::p_load(sf, sfdep, spdep, tmap, tidyverse, knitr) pacman
Take-home Exercise 1: Geospatial Analytics for Public Good
1. Overview
The digitization of urban infrastructures, such as buses and public utilities, generates datasets that, when analyzed through technologies like GPS, reveal valuable patterns in human movement. This information enhances urban management and aids both private and public transport providers in making informed decisions for a competitive edge in the evolving urban landscape. Hence there is value in performing analysis on such information, which is further showcased in this exercise.
1.1 Objectives
In this exercise, the focus will be to identify, analyse and compare the spatial patterns, through using of Geovisualisation and Analysis, and Local Indicators of Spatial Association (LISA) to uncover the spatial and spatio-temporal mobility patterns of public bus passengers in Singapore.
The specific tasks of this exercise are as follows:
Objective 1: Geovisualisation and Analysis
With reference to the time intervals provided in the table below, compute the passenger trips generated by origin at the hexagon level,
Peak hour period Bus tap on time Weekday morning peak 6am to 9am Weekday afternoon peak 5pm to 8pm Weekend/holiday morning peak 11am to 2pm Weekend/holiday evening peak 4pm to 7pm Display the geographical distribution of the passenger trips by using appropriate geovisualisation methods,
Describe the spatial patterns revealed by the geovisualisation (not more than 200 words per visual).
Objective 2: Local Indicators of Spatial Association (LISA) Analysis
Compute LISA of the passengers trips generate by origin at hexagon level.
Display the LISA maps of the passengers trips generate by origin at hexagon level. The maps should only display the significant (i.e. p-value < 0.05)
With reference to the analysis results, draw statistical conclusions (not more than 200 words per visual).
2. Installing and Loading the R Packages
For this exercise, in the following code chunk, p_load()
from pacman package is used to install and load the following R packages into the R environment:
sf for importing, managing, and processing geospatial data,
sfdep/spdep to compute spatial weights using appropriate functions
tmap for creating thematic maps,
tidyverse for performing data science tasks such as importing, wrangling and visualising data,
knitr for creating html table.
3. Data Preparation
3.1 Data
There are 2 datasets used, as outlined in sections 3.1 and 3.2
3.1.1 Apastial data
For the purpose of this take-home exercise, Passenger Volume by Origin Destination Bus Stops downloaded from LTA DataMall will be used. Relevant data for the month of August, September and Oct 2023 had been downloaded. For this exercise, we will observe this dataset for the time period of Oct 2023. This can reproduced later on by point to the csv file for the required month.
3.1.2 Geospatial data
Two geospatial data will be used in this study, they are:
Bus Stop Location from LTA DataMall. It provides information about all the bus stops currently being serviced by buses, including the bus stop code (identifier) and location coordinates.
hexagon, a hexagon layer of 250m (this distance is the perpendicular distance between the centre of the hexagon and its edges or in short “Apothem distance” ) should be created using Bus Stop Location and Passenger Volume by Origin Destination Bus Stops data.
3.2 Getting the Data Into R Environment
3.2.1 Importing the aspatial data
We will import the Passenger Volume By Origin Destination Bus Stops data set for Oct 2023 downloaded from LTA Datamall by using read_csv().
<- read_csv("data/aspatial/origin_destination_bus_202310.csv") odbus
Using glimpse(odbus), we can see that there are 5,694,297 rows of datapoints in this dataset.
A quick check of odbus tibble data frame also shows that the values in ORIGIN_PT_CODE and DESTINATON_PT_CODE are already in <char> type. Hence, no adjustments needed to the data type.
glimpse(odbus)
Rows: 5,694,297
Columns: 7
$ YEAR_MONTH <chr> "2023-10", "2023-10", "2023-10", "2023-10", "2023-…
$ DAY_TYPE <chr> "WEEKENDS/HOLIDAY", "WEEKDAY", "WEEKENDS/HOLIDAY",…
$ TIME_PER_HOUR <dbl> 16, 16, 14, 14, 17, 17, 17, 7, 14, 14, 10, 20, 20,…
$ PT_TYPE <chr> "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "…
$ ORIGIN_PT_CODE <chr> "04168", "04168", "80119", "80119", "44069", "2028…
$ DESTINATION_PT_CODE <chr> "10051", "10051", "90079", "90079", "17229", "2014…
$ TOTAL_TRIPS <dbl> 3, 5, 3, 5, 4, 1, 24, 2, 1, 7, 3, 2, 5, 1, 1, 1, 1…
3.2.2 Extracting the relevant study data from the aspatial data
For the purpose of this exercise, we will extract commuting flows based on the intervals denoted in section 1.1
However, I realized that the weekday afternoon peak stats later than weekend/holiday evening peak.
For purposes of consistency and comparison, I will rename peak hour period “Weekday afternoon peak” to “Weekday evening peak”
Peak hour period | Bus tap on time | Corresponding Table Name |
---|---|---|
Weekday morning peak | 6am to 9am | origin6_9 |
5pm to 8pm | origin17_20 | |
Weekend/holiday morning peak | 11am to 2pm | origin11_14 |
Weekend/holiday evening peak | 4pm to 7pm | origin16_19 |
The following data wrangling and transformation functions will be used:
<- odbus %>%
origin6_9 filter (DAY_TYPE == "WEEKDAY") %>%
filter (TIME_PER_HOUR >= 6 & TIME_PER_HOUR <=9) %>%
group_by(ORIGIN_PT_CODE) %>%
summarise(TRIPS = sum(TOTAL_TRIPS))
<- odbus %>%
origin17_20 filter (DAY_TYPE == "WEEKDAY") %>%
filter (TIME_PER_HOUR >= 17 & TIME_PER_HOUR <=20) %>%
group_by(ORIGIN_PT_CODE) %>%
summarise(TRIPS = sum(TOTAL_TRIPS))
<- odbus %>%
origin11_14 filter (DAY_TYPE == "WEEKENDS/HOLIDAY") %>%
filter (TIME_PER_HOUR >= 11 & TIME_PER_HOUR <=14) %>%
group_by(ORIGIN_PT_CODE) %>%
summarise(TRIPS = sum(TOTAL_TRIPS))
<- odbus %>%
origin16_19 filter (DAY_TYPE == "WEEKENDS/HOLIDAY") %>%
filter (TIME_PER_HOUR >= 16 & TIME_PER_HOUR <=19) %>%
group_by(ORIGIN_PT_CODE) %>%
summarise(TRIPS = sum(TOTAL_TRIPS))
We will save the output in rds format for future use.
write_rds(origin6_9, "data/rds/origin6_9.rds")
write_rds(origin17_20, "data/rds/origin17_20.rds")
write_rds(origin11_14, "data/rds/origin11_14.rds")
write_rds(origin16_19, "data/rds/origin16_19.rds")
A check on origin6_9 data table indicates the it is correctly mapped.
<- read_rds("data/rds/origin6_9.rds")
origin6_9 <- read_rds("data/rds/origin17_20.rds")
origin17_20 <- read_rds("data/rds/origin11_14.rds")
origin11_14 <- read_rds("data/rds/origin16_19.rds") origin16_19
kable(head(origin6_9))
ORIGIN_PT_CODE | TRIPS |
---|---|
01012 | 1770 |
01013 | 841 |
01019 | 1530 |
01029 | 2483 |
01039 | 2919 |
01059 | 1734 |
kable(head(origin17_20))
ORIGIN_PT_CODE | TRIPS |
---|---|
01012 | 8000 |
01013 | 7038 |
01019 | 3398 |
01029 | 9089 |
01039 | 12095 |
01059 | 2212 |
kable(head(origin11_14))
ORIGIN_PT_CODE | TRIPS |
---|---|
01012 | 2177 |
01013 | 1818 |
01019 | 1536 |
01029 | 3217 |
01039 | 5408 |
01059 | 1159 |
kable(head(origin16_19))
ORIGIN_PT_CODE | TRIPS |
---|---|
01012 | 3061 |
01013 | 2770 |
01019 | 1685 |
01029 | 4063 |
01039 | 7263 |
01059 | 1118 |
3.2.3 Exploratory data analysis on data
3.2.3.1 EDA on weekday morning peak data
Exploratory Data Analysis indicates following observations:
#Total trips during weekday morning peak for the month
sum(origin6_9$TRIPS)
[1] 25976410
#Maximum trips during weekday morning peak for the month from 1 origin
max(origin6_9$TRIPS)
[1] 357043
Checks in data notes that the highest no. of bus trip originates from Boon Lay Interchange (Loc_DESC)
#Minimum trips during weekday morning peak for the month from 1 origin
min (origin6_9$TRIPS)
[1] 1
#Median no. of trips during weekday morning peak from 1 origin
median(origin6_9$TRIPS)
[1] 2198
#Distribution check
hist(origin6_9$`TRIPS`)
Distribution is skewed heavily to the left.
3.2.3.2 EDA on weekday evening peak data
Exploratory Data Analysis indicates following observations:
#Total trips during weekday evening peak for the month
sum(origin17_20$TRIPS)
[1] 25075097
#Maximum trips during weekday evening peak for the month from 1 origin
max(origin17_20$TRIPS)
[1] 529081
Checks in data notes that the highest no. of bus trip originates from Boon Lay Interchange (Loc_DESC)
#Minimum trips during weekday evening peak for the month from 1 origin
min (origin17_20$TRIPS)
[1] 1
#Median no. of trips during weekday evening peak from 1 origin
median(origin17_20$TRIPS)
[1] 1972
hist(origin17_20$`TRIPS`)
Distribution is skewed heavily to the left.
3.2.3.3 EDA on Weekend/holiday morning peak data
Exploratory Data Analysis indicates following observations:
#Total trips during Weekend/holiday morning peak for the month
sum(origin11_14$TRIPS)
[1] 7737391
#Maximum trips during Weekend/holiday morning peak for the month from 1 origin
max(origin11_14$TRIPS)
[1] 103358
Checks in data notes that the highest no. of bus trip originates from Boon Lay Interchange (Loc_DESC)
#Minimum trips during Weekend/holiday morning peak for the month from 1 origin
min (origin11_14$TRIPS)
[1] 1
#Median no. of trips during Weekend/holiday morning peak from 1 origin
median(origin11_14$TRIPS)
[1] 666
hist(origin11_14$`TRIPS`)
Distribution is skewed heavily to the left.
3.2.3.4 EDA on Weekend/holiday evening peak data
Exploratory Data Analysis indicates following observations:
#Total trips during Weekend/holiday evening peak for the month
sum(origin16_19$TRIPS)
[1] 7769394
#Maximum trips during Weekend/holiday evening peak for the month from 1 origin
max(origin16_19$TRIPS)
[1] 144903
Checks in data notes that the highest no. of bus trip originates from Boon Lay Interchange (Loc_DESC)
#Minimum trips during Weekend/holiday evening peak for the month from 1 origin
min (origin16_19$TRIPS)
[1] 1
#Median no. of trips during Weekend/holiday evening peak from 1 origin
median(origin16_19$TRIPS)
[1] 629
hist(origin16_19$`TRIPS`)
Distribution is skewed heavily to the left.
3.2.3.5 EDA comparison across the different peak periods
Some observations noted for bus trips in Oct 2023:
All distributions are heavily skewed to the left.
Total bus trips for the month for both weekday peaks for both morning and afternoon are quite similar, 26,088,201 (morning) vs 25,151,947 (evening)
Total bus trips for the month for both weekend/holiday peaks for both morning and evening are quite similar, 7,766,064 (morning) vs 7,797,319 (evening)
Total bus trips during weekday peaks are circa 3 times more than bus trips during weekend/holiday peaks.
From the available data, the highest number of trips (529,081) for the month from across all peak periods occurred during weekday evening peak, and it originated from Boon Lay Interchange.
During all peak periods, the highest number of bus trips originates from Boon Lay Interchange. Based on public research, it is situated within Jurong Point Shopping Mall and integrated with the nearby Boon Lay MRT Station. This interchange also serves a variety of passengers, including those from Nanyang Technological University, Jurong Industrial Estate and Tuas Industrial Estate. It also has 27 bus services and it is among the largest and busiest bus interchange in Singapore with an affluence of more than 85,000 commuters every day. [1] This supports the observation that a high number of bus trips originates from this location.
3.2.3 Importing the geospatial data
The code chunk below
uses the st_read() function of sf package to import
Busstop
shapefile into R as a simple feature data frame calledbusstop
Assigning EPSG code 3414 to busstop data frame.
<- st_read(dsn = "data/geospatial", layer = "BusStop") %>%
busstop st_transform(crs = 3414)
Reading layer `BusStop' from data source
`D:\starweb84\ISSS624\Take-home_Ex\Take-home_Ex1\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 5161 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 3970.122 ymin: 26482.1 xmax: 48284.56 ymax: 52983.82
Projected CRS: SVY21
st_crs(busstop)
Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]
Before moving to the next step, we save the output into rds format as a good practice.
write_rds(busstop, "data/rds/busstop.csv")
3.3 Geospatial data wrangling
3.3.1 Data wrangling with first set of time interval data - Weekday morning peak
In this section, we are going to append the busstop data frame onto origin6_9 data frame first.
<- left_join(origin6_9 , busstop,
origin_data6_9 by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
rename(ORIGIN_BS = ORIGIN_PT_CODE)
We check for duplicating records
<- origin_data6_9 %>%
duplicate6_9 group_by_all() %>%
filter(n()>1) %>%
ungroup()
We use the code chunk below to retain the unique records.
<- unique(origin_data6_9) origin_data6_9
Using head(), we noticed that the origin_data6_9 does not appear to be in simple feature form.
head(origin_data6_9, n=5)
# A tibble: 5 × 5
ORIGIN_BS TRIPS BUS_ROOF_N LOC_DESC geometry
<chr> <dbl> <chr> <chr> <POINT [m]>
1 01012 1770 B03 HOTEL GRAND PACIFIC (30140.8 31031.95)
2 01013 841 B05 ST JOSEPH'S CH (30218.75 31126.49)
3 01019 1530 B04 BRAS BASAH CPLX (30187.77 31034.55)
4 01029 2483 B07 OPP NATL LIB (30345.83 31007.64)
5 01039 2919 B09 BUGIS CUBE (30471.08 31175.63)
In the following section, we will create a Choropleth map with a hexagon layer. The code utilises a function called st_make_grid, whcih needs to recognize origin_data as a simple feature form with geospatial information in order to process it. Hence, in anticipation of that, we will convert the data into simple feature form using the below code chunk.
<- st_as_sf (origin_data6_9) origin_data6_9
A check indicates it now to be in simple feature form
head(origin_data6_9, n=5)
Simple feature collection with 5 features and 4 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 30140.8 ymin: 31007.64 xmax: 30471.08 ymax: 31175.63
Projected CRS: SVY21 / Singapore TM
# A tibble: 5 × 5
ORIGIN_BS TRIPS BUS_ROOF_N LOC_DESC geometry
<chr> <dbl> <chr> <chr> <POINT [m]>
1 01012 1770 B03 HOTEL GRAND PACIFIC (30140.8 31031.95)
2 01013 841 B05 ST JOSEPH'S CH (30218.75 31126.49)
3 01019 1530 B04 BRAS BASAH CPLX (30187.77 31034.55)
4 01029 2483 B07 OPP NATL LIB (30345.83 31007.64)
5 01039 2919 B09 BUGIS CUBE (30471.08 31175.63)
We now replicate the same data wrangling for the other 3 datatables: origin17_20, origin11_14 and origin16_19.
3.3.2 Data wrangling with second set of time interval data - weekday evening peak
3.3.1 For origin17_20:
Append the busstop data frame onto origin17_20 data frame
Show the code
<- left_join(origin17_20 , busstop,
origin_data17_20 by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
rename(ORIGIN_BS = ORIGIN_PT_CODE)
We check for duplicating records
Show the code
<- origin_data17_20 %>%
duplicate17_20 group_by_all() %>%
filter(n()>1) %>%
ungroup()
We use the code chunk below to retain the unique records.
Show the code
<- unique(origin_data17_20) origin_data17_20
Using head(), we noticed that the origin_data17_20 does not appear to be in simple feature form.
Show the code
head(origin_data17_20, n=5)
# A tibble: 5 × 5
ORIGIN_BS TRIPS BUS_ROOF_N LOC_DESC geometry
<chr> <dbl> <chr> <chr> <POINT [m]>
1 01012 8000 B03 HOTEL GRAND PACIFIC (30140.8 31031.95)
2 01013 7038 B05 ST JOSEPH'S CH (30218.75 31126.49)
3 01019 3398 B04 BRAS BASAH CPLX (30187.77 31034.55)
4 01029 9089 B07 OPP NATL LIB (30345.83 31007.64)
5 01039 12095 B09 BUGIS CUBE (30471.08 31175.63)
In the following section, we will create a Choropleth map with a hexagon layer. The code utilises a function called st_make_grid, whcih needs to recognize origin_data as a simple feature form with geospatial information in order to process it. Hence, in anticipation of that, we will convert the data into simple feature form using the below code chunk.
Show the code
<- st_as_sf (origin_data17_20) origin_data17_20
A check indicates it now to be in simple feature form
Show the code
head(origin_data17_20, n=5)
Simple feature collection with 5 features and 4 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 30140.8 ymin: 31007.64 xmax: 30471.08 ymax: 31175.63
Projected CRS: SVY21 / Singapore TM
# A tibble: 5 × 5
ORIGIN_BS TRIPS BUS_ROOF_N LOC_DESC geometry
<chr> <dbl> <chr> <chr> <POINT [m]>
1 01012 8000 B03 HOTEL GRAND PACIFIC (30140.8 31031.95)
2 01013 7038 B05 ST JOSEPH'S CH (30218.75 31126.49)
3 01019 3398 B04 BRAS BASAH CPLX (30187.77 31034.55)
4 01029 9089 B07 OPP NATL LIB (30345.83 31007.64)
5 01039 12095 B09 BUGIS CUBE (30471.08 31175.63)
3.3.3 Data wrangling with third set of time interval data - Weekend/holiday morning peak
3.3.1 For origin11_14:
Append the busstop data frame onto origin11_14 data frame
Show the code
<- left_join(origin11_14 , busstop,
origin_data11_14 by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
rename(ORIGIN_BS = ORIGIN_PT_CODE)
We check for duplicating records
Show the code
<- origin_data11_14 %>%
duplicate11_14 group_by_all() %>%
filter(n()>1) %>%
ungroup()
We use the code chunk below to retain the unique records.
Show the code
<- unique(origin_data11_14) origin_data11_14
Using head(), we noticed that the origin_data11_14 does not appear to be in simple feature form.
Show the code
head(origin_data11_14, n=5)
# A tibble: 5 × 5
ORIGIN_BS TRIPS BUS_ROOF_N LOC_DESC geometry
<chr> <dbl> <chr> <chr> <POINT [m]>
1 01012 2177 B03 HOTEL GRAND PACIFIC (30140.8 31031.95)
2 01013 1818 B05 ST JOSEPH'S CH (30218.75 31126.49)
3 01019 1536 B04 BRAS BASAH CPLX (30187.77 31034.55)
4 01029 3217 B07 OPP NATL LIB (30345.83 31007.64)
5 01039 5408 B09 BUGIS CUBE (30471.08 31175.63)
In the following section, we will create a Choropleth map with a hexagon layer. The code utilises a function called st_make_grid, whcih needs to recognize origin_data as a simple feature form with geospatial information in order to process it. Hence, in anticipation of that, we will convert the data into simple feature form using the below code chunk.
Show the code
<- st_as_sf (origin_data11_14) origin_data11_14
A check indicates it now to be in simple feature form
Show the code
head(origin_data11_14, n=5)
Simple feature collection with 5 features and 4 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 30140.8 ymin: 31007.64 xmax: 30471.08 ymax: 31175.63
Projected CRS: SVY21 / Singapore TM
# A tibble: 5 × 5
ORIGIN_BS TRIPS BUS_ROOF_N LOC_DESC geometry
<chr> <dbl> <chr> <chr> <POINT [m]>
1 01012 2177 B03 HOTEL GRAND PACIFIC (30140.8 31031.95)
2 01013 1818 B05 ST JOSEPH'S CH (30218.75 31126.49)
3 01019 1536 B04 BRAS BASAH CPLX (30187.77 31034.55)
4 01029 3217 B07 OPP NATL LIB (30345.83 31007.64)
5 01039 5408 B09 BUGIS CUBE (30471.08 31175.63)
3.3.4 Data wrangling with fourth set of time interval data - Weekend/holiday evening peak
3.3.1 For origin16_19:
Append the busstop data frame onto origin16_19 data frame
Show the code
<- left_join(origin16_19 , busstop,
origin_data16_19 by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
rename(ORIGIN_BS = ORIGIN_PT_CODE)
We check for duplicating records
Show the code
<- origin_data16_19 %>%
duplicate16_19 group_by_all() %>%
filter(n()>1) %>%
ungroup()
We use the code chunk below to retain the unique records.
Show the code
<- unique(origin_data16_19) origin_data16_19
Using head(), we noticed that the origin_data16_19 does not appear to be in simple feature form.
Show the code
head(origin_data16_19, n=5)
# A tibble: 5 × 5
ORIGIN_BS TRIPS BUS_ROOF_N LOC_DESC geometry
<chr> <dbl> <chr> <chr> <POINT [m]>
1 01012 3061 B03 HOTEL GRAND PACIFIC (30140.8 31031.95)
2 01013 2770 B05 ST JOSEPH'S CH (30218.75 31126.49)
3 01019 1685 B04 BRAS BASAH CPLX (30187.77 31034.55)
4 01029 4063 B07 OPP NATL LIB (30345.83 31007.64)
5 01039 7263 B09 BUGIS CUBE (30471.08 31175.63)
In the following section, we will create a Choropleth map with a hexagon layer. The code utilises a function called st_make_grid, whcih needs to recognize origin_data as a simple feature form with geospatial information in order to process it. Hence, in anticipation of that, we will convert the data into simple feature form using the below code chunk.
Show the code
<- st_as_sf (origin_data16_19) origin_data16_19
A check indicates it now to be in simple feature form
Show the code
head(origin_data16_19, n=5)
Simple feature collection with 5 features and 4 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 30140.8 ymin: 31007.64 xmax: 30471.08 ymax: 31175.63
Projected CRS: SVY21 / Singapore TM
# A tibble: 5 × 5
ORIGIN_BS TRIPS BUS_ROOF_N LOC_DESC geometry
<chr> <dbl> <chr> <chr> <POINT [m]>
1 01012 3061 B03 HOTEL GRAND PACIFIC (30140.8 31031.95)
2 01013 2770 B05 ST JOSEPH'S CH (30218.75 31126.49)
3 01019 1685 B04 BRAS BASAH CPLX (30187.77 31034.55)
4 01029 4063 B07 OPP NATL LIB (30345.83 31007.64)
5 01039 7263 B09 BUGIS CUBE (30471.08 31175.63)
4. Choropleth Visualisation
4.1 Making the Grid
In this section, we will be creating hexagon grids to help in subsequent analysis.
The below code chunk shows the hexagon grid making for the first time interval using the data table origin_data6_9.
4.1.1 Making the Grid for Weekday morning peak data
# Apothem distance is distance from the centre of a regular polygon at right angles to any of its sides. As stated by the data requirement, we set the desired apothem distance at 250
<- 250
apothem_distance
# Calculate the side length
<- (2 * apothem_distance) / sqrt(3)
side_length
# Use the calculated side length in st_make_grid
<- st_make_grid(origin_data6_9, cellsize = c(side_length, side_length), what = "polygons", square = FALSE)
area_honeycomb_grid6_9
# To sf and add grid ID
= st_sf(area_honeycomb_grid6_9) %>%
honeycomb_grid_sf6_9 # add grid ID
mutate(grid_id = 1:length(lengths(area_honeycomb_grid6_9)))
# Use st_intersection to get a new dataset with intersecting points
<- st_intersection(honeycomb_grid_sf6_9, origin_data6_9)
intersections_data6_9
# Aggregate to sum the "TRIPS" values for each grid
<- aggregate(intersections_data6_9$TRIPS, by = list(intersections_data6_9$grid_id), sum, na.rm = TRUE)
sum_trips6_9
# Merge the result back to the honeycomb grid
colnames(sum_trips6_9) <- c("grid_id", "Sum_TRIPS")
<- merge(honeycomb_grid_sf6_9, sum_trips6_9, by.x = "grid_id", by.y = "grid_id", all.x = TRUE)
honeycomb_grid_sf6_9
# remove grid with value of 0
= filter(honeycomb_grid_sf6_9, Sum_TRIPS > 0) honeycomb_count6_9
This is replicated for the remaining 3 time intervals.
4.1.2 Making the Grid for weekday evening peak data
Show the code
# Apothem distance is distance from the centre of a regular polygon at right angles to any of its sides. As stated by the data requirement, we set the desired apothem distance at 250
<- 250
apothem_distance
# Calculate the side length
<- (2 * apothem_distance) / sqrt(3)
side_length
# Use the calculated side length in st_make_grid
<- st_make_grid(origin_data17_20, cellsize = c(side_length, side_length), what = "polygons", square = FALSE)
area_honeycomb_grid17_20
# To sf and add grid ID
= st_sf(area_honeycomb_grid17_20) %>%
honeycomb_grid_sf17_20 # add grid ID
mutate(grid_id = 1:length(lengths(area_honeycomb_grid17_20)))
# Use st_intersection to get a new dataset with intersecting points
<- st_intersection(honeycomb_grid_sf17_20, origin_data17_20)
intersections_data17_20
# Aggregate to sum the "TRIPS" values for each grid
<- aggregate(intersections_data17_20$TRIPS, by = list(intersections_data17_20$grid_id), sum, na.rm = TRUE)
sum_trips17_20
# Merge the result back to the honeycomb grid
colnames(sum_trips17_20) <- c("grid_id", "Sum_TRIPS")
<- merge(honeycomb_grid_sf17_20, sum_trips17_20, by.x = "grid_id", by.y = "grid_id", all.x = TRUE)
honeycomb_grid_sf17_20
# remove grid with value of 0
= filter(honeycomb_grid_sf17_20, Sum_TRIPS > 0) honeycomb_count17_20
4.1.3 Making the Grid for Weekend/holiday morning peak data
Show the code
# Apothem distance is distance from the centre of a regular polygon at right angles to any of its sides. As stated by the data requirement, we set the desired apothem distance at 250
<- 250
apothem_distance
# Calculate the side length
<- (2 * apothem_distance) / sqrt(3)
side_length
# Use the calculated side length in st_make_grid
<- st_make_grid(origin_data11_14, cellsize = c(side_length, side_length), what = "polygons", square = FALSE)
area_honeycomb_grid11_14
# To sf and add grid ID
= st_sf(area_honeycomb_grid11_14) %>%
honeycomb_grid_sf11_14 # add grid ID
mutate(grid_id = 1:length(lengths(area_honeycomb_grid11_14)))
# Use st_intersection to get a new dataset with intersecting points
<- st_intersection(honeycomb_grid_sf11_14, origin_data11_14)
intersections_data11_14
# Aggregate to sum the "TRIPS" values for each grid
<- aggregate(intersections_data11_14$TRIPS, by = list(intersections_data11_14$grid_id), sum, na.rm = TRUE)
sum_trips11_14
# Merge the result back to the honeycomb grid
colnames(sum_trips11_14) <- c("grid_id", "Sum_TRIPS")
<- merge(honeycomb_grid_sf11_14, sum_trips11_14, by.x = "grid_id", by.y = "grid_id", all.x = TRUE)
honeycomb_grid_sf11_14
# remove grid with value of 0
= filter(honeycomb_grid_sf11_14, Sum_TRIPS > 0) honeycomb_count11_14
4.1.4 Making the Grid for Weekend/holiday evening peak data
Show the code
# Apothem distance is distance from the centre of a regular polygon at right angles to any of its sides. As stated by the data requirement, we set the desired apothem distance at 250
<- 250
apothem_distance
# Calculate the side length
<- (2 * apothem_distance) / sqrt(3)
side_length
# Use the calculated side length in st_make_grid
<- st_make_grid(origin_data16_19, cellsize = c(side_length, side_length), what = "polygons", square = FALSE)
area_honeycomb_grid16_19
# To sf and add grid ID
= st_sf(area_honeycomb_grid16_19) %>%
honeycomb_grid_sf16_19 # add grid ID
mutate(grid_id = 1:length(lengths(area_honeycomb_grid16_19)))
# Use st_intersection to get a new dataset with intersecting points
<- st_intersection(honeycomb_grid_sf16_19, origin_data16_19)
intersections_data16_19
# Aggregate to sum the "TRIPS" values for each grid
<- aggregate(intersections_data16_19$TRIPS, by = list(intersections_data16_19$grid_id), sum, na.rm = TRUE)
sum_trips16_19
# Merge the result back to the honeycomb grid
colnames(sum_trips16_19) <- c("grid_id", "Sum_TRIPS")
<- merge(honeycomb_grid_sf16_19, sum_trips16_19, by.x = "grid_id", by.y = "grid_id", all.x = TRUE)
honeycomb_grid_sf16_19
# remove grid with value of 0
= filter(honeycomb_grid_sf16_19, Sum_TRIPS > 0) honeycomb_count16_19
4.2 Objective 1: Geovisualisation and analysis of passenger trips
4.2.1 Geovisualisation and analysis of passenger trips during weekday morning peak
The below code chunk creates the Choropleth map using tmap and the hexagon overlay.
tmap_mode("view")
= tm_shape(honeycomb_count6_9) +
map_honeycomb6_9 tm_fill(
col = "Sum_TRIPS",
palette = "Reds",
style = "jenks",
title = "Bus trips during weekday morning peak",
id = "grid_id",
showNA = FALSE,
alpha = 0.6,
popup.vars = c(
"No. of bus trips: " = "Sum_TRIPS"
),popup.format = list(
Sum_TRIPS = list(format = "f", digits = 0)
)+
) tm_borders(col = "grey40", lwd = 0.7)
map_honeycomb6_9
Geospatial visualization reveals distinctive patterns during weekday morning peaks (6am to 9pm), with a notable surge in the origination of bus trips emanating from residential heartlands like Tampines, Boon Lay, and SengKang. In contrast, fewer bus journeys commence from the bustling city center and industrial zones, where commercial and industrial spaces predominate over residential areas. This phenomenon aligns with the typical morning routine, wherein commuters embark on buses from their homes to workplaces during weekday peak hours.
Upon closer scrutiny, specific zones exhibit exceptionally high trip counts, particularly in proximity to key transit hubs such as Boon Lay Interchange, Woodlands MRT station, the Woodlands checkpoint, and major MRT-bus interchanges. These locations witness a heightened concentration of passengers, suggesting a correlation with areas where individuals assemble to transfer buses for diverse destinations.
While preliminary observations hint at a potential correlation between higher trip numbers and residential heartland areas characterized by numerous HDBs and condominiums, definitive conclusions await the overlay of demographic data. Further analysis incorporating demographic information is essential to validate whether these patterns correlate with income levels or specific residential types, providing a more comprehensive understanding of the dynamics influencing public transit usage in these regions.
4.2.2 Geovisualisation and analysis of passenger trips during weekday evening peak
The below code chunk creates the Choropleth map using tmap and the hexagon overlay.
tmap_mode("view")
= tm_shape(honeycomb_count17_20) +
map_honeycomb17_20 tm_fill(
col = "Sum_TRIPS",
palette = "Reds",
style = "jenks",
title = "Bus trips during weekday evening peak",
id = "grid_id",
showNA = FALSE,
alpha = 0.6,
popup.vars = c(
"No. of bus trips: " = "Sum_TRIPS"
),popup.format = list(
Sum_TRIPS = list(format = "f", digits = 0)
)+
) tm_borders(col = "grey40", lwd = 0.7)
map_honeycomb17_20
Geospatial visualization exposes a distinctive transit pattern during the weekday evening peak (5 pm to 8 pm), emphasizing the sustained importance of major transit hubs like Boon Lay Interchange and Woodlands MRT station. In the city center, a noticeable increase in bus trips is observed compared to the morning peak, with heightened colors indicating greater activity.
Conversely, residential heartlands experience a decline in originating bus trips during the evening peak, aligning with the post-office hours when commuters return home. Noteworthy exceptions include certain transit hubs, such as Boon Lay Interchange, witnessing a substantial 50% surge compared to the morning. This prompts a vital consideration: assessing whether an increased bus departure frequency is necessary from these hubs to meet the escalated demand during the weekday evening peak. Such analysis is crucial for optimizing transportation services and addressing heightened demand during specific time periods.
4.2.3 Geovisualisation and analysis of passenger trips during Weekend/holiday morning peak
The below code chunk creates the Choropleth map using tmap and the hexagon overlay.
tmap_mode("view")
= tm_shape(honeycomb_count11_14) +
map_honeycomb11_14 tm_fill(
col = "Sum_TRIPS",
palette = "Blues",
style = "jenks",
title = "Bus trips during Weekend/holiday morning peak",
id = "grid_id",
showNA = FALSE,
alpha = 0.6,
popup.vars = c(
"No. of bus trips: " = "Sum_TRIPS"
),popup.format = list(
Sum_TRIPS = list(format = "f", digits = 0)
)+
) tm_borders(col = "grey40", lwd = 0.7)
map_honeycomb11_14
Geospatial visualization reveals a consistent trend during weekend and holiday morning peaks (11 am to 2 pm), with a notable increase in bus trips originating from transit hubs. However, a distinctive difference is observed in the shades of blue at residential hubs, appearing visibly lighter compared to weekday morning peaks. The overall count of bus trips per zone has significantly decreased in comparison to weekday mornings. The cause of this decline remains uncertain—it could be attributed to a general reduction in weekend travel or a more evenly distributed ridership throughout the day, given the absence of the typical workday morning rush.
The ambiguity arises as weekends often entail fewer people commuting during the morning, possibly due to non-working or half-working days. A comprehensive investigation beyond the peak period is warranted to ascertain whether this decline represents an overall reduction in bus rides across various zones. Delving further into weekend time periods would provide valuable insights into travel patterns and help determine the factors contributing to the observed changes in bus trip frequencies
4.2.4 Geovisualisation and analysis of passenger trips during Weekend/holiday evening peak
The below code chunk creates the Choropleth map using tmap and the hexagon overlay.
tmap_mode("view")
= tm_shape(honeycomb_count16_19) +
map_honeycomb16_19 tm_fill(
col = "Sum_TRIPS",
palette = "Blues",
style = "jenks",
title = "Bus trips during Weekend/holiday evening peak",
id = "grid_id",
showNA = FALSE,
alpha = 0.6,
popup.vars = c(
"No. of bus trips: " = "Sum_TRIPS"
),popup.format = list(
Sum_TRIPS = list(format = "f", digits = 0)
)+
) tm_borders(col = "grey40", lwd = 0.7)
map_honeycomb16_19
Geospatial visualization illustrates a consistent trend during weekend and holiday evening peaks (4 pm to 7 pm), with an increased number of trips originating from transit hubs. However, a discernible decline in overall bus trips per zone, compared to weekday evenings, raises questions about the reasons behind this reduction. It remains unclear whether this decline is due to fewer people traveling on weekends or if there’s a more evenly distributed ridership throughout the day.To comprehensively understand these dynamics, additional research beyond peak hours during weekends is warranted.
Notably, during this period, heightened activity is observed in zones near Orchard Road and Somerset Road, indicating an increased number of trips, possibly from entertainment and shopping districts. This aligns with the expectation that people, having spent their weekends or holidays in these areas, are heading home during the evening peak. Consequently, bus operators can consider adjusting frequencies to accommodate the higher demand in these entertainment and shopping districts during weekend and holiday evenings.
5. Global and Local Measures of Spatial Association
5.1 Assigning spatial weights, and analyzing Global Spatial Autocorrelation with Moran’s I Test and Moran’s I Permutation Test
Firstly, we identify the spatial weights which is used to define the neighbourhood relationship between the geographical units.There are 2 main approaches to compute the spatial weights, namely, the contiguity approach and the distance approach. For this exercise, based on the observation of the geovisualization, we note that there are hexagons with no neighbors. Hence, we will use adaptive distance approach where shorter bandwidths (or distances) are used.
In the following code chunk, we use map_dbl() to transform the geometry of each hexagon by applying the function st_centroid() to each hexagon. We then access the longitude using [[1]]. Likewise, we perform the following to access the latitude of the hexagon, this time using [[2]] to access the latitude. Once we have latitude and longitude, we use cbind to put longitude and latitude into the same object.
We check the first few observations to see if things are formatted correctly.
For weekday morning peak
<- map_dbl(honeycomb_count6_9$geometry, ~st_centroid(.x)[[1]])
longitude6_9 <- map_dbl(honeycomb_count6_9$geometry, ~st_centroid(.x)[[2]])
latitude6_9 <- cbind(longitude6_9, latitude6_9)
coords6_9
head(coords6_9)
longitude6_9 latitude6_9
[1,] 3970.122 27982.1
[2,] 4403.134 28732.1
[3,] 4403.134 30732.1
[4,] 4691.809 28732.1
[5,] 4691.809 30232.1
[6,] 4691.809 31232.1
In the following code chunk, we define k = 8 to find the k-nearest neighbours using knearineigh() and knn2nb() to return a list of integer vectors containing neighbour number ids.
<- knn2nb(knearneigh(coords6_9, k = 8))
knn86_9 knn86_9
Neighbour list object:
Number of regions: 2769
Number of nonzero links: 22152
Percentage nonzero weights: 0.288913
Average number of links: 8
Non-symmetric neighbours list
Next, we will assign weights to each neighboring polygon by using binary assignment. This is achieved in the following code chunk
<- nb2listw(knn86_9,
wm6_9 style = "B",
zero.policy = TRUE)
moran.test(honeycomb_count6_9$Sum_TRIPS,
listw = wm6_9,
zero.policy = TRUE,
na.action = na.omit)
Moran I test under randomisation
data: honeycomb_count6_9$Sum_TRIPS
weights: wm6_9
Moran I statistic standard deviate = 14.205, p-value < 2.2e-16
alternative hypothesis: greater
sample estimates:
Moran I statistic Expectation Variance
1.265984e-01 -3.612717e-04 7.988238e-05
Since p-value is very small, < 0.05 (statistically significant) and the Moran I statistic (1.265984e-01) is positive, we reject the null hypothesis and conclude the no, of bus trips during the weekday morning peak period is spatially clustered.
set.seed(1234)
= moran.mc(honeycomb_count6_9$Sum_TRIPS,
bperm listw = wm6_9,
nsim = 999,
zero.policy = TRUE,
na.action = na.omit)
bperm
Monte-Carlo simulation of Moran I
data: honeycomb_count6_9$Sum_TRIPS
weights: wm6_9
number of simulations + 1: 1000
statistic = 0.1266, observed rank = 1000, p-value = 0.001
alternative hypothesis: greater
The Monte Carlo simulation generates a very small p-value, i.e. < 0.05 (thus statistically significant). Again, we can reject the null hypothesis and conclude that overall, the no, of bus trips during the weekday morning peak period is spatially clustered.
We repeat the above for the other 3 intervals.
For Weekday afternoon peak:
Show the code
<- map_dbl(honeycomb_count17_20$geometry, ~st_centroid(.x)[[1]])
longitude17_20 <- map_dbl(honeycomb_count17_20$geometry, ~st_centroid(.x)[[2]])
latitude17_20 <- cbind(longitude17_20, latitude17_20)
coords17_20
head(coords17_20)
longitude17_20 latitude17_20
[1,] 3970.122 27982.1
[2,] 4403.134 28732.1
[3,] 4403.134 30732.1
[4,] 4691.809 28732.1
[5,] 4691.809 30232.1
[6,] 4691.809 31232.1
Show the code
<- knn2nb(knearneigh(coords17_20, k = 8))
knn817_20 knn817_20
Neighbour list object:
Number of regions: 2769
Number of nonzero links: 22152
Percentage nonzero weights: 0.288913
Average number of links: 8
Non-symmetric neighbours list
Show the code
<- nb2listw(knn817_20,
wm17_20 style = "B",
zero.policy = TRUE)
moran.test(honeycomb_count17_20$Sum_TRIPS,
listw = wm17_20,
zero.policy = TRUE,
na.action = na.omit)
Moran I test under randomisation
data: honeycomb_count17_20$Sum_TRIPS
weights: wm17_20
Moran I statistic standard deviate = 6.1345, p-value = 4.271e-10
alternative hypothesis: greater
sample estimates:
Moran I statistic Expectation Variance
5.328283e-02 -3.612717e-04 7.646839e-05
Show the code
set.seed(1234)
= moran.mc(honeycomb_count17_20$Sum_TRIPS,
bperm listw = wm17_20,
nsim = 999,
zero.policy = TRUE,
na.action = na.omit)
bperm
Monte-Carlo simulation of Moran I
data: honeycomb_count17_20$Sum_TRIPS
weights: wm17_20
number of simulations + 1: 1000
statistic = 0.053283, observed rank = 1000, p-value = 0.001
alternative hypothesis: greater
From the Moran I test, Since p-value is very small, < 0.05 (statistically significant) and the Moran I statistic (5.328283e-02) is positive, we reject the null hypothesis and conclude the no, of bus trips during the weekday evening peak period is spatially clustered The Monte Carlo simulation generates a very small p-value, i.e. < 0.05 (thus statistically significant). Again, we can reject the null hypothesis and conclude that overall, the no, of bus trips during the weekday evening peak period is spatially clustered.
For Weekend/holiday morning peak:
Show the code
<- map_dbl(honeycomb_count11_14$geometry, ~st_centroid(.x)[[1]])
longitude11_14 <- map_dbl(honeycomb_count11_14$geometry, ~st_centroid(.x)[[2]])
latitude11_14 <- cbind(longitude11_14, latitude11_14)
coords11_14
head(coords11_14)
longitude11_14 latitude11_14
[1,] 4283.601 28732.1
[2,] 4572.276 28732.1
[3,] 4572.276 30732.1
[4,] 4572.276 31232.1
[5,] 4716.614 28482.1
[6,] 4860.951 30232.1
Show the code
<- knn2nb(knearneigh(coords11_14, k = 8))
knn811_14 knn811_14
Neighbour list object:
Number of regions: 2781
Number of nonzero links: 22248
Percentage nonzero weights: 0.2876663
Average number of links: 8
Non-symmetric neighbours list
Show the code
<- nb2listw(knn811_14,
wm11_14 style = "B",
zero.policy = TRUE)
moran.test(honeycomb_count11_14$Sum_TRIPS,
listw = wm11_14,
zero.policy = TRUE,
na.action = na.omit)
Moran I test under randomisation
data: honeycomb_count11_14$Sum_TRIPS
weights: wm11_14
Moran I statistic standard deviate = 12.109, p-value < 2.2e-16
alternative hypothesis: greater
sample estimates:
Moran I statistic Expectation Variance
1.079164e-01 -3.597122e-04 7.996141e-05
Show the code
set.seed(1234)
= moran.mc(honeycomb_count11_14$Sum_TRIPS,
bperm listw = wm11_14,
nsim = 999,
zero.policy = TRUE,
na.action = na.omit)
bperm
Monte-Carlo simulation of Moran I
data: honeycomb_count11_14$Sum_TRIPS
weights: wm11_14
number of simulations + 1: 1000
statistic = 0.10792, observed rank = 1000, p-value = 0.001
alternative hypothesis: greater
From the Moran I test, Since p-value is very small, < 0.05 (statistically significant) and the Moran I statistic (1.079164e-01) is positive, we reject the null hypothesis and conclude the no, of bus trips during the weekday evening peak period is spatially clustered The Monte Carlo simulation generates a very small p-value, i.e. < 0.05 (thus statistically significant). Again, we can reject the null hypothesis and conclude that overall, the no, of bus trips during the weekday evening peak period is spatially clustered.
For Weekend/holiday evening peak:
Show the code
<- map_dbl(honeycomb_count16_19$geometry, ~st_centroid(.x)[[1]])
longitude16_19 <- map_dbl(honeycomb_count16_19$geometry, ~st_centroid(.x)[[2]])
latitude16_19 <- cbind(longitude16_19, latitude16_19)
coords16_19
head(coords16_19)
longitude16_19 latitude16_19
[1,] 3970.122 27982.1
[2,] 4403.134 28732.1
[3,] 4403.134 30732.1
[4,] 4691.809 28732.1
[5,] 4691.809 30232.1
[6,] 4691.809 31232.1
Show the code
<- knn2nb(knearneigh(coords16_19, k = 8))
knn816_19 knn816_19
Neighbour list object:
Number of regions: 2753
Number of nonzero links: 22024
Percentage nonzero weights: 0.2905921
Average number of links: 8
Non-symmetric neighbours list
Show the code
<- nb2listw(knn816_19,
wm16_19 style = "B",
zero.policy = TRUE)
moran.test(honeycomb_count16_19$Sum_TRIPS,
listw = wm16_19,
zero.policy = TRUE,
na.action = na.omit)
Moran I test under randomisation
data: honeycomb_count16_19$Sum_TRIPS
weights: wm16_19
Moran I statistic standard deviate = 9.8687, p-value < 2.2e-16
alternative hypothesis: greater
sample estimates:
Moran I statistic Expectation Variance
8.709732e-02 -3.633721e-04 7.854322e-05
Show the code
set.seed(1234)
= moran.mc(honeycomb_count16_19$Sum_TRIPS,
bperm listw = wm16_19,
nsim = 999,
zero.policy = TRUE,
na.action = na.omit)
bperm
Monte-Carlo simulation of Moran I
data: honeycomb_count16_19$Sum_TRIPS
weights: wm16_19
number of simulations + 1: 1000
statistic = 0.087097, observed rank = 1000, p-value = 0.001
alternative hypothesis: greater
From the Moran I test, Since p-value is very small, < 0.05 (statistically significant) and the Moran I statistic (1.079164e-01) is positive, we reject the null hypothesis and conclude the no, of bus trips during the weekday evening peak period is spatially clustered The Monte Carlo simulation generates a very small p-value, i.e. < 0.05 (thus statistically significant). Again, we can reject the null hypothesis and conclude that overall, the no, of bus trips during the weekday evening peak period is spatially clustered.
5.2 Objective 2: Local Spatial Autocorrelation - computing LISA
In contrast to global spatial autocorrelation, which indicates whether a variable tends to cluster across the entire map, the global statistic doesn’t specify where these clusters occur. Local spatial autocorrelation, however, not only identifies the presence of clusters but also pinpoints their specific locations, along with spatial outliers.
The code chunks below are used to compute local Moran’s I/ LISA statistics
For weekday morning peak
<- order(honeycomb_count6_9$grid_id)
fips6_9 <- localmoran(honeycomb_count6_9$Sum_TRIPS, wm6_9)
localMI6_9 head(localMI6_9)
Ii E.Ii Var.Ii Z.Ii Pr(z != E(Ii))
1 2.106737 -0.0008208291 2.266893 1.399793 0.1615753
2 2.181515 -0.0008299501 2.292080 1.441480 0.1494493
3 2.160382 -0.0008252939 2.279222 1.431539 0.1522759
4 2.090476 -0.0008062695 2.226688 1.401467 0.1610743
5 1.993590 -0.0006501024 1.795434 1.488308 0.1366697
6 2.174175 -0.0008297708 2.291585 1.436787 0.1507786
The results can be interpreted as follows:
Ii: the local Moran’s I statistics
E.Ii: the expectation of local Moran’s I statistic under the random distribution hypothesis
Var.li: the variance of local Moran’s I statistic under the random distribution hypothesis
Z.li: the standard deviation of local Moran’s I statistic
Pr(z != E(Ii)): the p-value of local Moran’s I statistic
The code chunk below lists the content of the local Moran matrix derived
printCoefmat(data.frame(
localMI6_9[fips6_9,],row.names=honeycomb_count6_9$grid_id[fips6_9])
|> head(5) )
Ii E.Ii Var.Ii Z.Ii Pr.z....E.Ii..
58 2.1067e+00 -8.2083e-04 2.2669e+00 1.3998e+00 0.1616
221 2.1815e+00 -8.2995e-04 2.2921e+00 1.4415e+00 0.1494
225 2.1604e+00 -8.2529e-04 2.2792e+00 1.4315e+00 0.1523
329 2.0905e+00 -8.0627e-04 2.2267e+00 1.4015e+00 0.1611
332 1.9936e+00 -6.5010e-04 1.7954e+00 1.4883e+00 0.1367
334 2.1742e+00 -8.2977e-04 2.2916e+00 1.4368e+00 0.1508
386 2.2068e+00 -7.9465e-04 2.1946e+00 1.4902e+00 0.1362
390 2.1789e+00 -8.2852e-04 2.2881e+00 1.4410e+00 0.1496
438 2.2084e+00 -8.2780e-04 2.2861e+00 1.4611e+00 0.1440
440 2.1773e+00 -7.9359e-04 2.1917e+00 1.4712e+00 0.1412
444 2.0480e+00 -8.3768e-04 2.3134e+00 1.3470e+00 0.1780
496 1.9982e+00 -6.6318e-04 1.8316e+00 1.4769e+00 0.1397
499 1.9699e+00 -7.6889e-04 2.1235e+00 1.3524e+00 0.1763
500 7.0328e-01 -8.4465e-05 2.3329e-01 1.4562e+00 0.1453
547 2.2295e+00 -8.1211e-04 2.2428e+00 1.4892e+00 0.1364
548 2.2547e+00 -8.3354e-04 2.3020e+00 1.4866e+00 0.1371
550 1.8284e+00 -5.4331e-04 1.5005e+00 1.4931e+00 0.1354
551 2.1709e+00 -8.0910e-04 2.2345e+00 1.4528e+00 0.1463
553 1.7589e+00 -6.1118e-04 1.6880e+00 1.3543e+00 0.1756
554 1.9973e+00 -8.0680e-04 2.2282e+00 1.3386e+00 0.1807
604 2.2045e+00 -8.2655e-04 2.2827e+00 1.4596e+00 0.1444
606 2.2105e+00 -8.3462e-04 2.3050e+00 1.4565e+00 0.1452
609 2.0225e+00 -8.2601e-04 2.2812e+00 1.3396e+00 0.1804
656 2.2973e+00 -8.3894e-04 2.3169e+00 1.5098e+00 0.1311
657 2.2130e+00 -8.3390e-04 2.3030e+00 1.4588e+00 0.1446
660 2.1483e+00 -7.8084e-04 2.1565e+00 1.4634e+00 0.1433
664 2.2299e+00 -7.9605e-04 2.1985e+00 1.5044e+00 0.1325
707 1.7379e+00 -5.1453e-04 1.4211e+00 1.4583e+00 0.1447
712 2.1950e+00 -8.2547e-04 2.2797e+00 1.4543e+00 0.1459
719 2.2401e+00 -8.0574e-04 2.2252e+00 1.5022e+00 0.1330
720 1.9072e+00 -7.8974e-04 2.1810e+00 1.2919e+00 0.1964
763 2.2852e+00 -8.3426e-04 2.3040e+00 1.5061e+00 0.1320
764 2.2824e+00 -8.2708e-04 2.2842e+00 1.5107e+00 0.1309
766 2.2084e+00 -8.1016e-04 2.2374e+00 1.4769e+00 0.1397
771 2.2239e+00 -8.0786e-04 2.2311e+00 1.4894e+00 0.1364
774 9.8438e-01 -8.0168e-04 2.2140e+00 6.6210e-01 0.5079
817 2.1752e+00 -7.9587e-04 2.1980e+00 1.4678e+00 0.1422
821 2.2062e+00 -8.1211e-04 2.2428e+00 1.4737e+00 0.1406
823 1.9230e+00 -7.5582e-04 2.0874e+00 1.3315e+00 0.1830
824 2.0969e+00 -7.3931e-04 2.0418e+00 1.4680e+00 0.1421
826 2.2670e+00 -8.2136e-04 2.2684e+00 1.5057e+00 0.1321
869 1.6700e+00 -4.7007e-04 1.2983e+00 1.4661e+00 0.1426
872 2.2595e+00 -8.0768e-04 2.2306e+00 1.5134e+00 0.1302
873 2.2752e+00 -8.2047e-04 2.2659e+00 1.5120e+00 0.1305
879 2.2432e+00 -8.1673e-04 2.2556e+00 1.4941e+00 0.1351
881 1.5612e+00 -8.3750e-04 2.3129e+00 1.0271e+00 0.3044
883 1.2076e+00 -7.1016e-04 1.9613e+00 8.6277e-01 0.3883
885 1.2092e+00 -7.2232e-04 1.9949e+00 8.5663e-01 0.3916
928 2.2635e+00 -8.1300e-04 2.2453e+00 1.5111e+00 0.1308
933 2.2583e+00 -8.2780e-04 2.2861e+00 1.4941e+00 0.1351
935 1.5547e+00 -8.1744e-04 2.2575e+00 1.0353e+00 0.3005
936 1.5303e+00 -8.0380e-04 2.2199e+00 1.0277e+00 0.3041
938 -5.2301e+00 -4.5579e-03 1.2582e+01 -1.4732e+00 0.1407
981 2.2906e+00 -8.3642e-04 2.3099e+00 1.5077e+00 0.1316
986 2.1792e+00 -7.6079e-04 2.1011e+00 1.5039e+00 0.1326
988 1.5729e+00 -8.3588e-04 2.3085e+00 1.0358e+00 0.3003
989 -8.3944e-02 -1.6950e-06 4.6816e-03 -1.2268e+00 0.2199
991 1.2835e+00 -8.3336e-04 2.3015e+00 8.4657e-01 0.3972
992 1.2355e+00 -7.6286e-04 2.1068e+00 8.5175e-01 0.3944
1043 -9.2610e-01 -1.8057e-04 4.9873e-01 -1.3111e+00 0.1898
1089 2.2880e+00 -8.3426e-04 2.3040e+00 1.5079e+00 0.1316
1094 2.2693e+00 -8.1655e-04 2.2551e+00 1.5117e+00 0.1306
1097 1.5309e+00 -8.0574e-04 2.2252e+00 1.0268e+00 0.3045
1098 1.9207e+00 -8.0715e-04 2.2291e+00 1.2870e+00 0.1981
1148 2.2682e+00 -8.3588e-04 2.3085e+00 1.4934e+00 0.1353
1150 2.2685e+00 -8.1069e-04 2.2389e+00 1.5166e+00 0.1294
1151 1.8329e+00 -8.3696e-04 2.3114e+00 1.2061e+00 0.2278
1152 1.8553e+00 -7.6613e-04 2.1158e+00 1.2760e+00 0.2019
1202 2.2704e+00 -8.3678e-04 2.3109e+00 1.4940e+00 0.1352
1203 2.2762e+00 -8.3912e-04 2.3174e+00 1.4958e+00 0.1347
1204 1.8467e+00 -8.0521e-04 2.2238e+00 1.2389e+00 0.2154
1206 2.1584e+00 -7.7581e-04 2.1426e+00 1.4751e+00 0.1402
1207 1.2966e+00 -8.3013e-04 2.2926e+00 8.5688e-01 0.3915
1256 2.2846e+00 -8.3840e-04 2.3154e+00 1.5020e+00 0.1331
1259 2.2257e+00 -8.1336e-04 2.2463e+00 1.4856e+00 0.1374
1260 2.1975e+00 -8.1495e-04 2.2507e+00 1.4653e+00 0.1428
1310 9.8883e-01 -8.3696e-04 2.3114e+00 6.5095e-01 0.5151
1311 9.7962e-01 -8.3444e-04 2.3045e+00 6.4587e-01 0.5184
1312 2.2569e+00 -8.2816e-04 2.2871e+00 1.4929e+00 0.1355
1313 2.0446e+00 -6.7058e-04 1.8520e+00 1.5029e+00 0.1329
1314 2.0982e+00 -7.2953e-04 2.0148e+00 1.4787e+00 0.1392
1315 2.2693e+00 -8.3354e-04 2.3020e+00 1.4963e+00 0.1346
1365 8.9957e-01 -6.7753e-04 1.8712e+00 6.5812e-01 0.5105
1366 9.7483e-01 -8.3534e-04 2.3070e+00 6.4236e-01 0.5206
1367 2.2619e+00 -8.3858e-04 2.3159e+00 1.4869e+00 0.1370
1368 2.2277e+00 -8.2512e-04 2.2787e+00 1.4763e+00 0.1399
1369 2.2667e+00 -8.3426e-04 2.3040e+00 1.4939e+00 0.1352
1416 2.2548e+00 -8.1300e-04 2.2453e+00 1.5053e+00 0.1322
1419 -7.7325e+00 -9.9691e-03 2.7500e+01 -1.4726e+00 0.1409
1473 9.3516e-01 -7.8136e-04 2.1579e+00 6.3714e-01 0.5240
1474 9.7994e-01 -8.1816e-04 2.2595e+00 6.5246e-01 0.5141
1476 2.1808e+00 -7.8747e-04 2.1748e+00 1.4794e+00 0.1390
1525 2.2872e+00 -8.3013e-04 2.2926e+00 1.5112e+00 0.1307
1526 2.2416e+00 -8.3588e-04 2.3085e+00 1.4759e+00 0.1400
1527 9.1018e-01 -7.3779e-04 2.0376e+00 6.3814e-01 0.5234
1528 2.2625e+00 -8.3516e-04 2.3065e+00 1.4903e+00 0.1361
1529 2.1645e+00 -7.6492e-04 2.1125e+00 1.4897e+00 0.1363
1530 2.2390e+00 -8.3714e-04 2.3119e+00 1.4731e+00 0.1407
1579 2.2969e+00 -8.3840e-04 2.3154e+00 1.5100e+00 0.1310
1580 2.2934e+00 -8.3426e-04 2.3040e+00 1.5114e+00 0.1307
1581 9.5440e-01 -7.8467e-04 2.1671e+00 6.4886e-01 0.5164
1582 9.5246e-01 -7.9974e-04 2.2087e+00 6.4143e-01 0.5212
1583 2.2255e+00 -8.0239e-04 2.2160e+00 1.4956e+00 0.1348
1631 2.1740e+00 -7.4797e-04 2.0657e+00 1.5131e+00 0.1302
1633 2.2877e+00 -8.2404e-04 2.2758e+00 1.5170e+00 0.1293
1685 2.2744e+00 -8.2905e-04 2.2896e+00 1.5036e+00 0.1327
1686 2.2367e+00 -8.0627e-04 2.2267e+00 1.4994e+00 0.1338
1688 2.2825e+00 -8.2583e-04 2.2807e+00 1.5119e+00 0.1306
1689 2.0427e+00 -8.1211e-04 2.2428e+00 1.3645e+00 0.1724
1691 2.2285e+00 -8.0574e-04 2.2252e+00 1.4944e+00 0.1351
1740 2.2466e+00 -8.1211e-04 2.2428e+00 1.5007e+00 0.1334
1741 2.2755e+00 -8.2476e-04 2.2777e+00 1.5083e+00 0.1315
1742 1.8390e+00 -8.1958e-04 2.2634e+00 1.2229e+00 0.2214
1744 2.2267e+00 -7.9693e-04 2.2009e+00 1.5014e+00 0.1332
1794 2.2700e+00 -8.3390e-04 2.3030e+00 1.4963e+00 0.1346
1796 2.0599e+00 -8.0839e-04 2.2325e+00 1.3792e+00 0.1678
1797 6.3871e-01 -8.0117e-05 2.2128e-01 1.3580e+00 0.1745
1798 1.8497e+00 -8.3192e-04 2.2975e+00 1.2208e+00 0.2221
1848 2.2736e+00 -8.2708e-04 2.2842e+00 1.5049e+00 0.1324
1849 2.2847e+00 -8.3372e-04 2.3025e+00 1.5062e+00 0.1320
1851 1.8563e+00 -8.3031e-04 2.2931e+00 1.2264e+00 0.2200
1903 2.2120e+00 -7.7928e-04 2.1522e+00 1.5084e+00 0.1315
1905 3.9417e-01 -2.9423e-05 8.1266e-02 1.3828e+00 0.1667
1955 2.3034e+00 -8.3822e-04 2.3149e+00 1.5145e+00 0.1299
1958 1.8603e+00 -8.3282e-04 2.3000e+00 1.2272e+00 0.2197
2009 2.2816e+00 -8.3750e-04 2.3129e+00 1.5008e+00 0.1334
2010 2.2689e+00 -8.1371e-04 2.2472e+00 1.5141e+00 0.1300
2011 2.2667e+00 -8.2261e-04 2.2718e+00 1.5044e+00 0.1325
2014 1.8373e+00 -8.2708e-04 2.2842e+00 1.2162e+00 0.2239
2062 2.2756e+00 -8.3768e-04 2.3134e+00 1.4966e+00 0.1345
2063 2.2841e+00 -8.3768e-04 2.3134e+00 1.5022e+00 0.1330
2064 2.2359e+00 -7.9675e-04 2.2004e+00 1.5078e+00 0.1316
2065 2.2564e+00 -8.2565e-04 2.2802e+00 1.4948e+00 0.1350
2116 2.2049e+00 -7.7945e-04 2.1526e+00 1.5034e+00 0.1327
2117 2.2603e+00 -8.2512e-04 2.2787e+00 1.4979e+00 0.1342
2119 2.2547e+00 -8.1709e-04 2.2566e+00 1.5015e+00 0.1332
2120 2.2552e+00 -8.1744e-04 2.2575e+00 1.5015e+00 0.1332
2121 2.0290e+00 -8.2565e-04 2.2802e+00 1.3442e+00 0.1789
2170 2.1395e+00 -7.2785e-04 2.0101e+00 1.5095e+00 0.1312
2172 2.2767e+00 -8.2905e-04 2.2896e+00 1.5052e+00 0.1323
2176 2.0704e+00 -7.0172e-04 1.9380e+00 1.4878e+00 0.1368
2228 2.1817e+00 -7.6097e-04 2.1016e+00 1.5055e+00 0.1322
2229 2.2193e+00 -8.0027e-04 2.2101e+00 1.4934e+00 0.1353
2230 2.2184e+00 -8.1389e-04 2.2477e+00 1.4802e+00 0.1388
2277 2.2032e+00 -7.8520e-04 2.1685e+00 1.4967e+00 0.1345
2281 2.2306e+00 -8.1229e-04 2.2433e+00 1.4898e+00 0.1363
2283 2.2078e+00 -7.8659e-04 2.1724e+00 1.4985e+00 0.1340
2284 2.1789e+00 -7.8677e-04 2.1728e+00 1.4787e+00 0.1392
2332 2.2477e+00 -8.2690e-04 2.2837e+00 1.4879e+00 0.1368
2335 2.2185e+00 -8.0256e-04 2.2164e+00 1.4907e+00 0.1360
2336 2.2430e+00 -8.1460e-04 2.2497e+00 1.4960e+00 0.1347
2337 2.2618e+00 -8.3300e-04 2.3005e+00 1.4918e+00 0.1358
2338 2.1781e+00 -7.7546e-04 2.1416e+00 1.4889e+00 0.1365
2339 2.2439e+00 -8.3372e-04 2.3025e+00 1.4794e+00 0.1390
2392 1.1531e+00 -8.0009e-04 2.2096e+00 7.7625e-01 0.4376
2393 1.1148e+00 -7.5634e-04 2.0888e+00 7.7185e-01 0.4402
2443 2.1532e+00 -7.4593e-04 2.0601e+00 1.5007e+00 0.1334
2447 -3.3406e+00 -8.3732e-04 2.3124e+00 -2.1963e+00 0.0281
2495 2.2214e+00 -8.0344e-04 2.2189e+00 1.4918e+00 0.1357
2496 2.2395e+00 -8.1211e-04 2.2428e+00 1.4959e+00 0.1347
2497 2.2407e+00 -8.1318e-04 2.2458e+00 1.4957e+00 0.1347
2499 2.2592e+00 -8.3642e-04 2.3099e+00 1.4870e+00 0.1370
2501 -3.3496e+00 -8.3912e-04 2.3174e+00 -2.1998e+00 0.0278
2505 2.1420e+00 -8.2798e-04 2.2866e+00 1.4170e+00 0.1565
2549 2.2006e+00 -7.8607e-04 2.1709e+00 1.4941e+00 0.1351
2552 2.2385e+00 -8.0981e-04 2.2365e+00 1.4974e+00 0.1343
2553 2.2162e+00 -7.9359e-04 2.1917e+00 1.4975e+00 0.1343
2554 -3.3133e+00 -8.2601e-04 2.2812e+00 -2.1932e+00 0.0283
2555 6.2712e+00 -6.5059e-03 1.7955e+01 1.4815e+00 0.1385
2603 2.2713e+00 -8.3103e-04 2.2951e+00 1.4998e+00 0.1337
2605 2.2259e+00 -7.9816e-04 2.2043e+00 1.4998e+00 0.1337
2606 2.2616e+00 -8.3516e-04 2.3065e+00 1.4897e+00 0.1363
2607 2.2031e+00 -7.8084e-04 2.1565e+00 1.5007e+00 0.1334
2608 -1.7196e+01 -1.7884e-01 4.8290e+02 -7.7438e-01 0.4387
2609 -3.2580e+00 -7.9570e-04 2.1975e+00 -2.1973e+00 0.0280
2657 2.2106e+00 -7.8189e-04 2.1594e+00 1.5049e+00 0.1323
2658 2.2683e+00 -8.2852e-04 2.2881e+00 1.5001e+00 0.1336
2659 2.2645e+00 -8.2690e-04 2.2837e+00 1.4990e+00 0.1339
2660 2.2701e+00 -8.3804e-04 2.3144e+00 1.4927e+00 0.1355
2661 2.1514e+00 -7.4321e-04 2.0526e+00 1.5022e+00 0.1330
2663 -3.1993e+00 -7.5856e-04 2.0950e+00 -2.2098e+00 0.0271
2666 1.1987e+00 -7.9377e-04 2.1922e+00 8.1016e-01 0.4178
2667 2.1287e+00 -8.2119e-04 2.2679e+00 1.4141e+00 0.1573
2668 2.0011e+00 -8.3660e-04 2.3104e+00 1.3171e+00 0.1878
2715 2.2204e+00 -8.0168e-04 2.2140e+00 1.4928e+00 0.1355
2717 -3.2820e+00 -7.9184e-04 2.1868e+00 -2.2189e+00 0.0265
2719 8.4074e-01 -7.9798e-04 2.2038e+00 5.6687e-01 0.5708
2721 1.7600e+00 -6.1057e-04 1.6863e+00 1.3558e+00 0.1752
2722 1.7313e+00 -5.9924e-04 1.6550e+00 1.3462e+00 0.1782
2769 2.2567e+00 -8.3121e-04 2.2955e+00 1.4900e+00 0.1362
2770 -2.2416e+00 -8.2494e-04 2.2782e+00 -1.4846e+00 0.1377
2771 -2.2113e+00 -7.8904e-04 2.1791e+00 -1.4975e+00 0.1343
2774 7.7912e-01 -8.0981e-04 2.2365e+00 5.2153e-01 0.6020
2820 2.2849e+00 -8.3876e-04 2.3164e+00 1.5019e+00 0.1331
2821 2.2373e+00 -8.0221e-04 2.2155e+00 1.5037e+00 0.1327
2824 2.0687e+00 -6.9498e-04 1.9194e+00 1.4937e+00 0.1352
2825 2.1670e+00 -7.8747e-04 2.1748e+00 1.4699e+00 0.1416
2874 2.2426e+00 -8.0468e-04 2.2223e+00 1.5049e+00 0.1324
2877 2.1921e+00 -7.8694e-04 2.1733e+00 1.4875e+00 0.1369
2878 2.2645e+00 -8.3678e-04 2.3109e+00 1.4902e+00 0.1362
2879 2.1866e+00 -7.9482e-04 2.1951e+00 1.4764e+00 0.1398
2884 1.5715e+00 -5.5190e-04 1.5242e+00 1.2733e+00 0.2029
2885 1.6537e+00 -5.5351e-04 1.5287e+00 1.3380e+00 0.1809
2927 2.2686e+00 -8.2208e-04 2.2703e+00 1.5062e+00 0.1320
2929 2.2016e+00 -7.8642e-04 2.1719e+00 1.4944e+00 0.1351
2931 2.2599e+00 -8.3282e-04 2.3000e+00 1.4907e+00 0.1360
2932 2.2469e+00 -8.3300e-04 2.3005e+00 1.4819e+00 0.1384
2933 2.1052e+00 -7.6114e-04 2.1021e+00 1.4525e+00 0.1464
2936 -9.0554e-01 -5.7197e-04 1.5797e+00 -7.2003e-01 0.4715
2937 1.7255e+00 -6.8402e-04 1.8891e+00 1.2559e+00 0.2092
2985 2.0657e+00 -6.8402e-04 1.8891e+00 1.5034e+00 0.1327
2986 2.2400e+00 -8.3444e-04 2.3045e+00 1.4761e+00 0.1399
2987 2.1676e+00 -8.0680e-04 2.2282e+00 1.4527e+00 0.1463
2990 5.4225e-01 -3.7519e-03 1.0358e+01 1.6965e-01 0.8653
2991 -1.1662e+00 -4.6054e-04 1.2719e+00 -1.0336e+00 0.3013
2993 1.4693e+00 -4.0664e-04 1.1231e+00 1.3868e+00 0.1655
3035 2.2418e+00 -7.9535e-04 2.1965e+00 1.5132e+00 0.1302
3038 2.2470e+00 -8.2834e-04 2.2876e+00 1.4862e+00 0.1372
3040 2.0331e+00 -8.2065e-04 2.2664e+00 1.3510e+00 0.1767
3041 1.7247e+00 -5.7734e-04 1.5945e+00 1.3663e+00 0.1719
3043 4.7782e-01 -2.1852e-04 6.0353e-01 6.1534e-01 0.5383
3094 2.0188e+00 -7.7824e-04 2.1493e+00 1.3776e+00 0.1683
3095 1.9678e+00 -7.8345e-04 2.1637e+00 1.3383e+00 0.1808
3096 1.7174e+00 -7.2416e-04 1.9999e+00 1.2149e+00 0.2244
3098 1.6473e+00 -1.0479e-02 2.8905e+01 3.0834e-01 0.7578
3101 1.9178e+00 -7.2366e-04 1.9986e+00 1.3571e+00 0.1747
3150 2.8779e-01 -7.2970e-04 2.0152e+00 2.0324e-01 0.8389
3151 -2.0444e+00 -7.9517e-04 2.1960e+00 -1.3790e+00 0.1679
3152 1.8877e+00 -9.3600e-04 2.5849e+00 1.1747e+00 0.2401
3155 2.0585e+00 -8.0239e-04 2.2160e+00 1.3834e+00 0.1666
3198 2.2662e+00 -8.2905e-04 2.2896e+00 1.4982e+00 0.1341
3200 2.1764e+00 -8.3642e-04 2.3099e+00 1.4325e+00 0.1520
3202 1.8953e+00 -7.1331e-04 1.9700e+00 1.3508e+00 0.1767
3203 8.0045e-01 -1.1785e-04 3.2549e-01 1.4032e+00 0.1605
3206 -1.1266e+00 -4.0501e-04 1.1186e+00 -1.0648e+00 0.2870
3207 1.9789e+00 -4.6759e-04 1.2914e+00 1.7418e+00 0.0815
3209 1.5436e+00 -8.2995e-04 2.2921e+00 1.0201e+00 0.3077
3210 2.1266e+00 -8.3516e-04 2.3065e+00 1.4008e+00 0.1613
3252 2.2684e+00 -8.2852e-04 2.2881e+00 1.5002e+00 0.1336
3258 -3.0621e-01 -1.7406e-04 4.8074e-01 -4.4138e-01 0.6589
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14056 1.3187e+00 -4.6321e-04 1.2793e+00 1.1663e+00 0.2435
14057 1.7608e+00 -7.4644e-04 2.0615e+00 1.2269e+00 0.2199
14058 1.5258e+00 -6.5982e-04 1.8223e+00 1.1308e+00 0.2581
14060 -2.1667e-01 -3.0825e-04 8.5135e-01 -2.3449e-01 0.8146
14061 -4.8610e-01 -5.4796e-04 1.5134e+00 -3.9470e-01 0.6931
14062 5.3830e-02 -2.5200e-07 6.9602e-04 2.0404e+00 0.0413
14063 -9.6989e-01 -1.4680e-04 4.0546e-01 -1.5229e+00 0.1278
14064 1.2691e+00 -4.0623e-03 1.1214e+01 3.8019e-01 0.7038
14067 1.3230e+00 -2.8316e-04 7.8205e-01 1.4963e+00 0.1346
14109 1.3979e+00 -6.4361e-04 1.7775e+00 1.0490e+00 0.2942
14110 1.6813e+00 -7.6148e-04 2.1030e+00 1.1599e+00 0.2461
14112 1.8191e+00 -6.9219e-04 1.9117e+00 1.3162e+00 0.1881
14113 8.2040e-01 -7.0982e-04 1.9604e+00 5.8645e-01 0.5576
14114 -2.5213e+00 -3.5797e-03 9.8826e+00 -8.0088e-01 0.4232
14115 -2.0755e-01 -3.3984e-04 9.3860e-01 -2.1388e-01 0.8306
14117 6.2886e+00 -2.1142e-02 5.8240e+01 8.2680e-01 0.4084
14118 -1.0968e+00 -4.5063e-05 1.2446e-01 -3.1087e+00 0.0019
14120 3.6277e+00 -3.2847e-03 9.0686e+00 1.2057e+00 0.2279
14163 3.3002e-01 -2.2968e-05 6.3436e-02 1.3104e+00 0.1901
14166 2.0064e+00 -8.0645e-04 2.2272e+00 1.3450e+00 0.1786
14168 -1.1951e-01 -1.0112e-04 2.7928e-01 -2.2594e-01 0.8212
14170 8.6701e+00 -2.4159e-02 6.6526e+01 1.0659e+00 0.2864
14171 -3.3440e+00 -3.7069e-04 1.0238e+00 -3.3046e+00 0.0010
14172 1.8900e+00 -2.9801e-04 8.2308e-01 2.0836e+00 0.0372
14175 -5.0993e-01 -5.5659e-04 1.5372e+00 -4.1084e-01 0.6812
14220 2.0516e+00 -8.2619e-04 2.2817e+00 1.3587e+00 0.1742
14221 1.3035e+00 -7.9237e-04 2.1883e+00 8.8170e-01 0.3779
14222 1.2229e-03 -1.7210e-07 4.7533e-04 5.6099e-02 0.9553
14223 -2.2121e+00 -4.0929e-03 1.1299e+01 -6.5688e-01 0.5113
14226 -6.7013e-01 -1.8981e-05 5.2425e-02 -2.9267e+00 0.0034
14228 5.7279e+00 -1.0951e-02 3.0204e+01 1.0442e+00 0.2964
14229 1.4404e+00 -9.0353e-04 2.4953e+00 9.1243e-01 0.3615
14230 -6.4616e-01 -7.8102e-04 2.1570e+00 -4.3943e-01 0.6603
14273 1.3629e+00 -3.3106e-04 9.1435e-01 1.4257e+00 0.1540
14274 1.4587e+00 -7.5565e-04 2.0869e+00 1.0103e+00 0.3124
14276 -1.3611e-01 -6.3229e-04 1.7462e+00 -1.0252e-01 0.9183
14277 6.5522e-01 -1.6655e-04 4.6001e-01 9.6631e-01 0.3339
14278 1.3017e+00 -4.9758e-05 1.3743e-01 3.5114e+00 0.0004
14279 2.4263e+01 -5.7824e-02 1.5856e+02 1.9315e+00 0.0534
14280 2.1487e+00 -2.4866e-04 6.8678e-01 2.5931e+00 0.0095
14283 8.0106e-02 -2.3141e-03 6.3897e+00 3.2606e-02 0.9740
14328 1.3591e+00 -6.1211e-04 1.6905e+00 1.0458e+00 0.2957
14330 1.2779e-01 -1.2249e-04 3.3830e-01 2.1992e-01 0.8259
14333 -3.1253e-01 -2.9383e-06 8.1155e-03 -3.4692e+00 0.0005
14335 3.3178e+00 -1.5124e-03 4.1763e+00 1.6242e+00 0.1043
14336 2.5948e-01 -1.5781e-05 4.3586e-02 1.2430e+00 0.2139
14337 3.2380e-01 -1.6986e-04 4.6915e-01 4.7298e-01 0.6362
14338 3.3285e-02 -1.0514e-04 2.9038e-01 6.1963e-02 0.9506
14381 1.5357e+00 -8.2012e-04 2.2649e+00 1.0209e+00 0.3073
14382 -1.9306e+00 -6.7713e-04 1.8701e+00 -1.4113e+00 0.1582
14383 6.1325e-01 -5.4345e-04 1.5009e+00 5.0101e-01 0.6164
14384 9.2077e-02 -3.4792e-04 9.6091e-01 9.4286e-02 0.9249
14386 -5.4228e-02 -1.6554e-07 4.5722e-04 -2.5360e+00 0.0112
14390 -2.5656e-01 -1.5125e-04 4.1776e-01 -3.9671e-01 0.6916
14391 -1.0967e-01 -2.3750e-05 6.5596e-02 -4.2809e-01 0.6686
14436 1.3660e+00 -6.1782e-04 1.7063e+00 1.0462e+00 0.2955
14438 -5.7654e-01 -1.4753e-04 4.0746e-01 -9.0297e-01 0.3665
14439 2.1293e-02 -7.1939e-06 1.9869e-02 1.5111e-01 0.8799
14443 8.9410e-01 -4.0683e-03 1.1231e+01 2.6801e-01 0.7887
14444 -2.0047e-01 -2.9591e-04 8.1728e-01 -2.2142e-01 0.8248
14445 -4.5730e-02 -1.9527e-05 5.3933e-02 -1.9683e-01 0.8440
14489 1.6394e+00 -8.1069e-04 2.2389e+00 1.0962e+00 0.2730
14491 9.7366e-01 -8.1780e-04 2.2585e+00 6.4842e-01 0.5167
14494 -1.3015e-01 -6.8079e-06 1.8803e-02 -9.4909e-01 0.3426
14496 7.2505e-01 -2.5329e-03 6.9936e+00 2.7513e-01 0.7832
14497 -3.3265e-02 -2.3357e-05 6.4512e-02 -1.3088e-01 0.8959
14498 1.7322e-01 -2.3592e-04 6.5158e-01 2.1488e-01 0.8299
14500 7.6852e-02 -4.4032e-04 1.2161e+00 7.0089e-02 0.9441
14544 1.6746e+00 -8.1265e-04 2.2443e+00 1.1184e+00 0.2634
14545 1.6264e+00 -7.9219e-04 2.1878e+00 1.1001e+00 0.2713
14549 4.8752e-01 -4.7440e-04 1.3102e+00 4.2632e-01 0.6699
14550 -1.3139e-01 -6.7587e-05 1.8667e-01 -3.0396e-01 0.7612
14551 -1.8082e-01 -1.5975e-04 4.4122e-01 -2.7198e-01 0.7856
14552 5.5506e-01 -3.6472e-04 1.0073e+00 5.5340e-01 0.5800
14553 2.0001e-01 -2.6720e-04 7.3798e-01 2.3314e-01 0.8157
14598 2.2036e+00 -8.3013e-04 2.2926e+00 1.4559e+00 0.1454
14601 1.7184e+00 -8.3444e-04 2.3045e+00 1.1325e+00 0.2574
14602 5.8604e-01 -9.5381e-05 2.6344e-01 1.1420e+00 0.2535
14603 -5.3605e-01 -2.0404e-04 5.6355e-01 -7.1379e-01 0.4754
14604 1.0335e-01 -7.3627e-04 2.0334e+00 7.2994e-02 0.9418
14605 1.3126e-01 -7.0940e-06 1.9594e-02 9.3775e-01 0.3484
14651 2.2025e+00 -8.1087e-04 2.2394e+00 1.4724e+00 0.1409
14652 2.2120e+00 -8.0680e-04 2.2282e+00 1.4824e+00 0.1382
14653 2.1047e+00 -7.1864e-04 1.9847e+00 1.4944e+00 0.1351
14654 1.6033e+00 -8.1709e-04 2.2566e+00 1.0678e+00 0.2856
14655 1.7799e+00 -7.9640e-04 2.1994e+00 1.2007e+00 0.2299
14656 1.5819e+00 -6.6527e-04 1.8373e+00 1.1675e+00 0.2430
14657 1.0417e+00 -7.8642e-04 2.1719e+00 7.0739e-01 0.4793
14658 -4.8666e-02 -6.7916e-06 1.8758e-02 -3.5527e-01 0.7224
14659 1.1420e-01 -7.4287e-04 2.0516e+00 8.0251e-02 0.9360
14710 1.4449e+00 -7.7148e-04 2.1306e+00 9.9041e-01 0.3220
14711 7.2812e-01 -5.6707e-04 1.5661e+00 5.8227e-01 0.5604
14760 2.2260e+00 -8.1851e-04 2.2605e+00 1.4811e+00 0.1386
14763 1.4636e+00 -4.2082e-04 1.1622e+00 1.3580e+00 0.1745
14764 1.8178e+00 -8.0857e-04 2.2330e+00 1.2170e+00 0.2236
14765 8.0635e-01 -2.3486e-04 6.4868e-01 1.0015e+00 0.3166
14766 8.8109e-01 -4.2261e-04 1.1672e+00 8.1594e-01 0.4145
14767 1.2358e+00 -6.7575e-04 1.8662e+00 9.0512e-01 0.3654
14768 3.6920e-01 -6.8430e-05 1.8900e-01 8.4940e-01 0.3957
14769 -1.3912e-02 -6.5590e-08 1.8116e-04 -1.0336e+00 0.3013
14814 2.1338e+00 -7.4236e-04 2.0502e+00 1.4908e+00 0.1360
14817 1.9625e+00 -8.2601e-04 2.2812e+00 1.2999e+00 0.1936
14825 2.2027e+00 -8.0609e-04 2.2262e+00 1.4768e+00 0.1397
14877 1.2898e+00 -4.8833e-04 1.3487e+00 1.1111e+00 0.2665
14879 2.2044e+00 -8.0751e-04 2.2301e+00 1.4767e+00 0.1398
14926 1.9614e+00 -7.8189e-04 2.1594e+00 1.3353e+00 0.1818
14928 1.6024e+00 -7.1914e-04 1.9861e+00 1.1375e+00 0.2553
14931 1.7310e+00 -7.4389e-04 2.0544e+00 1.2082e+00 0.2270
14932 2.2142e+00 -8.0839e-04 2.2325e+00 1.4824e+00 0.1382
14933 2.1545e+00 -7.6509e-04 2.1130e+00 1.4827e+00 0.1381
14981 1.7930e+00 -7.2567e-04 2.0041e+00 1.2670e+00 0.2051
14982 1.4605e+00 -4.6994e-04 1.2979e+00 1.2824e+00 0.1997
14983 1.5472e+00 -7.4559e-04 2.0591e+00 1.0787e+00 0.2807
14985 1.5557e+00 -8.0733e-04 2.2296e+00 1.0424e+00 0.2972
14986 2.1548e+00 -8.2386e-04 2.2753e+00 1.4291e+00 0.1530
14987 2.2298e+00 -8.0203e-04 2.2150e+00 1.4988e+00 0.1339
15037 1.6985e+00 -8.2369e-04 2.2748e+00 1.1267e+00 0.2599
15039 1.5254e+00 -4.0564e-04 1.1203e+00 1.4416e+00 0.1494
15040 2.1360e+00 -7.9447e-04 2.1941e+00 1.4425e+00 0.1492
15092 2.9473e-01 -2.0137e-05 5.5618e-02 1.2498e+00 0.2114
15094 2.0946e+00 -7.6802e-04 2.1211e+00 1.4387e+00 0.1502
15095 2.2261e+00 -8.2959e-04 2.2911e+00 1.4712e+00 0.1412
15096 1.9846e+00 -6.6062e-04 1.8245e+00 1.4697e+00 0.1416
15146 1.8218e+00 -7.8834e-04 2.1772e+00 1.2352e+00 0.2167
15148 2.1603e+00 -8.1158e-04 2.2414e+00 1.4435e+00 0.1489
15149 2.2058e+00 -8.3354e-04 2.3020e+00 1.4544e+00 0.1458
15150 2.0981e+00 -8.3085e-04 2.2946e+00 1.3856e+00 0.1659
15204 2.0085e+00 -7.4916e-04 2.0690e+00 1.3969e+00 0.1625
15205 1.8935e+00 -7.9974e-04 2.2087e+00 1.2747e+00 0.2024
15247 1.0068e+00 -2.7396e-04 7.5664e-01 1.1577e+00 0.2470
15258 1.8184e+00 -7.2768e-04 2.0097e+00 1.2832e+00 0.1994
15302 -2.4915e-01 -2.8106e-05 7.7629e-02 -8.9414e-01 0.3712
15303 7.8009e-01 -4.2415e-04 1.1714e+00 7.2114e-01 0.4708
15312 1.7078e+00 -6.9350e-04 1.9153e+00 1.2345e+00 0.2170
15313 1.9363e+00 -8.1478e-04 2.2502e+00 1.2914e+00 0.1966
15420 1.2353e+00 -3.3470e-04 9.2439e-01 1.2852e+00 0.1987
15474 8.0740e-01 -1.3161e-04 3.6349e-01 1.3394e+00 0.1804
15512 8.6894e-01 -2.2226e-04 6.1385e-01 1.1094e+00 0.2673
15521 -1.5809e+00 -1.1811e-03 3.2616e+00 -8.7469e-01 0.3817
15528 1.1801e+00 -2.9165e-04 8.0550e-01 1.3152e+00 0.1884
15576 -5.7814e-01 -1.7019e-04 4.7004e-01 -8.4301e-01 0.3992
15582 1.8609e+00 -8.1247e-04 2.2438e+00 1.2429e+00 0.2139
15637 1.9074e+00 -8.3354e-04 2.3020e+00 1.2577e+00 0.2085
15690 1.9189e+00 -8.2995e-04 2.2921e+00 1.2680e+00 0.2048
15741 1.6761e+00 -5.4287e-04 1.4993e+00 1.3693e+00 0.1709
15745 1.9268e+00 -8.3804e-04 2.3144e+00 1.2671e+00 0.2051
15794 1.7019e+00 -5.6189e-04 1.5518e+00 1.3666e+00 0.1717
15798 1.8636e+00 -8.3426e-04 2.3040e+00 1.2283e+00 0.2193
15836 1.0251e+00 -3.2061e-04 8.8549e-01 1.0897e+00 0.2759
15849 1.9001e+00 -7.2232e-04 1.9949e+00 1.3458e+00 0.1784
15850 1.5059e+00 -4.5084e-04 1.2451e+00 1.3500e+00 0.1770
15903 1.8714e+00 -6.9744e-04 1.9262e+00 1.3489e+00 0.1774
15906 1.9171e+00 -8.3822e-04 2.3149e+00 1.2606e+00 0.2075
15959 1.4260e+00 -4.8586e-04 1.3419e+00 1.2314e+00 0.2182
15960 1.3702e+00 -3.9209e-04 1.0829e+00 1.3171e+00 0.1878
16012 1.7103e+00 -7.8241e-04 2.1608e+00 1.1640e+00 0.2444
16013 3.9309e-01 -3.0445e-05 8.4088e-02 1.3557e+00 0.1752
16066 1.7915e+00 -7.9570e-04 2.1975e+00 1.2091e+00 0.2266
16119 1.8639e+00 -7.0090e-04 1.9357e+00 1.3402e+00 0.1802
16173 1.9099e+00 -7.3088e-04 2.0185e+00 1.3448e+00 0.1787
16646 7.9182e-01 -7.0568e-04 1.9489e+00 5.6770e-01 0.5702
Ii E.Ii Var.Ii Z.Ii Pr.z....E.Ii..
58 2.106737 -0.0008208291 2.266893 1.399793 0.1615753
221 2.181515 -0.0008299501 2.292080 1.441480 0.1494493
225 2.160382 -0.0008252939 2.279222 1.431539 0.1522759
329 2.090476 -0.0008062695 2.226688 1.401467 0.1610743
332 1.993590 -0.0006501024 1.795434 1.488308 0.1366697
We will append the local Moran’s I dataframe (i.e. localMI) onto the honeycomb_count6_9 dataframe using the following code chunk.
<- cbind(honeycomb_count6_9, localMI6_9)%>%
honeycomb_count6_9.localMI rename(Pr.Ii = Pr.z....E.Ii..)
We repeat the same for the other intervals:
For weekday evening peak:
Show the code
<- order(honeycomb_count17_20$grid_id)
fips17_20 <- localmoran(honeycomb_count17_20$Sum_TRIPS, wm17_20 )
localMI17_20 head(localMI17_20)
Ii E.Ii Var.Ii Z.Ii Pr(z != E(Ii))
1 0.9504605 -0.0003767088 1.0404188 0.9321850 0.3512409
2 0.9923627 -0.0004015163 1.1089303 0.9427445 0.3458116
3 0.9565382 -0.0003855161 1.0647423 0.9273743 0.3537322
4 0.8004734 -0.0002546246 0.7032496 0.9548393 0.3396589
5 0.7187110 -0.0001874728 0.5177867 0.9990613 0.3177650
6 0.9515947 -0.0003900030 1.0771338 0.9172656 0.3590035
Show the code
printCoefmat(data.frame(
localMI17_20[fips17_20,],row.names=honeycomb_count17_20$grid_id[fips17_20])
|> head(5) )
Ii E.Ii Var.Ii Z.Ii Pr.z....E.Ii..
58 9.5046e-01 -3.7671e-04 1.0404e+00 9.3218e-01 0.3512
221 9.9236e-01 -4.0152e-04 1.1089e+00 9.4274e-01 0.3458
225 9.5654e-01 -3.8552e-04 1.0647e+00 9.2737e-01 0.3537
329 8.0047e-01 -2.5462e-04 7.0325e-01 9.5484e-01 0.3397
332 7.1871e-01 -1.8747e-04 5.1779e-01 9.9906e-01 0.3178
334 9.5159e-01 -3.9000e-04 1.0771e+00 9.1727e-01 0.3590
386 1.0182e+00 -3.8498e-04 1.0633e+00 9.8779e-01 0.3233
390 9.8822e-01 -3.7866e-04 1.0458e+00 9.6670e-01 0.3337
438 1.0113e+00 -3.8507e-04 1.0635e+00 9.8100e-01 0.3266
440 9.6660e-01 -3.6182e-04 9.9931e-01 9.6730e-01 0.3334
444 9.8980e-01 -4.0839e-04 1.1279e+00 9.3237e-01 0.3511
496 7.4711e-01 -2.1506e-04 5.9399e-01 9.6966e-01 0.3322
499 9.5254e-01 -4.0152e-04 1.1089e+00 9.0493e-01 0.3655
500 5.7202e-01 -1.4911e-04 4.1183e-01 8.9159e-01 0.3726
547 9.9045e-01 -3.5983e-04 9.9381e-01 9.9389e-01 0.3203
548 1.0216e+00 -3.9769e-04 1.0984e+00 9.7521e-01 0.3295
550 8.3829e-01 -2.7820e-04 7.6835e-01 9.5665e-01 0.3387
551 8.5554e-01 -3.0512e-04 8.4270e-01 9.3231e-01 0.3512
553 7.0896e-01 -2.4064e-04 6.6463e-01 8.6992e-01 0.3843
554 6.9326e-01 -2.3747e-04 6.5588e-01 8.5631e-01 0.3918
604 8.8798e-01 -3.0385e-04 8.3919e-01 9.6966e-01 0.3322
606 1.0102e+00 -3.9896e-04 1.1019e+00 9.6273e-01 0.3357
609 8.1465e-01 -3.5716e-04 9.8642e-01 8.2059e-01 0.4119
656 1.0670e+00 -4.0426e-04 1.1165e+00 1.0102e+00 0.3124
657 1.0112e+00 -4.0950e-04 1.1310e+00 9.5125e-01 0.3415
660 8.3552e-01 -2.9400e-04 8.1199e-01 9.2755e-01 0.3536
664 9.0475e-01 -3.2724e-04 9.0379e-01 9.5203e-01 0.3411
707 8.7113e-01 -2.8362e-04 7.8333e-01 9.8458e-01 0.3248
712 9.6303e-01 -3.8713e-04 1.0692e+00 9.3173e-01 0.3515
719 8.7360e-01 -2.8424e-04 7.8503e-01 9.8630e-01 0.3240
720 8.2282e-01 -2.5144e-04 6.9444e-01 9.8769e-01 0.3233
763 1.0618e+00 -3.9651e-04 1.0951e+00 1.0150e+00 0.3101
764 1.0282e+00 -3.6052e-04 9.9572e-01 1.0307e+00 0.3027
766 8.3524e-01 -2.5791e-04 7.1232e-01 9.8994e-01 0.3222
771 7.7329e-01 -2.7797e-04 7.6772e-01 8.8286e-01 0.3773
774 8.1132e-01 -3.5056e-04 9.6819e-01 8.2489e-01 0.4094
817 9.8529e-01 -3.4546e-04 9.5410e-01 1.0091e+00 0.3129
821 8.7909e-01 -3.0155e-04 8.3284e-01 9.6361e-01 0.3352
823 7.9908e-01 -3.1701e-04 8.7556e-01 8.5432e-01 0.3929
824 4.9218e-01 -1.0754e-04 2.9701e-01 9.0330e-01 0.3664
826 9.4221e-01 -3.3737e-04 9.3178e-01 9.7645e-01 0.3288
869 8.5842e-01 -2.8193e-04 7.7868e-01 9.7311e-01 0.3305
872 1.0227e+00 -3.5647e-04 9.8452e-01 1.0311e+00 0.3025
873 1.0513e+00 -3.9470e-04 1.0901e+00 1.0073e+00 0.3138
879 8.3675e-01 -3.2223e-04 8.8996e-01 8.8731e-01 0.3749
881 9.1705e-01 -4.0830e-04 1.1277e+00 8.6396e-01 0.3876
883 8.5938e-01 -3.9406e-04 1.0883e+00 8.2414e-01 0.4099
885 7.5070e-01 -2.7881e-04 7.7003e-01 8.5580e-01 0.3921
928 1.0077e+00 -3.6704e-04 1.0137e+00 1.0012e+00 0.3167
933 9.1744e-01 -3.9878e-04 1.1014e+00 8.7458e-01 0.3818
935 9.3085e-01 -3.8964e-04 1.0761e+00 8.9769e-01 0.3694
936 8.6236e-01 -3.4962e-04 9.6560e-01 8.7794e-01 0.3800
938 -2.0703e-01 -1.5953e-05 4.4063e-02 -9.8619e-01 0.3240
981 1.0332e+00 -3.9615e-04 1.0941e+00 9.8814e-01 0.3231
986 7.2342e-01 -2.2479e-04 6.2086e-01 9.1840e-01 0.3584
988 9.3126e-01 -4.0316e-04 1.1135e+00 8.8292e-01 0.3773
989 8.5373e-01 -3.1709e-04 8.7578e-01 9.1260e-01 0.3615
991 8.5699e-01 -3.9814e-04 1.0996e+00 8.1763e-01 0.4136
992 7.7609e-01 -3.0099e-04 8.3131e-01 8.5152e-01 0.3945
1043 1.8149e-01 -1.1590e-05 3.2010e-02 1.0145e+00 0.3104
1089 1.0391e+00 -4.0142e-04 1.1087e+00 9.8727e-01 0.3235
1094 7.9737e-01 -2.3628e-04 6.5258e-01 9.8735e-01 0.3235
1097 8.8253e-01 -3.7089e-04 1.0244e+00 8.7234e-01 0.3830
1098 9.0882e-01 -3.3487e-04 9.2486e-01 9.4536e-01 0.3445
1148 1.0115e+00 -3.7892e-04 1.0465e+00 9.8910e-01 0.3226
1150 8.1527e-01 -2.3362e-04 6.4525e-01 1.0152e+00 0.3100
1151 8.7347e-01 -3.9915e-04 1.1024e+00 8.3230e-01 0.4052
1152 8.2358e-01 -2.9580e-04 8.1696e-01 9.1151e-01 0.3620
1202 1.0189e+00 -3.8373e-04 1.0598e+00 9.9008e-01 0.3221
1203 1.0310e+00 -4.0252e-04 1.1117e+00 9.7819e-01 0.3280
1204 8.4855e-01 -3.3537e-04 9.2624e-01 8.8204e-01 0.3778
1206 7.4274e-01 -2.2411e-04 6.1898e-01 9.4435e-01 0.3450
1207 8.5296e-01 -4.0941e-04 1.1307e+00 8.0253e-01 0.4222
1256 1.0682e+00 -4.1144e-04 1.1363e+00 1.0024e+00 0.3161
1259 8.1032e-01 -2.5688e-04 7.0949e-01 9.6233e-01 0.3359
1260 9.0825e-01 -3.8373e-04 1.0598e+00 8.8262e-01 0.3774
1310 1.0490e+00 -4.1107e-04 1.1353e+00 9.8493e-01 0.3247
1311 1.0086e+00 -4.0968e-04 1.1315e+00 9.4857e-01 0.3428
1312 9.5317e-01 -3.8587e-04 1.0657e+00 9.2368e-01 0.3557
1313 6.3449e-01 -1.5461e-04 4.2703e-01 9.7118e-01 0.3315
1314 7.7177e-01 -2.5798e-04 7.1252e-01 9.1461e-01 0.3604
1315 1.0014e+00 -3.8114e-04 1.0527e+00 9.7643e-01 0.3289
1365 9.9915e-01 -3.8543e-04 1.0645e+00 9.6878e-01 0.3327
1366 1.0010e+00 -3.9253e-04 1.0841e+00 9.6172e-01 0.3362
1367 9.5835e-01 -3.8829e-04 1.0724e+00 9.2580e-01 0.3545
1368 9.4102e-01 -3.9018e-04 1.0776e+00 9.0687e-01 0.3645
1369 9.9615e-01 -3.9298e-04 1.0854e+00 9.5656e-01 0.3388
1416 7.6944e-01 -2.5412e-04 7.0184e-01 9.1875e-01 0.3582
1419 5.6028e-01 -1.1391e-04 3.1462e-01 9.9907e-01 0.3178
1473 9.8435e-01 -3.8391e-04 1.0603e+00 9.5633e-01 0.3389
1474 9.3834e-01 -3.4911e-04 9.6419e-01 9.5596e-01 0.3391
1476 7.6137e-01 -2.4277e-04 6.7050e-01 9.3011e-01 0.3523
1525 8.9248e-01 -3.0847e-04 8.5196e-01 9.6725e-01 0.3334
1526 1.0287e+00 -4.0161e-04 1.1092e+00 9.7714e-01 0.3285
1527 8.4706e-01 -2.8370e-04 7.8354e-01 9.5726e-01 0.3384
1528 9.7093e-01 -4.0950e-04 1.1310e+00 9.1336e-01 0.3611
1529 6.8681e-01 -2.0568e-04 5.6807e-01 9.1153e-01 0.3620
1530 9.2604e-01 -3.8106e-04 1.0524e+00 9.0305e-01 0.3665
1579 9.5428e-01 -3.9217e-04 1.0831e+00 9.1731e-01 0.3590
1580 1.0063e+00 -3.8008e-04 1.0497e+00 9.8253e-01 0.3258
1581 9.3642e-01 -3.5381e-04 9.7717e-01 9.4765e-01 0.3433
1582 8.4847e-01 -3.2773e-04 9.0516e-01 8.9216e-01 0.3723
1583 7.0936e-01 -2.1774e-04 6.0139e-01 9.1500e-01 0.3602
1631 6.1527e-01 -1.4789e-04 4.0846e-01 9.6294e-01 0.3356
1633 8.7276e-01 -2.7881e-04 7.7003e-01 9.9489e-01 0.3198
1685 8.6041e-01 -3.1799e-04 8.7825e-01 9.1846e-01 0.3584
1686 8.0521e-01 -2.9150e-04 8.0510e-01 8.9772e-01 0.3693
1688 9.0439e-01 -3.0536e-04 8.4336e-01 9.8513e-01 0.3246
1689 9.7428e-01 -3.5897e-04 9.9142e-01 9.7884e-01 0.3277
1691 7.6830e-01 -2.6975e-04 7.4502e-01 8.9043e-01 0.3732
1740 7.9967e-01 -2.6975e-04 7.4502e-01 9.2677e-01 0.3540
1741 9.2039e-01 -3.4605e-04 9.5574e-01 9.4181e-01 0.3463
1742 1.0320e+00 -4.0757e-04 1.1256e+00 9.7305e-01 0.3305
1744 7.7529e-01 -2.5158e-04 6.9484e-01 9.3039e-01 0.3522
1794 8.8523e-01 -3.7028e-04 1.0227e+00 8.7573e-01 0.3812
1796 9.4668e-01 -3.6678e-04 1.0130e+00 9.4096e-01 0.3467
1797 8.4169e-01 -2.5484e-04 7.0385e-01 1.0036e+00 0.3156
1798 8.8093e-01 -3.1104e-04 8.5905e-01 9.5079e-01 0.3417
1848 9.5558e-01 -3.9542e-04 1.0921e+00 9.1478e-01 0.3603
1849 9.4988e-01 -3.5854e-04 9.9023e-01 9.5492e-01 0.3396
1851 1.0088e+00 -3.8838e-04 1.0727e+00 9.7439e-01 0.3299
1903 7.3970e-01 -2.2548e-04 6.2275e-01 9.3763e-01 0.3484
1905 1.0001e+00 -3.7221e-04 1.0280e+00 9.8671e-01 0.3238
1955 1.0297e+00 -4.0097e-04 1.1074e+00 9.7890e-01 0.3276
1958 1.0289e+00 -3.9951e-04 1.1034e+00 9.7987e-01 0.3271
2009 1.0143e+00 -4.0399e-04 1.1157e+00 9.6064e-01 0.3367
2010 7.6839e-01 -2.1147e-04 5.8406e-01 1.0057e+00 0.3146
2011 9.2905e-01 -3.6295e-04 1.0024e+00 9.2829e-01 0.3533
2014 9.2785e-01 -4.0261e-04 1.1120e+00 8.8028e-01 0.3787
2062 1.0491e+00 -4.0922e-04 1.1302e+00 9.8721e-01 0.3235
2063 1.0233e+00 -4.0803e-04 1.1269e+00 9.6432e-01 0.3349
2064 7.9630e-01 -2.5042e-04 6.9165e-01 9.5779e-01 0.3382
2065 9.0411e-01 -3.6512e-04 1.0084e+00 9.0069e-01 0.3678
2116 8.3497e-01 -2.4398e-04 6.7384e-01 1.0175e+00 0.3089
2117 9.2640e-01 -3.4605e-04 9.5574e-01 9.4796e-01 0.3431
2119 8.4848e-01 -3.2166e-04 8.8838e-01 9.0055e-01 0.3678
2120 9.0303e-01 -3.3295e-04 9.1957e-01 9.4205e-01 0.3462
2121 8.6085e-01 -2.9291e-04 8.0897e-01 9.5743e-01 0.3384
2170 9.1906e-01 -3.0250e-04 8.3547e-01 1.0058e+00 0.3145
2172 9.4073e-01 -3.8794e-04 1.0714e+00 9.0921e-01 0.3632
2176 3.3381e-01 -5.8966e-05 1.6286e-01 8.2729e-01 0.4081
2228 8.0148e-01 -2.7208e-04 7.5144e-01 9.2489e-01 0.3550
2229 8.3038e-01 -3.2748e-04 9.0447e-01 8.7347e-01 0.3824
2230 7.1204e-01 -2.6454e-04 7.3062e-01 8.3333e-01 0.4047
2277 9.2246e-01 -3.1305e-04 8.6461e-01 9.9239e-01 0.3210
2281 6.7840e-01 -2.3244e-04 6.4199e-01 8.4698e-01 0.3970
2283 7.9454e-01 -2.8647e-04 7.9119e-01 8.9358e-01 0.3715
2284 5.9443e-01 -2.0810e-04 5.7476e-01 7.8435e-01 0.4328
2332 1.0237e+00 -4.1033e-04 1.1333e+00 9.6204e-01 0.3360
2335 7.1766e-01 -2.6033e-04 7.1900e-01 8.4667e-01 0.3972
2336 7.8786e-01 -2.8747e-04 7.9397e-01 8.8452e-01 0.3764
2337 9.0033e-01 -3.8150e-04 1.0537e+00 8.7748e-01 0.3802
2338 5.1357e-01 -1.2289e-04 3.3941e-01 8.8174e-01 0.3779
2339 8.0565e-01 -3.9651e-04 1.0951e+00 7.7025e-01 0.4411
2392 7.3836e-01 -3.5612e-04 9.8357e-01 7.4486e-01 0.4564
2393 3.4677e-01 -6.5396e-05 1.8062e-01 8.1608e-01 0.4145
2443 3.4387e-01 -5.8442e-05 1.6142e-01 8.5604e-01 0.3920
2447 1.0159e-01 -4.1079e-04 1.1345e+00 9.5760e-02 0.9237
2495 8.6723e-01 -3.2922e-04 9.0926e-01 9.0982e-01 0.3629
2496 8.3333e-01 -3.4216e-04 9.4500e-01 8.5759e-01 0.3911
2497 7.0454e-01 -2.5871e-04 7.1454e-01 8.3378e-01 0.4044
2499 8.8127e-01 -4.1153e-04 1.1366e+00 8.2701e-01 0.4082
2501 1.4136e-01 -4.1024e-04 1.1330e+00 1.3319e-01 0.8940
2505 -2.0561e-01 -3.5090e-04 9.6913e-01 -2.0850e-01 0.8348
2549 8.8583e-01 -3.3428e-04 9.2325e-01 9.2226e-01 0.3564
2552 6.6170e-01 -2.0922e-04 5.7785e-01 8.7074e-01 0.3839
2553 5.3472e-01 -1.4469e-04 3.9963e-01 8.4609e-01 0.3975
2554 6.0252e-02 -4.0692e-04 1.1239e+00 5.7219e-02 0.9544
2555 3.7510e-02 -8.2174e-06 2.2697e-02 2.4904e-01 0.8033
2603 1.0344e+00 -3.9452e-04 1.0896e+00 9.9138e-01 0.3215
2605 5.9487e-01 -1.6404e-04 4.5308e-01 8.8400e-01 0.3767
2606 7.5149e-01 -3.6234e-04 1.0007e+00 7.5157e-01 0.4523
2607 5.3643e-01 -1.3372e-04 3.6934e-01 8.8289e-01 0.3773
2608 -4.1536e+00 -8.0257e-03 2.2145e+01 -8.8095e-01 0.3783
2609 1.9623e-01 -3.8632e-04 1.0670e+00 1.9035e-01 0.8490
2657 9.3444e-01 -3.1491e-04 8.6974e-01 1.0023e+00 0.3162
2658 1.0277e+00 -3.8865e-04 1.0734e+00 9.9235e-01 0.3210
2659 9.1587e-01 -3.9253e-04 1.0841e+00 8.8000e-01 0.3789
2660 8.9716e-01 -4.1125e-04 1.1358e+00 8.4219e-01 0.3997
2661 6.4903e-01 -2.3140e-04 6.3911e-01 8.1215e-01 0.4167
2663 1.4603e-01 -4.0389e-04 1.1155e+00 1.3865e-01 0.8897
2666 4.4253e-02 -6.0086e-05 1.6596e-01 1.0878e-01 0.9134
2667 -3.0905e-02 -1.7029e-05 4.7035e-02 -1.4242e-01 0.8867
2668 9.0225e-02 -3.5458e-04 9.7930e-01 9.1532e-02 0.9271
2715 5.6229e-01 -1.6928e-04 4.6754e-01 8.2259e-01 0.4107
2717 1.0516e-01 -2.9989e-04 8.2826e-01 1.1588e-01 0.9077
2719 -2.9470e-01 -2.5332e-04 6.9964e-01 -3.5203e-01 0.7248
2721 -2.3788e+00 -4.3465e-03 1.1998e+01 -6.8550e-01 0.4930
2722 9.1268e-02 -2.1180e-04 5.8498e-01 1.1961e-01 0.9048
2769 6.1916e-01 -2.1707e-04 5.9954e-01 7.9992e-01 0.4238
2770 1.3716e-01 -3.8382e-04 1.0601e+00 1.3360e-01 0.8937
2771 2.0822e-01 -3.9153e-04 1.0814e+00 2.0061e-01 0.8410
2774 1.2327e-01 -3.2582e-04 8.9989e-01 1.3029e-01 0.8963
2820 1.0109e+00 -4.0646e-04 1.1226e+00 9.5446e-01 0.3398
2821 8.3731e-01 -3.3913e-04 9.3664e-01 8.6551e-01 0.3868
2824 6.4002e-01 -1.6527e-04 4.5647e-01 9.4754e-01 0.3434
2825 8.1564e-01 -3.1864e-04 8.8004e-01 8.6979e-01 0.3844
2874 9.6861e-01 -3.2988e-04 9.1109e-01 1.0151e+00 0.3101
2877 5.7177e-01 -1.5314e-04 4.2297e-01 8.7940e-01 0.3792
2878 8.5405e-01 -3.6975e-04 1.0212e+00 8.4550e-01 0.3978
2879 6.4856e-01 -1.9669e-04 5.4325e-01 8.8020e-01 0.3788
2884 6.9202e-02 -4.3305e-05 1.1961e-01 2.0022e-01 0.8413
2885 7.4920e-02 -2.5223e-04 6.9664e-01 9.0065e-02 0.9282
2927 1.0199e+00 -3.7494e-04 1.0355e+00 1.0026e+00 0.3160
2929 8.3762e-01 -2.8140e-04 7.7720e-01 9.5045e-01 0.3419
2931 8.5243e-01 -3.4749e-04 9.5973e-01 8.7048e-01 0.3840
2932 8.1831e-01 -3.3121e-04 9.1475e-01 8.5594e-01 0.3920
2933 6.7283e-01 -2.1526e-04 5.9454e-01 8.7287e-01 0.3827
2936 8.3877e-02 -1.0052e-04 2.7763e-01 1.5938e-01 0.8734
2937 1.1221e-01 -2.0470e-04 5.6536e-01 1.4950e-01 0.8812
2985 6.0912e-01 -1.6451e-04 4.5437e-01 9.0389e-01 0.3661
2986 8.8649e-01 -3.8686e-04 1.0685e+00 8.5799e-01 0.3909
2987 6.5806e-01 -2.2822e-04 6.3033e-01 8.2914e-01 0.4070
2990 2.6560e-02 -2.4013e-06 6.6323e-03 3.2616e-01 0.7443
2991 2.6503e-01 -2.9337e-04 8.1027e-01 2.9475e-01 0.7682
2993 2.1186e-01 -3.1293e-05 8.6432e-02 7.2074e-01 0.4711
3035 9.9682e-01 -3.6321e-04 1.0031e+00 9.9562e-01 0.3194
3038 9.1778e-01 -4.1181e-04 1.1374e+00 8.6096e-01 0.3893
3040 7.7631e-01 -3.1913e-04 8.8139e-01 8.2723e-01 0.4081
3041 5.4240e-01 -1.4584e-04 4.0281e-01 8.5484e-01 0.3926
3043 1.2035e-01 -2.6991e-05 7.4549e-02 4.4089e-01 0.6593
3094 7.3425e-01 -2.4149e-04 6.6698e-01 8.9936e-01 0.3685
3095 7.2574e-01 -2.7335e-04 7.5498e-01 8.3556e-01 0.4034
3096 6.2196e-01 -3.5949e-04 9.9285e-01 6.2455e-01 0.5323
3098 -4.2439e-01 -2.4539e-04 6.7775e-01 -5.1521e-01 0.6064
3101 5.9597e-01 -3.0242e-04 8.3525e-01 6.5244e-01 0.5141
3150 2.3874e-01 -9.2506e-05 2.5550e-01 4.7251e-01 0.6366
3151 3.1592e-01 -3.9805e-04 1.0994e+00 3.0168e-01 0.7629
3152 2.4573e-01 -1.7250e-04 4.7643e-01 3.5626e-01 0.7216
3155 1.0149e-01 -5.3180e-06 1.4688e-02 8.3745e-01 0.4023
3198 9.0940e-01 -3.3187e-04 9.1659e-01 9.5022e-01 0.3420
3200 6.9132e-01 -4.0610e-04 1.1216e+00 6.5316e-01 0.5137
3202 5.0823e-01 -1.5677e-04 4.3300e-01 7.7259e-01 0.4398
3203 5.3483e-01 -2.0869e-04 5.7640e-01 7.0473e-01 0.4810
3206 3.4172e-01 -3.1750e-04 8.7690e-01 3.6526e-01 0.7149
3207 1.1607e-01 -9.2024e-05 2.5417e-01 2.3040e-01 0.8178
3209 6.8282e-01 -3.6243e-04 1.0010e+00 6.8285e-01 0.4947
3210 6.8426e-01 -3.7644e-04 1.0397e+00 6.7144e-01 0.5019
3252 9.6322e-01 -3.7300e-04 1.0302e+00 9.4937e-01 0.3424
3258 -2.1883e-01 -1.2405e-04 3.4262e-01 -3.7364e-01 0.7087
3259 1.4883e-01 -1.1068e-04 3.0568e-01 2.6939e-01 0.7876
3260 2.8438e-03 -1.1023e-08 3.0445e-05 5.1541e-01 0.6063
3261 1.5391e-01 -8.2451e-05 2.2773e-01 3.2269e-01 0.7469
3263 3.1146e-01 -9.9561e-05 2.7498e-01 5.9415e-01 0.5524
3264 7.8674e-01 -3.8587e-04 1.0657e+00 7.6246e-01 0.4458
3265 3.6635e-01 -5.9457e-05 1.6422e-01 9.0419e-01 0.3659
3266 8.6805e-01 -3.3253e-04 9.1842e-01 9.0613e-01 0.3649
3306 9.4994e-01 -3.7795e-04 1.0438e+00 9.3015e-01 0.3523
3308 -1.1221e-01 -7.2773e-06 2.0100e-02 -7.9141e-01 0.4287
3310 7.3706e-01 -3.4911e-04 9.6419e-01 7.5098e-01 0.4527
3311 5.7112e-01 -3.0959e-04 8.5506e-01 6.1797e-01 0.5366
3312 3.6512e-02 -1.4809e-06 4.0903e-03 5.7092e-01 0.5681
3313 -4.3882e-02 -1.0722e-05 2.9615e-02 -2.5493e-01 0.7988
3314 8.6055e-02 -1.2913e-05 3.5666e-02 4.5574e-01 0.6486
3318 8.0736e-01 -4.1079e-04 1.1345e+00 7.5836e-01 0.4482
3320 9.2707e-01 -3.8650e-04 1.0675e+00 8.9767e-01 0.3694
3321 5.8667e-01 -1.3754e-04 3.7989e-01 9.5207e-01 0.3411
3322 1.0316e+00 -4.0234e-04 1.1112e+00 9.7899e-01 0.3276
3359 9.5090e-01 -3.7883e-04 1.0463e+00 9.3000e-01 0.3524
3360 8.4705e-01 -2.9057e-04 8.0252e-01 9.4586e-01 0.3442
3361 6.8151e-01 -4.1005e-04 1.1325e+00 6.4078e-01 0.5217
3362 2.0403e-01 -2.5867e-05 7.1443e-02 7.6343e-01 0.4452
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14168 -4.8978e-02 -2.4057e-04 6.6444e-01 -5.9791e-02 0.9523
14170 2.8909e+00 -5.3557e-03 1.4783e+01 7.5329e-01 0.4513
14171 -1.0636e+00 -1.3808e-04 3.8137e-01 -1.7221e+00 0.0850
14172 -4.7866e-02 -3.2503e-05 8.9773e-02 -1.5965e-01 0.8732
14175 1.8664e-01 -3.5081e-04 9.6890e-01 1.8997e-01 0.8493
14220 4.1786e-01 -3.4775e-04 9.6043e-01 4.2674e-01 0.6696
14221 4.4443e-01 -3.8785e-04 1.0712e+00 4.2979e-01 0.6673
14222 -1.9480e-02 -1.7340e-04 4.7891e-01 -2.7898e-02 0.9777
14223 -4.1294e-01 -1.0499e-04 2.8998e-01 -7.6664e-01 0.4433
14226 -8.9203e-01 -1.7244e-04 4.7626e-01 -1.2923e+00 0.1962
14228 -7.3029e-01 -1.0309e-03 2.8469e+00 -4.3221e-01 0.6656
14229 1.7742e-02 -5.0251e-05 1.3879e-01 4.7758e-02 0.9619
14230 1.8751e-01 -3.6044e-04 9.9548e-01 1.8829e-01 0.8506
14273 3.2703e-01 -1.0702e-04 2.9557e-01 6.0173e-01 0.5474
14274 2.7315e-01 -1.4900e-04 4.1152e-01 4.2602e-01 0.6701
14276 2.0832e-01 -3.7946e-04 1.0480e+00 2.0386e-01 0.8385
14277 -4.6654e-02 -8.2824e-05 2.2876e-01 -9.7371e-02 0.9224
14278 -5.2879e-01 -2.8992e-05 8.0075e-02 -1.8686e+00 0.0617
14279 5.2851e+00 -7.2175e-03 1.9917e+01 1.1859e+00 0.2357
14280 -2.1351e-01 -1.2243e-04 3.3815e-01 -3.6695e-01 0.7137
14283 4.7566e-02 -1.6991e-06 4.6930e-03 6.9436e-01 0.4875
14328 1.9493e-01 -4.3576e-05 1.2035e-01 5.6201e-01 0.5741
14330 -7.1937e-02 -1.8853e-04 5.2072e-01 -9.9429e-02 0.9208
14333 9.7615e-02 -1.1661e-06 3.2208e-03 1.7200e+00 0.0854
14335 -1.5429e-02 -1.4377e-05 3.9709e-02 -7.7355e-02 0.9383
14336 7.0919e-02 -1.4115e-04 3.8985e-01 1.1381e-01 0.9094
14337 3.1095e-01 -1.0052e-04 2.7763e-01 5.9034e-01 0.5550
14338 4.3047e-01 -1.4502e-04 4.0053e-01 6.8041e-01 0.4962
14381 4.3512e-01 -3.5905e-04 9.9166e-01 4.3730e-01 0.6619
14382 -5.8595e-01 -2.6467e-04 7.3100e-01 -6.8503e-01 0.4933
14383 2.8106e-01 -2.2336e-04 6.1691e-01 3.5812e-01 0.7203
14384 1.8141e-01 -2.0022e-04 5.5300e-01 2.4422e-01 0.8071
14386 -6.3961e-01 -1.8196e-04 5.0256e-01 -9.0198e-01 0.3671
14390 3.4555e-01 -9.0587e-05 2.5020e-01 6.9101e-01 0.4896
14391 4.2392e-01 -2.2651e-04 6.2559e-01 5.3625e-01 0.5918
14436 1.1364e-01 -1.7313e-05 4.7817e-02 5.1978e-01 0.6032
14438 -8.8924e-01 -6.2866e-04 1.7362e+00 -6.7439e-01 0.5001
14439 -1.4553e-01 -6.2764e-05 1.7335e-01 -3.4939e-01 0.7268
14443 -1.9478e-01 -1.2938e-04 3.5733e-01 -3.2562e-01 0.7447
14444 2.5205e-01 -2.4999e-04 6.9045e-01 3.0364e-01 0.7614
14445 4.0561e-01 -1.9669e-04 5.4325e-01 5.5057e-01 0.5819
14489 4.4471e-01 -3.2650e-04 9.0174e-01 4.6866e-01 0.6393
14491 1.2822e-01 -3.5992e-04 9.9405e-01 1.2896e-01 0.8974
14494 3.2477e-01 -1.9510e-04 5.3885e-01 4.4270e-01 0.6580
14496 -2.0361e-01 -8.5451e-05 2.3601e-01 -4.1894e-01 0.6753
14497 -1.5078e-02 -6.6141e-07 1.8268e-03 -3.5275e-01 0.7243
14498 3.4431e-01 -1.3032e-04 3.5994e-01 5.7412e-01 0.5659
14500 6.0949e-01 -3.2781e-04 9.0538e-01 6.4089e-01 0.5216
14544 3.7497e-01 -1.5889e-04 4.3885e-01 5.6626e-01 0.5712
14545 3.6709e-01 -2.5535e-04 7.0526e-01 4.3743e-01 0.6618
14549 4.5462e-01 -2.7245e-04 7.5248e-01 5.2440e-01 0.6000
14550 3.4638e-01 -1.1260e-04 3.1100e-01 6.2131e-01 0.5344
14551 2.2077e-01 -2.5368e-04 7.0064e-01 2.6405e-01 0.7917
14552 4.6245e-01 -3.3503e-04 9.2532e-01 4.8110e-01 0.6304
14553 2.3999e-01 -7.0887e-05 1.9579e-01 5.4254e-01 0.5874
14598 4.4953e-01 -2.6997e-04 7.4564e-01 5.2090e-01 0.6024
14601 2.3724e-01 -3.7441e-04 1.0341e+00 2.3367e-01 0.8152
14602 -9.0380e-01 -5.1897e-04 1.4333e+00 -7.5449e-01 0.4506
14603 2.6623e-01 -1.6068e-04 4.4378e-01 3.9989e-01 0.6892
14604 5.5488e-01 -3.9343e-04 1.0866e+00 5.3269e-01 0.5943
14605 -2.9107e-01 -4.7349e-05 1.3078e-01 -8.0474e-01 0.4210
14651 4.3827e-01 -1.2127e-04 3.3495e-01 7.5747e-01 0.4488
14652 5.1707e-01 -3.1120e-04 8.5950e-01 5.5807e-01 0.5768
14653 -7.2956e-01 -2.7387e-04 7.5640e-01 -8.3853e-01 0.4017
14654 2.2683e-01 -3.4664e-04 9.5738e-01 2.3218e-01 0.8164
14655 3.4301e-01 -1.5878e-04 4.3853e-01 5.1822e-01 0.6043
14656 1.0782e-01 -1.1373e-05 3.1413e-02 6.0840e-01 0.5429
14657 4.4540e-01 -3.7195e-04 1.0273e+00 4.3982e-01 0.6601
14658 1.9529e-01 -3.6710e-05 1.0139e-01 6.1342e-01 0.5396
14659 3.6406e-01 -3.8507e-04 1.0635e+00 3.5340e-01 0.7238
14710 4.4029e-01 -3.6321e-04 1.0031e+00 4.3996e-01 0.6600
14711 4.6887e-01 -1.7677e-04 4.8824e-01 6.7127e-01 0.5020
14760 4.8750e-01 -2.6863e-04 7.4193e-01 5.6628e-01 0.5712
14763 5.2503e-03 -3.4976e-08 9.6602e-05 5.3419e-01 0.5932
14764 2.6768e-01 -1.5552e-04 4.2954e-01 4.0866e-01 0.6828
14765 2.7579e-01 -1.1347e-04 3.1341e-01 4.9282e-01 0.6221
14766 2.8548e-01 -5.0025e-05 1.3817e-01 7.6815e-01 0.4424
14767 6.1932e-01 -3.2856e-04 9.0744e-01 6.5049e-01 0.5154
14768 1.6303e-01 -2.3839e-04 6.5840e-01 2.0122e-01 0.8405
14769 -2.4793e-01 -1.3845e-04 3.8238e-01 -4.0071e-01 0.6886
14814 3.4348e-01 -1.1611e-04 3.2069e-01 6.0675e-01 0.5440
14817 3.7028e-01 -3.4039e-04 9.4012e-01 3.8224e-01 0.7023
14825 7.9019e-01 -3.0416e-04 8.4007e-01 8.6246e-01 0.3884
14877 -7.5621e-01 -6.3784e-04 1.7616e+00 -5.6928e-01 0.5692
14879 4.7491e-01 -9.8246e-05 2.7135e-01 9.1187e-01 0.3618
14926 5.5403e-01 -1.8897e-04 5.2193e-01 7.6714e-01 0.4430
14928 7.7206e-01 -3.3930e-04 9.3710e-01 7.9790e-01 0.4249
14931 2.3609e-01 -2.1727e-04 6.0009e-01 3.0504e-01 0.7603
14932 7.9979e-01 -3.6148e-04 9.9835e-01 8.0081e-01 0.4232
14933 6.7238e-01 -2.0301e-04 5.6069e-01 8.9822e-01 0.3691
14981 6.0625e-01 -2.4341e-04 6.7227e-01 7.3970e-01 0.4595
14982 7.0661e-01 -3.0943e-04 8.5462e-01 7.6468e-01 0.4445
14983 8.4505e-01 -3.6792e-04 1.0161e+00 8.3868e-01 0.4017
14985 1.9868e-01 -2.0995e-04 5.7986e-01 2.6119e-01 0.7939
14986 7.1348e-01 -3.1636e-04 8.7376e-01 7.6362e-01 0.4451
14987 7.5219e-01 -2.5506e-04 7.0446e-01 8.9650e-01 0.3700
15037 9.1191e-01 -4.0766e-04 1.1259e+00 8.5980e-01 0.3899
15039 9.9391e-02 -1.1190e-05 3.0906e-02 5.6542e-01 0.5718
15040 6.2772e-01 -2.3064e-04 6.3701e-01 7.8678e-01 0.4314
15092 3.0918e-01 -1.1808e-04 3.2614e-01 5.4160e-01 0.5881
15094 5.8119e-01 -1.8202e-04 5.0273e-01 8.1994e-01 0.4122
15095 9.5418e-01 -4.0978e-04 1.1317e+00 8.9731e-01 0.3696
15096 8.6665e-01 -3.4554e-04 9.5434e-01 8.8749e-01 0.3748
15146 3.9577e-01 -2.6968e-04 7.4482e-01 4.5890e-01 0.6463
15148 8.5244e-01 -3.8803e-04 1.0717e+00 8.2382e-01 0.4100
15149 9.6186e-01 -4.0142e-04 1.1087e+00 9.1388e-01 0.3608
15150 8.8637e-01 -3.9361e-04 1.0871e+00 8.5050e-01 0.3950
15204 4.6829e-01 -9.3429e-05 2.5805e-01 9.2205e-01 0.3565
15205 6.2917e-01 -3.2395e-04 8.9471e-01 6.6550e-01 0.5057
15247 2.3056e-02 -3.4239e-06 9.4567e-03 2.3712e-01 0.8126
15258 6.8781e-01 -4.0371e-04 1.1150e+00 6.5176e-01 0.5146
15302 1.5741e-01 -3.1887e-04 8.8068e-01 1.6808e-01 0.8665
15303 -1.0511e-01 -3.5968e-05 9.9344e-02 -3.3337e-01 0.7389
15312 5.3253e-01 -2.1466e-04 5.9288e-01 6.9188e-01 0.4890
15313 6.7211e-01 -3.8088e-04 1.0519e+00 6.5568e-01 0.5120
15420 3.2603e-01 -7.3521e-05 2.0306e-01 7.2367e-01 0.4693
15474 -4.7235e-01 -9.7969e-05 2.7059e-01 -9.0786e-01 0.3640
15512 2.7598e-01 -1.2344e-04 3.4094e-01 4.7287e-01 0.6363
15521 3.6404e-01 -9.0445e-03 2.4953e+01 7.4688e-02 0.9405
15528 6.5940e-01 -2.9658e-04 8.1913e-01 7.2890e-01 0.4661
15576 -1.0383e-01 -7.0130e-03 1.9353e+01 -2.2007e-02 0.9824
15582 7.0844e-01 -3.4630e-04 9.5644e-01 7.2474e-01 0.4686
15637 7.9377e-01 -4.0399e-04 1.1157e+00 7.5185e-01 0.4521
15690 5.6097e-01 -3.6713e-04 1.0140e+00 5.5746e-01 0.5772
15741 1.1091e-01 -5.5961e-05 1.5456e-01 2.8225e-01 0.7778
15745 5.8562e-01 -4.1079e-04 1.1345e+00 5.5019e-01 0.5822
15794 1.8337e-01 -2.2500e-04 6.2143e-01 2.3289e-01 0.8158
15798 7.6760e-01 -3.9796e-04 1.0991e+00 7.3256e-01 0.4638
15836 3.5624e-01 -2.3133e-04 6.3892e-01 4.4596e-01 0.6556
15849 1.3470e-01 -9.1109e-05 2.5164e-01 2.6870e-01 0.7882
15850 -1.0883e+00 -1.7205e-03 4.7510e+00 -4.9853e-01 0.6181
15903 7.1670e-04 -1.6966e-09 4.6859e-06 3.3109e-01 0.7406
15906 6.5539e-01 -4.1024e-04 1.1330e+00 6.1610e-01 0.5378
15959 -1.3926e-03 -2.6115e-08 7.2131e-05 -1.6397e-01 0.8698
15960 -1.0083e+00 -4.7907e-04 1.3231e+00 -8.7617e-01 0.3809
16012 -1.3082e-02 -2.5886e-04 7.1495e-01 -1.5166e-02 0.9879
16013 1.5958e-01 -3.0568e-04 8.4424e-01 1.7401e-01 0.8619
16066 1.5363e-01 -2.0896e-04 5.7713e-01 2.0250e-01 0.8395
16119 1.3571e-01 -1.7914e-04 4.9478e-01 1.9318e-01 0.8468
16173 1.8886e-01 -2.5006e-04 6.9065e-01 2.2755e-01 0.8200
16646 -2.9956e-01 -2.8125e-04 7.7677e-01 -3.3957e-01 0.7342
Ii E.Ii Var.Ii Z.Ii Pr.z....E.Ii..
58 0.9504605 -0.0003767088 1.0404188 0.9321850 0.3512409
221 0.9923627 -0.0004015163 1.1089303 0.9427445 0.3458116
225 0.9565382 -0.0003855161 1.0647423 0.9273743 0.3537322
329 0.8004734 -0.0002546246 0.7032496 0.9548393 0.3396589
332 0.7187110 -0.0001874728 0.5177867 0.9990613 0.3177650
Show the code
<- cbind(honeycomb_count17_20, localMI17_20)%>%
honeycomb_count17_20.localMI rename(Pr.Ii = Pr.z....E.Ii..)
For weekend/holidays morning peak:
Show the code
<- order(honeycomb_count11_14$grid_id)
fips11_14 <- localmoran(honeycomb_count11_14$Sum_TRIPS, wm11_14)
localMI11_14 head(localMI11_14)
Ii E.Ii Var.Ii Z.Ii Pr(z != E(Ii))
1 1.562868 -0.0006466400 1.793631 1.167442 0.2430318
2 1.564357 -0.0006466400 1.793631 1.168554 0.2425835
3 1.585182 -0.0006343237 1.759471 1.195534 0.2318786
4 1.562521 -0.0006230598 1.728230 1.189045 0.2344221
5 1.509317 -0.0005722772 1.587380 1.198407 0.2307584
6 1.424700 -0.0004430645 1.228990 1.285536 0.1986051
Show the code
printCoefmat(data.frame(
localMI11_14[fips11_14,],row.names=honeycomb_count11_14$grid_id[fips11_14])
|> head(5) )
Ii E.Ii Var.Ii Z.Ii Pr.z....E.Ii..
5 1.5629e+00 -6.4664e-04 1.7936e+00 1.1674e+00 0.2430
113 1.5644e+00 -6.4664e-04 1.7936e+00 1.1686e+00 0.2426
117 1.5852e+00 -6.3432e-04 1.7595e+00 1.1955e+00 0.2319
118 1.5625e+00 -6.2306e-04 1.7282e+00 1.1890e+00 0.2344
167 1.5093e+00 -5.7228e-04 1.5874e+00 1.1984e+00 0.2308
224 1.4247e+00 -4.4306e-04 1.2290e+00 1.2855e+00 0.1986
280 1.2404e+00 -3.6885e-04 1.0231e+00 1.2266e+00 0.2200
282 1.5893e+00 -6.3763e-04 1.7686e+00 1.1955e+00 0.2319
283 1.3688e+00 -6.5667e-04 1.8215e+00 1.0147e+00 0.3103
330 1.6037e+00 -6.4902e-04 1.8002e+00 1.1957e+00 0.2318
331 1.7144e+00 -6.2680e-04 1.7386e+00 1.3007e+00 0.1934
332 1.6701e+00 -6.3574e-04 1.7634e+00 1.2582e+00 0.2083
334 1.0607e+00 -2.4636e-04 6.8337e-01 1.2834e+00 0.1993
337 1.3249e+00 -6.4664e-04 1.7936e+00 9.8978e-01 0.3223
388 1.5719e+00 -5.8987e-04 1.6362e+00 1.2294e+00 0.2189
389 1.5655e+00 -5.8806e-04 1.6311e+00 1.2262e+00 0.2201
392 -7.0873e-01 -1.1948e-04 3.3143e-01 -1.2309e+00 0.2184
440 1.7476e+00 -6.4998e-04 1.8029e+00 1.3021e+00 0.1929
445 8.9766e-01 -2.6248e-04 7.2808e-01 1.0523e+00 0.2927
446 1.2697e+00 -5.7317e-04 1.5899e+00 1.0075e+00 0.3137
447 1.4180e+00 -6.1236e-04 1.6986e+00 1.0885e+00 0.2764
491 1.0079e+00 -2.3246e-04 6.4481e-01 1.2555e+00 0.2093
496 1.6254e+00 -6.3574e-04 1.7634e+00 1.2245e+00 0.2208
498 1.6875e+00 -6.5189e-04 1.8082e+00 1.2554e+00 0.2093
499 1.2392e+00 -5.4879e-04 1.5222e+00 1.0048e+00 0.3150
501 1.3472e+00 -6.5811e-04 1.8255e+00 9.9763e-01 0.3185
503 1.7810e+00 -6.4141e-04 1.7791e+00 1.3357e+00 0.1816
547 1.7660e+00 -6.4426e-04 1.7870e+00 1.3215e+00 0.1863
548 1.7606e+00 -6.2353e-04 1.7295e+00 1.3392e+00 0.1805
549 1.7848e+00 -6.5859e-04 1.8268e+00 1.3210e+00 0.1865
550 1.6943e+00 -6.5763e-04 1.8241e+00 1.2549e+00 0.2095
557 1.7692e+00 -6.3480e-04 1.7608e+00 1.3338e+00 0.1823
605 1.7392e+00 -6.2213e-04 1.7256e+00 1.3245e+00 0.1853
607 1.3025e+00 -6.1793e-04 1.7140e+00 9.9539e-01 0.3195
608 1.1533e+00 -4.6500e-04 1.2898e+00 1.0159e+00 0.3097
610 1.8026e+00 -6.5763e-04 1.8241e+00 1.3352e+00 0.1818
612 1.5991e+00 -5.9946e-04 1.6628e+00 1.2405e+00 0.2148
653 1.0225e+00 -2.3994e-04 6.6556e-01 1.2537e+00 0.2100
656 1.7771e+00 -6.4521e-04 1.7897e+00 1.3289e+00 0.1839
657 1.7928e+00 -6.5715e-04 1.8228e+00 1.3284e+00 0.1841
658 1.7127e+00 -5.9717e-04 1.6564e+00 1.3312e+00 0.1831
663 1.7107e+00 -6.0635e-04 1.6819e+00 1.3196e+00 0.1870
664 1.6577e+00 -6.4047e-04 1.7765e+00 1.2442e+00 0.2134
666 1.6013e+00 -6.3621e-04 1.7647e+00 1.2059e+00 0.2279
667 1.5971e+00 -6.2915e-04 1.7451e+00 1.2095e+00 0.2265
709 1.6088e+00 -5.7946e-04 1.6073e+00 1.2694e+00 0.2043
711 1.7296e+00 -6.0267e-04 1.6717e+00 1.3382e+00 0.1808
717 1.7059e+00 -6.4189e-04 1.7805e+00 1.2790e+00 0.2009
719 1.6753e+00 -6.5763e-04 1.8241e+00 1.2409e+00 0.2146
720 1.6390e+00 -6.3952e-04 1.7739e+00 1.2311e+00 0.2183
722 4.7864e-01 -4.6814e-05 1.2986e-01 1.3283e+00 0.1841
772 1.6666e+00 -6.5763e-04 1.8241e+00 1.2344e+00 0.2170
773 1.6446e+00 -6.3291e-04 1.7556e+00 1.2417e+00 0.2143
775 1.6326e+00 -6.5476e-04 1.8161e+00 1.2120e+00 0.2255
776 1.5998e+00 -6.3009e-04 1.7477e+00 1.2106e+00 0.2260
777 1.5609e+00 -5.9397e-04 1.6476e+00 1.2165e+00 0.2238
819 1.7849e+00 -6.5332e-04 1.8122e+00 1.3264e+00 0.1847
820 1.7392e+00 -6.1421e-04 1.7037e+00 1.3329e+00 0.1826
825 1.6489e+00 -5.9033e-04 1.6374e+00 1.2891e+00 0.1974
827 7.6250e-01 -1.1666e-04 3.2361e-01 1.3406e+00 0.1801
831 1.6070e+00 -6.3668e-04 1.7660e+00 1.2097e+00 0.2264
873 1.7880e+00 -6.5093e-04 1.8055e+00 1.3311e+00 0.1831
878 1.5892e+00 -5.4267e-04 1.5053e+00 1.2958e+00 0.1951
880 1.6595e+00 -6.5811e-04 1.8255e+00 1.2288e+00 0.2192
881 1.6332e+00 -6.2259e-04 1.7269e+00 1.2433e+00 0.2138
882 1.7630e+00 -6.2774e-04 1.7412e+00 1.3365e+00 0.1814
884 1.6301e+00 -6.5811e-04 1.8255e+00 1.2070e+00 0.2274
932 1.7204e+00 -6.4331e-04 1.7844e+00 1.2884e+00 0.1976
934 1.5305e+00 -5.6915e-04 1.5787e+00 1.2185e+00 0.2230
936 1.7792e+00 -6.5811e-04 1.8255e+00 1.3173e+00 0.1877
989 1.6337e+00 -6.5045e-04 1.8042e+00 1.2167e+00 0.2237
990 1.7771e+00 -6.4616e-04 1.7923e+00 1.3279e+00 0.1842
1040 1.7386e+00 -6.5859e-04 1.8268e+00 1.2868e+00 0.1982
1042 1.7316e+00 -6.4759e-04 1.7963e+00 1.2925e+00 0.1962
1043 1.7067e+00 -6.0774e-04 1.6857e+00 1.3150e+00 0.1885
1044 1.7088e+00 -6.1793e-04 1.7140e+00 1.3057e+00 0.1917
1094 1.7461e+00 -6.5619e-04 1.8201e+00 1.2947e+00 0.1954
1096 1.7092e+00 -6.1607e-04 1.7088e+00 1.3080e+00 0.1909
1098 1.6654e+00 -5.7497e-04 1.5948e+00 1.3192e+00 0.1871
1099 1.7850e+00 -6.5428e-04 1.8148e+00 1.3255e+00 0.1850
1149 1.7587e+00 -6.5332e-04 1.8122e+00 1.3069e+00 0.1912
1151 1.7351e+00 -6.5189e-04 1.8082e+00 1.2908e+00 0.1968
1153 1.7436e+00 -6.4284e-04 1.7831e+00 1.3062e+00 0.1915
1200 1.6392e+00 -5.9992e-04 1.6640e+00 1.2712e+00 0.2037
1203 1.4325e+00 -4.1249e-04 1.1442e+00 1.3396e+00 0.1804
1205 1.5263e+00 -5.0456e-04 1.3995e+00 1.2906e+00 0.1968
1206 1.7113e+00 -6.3480e-04 1.7608e+00 1.2901e+00 0.1970
1257 1.7287e+00 -6.2915e-04 1.7451e+00 1.3091e+00 0.1905
1258 1.7413e+00 -6.4664e-04 1.7936e+00 1.3006e+00 0.1934
1260 1.5310e+00 -5.0624e-04 1.4042e+00 1.2924e+00 0.1962
1308 1.6245e+00 -5.9215e-04 1.6425e+00 1.2680e+00 0.2048
1310 1.7372e+00 -6.4664e-04 1.7936e+00 1.2976e+00 0.1944
1311 1.7527e+00 -6.5284e-04 1.8108e+00 1.3029e+00 0.1926
1312 1.7300e+00 -6.3905e-04 1.7726e+00 1.2999e+00 0.1936
1313 1.6035e+00 -5.5715e-04 1.5454e+00 1.2903e+00 0.1970
1314 1.6978e+00 -6.4047e-04 1.7765e+00 1.2743e+00 0.2026
1363 1.6824e+00 -6.0958e-04 1.6909e+00 1.2943e+00 0.1956
1365 1.7273e+00 -6.3197e-04 1.7529e+00 1.3051e+00 0.1919
1366 1.7052e+00 -6.3244e-04 1.7542e+00 1.2879e+00 0.1978
1367 1.6359e+00 -5.9443e-04 1.6488e+00 1.2745e+00 0.2025
1417 1.7531e+00 -6.5141e-04 1.8069e+00 1.3047e+00 0.1920
1419 1.7636e+00 -6.3999e-04 1.7752e+00 1.3242e+00 0.1854
1470 1.6187e+00 -6.0129e-04 1.6679e+00 1.2539e+00 0.2099
1472 1.6730e+00 -5.7766e-04 1.6023e+00 1.3221e+00 0.1861
1475 1.7034e+00 -6.1654e-04 1.7101e+00 1.3030e+00 0.1926
1523 1.3445e+00 -3.8778e-04 1.0756e+00 1.2967e+00 0.1947
1524 1.5131e+00 -5.0961e-04 1.4136e+00 1.2731e+00 0.2030
1525 1.7323e+00 -6.5476e-04 1.8161e+00 1.2859e+00 0.1985
1526 1.7670e+00 -6.4902e-04 1.8002e+00 1.3174e+00 0.1877
1528 1.6468e+00 -5.6336e-04 1.5626e+00 1.3178e+00 0.1876
1577 1.6442e+00 -6.0083e-04 1.6666e+00 1.2741e+00 0.2026
1578 1.6634e+00 -6.2633e-04 1.7373e+00 1.2625e+00 0.2068
1580 1.7233e+00 -6.1282e-04 1.6998e+00 1.3222e+00 0.1861
1581 1.7093e+00 -6.0313e-04 1.6730e+00 1.3220e+00 0.1862
1582 1.6792e+00 -5.8942e-04 1.6349e+00 1.3137e+00 0.1889
1583 1.7603e+00 -6.5332e-04 1.8122e+00 1.3081e+00 0.1908
1633 1.6281e+00 -5.4529e-04 1.5125e+00 1.3243e+00 0.1854
1634 1.7598e+00 -6.4998e-04 1.8029e+00 1.3111e+00 0.1898
1635 1.7369e+00 -6.1933e-04 1.7179e+00 1.3257e+00 0.1849
1686 1.6256e+00 -6.0728e-04 1.6845e+00 1.2530e+00 0.2102
1687 1.6572e+00 -5.9489e-04 1.6501e+00 1.2906e+00 0.1969
1688 1.7631e+00 -6.5045e-04 1.8042e+00 1.3131e+00 0.1892
1689 1.7088e+00 -6.0129e-04 1.6679e+00 1.3236e+00 0.1856
1739 1.7715e+00 -6.4521e-04 1.7897e+00 1.3247e+00 0.1853
1740 1.7463e+00 -6.5189e-04 1.8082e+00 1.2992e+00 0.1939
1741 1.7465e+00 -6.4284e-04 1.7831e+00 1.3084e+00 0.1907
1793 1.7615e+00 -6.5380e-04 1.8135e+00 1.3085e+00 0.1907
1794 1.6798e+00 -5.8715e-04 1.6286e+00 1.3167e+00 0.1879
1797 1.7776e+00 -6.5428e-04 1.8148e+00 1.3200e+00 0.1868
1798 1.7704e+00 -6.5763e-04 1.8241e+00 1.3113e+00 0.1897
1846 1.7357e+00 -6.5524e-04 1.8175e+00 1.2880e+00 0.1978
1848 1.5877e+00 -5.2795e-04 1.4644e+00 1.3124e+00 0.1894
1900 1.5833e+00 -5.2451e-04 1.4549e+00 1.3131e+00 0.1891
1902 1.7662e+00 -6.5715e-04 1.8228e+00 1.3087e+00 0.1906
1903 1.6716e+00 -5.8534e-04 1.6236e+00 1.3123e+00 0.1894
1904 1.7045e+00 -6.2073e-04 1.7218e+00 1.2995e+00 0.1938
1905 1.6949e+00 -5.9854e-04 1.6602e+00 1.3159e+00 0.1882
1906 1.7659e+00 -6.5859e-04 1.8268e+00 1.3070e+00 0.1912
1955 1.7632e+00 -6.5236e-04 1.8095e+00 1.3113e+00 0.1898
1957 1.7101e+00 -6.4331e-04 1.7844e+00 1.2807e+00 0.2003
1960 1.6901e+00 -5.9033e-04 1.6374e+00 1.3212e+00 0.1864
2009 1.6759e+00 -5.9671e-04 1.6552e+00 1.3031e+00 0.1925
2012 1.6273e+00 -5.6825e-04 1.5762e+00 1.2966e+00 0.1948
2013 1.6561e+00 -5.8670e-04 1.6274e+00 1.2986e+00 0.1941
2014 1.7101e+00 -6.2399e-04 1.7308e+00 1.3003e+00 0.1935
2062 1.5851e+00 -5.2580e-04 1.4585e+00 1.3129e+00 0.1892
2064 1.6983e+00 -6.1607e-04 1.7088e+00 1.2996e+00 0.1937
2068 1.6977e+00 -5.9717e-04 1.6564e+00 1.3196e+00 0.1870
2116 1.6211e+00 -5.6870e-04 1.5775e+00 1.2912e+00 0.1966
2120 1.6240e+00 -5.6915e-04 1.5787e+00 1.2929e+00 0.1960
2122 1.6838e+00 -5.9489e-04 1.6501e+00 1.3112e+00 0.1898
2172 1.6100e+00 -5.8353e-04 1.6186e+00 1.2660e+00 0.2055
2173 1.6099e+00 -5.7946e-04 1.6073e+00 1.2703e+00 0.2040
2175 1.6729e+00 -6.0728e-04 1.6845e+00 1.2894e+00 0.1972
2176 1.7212e+00 -6.1933e-04 1.7179e+00 1.3137e+00 0.1890
2231 9.9225e-01 -6.5189e-04 1.8082e+00 7.3839e-01 0.4603
2281 1.6221e+00 -5.9124e-04 1.6400e+00 1.2671e+00 0.2051
2284 1.0030e+00 -6.5189e-04 1.8082e+00 7.4642e-01 0.4554
2285 9.8071e-01 -6.3574e-04 1.7634e+00 7.3900e-01 0.4599
2334 1.6689e+00 -6.2306e-04 1.7282e+00 1.2699e+00 0.2041
2335 1.4390e+00 -4.4504e-04 1.2345e+00 1.2955e+00 0.1951
2336 1.6671e+00 -6.2540e-04 1.7347e+00 1.2662e+00 0.2054
2337 1.6339e+00 -5.6247e-04 1.5602e+00 1.3085e+00 0.1907
2387 1.6598e+00 -6.2774e-04 1.7412e+00 1.2583e+00 0.2083
2391 1.6174e+00 -5.3788e-04 1.4920e+00 1.3246e+00 0.1853
2392 9.8190e-01 -6.5524e-04 1.8175e+00 7.2882e-01 0.4661
2393 9.8492e-01 -6.4047e-04 1.7765e+00 7.3944e-01 0.4596
2397 1.3839e+00 -6.5284e-04 1.8108e+00 1.0289e+00 0.3035
2441 1.5725e+00 -5.5671e-04 1.5442e+00 1.2659e+00 0.2056
2442 1.6657e+00 -6.3291e-04 1.7556e+00 1.2577e+00 0.2085
2443 1.6628e+00 -5.9946e-04 1.6628e+00 1.2900e+00 0.1971
2444 1.6039e+00 -5.5892e-04 1.5503e+00 1.2886e+00 0.1975
2445 1.7424e+00 -6.4902e-04 1.8002e+00 1.2991e+00 0.1939
2446 9.6887e-01 -6.5811e-04 1.8255e+00 7.1758e-01 0.4730
2447 -4.4363e+00 -4.0359e-03 1.1190e+01 -1.3250e+00 0.1852
2450 8.0389e-01 -3.9370e-04 1.0921e+00 7.6964e-01 0.4415
2451 1.2714e+00 -5.3398e-04 1.4812e+00 1.0451e+00 0.2960
2452 1.3656e+00 -6.4807e-04 1.7976e+00 1.0191e+00 0.3082
2495 1.6129e+00 -5.7766e-04 1.6023e+00 1.2746e+00 0.2024
2497 1.7298e+00 -6.5811e-04 1.8255e+00 1.2808e+00 0.2003
2498 1.7451e+00 -6.4950e-04 1.8016e+00 1.3006e+00 0.1934
2500 8.7939e-01 -5.6291e-04 1.5614e+00 7.0421e-01 0.4813
2501 8.9811e-01 -6.1886e-04 1.7166e+00 6.8595e-01 0.4927
2503 7.8392e-01 -4.8995e-04 1.3590e+00 6.7286e-01 0.5010
2505 3.1130e-01 -2.5265e-05 7.0085e-02 1.1760e+00 0.2396
2506 9.6839e-01 -4.0228e-04 1.1159e+00 9.1711e-01 0.3591
2553 1.7184e+00 -6.3244e-04 1.7542e+00 1.2979e+00 0.1943
2554 1.7114e+00 -6.2353e-04 1.7295e+00 1.3018e+00 0.1930
2555 9.1380e-01 -6.2727e-04 1.7399e+00 6.9324e-01 0.4882
2609 6.8243e-01 -3.3996e-04 9.4300e-01 7.0311e-01 0.4820
2614 1.0093e+00 -4.8870e-04 1.3556e+00 8.6732e-01 0.3858
2659 1.7051e+00 -6.5572e-04 1.8188e+00 1.2648e+00 0.2059
2661 1.7191e+00 -6.3574e-04 1.7634e+00 1.2950e+00 0.1953
2663 1.6581e+00 -6.5572e-04 1.8188e+00 1.2299e+00 0.2187
2666 4.3604e-01 -2.0506e-04 5.6882e-01 5.7841e-01 0.5630
2668 9.2045e-01 -4.0869e-04 1.1337e+00 8.6487e-01 0.3871
2669 9.6257e-01 -3.3343e-04 9.2490e-01 1.0012e+00 0.3167
2711 1.5986e+00 -5.3615e-04 1.4872e+00 1.3113e+00 0.1898
2713 1.6863e+00 -5.9534e-04 1.6514e+00 1.3127e+00 0.1893
2715 1.7093e+00 -6.4521e-04 1.7897e+00 1.2782e+00 0.2012
2716 1.6187e+00 -5.5055e-04 1.5271e+00 1.3103e+00 0.1901
2717 1.5716e+00 -5.7991e-04 1.6086e+00 1.2396e+00 0.2151
2721 1.0251e+00 -4.0191e-04 1.1148e+00 9.7120e-01 0.3314
2769 1.5942e+00 -5.4093e-04 1.5004e+00 1.3019e+00 0.1930
2770 1.7252e+00 -6.3574e-04 1.7634e+00 1.2996e+00 0.1937
2771 1.6037e+00 -6.1561e-04 1.7076e+00 1.2277e+00 0.2196
2774 3.9303e-02 -4.0492e-04 1.1232e+00 3.7467e-02 0.9701
2776 1.1214e+00 -4.6986e-04 1.3033e+00 9.8266e-01 0.3258
2777 3.8428e-02 -4.1787e-07 1.1592e-03 1.1287e+00 0.2590
2825 1.5029e+00 -4.7923e-04 1.3293e+00 1.3040e+00 0.1922
2827 -2.8845e-01 -3.6593e-04 1.0150e+00 -2.8595e-01 0.7749
2828 4.4101e-01 -1.8904e-04 5.2437e-01 6.0928e-01 0.5423
2829 1.2389e+00 -5.3832e-04 1.4932e+00 1.0143e+00 0.3104
2877 1.4764e+00 -4.5138e-04 1.2520e+00 1.3199e+00 0.1869
2878 1.6846e+00 -6.3197e-04 1.7529e+00 1.2728e+00 0.2031
2879 1.5687e+00 -5.4267e-04 1.5053e+00 1.2790e+00 0.2009
2880 1.6478e+00 -6.3763e-04 1.7686e+00 1.2395e+00 0.2152
2882 -3.3282e-02 -7.2616e-06 2.0144e-02 -2.3445e-01 0.8146
2883 9.4591e-01 -5.2451e-04 1.4549e+00 7.8465e-01 0.4327
2885 1.1588e+00 -4.6178e-04 1.2809e+00 1.0243e+00 0.3057
2927 1.7052e+00 -6.3432e-04 1.7595e+00 1.2860e+00 0.1984
2932 1.5565e+00 -5.7631e-04 1.5986e+00 1.2315e+00 0.2181
2934 1.0562e+00 -6.0129e-04 1.6679e+00 8.1834e-01 0.4132
2935 -1.8550e-01 -1.1445e-04 3.1747e-01 -3.2901e-01 0.7421
2936 -7.3544e-02 -4.3483e-04 1.2061e+00 -6.6569e-02 0.9469
2982 1.6653e+00 -6.0083e-04 1.6666e+00 1.2904e+00 0.1969
2984 1.6344e+00 -6.5236e-04 1.8095e+00 1.2155e+00 0.2242
2986 1.6084e+00 -6.2868e-04 1.7438e+00 1.2185e+00 0.2230
2987 1.5344e+00 -6.3197e-04 1.7529e+00 1.1594e+00 0.2463
2988 1.5456e+00 -6.4379e-04 1.7857e+00 1.1571e+00 0.2472
2990 1.5753e-01 -3.0335e-03 8.4117e+00 5.5361e-02 0.9559
2991 -1.7240e-02 -1.6203e-04 4.4945e-01 -2.5473e-02 0.9797
2993 1.3127e+00 -5.7946e-04 1.6073e+00 1.0359e+00 0.3003
3036 1.7174e+00 -6.5141e-04 1.8069e+00 1.2781e+00 0.2012
3039 1.6497e+00 -6.3197e-04 1.7529e+00 1.2465e+00 0.2126
3040 1.5573e+00 -6.3103e-04 1.7503e+00 1.1776e+00 0.2390
3042 3.3548e-01 -3.4864e-04 9.6708e-01 3.4150e-01 0.7327
3043 -8.7264e-01 -4.5896e-04 1.2731e+00 -7.7299e-01 0.4395
3044 -3.1256e-01 -8.6382e-05 2.3962e-01 -6.3834e-01 0.5233
3047 1.1201e+00 -6.2540e-04 1.7347e+00 8.5089e-01 0.3948
3048 1.6804e+00 -6.5524e-04 1.8175e+00 1.2470e+00 0.2124
3049 1.5070e+00 -5.1981e-04 1.4418e+00 1.2554e+00 0.2093
3095 8.3720e-01 -1.6346e-04 4.5342e-01 1.2436e+00 0.2137
3097 -2.7196e-01 -3.9110e-04 1.0849e+00 -2.6073e-01 0.7943
3098 1.4933e+00 -3.0438e-03 8.4403e+00 5.1505e-01 0.6065
3099 6.4895e-02 -4.7305e-04 1.3122e+00 5.7066e-02 0.9545
3102 1.4933e+00 -6.5141e-04 1.8069e+00 1.1114e+00 0.2664
3104 1.5848e+00 -5.8082e-04 1.6111e+00 1.2490e+00 0.2116
3105 1.4798e+00 -4.9785e-04 1.3809e+00 1.2597e+00 0.2078
3145 1.4466e+00 -4.7270e-04 1.3112e+00 1.2638e+00 0.2063
3146 1.3688e+00 -4.2089e-04 1.1675e+00 1.2672e+00 0.2051
3147 1.3719e+00 -4.2899e-04 1.1900e+00 1.2580e+00 0.2084
3148 1.1720e+00 -3.2765e-04 9.0885e-01 1.2297e+00 0.2188
3149 1.3911e+00 -5.6380e-04 1.5639e+00 1.1129e+00 0.2658
3151 -5.1295e-01 -4.2196e-05 1.1705e-01 -1.4992e+00 0.1338
3152 3.7004e-01 -2.9139e-04 8.0829e-01 4.1192e-01 0.6804
3153 8.4530e-03 -4.7874e-07 1.3280e-03 2.3197e-01 0.8166
3155 1.0961e+00 -6.0820e-04 1.6870e+00 8.4434e-01 0.3985
3158 1.4180e+00 -4.5217e-04 1.2543e+00 1.2666e+00 0.2053
3159 1.6745e+00 -6.4189e-04 1.7805e+00 1.2554e+00 0.2093
3198 1.7000e+00 -6.1514e-04 1.7063e+00 1.3019e+00 0.1929
3199 1.4798e+00 -4.7637e-04 1.3214e+00 1.2877e+00 0.1978
3200 1.6281e+00 -6.5715e-04 1.8228e+00 1.2064e+00 0.2277
3202 1.6781e+00 -6.5715e-04 1.8228e+00 1.2434e+00 0.2137
3203 1.4242e+00 -5.9352e-04 1.6463e+00 1.1104e+00 0.2668
3204 3.9256e-01 -2.6674e-04 7.3991e-01 4.5668e-01 0.6479
3205 -2.5675e+00 -7.6508e-03 2.1203e+01 -5.5593e-01 0.5783
3206 1.9921e+00 -2.5541e-03 7.0828e+00 7.4951e-01 0.4536
3207 4.9882e-02 -7.3628e-06 2.0424e-02 3.4909e-01 0.7270
3208 -1.9609e-01 -1.5194e-04 4.2148e-01 -3.0181e-01 0.7628
3213 1.4124e+00 -4.3600e-04 1.2094e+00 1.2847e+00 0.1989
3214 1.6894e+00 -6.4569e-04 1.7910e+00 1.2628e+00 0.2066
3251 1.7112e+00 -6.2446e-04 1.7321e+00 1.3007e+00 0.1934
3252 1.6881e+00 -6.4807e-04 1.7976e+00 1.2596e+00 0.2078
3255 1.6095e+00 -6.4521e-04 1.7897e+00 1.2036e+00 0.2288
3257 1.3346e+00 -5.1046e-04 1.4159e+00 1.1221e+00 0.2618
3258 -2.2130e-01 -4.5177e-04 1.2532e+00 -1.9729e-01 0.8436
3259 2.0127e-01 -9.7088e-06 2.6932e-02 1.2265e+00 0.2200
3260 -5.7893e-01 -5.8488e-04 1.6223e+00 -4.5406e-01 0.6498
3261 -1.5531e+00 -2.4557e-03 6.8101e+00 -5.9420e-01 0.5524
3268 1.6753e+00 -6.3338e-04 1.7569e+00 1.2644e+00 0.2061
3269 1.6829e+00 -6.3999e-04 1.7752e+00 1.2636e+00 0.2064
3306 1.6566e+00 -6.0359e-04 1.6742e+00 1.2807e+00 0.2003
3308 1.4577e+00 -4.9244e-04 1.3659e+00 1.2477e+00 0.2121
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14066 7.0421e-01 -3.5703e-04 9.9035e-01 7.0799e-01 0.4790
14067 1.7083e-01 -4.5651e-04 1.2663e+00 1.5222e-01 0.8790
14113 8.0193e-01 -4.4464e-04 1.2334e+00 7.2249e-01 0.4700
14114 6.3451e-01 -2.5346e-04 7.0307e-01 7.5703e-01 0.4490
14115 1.3759e-01 -2.8167e-05 7.8134e-02 4.9234e-01 0.6225
14116 -7.5773e-01 -1.1505e-04 3.1914e-01 -1.3411e+00 0.1799
14118 -2.3841e-01 -4.0392e-05 1.1205e-01 -7.1213e-01 0.4764
14119 4.2253e-01 -3.2153e-04 8.9188e-01 4.4775e-01 0.6543
14120 6.1730e-01 -4.4216e-03 1.2259e+01 1.7757e-01 0.8591
14121 -1.2811e+00 -5.4529e-04 1.5125e+00 -1.0413e+00 0.2978
14122 1.5905e-02 -7.8896e-05 2.1886e-01 3.4166e-02 0.9727
14165 1.4220e+00 -6.4950e-04 1.8016e+00 1.0599e+00 0.2892
14167 8.8216e-01 -3.6027e-04 9.9934e-01 8.8281e-01 0.3773
14170 2.9629e+00 -1.0197e-03 2.8282e+00 1.7625e+00 0.0780
14171 1.8927e+00 -3.8351e-03 1.0633e+01 5.8160e-01 0.5608
14220 1.0248e+00 -3.0534e-04 8.4698e-01 1.1139e+00 0.2653
14222 -7.6577e-02 -2.1571e-06 5.9838e-03 -9.8991e-01 0.3222
14227 -1.9334e-02 -2.3579e-06 6.5407e-03 -2.3903e-01 0.8111
14228 -1.7149e-01 -2.1295e-05 5.9072e-02 -7.0549e-01 0.4805
14229 -1.9575e-01 -2.9749e-04 8.2522e-01 -2.1515e-01 0.8296
14230 2.9347e-01 -1.3296e-04 3.6883e-01 4.8345e-01 0.6288
14273 1.4819e+00 -6.5236e-04 1.8095e+00 1.1021e+00 0.2704
14274 1.9155e-01 -8.6400e-06 2.3967e-02 1.2374e+00 0.2160
14275 1.3079e+00 -6.0635e-04 1.6819e+00 1.0090e+00 0.3130
14276 6.7404e-01 -2.6491e-04 7.3483e-01 7.8661e-01 0.4315
14278 -2.5068e-02 -5.8190e-05 1.6142e-01 -6.2249e-02 0.9504
14280 -1.8383e-01 -2.5821e-04 7.1624e-01 -2.1691e-01 0.8283
14281 -2.1352e-01 -5.3986e-05 1.4975e-01 -5.5162e-01 0.5812
14282 -1.6149e-02 -2.4149e-05 6.6989e-02 -6.2301e-02 0.9503
14283 2.1829e-01 -1.6322e-04 4.5276e-01 3.2465e-01 0.7454
14284 4.3677e-01 -5.4616e-04 1.5150e+00 3.5530e-01 0.7224
14327 1.6555e+00 -6.3621e-04 1.7647e+00 1.2467e+00 0.2125
14328 1.4915e+00 -6.2446e-04 1.7321e+00 1.1338e+00 0.2569
14329 1.4944e+00 -6.3197e-04 1.7529e+00 1.1292e+00 0.2588
14331 3.4157e-01 -5.0203e-05 1.3926e-01 9.1542e-01 0.3600
14334 -2.5564e-05 -7.5680e-11 2.0994e-07 -5.5794e-02 0.9555
14335 -1.0490e-01 -8.2063e-05 2.2764e-01 -2.1969e-01 0.8261
14336 -1.8750e-01 -1.0950e-04 3.0374e-01 -3.4001e-01 0.7339
14337 1.5875e-01 -2.4753e-04 6.8663e-01 1.9188e-01 0.8478
14383 1.3805e+00 -6.4474e-04 1.7884e+00 1.0328e+00 0.3017
14386 2.9628e-01 -9.0607e-05 2.5134e-01 5.9116e-01 0.5544
14387 1.5755e-01 -4.4164e-05 1.2251e-01 4.5025e-01 0.6525
14388 1.8251e-01 -6.1190e-04 1.6973e+00 1.4056e-01 0.8882
14389 -1.0621e+00 -8.1585e-04 2.2629e+00 -7.0551e-01 0.4805
14392 8.1649e-01 -5.0792e-04 1.4089e+00 6.8831e-01 0.4913
14435 1.6596e+00 -5.6380e-04 1.5639e+00 1.3275e+00 0.1843
14436 1.5453e+00 -6.4616e-04 1.7923e+00 1.1548e+00 0.2482
14437 1.4436e+00 -5.4093e-04 1.5004e+00 1.1790e+00 0.2384
14438 1.2139e+00 -5.8488e-04 1.6223e+00 9.5351e-01 0.3403
14439 1.1841e+00 -5.8262e-04 1.6161e+00 9.3189e-01 0.3514
14440 1.1248e+00 -5.6469e-04 1.5663e+00 8.9916e-01 0.3686
14441 8.9042e-01 -3.9147e-04 1.0859e+00 8.5486e-01 0.3926
14443 3.5894e-01 -3.9779e-04 1.1034e+00 3.4208e-01 0.7323
14489 1.6791e+00 -6.0221e-04 1.6704e+00 1.2996e+00 0.1937
14490 1.7285e+00 -6.4855e-04 1.7989e+00 1.2892e+00 0.1973
14494 9.9134e-01 -5.0624e-04 1.4042e+00 8.3701e-01 0.4026
14496 9.2253e-01 -5.9534e-04 1.6514e+00 7.1836e-01 0.4725
14544 1.6572e+00 -5.9854e-04 1.6602e+00 1.2866e+00 0.1982
14545 1.7284e+00 -6.4807e-04 1.7976e+00 1.2896e+00 0.1972
14547 1.2719e+00 -4.7964e-04 1.3304e+00 1.1031e+00 0.2700
14549 7.8509e-01 -3.0730e-04 8.5243e-01 8.5067e-01 0.3950
14550 2.8005e-01 -2.6024e-05 7.2189e-02 1.0424e+00 0.2972
14551 9.8781e-01 -5.7317e-04 1.5899e+00 7.8387e-01 0.4331
14552 8.1888e-01 -6.2587e-04 1.7360e+00 6.2198e-01 0.5340
14598 1.5228e+00 -4.8623e-04 1.3487e+00 1.3117e+00 0.1896
14602 1.3030e+00 -5.5937e-04 1.5516e+00 1.0465e+00 0.2953
14603 9.8612e-01 -3.3377e-04 9.2585e-01 1.0252e+00 0.3053
14604 1.3824e+00 -6.2774e-04 1.7412e+00 1.0481e+00 0.2946
14606 4.3841e-01 -4.7328e-05 1.3129e-01 1.2101e+00 0.2262
14655 1.4472e+00 -5.7766e-04 1.6023e+00 1.1438e+00 0.2527
14658 1.0529e+00 -3.6454e-04 1.0112e+00 1.0474e+00 0.2949
14660 7.9329e-01 -3.8999e-04 1.0818e+00 7.6309e-01 0.4454
14661 9.8471e-01 -2.6582e-04 7.3737e-01 1.1470e+00 0.2514
14663 1.6252e+00 -5.5937e-04 1.5516e+00 1.3052e+00 0.1918
14709 1.6356e+00 -6.3244e-04 1.7542e+00 1.2354e+00 0.2167
14710 1.3934e+00 -5.4791e-04 1.5198e+00 1.1307e+00 0.2582
14712 1.2961e+00 -5.3096e-04 1.4728e+00 1.0685e+00 0.2853
14715 1.5020e+00 -6.3621e-04 1.7647e+00 1.1311e+00 0.2580
14716 1.7406e+00 -6.5332e-04 1.8122e+00 1.2935e+00 0.1958
14717 1.6216e+00 -5.7811e-04 1.6036e+00 1.2810e+00 0.2002
14765 1.2506e+00 -5.6469e-04 1.5663e+00 9.9969e-01 0.3175
14766 1.1968e+00 -4.5576e-04 1.2642e+00 1.0648e+00 0.2870
14767 1.4807e+00 -5.5627e-04 1.5430e+00 1.1925e+00 0.2331
14770 1.6558e+00 -6.4094e-04 1.7778e+00 1.2423e+00 0.2141
14771 1.6776e+00 -6.0129e-04 1.6679e+00 1.2994e+00 0.1938
14821 1.4945e+00 -6.4902e-04 1.8002e+00 1.1143e+00 0.2651
14823 1.5314e+00 -5.4704e-04 1.5174e+00 1.2437e+00 0.2136
14824 1.6251e+00 -5.8353e-04 1.6186e+00 1.2778e+00 0.2013
14876 1.3169e+00 -5.2709e-04 1.4620e+00 1.0896e+00 0.2759
14877 1.6251e+00 -6.3857e-04 1.7713e+00 1.2215e+00 0.2219
14878 1.6641e+00 -5.9946e-04 1.6628e+00 1.2910e+00 0.1967
14932 1.6616e+00 -6.0359e-04 1.6742e+00 1.2846e+00 0.1989
14933 1.6583e+00 -6.2962e-04 1.7464e+00 1.2553e+00 0.2094
14934 1.4604e+00 -6.0912e-04 1.6896e+00 1.1240e+00 0.2610
14984 1.4249e+00 -5.0750e-04 1.4077e+00 1.2013e+00 0.2296
14986 1.5208e+00 -4.8870e-04 1.3556e+00 1.3066e+00 0.1913
14988 1.3130e+00 -4.7760e-04 1.3248e+00 1.1412e+00 0.2538
14989 1.4873e+00 -6.4426e-04 1.7870e+00 1.1130e+00 0.2657
15038 1.6817e+00 -6.3905e-04 1.7726e+00 1.2636e+00 0.2064
15086 4.8221e-01 -1.3863e-04 3.8456e-01 7.7781e-01 0.4367
15096 1.3583e+00 -5.1555e-04 1.4300e+00 1.1363e+00 0.2558
15097 6.8872e-01 -5.3745e-04 1.4908e+00 5.6451e-01 0.5724
15139 3.8293e-01 -3.8279e-05 1.0618e-01 1.1752e+00 0.2399
15195 6.4570e-01 -5.4180e-04 1.5028e+00 5.2715e-01 0.5981
15204 1.2121e-01 -1.0796e-05 2.9947e-02 7.0046e-01 0.4836
15205 7.5844e-01 -6.1190e-04 1.6973e+00 5.8264e-01 0.5601
15258 6.9264e-01 -5.3269e-04 1.4776e+00 5.7025e-01 0.5685
15305 -6.1944e-01 -9.1209e-04 2.5299e+00 -3.8887e-01 0.6974
15312 7.8634e-01 -6.5524e-04 1.8175e+00 5.8377e-01 0.5594
15366 -3.6469e+00 -3.6281e-03 1.0060e+01 -1.1487e+00 0.2507
15404 -4.1912e-01 -4.7826e-05 1.3267e-01 -1.1505e+00 0.2499
15413 -4.9308e-02 -1.8368e-05 5.0952e-02 -2.1836e-01 0.8271
15421 7.9762e-01 -6.3668e-04 1.7660e+00 6.0068e-01 0.5481
15468 -2.0706e+00 -3.9425e-03 1.0931e+01 -6.2507e-01 0.5319
15529 9.2682e-01 -5.7721e-04 1.6011e+00 7.3293e-01 0.4636
15582 8.9675e-01 -6.5380e-04 1.8135e+00 6.6639e-01 0.5052
15620 1.1289e+00 -5.9900e-04 1.6615e+00 8.7626e-01 0.3809
15633 7.2185e-01 -1.5824e-04 4.3894e-01 1.0898e+00 0.2758
15673 1.1659e+00 -6.4855e-04 1.7989e+00 8.6974e-01 0.3844
15687 1.1229e+00 -4.2281e-04 1.1728e+00 1.0373e+00 0.2996
15690 8.2363e-01 -6.2026e-04 1.7205e+00 6.2840e-01 0.5297
15742 8.9415e-01 -2.5286e-04 7.0142e-01 1.0679e+00 0.2855
15743 1.1404e+00 -3.6777e-04 1.0201e+00 1.1294e+00 0.2587
15797 8.6091e-01 -1.8596e-04 5.1584e-01 1.1989e+00 0.2306
15798 1.3960e+00 -4.8953e-04 1.3579e+00 1.1984e+00 0.2308
15852 1.5031e+00 -6.5715e-04 1.8228e+00 1.1138e+00 0.2654
15903 1.2509e+00 -5.4354e-04 1.5077e+00 1.0192e+00 0.3081
15904 1.3604e+00 -5.4704e-04 1.5174e+00 1.1048e+00 0.2692
15958 1.3254e+00 -6.2353e-04 1.7295e+00 1.0083e+00 0.3133
16065 1.2903e+00 -5.8488e-04 1.6223e+00 1.0135e+00 0.3108
16430 4.0602e-01 -5.5099e-04 1.5283e+00 3.2887e-01 0.7423
Ii E.Ii Var.Ii Z.Ii Pr.z....E.Ii..
5 1.562868 -0.0006466400 1.793631 1.167442 0.2430318
113 1.564357 -0.0006466400 1.793631 1.168554 0.2425835
117 1.585182 -0.0006343237 1.759471 1.195534 0.2318786
118 1.562521 -0.0006230598 1.728230 1.189045 0.2344221
167 1.509317 -0.0005722772 1.587380 1.198407 0.2307584
Show the code
<- cbind(honeycomb_count11_14, localMI11_14)%>%
honeycomb_count11_14.localMI rename(Pr.Ii = Pr.z....E.Ii..)
For weekend/holidays evening peak:
Show the code
<- order(honeycomb_count16_19$grid_id)
fips16_19 <- localmoran(honeycomb_count16_19$Sum_TRIPS, wm16_19)
localMI16_19 head(localMI16_19)
Ii E.Ii Var.Ii Z.Ii Pr(z != E(Ii))
1 1.1210198 -0.0004634753 1.2726271 0.9941278 0.3201607
2 1.1800130 -0.0004778890 1.3122025 1.0305337 0.3027595
3 1.0835925 -0.0004486119 1.2318170 0.9767257 0.3287049
4 1.0167585 -0.0003699751 1.0159028 1.0091361 0.3129094
5 0.9513416 -0.0002875336 0.7895375 1.0709800 0.2841784
6 1.0912541 -0.0004638159 1.2735623 0.9673872 0.3333505
Show the code
printCoefmat(data.frame(
localMI16_19[fips16_19,],row.names=honeycomb_count16_19$grid_id[fips16_19])
|> head(5) )
Ii E.Ii Var.Ii Z.Ii Pr.z....E.Ii..
58 1.1210e+00 -4.6348e-04 1.2726e+00 9.9413e-01 0.3202
221 1.1800e+00 -4.7789e-04 1.3122e+00 1.0305e+00 0.3028
225 1.0836e+00 -4.4861e-04 1.2318e+00 9.7673e-01 0.3287
329 1.0168e+00 -3.6998e-04 1.0159e+00 1.0091e+00 0.3129
332 9.5134e-01 -2.8753e-04 7.8954e-01 1.0710e+00 0.2842
334 1.0913e+00 -4.6382e-04 1.2736e+00 9.6739e-01 0.3334
386 1.1987e+00 -4.3795e-04 1.2026e+00 1.0935e+00 0.2742
390 1.1121e+00 -4.6586e-04 1.2792e+00 9.8369e-01 0.3253
438 1.1868e+00 -4.6450e-04 1.2754e+00 1.0512e+00 0.2931
440 1.1561e+00 -4.4493e-04 1.2217e+00 1.0464e+00 0.2954
444 9.7878e-01 -4.7927e-04 1.3160e+00 8.5363e-01 0.3933
496 7.5478e-01 -1.9112e-04 5.2481e-01 1.0421e+00 0.2973
499 9.1833e-01 -4.3103e-04 1.1835e+00 8.4452e-01 0.3984
500 -3.8346e-01 -5.5764e-05 1.5313e-01 -9.7979e-01 0.3272
547 1.2068e+00 -4.4127e-04 1.2117e+00 1.0968e+00 0.2727
548 1.2360e+00 -4.7100e-04 1.2933e+00 1.0872e+00 0.2769
550 6.6459e-01 -1.4489e-04 3.9787e-01 1.0538e+00 0.2920
551 9.8901e-01 -3.6724e-04 1.0084e+00 9.8525e-01 0.3245
553 6.0149e-01 -1.8612e-04 5.1109e-01 8.4162e-01 0.4000
554 8.1527e-01 -3.6181e-04 9.9347e-01 8.1831e-01 0.4132
604 1.0938e+00 -4.2612e-04 1.1701e+00 1.0116e+00 0.3117
606 1.1521e+00 -4.7100e-04 1.2933e+00 1.0135e+00 0.3108
609 8.5737e-01 -4.0516e-04 1.1125e+00 8.1325e-01 0.4161
656 1.2744e+00 -4.7616e-04 1.3075e+00 1.1149e+00 0.2649
657 1.1513e+00 -4.7997e-04 1.3179e+00 1.0033e+00 0.3157
660 1.0058e+00 -3.6271e-04 9.9595e-01 1.0082e+00 0.3133
664 1.2195e+00 -4.4493e-04 1.2217e+00 1.1037e+00 0.2697
707 8.1013e-01 -2.1362e-04 5.8657e-01 1.0581e+00 0.2900
712 1.1062e+00 -4.6245e-04 1.2698e+00 9.8203e-01 0.3261
719 1.2289e+00 -4.3564e-04 1.1962e+00 1.1240e+00 0.2610
720 1.1875e+00 -4.1444e-04 1.1380e+00 1.1136e+00 0.2655
763 1.2605e+00 -4.7340e-04 1.2999e+00 1.1060e+00 0.2687
764 1.2341e+00 -4.4928e-04 1.2337e+00 1.1115e+00 0.2663
766 1.1028e+00 -4.0867e-04 1.1221e+00 1.0415e+00 0.2977
771 1.1227e+00 -4.2221e-04 1.1593e+00 1.0431e+00 0.2969
774 8.4610e-01 -4.2026e-04 1.1540e+00 7.8802e-01 0.4307
817 1.1091e+00 -3.8317e-04 1.0521e+00 1.0817e+00 0.2794
821 1.0615e+00 -3.8908e-04 1.0684e+00 1.0274e+00 0.3042
823 8.5363e-01 -4.0452e-04 1.1108e+00 8.1034e-01 0.4177
824 7.8522e-01 -2.1524e-04 5.9103e-01 1.0217e+00 0.3069
826 1.2517e+00 -4.6382e-04 1.2736e+00 1.1096e+00 0.2672
869 8.3438e-01 -2.3155e-04 6.3581e-01 1.0467e+00 0.2952
872 1.1893e+00 -4.1864e-04 1.1495e+00 1.1096e+00 0.2672
873 1.2213e+00 -4.4194e-04 1.2135e+00 1.1091e+00 0.2674
879 1.1377e+00 -4.3169e-04 1.1853e+00 1.0454e+00 0.2959
881 1.0099e+00 -4.8240e-04 1.3246e+00 8.7788e-01 0.3800
883 8.7115e-01 -4.5568e-04 1.2512e+00 7.7921e-01 0.4359
885 8.2209e-01 -4.0835e-04 1.1213e+00 7.7675e-01 0.4373
928 1.1666e+00 -4.0611e-04 1.1151e+00 1.1051e+00 0.2691
933 1.1898e+00 -4.7237e-04 1.2971e+00 1.0451e+00 0.2960
935 1.0242e+00 -4.7893e-04 1.3151e+00 8.9351e-01 0.3716
936 1.0062e+00 -4.7962e-04 1.3170e+00 8.7720e-01 0.3804
938 -1.6427e+00 -8.0588e-04 2.2127e+00 -1.1038e+00 0.2697
981 1.2339e+00 -4.6620e-04 1.2801e+00 1.0910e+00 0.2753
986 1.1019e+00 -3.9472e-04 1.0838e+00 1.0588e+00 0.2897
988 1.0147e+00 -4.8031e-04 1.3189e+00 8.8395e-01 0.3767
989 9.5315e-01 -4.0039e-04 1.0994e+00 9.0941e-01 0.3631
991 8.9016e-01 -4.8031e-04 1.3189e+00 7.7554e-01 0.4380
992 7.9003e-01 -3.7119e-04 1.0192e+00 7.8291e-01 0.4337
1043 -8.1502e-01 -1.8987e-04 5.2137e-01 -1.1285e+00 0.2591
1089 1.2469e+00 -4.7754e-04 1.3113e+00 1.0893e+00 0.2760
1094 1.0899e+00 -3.5254e-04 9.6802e-01 1.1081e+00 0.2678
1097 9.9433e-01 -4.5872e-04 1.2596e+00 8.8638e-01 0.3754
1098 1.2180e+00 -4.4962e-04 1.2346e+00 1.0966e+00 0.2728
1148 1.2256e+00 -4.4761e-04 1.2291e+00 1.1059e+00 0.2688
1150 1.1698e+00 -3.9252e-04 1.0778e+00 1.1272e+00 0.2597
1151 9.7922e-01 -4.7272e-04 1.2980e+00 8.5991e-01 0.3898
1152 1.1951e+00 -4.5906e-04 1.2605e+00 1.0648e+00 0.2869
1202 1.2439e+00 -4.7547e-04 1.3056e+00 1.0891e+00 0.2761
1203 1.2569e+00 -4.7375e-04 1.3008e+00 1.1024e+00 0.2703
1204 9.7823e-01 -4.4560e-04 1.2236e+00 8.8477e-01 0.3763
1206 1.1549e+00 -4.1477e-04 1.1389e+00 1.0826e+00 0.2790
1207 8.7980e-01 -4.7858e-04 1.3141e+00 7.6790e-01 0.4425
1259 1.1669e+00 -4.0899e-04 1.1230e+00 1.1015e+00 0.2707
1260 1.2009e+00 -4.6450e-04 1.2754e+00 1.0638e+00 0.2874
1310 1.1914e+00 -4.7651e-04 1.3084e+00 1.0420e+00 0.2974
1311 1.1775e+00 -4.7582e-04 1.3065e+00 1.0306e+00 0.3027
1312 1.2029e+00 -4.4761e-04 1.2291e+00 1.0854e+00 0.2777
1313 1.0049e+00 -3.0468e-04 8.3662e-01 1.0990e+00 0.2718
1314 1.0263e+00 -3.3843e-04 9.2927e-01 1.0650e+00 0.2869
1315 1.1831e+00 -4.2188e-04 1.1584e+00 1.0996e+00 0.2715
1365 1.1466e+00 -4.3300e-04 1.1890e+00 1.0520e+00 0.2928
1366 1.1906e+00 -4.8031e-04 1.3189e+00 1.0372e+00 0.2997
1367 1.2322e+00 -4.7858e-04 1.3141e+00 1.0753e+00 0.2822
1368 1.1835e+00 -4.6177e-04 1.2680e+00 1.0515e+00 0.2931
1369 1.2044e+00 -4.6008e-04 1.2633e+00 1.0720e+00 0.2837
1416 9.6692e-01 -3.4280e-04 9.4130e-01 9.9697e-01 0.3188
1419 4.6598e-01 -6.3548e-05 1.7450e-01 1.1157e+00 0.2646
1473 1.1672e+00 -4.6997e-04 1.2905e+00 1.0279e+00 0.3040
1474 1.1569e+00 -4.4694e-04 1.2272e+00 1.0447e+00 0.2961
1476 9.9650e-01 -3.2034e-04 8.7962e-01 1.0628e+00 0.2879
1525 1.1180e+00 -3.9252e-04 1.0778e+00 1.0773e+00 0.2814
1526 1.2481e+00 -4.6894e-04 1.2876e+00 1.1003e+00 0.2712
1527 1.1510e+00 -4.5804e-04 1.2577e+00 1.0267e+00 0.3045
1528 1.2486e+00 -4.7823e-04 1.3132e+00 1.0900e+00 0.2757
1529 1.0293e+00 -3.4310e-04 9.4210e-01 1.0608e+00 0.2888
1530 1.1423e+00 -4.4560e-04 1.2236e+00 1.0331e+00 0.3016
1579 1.1860e+00 -4.7858e-04 1.3141e+00 1.0350e+00 0.3007
1580 1.2129e+00 -4.5197e-04 1.2410e+00 1.0891e+00 0.2761
1581 1.0858e+00 -3.9566e-04 1.0864e+00 1.0421e+00 0.2974
1582 1.1225e+00 -4.5264e-04 1.2429e+00 1.0073e+00 0.3138
1583 1.0979e+00 -3.8535e-04 1.0581e+00 1.0677e+00 0.2856
1631 6.6110e-01 -1.4092e-04 3.8696e-01 1.0630e+00 0.2878
1633 1.1583e+00 -4.0071e-04 1.1003e+00 1.1046e+00 0.2693
1685 1.0522e+00 -3.9472e-04 1.0838e+00 1.0111e+00 0.3120
1686 9.9565e-01 -3.6603e-04 1.0051e+00 9.9350e-01 0.3205
1688 1.2081e+00 -4.4160e-04 1.2126e+00 1.0975e+00 0.2724
1689 1.2471e+00 -4.6997e-04 1.2905e+00 1.0982e+00 0.2721
1691 1.1165e+00 -4.0835e-04 1.1213e+00 1.0547e+00 0.2915
1740 9.6405e-01 -3.2517e-04 8.9288e-01 1.0206e+00 0.3075
1741 1.1130e+00 -3.9252e-04 1.0778e+00 1.0725e+00 0.2835
1742 1.2340e+00 -4.7375e-04 1.3008e+00 1.0824e+00 0.2791
1744 1.1251e+00 -3.9189e-04 1.0761e+00 1.0850e+00 0.2779
1794 1.0862e+00 -4.4828e-04 1.2309e+00 9.7943e-01 0.3274
1796 1.1874e+00 -4.4861e-04 1.2318e+00 1.0703e+00 0.2845
1797 1.0878e+00 -3.4280e-04 9.4130e-01 1.1216e+00 0.2620
1798 1.1704e+00 -4.1929e-04 1.1513e+00 1.0912e+00 0.2752
1848 1.1694e+00 -4.6723e-04 1.2829e+00 1.0328e+00 0.3017
1849 1.2198e+00 -4.6655e-04 1.2811e+00 1.0781e+00 0.2810
1851 1.2279e+00 -4.5399e-04 1.2466e+00 1.1002e+00 0.2712
1903 1.0007e+00 -3.3610e-04 9.2289e-01 1.0420e+00 0.2974
1905 1.2406e+00 -4.6042e-04 1.2642e+00 1.1038e+00 0.2697
1955 1.2252e+00 -4.6997e-04 1.2905e+00 1.0790e+00 0.2806
1958 1.2664e+00 -4.8031e-04 1.3189e+00 1.1031e+00 0.2700
2009 1.2035e+00 -4.7754e-04 1.3113e+00 1.0514e+00 0.2931
2010 1.0674e+00 -3.4603e-04 9.5017e-01 1.0954e+00 0.2733
2011 1.1397e+00 -4.2351e-04 1.1629e+00 1.0572e+00 0.2904
2014 1.2094e+00 -4.8066e-04 1.3198e+00 1.0532e+00 0.2923
2062 1.2250e+00 -4.7997e-04 1.3179e+00 1.0675e+00 0.2858
2063 1.2037e+00 -4.7789e-04 1.3122e+00 1.0513e+00 0.2931
2064 9.5487e-01 -2.8299e-04 7.7707e-01 1.0835e+00 0.2786
2065 1.1798e+00 -4.6723e-04 1.2829e+00 1.0420e+00 0.2974
2116 9.5770e-01 -2.7506e-04 7.5530e-01 1.1023e+00 0.2703
2117 1.1060e+00 -4.1864e-04 1.1495e+00 1.0320e+00 0.3021
2119 1.1640e+00 -4.6143e-04 1.2670e+00 1.0345e+00 0.3009
2120 1.2046e+00 -4.4694e-04 1.2272e+00 1.0878e+00 0.2767
2121 1.2056e+00 -4.4061e-04 1.2098e+00 1.0965e+00 0.2729
2170 1.0218e+00 -3.1780e-04 8.7263e-01 1.0942e+00 0.2739
2172 1.1583e+00 -4.3762e-04 1.2016e+00 1.0570e+00 0.2905
2176 8.9874e-01 -2.4796e-04 6.8087e-01 1.0895e+00 0.2759
2228 1.0817e+00 -3.6876e-04 1.0126e+00 1.0753e+00 0.2822
2229 1.1255e+00 -4.1412e-04 1.1371e+00 1.0559e+00 0.2910
2230 1.1014e+00 -3.9818e-04 1.0934e+00 1.0537e+00 0.2920
2277 1.1361e+00 -4.1541e-04 1.1407e+00 1.0641e+00 0.2873
2281 1.0495e+00 -3.8039e-04 1.0445e+00 1.0273e+00 0.3043
2283 1.1902e+00 -4.4160e-04 1.2126e+00 1.0813e+00 0.2796
2284 1.1091e+00 -3.9724e-04 1.0908e+00 1.0623e+00 0.2881
2332 1.2049e+00 -4.7927e-04 1.3160e+00 1.0507e+00 0.2934
2335 1.0874e+00 -4.1994e-04 1.1531e+00 1.0130e+00 0.3111
2336 1.0322e+00 -3.4633e-04 9.5097e-01 1.0589e+00 0.2897
2337 1.1649e+00 -4.4293e-04 1.2162e+00 1.0567e+00 0.2907
2338 1.0567e+00 -3.5432e-04 9.7292e-01 1.0716e+00 0.2839
2339 1.2126e+00 -4.8135e-04 1.3217e+00 1.0552e+00 0.2913
2392 1.1084e+00 -4.6655e-04 1.2811e+00 9.7975e-01 0.3272
2393 1.0401e+00 -4.2972e-04 1.1799e+00 9.5787e-01 0.3381
2443 8.0405e-01 -2.1780e-04 5.9806e-01 1.0400e+00 0.2983
2447 -7.6527e-02 -4.8205e-04 1.3236e+00 -6.6098e-02 0.9473
2495 1.1625e+00 -4.5466e-04 1.2484e+00 1.0408e+00 0.2980
2496 1.1182e+00 -4.2612e-04 1.1701e+00 1.0341e+00 0.3011
2497 1.0136e+00 -3.6603e-04 1.0051e+00 1.0114e+00 0.3118
2499 1.2100e+00 -4.8205e-04 1.3236e+00 1.0522e+00 0.2927
2501 -6.2182e-02 -4.8101e-04 1.3208e+00 -5.3689e-02 0.9572
2505 7.9270e-01 -4.6450e-04 1.2754e+00 7.0232e-01 0.4825
2549 1.0776e+00 -3.8628e-04 1.0607e+00 1.0467e+00 0.2952
2552 1.0680e+00 -4.1509e-04 1.1398e+00 1.0008e+00 0.3169
2553 1.0166e+00 -3.1977e-04 8.7806e-01 1.0853e+00 0.2778
2554 -1.1221e-01 -4.8066e-04 1.3198e+00 -9.7253e-02 0.9225
2555 1.3157e-02 -1.5382e-05 4.2240e-02 6.4093e-02 0.9489
2603 1.1898e+00 -4.4094e-04 1.2107e+00 1.0817e+00 0.2794
2605 1.0008e+00 -3.3350e-04 9.1574e-01 1.0461e+00 0.2955
2606 1.1824e+00 -4.7513e-04 1.3046e+00 1.0356e+00 0.3004
2607 9.8547e-01 -2.9374e-04 8.0657e-01 1.0976e+00 0.2724
2608 -7.0921e+00 -1.9324e-02 5.2934e+01 -9.7212e-01 0.3310
2609 -6.7044e-02 -3.5432e-04 9.7292e-01 -6.7611e-02 0.9461
2657 1.0818e+00 -3.5731e-04 9.8112e-01 1.0926e+00 0.2746
2658 1.1968e+00 -4.4694e-04 1.2272e+00 1.0807e+00 0.2798
2659 1.1531e+00 -4.5635e-04 1.2531e+00 1.0305e+00 0.3028
2661 1.1075e+00 -4.2383e-04 1.1638e+00 1.0270e+00 0.3044
2663 -1.2485e-01 -4.7513e-04 1.3046e+00 -1.0889e-01 0.9133
2666 4.4913e-01 -2.4871e-04 6.8292e-01 5.4378e-01 0.5866
2667 6.8832e-01 -3.6120e-04 9.9182e-01 6.9151e-01 0.4892
2668 7.1881e-01 -4.5872e-04 1.2596e+00 6.4089e-01 0.5216
2715 1.0913e+00 -4.0484e-04 1.1116e+00 1.0355e+00 0.3004
2717 -8.9390e-02 -3.3988e-04 9.3327e-01 -9.2178e-02 0.9266
2719 4.1845e-01 -3.3205e-04 9.1178e-01 4.3858e-01 0.6610
2721 -2.3776e-01 -2.5956e-05 7.1275e-02 -8.9047e-01 0.3732
2722 5.5515e-01 -2.4374e-04 6.6929e-01 6.7888e-01 0.4972
2769 1.1466e+00 -4.5669e-04 1.2540e+00 1.0243e+00 0.3057
2770 1.6211e-02 -4.6279e-04 1.2708e+00 1.4791e-02 0.9882
2771 4.3884e-03 -4.5096e-04 1.2383e+00 4.3489e-03 0.9965
2774 2.2193e-01 -6.9217e-05 1.9007e-01 5.0921e-01 0.6106
2820 1.2332e+00 -4.8170e-04 1.3227e+00 1.0727e+00 0.2834
2821 1.1445e+00 -4.2644e-04 1.1710e+00 1.0581e+00 0.2900
2824 1.0761e+00 -3.4721e-04 9.5340e-01 1.1025e+00 0.2703
2825 1.0875e+00 -3.7547e-04 1.0310e+00 1.0714e+00 0.2840
2874 1.1343e+00 -3.8939e-04 1.0692e+00 1.0973e+00 0.2725
2877 8.8773e-01 -2.4796e-04 6.8087e-01 1.0761e+00 0.2819
2878 1.1932e+00 -4.6279e-04 1.2708e+00 1.0589e+00 0.2897
2879 1.1673e+00 -4.4627e-04 1.2254e+00 1.0549e+00 0.2915
2884 4.4900e-01 -1.8677e-04 5.1287e-01 6.2723e-01 0.5305
2885 5.4248e-01 -2.4771e-04 6.8019e-01 6.5806e-01 0.5105
2927 1.1869e+00 -4.3829e-04 1.2035e+00 1.0823e+00 0.2791
2929 1.1078e+00 -4.1027e-04 1.1265e+00 1.0441e+00 0.2964
2931 1.1563e+00 -4.4895e-04 1.2327e+00 1.0418e+00 0.2975
2932 1.2141e+00 -4.5872e-04 1.2596e+00 1.0822e+00 0.2791
2933 1.1481e+00 -4.2416e-04 1.1647e+00 1.0643e+00 0.2872
2936 9.1726e-02 -1.3060e-04 3.5863e-01 1.5339e-01 0.8781
2937 4.4878e-01 -1.8656e-04 5.1227e-01 6.2728e-01 0.5305
2985 8.8036e-01 -2.4523e-04 6.7337e-01 1.0731e+00 0.2832
2986 1.1774e+00 -4.6177e-04 1.2680e+00 1.0460e+00 0.2956
2987 1.1114e+00 -3.9629e-04 1.0882e+00 1.0658e+00 0.2865
2990 -1.8701e-01 -9.9340e-05 2.7278e-01 -3.5787e-01 0.7204
2991 5.7406e-02 -3.7333e-04 1.0251e+00 5.7067e-02 0.9545
2993 1.6452e-01 -1.1722e-05 3.2189e-02 9.1706e-01 0.3591
3035 1.2130e+00 -4.4761e-04 1.2291e+00 1.0946e+00 0.2737
3038 1.1890e+00 -4.8101e-04 1.3208e+00 1.0350e+00 0.3007
3040 1.1103e+00 -4.4194e-04 1.2135e+00 1.0083e+00 0.3133
3041 9.4658e-01 -3.0634e-04 8.4118e-01 1.0324e+00 0.3019
3043 1.1927e-01 -7.8456e-05 2.1544e-01 2.5713e-01 0.7971
3094 1.0680e+00 -3.9724e-04 1.0908e+00 1.0230e+00 0.3063
3095 1.0795e+00 -4.2058e-04 1.1549e+00 1.0049e+00 0.3149
3096 9.5484e-01 -4.4027e-04 1.2089e+00 8.6882e-01 0.3849
3098 -9.2412e-01 -1.7211e-03 4.7251e+00 -4.2434e-01 0.6713
3101 8.3890e-01 -3.1302e-04 8.5952e-01 9.0520e-01 0.3654
3150 6.2964e-01 -4.1316e-04 1.1345e+00 5.9154e-01 0.5542
3151 6.7512e-02 -4.5601e-04 1.2521e+00 6.0741e-02 0.9516
3152 -1.4735e-02 -1.2015e-04 3.2994e-01 -2.5443e-02 0.9797
3155 9.7802e-01 -3.9283e-04 1.0787e+00 9.4206e-01 0.3462
3198 1.1180e+00 -3.8441e-04 1.0555e+00 1.0886e+00 0.2763
3200 1.0784e+00 -4.8205e-04 1.3236e+00 9.3780e-01 0.3483
3202 8.6134e-01 -3.0000e-04 8.2378e-01 9.4933e-01 0.3425
3203 5.5964e-01 -1.3590e-04 3.7317e-01 9.1635e-01 0.3595
3206 1.0330e-01 -2.4920e-04 6.8429e-01 1.2517e-01 0.9004
3207 -1.7235e-02 -2.3030e-06 6.3241e-03 -2.1670e-01 0.8284
3209 9.6265e-01 -4.7651e-04 1.3084e+00 8.4200e-01 0.3998
3210 1.0839e+00 -4.6963e-04 1.2895e+00 9.5488e-01 0.3396
3252 1.1586e+00 -4.5466e-04 1.2484e+00 1.0373e+00 0.2996
3258 3.1919e-02 -9.1271e-05 2.5063e-01 6.3941e-02 0.9490
3259 -5.7101e-02 -1.1535e-04 3.1674e-01 -1.0125e-01 0.9193
3260 -5.6075e-02 -1.9418e-05 5.3322e-02 -2.4275e-01 0.8082
3261 -4.1265e-03 -6.2417e-06 1.7140e-02 -3.1472e-02 0.9749
3263 8.4365e-01 -3.8970e-04 1.0701e+00 8.1594e-01 0.4145
3264 1.2017e+00 -4.5804e-04 1.2577e+00 1.0720e+00 0.2837
3265 1.0326e+00 -3.8163e-04 1.0479e+00 1.0091e+00 0.3129
3266 9.4703e-01 -3.1134e-04 8.5492e-01 1.0246e+00 0.3056
3306 1.1773e+00 -4.3795e-04 1.2026e+00 1.0740e+00 0.2828
3308 7.4690e-01 -2.0583e-04 5.6519e-01 9.9377e-01 0.3203
3310 9.7613e-01 -4.4794e-04 1.2300e+00 8.8056e-01 0.3786
3311 6.2351e-01 -1.8742e-04 5.1465e-01 8.6940e-01 0.3846
3312 4.5360e-01 -1.4969e-04 4.1105e-01 7.0773e-01 0.4791
3313 -6.8986e-04 -1.8437e-05 5.0627e-02 -2.9840e-03 0.9976
3314 -8.7123e-02 -3.6337e-05 9.9781e-02 -2.7569e-01 0.7828
3318 1.2282e+00 -4.8170e-04 1.3227e+00 1.0684e+00 0.2853
3320 1.1104e+00 -4.4061e-04 1.2098e+00 1.0100e+00 0.3125
3321 4.9130e-01 -7.4445e-05 2.0442e-01 1.0868e+00 0.2771
3322 1.1316e+00 -4.4560e-04 1.2236e+00 1.0234e+00 0.3061
3359 1.1967e+00 -4.5466e-04 1.2484e+00 1.0714e+00 0.2840
3360 1.1750e+00 -4.3597e-04 1.1971e+00 1.0743e+00 0.2827
3362 8.1687e-01 -2.3858e-04 6.5513e-01 1.0095e+00 0.3127
3363 7.8978e-01 -2.5523e-04 7.0085e-01 9.4370e-01 0.3453
3364 6.1119e-01 -1.5595e-04 4.2823e-01 9.3422e-01 0.3502
3365 6.9615e-01 -3.5850e-04 9.8440e-01 7.0200e-01 0.4827
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3367 -4.7390e-01 -3.6211e-04 9.9430e-01 -4.7490e-01 0.6349
3368 1.0695e-02 -6.1477e-07 1.6882e-03 2.6030e-01 0.7946
3369 6.8760e-02 -3.1985e-04 8.7827e-01 7.3712e-02 0.9412
3375 1.1526e+00 -4.6791e-04 1.2848e+00 1.0172e+00 0.3090
3376 1.1194e+00 -4.3432e-04 1.1926e+00 1.0254e+00 0.3052
3377 1.2033e+00 -4.8240e-04 1.3246e+00 1.0460e+00 0.2956
3414 1.2187e+00 -4.6586e-04 1.2792e+00 1.0780e+00 0.2810
3415 9.4915e-01 -3.1106e-04 8.5415e-01 1.0273e+00 0.3043
3416 8.2971e-01 -2.6210e-04 7.1971e-01 9.7833e-01 0.3279
3418 1.0470e+00 -4.7582e-04 1.3065e+00 9.1640e-01 0.3595
3419 8.5264e-01 -3.2717e-04 8.9837e-01 8.9992e-01 0.3682
3420 1.5562e-01 -2.9184e-04 8.0137e-01 1.7416e-01 0.8617
3421 -2.0146e+00 -6.0809e-03 1.6685e+01 -4.9170e-01 0.6229
3422 4.2560e-01 -5.7592e-04 1.5814e+00 3.3890e-01 0.7347
3423 -4.3855e-02 -5.2928e-06 1.4534e-02 -3.6373e-01 0.7161
3432 1.1941e+00 -4.8101e-04 1.3208e+00 1.0394e+00 0.2986
3468 1.2218e+00 -4.6860e-04 1.2867e+00 1.0776e+00 0.2812
3471 1.0417e+00 -4.4928e-04 1.2337e+00 9.3830e-01 0.3481
3474 -3.2821e-01 -4.7789e-04 1.3122e+00 -2.8610e-01 0.7748
3475 -1.3997e-01 -3.1082e-05 8.5351e-02 -4.7898e-01 0.6319
3477 1.4373e-01 -3.3618e-04 9.2310e-01 1.4994e-01 0.8808
3485 1.1740e+00 -4.5568e-04 1.2512e+00 1.0500e+00 0.2937
3488 1.2122e+00 -4.3531e-04 1.1953e+00 1.1092e+00 0.2674
3522 1.1172e+00 -3.8194e-04 1.0487e+00 1.0913e+00 0.2751
3527 9.2812e-01 -3.8441e-04 1.0555e+00 9.0374e-01 0.3661
3529 -2.6722e-03 -1.8727e-05 5.1425e-02 -1.1701e-02 0.9907
3531 4.4182e-02 -1.0364e-04 2.8460e-01 8.3014e-02 0.9338
3532 -3.4991e-01 -2.6287e-04 7.2182e-01 -4.1155e-01 0.6807
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14444 1.4546e-01 -2.3227e-04 6.3780e-01 1.8243e-01 0.8552
14445 2.6335e-01 -1.6762e-04 4.6027e-01 3.8842e-01 0.6977
14489 8.2325e-01 -4.4027e-04 1.2089e+00 7.4914e-01 0.4538
14491 5.5573e-01 -3.8690e-04 1.0624e+00 5.3955e-01 0.5895
14494 3.6668e-01 -1.2329e-04 3.3856e-01 6.3040e-01 0.5284
14496 -1.6337e-01 -2.7330e-04 7.5045e-01 -1.8827e-01 0.8507
14497 -5.2189e-02 -1.4542e-05 3.9932e-02 -2.6109e-01 0.7940
14498 3.3784e-01 -1.6093e-04 4.4190e-01 5.0846e-01 0.6111
14500 4.5395e-01 -3.4251e-04 9.4049e-01 4.6844e-01 0.6395
14544 8.5941e-01 -4.2742e-04 1.1736e+00 7.9368e-01 0.4274
14545 9.1641e-01 -4.6620e-04 1.2801e+00 8.1037e-01 0.4177
14549 4.9349e-01 -2.7193e-04 7.4668e-01 5.7142e-01 0.5677
14550 9.5551e-02 -1.0154e-05 2.7882e-02 5.7230e-01 0.5671
14551 9.1621e-02 -2.7036e-04 7.4239e-01 1.0665e-01 0.9151
14552 5.3095e-01 -3.8814e-04 1.0658e+00 5.1468e-01 0.6068
14553 4.5910e-01 -2.1177e-04 5.8151e-01 6.0232e-01 0.5470
14598 1.1480e+00 -4.7100e-04 1.2933e+00 1.0099e+00 0.3126
14601 6.6494e-01 -4.4127e-04 1.2117e+00 6.0448e-01 0.5455
14602 -9.9752e-02 -4.3645e-06 1.1985e-02 -9.1114e-01 0.3622
14603 2.3766e-01 -6.1051e-05 1.6764e-01 5.8059e-01 0.5615
14604 5.1443e-01 -4.5838e-04 1.2586e+00 4.5895e-01 0.6463
14605 -1.5369e-01 -1.2507e-05 3.4345e-02 -8.2924e-01 0.4070
14651 9.2416e-01 -2.9428e-04 8.0806e-01 1.0284e+00 0.3038
14652 1.1479e+00 -4.4694e-04 1.2272e+00 1.0366e+00 0.2999
14653 1.0285e+00 -3.3930e-04 9.3167e-01 1.0659e+00 0.2865
14654 6.8093e-01 -4.0899e-04 1.1230e+00 6.4294e-01 0.5203
14655 5.7706e-01 -2.2108e-04 6.0706e-01 7.4091e-01 0.4587
14656 6.5152e-01 -2.2963e-04 6.3054e-01 8.2078e-01 0.4118
14657 7.0955e-01 -4.0931e-04 1.1239e+00 6.6968e-01 0.5031
14658 1.6483e-01 -3.1436e-05 8.6322e-02 5.6113e-01 0.5747
14659 3.0317e-01 -4.3103e-04 1.1835e+00 2.7907e-01 0.7802
14710 8.0897e-01 -4.5669e-04 1.2540e+00 7.2282e-01 0.4698
14711 5.6186e-01 -2.4671e-04 6.7745e-01 6.8293e-01 0.4947
14760 1.1341e+00 -4.3465e-04 1.1935e+00 1.0385e+00 0.2990
14763 -4.2876e-02 -9.3314e-07 2.5624e-03 -8.4699e-01 0.3970
14764 6.5220e-01 -2.9049e-04 7.9766e-01 7.3057e-01 0.4650
14765 6.3125e-01 -2.6906e-04 7.3882e-01 7.3471e-01 0.4625
14766 5.5746e-01 -1.6598e-04 4.5578e-01 8.2597e-01 0.4088
14767 7.7155e-01 -3.8752e-04 1.0641e+00 7.4833e-01 0.4543
14768 5.0369e-01 -2.8566e-04 7.8439e-01 5.6904e-01 0.5693
14769 2.7273e-01 -6.6739e-05 1.8326e-01 6.3724e-01 0.5240
14814 9.1626e-01 -2.7114e-04 7.4453e-01 1.0622e+00 0.2881
14817 7.7695e-01 -4.6008e-04 1.2633e+00 6.9167e-01 0.4891
14877 2.2357e-01 -3.0380e-05 8.3424e-02 7.7416e-01 0.4388
14926 9.7060e-01 -3.5761e-04 9.8194e-01 9.7984e-01 0.3272
14928 9.2287e-01 -3.9033e-04 1.0718e+00 8.9180e-01 0.3725
14981 8.8337e-01 -3.2946e-04 9.0467e-01 9.2910e-01 0.3528
14982 9.4536e-01 -3.7639e-04 1.0335e+00 9.3027e-01 0.3522
14983 1.0213e+00 -4.0611e-04 1.1151e+00 9.6756e-01 0.3333
14985 7.9265e-01 -4.4360e-04 1.2181e+00 7.1861e-01 0.4724
15037 1.1228e+00 -4.6620e-04 1.2801e+00 9.9283e-01 0.3208
15039 4.2892e-01 -1.0344e-04 2.8404e-01 8.0499e-01 0.4208
15092 7.4802e-01 -2.6725e-04 7.3384e-01 8.7350e-01 0.3824
15094 6.1044e-01 -1.6497e-04 4.5299e-01 9.0723e-01 0.3643
15095 1.0746e+00 -4.7444e-04 1.3027e+00 9.4195e-01 0.3462
15096 1.1719e+00 -4.4527e-04 1.2226e+00 1.0602e+00 0.2890
15146 7.7866e-01 -3.1921e-04 8.7651e-01 8.3205e-01 0.4054
15148 9.5730e-01 -3.6150e-04 9.9264e-01 9.6121e-01 0.3364
15149 1.0916e+00 -4.6894e-04 1.2876e+00 9.6235e-01 0.3359
15150 1.0505e+00 -4.3630e-04 1.1980e+00 9.6016e-01 0.3370
15204 9.4599e-01 -3.3755e-04 9.2688e-01 9.8295e-01 0.3256
15205 3.6316e-01 -3.5641e-04 9.7866e-01 3.6746e-01 0.7133
15247 1.5873e-02 -2.3946e-07 6.5756e-04 6.1903e-01 0.5359
15258 3.9390e-01 -4.6109e-04 1.2661e+00 3.5048e-01 0.7260
15302 1.6187e-01 -1.8019e-04 4.9478e-01 2.3038e-01 0.8178
15303 -2.3763e-01 -1.2719e-04 3.4926e-01 -4.0188e-01 0.6878
15312 3.5803e-01 -3.7547e-04 1.0310e+00 3.5298e-01 0.7241
15313 3.7404e-01 -4.3333e-04 1.1899e+00 3.4330e-01 0.7314
15420 1.0430e-01 -2.0459e-05 5.6180e-02 4.4013e-01 0.6598
15474 -3.3914e+00 -4.9889e-03 1.3691e+01 -9.1521e-01 0.3601
15512 -6.8392e-01 -3.4906e-04 9.5848e-01 -6.9822e-01 0.4850
15521 1.8757e+00 -1.5106e-02 4.1402e+01 2.9386e-01 0.7689
15528 2.9292e-01 -2.7612e-04 7.5818e-01 3.3673e-01 0.7363
15576 -4.9585e-01 -1.9207e-02 5.2616e+01 -6.5710e-02 0.9476
15582 3.2948e-01 -3.7455e-04 1.0285e+00 3.2525e-01 0.7450
15637 3.6443e-01 -4.4393e-04 1.2190e+00 3.3048e-01 0.7410
15690 3.1607e-01 -2.6725e-04 7.3384e-01 3.6928e-01 0.7119
15741 -1.6867e-01 -3.4928e-04 9.5907e-01 -1.7188e-01 0.8635
15745 3.8057e-01 -4.7513e-04 1.3046e+00 3.3361e-01 0.7387
15794 -1.7645e-01 -3.8877e-04 1.0675e+00 -1.7040e-01 0.8647
15798 9.9858e-01 -4.1573e-04 1.1415e+00 9.3501e-01 0.3498
15836 4.9462e-01 -4.7582e-04 1.3065e+00 4.3315e-01 0.6649
15849 -2.4357e-01 -3.5880e-04 9.8523e-01 -2.4503e-01 0.8064
15850 2.6491e-01 -3.1881e-05 8.7544e-02 8.9546e-01 0.3705
15903 7.7871e-01 -3.3465e-04 9.1892e-01 8.1269e-01 0.4164
15906 1.0376e+00 -4.7893e-04 1.3151e+00 9.0519e-01 0.3654
15959 5.9165e-01 -1.8397e-04 5.0518e-01 8.3269e-01 0.4050
15960 2.7627e-01 -3.2780e-05 9.0014e-02 9.2095e-01 0.3571
16013 8.3261e-01 -3.8317e-04 1.0521e+00 8.1209e-01 0.4167
16646 -6.3440e-01 -4.8066e-04 1.3198e+00 -5.5180e-01 0.5811
Ii E.Ii Var.Ii Z.Ii Pr.z....E.Ii..
58 1.1210198 -0.0004634753 1.2726271 0.9941278 0.3201607
221 1.1800130 -0.0004778890 1.3122025 1.0305337 0.3027595
225 1.0835925 -0.0004486119 1.2318170 0.9767257 0.3287049
329 1.0167585 -0.0003699751 1.0159028 1.0091361 0.3129094
332 0.9513416 -0.0002875336 0.7895375 1.0709800 0.2841784
Show the code
<- cbind(honeycomb_count16_19, localMI16_19)%>%
honeycomb_count16_19.localMI rename(Pr.Ii = Pr.z....E.Ii..)
5.3 Creating a LISA Cluster Map
The following outlines the steps to prepare a LISA cluster map.
We will first derive the spatially lagged variable of interest and center the spatially lagged variable around its mean.
$lag_pct_nf <- lag.listw(wm6_9, honeycomb_count6_9$Sum_TRIPS)
honeycomb_count6_9<- honeycomb_count6_9$lag_pct_nf - mean(honeycomb_count6_9$lag_pct_nf) DV6_9
In the code chunk below, we 1) set a statistical significance level for the local Moran, 2) define the low-low (1), low-high (2), high-low (3) and high-high (4) categories and 3) create an additional category for LGAs with no statistically significant autocorrelation
<- localMI6_9[,1] - mean(localMI6_9[,1])
LM_I6_9 <- 0.05
signif <- vector(mode="numeric",length=nrow(localMI6_9))
Sum_TRIPS6_9 <0 & LM_I6_9>0] <- 1
Sum_TRIPS6_9[DV6_9 >0 & LM_I6_9<0] <- 2
Sum_TRIPS6_9[DV6_9 <0 & LM_I6_9<0] <- 3
Sum_TRIPS6_9[DV6_9 >0 & LM_I6_9>0] <- 4
Sum_TRIPS6_9[DV6_9 5]>signif] <- 0 Sum_TRIPS6_9[localMI6_9[,
Repeat the same for the other intervals
For weekday evening peak:
Show the code
$lag_pct_nf <- lag.listw(wm17_20, honeycomb_count17_20$Sum_TRIPS)
honeycomb_count17_20<- honeycomb_count17_20$lag_pct_nf - mean(honeycomb_count17_20$lag_pct_nf)
DV17_20
<- localMI17_20[,1] - mean(localMI17_20[,1])
LM_I17_20 <- 0.05
signif <- vector(mode="numeric",length=nrow(localMI17_20))
Sum_TRIPS17_20 <0 & LM_I17_20>0] <- 1
Sum_TRIPS17_20[DV17_20 >0 & LM_I17_20<0] <- 2
Sum_TRIPS17_20[DV17_20<0 & LM_I17_20<0] <- 3
Sum_TRIPS17_20[DV17_20 >0 & LM_I17_20>0] <- 4
Sum_TRIPS17_20[DV17_20 5]>signif] <- 0 Sum_TRIPS17_20[localMI17_20[,
For weekend/holidays morning peak:
Show the code
$lag_pct_nf <- lag.listw(wm11_14, honeycomb_count11_14$Sum_TRIPS)
honeycomb_count11_14<- honeycomb_count11_14$lag_pct_nf - mean(honeycomb_count11_14$lag_pct_nf)
DV11_14
<- localMI11_14[,1] - mean(localMI11_14[,1])
LM_I11_14 <- 0.05
signif <- vector(mode="numeric",length=nrow(localMI11_14))
Sum_TRIPS11_14 <0 & LM_I11_14>0] <- 1
Sum_TRIPS11_14[DV11_14 >0 & LM_I11_14<0] <- 2
Sum_TRIPS11_14[DV11_14 <0 & LM_I11_14<0] <- 3
Sum_TRIPS11_14[DV11_14 >0 & LM_I11_14>0] <- 4
Sum_TRIPS11_14[DV11_14 5]>signif] <- 0 Sum_TRIPS11_14[localMI11_14[,
For weekend/holidays evening peak:
Show the code
$lag_pct_nf <- lag.listw(wm16_19, honeycomb_count16_19$Sum_TRIPS)
honeycomb_count16_19<- honeycomb_count16_19$lag_pct_nf - mean(honeycomb_count16_19$lag_pct_nf)
DV16_19
<- localMI16_19[,1] - mean(localMI16_19[,1])
LM_I16_19 <- 0.05
signif <- vector(mode="numeric",length=nrow(localMI16_19))
Sum_TRIPS16_19 <0 & LM_I16_19>0] <- 1
Sum_TRIPS16_19[DV16_19 >0 & LM_I16_19<0] <- 2
Sum_TRIPS16_19[DV16_19 <0 & LM_I16_19<0] <- 3
Sum_TRIPS16_19[DV16_19 >0 & LM_I16_19>0] <- 4
Sum_TRIPS16_19[DV16_19 5]>signif] <- 0 Sum_TRIPS16_19[localMI16_19[,
5.3.1 Plotting LISA map
5.3.1.1 LISA Map for weekday morning peak
The code chunk below is used to plot the LISA Map for weekday morning peak
$Sum_TRIPS <- Sum_TRIPS6_9
honeycomb_count6_9.localMI<- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
colors <- c("insignificant", "low-low", "low-high", "high-low", "high-high")
clusters
tmap_mode("view")
<- tm_shape(honeycomb_count6_9.localMI) +
LISA6_9 tm_fill(col = "Sum_TRIPS",
style = "cat",
palette = colors[c(sort(unique(Sum_TRIPS6_9)))+1],
labels = clusters[c(sort(unique(Sum_TRIPS6_9)))+1]) +
tm_borders(alpha=0.7)
LISA6_9
During the weekday morning peak (6am to 9am), statistically significant clusters emerge in major residential areas and near MRT stations with connecting services like LRT or bus interchanges. There are circa 11 high-high clusters. Prominent high-high zones appear at transit hubs, including Woodlands Checkpoint, Boon Lay MRT/Interchange, Bukit Panjang MRT, Toa Payoh MRT/Interchange, and Bedok MRT/Interchange. These high-high clusters are often surrounded by similar clusters and some low-high clusters, suggesting a potential proximity limit for bus travelers.
City areas and industrial zones show statistical insignificance during this period due to lower activity levels. Excluding Woodlands Checkpoint, the identified high-high zones predominantly lie in residential areas, indicating a reliance on buses for morning commutes. The presence of high values in these zones may also be attributed to individuals taking buses after clearing the checkpoint to reach workplaces, emphasizing the significance of transit hubs during the morning peak. Further investigation is necessary for conclusive insights into these patterns.
Repeat the same for the other intervals
5.3.1.2 LISA Map for weekday evening peak
$Sum_TRIPS <- Sum_TRIPS17_20
honeycomb_count17_20.localMI<- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
colors <- c("insignificant", "low-low", "low-high", "high-low", "high-high")
clusters
tmap_mode("view")
<- tm_shape(honeycomb_count17_20.localMI) +
LISA17_20 tm_fill(col = "Sum_TRIPS",
style = "cat",
palette = colors[c(sort(unique(Sum_TRIPS17_20)))+1],
labels = clusters[c(sort(unique(Sum_TRIPS17_20)))+1]) +
tm_borders(alpha=0.7)
LISA17_20
During the weekday evening peak (5pm to 8pm), statistical significant clusters mostly showed up at major residential areas, MRT stations in the east side of Singapore,. The no. of high-high clusters have visibily decreased suggesting a potential shift in preference away from buses during this period. A comprehensive study of alternative public transport choices could offer deeper insights into this trend.
Transit hubs, including Woodlands Checkpoint, Toa Payoh MRT/Interchange, Tampines MRT/Interchange, and Bedok MRT/Interchange, continue to exhibit prominent high-high zones. These clusters are surrounded by similar high-high clusters and some low-high clusters, emphasizing their central role in evening commutes.
Additionally, a high-high cluster emerges along Orchard Rd, likely representing individuals commuting back home after dinner or evening activities in the district. Further analysis may reveal patterns in transportation choices during the weekday evening peak, guiding potential adjustments in bus services.
5.3.1.3 LISA Map for weekend/holidays morning peak
$Sum_TRIPS <- Sum_TRIPS11_14
honeycomb_count11_14.localMI<- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
colors <- c("insignificant", "low-low", "low-high", "high-low", "high-high")
clusters
tmap_mode("view")
<- tm_shape(honeycomb_count11_14.localMI) +
LISA11_14 tm_fill(col = "Sum_TRIPS",
style = "cat",
palette = colors[c(sort(unique(Sum_TRIPS11_14)))+1],
labels = clusters[c(sort(unique(Sum_TRIPS11_14)))+1]) +
tm_borders(alpha=0.7)
LISA11_14
During the weekend morning peak (11am to 2pm), statistically significant clusters showed up mostly at major residential areas, MRT stations in the east side of Singapore, and the city fringe. Notably, high-high clusters appear with specific focus areas near heartland malls in Hougang, Bukit Panjang, Bugis MRT/Bugis Junction, and Bukit Panjang MRT/Junction10.
Observations near Bugis and Bukit Panjang noted they are strategically located near shopping malls and places of worship. This suggest that post-worship and lunch, passengers utilize transportation from these areas to return home or visit other places. Conducting further demographic studies could offer valuable insights into the commuting habits of passengers during weekend mornings, using these locations as test sites.
Transit hubs like Woodlands Checkpoint, Toa Payoh MRT/Interchange, Tampines MRT/Interchange, and Bedok MRT/Interchange maintain high-high zones, surrounded by similar clusters and some low-high clusters.
5.3.14 LISA Map for weekend/holidays evening peak
$Sum_TRIPS <- Sum_TRIPS16_19
honeycomb_count16_19.localMI<- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
colors <- c("insignificant", "low-low", "low-high", "high-low", "high-high")
clusters
tmap_mode("view")
<- tm_shape(honeycomb_count16_19.localMI) +
LISA16_19 tm_fill(col = "Sum_TRIPS",
style = "cat",
palette = colors[c(sort(unique(Sum_TRIPS16_19)))+1],
labels = clusters[c(sort(unique(Sum_TRIPS16_19)))+1]) +
tm_borders(alpha=0.7)
LISA16_19
During the weekend evening peak (4 pm to 7 pm), significant clusters emerge predominantly in major residential areas, MRT stations on the east side of Singapore, and near shopping/entertainment districts. Notably, Bugis and Orchard Road exhibit significant clusters of high-high zones, indicating increased bus trips from these areas and a potentially higher population density during this peak period.
To comprehend the reasons behind this surge, an in-depth study of bus trips specific to these zones during the weekend evening peak is crucial. Such research should encompass demographics and transport preferences to facilitate informed policy-making. Transit hubs like Woodlands Checkpoint, Toa Payoh MRT/Interchange, Tampines MRT/Interchange, and Bedok MRT/Interchange consistently maintain high-high zones, surrounded by similar clusters and some low-high clusters.
6. Conclusion
Spatial data analysis, complemented by effective visualization, facilitates swift pattern recognition and aids policymakers in pinpointing areas for deeper investigation. However, for meaningful discussions, spatial data analysis should be accompanied by domain expertise and an understanding of the specific field under consideration. While the analysis reveals relationships and clusters, it’s crucial to acknowledge that assumptions are made based on the available data. Despite this limitation, spatial analysis offers a rapid comprehension of distribution, relationships, and clustering patterns, serving as a valuable tool for informed decision-making.
7. Future Works
The analysis reveals information gaps that hinder a comprehensive understanding of commuter trends and habits. To enhance the depth of spatial information on public transport, collaboration with transport authorities is recommended. Exploring other modes of public transport and their spatial dynamics will contribute to a more holistic view. It’s important to note that the study focuses solely on bus rides during peak periods in October 2023, leaving room for expansion to cover additional months or a broader time frame each month. To refine the transport system, policymakers should consider comparing spatial observations with demographic factors, allowing for tailored adjustments to meet the nation’s evolving needs.