1.0 Overview

This report focuses on creating interactive visualisations for second order spatial point pattern analysis, to allow analysts to better explore and draw insights from the results.

The analysis aims to characterize spatial point patterns of childcare centres in Singapore using distance-based methods. Also known as second order property of the point pattern, it examines the stochastic dependence between observed point processes (presence of childcare centres) by comparing distances between points in the dataset with that of theoretical models (poisson processes).

The research question related to this topic:

Is the occurrence of an event dependent on the presence of other events?

A step-by-step implementation of second-order point pattern analysis in R can be found in Professor Kam Tin Seong’s In-class tutorial

2.0 Installing Required Packages

The list of packages required for this exercise is given below:

spatstat: A package for statistical analysis of spatial data, specifically Spatial Point Pattern Analysis.
rgdal: Used to import geospatial data and output as spatial class objects from sp package
maptools,ggplot2,ggthemes,plotly: Packages used to plot interactive visualisations for distance-based summary statistics and testing

packages = c('rgdal', 'maptools', 'spatstat','ggplot2','ggthemes','plotly')
for (p in packages){
if(!require(p, character.only = T)){
install.packages(p)
}
library(p,character.only = T)
}

3.0 Data Preparation

3.1 Data source

Two data sets will be used for this exercise, both of which can be downloaded from data.gov.sg.

Childcare centres geospatial data: Original data is in KML format and was converted into ESRI shapefile format
URA Planning Subzone boundary geospatial data: Original data is in ESRI shapefile format

3.2 Reading in shapefiles

readORG() of rgdal package is used to read in the shapefiles. The output is a SpatialPolygonsDataframe object of the sp package.

childcare <- readOGR(dsn = "data", layer="CHILDCARE")
mpsz = readOGR(dsn = "data", layer="MP14_SUBZONE_WEB_PL")

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\denis\OneDrive\Desktop\MITB\Term 3\IS415- Geospatial Analytics\In-class exercises\In-class_Ex08 supplementary\data", layer: "CHILDCARE"
## with 1312 features
## It has 18 fields
## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\denis\OneDrive\Desktop\MITB\Term 3\IS415- Geospatial Analytics\In-class exercises\In-class_Ex08 supplementary\data", layer: "MP14_SUBZONE_WEB_PL"
## with 323 features
## It has 15 fields

3.2 Creating `ppp` objects

Spatstat package will be used to perform point pattern analysis. A new class of object ppp will created to use spatstat functions. However since there is no direct way to convert SpatialDataFrame into ppp, it is necessary to first convert the SpatialDataFrame into Spatial object. This can be achieved using as() function.

childcare_sp <- as(childcare, "SpatialPoints")

as.ppp() function of spatstat is then used to convert the spatial data into spatstat’s ppp object format.

childcare_ppp <- as(childcare_sp, "ppp")
childcare_ppp

## Planar point pattern: 1312 points
## window: rectangle = [11203.01, 45404.24] x [25667.6, 49300.88] units

3.3 Checking for duplicated spatial point events

duplicated(childcare_ppp)

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The print out above shows that there are several duplication point events (i.e. TRUE). Duplicated points must be avoided when doing statistical test as the number of points used to compute the Poisson distribution will be different from the distribution of observed events, and this renders the test inaccurate.

While there are several methods to treat duplicated point events, this exercise implements the jittering approach, which is to apply random displacements to each point in a point pattern.

childcare_ppp_jit <- rjitter(childcare_ppp, retry=TRUE, nsim=1, drop=TRUE)

# check that there are no more duplicated points
duplicated(childcare_ppp_jit)

##    [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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The ppp object before and after jittering is plotted side-by-side for a quick visual comparison.

par(mfrow=c(1,2))
plot(childcare_ppp)
plot(childcare_ppp_jit)

3.4 Extracting study area

There are several non-residential planning areas in Singapore, such as the Central Water Catchment Area. Naturally, there would be no childcare centres located in those planning areas, resulting in empty regions within the area of study. As such, it may be more meaningful to analyse the spatial distribution of childcare centres within a planning area instead of Singapore as a whole.

The code chunk below is used to extract the polygons of individual planning areas. The output is a SpatialPolygonsDataFrame object.

For this study, Tampines is extracted for analysis.

tm = mpsz[mpsz@data$PLN_AREA_N == "TAMPINES",]

The SpatialPolygonsDataFrame object is then converted to SpatialPolygons object, before further converting it to owin objects, which is required by spatstat to define the boundaries of the study area (i.e. Tampines).

tm_sp = as(tm, "SpatialPolygons")

tm_owin = as(tm_sp, "owin")

The final ppp object is then created using the code chunk below, using the owin object derived above.

childcare_tm_ppp = childcare_ppp_jit[tm_owin]

4.0 Second-order Point Pattern Analysis- A Brief Introduction

4.1 Nearest-neighbour distance & G-function

The nearest-neighbour distance is the measure of distance from each point to its nearest neighbour. G-function measures the distribution of distances from an arbitrary event to its nearest neighbour.

Gest() of spatstat package is used to compute the G-function statistics.

G_TM = Gest(childcare_tm_ppp, correction = "border")
plot(G_TM)

4.2 empty space distance & F-function

Empty space distance is the measure of distance from a fixed reference location in the study window to the nearest data point, while the F function is the cumulative distribution function of the empty space distance.

Fest() of spatstat package is used to compute the F-function statistics.

F_tm.csr <- envelope(childcare_tm_ppp, Fest, correction = "all", nsim = 999)
plot(F_tm.csr)

## 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.

4.3 Pairwise distance & K-function (and L-function)

Pairwise distance is the measure of the distance between all distinct pairs of points in the pattern. The K function computes cumulative average number of points that lie closer than a distance r, standardized by dividing by the intensity of the study region.

A commonly-used variarion of K-function is the L-function, which transforms the theoretical Possion K-function to a straight line. The purpose is to make visual assessment of deviation easier.

Kest() and Lest() of spatstat package is used to compute the K-function and L-function statistics, respectively.

K_tm = Kest(childcare_tm_ppp, correction = "Ripley")
plot(K_tm, . -r ~ r, 
     ylab= "K(d)-r", xlab = "d(m)", 
     xlim=c(0,1000))

L_tm = Lest(childcare_tm_ppp, correction = "Ripley")
plot(L_tm, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)", 
     xlim=c(0,1000))

4.4 Performing Complete Spatial Randomness Test

The summary statistics such as K, L, F and G-functions can be used for hypothesis testing to assess if a point pattern exhibits statistically significant clustering or segregation as compared a spatially random Poisson process.

Onr approach is using Monte carlo simulation to construct an envelope of simulated curves of random point patterns. The envelope forms the acceptance interval for the hypothesis test. envelope() function of spatstat package is used to perform the Monte Carlo simulation.

The null and alternative hypotheses are stated below:

Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.

H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.

The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001 (the alpha value is dependent on the number of simulations performed, as indicated in the nsim argument).

L_tm.csr <- envelope(childcare_tm_ppp, Lest, nsim = 999, rank = 1, glocal=TRUE)
plot(L_tm.csr, . - r ~ r, 
     xlab="d", ylab="L(d)-r", xlim=c(0,500))

## Generating 999 simulations of CSR  ...
## 1, 2, 3, ......10 [etd 4:07] .........20 [etd 3:43] .........
## 30 [etd 3:37] .........40 [etd 3:29] .........50 [etd 3:21] ........
## .60 [etd 3:17] .........70 [etd 3:16] .........80 [etd 3:18] .......
## ..90 [etd 3:15] .........100 [etd 3:13] .........110 [etd 3:13] ......
## ...120 [etd 3:11] .........130 [etd 3:11] .........140 [etd 3:08] .....
## ....150 [etd 3:08] .........160 [etd 3:05] .........170 [etd 3:03] ....
## .....180 [etd 3:00] .........190 [etd 2:57] .........200 [etd 2:54] ...
## ......210 [etd 2:52] .........220 [etd 2:50] .........230 [etd 2:47] ..
## .......240 [etd 2:45] .........250 [etd 2:44] .........260 [etd 2:41] .
## ........270 [etd 2:39] .........280 [etd 2:36] .........290
##  [etd 2:35] .........300 [etd 2:33] .........310 [etd 2:30] .........
## 320 [etd 2:28] .........330 [etd 2:27] .........340 [etd 2:25] ........
## .350 [etd 2:22] .........360 [etd 2:20] .........370 [etd 2:17] .......
## ..380 [etd 2:15] .........390 [etd 2:12] .........400 [etd 2:10] ......
## ...410 [etd 2:08] .........420 [etd 2:06] .........430 [etd 2:03] .....
## ....440 [etd 2:01] .........450 [etd 1:59] .........460 [etd 1:57] ....
## .....470 [etd 1:55] .........480 [etd 1:53] .........490 [etd 1:51] ...
## ......500 [etd 1:49] .........510 [etd 1:46] .........520 [etd 1:44] ..
## .......530 [etd 1:42] .........540 [etd 1:40] .........550 [etd 1:37] .
## ........560 [etd 1:35] .........570 [etd 1:33] .........580
##  [etd 1:31] .........590 [etd 1:28] .........600 [etd 1:26] .........
## 610 [etd 1:24] .........620 [etd 1:22] .........630 [etd 1:20] ........
## .640 [etd 1:18] .........650 [etd 1:16] .........660 [etd 1:14] .......
## ..670 [etd 1:12] .........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 48 sec] ...
## ......790 [etd 45 sec] .........800 [etd 43 sec] .........810 [etd 41 sec] ..
## .......820 [etd 39 sec] .........830 [etd 37 sec] .........840 [etd 35 sec] .
## ........850 [etd 32 sec] .........860 [etd 30 sec] .........870
##  [etd 28 sec] .........880 [etd 26 sec] .........890 [etd 24 sec] .........
## 900 [etd 22 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.

5.0 Building an interative plot with ggplotly

The previous code chunks uses plot() to visualise the envelopes of the second-order summary statistics (such as L-function). The output is a static plot, therefore it can be difficult to make accurate guesstimates of the statistics and the corresponding distance, r.

The below code chunk converts the output (which is in a list form) into a dataframe, which can be used to generate a similar plot using appropriate aesthetic mappings from ggplot package. Finally, ggplotly() is used to convert the ggplot into an interactive plotly visualisation.

The codes were referenced from a R-blogger article. Further modifications were made to enhance the user experience by customizing the tooltips for greater clarity and intuition.

title <- "Pairwise Distance: L function"

Lcsr_df <- as.data.frame(L_tm.csr)

colour=c("#0D657D","#ee770d","#D3D3D3")
csr_plot <- ggplot(Lcsr_df, aes(r, obs-r))+
  # plot observed value
  geom_line(colour=c("#4d4d4d"))+
  geom_line(aes(r,theo-r), colour="red", linetype = "dashed")+
  # plot simulation envelopes
  geom_ribbon(aes(ymin=lo-r,ymax=hi-r),alpha=0.1, colour=c("#91bfdb")) +
  xlab("Distance r (m)") +
  ylab("L(r)-r") +
  geom_rug(data=Lcsr_df[Lcsr_df$obs > Lcsr_df$hi,], sides="b", colour=colour[1])  +
  geom_rug(data=Lcsr_df[Lcsr_df$obs < Lcsr_df$lo,], sides="b", colour=colour[2]) +
  geom_rug(data=Lcsr_df[Lcsr_df$obs >= Lcsr_df$lo & Lcsr_df$obs <= Lcsr_df$hi,], sides="b", color=colour[3]) +
  theme_tufte()+
  ggtitle(title)

text1<-"Significant clustering"
text2<-"Significant segregation"
text3<-"Not significant clustering/segregation"

# the below conditional statement is required to ensure that the labels (text1/2/3) are assigned to the correct traces
if (nrow(Lcsr_df[Lcsr_df$obs > Lcsr_df$hi,])==0){ 
  if (nrow(Lcsr_df[Lcsr_df$obs < Lcsr_df$lo,])==0){ 
    ggplotly(csr_plot, dynamicTicks=T) %>%
      style(text = text3, traces = 4) %>%
      rangeslider() 
  }else if (nrow(Lcsr_df[Lcsr_df$obs >= Lcsr_df$lo & Lcsr_df$obs <= Lcsr_df$hi,])==0){ 
    ggplotly(csr_plot, dynamicTicks=T) %>%
      style(text = text2, traces = 4) %>%
      rangeslider() 
  }else {
    ggplotly(csr_plot, dynamicTicks=T) %>%
      style(text = text2, traces = 4) %>%
      style(text = text3, traces = 5) %>%
      rangeslider() 
  }
} else if (nrow(Lcsr_df[Lcsr_df$obs < Lcsr_df$lo,])==0){
  if (nrow(Lcsr_df[Lcsr_df$obs >= Lcsr_df$lo & Lcsr_df$obs <= Lcsr_df$hi,])==0){
    ggplotly(csr_plot, dynamicTicks=T) %>%
      style(text = text1, traces = 4) %>%
      rangeslider() 
  } else{
    ggplotly(csr_plot, dynamicTicks=T) %>%
      style(text = text1, traces = 4) %>%
      style(text = text3, traces = 5) %>%
      rangeslider()
  }
} else{
  ggplotly(csr_plot, dynamicTicks=T) %>%
    style(text = text1, traces = 4) %>%
    style(text = text2, traces = 5) %>%
    style(text = text3, traces = 6) %>%
    rangeslider()
  }

The main features of the above visualisation:

The observed and theoretical values of L(r)-r (including the upper and lower curves of the simulated envelope) can be found in the tooltip upon hovering the cursor over the geometry layers.
The range slider below the plot enables users to pan and zoom in to a specific range of distance.
The colored bands at the bottom of the line graph gives a clearer indication of significant or insignificant spatial segregation/ clustering at distance r. Dark green bands indicate significant clustering, orange indicate significant segregation, while grey indicates insignificant clustering/segregation. Tooltips were added to provide color legend information.

6.0 References

Professor Kam Tin Seong’s In-class tutorial
QuantumPlots with ggplot2 and spatstat ( R-blogger Article )

Interactive Plotting of Second-order Spatial Point Patterns Analysis: Childcare Centres in Singapore

Denise Adele Chua
View my tableau public account

13 May 2020 (Updated: 2020-05-15)

1.0 Overview

2.0 Installing Required Packages

3.0 Data Preparation

3.1 Data source

3.2 Reading in shapefiles

3.2 Creating `ppp` objects

3.3 Checking for duplicated spatial point events

3.4 Extracting study area

4.0 Second-order Point Pattern Analysis- A Brief Introduction

4.1 Nearest-neighbour distance & G-function

4.2 empty space distance & F-function

4.3 Pairwise distance & K-function (and L-function)

4.4 Performing Complete Spatial Randomness Test

5.0 Building an interative plot with ggplotly

6.0 References

Interactive Plotting of Second-order Spatial Point Patterns Analysis: Childcare Centres in Singapore

Denise Adele Chua View my tableau public account

13 May 2020 (Updated: 2020-05-15)

1.0 Overview

2.0 Installing Required Packages

3.0 Data Preparation

3.1 Data source

3.2 Reading in shapefiles

3.2 Creating ppp objects

3.3 Checking for duplicated spatial point events

3.4 Extracting study area

4.0 Second-order Point Pattern Analysis- A Brief Introduction

4.1 Nearest-neighbour distance & G-function

4.2 empty space distance & F-function

4.3 Pairwise distance & K-function (and L-function)

4.4 Performing Complete Spatial Randomness Test

5.0 Building an interative plot with ggplotly

6.0 References

Denise Adele Chua
View my tableau public account

3.2 Creating `ppp` objects