pacman::p_load(tmap, sf, dplyr, DT, sp,
stplanr, performance, mapview,
ggpubr, tidyverse, httr,
units, reshape2)Take-home Exercise 2: Analyzing the Dynamics of Bus Commute Flow and Spatial Interaction in Singapore
Setting the Scene
The inquiry focuses on the key motivators prompting city residents to rise early for their daily commutes from home to work, and the consequences of discontinuing public bus services along specific routes. These issues represent significant challenges for transport operators and urban planners.
Traditionally, understanding these dynamics involved conducting extensive commuter surveys. These surveys, however, are expensive, time-intensive, and laborious. Moreover, the data collected often requires extensive processing and analysis, leading to reports that are frequently outdated by the time they are completed.
With the digitalization of urban infrastructure, including public buses, mass rapid transit systems, public utilities, and roads, new opportunities for data collection arise. The integration of pervasive computing technologies like GPS in vehicles and SMART cards among public transport users allows for detailed tracking of movement patterns across time and space.
Despite this, the rapid accumulation of geospatial data has overwhelmed planners’ capacity to effectively analyze and convert it into valuable insights. This inefficiency negatively impacts the return on investment in data collection and management.
Motivation and Objective
The purpose of this take-home project is twofold. First, it addresses the gap in applied research demonstrating the integration, analysis, and modeling of the increasingly available open data for effective policy-making. Despite the abundance of such data, there is a noticeable absence of practical studies showcasing its potential use in policy decisions.
Second, the project aims to fill the void in practical research illustrating the application of geospatial data science and analysis (GDSA) in decision-making processes.
Therefore, the assignment involves conducting a case study to showcase the value of GDSA. This will involve synthesizing publicly accessible data from various sources to construct spatial interaction models. These models will be used to identify and analyze factors influencing the urban mobility patterns of public bus transit.
1.Getting Started
The code snippet shown is responsible for loading various packages that provide essential tools and functions for the analysis.
pacman::p_load: This function from thepacmanpackage streamlines the process of loading multiple R packages. If a package is not already installed,p_loadwill install it before loading.tmap: Utilized for creating thematic maps, essential in visualizing geospatial data.sf: Stands for “simple features” and is used for handling and analyzing geospatial data.dplyr: A part of thetidyversecollection, this package is instrumental in data manipulation tasks like filtering, selecting, and summarizing data.DT: Provides an R interface to the JavaScript library “DataTables”, enabling interactive display of data in tables.sp: Offers classes and methods for spatial data, crucial for handling spatial points, lines, and polygons.stplanr: Specifically designed for sustainable transport planning with spatial data.performance: Useful for assessing and comparing the performance of statistical models.mapview: Facilitates interactive viewing of spatial data in R.ggpubr: A part of theggplot2ecosystem, this package provides additional functions for creating publication-ready plots.tidyverse: A collection of R packages designed for data science, providing tools for data manipulation, visualization, and more.httr: Used for working with HTTP protocols to access web resources.units: Deals with measurement units, crucial for handling and converting between different units of measurement in spatial data.reshape2: Aids in reshaping data, transitioning between wide and long formats, which is often necessary in data analysis.
Each of these packages plays a specific role in the analysis, ranging from data manipulation and visualization to handling spatial and web-based data.
2.Data Importing
2.1Geospatial Data Importing
This R code snippet is focused on importing and transforming geospatial data related to Singapore’s bus stops and Metropolitan Planning Strategy Zones (MPSZ) for the year 2019. Using st_read from the sf package, it loads the BusStop and MPSZ-2019 layers from a specified directory (data/geospatial). Both datasets are then transformed to the local Singapore coordinate reference system (CRS code 3414) using st_transform.
busstop <- st_read(dsn = "data/geospatial",
layer = "BusStop") %>%
st_transform(crs = 3414)Reading layer `BusStop' from data source
`D:\KathyChiu77\ISSS624\Take-home Ex\Take-home Ex 2\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: SVY21mpsz <- st_read(dsn = "data/geospatial",
layer = "MPSZ-2019") %>%
st_transform(crs = 3414)Reading layer `MPSZ-2019' from data source
`D:\KathyChiu77\ISSS624\Take-home Ex\Take-home Ex 2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS: WGS 84Display and grasp the basic situation of geospatial dataset mpsz.
mpszSimple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21 / Singapore TM
First 10 features:
SUBZONE_N SUBZONE_C PLN_AREA_N PLN_AREA_C REGION_N
1 MARINA EAST MESZ01 MARINA EAST ME CENTRAL REGION
2 INSTITUTION HILL RVSZ05 RIVER VALLEY RV CENTRAL REGION
3 ROBERTSON QUAY SRSZ01 SINGAPORE RIVER SR CENTRAL REGION
4 JURONG ISLAND AND BUKOM WISZ01 WESTERN ISLANDS WI WEST REGION
5 FORT CANNING MUSZ02 MUSEUM MU CENTRAL REGION
6 MARINA EAST (MP) MPSZ05 MARINE PARADE MP CENTRAL REGION
7 SUDONG WISZ03 WESTERN ISLANDS WI WEST REGION
8 SEMAKAU WISZ02 WESTERN ISLANDS WI WEST REGION
9 SOUTHERN GROUP SISZ02 SOUTHERN ISLANDS SI CENTRAL REGION
10 SENTOSA SISZ01 SOUTHERN ISLANDS SI CENTRAL REGION
REGION_C geometry
1 CR MULTIPOLYGON (((33222.98 29...
2 CR MULTIPOLYGON (((28481.45 30...
3 CR MULTIPOLYGON (((28087.34 30...
4 WR MULTIPOLYGON (((14557.7 304...
5 CR MULTIPOLYGON (((29542.53 31...
6 CR MULTIPOLYGON (((35279.55 30...
7 WR MULTIPOLYGON (((15772.59 21...
8 WR MULTIPOLYGON (((19843.41 21...
9 CR MULTIPOLYGON (((30870.53 22...
10 CR MULTIPOLYGON (((26879.04 26...Export and save in rds format for later use.
mpsz <- write_rds(mpsz, "data/rds/mpsz.rds")2.2Aspatial Data Importing
This line of R code is used for importing an aspatial dataset named origin_destination_bus_202310.csv from a specified directory (data/aspatial). The function read_csv from the tidyverse package efficiently reads the CSV file, converting it into a dataframe. This dataset likely contains origin-destination information for bus routes in October, 2023.
odbus <- read_csv("data/aspatial/origin_destination_bus_202310.csv")The glimpse(odbus) function provides a quick overview of the structure and contents of the odbus dataframe, summarizing its columns, data types, and a few initial entries.
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…This code converts the ORIGIN_PT_CODE and DESTINATION_PT_CODE columns in the odbus dataframe to factors, categorizing unique bus stop codes for analysis.
odbus$ORIGIN_PT_CODE <- as.factor(odbus$ORIGIN_PT_CODE)
odbus$DESTINATION_PT_CODE <- as.factor(odbus$DESTINATION_PT_CODE) 2.3Extracting the Study Data
2.3.1Extracting the Trips Volume of Weekday Morning Peak
This code snippet filters and summarizes the odbus dataframe to extract data on bus trips during weekday morning peak hours (6 to 9 AM). It selects records marked as WEEKDAY, groups them by origin and destination bus stop codes, and then calculates the total number of trips between each stop pair in this time frame.
weekday6_9 <- odbus %>%
filter(DAY_TYPE == "WEEKDAY") %>%
filter(TIME_PER_HOUR >= 6 &
TIME_PER_HOUR <= 9) %>%
group_by(ORIGIN_PT_CODE,
DESTINATION_PT_CODE) %>%
summarise(TRIPS = sum(TOTAL_TRIPS))The datatable(weekday6_9) function creates an interactive table display of the weekday6_9 dataframe, facilitating easy exploration and analysis of the data.
datatable(weekday6_9)The write_rds(weekday6_9, "data/rds/weekday6_9.rds") function saves the weekday6_9 dataframe to a file named weekday6_9.rds for future use.
write_rds(weekday6_9, "data/rds/weekday6_9.rds")The read_rds("data/rds/weekday6_9.rds") function loads the previously saved weekday6_9 dataframe back into the R environment.
weekday6_9 <- read_rds("data/rds/weekday6_9.rds")2.3.2Extracting the Trips Volume of Weekday Afternoon Peak
Repeat the process above for weekday afternoon peak (5-8 PM).
weekday17_20 <- odbus %>%
filter(DAY_TYPE == "WEEKDAY") %>%
filter(TIME_PER_HOUR >= 17 &
TIME_PER_HOUR <= 20) %>%
group_by(ORIGIN_PT_CODE,
DESTINATION_PT_CODE) %>%
summarise(TRIPS = sum(TOTAL_TRIPS))datatable(weekday17_20)write_rds(weekday17_20, "data/rds/weekday17_20.rds")weekday17_20 <- read_rds("data/rds/weekday17_20.rds")2.3.3Extracting the Trips Volume of Weekend/Holiday Morning Peak
Repeat the process above for weekend/holiday morning peak (11 AM-2 PM).
weekend11_14 <- odbus %>%
filter(DAY_TYPE == "WEEKENDS/HOLIDAY") %>%
filter(TIME_PER_HOUR >= 11 &
TIME_PER_HOUR <= 14) %>%
group_by(ORIGIN_PT_CODE,
DESTINATION_PT_CODE) %>%
summarise(TRIPS = sum(TOTAL_TRIPS))datatable(weekend11_14)write_rds(weekend11_14, "data/rds/weekend11_14.rds")weekend11_14 <- read_rds("data/rds/weekend11_14.rds")2.3.4Extracting the Trips Volume of Weekend/Holiday Evening Peak
Repeat the process above for weekend/holiday evening peak (4-7 PM).
weekend16_19 <- odbus %>%
filter(DAY_TYPE == "WEEKENDS/HOLIDAY") %>%
filter(TIME_PER_HOUR >= 16 &
TIME_PER_HOUR <= 19) %>%
group_by(ORIGIN_PT_CODE,
DESTINATION_PT_CODE) %>%
summarise(TRIPS = sum(TOTAL_TRIPS))datatable(weekend16_19)write_rds(weekend16_19, "data/rds/weekend16_19.rds")weekend16_19 <- read_rds("data/rds/weekend16_19.rds")4.Geospatial Data Wrangling
4.1Combining busstop and mpsz
The code st_intersection(busstop, mpsz) combines the busstop and mpsz datasets to retain only those bus stops located within the boundaries of Singapore’s metropolitan planning zones. The select(BUS_STOP_N, SUBZONE_C) part then extracts specific columns, namely bus stop IDs and subzone codes, from the intersected dataset.
busstop_mpsz <- st_intersection(busstop, mpsz) %>%
select(BUS_STOP_N, SUBZONE_C)The mapview(busstop_mpsz) function creates an interactive map displaying the spatial data from the busstop_mpsz dataframe, visualizing the locations of bus stops within Singapore’s planning zones.
mapview(busstop_mpsz)4.2Creating Hexagon Layer
The code st_make_grid(mpsz, cellsize = 2 * 375 / sqrt(3), square = FALSE) generates a hexagonal grid overlay on the mpsz spatial data. Each hexagon in the grid has a perpendicular distance from its center to its edges of 375 meters, effectively creating a hexagonal pattern to represent Traffic Analysis Zones (TAZs).
hex_grid <- st_make_grid(mpsz, cellsize = 2 * 375 / sqrt(3), square = FALSE)This code converts the hex_grid object into a simple features (sf) dataframe hex_grid_sf, and then adds a new column hex_id that assigns a unique identifier to each hexagon in the grid.
hex_grid_sf <- st_sf(geometry = hex_grid) %>%
mutate(hex_id = 1:length(hex_grid))This code calculates the number of bus stops within each hexagon of the hex_grid_sf grid. It uses st_intersects to identify which bus stops (busstop_mpsz) fall within each hexagon, and then applies a function to count these stops for each hexagon, handling any missing values (na.rm = TRUE).
busstop_counts <- st_intersects(hex_grid_sf, busstop_mpsz, sparse = FALSE) %>%
apply(1, function(x) sum(x, na.rm = TRUE))This step assigns the computed bus stop counts (busstop_counts) to a new column bus_stop_count in the hex_grid_sf dataframe, effectively adding the number of bus stops within each hexagon to the grid data.
hex_grid_sf$bus_stop_count <- busstop_countsThis code filters the hex_grid_sf dataframe to keep only those hexagons that have one or more bus stops, effectively removing hexagons with no bus stop presence.
hex_grid_sf <- hex_grid_sf %>%
filter(bus_stop_count > 0)This code creates a visual map in R using the tmap package. It overlays hexagons from hex_grid_sf onto the mpsz spatial layout, coloring them based on the count of bus stops in each hexagon. The map features a legend, titles, and styling details for clarity and visual appeal. The final map displays the distribution of bus stops across Singapore, with additional borders for context and credits for data sources.
tmap_options(check.and.fix = TRUE)
map_hexagon <- tm_shape(hex_grid_sf) +
tm_polygons(
col = "bus_stop_count",
palette = "Purples",
style = "cont",
title = "Number of Bus Stops",
id = "hex_id",
showNA = FALSE,
alpha = 0.6,
popup.vars = c("Number of Bus Stops" = "bus_stop_count"),
popup.format = list(bus_stop_count = list(format = "f", digits = 0))
) +
tm_shape(mpsz) +
tm_borders(col = "grey75", lwd = 0.7) +
tm_layout(
main.title = "Bus Stop Distribution in Singapore",
main.title.size = 1.5,
legend.title.size = 1,
legend.text.size = 0.8,
legend.position = c("left", "bottom"),
frame = FALSE,
inner.margins = c(0.05, 0.05, 0.05, 0.05)
) +
tm_credits("Data Source: LTA DataMall, Data.gov.sg", position = c("RIGHT", "BOTTOM"), size = 0.8) +
tm_view(view.legend.position = c("left", "bottom"))
map_hexagon
Observations from the map:
Blank Areas: The absence of hexagons in certain parts of the map suggests these are areas with no bus stops. These could be non-residential areas, such as industrial zones, green spaces, or water bodies where public bus services are not necessary or practical.
Bus Stop-Dense Areas: Regions densely packed with hexagons indicate a high concentration of bus stops. These areas are likely to be highly urbanized with significant residential and commercial activities, necessitating a greater number of bus stops to accommodate the public transport needs of the population.
The distribution pattern reflects the urban planning and public transportation infrastructure of Singapore, designed to cater to areas with high commuter demand while excluding zones where bus stops are not viable.
4.3Correspondence of Hexagon and Bus Stop ID
The code creates a new dataset busstop_hex by intersecting busstop locations with the hex_grid_sf to assign a hex_id to each bus stop. It then selects the bus stop number and corresponding hex_id, and removes the spatial geometry data for a simple reference table. The final step omits any entries with missing values to ensure a clean dataset for merging with other data based on hexagon and bus stop IDs.
busstop_hex <- st_intersection(busstop, hex_grid_sf) %>%
select(BUS_STOP_N, hex_id) %>%
st_drop_geometry()busstop_hex <- na.omit(busstop_hex)The head(busstop_hex) function displays the first few rows of the busstop_hex dataframe for a quick preview of its structure and data.
head(busstop_hex) BUS_STOP_N hex_id
3269 25059 393
254 26379 444
2570 25751 488
4203 26389 490
2403 26369 491
2897 25761 535Export and save busstop_hex in rds format for future use.
write_rds(busstop_hex, "data/rds/busstop_hex.rds") Remove items no longer needed from R environment to free memory and avoid redundancy.
rm(hex_grid, map_hexagon, odbus, busstop_counts)5.Preparing Commute Flow Data
5.1Weekday Morning Peak Flow
The code merges flow data from weekday6_9 with bus stop IDs from busstop_hex based on common origin bus stop numbers, then renames the key columns for clarity, assigning hex IDs to origin points and preserving destination bus stop codes.
weekday_morning_od <- left_join(weekday6_9 , busstop_hex,
by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
rename(ORIGIN_BS = ORIGIN_PT_CODE,
ORIGIN_HEX = hex_id,
DESTIN_BS = DESTINATION_PT_CODE)Before continue, it is a good practice for us to check for duplicating records (It can be judged based on data frame is blank or not).
duplicate <- weekday_morning_od %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()If duplicated records are found, the code chunk below will be used to retain the unique records.
weekday_morning_od <- unique(weekday_morning_od)This code further enhances the weekday_morning_od dataframe by joining it with the busstop_hex dataframe to append hex_id information corresponding to the destination bus stops, linking each trip’s endpoint to its respective hexagonal spatial zone.
weekday_morning_od <- left_join(weekday_morning_od , busstop_hex,
by = c("DESTIN_BS" = "BUS_STOP_N"))duplicate <- weekday_morning_od %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()weekday_morning_od <- unique(weekday_morning_od)This step renames the destination hex ID column for clarity, removes any rows with missing data, then groups the data by origin and destination hex IDs, and summarizes it to calculate the total number of trips made during the weekday morning peak hours between each hexagon pair.
weekday_morning_od <- weekday_morning_od %>%
rename(DESTIN_HEX = hex_id) %>%
drop_na() %>%
group_by(ORIGIN_HEX, DESTIN_HEX) %>%
summarise(WEEKDAY_MORNING_PEAK = sum(TRIPS))It is time to save the output into an rds file format.
write_rds(weekday_morning_od, "data/rds/weekday_morning_od.rds")weekday_morning_od <- read_rds("data/rds/weekday_morning_od.rds")5.2Weekday Afternoon Peak Flow
Repeat the process above for weekday afternoon peak (5-8 PM).
weekday_afternoon_od <- left_join(weekday17_20 , busstop_hex,
by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
rename(ORIGIN_BS = ORIGIN_PT_CODE,
ORIGIN_HEX = hex_id,
DESTIN_BS = DESTINATION_PT_CODE)duplicate <- weekday_afternoon_od %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()weekday_afternoon_od <- unique(weekday_afternoon_od)weekday_afternoon_od <- left_join(weekday_afternoon_od , busstop_hex,
by = c("DESTIN_BS" = "BUS_STOP_N"))duplicate <- weekday_afternoon_od %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()weekday_afternoon_od <- unique(weekday_afternoon_od)weekday_afternoon_od <- weekday_afternoon_od %>%
rename(DESTIN_HEX = hex_id) %>%
drop_na() %>%
group_by(ORIGIN_HEX, DESTIN_HEX) %>%
summarise(WEEKDAY_AFTERNOON_PEAK = sum(TRIPS))write_rds(weekday_afternoon_od, "data/rds/weekday_afternoon_od.rds")weekday_afternoon_od <- read_rds("data/rds/weekday_afternoon_od.rds")5.3Weekend Morning Peak Flow
Repeat the process above for weekend/holiday morning peak (11 AM-2 PM).
weekend_morning_od <- left_join(weekend11_14 , busstop_hex,
by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
rename(ORIGIN_BS = ORIGIN_PT_CODE,
ORIGIN_HEX = hex_id,
DESTIN_BS = DESTINATION_PT_CODE)duplicate <- weekend_morning_od %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()weekend_morning_od <- unique(weekend_morning_od)weekend_morning_od <- left_join(weekend_morning_od , busstop_hex,
by = c("DESTIN_BS" = "BUS_STOP_N"))duplicate <- weekend_morning_od %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()weekend_morning_od <- unique(weekend_morning_od)weekend_morning_od <- weekend_morning_od %>%
rename(DESTIN_HEX = hex_id) %>%
drop_na() %>%
group_by(ORIGIN_HEX, DESTIN_HEX) %>%
summarise(WEEKEND_MORNING_PEAK = sum(TRIPS))write_rds(weekend_morning_od, "data/rds/weekend_morning_od.rds")weekend_morning_od <- read_rds("data/rds/weekend_morning_od.rds")5.4Weekend Evening Peak Flow
Repeat the process above for weekend/holiday evening peak (4-7 PM).
weekend_evening_od <- left_join(weekend16_19 , busstop_hex,
by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
rename(ORIGIN_BS = ORIGIN_PT_CODE,
ORIGIN_HEX = hex_id,
DESTIN_BS = DESTINATION_PT_CODE)duplicate <- weekend_evening_od %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()weekend_evening_od <- unique(weekend_evening_od)weekend_evening_od <- left_join(weekend_evening_od , busstop_hex,
by = c("DESTIN_BS" = "BUS_STOP_N"))duplicate <- weekend_evening_od %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()weekend_evening_od <- unique(weekend_evening_od)weekend_evening_od <- weekend_evening_od %>%
rename(DESTIN_HEX = hex_id) %>%
drop_na() %>%
group_by(ORIGIN_HEX, DESTIN_HEX) %>%
summarise(WEEKEND_EVENING_PEAK = sum(TRIPS))write_rds(weekend_evening_od, "data/rds/weekend_evening_od.rds")weekend_evening_od <- read_rds("data/rds/weekend_evening_od.rds")Remove items no longer needed to free memory and avoid redundancy.
rm(weekday6_9, weekday17_20, weekend11_14, weekend16_19)6.Visualising Commute Flow
6.1Removing Intra-zonal Flows
The code filters out intra-zonal flows from four separate data frames by excluding rows where the origin hexagon (ORIGIN_HEX) is the same as the destination hexagon (DESTIN_HEX). This step is crucial for analysis as it removes trips that start and end within the same traffic analysis zone, focusing the study on inter-zonal movements which are more significant for understanding commuting patterns and the broader transportation network efficiency.
weekday_morning_od1 <- weekday_morning_od[weekday_morning_od$ORIGIN_HEX!=weekday_morning_od$DESTIN_HEX,]weekday_afternoon_od1 <- weekday_afternoon_od[weekday_afternoon_od$ORIGIN_HEX!=weekday_afternoon_od$DESTIN_HEX,]weekend_morning_od1 <- weekend_morning_od[weekend_morning_od$ORIGIN_HEX!=weekend_morning_od$DESTIN_HEX,]weekend_evening_od1 <- weekend_evening_od[weekend_evening_od$ORIGIN_HEX!=weekend_evening_od$DESTIN_HEX,]6.2Creating the Desire Lines
The code uses the od2line function to transform the inter-zonal flow data from each time period into desire lines, which are spatial representations of the volume and direction of trips between different hexagons. These lines are prepared for visualization, allowing us to graphically depict and analyze commuting patterns for different times of the day and week on a map.
weekday_morning_flowLine <- od2line(flow = weekday_morning_od1,
zones = hex_grid_sf,
zone_code = "hex_id")weekday_afternoon_flowLine <- od2line(flow = weekday_afternoon_od1,
zones = hex_grid_sf,
zone_code = "hex_id")weekend_morning_flowLine <- od2line(flow = weekend_morning_od1,
zones = hex_grid_sf,
zone_code = "hex_id")weekend_evening_flowLine <- od2line(flow = weekend_evening_od1,
zones = hex_grid_sf,
zone_code = "hex_id")6.3Visualising the Desire Lines
6.3.1Weekday Morning Peak Commute Flow Map
This visualization code uses the tmap package to plot the hexagonal grid as a base, draws the boundaries of the metropolitan planning zones (MPZ), and overlays the desire lines representing high-volume weekday morning commute flows in Singapore. The lines are styled to vary in width and color intensity based on the volume of commutes, with thicker, darker lines indicating higher numbers of trips.
tm_shape(hex_grid_sf) +
tm_polygons(
border.col = "grey50",
border.alpha = 0.6,
alpha = 0.1
) +
tm_shape(weekday_morning_flowLine %>%
filter(WEEKDAY_MORNING_PEAK >= 5000)) +
tm_lines(
lwd = "WEEKDAY_MORNING_PEAK",
style = "quantile",
scale = c(0.1, 1, 3, 5, 7, 10),
n = 6,
alpha = 0.5,
palette = "Blues"
) +
tm_shape(mpsz) +
tm_borders(
col = "darkblue",
alpha = 0.1,
lwd = 1.5
) +
tm_layout(
main.title = "Weekday Morning Commute Flows in Singapore",
main.title.position = "center",
main.title.size = 1.0,
legend.title.size = 0.8,
legend.text.size = 0.7,
legend.position = c("left", "bottom"),
frame = FALSE,
inner.margins = c(0.05, 0.05, 0.05, 0.05)
) +
tm_credits("Source: LTA DataMall", position = c("RIGHT", "BOTTOM"), size = 0.5)
Insight from the Map:
The “Weekday Morning Commute Flows in Singapore” map reveals significant commuter traffic between various regions during peak morning hours. The thicker, darker lines suggest heavy flow between central business districts and outlying residential areas, indicating a typical urban commute pattern where many residents travel towards city centers for work. Areas with dense hexagon clusters, likely representing central and suburban residential zones, show extensive outward flow, highlighting these as key commuter hubs. Conversely, some regions exhibit sparse lines, suggesting lower population density or less reliance on public bus transit.
6.3.2Weekday Afternoon Peak Commute Flow Map
tm_shape(hex_grid_sf) +
tm_polygons(
border.col = "grey50",
border.alpha = 0.6,
alpha = 0.1
) +
tm_shape(weekday_afternoon_flowLine %>%
filter(WEEKDAY_AFTERNOON_PEAK >= 5000)) +
tm_lines(
lwd = "WEEKDAY_AFTERNOON_PEAK",
style = "quantile",
scale = c(0.1, 1, 3, 5, 7, 10),
n = 6,
alpha = 0.5,
palette = "Blues"
) +
tm_shape(mpsz) +
tm_borders(
col = "darkblue",
alpha = 0.1,
lwd = 1.5
) +
tm_layout(
main.title = "Weekday Afternoon Commute Flows in Singapore",
main.title.position = "center",
main.title.size = 1.0,
legend.title.size = 0.8,
legend.text.size = 0.7,
legend.position = c("left", "bottom"),
frame = FALSE,
inner.margins = c(0.05, 0.05, 0.05, 0.05)
) +
tm_credits("Source: LTA DataMall", position = c("RIGHT", "BOTTOM"), size = 0.5)
Insight from the Map:
The “Weekday Afternoon Commute Flows in Singapore” map suggests a reverse commute pattern from the morning, with significant flows from central areas to the outskirts, likely as people return home from work. The dense lines indicate high traffic volumes, particularly from the CBD and other employment hubs to residential districts. The distribution and volume of these lines can indicate areas with a high demand for evening public transportation services, and such insights could inform enhancements to bus service capacity and frequency to meet commuter needs during peak hours.
6.3.3Weekend Morning Peak Commute Flow Map
tm_shape(hex_grid_sf) +
tm_polygons(
border.col = "grey50",
border.alpha = 0.6,
alpha = 0.1
) +
tm_shape(weekend_morning_flowLine %>%
filter(WEEKEND_MORNING_PEAK >= 3000)) +
tm_lines(
lwd = "WEEKEND_MORNING_PEAK",
style = "quantile",
scale = c(0.1, 1, 3, 5, 7, 13, 15),
n = 7,
alpha = 0.5,
palette = "Blues"
) +
tm_shape(mpsz) +
tm_borders(
col = "darkblue",
alpha = 0.1,
lwd = 1.5
) +
tm_layout(
main.title = "Weekend Morning Commute Flows in Singapore",
main.title.position = "center",
main.title.size = 1.0,
legend.title.size = 0.8,
legend.text.size = 0.7,
legend.position = c("left", "bottom"),
frame = FALSE,
inner.margins = c(0.05, 0.05, 0.05, 0.05)
) +
tm_credits("Source: LTA DataMall", position = c("RIGHT", "BOTTOM"), size = 0.5)
Insight from the Map:
The “Weekend Morning Commute Flows in Singapore” map shows a noticeable reduction in volume and fewer dense flow lines compared to weekdays, reflecting a typical decrease in commuting activity during weekends. The flows that are present may indicate travel to weekend-specific destinations like markets, recreational areas, or places of worship. The patterns suggest that the weekend movement is more dispersed and possibly oriented towards leisure or non-work-related activities, contrasting the concentrated, work-directed flows of weekday mornings.
6.3.4Weekend Evening Peak Commute Flow Map
tm_shape(hex_grid_sf) +
tm_polygons(
border.col = "grey50",
border.alpha = 0.6,
alpha = 0.1
) +
tm_shape(weekend_evening_flowLine %>%
filter(WEEKEND_EVENING_PEAK >= 3000)) +
tm_lines(
lwd = "WEEKEND_EVENING_PEAK",
style = "quantile",
scale = c(0.1, 1, 3, 5, 7, 10),
n = 6,
alpha = 0.5,
palette = "Blues"
) +
tm_shape(mpsz) +
tm_borders(
col = "darkblue",
alpha = 0.1,
lwd = 1.5
) +
tm_layout(
main.title = "Weekend Evening Commute Flows in Singapore",
main.title.position = "center",
main.title.size = 1.0,
legend.title.size = 0.8,
legend.text.size = 0.7,
legend.position = c("left", "bottom"),
frame = FALSE,
inner.margins = c(0.05, 0.05, 0.05, 0.05)
) +
tm_credits("Source: LTA DataMall", position = c("RIGHT", "BOTTOM"), size = 0.5)
Insight from the Map:
The “Weekend Evening Commute Flows in Singapore” map likely indicates an increase in volume compared to the morning, with more pronounced traffic flows towards residential areas and perhaps popular evening destinations. This contrasts with weekday evenings, where the flow would primarily be homeward from work centers. The patterns may suggest leisure and social activities are influencing travel, with possibly greater flows to entertainment or dining hubs and a more dispersed pattern as people return from various activities across the city.
rm(duplicate, weekday_morning_flowLine, weekday_morning_od, weekday_morning_od1,
weekend_morning_flowLine, weekend_morning_od, weekend_morning_od1,
weekend_evening_flowLine, weekend_evening_od, weekend_evening_od1)7.Attractiveness Factors
In the subsequent section, we will delve into a targeted analysis of the weekday afternoon peak period. The reason for this focus stems from the comprehensive nature of commute drivers during this time. On weekday afternoons, residents are not only heading home from work or school but often transition to leisure activities such as shopping or entertainment venues directly. This complexity presents a rich tapestry of commuting patterns worthy of in-depth examination.
7.1Entertainment Distribution Integration
Entertainment distribution is considered an attractiveness factor because these venues often draw people to travel to them, influencing commuting and traffic flows. The provided code reads in the entertn geospatial data and then calculates the count of entertainment venues within each hexagon of the hex_grid_sf grid, integrating this data to quantify the level of entertainment-related attractiveness of different areas.
entertn <- st_read(dsn = "data/geospatial",
layer = "entertn")Reading layer `entertn' from data source
`D:\KathyChiu77\ISSS624\Take-home Ex\Take-home Ex 2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 114 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 10809.34 ymin: 26528.63 xmax: 41600.62 ymax: 46375.77
Projected CRS: SVY21 / Singapore TMhex_grid_sf$entertn_count <- lengths(st_intersects(hex_grid_sf, entertn))7.2Food & Beverage Distribution Integration
Food and beverage (F&B) venues act as attractiveness factors because they are destinations that people may frequently visit after work, thus influencing traffic and transportation patterns within an area.
FB <- st_read(dsn = "data/geospatial",
layer = "F&B")Reading layer `F&B' from data source
`D:\KathyChiu77\ISSS624\Take-home Ex\Take-home Ex 2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 1919 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 6010.495 ymin: 25343.27 xmax: 45462.43 ymax: 48796.21
Projected CRS: SVY21 / Singapore TMhex_grid_sf$FB_count <- lengths(st_intersects(hex_grid_sf, FB))7.3Leisure & Recreation Distribution Integration
Leisure and recreation spots are included in the study of weekday afternoon peak times because they are popular destinations that contribute to the flow of people and the overall demand for transportation services during these periods.
lere <- st_read(dsn = "data/geospatial",
layer = "Liesure&Recreation")Reading layer `Liesure&Recreation' from data source
`D:\KathyChiu77\ISSS624\Take-home Ex\Take-home Ex 2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 1217 features and 30 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 6010.495 ymin: 25134.28 xmax: 48439.77 ymax: 50078.88
Projected CRS: SVY21 / Singapore TMhex_grid_sf$lere_count <- lengths(st_intersects(hex_grid_sf, lere))7.4Retail Distribution Integration
Retail locations are included in the analysis because they are key destinations that attract shoppers, impacting people’s movement and transit patterns, especially during peak times.
retail <- st_read(dsn = "data/geospatial",
layer = "Retails")Reading layer `Retails' from data source
`D:\KathyChiu77\ISSS624\Take-home Ex\Take-home Ex 2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 37635 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 4737.982 ymin: 25171.88 xmax: 48265.04 ymax: 50135.28
Projected CRS: SVY21 / Singapore TMhex_grid_sf$retail_count <- lengths(st_intersects(hex_grid_sf, retail))7.5Train Exits Distribution Integration
trainexits <- st_read(dsn = "data/geospatial",
layer = "Train_Station_Exit_Layer")Reading layer `Train_Station_Exit_Layer' from data source
`D:\KathyChiu77\ISSS624\Take-home Ex\Take-home Ex 2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 565 features and 2 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 6134.086 ymin: 27499.7 xmax: 45356.36 ymax: 47865.92
Projected CRS: SVY21The code transforms the coordinates of train exit locations to match the coordinate reference system of the hexagonal grid and then counts the number of train exits within each hexagon. This reflects the influence of proximity to train stations on bus ridership, as people often use buses to access MRT stations in Singapore.
trainexits <- st_transform(trainexits, st_crs(hex_grid_sf))
hex_grid_sf$trainexits_count <- lengths(st_intersects(hex_grid_sf, trainexits))7.6Residence Distribution Integration
The code reads a CSV file containing housing data (hdb.csv), filters for entries marked as residential (Y), selects columns for latitude, longitude, and total dwelling units, and removes any rows with missing data. This prepares a dataset of residential locations and their capacity, which is important for analyzing homebound travel patterns.
hdb <- read_csv("data/aspatial/hdb.csv")residential <- hdb %>%
filter(residential == "Y") %>%
select(lat, lng, total_dwelling_units) %>%
na.omit()This step converts the residential dataframe into a spatial dataframe with longitude and latitude coordinates, sets its coordinate reference system (CRS) to WGS 84 (CRS 4326), and then transforms it to match the CRS of the hex_grid_sf for compatibility in subsequent spatial merging.
residential <- st_as_sf(residential,
coords = c("lng", "lat"),
crs = 4326) %>%
st_transform(crs = st_crs(hex_grid_sf))This step calculates the total number of dwelling units from the residential data within each hexagon of the hex_grid_sf grid. It uses spatial intersection to identify which residential entries fall into each hexagon and then sums the total_dwelling_units for those entries, assigning this sum to a new residential_count column in the hex grid.
intersections <- st_intersects(hex_grid_sf, residential, sparse = TRUE)
hex_grid_sf$residential_count <- mapply(function(index, residential) {
sum(residential$total_dwelling_units[index], na.rm = TRUE)
}, intersections, MoreArgs = list(residential = residential))rm(intersections)8.Propulsive Factors
To understand the propulsive factors behind bus commute flow, we focus on several key factors. Firstly, the density of bus stops, as captured by bus_stop_count, indicates the convenience and accessibility of bus services. Secondly, the distribution of businesses and schools sheds light on major daily locations, as these are places where people work and study, often traveling from these places during weekday afternoons. Additionally, we include the distribution of financial services, recognizing that these often coincide with business hubs and can be significant in influencing commuting patterns.
8.1Business Distribution Integration
business <- st_read(dsn = "data/geospatial",
layer = "Business")Reading layer `Business' from data source
`D:\KathyChiu77\ISSS624\Take-home Ex\Take-home Ex 2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 6550 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 3669.148 ymin: 25408.41 xmax: 47034.83 ymax: 50148.54
Projected CRS: SVY21 / Singapore TMhex_grid_sf$business_count <- lengths(st_intersects(hex_grid_sf, business))8.2School Distribution Integration
This code snippet queries an API to gather information about schools in Singapore. It first reads a CSV file listing school postal codes, then iterates through these codes, sending a request to the OneMap API for each. For postal codes with found data, it appends relevant details to the found dataframe. If no data is found for a postal code, it adds that code to the not_found dataframe.
url<-"https://www.onemap.gov.sg/api/common/elastic/search"
csv<-read_csv("data/aspatial/Generalinformationofschools.csv")
postcodes<-csv$`postal_code`
found<-data.frame()
not_found<-data.frame()
for(postcode in postcodes){
query<-list('searchVal'=postcode,'returnGeom'='Y','getAddrDetails'='Y','pageNum'='1')
res<- GET(url,query=query)
if((content(res)$found)!=0){
found<-rbind(found,data.frame(content(res))[4:13])
} else{
not_found = data.frame(postcode)
}
}The next step merges the original school information from the csv file with the data retrieved from the API (found), matching entries based on postal codes. The merged data, which now includes enhanced details for each school, is saved to a new CSV file schools.csv. Additionally, postal codes for which no data was found are saved in a separate file not_found.csv, allowing for further review or data acquisition efforts.
merged = merge(csv, found, by.x = 'postal_code', by.y = 'results.POSTAL', all = TRUE)
write.csv(merged, file = "data/aspatial/schools.csv")
write.csv(not_found, file = "data/aspatial/not_found.csv")The code below initially reads the enhanced schools.csv file and renames latitude and longitude columns for clarity. It then selects specific columns, including postal code, school name, latitude, and longitude. Following this, it filters out any schools with missing latitude or longitude data. Finally, the filtered dataset is converted into a spatial dataframe with a coordinate reference system (CRS) of WGS 84 (CRS 4326) and then transformed to match Singapore’s local CRS (3414) for spatial analysis compatibility.
schools <- read_csv("data/aspatial/schools.csv") %>%
rename(latitude = "results.LATITUDE",
longitude = "results.LONGITUDE")%>%
select(postal_code, school_name, latitude, longitude)schools <- schools %>%
filter(!is.na(longitude) & !is.na(latitude)) %>%
st_as_sf(coords = c("longitude", "latitude"), crs = 4326) %>%
st_transform(crs = 3414)hex_grid_sf$school_count <- lengths(st_intersects(hex_grid_sf, schools))rm(csv, found, merged, not_found, query, res,
postcode, postcodes, url)8.3Financial Service Distribution Integration
finserv <- st_read(dsn = "data/geospatial",
layer = "FinServ")Reading layer `FinServ' from data source
`D:\KathyChiu77\ISSS624\Take-home Ex\Take-home Ex 2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 3320 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 4881.527 ymin: 25171.88 xmax: 46526.16 ymax: 49338.02
Projected CRS: SVY21 / Singapore TMhex_grid_sf$finserv_count <- lengths(st_intersects(hex_grid_sf, finserv))8.4Final Check of Integrated Data
Before moving to next section, we may kindly check the basic structure and content of integrated data hex_grid_sf.
datatable(hex_grid_sf)9.Computing Distance Matrix
9.1Converting from sf Data.table to Spatial Polygons Data.frame
This conversion is necessary for compatibility with spatial functions or methods that specifically require data in the sp format, rather than the sf format.
hex_grid_sp <- as(hex_grid_sf, "Spatial")
hex_grid_spclass : SpatialPolygonsDataFrame
features : 1853
extent : 3966.576, 48566.88, 26373.72, 50123.72 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 11
names : hex_id, bus_stop_count, entertn_count, FB_count, lere_count, retail_count, trainexits_count, residential_count, business_count, school_count, finserv_count
min values : 393, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
max values : 9988, 13, 8, 71, 26, 986, 9, 3531, 60, 4, 91 9.2 Computing the Distance Matrix
The spDists function computes distances between each pair of hexagons in the grid. The parameter longlat = FALSE indicates that the distances are calculated in a planar manner, suitable for the coordinate system used. The final line displays the first 10 rows and columns of this distance matrix for a quick inspection of the calculated distances.
dist <- spDists(hex_grid_sp,
longlat = FALSE)
head(dist, n=c(10, 10)) [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.0000 2633.9134 866.0254 2291.2878 3031.0889 750.0000 1984.3135
[2,] 2633.9134 0.0000 1887.4586 433.0127 433.0127 2291.2878 866.0254
[3,] 866.0254 1887.4586 0.0000 1500.0000 2250.0000 433.0127 1145.6439
[4,] 2291.2878 433.0127 1500.0000 0.0000 750.0000 1887.4586 433.0127
[5,] 3031.0889 433.0127 2250.0000 750.0000 0.0000 2633.9134 1145.6439
[6,] 750.0000 2291.2878 433.0127 1887.4586 2633.9134 0.0000 1500.0000
[7,] 1984.3135 866.0254 1145.6439 433.0127 1145.6439 1500.0000 0.0000
[8,] 4175.8233 1561.2495 3381.9373 1887.4586 1145.6439 3750.0000 2250.0000
[9,] 1732.0508 1299.0381 866.0254 866.0254 1561.2495 1145.6439 433.0127
[10,] 2410.9127 750.0000 1561.2495 433.0127 866.0254 1887.4586 433.0127
[,8] [,9] [,10]
[1,] 4175.823 1732.0508 2410.9127
[2,] 1561.249 1299.0381 750.0000
[3,] 3381.937 866.0254 1561.2495
[4,] 1887.459 866.0254 433.0127
[5,] 1145.644 1561.2495 866.0254
[6,] 3750.000 1145.6439 1887.4586
[7,] 2250.000 433.0127 433.0127
[8,] 0.000 2633.9134 1887.4586
[9,] 2633.913 0.0000 750.0000
[10,] 1887.459 750.0000 0.00009.3Labeling Column and Row Headers of the Distance Matrix
This code assigns the hex_id values from the hex_grid_sf dataframe as both column and row headers for the distance matrix dist. By doing so, each row and column in the matrix is clearly labeled with the corresponding hexagon’s identifier, making it easier to interpret the distances between specific hexagons.
hex_names <- hex_grid_sf$hex_idcolnames(dist) <- paste0(hex_names)
rownames(dist) <- paste0(hex_names)9.4Pivoting Distance Value by HEX_ID
The code transforms the distance matrix dist into a long format data frame distPair using the melt function. Each row in distPair represents a pair of hexagons with their corresponding distance.
distPair <- melt(dist) %>%
rename(dist = value)
head(distPair, 10) Var1 Var2 dist
1 393 393 0.0000
2 444 393 2633.9134
3 488 393 866.0254
4 490 393 2291.2878
5 491 393 3031.0889
6 535 393 750.0000
7 537 393 1984.3135
8 540 393 4175.8233
9 583 393 1732.0508
10 584 393 2410.91279.5Updating Intra-zonal Distances
This code filters the distPair dataframe to exclude distances of zero (indicating the same hexagon), and then provides a statistical summary of the remaining non-zero distances.
distPair %>%
filter(dist > 0) %>%
summary() Var1 Var2 dist
Min. : 393 Min. : 393 Min. : 433
1st Qu.:3694 1st Qu.:3694 1st Qu.: 7949
Median :5474 Median :5474 Median :12933
Mean :5236 Mean :5236 Mean :13705
3rd Qu.:6837 3rd Qu.:6837 3rd Qu.:18407
Max. :9988 Max. :9988 Max. :44478 We then replace the distance of 0 by 200 which would not affect the minimum distance that is 433.
distPair$dist <- ifelse(distPair$dist == 0,
200, distPair$dist)Let’s check the statistical summary of distPair again.
distPair %>%
summary() Var1 Var2 dist
Min. : 393 Min. : 393 Min. : 200
1st Qu.:3694 1st Qu.:3694 1st Qu.: 7949
Median :5474 Median :5474 Median :12933
Mean :5236 Mean :5236 Mean :13698
3rd Qu.:6837 3rd Qu.:6837 3rd Qu.:18407
Max. :9988 Max. :9988 Max. :44478 Rename the Var1 and Var2 as orig and dest respectively which are short for origin and destination.
distPair <- distPair %>%
rename(orig = Var1,
dest = Var2)Export and save the distPair in rds format.
write_rds(distPair, "data/rds/distPair.rds") 10.Creating Complete Data for Spatial Interaction Modeling
This code converts the ORIGIN_HEX and DESTIN_HEX columns in the weekday_afternoon_od1 dataframe, as well as the orig and dest columns in the distPair dataframe, into factors. This conversion is essential for spatial interaction modeling, as it ensures that these columns, representing hexagon identifiers, are treated as categorical variables rather than numeric values.
weekday_afternoon_od1$ORIGIN_HEX <- as.factor(weekday_afternoon_od1$ORIGIN_HEX)
weekday_afternoon_od1$DESTIN_HEX <- as.factor(weekday_afternoon_od1$DESTIN_HEX)
distPair$orig <- as.factor(distPair$orig)
distPair$dest <- as.factor(distPair$dest)The code below adds distance information to each origin-destination pair in the weekday_afternoon_od1 data.
weekday_afternoon_od2 <- weekday_afternoon_od1 %>%
left_join (distPair,
by = c("ORIGIN_HEX" = "orig",
"DESTIN_HEX" = "dest"))The code converts the hex_grid_sf simple features (sf) object into a regular dataframe named hex_grid_df. It then selects specific columns related to various counts (like bus stops, businesses, schools, financial services, etc.) and the hexagon ID (hex_id).
hex_grid_df <- as.data.frame(hex_grid_sf) %>%
select(hex_id, bus_stop_count, business_count, school_count, finserv_count,
entertn_count, FB_count, lere_count, retail_count, trainexits_count, residential_count) %>%
mutate(hex_id = as.character(hex_id))origin_factors is created by selecting relevant columns from hex_grid_df that represent factors at the origin hexagons (like bus stop count, business count, etc.).
origin_factors <- hex_grid_df %>%
select(hex_id, bus_stop_count, business_count, school_count, finserv_count)
weekday_afternoon_od2 <- weekday_afternoon_od2 %>%
mutate(ORIGIN_HEX = as.character(ORIGIN_HEX),
DESTIN_HEX = as.character(DESTIN_HEX))This join adds the origin-specific factors to each row based on the origin hexagon ID, enriching the dataset with contextual information about the origin locations.
weekday_afternoon_od2_with_origin <- weekday_afternoon_od2 %>%
left_join(origin_factors, by = c("ORIGIN_HEX" = "hex_id"))destin_factors is created by selecting columns from hex_grid_df that represent factors at destination hexagons, such as counts of entertainment venues, food and beverage outlets, leisure and recreation spots, retail locations, train exits, and residential units.
destin_factors <- hex_grid_df %>%
select(hex_id, entertn_count, FB_count, lere_count, retail_count, trainexits_count, residential_count)This step adds destination-specific contextual information to each row in the dataset, based on the destination hexagon ID, thus completing the dataset with both origin and destination factors
weekday_afternoon_od2_complete <- weekday_afternoon_od2_with_origin %>%
left_join(destin_factors, by = c("DESTIN_HEX" = "hex_id"))glimpse(weekday_afternoon_od2_complete)Rows: 161,671
Columns: 14
Groups: ORIGIN_HEX [1,808]
$ ORIGIN_HEX <chr> "393", "393", "393", "393", "393", "393", "393"…
$ DESTIN_HEX <chr> "535", "585", "723", "770", "779", "824", "827"…
$ WEEKDAY_AFTERNOON_PEAK <dbl> 3, 34, 182, 1, 1, 18, 6, 145, 2, 16, 250, 23, 2…
$ dist <dbl> 750.000, 3122.499, 1561.249, 1887.459, 7697.402…
$ bus_stop_count <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ business_count <int> 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0,…
$ school_count <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ finserv_count <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ entertn_count <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$ FB_count <int> 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0,…
$ lere_count <int> 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0,…
$ retail_count <int> 0, 1, 0, 0, 0, 0, 3, 0, 2, 0, 3, 9, 2, 1, 0, 0,…
$ trainexits_count <int> 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0,…
$ residential_count <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…Export the complete dataset and name it as SIM_data for later use.
write_rds(weekday_afternoon_od2_complete, "data/rds/SIM_data.rds")rm(business, busstop, busstop_hex, busstop_mpsz, destin_factors, dist, distPair, entertn, FB, finserv, hdb, hex_grid_df, hex_grid_sf, hex_grid_sp, lere, mpsz, origin_factors, residential, retail, schools, trainexits, weekday_afternoon_flowLine, weekday_afternoon_od, weekday_afternoon_od1, weekday_afternoon_od2, weekday_afternoon_od2_complete, weekday_afternoon_od2_with_origin, hex_names)11.Calibrating Spatial Interaction Models
11.1Importing the Modelling Data
The first step to calibrate Spatial Interaction Models is importing the modelling data by using the code chunk below.
SIM_data <- read_rds("data/rds/SIM_data.rds")11.2Visualising the Dependent Variable
After plotting the distribution of dependent variable, the bus travel volume during weekday afternoon peak, it’s obvious that the distribution is highly skewed and not resemble bell shape or also known as normal distribution.
ggplot(data = SIM_data, aes(x = WEEKDAY_AFTERNOON_PEAK)) +
geom_histogram(binwidth = 100) +
xlab("Volume of Weekday Afternoon Peak") +
ylab("Count") +
ggtitle("Distribution of Weekday Afternoon Peak Volumes")
Next, let us visualise the relation between the dependent variable and one of the key independent variable in Spatial Interaction Model, namely distance.
ggplot(data = SIM_data, aes(x = dist, y = WEEKDAY_AFTERNOON_PEAK)) +
geom_point(alpha = 0.5) +
geom_smooth(method = "lm", se = FALSE) +
xlab("Distance Between Hexagons") +
ylab("Volume of Weekday Afternoon Peak") +
ggtitle("Relationship Between Distance and Weekday Afternoon Peak Volume")
Notice that their relationship hardly resemble linear relationship.
On the other hand, if we plot the scatter plot by using the log transformed version of both variables, we can see that their relationship is more resemble linear relationship.
ggplot(data = SIM_data, aes(x = log(dist), y = log(WEEKDAY_AFTERNOON_PEAK))) +
geom_point(alpha = 0.5) +
geom_smooth(method = "lm", se = FALSE, color = "lightblue") +
xlab("Log of Distance Between Hexagons") +
ylab("Log of Volume of Weekday Afternoon Peak") +
ggtitle("Log-Log Relationship Between Distance and Volume of Weekday Afternoon Peak") +
theme_minimal()
11.3Checking and Replacing Variables with Zero Values
Since Poisson Regression is based of log and log 0 is undefined, it is important for us to ensure that no 0 values in the explanatory variables.
In the code chunk below, summary() is used to compute the summary statistics of all variables in SIM_data data frame.
summary(SIM_data) ORIGIN_HEX DESTIN_HEX WEEKDAY_AFTERNOON_PEAK dist
Length:161671 Length:161671 Min. : 1.0 Min. : 433
Class :character Class :character 1st Qu.: 4.0 1st Qu.: 2411
Mode :character Mode :character Median : 18.0 Median : 4684
Mean : 148.4 Mean : 5658
3rd Qu.: 73.0 3rd Qu.: 8020
Max. :59391.0 Max. :25159
bus_stop_count business_count school_count finserv_count
Min. : 1.000 Min. : 0.000 Min. :0.0000 Min. : 0.000
1st Qu.: 2.000 1st Qu.: 0.000 1st Qu.:0.0000 1st Qu.: 0.000
Median : 3.000 Median : 0.000 Median :0.0000 Median : 1.000
Mean : 3.401 Mean : 2.556 Mean :0.1806 Mean : 3.944
3rd Qu.: 4.000 3rd Qu.: 2.000 3rd Qu.:0.0000 3rd Qu.: 4.000
Max. :13.000 Max. :60.000 Max. :4.0000 Max. :91.000
entertn_count FB_count lere_count retail_count
Min. :0.0000 Min. : 0.000 Min. : 0.0000 Min. : 0.00
1st Qu.:0.0000 1st Qu.: 0.000 1st Qu.: 0.0000 1st Qu.: 2.00
Median :0.0000 Median : 0.000 Median : 0.0000 Median : 7.00
Mean :0.1352 Mean : 2.135 Mean : 0.8934 Mean : 38.84
3rd Qu.:0.0000 3rd Qu.: 1.000 3rd Qu.: 1.0000 3rd Qu.: 31.00
Max. :8.0000 Max. :71.000 Max. :26.0000 Max. :986.00
trainexits_count residential_count
Min. :0.0000 Min. : 0.0
1st Qu.:0.0000 1st Qu.: 0.0
Median :0.0000 Median : 219.0
Mean :0.6436 Mean : 674.6
3rd Qu.:0.0000 3rd Qu.:1264.0
Max. :9.0000 Max. :3531.0 After knowing variables with 0 values, we should use the code below to replace all 0 values to 0.99.
SIM_data$business_count <- ifelse(
SIM_data$business_count == 0,
0.99, SIM_data$business_count)
SIM_data$school_count <- ifelse(
SIM_data$school_count == 0,
0.99, SIM_data$school_count)
SIM_data$finserv_count <- ifelse(
SIM_data$finserv_count == 0,
0.99, SIM_data$finserv_count)
SIM_data$entertn_count <- ifelse(
SIM_data$entertn_count == 0,
0.99, SIM_data$entertn_count)
SIM_data$FB_count <- ifelse(
SIM_data$FB_count == 0,
0.99, SIM_data$FB_count)
SIM_data$lere_count <- ifelse(
SIM_data$lere_count == 0,
0.99, SIM_data$lere_count)
SIM_data$retail_count <- ifelse(
SIM_data$retail_count == 0,
0.99, SIM_data$retail_count)
SIM_data$trainexits_count <- ifelse(
SIM_data$trainexits_count == 0,
0.99, SIM_data$trainexits_count)
SIM_data$residential_count <- ifelse(
SIM_data$residential_count == 0,
0.99, SIM_data$residential_count)Let’s run summary() again for double check.
summary(SIM_data) ORIGIN_HEX DESTIN_HEX WEEKDAY_AFTERNOON_PEAK dist
Length:161671 Length:161671 Min. : 1.0 Min. : 433
Class :character Class :character 1st Qu.: 4.0 1st Qu.: 2411
Mode :character Mode :character Median : 18.0 Median : 4684
Mean : 148.4 Mean : 5658
3rd Qu.: 73.0 3rd Qu.: 8020
Max. :59391.0 Max. :25159
bus_stop_count business_count school_count finserv_count
Min. : 1.000 Min. : 0.990 Min. :0.990 Min. : 0.990
1st Qu.: 2.000 1st Qu.: 0.990 1st Qu.:0.990 1st Qu.: 0.990
Median : 3.000 Median : 0.990 Median :0.990 Median : 1.000
Mean : 3.401 Mean : 3.138 Mean :1.019 Mean : 4.391
3rd Qu.: 4.000 3rd Qu.: 2.000 3rd Qu.:0.990 3rd Qu.: 4.000
Max. :13.000 Max. :60.000 Max. :4.000 Max. :91.000
entertn_count FB_count lere_count retail_count
Min. :0.990 Min. : 0.990 Min. : 0.990 Min. : 0.99
1st Qu.:0.990 1st Qu.: 0.990 1st Qu.: 0.990 1st Qu.: 2.00
Median :0.990 Median : 0.990 Median : 0.990 Median : 7.00
Mean :1.045 Mean : 2.862 Mean : 1.539 Mean : 38.99
3rd Qu.:0.990 3rd Qu.: 1.000 3rd Qu.: 1.000 3rd Qu.: 31.00
Max. :8.000 Max. :71.000 Max. :26.000 Max. :986.00
trainexits_count residential_count
Min. :0.990 Min. : 0.99
1st Qu.:0.990 1st Qu.: 0.99
Median :0.990 Median : 219.00
Mean :1.399 Mean : 675.02
3rd Qu.:0.990 3rd Qu.:1264.00
Max. :9.000 Max. :3531.00 11.4Unconstrained Spatial Interaction Model
The model is “unconstrained” because it doesn’t impose any limitations on the total outflow from an origin or the total inflow to a destination, allowing them to vary freely based on the underlying variables.
The code chunk used to calibrate to model is shown as below. Specifically, we should export and save uncSIM to ensure reproducibility as it commonly takes long to run for large dataset.
uncSIM <- glm(formula = WEEKDAY_AFTERNOON_PEAK ~
log(bus_stop_count) +
log(business_count) +
log(school_count) +
log(finserv_count) +
log(entertn_count) +
log(FB_count) +
log(lere_count) +
log(retail_count) +
log(trainexits_count) +
log(residential_count) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
write_rds(uncSIM, "data/rds/uncSIM.rds")uncSIM <- read_rds("data/rds/uncSIM.rds")
uncSIM
Call: glm(formula = WEEKDAY_AFTERNOON_PEAK ~ log(bus_stop_count) +
log(business_count) + log(school_count) + log(finserv_count) +
log(entertn_count) + log(FB_count) + log(lere_count) + log(retail_count) +
log(trainexits_count) + log(residential_count) + log(dist),
family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)
Coefficients:
(Intercept) log(bus_stop_count) log(business_count)
11.67689 0.40019 -0.06794
log(school_count) log(finserv_count) log(entertn_count)
-0.31202 0.42704 0.05788
log(FB_count) log(lere_count) log(retail_count)
-0.17995 -0.10079 0.05820
log(trainexits_count) log(residential_count) log(dist)
0.69347 0.12209 -1.04916
Degrees of Freedom: 161670 Total (i.e. Null); 161659 Residual
Null Deviance: 96290000
Residual Deviance: 59350000 AIC: 6013000011.5R-squared Function
The provided R function CalcRSquared calculates the coefficient of determination, commonly known as R-squared (R²), to assess the goodness of fit for a statistical model.
Inside the function, it computes the correlation coefficient r between the observed and estimated values, then squares this value to obtain R².
CalcRSquared <- function(observed,estimated){
r <- cor(observed,estimated)
R2 <- r^2
R2
}Next, we will compute the R-squared of the unconstrained SIM by using the code chunk below.
CalcRSquared(uncSIM$data$WEEKDAY_AFTERNOON_PEAK, uncSIM$fitted.values)[1] 0.1063576The function r2_mcfadden calculates McFadden’s R-squared for the provided uncSIM model, which is the unconstrained model in this context. McFadden’s R-squared is a measure of goodness of fit for logistic regression models and is interpreted as the proportion of the log likelihood explained by the model. Unlike the traditional R-squared, McFadden’s R-squared typically provides smaller values; values between 0.2 to 0.4 can indicate a good fit.
r2_mcfadden(uncSIM)# R2 for Generalized Linear Regression
R2: 0.381
adj. R2: 0.38111.6Origin Constrained Spatial Interaction Model
The origin (production) constrained model predicts flows from origins to various destinations while ensuring that the sum of the flows from each origin matches the observed total outflows for that origin.
The code chunk below is adjusted accordingly:
orcSIM <- glm(formula = WEEKDAY_AFTERNOON_PEAK ~
ORIGIN_HEX +
log(entertn_count) +
log(FB_count) +
log(lere_count) +
log(retail_count) +
log(trainexits_count) +
log(residential_count) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
write_rds(orcSIM, "data/rds/orcSIM.rds")orcSIM <- read_rds("data/rds/orcSIM.rds")
orcSIM
Call: glm(formula = WEEKDAY_AFTERNOON_PEAK ~ ORIGIN_HEX + log(entertn_count) +
log(FB_count) + log(lere_count) + log(retail_count) + log(trainexits_count) +
log(residential_count) + log(dist), family = poisson(link = "log"),
data = SIM_data, na.action = na.exclude)
Coefficients:
(Intercept) ORIGIN_HEX1012 ORIGIN_HEX1013
12.2146119 -1.1232728 0.0834191
ORIGIN_HEX1014 ORIGIN_HEX1058 ORIGIN_HEX1059
0.6124842 -3.6957314 -0.6714203
ORIGIN_HEX1060 ORIGIN_HEX1061 ORIGIN_HEX1104
-0.5027015 -0.2213456 1.3164351
ORIGIN_HEX1106 ORIGIN_HEX1107 ORIGIN_HEX1108
0.4673144 1.2099413 0.1395859
ORIGIN_HEX1152 ORIGIN_HEX1153 ORIGIN_HEX1154
-1.0968668 -0.5082854 0.8594057
ORIGIN_HEX1199 ORIGIN_HEX1200 ORIGIN_HEX1201
-0.6125329 0.1508162 0.5123503
ORIGIN_HEX1202 ORIGIN_HEX1244 ORIGIN_HEX1245
0.3357323 1.3788573 0.6675282
ORIGIN_HEX1246 ORIGIN_HEX1247 ORIGIN_HEX1291
-0.3714249 -0.4101895 1.6401911
ORIGIN_HEX1292 ORIGIN_HEX1293 ORIGIN_HEX1295
1.2503401 1.5477108 0.2113326
ORIGIN_HEX1338 ORIGIN_HEX1339 ORIGIN_HEX1340
1.6483118 -0.2701012 -0.0671674
ORIGIN_HEX1341 ORIGIN_HEX1385 ORIGIN_HEX1386
0.6648272 0.3461467 -1.3002130
ORIGIN_HEX1387 ORIGIN_HEX1388 ORIGIN_HEX1433
0.5593144 -1.5967428 1.3470366
ORIGIN_HEX1434 ORIGIN_HEX1479 ORIGIN_HEX1480
-1.1888456 -0.0513426 1.5276145
ORIGIN_HEX1481 ORIGIN_HEX1525 ORIGIN_HEX1526
0.6237632 1.5438707 -0.9104852
ORIGIN_HEX1527 ORIGIN_HEX1528 ORIGIN_HEX1529
1.2066114 0.8178755 1.1631925
ORIGIN_HEX1573 ORIGIN_HEX1574 ORIGIN_HEX1575
0.1021890 -1.6188279 1.4591288
ORIGIN_HEX1619 ORIGIN_HEX1621 ORIGIN_HEX1622
0.9872447 2.6350589 0.1417837
ORIGIN_HEX1623 ORIGIN_HEX1666 ORIGIN_HEX1668
1.9846656 1.1502891 0.4249987
ORIGIN_HEX1669 ORIGIN_HEX1670 ORIGIN_HEX1671
1.0466328 0.8519089 -1.3363757
ORIGIN_HEX1715 ORIGIN_HEX1717 ORIGIN_HEX1718
1.0875148 -0.4159235 2.0813279
ORIGIN_HEX1761 ORIGIN_HEX1762 ORIGIN_HEX1763
0.7785746 1.2993884 2.3826871
ORIGIN_HEX1764 ORIGIN_HEX1765 ORIGIN_HEX1768
-3.3052426 -2.4649452 -0.5687006
ORIGIN_HEX1808 ORIGIN_HEX1809 ORIGIN_HEX1810
0.8247703 0.5879864 1.6827475
ORIGIN_HEX1811 ORIGIN_HEX1812 ORIGIN_HEX1814
-1.2049275 -1.2436807 1.2992878
ORIGIN_HEX1815 ORIGIN_HEX1855 ORIGIN_HEX1856
-0.6022784 1.2201632 -0.6488613
ORIGIN_HEX1857 ORIGIN_HEX1858 ORIGIN_HEX1859
1.3868157 1.6168154 1.5906235
ORIGIN_HEX1861 ORIGIN_HEX1862 ORIGIN_HEX1903
1.6875438 2.5260569 -0.9773752
ORIGIN_HEX1904 ORIGIN_HEX1905 ORIGIN_HEX1906
1.1607129 -1.6120253 -1.2186386
ORIGIN_HEX1907 ORIGIN_HEX1909 ORIGIN_HEX1950
-0.1349058 0.2826431 -2.3107875
ORIGIN_HEX1952 ORIGIN_HEX1953 ORIGIN_HEX1955
1.7654787 -0.6232722 2.0091364
ORIGIN_HEX1956 ORIGIN_HEX1957 ORIGIN_HEX1996
0.2970540 -0.3343039 0.3600461
ORIGIN_HEX1997 ORIGIN_HEX1998 ORIGIN_HEX1999
-0.0442811 1.7923203 0.2805291
ORIGIN_HEX2000 ORIGIN_HEX2003 ORIGIN_HEX2046
-0.7633798 -0.0990055 -0.3938473
ORIGIN_HEX2047 ORIGIN_HEX2049 ORIGIN_HEX2050
1.1862402 0.8174522 -0.1415366
ORIGIN_HEX2051 ORIGIN_HEX2090 ORIGIN_HEX2092
1.2559151 -0.2674990 1.8823655
ORIGIN_HEX2093 ORIGIN_HEX2094 ORIGIN_HEX2095
0.1352920 -0.4729770 -0.0751354
ORIGIN_HEX2096 ORIGIN_HEX2139 ORIGIN_HEX2140
-1.1432896 -2.4592280 1.6702654
ORIGIN_HEX2141 ORIGIN_HEX2142 ORIGIN_HEX2143
-0.0843711 -0.1356914 0.7089135
ORIGIN_HEX2145 ORIGIN_HEX2146 ORIGIN_HEX2184
1.3588908 -1.3799040 0.0931636
ORIGIN_HEX2187 ORIGIN_HEX2189 ORIGIN_HEX2190
-0.6736008 -1.6585222 0.1304956
ORIGIN_HEX2192 ORIGIN_HEX2193 ORIGIN_HEX2194
-1.1777504 0.9474195 0.0004905
ORIGIN_HEX2232 ORIGIN_HEX2233 ORIGIN_HEX2234
0.2344905 1.5635186 1.0494823
ORIGIN_HEX2235 ORIGIN_HEX2236 ORIGIN_HEX2237
0.4438395 -0.3809052 0.2469121
ORIGIN_HEX2238 ORIGIN_HEX2239 ORIGIN_HEX2241
0.6055828 0.4171301 -1.8325487
ORIGIN_HEX2242 ORIGIN_HEX2278 ORIGIN_HEX2279
-0.4236908 -0.2278623 0.6966419
ORIGIN_HEX2280 ORIGIN_HEX2281 ORIGIN_HEX2282
1.4514008 0.5754270 0.3590999
ORIGIN_HEX2283 ORIGIN_HEX2284 ORIGIN_HEX2288
1.5845045 -0.0734321 0.1675462
ORIGIN_HEX2289 ORIGIN_HEX2290 ORIGIN_HEX2326
-1.9426846 -3.6744967 -0.8393572
ORIGIN_HEX2327 ORIGIN_HEX2328 ORIGIN_HEX2329
1.1992830 -1.1457234 0.5989836
ORIGIN_HEX2330 ORIGIN_HEX2331 ORIGIN_HEX2332
-0.1568768 0.6016083 0.7699250
ORIGIN_HEX2337 ORIGIN_HEX2340 ORIGIN_HEX2341
-1.2387776 -1.0026606 -3.1148913
ORIGIN_HEX2342 ORIGIN_HEX2372 ORIGIN_HEX2376
-1.2525360 0.4220926 -2.1631551
ORIGIN_HEX2377 ORIGIN_HEX2378 ORIGIN_HEX2379
0.2903871 -0.0614725 0.6377149
ORIGIN_HEX2382 ORIGIN_HEX2386 ORIGIN_HEX2387
-3.1910650 -1.4074848 -5.2715931
ORIGIN_HEX2389 ORIGIN_HEX2421 ORIGIN_HEX2422
-0.1426100 0.5355638 1.6328897
ORIGIN_HEX2423 ORIGIN_HEX2424 ORIGIN_HEX2425
0.4999534 -2.2434270 -0.4138955
ORIGIN_HEX2426 ORIGIN_HEX2436 ORIGIN_HEX2437
-0.0189230 1.0224484 -1.7137900
ORIGIN_HEX2466 ORIGIN_HEX2470 ORIGIN_HEX2471
-0.3324475 0.7160412 3.1010085
ORIGIN_HEX2472 ORIGIN_HEX2473 ORIGIN_HEX2476
0.2559324 1.0153091 -3.1315670
ORIGIN_HEX2484 ORIGIN_HEX2515 ORIGIN_HEX2516
-0.9226008 0.0830500 0.4198018
ORIGIN_HEX2518 ORIGIN_HEX2519 ORIGIN_HEX2520
-2.6558177 -0.4908226 -1.1617722
ORIGIN_HEX2532 ORIGIN_HEX2533 ORIGIN_HEX2534
-2.4978366 -0.6334217 -0.1609490
ORIGIN_HEX2562 ORIGIN_HEX2563 ORIGIN_HEX2564
-0.0182499 0.8234200 1.3195002
ORIGIN_HEX2565 ORIGIN_HEX2566 ORIGIN_HEX2567
-1.8830530 -0.5882415 -0.4802982
ORIGIN_HEX2570 ORIGIN_HEX2579 ORIGIN_HEX2609
-4.2327829 -3.8214580 -0.0907136
ORIGIN_HEX2611 ORIGIN_HEX2612 ORIGIN_HEX2613
0.3898628 0.3640899 -0.5721390
ORIGIN_HEX2614 ORIGIN_HEX2655 ORIGIN_HEX2657
0.7980937 -0.5860837 -0.3887114
ORIGIN_HEX2658 ORIGIN_HEX2660 ORIGIN_HEX2661
1.3442512 0.7700844 -0.7084062
ORIGIN_HEX2664 ORIGIN_HEX2703 ORIGIN_HEX2705
-0.5157909 -2.3180451 -0.4601412
ORIGIN_HEX2706 ORIGIN_HEX2707 ORIGIN_HEX2708
0.5500602 -0.4117198 -0.8756490
ORIGIN_HEX2712 ORIGIN_HEX2752 ORIGIN_HEX2753
0.4656846 -0.1345038 -0.0942630
ORIGIN_HEX2754 ORIGIN_HEX2755 ORIGIN_HEX2758
-0.7419777 0.1006397 -0.0216992
ORIGIN_HEX2797 ORIGIN_HEX2798 ORIGIN_HEX2799
0.7094211 -1.0773740 -0.2653153
ORIGIN_HEX2800 ORIGIN_HEX2802 ORIGIN_HEX2806
-0.7333003 0.8382372 0.8390265
ORIGIN_HEX2843 ORIGIN_HEX2844 ORIGIN_HEX2845
0.9410683 -0.1103087 0.6087839
ORIGIN_HEX2846 ORIGIN_HEX2847 ORIGIN_HEX2848
-0.5875411 0.1872471 2.4708727
ORIGIN_HEX2849 ORIGIN_HEX2891 ORIGIN_HEX2893
-0.3609997 0.9092353 0.3249502
ORIGIN_HEX2894 ORIGIN_HEX2895 ORIGIN_HEX2896
0.6591408 -0.7842087 -1.0554792
ORIGIN_HEX2897 ORIGIN_HEX2900 ORIGIN_HEX2937
-0.6836332 0.9182720 0.3773590
ORIGIN_HEX2939 ORIGIN_HEX2940 ORIGIN_HEX2941
0.4129201 0.2143413 -0.7182327
ORIGIN_HEX2942 ORIGIN_HEX2943 ORIGIN_HEX2987
-1.0721704 0.7460494 -0.8310831
ORIGIN_HEX2988 ORIGIN_HEX2990 ORIGIN_HEX2994
-0.6971969 -0.1935696 -2.3405647
ORIGIN_HEX3031 ORIGIN_HEX3033 ORIGIN_HEX3036
0.6062849 -0.3812143 -0.9961095
ORIGIN_HEX3084 ORIGIN_HEX3125 ORIGIN_HEX3129
0.2732330 -0.2696515 -2.7185448
ORIGIN_HEX3130 ORIGIN_HEX3135 ORIGIN_HEX3172
0.3905817 -1.2462760 1.2958032
ORIGIN_HEX3173 ORIGIN_HEX3176 ORIGIN_HEX3177
0.9492186 -2.9362429 0.6116500
ORIGIN_HEX3182 ORIGIN_HEX3218 ORIGIN_HEX3220
-1.0390481 0.2216831 0.4569443
ORIGIN_HEX3221 ORIGIN_HEX3223 ORIGIN_HEX3224
-3.9730883 -0.9420276 0.4114902
ORIGIN_HEX3225 ORIGIN_HEX3229 ORIGIN_HEX3238
-1.3968761 0.5142262 -0.9948517
ORIGIN_HEX3266 ORIGIN_HEX3268 ORIGIN_HEX3269
-0.0214121 0.8779738 -1.5961636
ORIGIN_HEX3270 ORIGIN_HEX3271 ORIGIN_HEX3272
0.3971190 0.1776396 -1.3151783
ORIGIN_HEX3273 ORIGIN_HEX3276 ORIGIN_HEX3277
0.6430561 0.2161216 -0.0136848
ORIGIN_HEX3312 ORIGIN_HEX3314 ORIGIN_HEX3316
0.2882789 -2.6345576 0.0599729
ORIGIN_HEX3317 ORIGIN_HEX3318 ORIGIN_HEX3319
-0.6876372 -0.8603021 -0.1459794
ORIGIN_HEX3320 ORIGIN_HEX3322 ORIGIN_HEX3323
0.4940919 -1.6540433 0.3697562
ORIGIN_HEX3325 ORIGIN_HEX3362 ORIGIN_HEX3363
-1.7356942 -0.1762301 -1.5297922
ORIGIN_HEX3364 ORIGIN_HEX3365 ORIGIN_HEX3366
1.9158610 0.2627902 0.3058646
ORIGIN_HEX3367 ORIGIN_HEX3368 ORIGIN_HEX3370
0.1188548 -0.2288376 0.0830823
ORIGIN_HEX3371 ORIGIN_HEX3372 ORIGIN_HEX3406
-0.2711702 -1.4751295 -1.1132599
ORIGIN_HEX3408 ORIGIN_HEX3409 ORIGIN_HEX3410
-1.2127302 0.2939776 -0.1290954
ORIGIN_HEX3411 ORIGIN_HEX3412 ORIGIN_HEX3413
-0.3270765 -0.2095660 -0.0454839
ORIGIN_HEX3414 ORIGIN_HEX3415 ORIGIN_HEX3416
-0.5022096 -0.6678825 -0.6082427
ORIGIN_HEX3417 ORIGIN_HEX3418 ORIGIN_HEX3419
0.1264543 2.6952521 0.5780081
ORIGIN_HEX3426 ORIGIN_HEX3453 ORIGIN_HEX3456
-0.4380904 -0.6501199 0.1226379
ORIGIN_HEX3457 ORIGIN_HEX3458 ORIGIN_HEX3459
-1.2418845 0.8096226 -0.5891016
ORIGIN_HEX3460 ORIGIN_HEX3461 ORIGIN_HEX3462
0.2411234 -2.6615380 -0.3067930
ORIGIN_HEX3463 ORIGIN_HEX3464 ORIGIN_HEX3465
-1.9692455 0.5448568 -2.4696135
ORIGIN_HEX3466 ORIGIN_HEX3467 ORIGIN_HEX3468
-1.3892184 -0.5422293 -0.2770123
ORIGIN_HEX3472 ORIGIN_HEX3473 ORIGIN_HEX3499
-0.8606317 -0.3139224 0.1108829
ORIGIN_HEX3502 ORIGIN_HEX3503 ORIGIN_HEX3504
-0.2826157 0.0642999 0.7549507
ORIGIN_HEX3505 ORIGIN_HEX3506 ORIGIN_HEX3507
0.0318715 0.0744326 -0.7701441
ORIGIN_HEX3508 ORIGIN_HEX3509 ORIGIN_HEX3511
-0.3879061 -0.4118409 -0.8794052
ORIGIN_HEX3512 ORIGIN_HEX3513 ORIGIN_HEX3514
-2.6736844 -0.1655829 2.2431147
ORIGIN_HEX3518 ORIGIN_HEX3519 ORIGIN_HEX3547
-0.4201076 -0.6117609 1.0466494
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ORIGIN_HEX7218 ORIGIN_HEX7222 ORIGIN_HEX7223
0.2435782 -1.4766816 -1.1197872
ORIGIN_HEX7224 ORIGIN_HEX7225 ORIGIN_HEX7226
0.0107776 -1.5058850 -0.1058206
ORIGIN_HEX7227 ORIGIN_HEX7228 ORIGIN_HEX7229
0.7838593 1.8034479 -1.6887132
ORIGIN_HEX723 ORIGIN_HEX7230 ORIGIN_HEX725
1.0852253 -0.7791157 0.0919991
ORIGIN_HEX726 ORIGIN_HEX7260 ORIGIN_HEX7261
-0.4065617 1.0598418 -0.0494953
ORIGIN_HEX7262 ORIGIN_HEX7264 ORIGIN_HEX7265
1.2230029 0.9159733 0.0373724
ORIGIN_HEX727 ORIGIN_HEX7271 ORIGIN_HEX7272
1.1836077 -0.0281868 -0.7093912
ORIGIN_HEX7273 ORIGIN_HEX7274 ORIGIN_HEX7275
-0.5003433 -0.4764360 0.8291770
ORIGIN_HEX7277 ORIGIN_HEX728 ORIGIN_HEX7307
0.1070323 1.4510122 1.7308449
ORIGIN_HEX7308 ORIGIN_HEX7309 ORIGIN_HEX731
0.3579977 -0.3769523 0.1819044
ORIGIN_HEX7310 ORIGIN_HEX7311 ORIGIN_HEX7312
1.1619960 0.0421492 0.9201430
ORIGIN_HEX7316 ORIGIN_HEX7319 ORIGIN_HEX7320
-1.2530311 -2.0186699 -0.7869755
ORIGIN_HEX7321 ORIGIN_HEX7322 ORIGIN_HEX7323
2.0281550 -0.7009741 -0.5310195
ORIGIN_HEX7324 ORIGIN_HEX7354 ORIGIN_HEX7355
-2.7267655 -0.2215294 -0.5384721
ORIGIN_HEX7356 ORIGIN_HEX7358 ORIGIN_HEX7359
-0.7539896 -0.9435706 -1.7291950
ORIGIN_HEX7363 ORIGIN_HEX7366 ORIGIN_HEX7367
0.7994475 -0.6686776 -0.6961608
ORIGIN_HEX7368 ORIGIN_HEX7369 ORIGIN_HEX7371
-0.7043237 -1.5237760 -3.3933048
ORIGIN_HEX7402 ORIGIN_HEX7403 ORIGIN_HEX7404
-0.0918158 -0.3878563 -0.9980713
ORIGIN_HEX7406 ORIGIN_HEX7411 ORIGIN_HEX7414
1.1911120 1.0389003 0.0869185
ORIGIN_HEX7415 ORIGIN_HEX7416 ORIGIN_HEX7418
-0.6996361 -0.3342751 -2.2131131
ORIGIN_HEX7448 ORIGIN_HEX7449 ORIGIN_HEX7450
0.1684596 -0.2935745 -0.1038257
ORIGIN_HEX7451 ORIGIN_HEX7452 ORIGIN_HEX7453
-1.1901804 0.5252559 -1.1632728
ORIGIN_HEX7458 ORIGIN_HEX7461 ORIGIN_HEX7462
0.7507511 -0.2854394 -0.3478347
ORIGIN_HEX7463 ORIGIN_HEX7465 ORIGIN_HEX7496
-0.0013636 0.1108216 -0.3884646
ORIGIN_HEX7498 ORIGIN_HEX7499 ORIGIN_HEX7500
1.8143963 0.4551627 0.2033350
ORIGIN_HEX7501 ORIGIN_HEX7506 ORIGIN_HEX7509
-0.2206504 -2.5574910 -0.0907273
ORIGIN_HEX7510 ORIGIN_HEX7542 ORIGIN_HEX7543
-0.3076071 0.1597786 -0.9755278
ORIGIN_HEX7544 ORIGIN_HEX7545 ORIGIN_HEX7546
-1.5666799 -1.1429411 -0.1480710
ORIGIN_HEX7547 ORIGIN_HEX7553 ORIGIN_HEX7555
0.2361290 -3.6928012 -0.7320927
ORIGIN_HEX7556 ORIGIN_HEX7590 ORIGIN_HEX7591
-0.9926280 -0.2937250 -1.3367075
ORIGIN_HEX7592 ORIGIN_HEX7594 ORIGIN_HEX7595
-0.7282577 1.0844705 -1.1917117
ORIGIN_HEX7603 ORIGIN_HEX7604 ORIGIN_HEX7637
-1.8395074 -0.3838613 -1.2028512
ORIGIN_HEX7638 ORIGIN_HEX7639 ORIGIN_HEX7641
-2.7908455 0.5483088 -0.9900580
ORIGIN_HEX7647 ORIGIN_HEX7650 ORIGIN_HEX7684
0.2265507 -0.1421807 -0.2198241
ORIGIN_HEX7685 ORIGIN_HEX7686 ORIGIN_HEX7687
-0.4245327 1.2109593 0.5110082
ORIGIN_HEX7694 ORIGIN_HEX770 ORIGIN_HEX771
1.0926813 1.2062894 0.2712084
ORIGIN_HEX773 ORIGIN_HEX7731 ORIGIN_HEX7732
1.8458553 -0.0407189 -0.8929198
ORIGIN_HEX7733 ORIGIN_HEX7734 ORIGIN_HEX7735
-0.3590890 0.4536808 0.4912278
ORIGIN_HEX7740 ORIGIN_HEX775 ORIGIN_HEX777
-0.4368592 0.1869157 0.0902784
ORIGIN_HEX7778 ORIGIN_HEX7779 ORIGIN_HEX778
-0.2491674 -1.8008499 0.0772794
ORIGIN_HEX7780 ORIGIN_HEX7781 ORIGIN_HEX7787
0.2594624 0.1976078 -0.6937104
ORIGIN_HEX779 ORIGIN_HEX7825 ORIGIN_HEX7826
-2.2525543 -0.4137566 -0.3862058
ORIGIN_HEX7828 ORIGIN_HEX7829 ORIGIN_HEX7831
0.0817001 -0.3509552 -1.2473942
ORIGIN_HEX7833 ORIGIN_HEX7834 ORIGIN_HEX7872
-0.8671051 0.6231563 -0.2272530
ORIGIN_HEX7873 ORIGIN_HEX7874 ORIGIN_HEX7875
-0.4777802 0.8186305 -0.4837522
ORIGIN_HEX7876 ORIGIN_HEX7878 ORIGIN_HEX7879
-0.3868623 0.4730541 -1.1891829
ORIGIN_HEX7881 ORIGIN_HEX7919 ORIGIN_HEX7920
-2.3689041 -0.2419391 -0.1805710
ORIGIN_HEX7921 ORIGIN_HEX7922 ORIGIN_HEX7923
2.4629885 0.0293314 -0.7153594
ORIGIN_HEX7925 ORIGIN_HEX7926 ORIGIN_HEX7927
0.0950991 -0.0049583 0.1861349
ORIGIN_HEX7928 ORIGIN_HEX7967 ORIGIN_HEX7968
1.5353544 -1.1121005 -2.0586349
ORIGIN_HEX7969 ORIGIN_HEX7970 ORIGIN_HEX7972
-0.1129135 0.5697368 1.2199448
ORIGIN_HEX7973 ORIGIN_HEX7974 ORIGIN_HEX7976
0.5320125 0.2431154 1.0369980
ORIGIN_HEX8013 ORIGIN_HEX8014 ORIGIN_HEX8015
-0.2866538 0.3802984 0.0967910
ORIGIN_HEX8016 ORIGIN_HEX8017 ORIGIN_HEX8018
0.4830874 0.9348986 -0.4788981
ORIGIN_HEX8019 ORIGIN_HEX8020 ORIGIN_HEX8021
0.2108282 -0.1053991 -0.6433935
ORIGIN_HEX8023 ORIGIN_HEX8061 ORIGIN_HEX8062
1.5264307 -0.6102569 -0.1392338
ORIGIN_HEX8063 ORIGIN_HEX8065 ORIGIN_HEX8066
-0.1591577 -1.4883894 -0.2876854
ORIGIN_HEX8067 ORIGIN_HEX8068 ORIGIN_HEX8070
-0.1750988 0.2665212 -0.2400799
ORIGIN_HEX8071 ORIGIN_HEX8108 ORIGIN_HEX8109
-1.4946598 -1.1593907 -0.8985429
ORIGIN_HEX8110 ORIGIN_HEX8112 ORIGIN_HEX8113
0.4609203 1.2611992 -0.3335546
ORIGIN_HEX8114 ORIGIN_HEX8115 ORIGIN_HEX8116
-0.7193355 -0.7132643 -1.4482160
ORIGIN_HEX8117 ORIGIN_HEX8155 ORIGIN_HEX8156
-0.2268583 -0.3328154 -0.8759897
ORIGIN_HEX8157 ORIGIN_HEX8158 ORIGIN_HEX8160
0.0241561 -0.4503147 0.3107647
ORIGIN_HEX8161 ORIGIN_HEX8162 ORIGIN_HEX8163
-0.0389856 -0.8871568 -1.4739588
ORIGIN_HEX8164 ORIGIN_HEX8165 ORIGIN_HEX818
-0.3143066 -0.4791083 1.1369908
ORIGIN_HEX819 ORIGIN_HEX820 ORIGIN_HEX8203
0.2824713 -0.5611867 0.1838596
ORIGIN_HEX8207 ORIGIN_HEX8208 ORIGIN_HEX8209
1.0399887 -2.5092773 0.0270227
ORIGIN_HEX8210 ORIGIN_HEX8211 ORIGIN_HEX823
-0.1307716 0.3937173 1.0363137
ORIGIN_HEX824 ORIGIN_HEX8249 ORIGIN_HEX825
1.3835257 -1.0848553 -1.8938836
ORIGIN_HEX8250 ORIGIN_HEX8252 ORIGIN_HEX8254
0.3904125 0.1012029 -0.3222262
ORIGIN_HEX8255 ORIGIN_HEX8256 ORIGIN_HEX8258
2.6171486 -0.7698408 -0.9525040
ORIGIN_HEX8259 ORIGIN_HEX826 ORIGIN_HEX827
-0.8939885 -1.0787833 0.9945789
ORIGIN_HEX828 ORIGIN_HEX8296 ORIGIN_HEX8297
0.7874725 -0.0814198 1.6032205
ORIGIN_HEX8298 ORIGIN_HEX8299 ORIGIN_HEX8300
0.1025655 0.5370791 0.1554585
ORIGIN_HEX8301 ORIGIN_HEX8302 ORIGIN_HEX8304
0.9991954 -0.9319055 -0.1929707
ORIGIN_HEX8305 ORIGIN_HEX8344 ORIGIN_HEX8345
-2.2067185 -1.5294690 1.1632939
ORIGIN_HEX8346 ORIGIN_HEX8347 ORIGIN_HEX8348
-0.5696555 0.2353310 -0.4319985
ORIGIN_HEX8349 ORIGIN_HEX8351 ORIGIN_HEX8352
-0.9459308 -0.9957529 -1.3952910
ORIGIN_HEX8353 ORIGIN_HEX8389 ORIGIN_HEX8390
-0.8871489 -0.6860503 -1.2296830
ORIGIN_HEX8391 ORIGIN_HEX8392 ORIGIN_HEX8393
-0.8430484 0.3938930 0.9200548
ORIGIN_HEX8394 ORIGIN_HEX8395 ORIGIN_HEX8396
-0.8390818 -1.8525277 -0.5302077
ORIGIN_HEX8398 ORIGIN_HEX8439 ORIGIN_HEX8440
2.4127134 -0.1853154 1.2037616
ORIGIN_HEX8441 ORIGIN_HEX8442 ORIGIN_HEX8443
1.4971431 -0.1668903 -0.1034493
ORIGIN_HEX8444 ORIGIN_HEX8445 ORIGIN_HEX8484
0.1196136 -0.5320207 -0.6898594
ORIGIN_HEX8485 ORIGIN_HEX8486 ORIGIN_HEX8488
-1.5478549 0.3215129 -0.4892414
ORIGIN_HEX8489 ORIGIN_HEX8490 ORIGIN_HEX8532
0.6304819 -0.8349642 0.4104595
ORIGIN_HEX8534 ORIGIN_HEX8535 ORIGIN_HEX8536
-1.4487432 -0.9159027 -0.9674001
ORIGIN_HEX8537 ORIGIN_HEX8538 ORIGIN_HEX8539
1.4224652 0.1146611 0.0860293
ORIGIN_HEX8540 ORIGIN_HEX8580 ORIGIN_HEX8581
0.6784089 0.0914039 -2.7720896
ORIGIN_HEX8582 ORIGIN_HEX8583 ORIGIN_HEX8584
0.2450316 -0.9308679 0.4307525
ORIGIN_HEX8585 ORIGIN_HEX8586 ORIGIN_HEX8587
-0.6915903 -0.9368247 0.3063461
ORIGIN_HEX8628 ORIGIN_HEX8629 ORIGIN_HEX8631
-0.7479388 0.5065877 0.1038980
ORIGIN_HEX8633 ORIGIN_HEX8634 ORIGIN_HEX866
0.2287688 -0.1996324 -0.5056586
ORIGIN_HEX867 ORIGIN_HEX8674 ORIGIN_HEX8675
0.6689957 0.3497376 -1.2009111
ORIGIN_HEX8676 ORIGIN_HEX8677 ORIGIN_HEX8679
0.1395859 -0.2095949 -0.0583122
ORIGIN_HEX8680 ORIGIN_HEX8681 ORIGIN_HEX870
0.2849556 0.6207966 0.5650486
ORIGIN_HEX872 ORIGIN_HEX8721 ORIGIN_HEX8722
-0.4675838 0.4077646 1.0533095
ORIGIN_HEX8723 ORIGIN_HEX8724 ORIGIN_HEX8725
-2.5082639 1.0631694 0.1969713
ORIGIN_HEX8726 ORIGIN_HEX8727 ORIGIN_HEX8728
-0.1822067 0.2171370 -0.7912455
ORIGIN_HEX873 ORIGIN_HEX874 ORIGIN_HEX8768
-1.8528557 -0.5934425 -0.3409253
ORIGIN_HEX8769 ORIGIN_HEX8771 ORIGIN_HEX8772
-1.0295736 0.8567672 0.5125111
ORIGIN_HEX8773 ORIGIN_HEX8774 ORIGIN_HEX8775
0.1540031 0.1376678 -0.5707086
ORIGIN_HEX8815 ORIGIN_HEX8816 ORIGIN_HEX8817
1.6638593 1.0866118 -1.1818219
ORIGIN_HEX8818 ORIGIN_HEX8819 ORIGIN_HEX8820
1.0935691 -0.0931318 -2.2924554
ORIGIN_HEX8862 ORIGIN_HEX8864 ORIGIN_HEX8865
-0.2508749 1.0403730 0.9547658
ORIGIN_HEX8866 ORIGIN_HEX8867 ORIGIN_HEX8868
0.4939943 -2.4029941 0.4070722
ORIGIN_HEX8910 ORIGIN_HEX8912 ORIGIN_HEX8914
0.2833308 0.6469146 -0.2841290
ORIGIN_HEX8915 ORIGIN_HEX8916 ORIGIN_HEX8917
-1.2813029 -1.8777404 0.9378051
ORIGIN_HEX8959 ORIGIN_HEX8961 ORIGIN_HEX8962
0.7248720 -1.7139033 1.0501780
ORIGIN_HEX8963 ORIGIN_HEX8964 ORIGIN_HEX9007
-0.2406197 0.8702391 0.3041815
ORIGIN_HEX9008 ORIGIN_HEX9010 ORIGIN_HEX9011
-0.3427615 0.0381626 0.1652927
ORIGIN_HEX9055 ORIGIN_HEX9056 ORIGIN_HEX9057
-2.6198357 -0.3842371 -0.2883586
ORIGIN_HEX9103 ORIGIN_HEX9105 ORIGIN_HEX9106
-0.4685461 -3.2553658 -0.9640589
ORIGIN_HEX914 ORIGIN_HEX9145 ORIGIN_HEX9150
0.4845335 0.9431767 -0.4778007
ORIGIN_HEX9152 ORIGIN_HEX9153 ORIGIN_HEX917
-0.0148354 -0.7258198 1.1378494
ORIGIN_HEX919 ORIGIN_HEX9193 ORIGIN_HEX920
0.6412568 1.1885996 -0.0375516
ORIGIN_HEX9200 ORIGIN_HEX9240 ORIGIN_HEX9246
-2.6953807 0.2474209 -0.2473385
ORIGIN_HEX9247 ORIGIN_HEX9283 ORIGIN_HEX9289
-1.5711944 1.9639678 1.7137229
ORIGIN_HEX9294 ORIGIN_HEX9340 ORIGIN_HEX9383
0.9764877 -0.1679859 1.4978247
ORIGIN_HEX9384 ORIGIN_HEX9388 ORIGIN_HEX9432
2.2841954 -0.8250644 0.9103273
ORIGIN_HEX9471 ORIGIN_HEX9480 ORIGIN_HEX9482
1.5664694 0.7871702 -2.7152770
ORIGIN_HEX9526 ORIGIN_HEX9527 ORIGIN_HEX9575
0.3921877 1.9647531 0.9330241
ORIGIN_HEX9576 ORIGIN_HEX9621 ORIGIN_HEX9622
0.5329091 1.0448569 1.6385604
ORIGIN_HEX965 ORIGIN_HEX966 ORIGIN_HEX9668
1.3768148 -1.3392508 0.9939970
ORIGIN_HEX9714 ORIGIN_HEX9988 log(entertn_count)
1.1319527 1.5855659 0.1242313
log(FB_count) log(lere_count) log(retail_count)
-0.1023757 -0.0643380 0.0907983
log(trainexits_count) log(residential_count) log(dist)
0.7528727 0.1249424 -1.0917845
Degrees of Freedom: 161670 Total (i.e. Null); 159856 Residual
Null Deviance: 96290000
Residual Deviance: 41900000 AIC: 42690000CalcRSquared(orcSIM$data$WEEKDAY_AFTERNOON_PEAK, orcSIM$fitted.values)[1] 0.2306263r2_mcfadden(orcSIM)# R2 for Generalized Linear Regression
R2: 0.560
adj. R2: 0.56011.7Destination Constrained Spatial Interaction Model
The destination (attraction) constrained model predicts flows to destinations by applying a balancing factor to ensure that the total predicted inflows to each destination match the observed inflows. Unlike the origin constrained model, this model accounts for the capacity or attractiveness of each destination to attract inflows.
The code chunk is adjusted accordingly as below:
decSIM <- glm(formula = WEEKDAY_AFTERNOON_PEAK ~
DESTIN_HEX +
log(bus_stop_count) +
log(business_count) +
log(school_count) +
log(finserv_count) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
write_rds(decSIM, "data/rds/decSIM.rds")decSIM <- read_rds("data/rds/decSIM.rds")
decSIM
Call: glm(formula = WEEKDAY_AFTERNOON_PEAK ~ DESTIN_HEX + log(bus_stop_count) +
log(business_count) + log(school_count) + log(finserv_count) +
log(dist), family = poisson(link = "log"), data = SIM_data,
na.action = na.exclude)
Coefficients:
(Intercept) DESTIN_HEX1012 DESTIN_HEX1013
8.447842 -0.620665 1.552959
DESTIN_HEX1014 DESTIN_HEX1058 DESTIN_HEX1059
2.390755 1.632665 1.336681
DESTIN_HEX1060 DESTIN_HEX1061 DESTIN_HEX1104
2.318986 2.457471 2.632307
DESTIN_HEX1106 DESTIN_HEX1107 DESTIN_HEX1108
5.498398 3.840852 2.517246
DESTIN_HEX1152 DESTIN_HEX1153 DESTIN_HEX1154
3.831611 1.413679 2.608004
DESTIN_HEX1199 DESTIN_HEX1200 DESTIN_HEX1201
-0.825045 3.481625 2.737735
DESTIN_HEX1202 DESTIN_HEX1244 DESTIN_HEX1245
4.202204 0.917208 2.388941
DESTIN_HEX1246 DESTIN_HEX1247 DESTIN_HEX1291
1.152274 0.070541 3.214181
DESTIN_HEX1292 DESTIN_HEX1293 DESTIN_HEX1295
2.734613 -0.283585 1.604892
DESTIN_HEX1338 DESTIN_HEX1339 DESTIN_HEX1340
2.826374 2.018304 4.924653
DESTIN_HEX1341 DESTIN_HEX1385 DESTIN_HEX1386
2.385585 2.455026 2.678016
DESTIN_HEX1387 DESTIN_HEX1388 DESTIN_HEX1433
1.955599 0.561984 2.198688
DESTIN_HEX1434 DESTIN_HEX1479 DESTIN_HEX1480
3.879328 1.390610 2.575423
DESTIN_HEX1481 DESTIN_HEX1525 DESTIN_HEX1526
2.701184 3.350146 1.252878
DESTIN_HEX1527 DESTIN_HEX1528 DESTIN_HEX1529
3.437638 3.094626 3.580964
DESTIN_HEX1573 DESTIN_HEX1574 DESTIN_HEX1575
3.590325 1.432800 2.448803
DESTIN_HEX1619 DESTIN_HEX1621 DESTIN_HEX1622
3.753948 2.967183 4.021489
DESTIN_HEX1623 DESTIN_HEX1666 DESTIN_HEX1668
3.936538 3.175880 2.541494
DESTIN_HEX1669 DESTIN_HEX1670 DESTIN_HEX1671
2.382142 2.186917 2.216756
DESTIN_HEX1715 DESTIN_HEX1717 DESTIN_HEX1718
2.172002 0.146129 3.143800
DESTIN_HEX1761 DESTIN_HEX1762 DESTIN_HEX1763
3.413622 2.405183 1.449493
DESTIN_HEX1764 DESTIN_HEX1765 DESTIN_HEX1768
2.081198 1.733104 1.064033
DESTIN_HEX1808 DESTIN_HEX1809 DESTIN_HEX1810
2.970521 1.520056 0.247839
DESTIN_HEX1811 DESTIN_HEX1812 DESTIN_HEX1814
3.891577 1.520545 2.515835
DESTIN_HEX1815 DESTIN_HEX1855 DESTIN_HEX1856
1.815298 2.880625 2.336006
DESTIN_HEX1857 DESTIN_HEX1858 DESTIN_HEX1859
2.304166 2.001847 6.049929
DESTIN_HEX1861 DESTIN_HEX1862 DESTIN_HEX1903
4.170026 4.675106 -1.621048
DESTIN_HEX1904 DESTIN_HEX1905 DESTIN_HEX1906
2.698382 0.502234 2.169203
DESTIN_HEX1907 DESTIN_HEX1909 DESTIN_HEX1950
2.734840 4.165344 1.137720
DESTIN_HEX1952 DESTIN_HEX1953 DESTIN_HEX1955
1.145970 2.659216 3.390037
DESTIN_HEX1956 DESTIN_HEX1957 DESTIN_HEX1996
3.152196 4.454993 3.006570
DESTIN_HEX1997 DESTIN_HEX1998 DESTIN_HEX1999
2.417170 3.568262 2.484697
DESTIN_HEX2000 DESTIN_HEX2003 DESTIN_HEX2046
1.806949 1.797842 0.282109
DESTIN_HEX2047 DESTIN_HEX2049 DESTIN_HEX2050
2.087621 5.407134 4.766394
DESTIN_HEX2051 DESTIN_HEX2090 DESTIN_HEX2092
4.705234 1.567164 3.584444
DESTIN_HEX2093 DESTIN_HEX2094 DESTIN_HEX2095
1.734036 2.643815 3.880151
DESTIN_HEX2096 DESTIN_HEX2139 DESTIN_HEX2140
4.562976 2.948328 2.988491
DESTIN_HEX2141 DESTIN_HEX2142 DESTIN_HEX2143
2.357160 3.076807 5.310905
DESTIN_HEX2145 DESTIN_HEX2146 DESTIN_HEX2184
1.883199 -0.237729 2.817487
DESTIN_HEX2187 DESTIN_HEX2189 DESTIN_HEX2190
1.584625 3.706179 5.492825
DESTIN_HEX2192 DESTIN_HEX2193 DESTIN_HEX2194
0.509126 2.561649 2.168302
DESTIN_HEX2232 DESTIN_HEX2233 DESTIN_HEX2234
0.977301 2.948816 2.418126
DESTIN_HEX2235 DESTIN_HEX2236 DESTIN_HEX2237
3.894553 3.402209 4.872929
DESTIN_HEX2238 DESTIN_HEX2239 DESTIN_HEX2241
6.063297 2.616972 0.688119
DESTIN_HEX2242 DESTIN_HEX2278 DESTIN_HEX2279
1.871787 2.287898 2.575728
DESTIN_HEX2280 DESTIN_HEX2281 DESTIN_HEX2282
3.306797 2.658118 3.631304
DESTIN_HEX2283 DESTIN_HEX2284 DESTIN_HEX2288
5.708689 4.968754 3.007444
DESTIN_HEX2289 DESTIN_HEX2290 DESTIN_HEX2326
0.855073 0.805451 1.603713
DESTIN_HEX2327 DESTIN_HEX2328 DESTIN_HEX2329
2.018416 -0.465983 2.383474
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4.774918 4.714177 1.116856
DESTIN_HEX6789 DESTIN_HEX679 DESTIN_HEX6790
3.350293 2.131223 4.114785
DESTIN_HEX6791 DESTIN_HEX6792 DESTIN_HEX6793
3.938149 2.900804 3.541162
DESTIN_HEX6794 DESTIN_HEX6796 DESTIN_HEX6797
3.263110 2.666353 4.288651
DESTIN_HEX6798 DESTIN_HEX680 DESTIN_HEX6800
2.869259 -0.047604 4.752760
DESTIN_HEX6801 DESTIN_HEX6802 DESTIN_HEX681
4.358814 4.718417 1.696395
DESTIN_HEX682 DESTIN_HEX6837 DESTIN_HEX6838
3.252382 3.544971 4.160045
DESTIN_HEX6839 DESTIN_HEX6841 DESTIN_HEX6843
4.367769 4.207336 2.796294
DESTIN_HEX6846 DESTIN_HEX6847 DESTIN_HEX6848
4.772724 3.863658 3.666921
DESTIN_HEX6850 DESTIN_HEX6851 DESTIN_HEX6885
4.328784 4.310878 3.736440
DESTIN_HEX6886 DESTIN_HEX6887 DESTIN_HEX6888
3.862276 3.666466 3.500949
DESTIN_HEX6889 DESTIN_HEX6891 DESTIN_HEX6892
3.127904 5.042587 3.450400
DESTIN_HEX6893 DESTIN_HEX6894 DESTIN_HEX6895
4.851118 4.363632 4.946476
DESTIN_HEX6896 DESTIN_HEX6897 DESTIN_HEX6898
1.829313 5.430966 2.593809
DESTIN_HEX6931 DESTIN_HEX6932 DESTIN_HEX6933
3.275579 4.530725 2.656719
DESTIN_HEX6934 DESTIN_HEX6935 DESTIN_HEX6936
1.894406 3.354669 4.200157
DESTIN_HEX6938 DESTIN_HEX6939 DESTIN_HEX6940
1.479022 4.487533 3.500669
DESTIN_HEX6941 DESTIN_HEX6942 DESTIN_HEX6943
3.648603 4.209821 3.668199
DESTIN_HEX6944 DESTIN_HEX6945 DESTIN_HEX6946
3.432091 3.686582 5.306487
DESTIN_HEX6979 DESTIN_HEX6980 DESTIN_HEX6981
3.177733 5.159727 3.413935
DESTIN_HEX6982 DESTIN_HEX6984 DESTIN_HEX6985
1.439172 1.712966 4.655276
DESTIN_HEX6986 DESTIN_HEX6987 DESTIN_HEX6988
3.808234 4.743712 5.402220
DESTIN_HEX6989 DESTIN_HEX6990 DESTIN_HEX6991
5.110252 3.199704 4.595012
DESTIN_HEX6992 DESTIN_HEX7025 DESTIN_HEX7026
5.188817 3.070830 3.538897
DESTIN_HEX7027 DESTIN_HEX7029 DESTIN_HEX7030
4.156221 3.812198 2.938219
DESTIN_HEX7031 DESTIN_HEX7033 DESTIN_HEX7034
1.558390 3.227114 4.155727
DESTIN_HEX7035 DESTIN_HEX7036 DESTIN_HEX7037
3.362618 3.872495 5.165650
DESTIN_HEX7038 DESTIN_HEX7039 DESTIN_HEX7040
4.190070 4.295476 5.744356
DESTIN_HEX7072 DESTIN_HEX7073 DESTIN_HEX7074
3.179494 3.473587 4.046274
DESTIN_HEX7075 DESTIN_HEX7076 DESTIN_HEX7077
2.169745 2.359161 2.637294
DESTIN_HEX7081 DESTIN_HEX7082 DESTIN_HEX7083
4.342963 2.917042 3.630027
DESTIN_HEX7084 DESTIN_HEX7085 DESTIN_HEX7086
4.562461 5.312009 4.755701
DESTIN_HEX7087 DESTIN_HEX7119 DESTIN_HEX7120
4.992759 3.556804 3.503517
DESTIN_HEX7123 DESTIN_HEX7124 DESTIN_HEX7125
1.718489 3.632890 2.894625
DESTIN_HEX7128 DESTIN_HEX7129 DESTIN_HEX7130
1.720396 3.938325 3.786226
DESTIN_HEX7131 DESTIN_HEX7132 DESTIN_HEX7133
4.353008 4.334132 3.045996
DESTIN_HEX7134 DESTIN_HEX7135 DESTIN_HEX7166
5.043491 4.887392 3.571828
DESTIN_HEX7167 DESTIN_HEX7168 DESTIN_HEX7169
3.917807 3.623274 1.803171
DESTIN_HEX7170 DESTIN_HEX7172 DESTIN_HEX7173
3.942481 2.395805 3.104703
DESTIN_HEX7175 DESTIN_HEX7176 DESTIN_HEX7177
3.659462 4.288562 4.326463
DESTIN_HEX7178 DESTIN_HEX7179 DESTIN_HEX7181
4.718874 4.429119 3.512504
DESTIN_HEX7182 DESTIN_HEX7213 DESTIN_HEX7214
2.777079 4.056257 3.559326
DESTIN_HEX7215 DESTIN_HEX7217 DESTIN_HEX7218
3.673376 4.720132 3.465954
DESTIN_HEX7222 DESTIN_HEX7223 DESTIN_HEX7224
1.703596 3.493678 4.908233
DESTIN_HEX7225 DESTIN_HEX7226 DESTIN_HEX7227
2.847793 4.370361 5.118873
DESTIN_HEX7228 DESTIN_HEX7229 DESTIN_HEX723
5.378461 3.001434 5.643181
DESTIN_HEX7230 DESTIN_HEX725 DESTIN_HEX726
4.266665 2.660921 2.278061
DESTIN_HEX7260 DESTIN_HEX7261 DESTIN_HEX7262
4.000188 3.477563 4.425708
DESTIN_HEX7264 DESTIN_HEX7265 DESTIN_HEX727
4.499389 3.152992 3.311477
DESTIN_HEX7271 DESTIN_HEX7272 DESTIN_HEX7273
4.677017 4.509064 4.611996
DESTIN_HEX7274 DESTIN_HEX7275 DESTIN_HEX7277
4.420724 4.396126 5.534651
DESTIN_HEX728 DESTIN_HEX7307 DESTIN_HEX7308
1.462661 5.039592 3.887137
DESTIN_HEX7309 DESTIN_HEX731 DESTIN_HEX7310
3.615217 1.290530 4.991248
DESTIN_HEX7311 DESTIN_HEX7312 DESTIN_HEX7316
4.297197 2.943226 0.709071
DESTIN_HEX7319 DESTIN_HEX7320 DESTIN_HEX7321
2.946397 3.767922 6.334334
DESTIN_HEX7322 DESTIN_HEX7323 DESTIN_HEX7324
3.947402 3.068809 2.200935
DESTIN_HEX7354 DESTIN_HEX7355 DESTIN_HEX7356
3.473453 3.930117 3.235233
DESTIN_HEX7358 DESTIN_HEX7359 DESTIN_HEX7363
4.097268 2.222180 2.131695
DESTIN_HEX7366 DESTIN_HEX7367 DESTIN_HEX7368
4.263979 4.374363 4.042753
DESTIN_HEX7369 DESTIN_HEX7371 DESTIN_HEX7402
2.899032 2.029499 3.345280
DESTIN_HEX7403 DESTIN_HEX7404 DESTIN_HEX7406
3.317015 2.723656 4.876100
DESTIN_HEX7411 DESTIN_HEX7414 DESTIN_HEX7415
2.287844 5.238970 3.828234
DESTIN_HEX7416 DESTIN_HEX7418 DESTIN_HEX7448
4.196048 -0.249919 4.320075
DESTIN_HEX7449 DESTIN_HEX7450 DESTIN_HEX7451
4.018957 4.295648 3.414997
DESTIN_HEX7452 DESTIN_HEX7453 DESTIN_HEX7458
5.265288 1.988716 1.929544
DESTIN_HEX7461 DESTIN_HEX7462 DESTIN_HEX7463
4.059574 4.797977 5.513973
DESTIN_HEX7465 DESTIN_HEX7496 DESTIN_HEX7498
4.270713 3.824271 4.324409
DESTIN_HEX7499 DESTIN_HEX7500 DESTIN_HEX7501
5.275641 4.258167 2.034017
DESTIN_HEX7506 DESTIN_HEX7509 DESTIN_HEX7510
0.685718 5.168585 3.972661
DESTIN_HEX7542 DESTIN_HEX7543 DESTIN_HEX7544
4.646184 2.886156 2.507924
DESTIN_HEX7545 DESTIN_HEX7546 DESTIN_HEX7547
2.894553 4.920285 4.051167
DESTIN_HEX7553 DESTIN_HEX7555 DESTIN_HEX7556
-0.194925 3.797735 3.803344
DESTIN_HEX7590 DESTIN_HEX7591 DESTIN_HEX7592
2.936958 0.161755 3.198596
DESTIN_HEX7594 DESTIN_HEX7595 DESTIN_HEX7603
4.489857 0.879255 3.002148
DESTIN_HEX7604 DESTIN_HEX7637 DESTIN_HEX7638
5.314773 2.519203 1.639462
DESTIN_HEX7639 DESTIN_HEX7641 DESTIN_HEX7647
4.251150 3.584329 0.979978
DESTIN_HEX7650 DESTIN_HEX7684 DESTIN_HEX7685
5.263694 3.297677 2.725447
DESTIN_HEX7686 DESTIN_HEX7687 DESTIN_HEX7694
4.136191 4.459324 3.126119
DESTIN_HEX770 DESTIN_HEX771 DESTIN_HEX773
4.262195 -0.550527 2.346175
DESTIN_HEX7731 DESTIN_HEX7732 DESTIN_HEX7733
3.475218 3.539671 4.577166
DESTIN_HEX7734 DESTIN_HEX7735 DESTIN_HEX7740
5.571465 4.680107 0.960854
DESTIN_HEX775 DESTIN_HEX777 DESTIN_HEX7778
3.005493 0.926771 3.771064
DESTIN_HEX7779 DESTIN_HEX778 DESTIN_HEX7780
2.801780 1.805080 4.158760
DESTIN_HEX7781 DESTIN_HEX7787 DESTIN_HEX779
5.079275 1.896746 2.425890
DESTIN_HEX7825 DESTIN_HEX7826 DESTIN_HEX7828
3.430439 4.254651 5.331552
DESTIN_HEX7829 DESTIN_HEX7831 DESTIN_HEX7833
4.028028 3.329300 1.674015
DESTIN_HEX7834 DESTIN_HEX7872 DESTIN_HEX7873
1.881086 3.782676 2.928203
DESTIN_HEX7874 DESTIN_HEX7875 DESTIN_HEX7876
4.570602 3.751502 4.513224
DESTIN_HEX7878 DESTIN_HEX7879 DESTIN_HEX7881
5.026533 2.514670 2.459191
DESTIN_HEX7919 DESTIN_HEX7920 DESTIN_HEX7921
3.159697 2.030988 5.855011
DESTIN_HEX7922 DESTIN_HEX7923 DESTIN_HEX7925
4.750972 3.858075 4.504450
DESTIN_HEX7926 DESTIN_HEX7927 DESTIN_HEX7928
3.247137 3.977551 4.064549
DESTIN_HEX7967 DESTIN_HEX7968 DESTIN_HEX7969
2.726575 1.737312 3.701111
DESTIN_HEX7970 DESTIN_HEX7972 DESTIN_HEX7973
4.806094 4.765098 5.279707
DESTIN_HEX7974 DESTIN_HEX7976 DESTIN_HEX8013
3.919916 4.709924 4.043408
DESTIN_HEX8014 DESTIN_HEX8015 DESTIN_HEX8016
3.923450 4.465267 4.780293
DESTIN_HEX8017 DESTIN_HEX8018 DESTIN_HEX8019
4.202639 3.645675 4.862858
DESTIN_HEX8020 DESTIN_HEX8021 DESTIN_HEX8023
4.643608 3.435187 5.529111
DESTIN_HEX8061 DESTIN_HEX8062 DESTIN_HEX8063
3.359563 3.617550 3.925736
DESTIN_HEX8065 DESTIN_HEX8066 DESTIN_HEX8067
1.492068 3.577083 4.305582
DESTIN_HEX8068 DESTIN_HEX8070 DESTIN_HEX8071
5.049595 4.137568 3.277774
DESTIN_HEX8108 DESTIN_HEX8109 DESTIN_HEX8110
3.028855 4.568088 5.251864
DESTIN_HEX8112 DESTIN_HEX8113 DESTIN_HEX8114
4.666181 3.866658 4.269615
DESTIN_HEX8115 DESTIN_HEX8116 DESTIN_HEX8117
4.524722 3.499233 4.165884
DESTIN_HEX8155 DESTIN_HEX8156 DESTIN_HEX8157
3.956453 3.877814 4.878435
DESTIN_HEX8158 DESTIN_HEX8160 DESTIN_HEX8161
3.806453 4.278471 3.748676
DESTIN_HEX8162 DESTIN_HEX8163 DESTIN_HEX8164
4.533055 4.089768 4.142505
DESTIN_HEX8165 DESTIN_HEX818 DESTIN_HEX819
3.983319 3.172195 2.871507
DESTIN_HEX820 DESTIN_HEX8203 DESTIN_HEX8207
2.388386 4.548906 4.526246
DESTIN_HEX8208 DESTIN_HEX8209 DESTIN_HEX8210
2.689552 4.853052 4.523534
DESTIN_HEX8211 DESTIN_HEX823 DESTIN_HEX824
5.104189 2.673253 3.492647
DESTIN_HEX8249 DESTIN_HEX825 DESTIN_HEX8250
2.645354 0.836546 4.832411
DESTIN_HEX8252 DESTIN_HEX8254 DESTIN_HEX8255
2.394940 3.993045 5.946852
DESTIN_HEX8256 DESTIN_HEX8258 DESTIN_HEX8259
3.866743 3.522489 2.132961
DESTIN_HEX826 DESTIN_HEX827 DESTIN_HEX828
0.812886 5.279107 3.145135
DESTIN_HEX8296 DESTIN_HEX8297 DESTIN_HEX8298
3.935007 5.245973 3.901539
DESTIN_HEX8299 DESTIN_HEX8300 DESTIN_HEX8301
1.975025 2.959926 4.423813
DESTIN_HEX8302 DESTIN_HEX8304 DESTIN_HEX8305
3.525896 4.084234 2.466527
DESTIN_HEX8344 DESTIN_HEX8345 DESTIN_HEX8346
2.869580 4.489238 2.128779
DESTIN_HEX8347 DESTIN_HEX8348 DESTIN_HEX8349
4.371697 4.246721 3.226941
DESTIN_HEX8351 DESTIN_HEX8352 DESTIN_HEX8353
3.752957 2.939601 2.524785
DESTIN_HEX8389 DESTIN_HEX8390 DESTIN_HEX8391
3.368545 2.177593 2.062215
DESTIN_HEX8392 DESTIN_HEX8393 DESTIN_HEX8394
2.335908 3.148335 3.441021
DESTIN_HEX8395 DESTIN_HEX8396 DESTIN_HEX8398
3.077094 4.224444 5.607132
DESTIN_HEX8439 DESTIN_HEX8440 DESTIN_HEX8441
2.936098 3.375563 5.076888
DESTIN_HEX8442 DESTIN_HEX8443 DESTIN_HEX8444
4.187927 4.577425 4.914531
DESTIN_HEX8445 DESTIN_HEX8484 DESTIN_HEX8485
4.022784 2.676235 2.639026
DESTIN_HEX8486 DESTIN_HEX8488 DESTIN_HEX8489
2.420409 3.310384 4.981806
DESTIN_HEX8490 DESTIN_HEX8532 DESTIN_HEX8534
3.516090 4.103957 1.974126
DESTIN_HEX8535 DESTIN_HEX8536 DESTIN_HEX8537
3.893380 3.450181 4.823229
DESTIN_HEX8538 DESTIN_HEX8539 DESTIN_HEX8540
5.192026 4.845422 4.616494
DESTIN_HEX8580 DESTIN_HEX8581 DESTIN_HEX8582
3.014003 1.006853 4.883081
DESTIN_HEX8583 DESTIN_HEX8584 DESTIN_HEX8585
4.161150 4.682032 4.044679
DESTIN_HEX8586 DESTIN_HEX8587 DESTIN_HEX8628
4.429718 5.031460 2.057552
DESTIN_HEX8629 DESTIN_HEX8631 DESTIN_HEX8633
4.165277 5.030084 4.645113
DESTIN_HEX8634 DESTIN_HEX866 DESTIN_HEX867
4.386412 1.212021 2.738903
DESTIN_HEX8674 DESTIN_HEX8675 DESTIN_HEX8676
2.630184 1.909263 3.548578
DESTIN_HEX8677 DESTIN_HEX8679 DESTIN_HEX8680
4.837473 4.241349 5.280697
DESTIN_HEX8681 DESTIN_HEX870 DESTIN_HEX872
5.319091 2.956168 5.000253
DESTIN_HEX8721 DESTIN_HEX8722 DESTIN_HEX8723
-0.899206 4.613156 1.482555
DESTIN_HEX8724 DESTIN_HEX8725 DESTIN_HEX8726
4.009962 5.498311 4.055204
DESTIN_HEX8727 DESTIN_HEX8728 DESTIN_HEX873
4.119307 3.518273 -0.310447
DESTIN_HEX874 DESTIN_HEX8768 DESTIN_HEX8769
1.256921 0.305644 1.708929
DESTIN_HEX8771 DESTIN_HEX8772 DESTIN_HEX8773
3.421797 5.182754 4.466746
DESTIN_HEX8774 DESTIN_HEX8775 DESTIN_HEX8815
2.993404 2.705393 2.758938
DESTIN_HEX8816 DESTIN_HEX8817 DESTIN_HEX8818
2.633945 1.418880 2.727873
DESTIN_HEX8819 DESTIN_HEX8820 DESTIN_HEX8862
3.731896 2.680923 1.556724
DESTIN_HEX8864 DESTIN_HEX8865 DESTIN_HEX8866
3.447902 2.789398 4.300739
DESTIN_HEX8867 DESTIN_HEX8868 DESTIN_HEX8910
2.231333 2.856633 2.367386
DESTIN_HEX8912 DESTIN_HEX8914 DESTIN_HEX8915
2.165090 2.930028 3.005237
DESTIN_HEX8916 DESTIN_HEX8917 DESTIN_HEX8959
1.994902 2.000103 2.670687
DESTIN_HEX8961 DESTIN_HEX8962 DESTIN_HEX8963
1.090554 4.434702 0.860711
DESTIN_HEX8964 DESTIN_HEX9007 DESTIN_HEX9008
2.110800 3.130017 3.296397
DESTIN_HEX9010 DESTIN_HEX9011 DESTIN_HEX9055
2.183768 1.266038 2.239909
DESTIN_HEX9056 DESTIN_HEX9057 DESTIN_HEX9103
1.147209 1.958921 4.112103
DESTIN_HEX9105 DESTIN_HEX9106 DESTIN_HEX914
0.237506 1.935979 2.482588
DESTIN_HEX9145 DESTIN_HEX9150 DESTIN_HEX9152
3.036572 1.537170 2.510228
DESTIN_HEX9153 DESTIN_HEX917 DESTIN_HEX919
1.995798 1.386993 2.611186
DESTIN_HEX9193 DESTIN_HEX920 DESTIN_HEX9200
4.409097 2.475983 2.251822
DESTIN_HEX9240 DESTIN_HEX9246 DESTIN_HEX9247
2.876733 3.454556 1.498770
DESTIN_HEX9283 DESTIN_HEX9289 DESTIN_HEX9294
5.995056 5.246427 4.282646
DESTIN_HEX9340 DESTIN_HEX9383 DESTIN_HEX9384
3.314723 3.773648 5.357045
DESTIN_HEX9388 DESTIN_HEX9432 DESTIN_HEX9471
3.547093 3.073919 5.317497
DESTIN_HEX9480 DESTIN_HEX9482 DESTIN_HEX9526
2.930234 1.407781 2.661234
DESTIN_HEX9527 DESTIN_HEX9575 DESTIN_HEX9576
2.573861 3.287680 1.593254
DESTIN_HEX9621 DESTIN_HEX9622 DESTIN_HEX965
2.204027 4.332383 2.271311
DESTIN_HEX966 DESTIN_HEX9668 DESTIN_HEX9714
1.185902 3.104254 3.150867
DESTIN_HEX9988 log(bus_stop_count) log(business_count)
3.501863 0.366795 0.002257
log(school_count) log(finserv_count) log(dist)
-0.273443 0.493462 -1.081710
Degrees of Freedom: 161670 Total (i.e. Null); 159856 Residual
Null Deviance: 96290000
Residual Deviance: 45520000 AIC: 46310000CalcRSquared(decSIM$data$WEEKDAY_AFTERNOON_PEAK, decSIM$fitted.values)[1] 0.1856562r2_mcfadden(decSIM)# R2 for Generalized Linear Regression
R2: 0.523
adj. R2: 0.52311.8Doubly Constrained Spatial Interaction Model
The doubly constrained model ensures that the predicted flows both from origins (Oi) and to destinations (Dj) match observed totals by applying balancing factors (Ai for origins and Bj for destinations) along with the influence of distance (dij).
The code chunk is changed correspondingly as below:
dbcSIM <- glm(formula = WEEKDAY_AFTERNOON_PEAK ~
ORIGIN_HEX +
DESTIN_HEX +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
write_rds(dbcSIM, "data/rds/dbcSIM.rds")dbcSIM <- read_rds("data/rds/dbcSIM.rds")
dbcSIM
Call: glm(formula = WEEKDAY_AFTERNOON_PEAK ~ ORIGIN_HEX + DESTIN_HEX +
log(dist), family = poisson(link = "log"), data = SIM_data,
na.action = na.exclude)
Coefficients:
(Intercept) ORIGIN_HEX1012 ORIGIN_HEX1013 ORIGIN_HEX1014 ORIGIN_HEX1058
8.7209518 -0.8816039 0.3264009 0.5528511 -4.2027183
ORIGIN_HEX1059 ORIGIN_HEX1060 ORIGIN_HEX1061 ORIGIN_HEX1104 ORIGIN_HEX1106
-0.8834993 -0.8184197 -0.2517575 1.3068727 1.7232583
ORIGIN_HEX1107 ORIGIN_HEX1108 ORIGIN_HEX1152 ORIGIN_HEX1153 ORIGIN_HEX1154
1.2963036 0.3314767 -0.8945535 -0.3790338 1.2225328
ORIGIN_HEX1199 ORIGIN_HEX1200 ORIGIN_HEX1201 ORIGIN_HEX1202 ORIGIN_HEX1244
0.3866662 0.0170405 0.7711185 -0.2608678 1.8840289
ORIGIN_HEX1245 ORIGIN_HEX1246 ORIGIN_HEX1247 ORIGIN_HEX1291 ORIGIN_HEX1292
0.8351036 -0.9986651 -0.4453742 3.1736232 2.0354568
ORIGIN_HEX1293 ORIGIN_HEX1295 ORIGIN_HEX1338 ORIGIN_HEX1339 ORIGIN_HEX1340
1.2543444 0.2428771 0.8689960 0.1273712 0.6762757
ORIGIN_HEX1341 ORIGIN_HEX1385 ORIGIN_HEX1386 ORIGIN_HEX1387 ORIGIN_HEX1388
0.7287095 -0.4290908 -0.8039356 1.1763782 -2.0404032
ORIGIN_HEX1433 ORIGIN_HEX1434 ORIGIN_HEX1479 ORIGIN_HEX1480 ORIGIN_HEX1481
2.0143888 -1.1991310 -0.8311869 2.7097656 0.9206473
ORIGIN_HEX1525 ORIGIN_HEX1526 ORIGIN_HEX1527 ORIGIN_HEX1528 ORIGIN_HEX1529
2.3123863 -1.6994128 1.5654513 0.7268888 1.1298185
ORIGIN_HEX1573 ORIGIN_HEX1574 ORIGIN_HEX1575 ORIGIN_HEX1619 ORIGIN_HEX1621
0.7993031 -0.7847872 1.4151693 1.7549700 1.8292167
ORIGIN_HEX1622 ORIGIN_HEX1623 ORIGIN_HEX1666 ORIGIN_HEX1668 ORIGIN_HEX1669
0.3499279 1.6995988 1.7824566 1.2305950 1.0853798
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DESTIN_HEX4913 DESTIN_HEX4925 DESTIN_HEX4926 DESTIN_HEX4930 DESTIN_HEX4931
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DESTIN_HEX4932 DESTIN_HEX4933 DESTIN_HEX4953 DESTIN_HEX4954 DESTIN_HEX4955
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DESTIN_HEX5026 DESTIN_HEX5027 DESTIN_HEX5028 DESTIN_HEX5047 DESTIN_HEX5048
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DESTIN_HEX5286 DESTIN_HEX5298 DESTIN_HEX5301 DESTIN_HEX5307 DESTIN_HEX5308
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DESTIN_HEX5309 DESTIN_HEX5328 DESTIN_HEX5329 DESTIN_HEX5330 DESTIN_HEX5331
4.5235840 3.3576605 5.0082090 4.2296242 4.1412444
DESTIN_HEX5333 DESTIN_HEX5336 DESTIN_HEX5339 DESTIN_HEX5349 DESTIN_HEX535
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DESTIN_HEX5350 DESTIN_HEX5354 DESTIN_HEX5355 DESTIN_HEX5356 DESTIN_HEX537
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DESTIN_HEX5373 DESTIN_HEX5375 DESTIN_HEX5377 DESTIN_HEX5378 DESTIN_HEX5379
4.7231677 4.1800455 4.1447967 3.5823810 3.9866788
DESTIN_HEX5380 DESTIN_HEX5382 DESTIN_HEX5383 DESTIN_HEX5397 DESTIN_HEX5398
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DESTIN_HEX5399 DESTIN_HEX540 DESTIN_HEX5400 DESTIN_HEX5401 DESTIN_HEX5402
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DESTIN_HEX5403 DESTIN_HEX5422 DESTIN_HEX5423 DESTIN_HEX5424 DESTIN_HEX5425
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DESTIN_HEX5426 DESTIN_HEX5428 DESTIN_HEX5429 DESTIN_HEX5430 DESTIN_HEX5433
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DESTIN_HEX5436 DESTIN_HEX5437 DESTIN_HEX5438 DESTIN_HEX5439 DESTIN_HEX5442
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DESTIN_HEX5450 DESTIN_HEX5469 DESTIN_HEX5470 DESTIN_HEX5471 DESTIN_HEX5472
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DESTIN_HEX5490 DESTIN_HEX5492 DESTIN_HEX5493 DESTIN_HEX5495 DESTIN_HEX5496
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0.8870594 4.1037408 4.4946583 3.5801613 3.3244521
DESTIN_HEX5568 DESTIN_HEX5569 DESTIN_HEX5570 DESTIN_HEX5571 DESTIN_HEX5573
4.8880951 2.4231011 4.0333284 3.0900187 1.7435581
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3.2324151 4.1289390 4.8330789 6.1506253 3.7650882
DESTIN_HEX6186 DESTIN_HEX6188 DESTIN_HEX6189 DESTIN_HEX6192 DESTIN_HEX6195
1.0178855 3.6926315 5.0392979 3.1496564 0.3797486
DESTIN_HEX6222 DESTIN_HEX6223 DESTIN_HEX6224 DESTIN_HEX6226 DESTIN_HEX6227
-0.6590108 4.5621556 3.5031153 4.6637302 4.2079756
DESTIN_HEX6228 DESTIN_HEX6229 DESTIN_HEX6230 DESTIN_HEX6231 DESTIN_HEX6232
4.6585405 4.3604463 4.9287869 5.1225133 0.7940821
DESTIN_HEX6233 DESTIN_HEX6234 DESTIN_HEX6235 DESTIN_HEX6237 DESTIN_HEX6239
3.6102099 2.9483460 4.1195504 1.6056854 3.6393690
DESTIN_HEX6241 DESTIN_HEX6242 DESTIN_HEX6272 DESTIN_HEX6273 DESTIN_HEX6274
2.0868903 0.3240889 3.5717754 4.4739095 4.7650499
DESTIN_HEX6275 DESTIN_HEX6276 DESTIN_HEX6278 DESTIN_HEX6279 DESTIN_HEX6280
3.9288659 5.8126471 5.6794483 2.7782532 2.9598601
DESTIN_HEX6281 DESTIN_HEX6283 DESTIN_HEX6284 DESTIN_HEX6286 DESTIN_HEX6289
3.7203909 2.7906850 3.1280743 2.7992922 1.4764234
DESTIN_HEX6290 DESTIN_HEX630 DESTIN_HEX6315 DESTIN_HEX6316 DESTIN_HEX632
2.2307170 2.6519748 3.7433661 1.9806640 6.1710473
DESTIN_HEX6320 DESTIN_HEX6321 DESTIN_HEX6322 DESTIN_HEX6323 DESTIN_HEX6324
4.3716312 4.3298702 5.0347321 4.9849007 1.9660676
DESTIN_HEX6326 DESTIN_HEX6327 DESTIN_HEX6328 DESTIN_HEX633 DESTIN_HEX6330
2.9604093 2.9331220 3.9884079 2.4147355 3.5119978
DESTIN_HEX6331 DESTIN_HEX6337 DESTIN_HEX635 DESTIN_HEX6364 DESTIN_HEX6368
3.7032036 1.2490355 5.4975591 3.1481818 3.0966706
DESTIN_HEX6369 DESTIN_HEX6370 DESTIN_HEX6371 DESTIN_HEX6372 DESTIN_HEX6373
2.7727966 4.5695769 4.7463924 4.5905580 2.7630652
DESTIN_HEX6374 DESTIN_HEX6375 DESTIN_HEX6376 DESTIN_HEX6377 DESTIN_HEX6378
3.0274536 3.9317635 5.3493610 3.3223592 3.5748536
DESTIN_HEX6380 DESTIN_HEX6382 DESTIN_HEX6385 DESTIN_HEX6413 DESTIN_HEX6415
3.4742250 1.4561156 1.9850694 4.4828658 3.4513382
DESTIN_HEX6416 DESTIN_HEX6417 DESTIN_HEX6418 DESTIN_HEX6420 DESTIN_HEX6421
2.8432366 4.4987779 5.5418511 3.3893213 3.7683763
DESTIN_HEX6422 DESTIN_HEX6423 DESTIN_HEX6424 DESTIN_HEX6425 DESTIN_HEX6427
3.4169079 1.2444095 1.7031749 3.4524874 3.2769159
DESTIN_HEX6429 DESTIN_HEX6458 DESTIN_HEX6463 DESTIN_HEX6464 DESTIN_HEX6465
1.6672228 2.4578392 5.1139413 5.0888224 4.2440943
DESTIN_HEX6466 DESTIN_HEX6467 DESTIN_HEX6468 DESTIN_HEX6469 DESTIN_HEX6470
4.6564616 3.3228095 3.8051986 4.6073903 3.2852103
DESTIN_HEX6471 DESTIN_HEX6472 DESTIN_HEX6474 DESTIN_HEX6475 DESTIN_HEX6476
5.2129570 3.2164119 5.6165826 3.6783255 5.2595228
DESTIN_HEX6477 DESTIN_HEX6507 DESTIN_HEX6509 DESTIN_HEX6510 DESTIN_HEX6511
2.9948860 4.4952586 5.0633485 2.7731165 4.6020386
DESTIN_HEX6513 DESTIN_HEX6514 DESTIN_HEX6515 DESTIN_HEX6516 DESTIN_HEX6517
5.4377767 4.1341526 6.2180162 4.6303022 4.4362467
DESTIN_HEX6518 DESTIN_HEX6519 DESTIN_HEX6520 DESTIN_HEX6521 DESTIN_HEX6522
6.0186174 3.2391255 5.0966941 5.2315314 3.6080436
DESTIN_HEX6523 DESTIN_HEX6524 DESTIN_HEX6555 DESTIN_HEX6556 DESTIN_HEX6557
1.6593955 2.4556758 5.1419202 3.5398731 3.9032010
DESTIN_HEX6558 DESTIN_HEX6559 DESTIN_HEX6561 DESTIN_HEX6562 DESTIN_HEX6563
2.9628851 3.4981703 3.0474097 5.0237816 3.6868384
DESTIN_HEX6564 DESTIN_HEX6565 DESTIN_HEX6566 DESTIN_HEX6568 DESTIN_HEX6569
4.3162272 5.2027103 3.6517222 5.1548757 4.6909751
DESTIN_HEX6570 DESTIN_HEX6571 DESTIN_HEX6601 DESTIN_HEX6603 DESTIN_HEX6605
5.7442625 1.8184377 2.6279200 4.6845937 2.7144583
DESTIN_HEX6606 DESTIN_HEX6607 DESTIN_HEX6608 DESTIN_HEX6609 DESTIN_HEX6610
3.7950082 3.6169424 3.2903615 4.0812339 3.2159316
DESTIN_HEX6611 DESTIN_HEX6612 DESTIN_HEX6613 DESTIN_HEX6614 DESTIN_HEX6615
3.9281707 5.1544550 4.0705484 2.2478998 5.6165781
DESTIN_HEX6616 DESTIN_HEX6649 DESTIN_HEX6650 DESTIN_HEX6651 DESTIN_HEX6652
5.5125053 -0.0519043 4.2027869 4.7365735 1.5081372
DESTIN_HEX6653 DESTIN_HEX6654 DESTIN_HEX6655 DESTIN_HEX6656 DESTIN_HEX6657
3.4897017 5.5492789 4.4310917 2.1512904 4.7461574
DESTIN_HEX6659 DESTIN_HEX6660 DESTIN_HEX6661 DESTIN_HEX6663 DESTIN_HEX6695
4.5387998 5.5188021 4.3784236 5.3266245 2.1644065
DESTIN_HEX6696 DESTIN_HEX6697 DESTIN_HEX6698 DESTIN_HEX6699 DESTIN_HEX6700
1.1065215 5.1842247 4.2715546 2.3976601 4.0528618
DESTIN_HEX6702 DESTIN_HEX6703 DESTIN_HEX6706 DESTIN_HEX6707 DESTIN_HEX6708
3.6598983 4.8272082 4.7508875 5.3725730 6.0163648
DESTIN_HEX6709 DESTIN_HEX6744 DESTIN_HEX6745 DESTIN_HEX6746 DESTIN_HEX6747
5.0292209 3.4473233 5.4952437 4.4300439 3.7559614
DESTIN_HEX6749 DESTIN_HEX6750 DESTIN_HEX6751 DESTIN_HEX6753 DESTIN_HEX6754
3.5975030 3.6303793 3.7844756 5.0203667 5.5136709
DESTIN_HEX6755 DESTIN_HEX6757 DESTIN_HEX678 DESTIN_HEX6789 DESTIN_HEX679
5.2300698 5.4875353 0.7446376 4.0062034 2.1495080
DESTIN_HEX6790 DESTIN_HEX6791 DESTIN_HEX6792 DESTIN_HEX6793 DESTIN_HEX6794
4.8526455 4.7802075 3.4750828 4.0340393 3.5596101
DESTIN_HEX6796 DESTIN_HEX6797 DESTIN_HEX6798 DESTIN_HEX680 DESTIN_HEX6800
3.2889134 4.8486425 3.4668225 -0.4304163 5.4654543
DESTIN_HEX6801 DESTIN_HEX6802 DESTIN_HEX681 DESTIN_HEX682 DESTIN_HEX6837
5.0838959 5.3236800 1.1962535 2.9789649 4.2170880
DESTIN_HEX6838 DESTIN_HEX6839 DESTIN_HEX6841 DESTIN_HEX6843 DESTIN_HEX6846
4.8303756 4.9534915 4.7503775 3.2242804 5.6530210
DESTIN_HEX6847 DESTIN_HEX6848 DESTIN_HEX6850 DESTIN_HEX6851 DESTIN_HEX6885
4.4946591 4.2829482 5.0956348 4.9204512 4.5711500
DESTIN_HEX6886 DESTIN_HEX6887 DESTIN_HEX6888 DESTIN_HEX6889 DESTIN_HEX6891
4.4675034 4.2054458 3.9316895 3.6461931 5.6010384
DESTIN_HEX6892 DESTIN_HEX6893 DESTIN_HEX6894 DESTIN_HEX6895 DESTIN_HEX6896
4.0542397 5.4737967 4.9568566 5.4466658 2.6526970
DESTIN_HEX6897 DESTIN_HEX6898 DESTIN_HEX6931 DESTIN_HEX6932 DESTIN_HEX6933
6.1395477 3.2906014 4.1566528 5.3097992 3.2339284
DESTIN_HEX6934 DESTIN_HEX6935 DESTIN_HEX6936 DESTIN_HEX6938 DESTIN_HEX6939
2.4502664 3.9045538 4.5423044 1.7971732 5.1454490
DESTIN_HEX6940 DESTIN_HEX6941 DESTIN_HEX6942 DESTIN_HEX6943 DESTIN_HEX6944
4.1547641 4.2927073 4.8564606 4.1403322 4.0565576
DESTIN_HEX6945 DESTIN_HEX6946 DESTIN_HEX6979 DESTIN_HEX6980 DESTIN_HEX6981
4.3289787 6.2667108 3.8621892 5.8457302 3.9404791
DESTIN_HEX6982 DESTIN_HEX6984 DESTIN_HEX6985 DESTIN_HEX6986 DESTIN_HEX6987
1.1694082 2.0574821 5.2376739 4.4392902 5.3892707
DESTIN_HEX6988 DESTIN_HEX6989 DESTIN_HEX6990 DESTIN_HEX6991 DESTIN_HEX6992
6.1537051 5.2130858 3.9010530 5.2655812 5.4822639
DESTIN_HEX7025 DESTIN_HEX7026 DESTIN_HEX7027 DESTIN_HEX7029 DESTIN_HEX7030
3.8994194 4.1965528 4.7699923 4.2299180 2.9474758
DESTIN_HEX7031 DESTIN_HEX7033 DESTIN_HEX7034 DESTIN_HEX7035 DESTIN_HEX7036
1.9032327 3.7545679 4.7336382 3.9458944 4.4696814
DESTIN_HEX7037 DESTIN_HEX7038 DESTIN_HEX7039 DESTIN_HEX7040 DESTIN_HEX7072
5.9127520 4.7673751 4.9013429 6.6669622 3.8780893
DESTIN_HEX7073 DESTIN_HEX7074 DESTIN_HEX7075 DESTIN_HEX7076 DESTIN_HEX7077
4.1405218 4.6990776 2.4469074 2.4253693 2.9267841
DESTIN_HEX7081 DESTIN_HEX7082 DESTIN_HEX7083 DESTIN_HEX7084 DESTIN_HEX7085
4.9274433 3.3512857 4.1930610 4.9834311 6.2565326
DESTIN_HEX7086 DESTIN_HEX7087 DESTIN_HEX7119 DESTIN_HEX7120 DESTIN_HEX7123
5.0338928 5.6557054 4.3095429 4.1430013 2.0329324
DESTIN_HEX7124 DESTIN_HEX7125 DESTIN_HEX7128 DESTIN_HEX7129 DESTIN_HEX7130
3.7331848 3.0374903 2.0524348 4.6966302 4.5664136
DESTIN_HEX7131 DESTIN_HEX7132 DESTIN_HEX7133 DESTIN_HEX7134 DESTIN_HEX7135
5.0908935 4.9412602 3.5070585 5.7066947 6.0019797
DESTIN_HEX7166 DESTIN_HEX7167 DESTIN_HEX7168 DESTIN_HEX7169 DESTIN_HEX7170
4.2694538 4.5622013 4.0240992 1.9569061 4.3132345
DESTIN_HEX7172 DESTIN_HEX7173 DESTIN_HEX7175 DESTIN_HEX7176 DESTIN_HEX7177
1.9492433 2.8321706 4.3149980 5.0991395 4.8277320
DESTIN_HEX7178 DESTIN_HEX7179 DESTIN_HEX7181 DESTIN_HEX7182 DESTIN_HEX7213
5.3843179 4.9896455 4.2016947 3.8977871 4.7505233
DESTIN_HEX7214 DESTIN_HEX7215 DESTIN_HEX7217 DESTIN_HEX7218 DESTIN_HEX7222
4.1715351 4.2906737 4.9338098 3.4906329 1.9501310
DESTIN_HEX7223 DESTIN_HEX7224 DESTIN_HEX7225 DESTIN_HEX7226 DESTIN_HEX7227
4.2948697 5.7692118 3.8144488 5.0842218 5.6496036
DESTIN_HEX7228 DESTIN_HEX7229 DESTIN_HEX723 DESTIN_HEX7230 DESTIN_HEX725
6.2776609 4.1052063 6.2006158 5.3748515 2.7347412
DESTIN_HEX726 DESTIN_HEX7260 DESTIN_HEX7261 DESTIN_HEX7262 DESTIN_HEX7264
2.2373158 4.6721777 4.1375519 4.9575663 4.8332085
DESTIN_HEX7265 DESTIN_HEX727 DESTIN_HEX7271 DESTIN_HEX7272 DESTIN_HEX7273
3.4757049 3.1530280 5.6035783 5.3450187 5.3836914
DESTIN_HEX7274 DESTIN_HEX7275 DESTIN_HEX7277 DESTIN_HEX728 DESTIN_HEX7307
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DESTIN_HEX7308 DESTIN_HEX7309 DESTIN_HEX731 DESTIN_HEX7310 DESTIN_HEX7311
4.6150275 4.0577996 1.7728141 5.3694664 4.6499846
DESTIN_HEX7312 DESTIN_HEX7316 DESTIN_HEX7319 DESTIN_HEX7320 DESTIN_HEX7321
3.1355073 1.0123688 3.7074446 4.7886384 7.0975901
DESTIN_HEX7322 DESTIN_HEX7323 DESTIN_HEX7324 DESTIN_HEX7354 DESTIN_HEX7355
4.6473424 4.2204204 3.3641779 4.1245615 4.4317381
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5.2223265 4.5848707 3.6027473 3.3592973 3.9626289
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3.8046733 3.2296518 5.1020842 2.2201491 6.3537756
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4.6092150 3.1228620 5.6771659 2.2126709 1.7819767
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5.1286360 5.4982882 6.5429782 5.7042095 4.4973166
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DESTIN_HEX7509 DESTIN_HEX7510 DESTIN_HEX7542 DESTIN_HEX7543 DESTIN_HEX7544
5.8705979 5.0297556 5.2117557 3.6556406 2.7436799
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2.6555995 5.0216190 4.3726109 -0.4811079 4.6200182
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4.9123406 3.6236083 0.7862709 3.5258518 4.9335155
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DESTIN_HEX7734 DESTIN_HEX7735 DESTIN_HEX7740 DESTIN_HEX775 DESTIN_HEX777
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4.4395171 2.8243826 2.0121522 4.6114967 5.5120143
DESTIN_HEX7787 DESTIN_HEX779 DESTIN_HEX7825 DESTIN_HEX7826 DESTIN_HEX7828
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DESTIN_HEX7829 DESTIN_HEX7831 DESTIN_HEX7833 DESTIN_HEX7834 DESTIN_HEX7872
4.3897038 3.5886133 1.8031738 1.6830704 4.3214085
DESTIN_HEX7873 DESTIN_HEX7874 DESTIN_HEX7875 DESTIN_HEX7876 DESTIN_HEX7878
3.6097653 4.9733419 4.0195505 5.0577933 5.4400737
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2.7671400 1.9556745 3.9813443 2.5155164 6.4839269
DESTIN_HEX7922 DESTIN_HEX7923 DESTIN_HEX7925 DESTIN_HEX7926 DESTIN_HEX7927
5.1600003 4.1305939 4.8637150 3.5788043 4.2755270
DESTIN_HEX7928 DESTIN_HEX7967 DESTIN_HEX7968 DESTIN_HEX7969 DESTIN_HEX7970
4.3583621 3.3555775 1.8641089 4.0897224 5.1689938
DESTIN_HEX7972 DESTIN_HEX7973 DESTIN_HEX7974 DESTIN_HEX7976 DESTIN_HEX8013
5.2075444 5.5934478 4.1778395 5.0321342 4.6751396
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4.5718808 4.8370937 5.3063225 4.6549235 3.9451493
DESTIN_HEX8019 DESTIN_HEX8020 DESTIN_HEX8021 DESTIN_HEX8023 DESTIN_HEX8061
5.2960864 4.9524372 3.6326160 6.0499924 3.9858101
DESTIN_HEX8062 DESTIN_HEX8063 DESTIN_HEX8065 DESTIN_HEX8066 DESTIN_HEX8067
4.0380146 4.4038675 1.7837311 3.8683683 4.5639929
DESTIN_HEX8068 DESTIN_HEX8070 DESTIN_HEX8071 DESTIN_HEX8108 DESTIN_HEX8109
5.4172845 4.5070889 3.5486024 3.2108511 4.9975895
DESTIN_HEX8110 DESTIN_HEX8112 DESTIN_HEX8113 DESTIN_HEX8114 DESTIN_HEX8115
5.7421041 5.1143545 4.2581858 4.6037762 4.8237608
DESTIN_HEX8116 DESTIN_HEX8117 DESTIN_HEX8155 DESTIN_HEX8156 DESTIN_HEX8157
3.8452265 4.6001105 4.5953703 4.2427643 5.3904178
DESTIN_HEX8158 DESTIN_HEX8160 DESTIN_HEX8161 DESTIN_HEX8162 DESTIN_HEX8163
4.1308954 4.6818893 3.9275972 4.7119074 4.4006573
DESTIN_HEX8164 DESTIN_HEX8165 DESTIN_HEX818 DESTIN_HEX819 DESTIN_HEX820
4.6641112 4.4363987 1.8656390 2.9764237 2.3205573
DESTIN_HEX8203 DESTIN_HEX8207 DESTIN_HEX8208 DESTIN_HEX8209 DESTIN_HEX8210
4.9293886 4.8590811 3.2939479 5.2322882 4.9904481
DESTIN_HEX8211 DESTIN_HEX823 DESTIN_HEX824 DESTIN_HEX8249 DESTIN_HEX825
5.6209738 2.5979235 2.8299429 3.2532258 0.8908424
DESTIN_HEX8250 DESTIN_HEX8252 DESTIN_HEX8254 DESTIN_HEX8255 DESTIN_HEX8256
5.3030375 2.6520588 4.3252224 6.5772710 4.0736099
DESTIN_HEX8258 DESTIN_HEX8259 DESTIN_HEX826 DESTIN_HEX827 DESTIN_HEX828
3.9031872 2.7381395 1.1072454 5.7659308 3.4112234
DESTIN_HEX8296 DESTIN_HEX8297 DESTIN_HEX8298 DESTIN_HEX8299 DESTIN_HEX8300
4.5002142 5.6996823 4.3168747 2.2005582 3.1287379
DESTIN_HEX8301 DESTIN_HEX8302 DESTIN_HEX8304 DESTIN_HEX8305 DESTIN_HEX8344
4.5649444 3.5218366 4.4696695 2.8016742 3.2551980
DESTIN_HEX8345 DESTIN_HEX8346 DESTIN_HEX8347 DESTIN_HEX8348 DESTIN_HEX8349
5.0486306 2.4340612 4.6164988 4.5760323 3.3725105
DESTIN_HEX8351 DESTIN_HEX8352 DESTIN_HEX8353 DESTIN_HEX8389 DESTIN_HEX8390
3.9581833 3.0978872 2.9627468 3.0667451 2.8165226
DESTIN_HEX8391 DESTIN_HEX8392 DESTIN_HEX8393 DESTIN_HEX8394 DESTIN_HEX8395
3.2027231 2.4114231 3.4082406 3.5956040 3.2167791
DESTIN_HEX8396 DESTIN_HEX8398 DESTIN_HEX8439 DESTIN_HEX8440 DESTIN_HEX8441
4.5045760 6.2529855 3.3384065 3.8459593 5.3829289
DESTIN_HEX8442 DESTIN_HEX8443 DESTIN_HEX8444 DESTIN_HEX8445 DESTIN_HEX8484
4.5631121 4.9210968 5.3239063 4.2582668 3.2635705
DESTIN_HEX8485 DESTIN_HEX8486 DESTIN_HEX8488 DESTIN_HEX8489 DESTIN_HEX8490
3.2824026 2.7742633 3.5567135 5.4163101 3.7643182
DESTIN_HEX8532 DESTIN_HEX8534 DESTIN_HEX8535 DESTIN_HEX8536 DESTIN_HEX8537
4.8535382 2.3270560 4.1666371 3.6490404 5.3194975
DESTIN_HEX8538 DESTIN_HEX8539 DESTIN_HEX8540 DESTIN_HEX8580 DESTIN_HEX8581
5.5753545 5.3538659 5.0333532 3.1170637 1.4417135
DESTIN_HEX8582 DESTIN_HEX8583 DESTIN_HEX8584 DESTIN_HEX8585 DESTIN_HEX8586
5.2300376 4.6152005 5.0998674 4.5587344 4.8147781
DESTIN_HEX8587 DESTIN_HEX8628 DESTIN_HEX8629 DESTIN_HEX8631 DESTIN_HEX8633
5.1590530 2.4488243 4.5359622 5.5039912 5.1381547
DESTIN_HEX8634 DESTIN_HEX866 DESTIN_HEX867 DESTIN_HEX8674 DESTIN_HEX8675
4.7232262 1.1523793 1.9147236 2.6936578 2.1458419
DESTIN_HEX8676 DESTIN_HEX8677 DESTIN_HEX8679 DESTIN_HEX8680 DESTIN_HEX8681
3.8056743 5.3944193 4.7971934 5.7952476 5.6493015
DESTIN_HEX870 DESTIN_HEX872 DESTIN_HEX8721 DESTIN_HEX8722 DESTIN_HEX8723
2.2510151 5.5453843 -0.9876780 4.7275824 1.7542805
DESTIN_HEX8724 DESTIN_HEX8725 DESTIN_HEX8726 DESTIN_HEX8727 DESTIN_HEX8728
4.4162965 5.4663378 4.5595626 4.5375539 3.6377447
DESTIN_HEX873 DESTIN_HEX874 DESTIN_HEX8768 DESTIN_HEX8769 DESTIN_HEX8771
-0.4233694 1.1643586 0.2387770 1.8608855 3.3044117
DESTIN_HEX8772 DESTIN_HEX8773 DESTIN_HEX8774 DESTIN_HEX8775 DESTIN_HEX8815
5.2801325 4.8018136 3.1516845 2.9217890 2.8607349
DESTIN_HEX8816 DESTIN_HEX8817 DESTIN_HEX8818 DESTIN_HEX8819 DESTIN_HEX8820
2.6468505 1.7532837 1.8807388 3.7283580 3.1221765
DESTIN_HEX8862 DESTIN_HEX8864 DESTIN_HEX8865 DESTIN_HEX8866 DESTIN_HEX8867
1.8315950 2.7049437 2.1714108 4.5111766 2.5860852
DESTIN_HEX8868 DESTIN_HEX8910 DESTIN_HEX8912 DESTIN_HEX8914 DESTIN_HEX8915
3.0390411 2.4753274 1.3142224 3.2723508 3.1053101
DESTIN_HEX8916 DESTIN_HEX8917 DESTIN_HEX8959 DESTIN_HEX8961 DESTIN_HEX8962
2.3366815 1.9871027 2.3572699 1.5282740 4.2676011
DESTIN_HEX8963 DESTIN_HEX8964 DESTIN_HEX9007 DESTIN_HEX9008 DESTIN_HEX9010
0.6084691 2.1960287 2.9063043 3.5002873 2.4125914
DESTIN_HEX9011 DESTIN_HEX9055 DESTIN_HEX9056 DESTIN_HEX9057 DESTIN_HEX9103
1.6887608 2.5328127 1.4404796 2.1471001 4.6113701
DESTIN_HEX9105 DESTIN_HEX9106 DESTIN_HEX914 DESTIN_HEX9145 DESTIN_HEX9150
0.2868241 2.3434539 2.6487482 3.1234061 1.8808858
DESTIN_HEX9152 DESTIN_HEX9153 DESTIN_HEX917 DESTIN_HEX919 DESTIN_HEX9193
2.7496225 2.4314684 0.7894815 3.2217161 4.5984970
DESTIN_HEX920 DESTIN_HEX9200 DESTIN_HEX9240 DESTIN_HEX9246 DESTIN_HEX9247
2.3642959 2.6326960 2.9287739 3.6134821 1.7184615
DESTIN_HEX9283 DESTIN_HEX9289 DESTIN_HEX9294 DESTIN_HEX9340 DESTIN_HEX9383
6.0226879 5.7685354 4.9359247 3.7758461 3.7910464
DESTIN_HEX9384 DESTIN_HEX9388 DESTIN_HEX9432 DESTIN_HEX9471 DESTIN_HEX9480
5.6492497 3.3584586 2.7532063 4.7627330 2.3945719
DESTIN_HEX9482 DESTIN_HEX9526 DESTIN_HEX9527 DESTIN_HEX9575 DESTIN_HEX9576
1.1138212 2.2028286 2.2637589 2.6121430 1.1467685
DESTIN_HEX9621 DESTIN_HEX9622 DESTIN_HEX965 DESTIN_HEX966 DESTIN_HEX9668
1.4295567 4.0686291 2.1646485 1.2053448 2.2143921
DESTIN_HEX9714 DESTIN_HEX9988 log(dist)
2.4806693 3.4955293 -1.2091797
Degrees of Freedom: 161670 Total (i.e. Null); 158053 Residual
Null Deviance: 96290000
Residual Deviance: 28500000 AIC: 29290000CalcRSquared(dbcSIM$data$WEEKDAY_AFTERNOON_PEAK, dbcSIM$fitted.values)[1] 0.4406584r2_mcfadden(dbcSIM)# R2 for Generalized Linear Regression
R2: 0.698
adj. R2: 0.69811.9Model Comparison
Create a list called model_list by using the code chunk below.
model_list <- list(unconstrained=uncSIM,
originConstrained=orcSIM,
destinationConstrained=decSIM,
doublyConstrained=dbcSIM)Next, we will compute the RMSE of all the models in model_list file by using the code chunk below.
compare_performance(model_list,
metrics = "RMSE")# Comparison of Model Performance Indices
Name | Model | RMSE
----------------------------------------
unconstrained | glm | 729.068
originConstrained | glm | 678.683
destinationConstrained | glm | 696.998
doublyConstrained | glm | 576.958The print above reveals that doubly constrained SIM is the best model among all the four SIMs because it has the smallest RMSE value of 576.958.
11.11Visualizing Fitted
We are going to visualize the observed values and the fitted values of all models in this section. Firstly, we need to extract the fitted values from each model by using the code below.
df <- as.data.frame(uncSIM$fitted.values) %>%
round(digits = 0)Next, we will join the fitted values to SIM_data data frame and name them appropriately.
SIM_data <- SIM_data %>%
cbind(df) %>%
rename(uncWEEKDAY_AFTERNOON_PEAK = "uncSIM$fitted.values")Repeat the process for orcSIM.
df <- as.data.frame(orcSIM$fitted.values) %>%
round(digits = 0)SIM_data <- SIM_data %>%
cbind(df) %>%
rename(orcWEEKDAY_AFTERNOON_PEAK = "orcSIM$fitted.values")Repeat the process for decSIM.
df <- as.data.frame(decSIM$fitted.values) %>%
round(digits = 0)SIM_data <- SIM_data %>%
cbind(df) %>%
rename(decWEEKDAY_AFTERNOON_PEAK = "decSIM$fitted.values")Repeat the process for dbcSIM.
df <- as.data.frame(dbcSIM$fitted.values) %>%
round(digits = 0)SIM_data <- SIM_data %>%
cbind(df) %>%
rename(dbcWEEKDAY_AFTERNOON_PEAK = "dbcSIM$fitted.values")unc_p <- ggplot(data = SIM_data,
aes(x = uncWEEKDAY_AFTERNOON_PEAK,
y = WEEKDAY_AFTERNOON_PEAK)) +
geom_point() +
geom_smooth(method = lm)
orc_p <- ggplot(data = SIM_data,
aes(x = orcWEEKDAY_AFTERNOON_PEAK,
y = WEEKDAY_AFTERNOON_PEAK)) +
geom_point() +
geom_smooth(method = lm)
dec_p <- ggplot(data = SIM_data,
aes(x = decWEEKDAY_AFTERNOON_PEAK,
y = WEEKDAY_AFTERNOON_PEAK)) +
geom_point() +
geom_smooth(method = lm)
dbc_p <- ggplot(data = SIM_data,
aes(x = dbcWEEKDAY_AFTERNOON_PEAK,
y = WEEKDAY_AFTERNOON_PEAK)) +
geom_point() +
geom_smooth(method = lm)
ggarrange(unc_p, orc_p, dec_p, dbc_p,
ncol = 2,
nrow = 2)
The trend line of dbcSIM indicates a stronger relationship with a steeper slope, suggesting this model may be capturing the variance in the observed data more effectively.