = TRUE) %>%
  mutate(neighbourhood = toupper(neighbourhood)) %>% 
  mutate(neighbourhood = factor(neighbourhood, level=levels(sgmap$PLN_AREA_N)))

Merge the data using the neighbourhood groups e.g Pasir Ris, Tampines etc

Merge the basemap with the average location reviews

sgmap_locationreviews <- left_join(sgmap, avg_location_reviews, 
                                   by = c("PLN_AREA_N" = "neighbourhood"))

## Warning: Column `PLN_AREA_N`/`neighbourhood` joining character vector and
## factor, coercing into character vector

Merge the basemap & location review with the average price

sgmap_locationreviews_price <- left_join(sgmap_locationreviews, avg_price, 
                                         by = c("PLN_AREA_N" = "neighbourhood"))

## Warning: Column `PLN_AREA_N`/`neighbourhood` joining character vector and
## factor, coercing into character vector

Generate both graphs together for easy comparison

sgmap_locationanalysis_graph <- tm_shape(sgmap_locationreviews_price) + 
  tm_fill(c("avg_loc_review", "avg_price"), style = "quantile", palette = "Blues",
          title=c("Average Location Score", "Average Price")) +
  tm_layout(panel.labels = c("Average Location Score by Neighbourhood", 
                             "Average Price by Neighbourhood"), legend.position = c("right", "bottom")) +
  tm_borders(alpha = 0.2)
print(sgmap_locationanalysis_graph)

## Warning: The shape sgmap_locationreviews_price is invalid. See sf::st_is_valid

At first glance, this data shows us that the East and North regions have higher prices despite being usually populated by local residents. Neighbourhoods in the Central region are shown to be the “sweet spot”, where the location score is high and the average price is low.

DEMAND per neighborhood

Total reviews as a proxy for demand per neighbourhood

totalreview_neighbourhood <- listings %>%
  select(neighbourhood, number_of_reviews) %>% 
  group_by(neighbourhood) %>% 
  summarise(avg_totalreviews = mean(number_of_reviews), na.rm=TRUE) %>%
  mutate(neighbourhood = toupper(neighbourhood)) %>% 
  mutate(neighbourhood = factor(neighbourhood, level=levels(sgmap$PLN_AREA_N)))

sgmap_totalreviews <- left_join(sgmap, totalreview_neighbourhood, 
                                by = c("PLN_AREA_N" = "neighbourhood"))

## Warning: Column `PLN_AREA_N`/`neighbourhood` joining character vector and
## factor, coercing into character vector

Plotting Average Demand by Neighbourhood

avg_demand_graph <- tm_shape(sgmap_totalreviews) + 
  tm_fill("avg_totalreviews", style = "quantile", 
          legend.hist = F, title="Average No. of Reviews") + 
  tm_layout(main.title="Average Demand by Neighbourhood", 
            legend.position = c("right", "bottom"), frame = F) + 
  tm_borders(alpha = 0.2)
print(avg_demand_graph)

## Warning: The shape sgmap_totalreviews is invalid. See sf::st_is_valid

This graph above was plotted by mapping out the average demand per neighbourhood using the number of unique listings as a proxy. It is intriguing to note that the demand for Airbnb’s is particularly high in the East region. This could be due to the location being near the airport, and travellers wants convenience right after they touch down in Singapore.

Taking into account that the North and West regions have relatively little listings, the data is mildly skewed. Taking this into account, the average location score and average prices were plotted after removing outliners (neighbourhoods with zero or one listing).

With the analysis conducted above, we can have a rough idea of the different factors that affect Airbnb, such as,

Which area is the best?

Which area is expensive?

Through plotting geospatial graph, we can have a visualisation of the different areas on the map that may have better demand, or better location score.

There are many more analysis that can be conducted, such as Demand and Price analysis. This includes seasonality in demand, seasonality in prices. Consumer analysis can also be conducted, such as how to appeal the Airbnb to users. However, these analysis are not geospatial in nature, and hence it will not be analysed in this report.