1 Overview

In this hands-on exercise, you will gain hands-on experience on using appropriate R functions to analyse spatial point events. The case study aims to discover the spatial point processes of childecare centres in Singapore.

1.1 The research questions

The specific questions we would like to answer are as follows:

are the childcare centre centres in a planning area randomly distributed?
if the answer is not, then the next logical question is where are the locations with higher concentration of childcare centres?

1.2 The data

To provide answers to the questions above, two data sets will be used. They are:

Childcare centre: this data is downloaded from www.data.gov.sg. The original data is in KML format. It has been coverted into ESRI shapefile format.
URA Planning Subzone boundary data (i.e. MP14_SUBZONE_WEB_PL). It is in ESRI shapefile format.

2 Installing and Loading the R packages

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

3 Spatial Data Wrangling

3.1 Importing the spatial data

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

## OGR data source with driver: ESRI Shapefile 
## Source: "D:\IS415-AY2020-21T1\03-Hands-on Exercises\Hands-on_Ex05_SPPA-2ndOrder\data", layer: "CHILDCARE"
## with 1312 features
## It has 18 fields

mpsz = readOGR(dsn = "data", layer="MP14_SUBZONE_WEB_PL")

## OGR data source with driver: ESRI Shapefile 
## Source: "D:\IS415-AY2020-21T1\03-Hands-on Exercises\Hands-on_Ex05_SPPA-2ndOrder\data", layer: "MP14_SUBZONE_WEB_PL"
## with 323 features
## It has 15 fields

3.2 Converting the spatial point data frame into generic sp format

spatstat requires the analytical data in ppp object form. There is no direct way to convert a SpatialDataFrame into ppp object. We need to convert the SpatialDataFrame into Spatial object first.

The codes below will convert the SpatialPoint and SpatialPolygon data frame into generic spatialpoints and spatialpolygons objects.

childcare_sp <- as(childcare, "SpatialPoints")

3.3 Converting the generic sp format into spatstat’s ppp format

Now, we will use as.ppp() function to convert the spatial data into spatstat’s ppp object format.

childcare_ppp <- as(childcare_sp, "ppp")

3.4 Checking for duplicated saptial point events

The code chunk below is used to check if there is any duplicated point events.

duplicated(childcare_ppp)

The print out above shows that there are several duplication point events (i.e. TRUE)

The code chunk uses unique() to eliminate duplicate point events.

childcare_ppp_u <- unique(childcare_ppp)
duplicated(childcare_ppp_u)

Notice that there are nomore duplicated point events in childcare_ppp_u object.

Warning: In practice, it is not advisible to merely dropping the duplicated point events. We should study the context carefully. A better approach is to use the jittering approach discussed in previous hands-on exercise to address the issue.

The code chunk below implements the jittering approach.

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

Then, use the code chunk below to ensure that all duplicated point events have been jittered.

duplicated(childcare_ppp_jit)

3.5 Extracting study area

The code chunk below will be used to extract the target planning areas.

pg = mpsz[mpsz@data$PLN_AREA_N == "PUNGGOL",]
tm = mpsz[mpsz@data$PLN_AREA_N == "TAMPINES",]
ck = mpsz[mpsz@data$PLN_AREA_N == "CHOA CHU KANG",]
jw = mpsz[mpsz@data$PLN_AREA_N == "JURONG WEST",]

Plotting target planning areas

plot(pg)

plot(tm)

plot(ck)

plot(jw)

3.6 Converting the spatial point data frame into generic sp format

Next, we will convert these SpatialPolygonDataFrame into generic spatialpolygons objects

childcare_sp = as(childcare, "SpatialPoints")
pg_sp = as(pg, "SpatialPolygons")
tm_sp = as(tm, "SpatialPolygons")
ck_sp = as(ck, "SpatialPolygons")
jw_sp = as(jw, "SpatialPolygons")

3.7 Creating owin object

Now, we will convert these SpatialPolygons objects into owin objects that is required by spatstat.

pg_owin = as(pg_sp, "owin")
tm_owin = as(tm_sp, "owin")
ck_owin = as(ck_sp, "owin")
jw_owin = as(jw_sp, "owin")

3.8 Combining childcare points and the study area

By doing the code below, we are able to extract childcare that is within the specific region to do our analysis later on.

childcare_pg_ppp = childcare_ppp_jit[pg_owin]
childcare_tm_ppp = childcare_ppp_jit[tm_owin]
childcare_ck_ppp = childcare_ppp_jit[ck_owin]
childcare_jw_ppp = childcare_ppp_jit[jw_owin]

3.9 Visualising the ppp objects

It is a good practice to examine the output ppp objects visually. The code chunk below can be used to plot the ppp objected created in the earlier step.

plot(childcare_ck_ppp)

plot(childcare_jw_ppp)

plot(childcare_pg_ppp)

plot(childcare_tm_ppp)

4 Analysing Spatial Point Process Using G-Function

The G function measures the distribution of the distances from an arbitrary event to its nearest event. In this section, you will learn how to compute G-function estimation by using Gest() of spatstat package. You will also learn how to perform monta carlo simulation test using envelope() of spatstat package.

4.1 Choa Chu Kang planning area

4.1.1 Computing G-function estimation

The code chunk below is used to compute G-function using Gest() of spatat package.

G_CK = Gest(childcare_ck_ppp, correction = "border")
plot(G_CK)

4.1.2 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 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.

Monte Carlo test with G-fucntion

G_CK.csr <- envelope(childcare_ck_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(G_CK.csr)

4.2 Tampines planning area

4.2.1 Computing G-function estimation

G_tm = Gest(childcare_tm_ppp, correction = "best")
plot(G_tm)

4.2.2 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 childcare services at Tampines are randomly distributed.

H1= The distribution of childcare services at Tampines are not randomly distributed.

The null hypothesis will be rejected is p-value is smaller than alpha value of 0.001.

The code chunk below is used to perform the hypothesis testing.

G_tm.csr <- envelope(childcare_tm_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(G_tm.csr)

5 Analysing Spatial Point Process Using F-Function

The F function estimates the empty space function F(r) or its hazard rate h(r) from a point pattern in a window of arbitrary shape. In this section, you will learn how to compute F-function estimation by using Fest() of spatstat package. You will also learn how to perform monta carlo simulation test using envelope() of spatstat package.

5.1 Choa Chu Kang planning area

5.1.1 Computing F-function estimation

The code chunk below is used to compute F-function using Fest() of spatat package.

F_CK = Fest(childcare_ck_ppp)
plot(F_CK)

5.1.2 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 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.

Monte Carlo test with F-fucntion

F_CK.csr <- envelope(childcare_ck_ppp, Fest, 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(F_CK.csr)

5.2 Tampines planning area

5.2.1 Computing F-function estimation

Monte Carlo test with F-fucntion

F_tm = Fest(childcare_tm_ppp, correction = "best")
plot(F_tm)

5.2.2 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 childcare services at Tampines are randomly distributed.

H1= The distribution of childcare services at Tampines are not randomly distributed.

The null hypothesis will be rejected is p-value is smaller than alpha value of 0.001.

The code chunk below is used to perform the hypothesis testing.

F_tm.csr <- envelope(childcare_tm_ppp, Fest, 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(F_tm.csr)

6 Analysing Spatial Point Process Using K-Function

K-function measures the number of events found up to a given distance of any particular event. In this section, you will learn how to compute K-function estimates by using Kest() of spatstat package. You will also learn how to perform monta carlo simulation test using envelope() of spatstat package.

6.1 Choa Chu Kang planning area

6.1.1 Computing K-fucntion estimate

K_ck = Kest(childcare_ck_ppp, correction = "Ripley")
plot(K_ck, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

6.1.2 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 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 code chunk below is used to perform the hypothesis testing.

K_ck.csr <- envelope(childcare_ck_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)

## Generating 99 simulations of CSR  ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
## 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
## 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.
## 
## Done.

plot(K_ck.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

6.2 Tampines planning area

6.2.1 Computing K-fucntion estimation

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

6.2.2 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 childcare services at Tampines are randomly distributed.

H1= The distribution of childcare services at Tampines are not randomly distributed.

The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.

The code chunk below is used to perform the hypothesis testing.

K_tm.csr <- envelope(childcare_tm_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)

## Generating 99 simulations of CSR  ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
## 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
## 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.
## 
## Done.

plot(K_tm.csr, . - r ~ r, 
     xlab="d", ylab="K(d)-r", xlim=c(0,500))

7 Analysing Spatial Point Process Using L-Function

In this section, you will learn how to compute L-function estimation by using Lest() of spatstat package. You will also learn how to perform monta carlo simulation test using envelope() of spatstat package.

7.1 Choa Chu Kang planning area

7.1.1 Computing L Fucntion estimation

L_ck = Lest(childcare_ck_ppp, correction = "Ripley")
plot(L_ck, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

7.1.2 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 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 if smaller than alpha value of 0.001.

The code chunk below is used to perform the hypothesis testing.

L_ck.csr <- envelope(childcare_ck_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)

## Generating 99 simulations of CSR  ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
## 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
## 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.
## 
## Done.

plot(L_ck.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

7.2 Tampines planning area

7.2.1 Computing L-fucntion estimate

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

7.2.2 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 childcare services at Tampines are randomly distributed.

H1= The distribution of childcare services at Tampines are not randomly distributed.

The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.

The code chunk below will be used to perform the hypothesis testing.

L_tm.csr <- envelope(childcare_tm_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)

## Generating 99 simulations of CSR  ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
## 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
## 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,  99.
## 
## Done.

Then, plot the model output by using the code chun below.

plot(L_tm.csr, . - r ~ r, 
     xlab="d", ylab="L(d)-r", xlim=c(0,500))

IS415 Hands-on Exercise 5:Second-order Analysis of Spatial Point Patterns

Dr. Kam Tin SeongAssoc. Professor of Information Systems (Practice)

2019/03/11 (updated: 2020-09-01)

1 Overview

1.1 The research questions

1.2 The data

2 Installing and Loading the R packages

3 Spatial Data Wrangling

3.1 Importing the spatial data

3.2 Converting the spatial point data frame into generic sp format

3.3 Converting the generic sp format into spatstat’s ppp format

3.4 Checking for duplicated saptial point events

3.5 Extracting study area

3.6 Converting the spatial point data frame into generic sp format

3.7 Creating owin object

3.8 Combining childcare points and the study area

3.9 Visualising the ppp objects

4 Analysing Spatial Point Process Using G-Function

4.1 Choa Chu Kang planning area

4.1.1 Computing G-function estimation

4.1.2 Performing Complete Spatial Randomness Test

4.2 Tampines planning area

4.2.1 Computing G-function estimation

4.2.2 Performing Complete Spatial Randomness Test

5 Analysing Spatial Point Process Using F-Function

5.1 Choa Chu Kang planning area

5.1.1 Computing F-function estimation

5.1.2 Performing Complete Spatial Randomness Test

5.2 Tampines planning area

5.2.1 Computing F-function estimation

5.2.2 Performing Complete Spatial Randomness Test

6 Analysing Spatial Point Process Using K-Function

6.1 Choa Chu Kang planning area

6.1.1 Computing K-fucntion estimate

6.1.2 Performing Complete Spatial Randomness Test

6.2 Tampines planning area

6.2.1 Computing K-fucntion estimation

6.2.2 Performing Complete Spatial Randomness Test

7 Analysing Spatial Point Process Using L-Function

7.1 Choa Chu Kang planning area

7.1.1 Computing L Fucntion estimation

7.1.2 Performing Complete Spatial Randomness Test

7.2 Tampines planning area

7.2.1 Computing L-fucntion estimate

7.2.2 Performing Complete Spatial Randomness Test

IS415 Hands-on Exercise 5:
Second-order Analysis of Spatial Point Patterns

Dr. Kam Tin Seong
Assoc. Professor of Information Systems (Practice)