Code
pacman::p_load(tidyverse, sf, httr, tmap, dplyr)In-class Exercise 4 - Geospatial Data Science and Spatial Interaction Model with R
1 Geospatial Data Science with R
1.1 Overview
In this exercise, we are going to do the following: - Performing geocoding using data downloaded from data.gov.sg - Calibrating Geographically Weighted Poisson Regression - perform point-in-polygon count analysis - append the propulsiveness and attractiveness variables onto a flow data.
1.2 Getting Started
Packages Explanations
tidyverse: A collection of R packages designed for data science that makes it easier to import, tidy, transform, visualize, and model data.
sf: An R package that simplifies handling and manipulating geospatial data, providing simple features access for geographic data operations.
httr: A user-friendly package to make working with HTTP requests easier, providing useful tools for interacting with APIs and web services directly from R.
tmap: An R package for creating thematic maps that can be static or interactive, offering a structured and comprehensive approach to visualizing spatial data.
1.2.1 Geocoding using SLA API
Geocoding is the conversion of an address or postal code into geographic coordinates, typically latitude and longitude. The Singapore Land Authority offers the OneMap API, specifically the Search API, which retrieves latitude, longitude, and x,y coordinates for a given address or postal code.
To perform geocoding using the SLA OneMap API, the provided code, written in R, reads input data from a CSV file using the read_csv function from the readr package. The httr package’s HTTP call functions are then used to send individual records to the OneMap geocoding server.
The geocoding process creates two data frames: found for successfully geocoded records and not_found for those that failed. The found data table is joined with the initial CSV data table using a unique identifier (POSTAL) and saved as a new CSV file named found.
Code
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)
}
}
Functions
- read_csv from readr package reads a CSV file into R, creating a data frame.
- A
forloop in base R iterates over each postcode inpostcodes. - GET from httr package sends an HTTP GET request to a specified URL. Here, it is used to query a web API with specific parameters for each postcode.
- content from httr package extracts content from a response object returned by
GET. It’s used to extract data from the API response. - rbind from base R combines data frames by rows. In this code, it’s used to append new rows to
foundornot_found. - The code checks if each postcode has corresponding data in the API response (
found) or not (not_found), and constructs two separate data frames accordingly.
First, let’s check the Resulting Variables ::: panel-tabset #### url
Code
url[1] "https://www.onemap.gov.sg/api/common/elastic/search"csv
Code
glimpse(csv)Rows: 346
Columns: 31
$ school_name <chr> "ADMIRALTY PRIMARY SCHOOL", "ADMIRALTY SECONDARY SC…
$ url_address <chr> "https://admiraltypri.moe.edu.sg/", "http://www.adm…
$ address <chr> "11 WOODLANDS CIRCLE", "31 WOODLANDS CRESCENT",…
$ postal_code <chr> "738907", "737916", "768643", "768928", "579646", "…
$ telephone_no <chr> "63620598", "63651733", "67592906", "67585384", "64…
$ telephone_no_2 <chr> "na", "63654596", "na", "na", "na", "na", "na", "na…
$ fax_no <chr> "63627512", "63652774", "67592927", "67557778", "64…
$ fax_no_2 <chr> "na", "na", "na", "na", "na", "na", "na", "na", "na…
$ email_address <chr> "ADMIRALTY_PS@MOE.EDU.SG", "Admiralty_SS@moe.edu.sg…
$ mrt_desc <chr> "Admiralty Station", "ADMIRALTY MRT", "Yishun", "CA…
$ bus_desc <chr> "TIBS 965, 964, 913", "904", "Yishun Ring Road - 81…
$ principal_name <chr> "MR PEK WEE HAUR", "MR LAM YUI- P'NG", "MISS ONG LE…
$ first_vp_name <chr> "MDM CHUA MUI LING", "MR NG SONG LIM STEVEN", "MADA…
$ second_vp_name <chr> "MDM NUR SABARIAH BTE MOHD IBRAHIM", "MR SHEIK ALAU…
$ third_vp_name <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL", "NU…
$ fourth_vp_name <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL", "NU…
$ fifth_vp_name <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL", "NU…
$ sixth_vp_name <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL", "NU…
$ dgp_code <chr> "WOODLANDS", "WOODLANDS", "YISHUN", "YISHUN", "BISH…
$ zone_code <chr> "NORTH", "NORTH", "NORTH", "NORTH", "SOUTH", "SOUTH…
$ type_code <chr> "GOVERNMENT SCHOOL", "GOVERNMENT SCHOOL", "GOVERNME…
$ nature_code <chr> "CO-ED SCHOOL", "CO-ED SCHOOL", "CO-ED SCHOOL", "CO…
$ session_code <chr> "FULL DAY", "SINGLE SESSION", "SINGLE SESSION", "SI…
$ mainlevel_code <chr> "PRIMARY", "SECONDARY", "PRIMARY", "SECONDARY", "PR…
$ sap_ind <chr> "No", "No", "No", "No", "Yes", "No", "No", "No", "N…
$ autonomous_ind <chr> "No", "No", "No", "No", "No", "No", "No", "No", "Ye…
$ gifted_ind <chr> "No", "No", "No", "No", "No", "No", "No", "No", "No…
$ ip_ind <chr> "No", "No", "No", "No", "No", "No", "No", "No", "No…
$ mothertongue1_code <chr> "Chinese", "Chinese", "Chinese", "Chinese", "Chines…
$ mothertongue2_code <chr> "Malay", "Malay", "Malay", "Malay", "na", "Malay", …
$ mothertongue3_code <chr> "Tamil", "Tamil", "Tamil", "Tamil", "na", "Tamil", …postcodes
Code
glimpse(postcodes) chr [1:346] "738907" "737916" "768643" "768928" "579646" "159016" "544969" ...found
Code
glimpse(found)Rows: 345
Columns: 10
$ results.SEARCHVAL <chr> "THE LEARNING HARBOUR @ ADMIRALTY PRIMARY SCHOOL", "…
$ results.BLK_NO <chr> "11", "31", "10", "751", "100", "2A", "31", "19", "1…
$ results.ROAD_NAME <chr> "WOODLANDS CIRCLE", "WOODLANDS CRESCENT", "YISHUN ST…
$ results.BUILDING <chr> "THE LEARNING HARBOUR @ ADMIRALTY PRIMARY SCHOOL", "…
$ results.ADDRESS <chr> "11 WOODLANDS CIRCLE THE LEARNING HARBOUR @ ADMIRALT…
$ results.POSTAL <chr> "738907", "737916", "768643", "768928", "579646", "1…
$ results.X <chr> "24315.9398124339", "24559.0472937012", "27958.13714…
$ results.Y <chr> "47135.3542042952", "47504.7873554379", "46096.26276…
$ results.LATITUDE <chr> "1.44254963931583", "1.44589068910993", "1.433152715…
$ results.LONGITUDE <chr> "103.800213682734", "103.802398196596", "103.8329424…not_found
Code
glimpse(not_found)Rows: 1
Columns: 1
$ postcode <chr> "677741":::
Next, we combine both found and not_found into a single tibble dataframe.
Code
merged = merge(csv, found, by.x = 'postal_code', by.y = 'results.POSTAL', all = TRUE)
# manually add the Zhenghua Secondary School data
merged[merged$school_name == "ZHENGHUA SECONDARY SCHOOL", "results.LATITUDE"] <- 1.3887
merged[merged$school_name == "ZHENGHUA SECONDARY SCHOOL", "results.LONGITUDE"] <- 103.7652
write.csv(merged, file = "../data/aspatial/schools.csv")
write.csv(not_found, file = "../data/aspatial/not_found.csv")
# check the output
glimpse(merged)Rows: 350
Columns: 40
$ postal_code <chr> "088256", "099138", "099757", "099840", "109100", "…
$ school_name <chr> "CANTONMENT PRIMARY SCHOOL", "CHIJ ST. THERESA'S CO…
$ url_address <chr> "http://www.cantonmentpri.moe.edu.sg", "http://www.…
$ address <chr> "1 Cantonment Close", "160 LOWER DELTA ROAD", "…
$ telephone_no <chr> "65119555", "64775777", "62730096", "62733937", "62…
$ telephone_no_2 <chr> "na", "na", "na", "na", "na", "na", "na", "na", "na…
$ fax_no <chr> "65119556", "64775700", "62731710", "62763083", "62…
$ fax_no_2 <chr> "na", "na", "na", "na", "na", "na", "na", "na", "na…
$ email_address <chr> "cantonment_ps@moe.edu.sg", "CHIJSTCS@MOE.EDU.SG", …
$ mrt_desc <chr> "Tanjong Pagar Outram Park", "HARBOURFRONT MRT, TIO…
$ bus_desc <chr> "75, 167, 196", "65, 121, 123, 123M, 124, 131, 131M…
$ principal_name <chr> "MRS MANOKARA SUGUNAVATHI", "MDM TAN MEI MEI JENNY"…
$ first_vp_name <chr> "MRS AUDREA CHIN", "MDM ONG LEE LEE", "MS NG CHIOU …
$ second_vp_name <chr> "MISS CHENG SHIN MIIN", "MISS KUO ZHAOYAN, FELICIA"…
$ third_vp_name <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL", "NU…
$ fourth_vp_name <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL", "NU…
$ fifth_vp_name <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL", "NU…
$ sixth_vp_name <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL", "NU…
$ dgp_code <chr> "BUKIT MERAH", "BUKIT MERAH", "BUKIT MERAH", "BUKIT…
$ zone_code <chr> "SOUTH", "SOUTH", "SOUTH", "SOUTH", "SOUTH", "SOUTH…
$ type_code <chr> "GOVERNMENT SCHOOL", "GOVERNMENT-AIDED SCH", "GOVER…
$ nature_code <chr> "CO-ED SCHOOL", "GIRLS' SCHOOL", "GIRLS' SCHOOL", "…
$ session_code <chr> "SINGLE SESSION", "SINGLE SESSION", "SINGLE SESSION…
$ mainlevel_code <chr> "PRIMARY", "SECONDARY", "PRIMARY", "PRIMARY", "PRIM…
$ sap_ind <chr> "No", "No", "No", "No", "No", "No", "No", "No", "Ye…
$ autonomous_ind <chr> "No", "No", "No", "No", "No", "No", "No", "No", "No…
$ gifted_ind <chr> "No", "No", "No", "No", "No", "No", "No", "No", "Ye…
$ ip_ind <chr> "No", "No", "No", "No", "No", "No", "No", "No", "No…
$ mothertongue1_code <chr> "Chinese", "Chinese", "Chinese", "Chinese", "Chines…
$ mothertongue2_code <chr> "Malay", "Malay", "Malay", "Malay", "Malay", "Malay…
$ mothertongue3_code <chr> "Tamil", "Tamil", "Tamil", "Tamil", "Tamil", "na", …
$ results.SEARCHVAL <chr> "KIDZ TREEHOUSE @ CANTONMENT", "CHIJ SAINT THERESA'…
$ results.BLK_NO <chr> "1", "160", "1", "1", "91", "147", "301", "50", "30…
$ results.ROAD_NAME <chr> "CANTONMENT CLOSE", "LOWER DELTA ROAD", "BUKIT TERE…
$ results.BUILDING <chr> "KIDZ TREEHOUSE @ CANTONMENT", "CHIJ SAINT THERESA'…
$ results.ADDRESS <chr> "1 CANTONMENT CLOSE KIDZ TREEHOUSE @ CANTONMENT SIN…
$ results.X <chr> "28748.1620587641", "26789.3781491434", "27402.9654…
$ results.Y <chr> "28659.9995642845", "28647.4426490944", "28579.8478…
$ results.LATITUDE <chr> "1.27546534984202", "1.27535177510054", "1.27474048…
$ results.LONGITUDE <chr> "103.840041087946", "103.822440701642", "103.827954…
Functions
- merge from base R combines two data frames by matching rows based on specified columns. In this code,
csvandfoundare merged usingpostal_codefromcsvandresults.POSTALfromfound, with theall = TRUEoption to include all rows from both data frames. - The manual addition of data for “ZHENGHUA SECONDARY SCHOOL” is performed using base R’s subsetting and assignment operations.
- write.csv from base R writes a data frame to a CSV file.
- glimpse from dplyr package provides a transposed summary of the data frame, offering a quick look at its structure and contents.
1.2.2 Importing and tidying schools data
In this sub-section, you will import schools.csv into R environment and at the same time tidying the data by selecting only the necessary fields as well as rename some fields.
Code
# re-import the correct dataset as schools
schools <- read_csv("../data/aspatial/schools.csv")
schools <- schools %>%
rename(latitude = "results.LATITUDE",
longitude = "results.LONGITUDE")
schools <- schools %>%
select(`postal_code`, `school_name`, `latitude`, `longitude`)
# check the output
glimpse(schools)Rows: 350
Columns: 4
$ postal_code <chr> "088256", "099138", "099757", "099840", "109100", "127368"…
$ school_name <chr> "CANTONMENT PRIMARY SCHOOL", "CHIJ ST. THERESA'S CONVENT",…
$ latitude <dbl> 1.275465, 1.275352, 1.274740, 1.274958, 1.276128, 1.301228…
$ longitude <dbl> 103.8400, 103.8224, 103.8280, 103.8242, 103.8086, 103.7649…
Functions
- read_csv from readr package reads a CSV file into R, creating a data frame.
- rename from dplyr package changes the names of specific columns in a data frame for clarity or convenience. Here, it renames
results.LATITUDEtolatitudeandresults.LONGITUDEtolongitude. - select from dplyr package is used to subset specific columns from the data frame, retaining only the
postal_code,school_name,latitude, andlongitudecolumns. - glimpse from dplyr package provides a quick overview of the data frame’s structure, including column types and the first few entries in each column.
1.2.3 Converting an aspatial data into sf tibble data.frame
Next, you will convert schools tibble data.frame data into a simple feature tibble data.frame called schools_sf by using values in latitude and longitude fields.
Code
schools_sf <- st_as_sf(schools,
coords = c("longitude", "latitude"),
crs = 4326) %>%
st_transform(crs = 3414)
# check the output
glimpse(schools_sf)Rows: 350
Columns: 3
$ postal_code <chr> "088256", "099138", "099757", "099840", "109100", "127368"…
$ school_name <chr> "CANTONMENT PRIMARY SCHOOL", "CHIJ ST. THERESA'S CONVENT",…
$ geometry <POINT [m]> POINT (28748.16 28660), POINT (26789.38 28647.44), P…
Functions
- st_as_sf from sf package converts a data frame to a simple features (sf) object, specifying the coordinates for spatial data. In this code,
longitudeandlatitudecolumns are used for coordinates. - st_transform from sf package transforms the coordinate reference system (CRS) of the sf object. Here, it converts CRS to 3414.
- glimpse from dplyr package provides a transposed summary of the sf object, giving a quick look at its structure, including geometry type and the first few entries in each column.
1.2.4 Plotting a point simple feature layer
To ensure that schools sf tibble data.frame has been projected and converted correctly, you can plot the schools point data for visual inspection.
First, import MPSZ-2019 shapefile into R as sf tibble data.frame and name it mpsz.
Code
mpsz <- st_read(dsn = "../data/geospatial/",
layer = "MPSZ-2019") %>%
st_transform(crs = 3414)Reading layer `MPSZ-2019' from data source `C:\ameernoor\ISSS624\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 84Code
# check the output
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...Next, create a point symbol map showing the location of schools with OSM as the background map.
Code
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
tm_polygons() +
tm_shape(schools_sf) +
tm_dots()
Functions
- tmap_options from tmap package sets options for tmap functions. In this case, it’s set to automatically check and fix invalid polygons in spatial data.
- tm_shape from tmap package prepares spatial data for plotting. It is used twice in this code: first for the
mpszdataset and then forschools_sf. - tm_polygons from tmap package adds a layer of polygons to the map, in this case, for the
mpszdata. - tm_dots from tmap package adds a layer of dots to the map, here representing the
schools_sfdata. - This code snippet creates a thematic map that combines polygons from
mpszand dots representing schools fromschools_sf.
1.2.5 Create Interactive Map
Code
tmap_mode("plot")
tm_shape(schools_sf) +
tm_dots() +
tm_view(set.zoom.limits = c(11,14))
Code
# turn off the interactive layer setting for next codes
tmap_mode("plot")
Functions
- tmap_mode from tmap package sets the mode for creating maps. Initially, it’s set to
"view"for interactive maps. - tm_shape from tmap package prepares the spatial data (here
schools_sf) for plotting. - tm_dots from tmap package adds a layer of dots to represent spatial points on the map.
- tm_view from tmap package customizes the interactive map view, including setting zoom limits.
- The code snippet creates an interactive map displaying schools as dots.
- Finally,
tmap_mode("plot")switches back to static plotting mode, stopping the interactive layer.
1.2.6 Performing point-in-polygon count process
Next, we will count the number of schools located inside the planning subzones.
Code
mpsz$`SCHOOL_COUNT`<- lengths(
st_intersects(
mpsz, schools_sf))
# check the summary statistics of the derived variabled
summary(mpsz$`SCHOOL_COUNT`) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000 0.000 0.000 1.054 2.000 12.000
Functions
- st_intersects from sf package is used to find the intersection between two spatial objects, here
mpszandschools_sf. It returns a list indicating which geometries fromschools_sfintersect with each geometry inmpsz. - lengths from base R calculates the lengths of the elements in a list, in this case, the number of schools intersecting with each polygon in
mpsz. - The assignment operation (
mpsz$SCHOOL_COUNT <-) creates a new column in thempszdata frame, storing the count of schools intersecting with each area. - summary from base R provides a summary of the
SCHOOL_COUNTvariable, typically giving minimum, maximum, mean, and other useful statistics.
The summary statistics above reveals that there are excessive 0 values in SCHOOL_COUNT field. If log() is going to use to transform this field, additional step is required to ensure that all 0 will be replaced with a value between 0 and 1 but not 0 neither 1.
1.3 Data Integration and Final Touch-up
1.3.1 Count Number of Business Points in each Planning Subzone.
Code
business_sf <- st_read(dsn = "../data/geospatial",
layer = "Business")Reading layer `Business' from data source `C:\ameernoor\ISSS624\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 TM
Functions
- st_read from sf package is used for reading spatial vector data into R. It imports data from a specified data source (
dsn) and layer (layer). In this code, the function is reading the “Business” layer from the data source located at"../data/geospatial", converting it into ansf(simple features) object suitable for spatial analysis in R.
Code
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
tm_polygons() +
tm_shape(business_sf) +
tm_dots()
Functions
- tmap_options from tmap package sets options for tmap functions. Here, it’s configured to automatically check and fix invalid polygons in spatial data.
- tm_shape from tmap package prepares spatial data for plotting. It’s used twice in this code: first for the
mpszdataset and then forbusiness_sf. - tm_polygons from tmap package adds a layer of polygons to the map, representing the
mpszdata. - tm_dots from tmap package adds a layer of dots to the map, here representing the
business_sfdata. - This code snippet creates a thematic map that combines polygonal representations of
mpszand dots representing business locations frombusiness_sf.
note that for plotting layers of map, the polygons must always come first
Code
mpsz$`BUSINESS_COUNT`<- lengths(
st_intersects(
mpsz, business_sf))
# check the summary statistics of the new variable
summary(mpsz$`BUSINESS_COUNT`) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00 0.00 2.00 19.73 13.00 307.00
Functions
- st_intersects from sf package is used to find the intersections between two spatial objects, in this case,
mpszandbusiness_sf. It determines which geometries frombusiness_sfintersect with each geometry inmpszand returns a list indicating these intersections. - lengths from base R calculates the lengths of the elements in a list. Here, it’s used to count the number of business locations intersecting with each area in
mpsz. - The assignment operation (
mpsz$BUSINESS_COUNT <-) adds a new column to thempszdata frame, which stores the count of business locations intersecting with each area. - summary from base R provides a summary of the
BUSINESS_COUNTvariable, giving a statistical overview including minimum, maximum, mean, and other useful metrics.
1.3.2 Append School and Business Counts
Next, import the flow_data.rds from Hands-on Exercise 3.
Code
flow_data <- read_rds("../data/rds/flow_data_tidy.rds")
# check the output
glimpse(flow_data)Rows: 14,734
Columns: 13
$ ORIGIN_SZ <chr> "AMSZ01", "AMSZ01", "AMSZ01", "AMSZ01", "AMSZ01", "AMS…
$ DESTIN_SZ <chr> "AMSZ01", "AMSZ02", "AMSZ03", "AMSZ04", "AMSZ05", "AMS…
$ MORNING_PEAK <dbl> 1998, 8289, 8971, 2252, 6136, 2148, 1620, 1925, 1773, …
$ dist <dbl> 50.0000, 810.4491, 1360.9294, 840.4432, 1076.7916, 805…
$ ORIGIN_AGE7_12 <dbl> 310, 310, 310, 310, 310, 310, 310, 310, 310, 310, 310,…
$ ORIGIN_AGE13_24 <dbl> 710, 710, 710, 710, 710, 710, 710, 710, 710, 710, 710,…
$ ORIGIN_AGE25_64 <dbl> 2780, 2780, 2780, 2780, 2780, 2780, 2780, 2780, 2780, …
$ DESTIN_AGE7_12 <dbl> 310.00, 1140.00, 1010.00, 980.00, 810.00, 1050.00, 420…
$ DESTIN_AGE13_24 <dbl> 710.00, 2770.00, 2650.00, 2000.00, 1920.00, 2390.00, 1…
$ DESTIN_AGE25_64 <dbl> 2780.00, 15700.00, 14240.00, 11320.00, 9650.00, 12460.…
$ SCHOOL_COUNT <dbl> 0.99, 2.00, 2.00, 1.00, 3.00, 2.00, 0.99, 0.99, 3.00, …
$ RETAIL_COUNT <dbl> 1.00, 0.99, 6.00, 0.99, 0.99, 0.99, 1.00, 117.00, 0.99…
$ geometry <LINESTRING [m]> LINESTRING (29501.77 39419...., LINESTRING …
Functions
- read_rds from base R reads an R object stored in RDS format and restores it. In this code, it’s used to load the
flow_dataobject from an RDS file located at"../data/rds/flow_data_tidy.rds". - glimpse from dplyr package provides a transposed summary of the data frame, offering a quick look at its structure, including the types of columns and the first few entries in each column.
This is an sf tibble data.frame and the features are polylines linking the centroid of origins and destination planning subzone.
Next, append SCHOOL_COUNT and BUSINESS_COUNT into flow_data sf tibble data.frame.
Code
mpsz_tidy <- mpsz %>%
select(SUBZONE_C, SCHOOL_COUNT, BUSINESS_COUNT) %>%
st_drop_geometry()
# check the output
glimpse(mpsz_tidy)Rows: 332
Columns: 3
$ SUBZONE_C <chr> "MESZ01", "RVSZ05", "SRSZ01", "WISZ01", "MUSZ02", "MPSZ…
$ SCHOOL_COUNT <int> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 0…
$ BUSINESS_COUNT <int> 0, 6, 4, 5, 7, 0, 0, 0, 0, 1, 11, 15, 1, 10, 1, 17, 6, …
Functions
- st_drop_geometry from sf package is used to remove the geometry column from a spatial object, converting it into a regular data frame.
- select from dplyr package subsets specific columns in a data frame. In this case, it retains
SUBZONE_C,SCHOOL_COUNT, andBUSINESS_COUNT. - glimpse from dplyr package provides a quick overview of the data frame’s structure, including column types and the first few entries in each column.
Next, append SCHOOL_COUNT and BUSINESS_COUNT fields from mpsz_tidy data.frame into flow_data sf tibble data.frame
Code
flow_data <- flow_data %>%
left_join(mpsz_tidy,
by = c("DESTIN_SZ" = "SUBZONE_C")) %>%
rename(TRIPS = MORNING_PEAK, DIST = dist)
Functions
- left_join from dplyr package merges two data frames based on matching values in their columns. Here,
flow_datais joined withmpsz_tidyusing theDESTIN_SZcolumn fromflow_dataandSUBZONE_Cfrommpsz_tidy. This function retains all rows fromflow_dataand adds matching rows frommpsz_tidy. - rename from dplyr package changes the names of specific columns in a data frame for clarity or convenience. In this code,
MORNING_PEAKis renamed toTRIPSanddisttoDIST.
Note that unique join field is DESTIN_SZ and SUBZONE_C. Destination is chosen as the unique field as it represents the attracting zone in a morning peak trips.
1.3.3 Checking for 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. Summary() of Base R is used to compute the summary statistics of all variables in wd_od data frame.
Code
summary(flow_data) ORIGIN_SZ DESTIN_SZ TRIPS DIST
Length:14734 Length:14734 Min. : 1 Min. : 50
Class :character Class :character 1st Qu.: 14 1st Qu.: 3346
Mode :character Mode :character Median : 76 Median : 6067
Mean : 1021 Mean : 6880
3rd Qu.: 426 3rd Qu.: 9729
Max. :232187 Max. :26136
ORIGIN_AGE7_12 ORIGIN_AGE13_24 ORIGIN_AGE25_64 DESTIN_AGE7_12
Min. : 0.99 Min. : 0.99 Min. : 0.99 Min. : 0.99
1st Qu.: 240.00 1st Qu.: 440.00 1st Qu.: 2200.00 1st Qu.: 240.00
Median : 700.00 Median : 1350.00 Median : 6810.00 Median : 720.00
Mean :1031.86 Mean : 2268.84 Mean :10487.62 Mean :1033.40
3rd Qu.:1480.00 3rd Qu.: 3260.00 3rd Qu.:15770.00 3rd Qu.:1500.00
Max. :6340.00 Max. :16380.00 Max. :74610.00 Max. :6340.00
DESTIN_AGE13_24 DESTIN_AGE25_64 SCHOOL_COUNT.x RETAIL_COUNT
Min. : 0.99 Min. : 0.99 Min. : 0.990 Min. : 0.99
1st Qu.: 460.00 1st Qu.: 2200.00 1st Qu.: 0.990 1st Qu.: 0.99
Median : 1420.00 Median : 7030.00 Median : 1.000 Median : 3.00
Mean : 2290.35 Mean :10574.46 Mean : 1.987 Mean : 16.47
3rd Qu.: 3260.00 3rd Qu.:15830.00 3rd Qu.: 2.000 3rd Qu.: 12.00
Max. :16380.00 Max. :74610.00 Max. :12.000 Max. :307.00
SCHOOL_COUNT.y BUSINESS_COUNT geometry
Min. : 0.000 Min. : 0.00 LINESTRING :14734
1st Qu.: 0.000 1st Qu.: 0.00 epsg:3414 : 0
Median : 1.000 Median : 3.00 +proj=tmer...: 0
Mean : 1.583 Mean : 16.17
3rd Qu.: 2.000 3rd Qu.: 12.00
Max. :12.000 Max. :307.00 The print report above reveals that variables ORIGIN_AGE7_12, ORIGIN_AGE13_24, ORIGIN_AGE25_64, DESTIN_AGE7_12, DESTIN_AGE13_24, DESTIN_AGE25_64 consist of 0 values. To prepare the data for poisson regression, replae zero values to 0.99
Code
# Check if there are any zero values in SCHOOL_COUNT and BUSINESS_COUNT
if (any(flow_data$SCHOOL_COUNT == 0)) {
flow_data$SCHOOL_COUNT <- ifelse(flow_data$SCHOOL_COUNT == 0, 0.99, flow_data$SCHOOL_COUNT)
}
if (any(flow_data$BUSINESS_COUNT == 0)) {
flow_data$BUSINESS_COUNT <- ifelse(flow_data$BUSINESS_COUNT == 0, 0.99, flow_data$BUSINESS_COUNT)
}
# run summary to check:
summary(flow_data) ORIGIN_SZ DESTIN_SZ TRIPS DIST
Length:14734 Length:14734 Min. : 1 Min. : 50
Class :character Class :character 1st Qu.: 14 1st Qu.: 3346
Mode :character Mode :character Median : 76 Median : 6067
Mean : 1021 Mean : 6880
3rd Qu.: 426 3rd Qu.: 9729
Max. :232187 Max. :26136
ORIGIN_AGE7_12 ORIGIN_AGE13_24 ORIGIN_AGE25_64 DESTIN_AGE7_12
Min. : 0.99 Min. : 0.99 Min. : 0.99 Min. : 0.99
1st Qu.: 240.00 1st Qu.: 440.00 1st Qu.: 2200.00 1st Qu.: 240.00
Median : 700.00 Median : 1350.00 Median : 6810.00 Median : 720.00
Mean :1031.86 Mean : 2268.84 Mean :10487.62 Mean :1033.40
3rd Qu.:1480.00 3rd Qu.: 3260.00 3rd Qu.:15770.00 3rd Qu.:1500.00
Max. :6340.00 Max. :16380.00 Max. :74610.00 Max. :6340.00
DESTIN_AGE13_24 DESTIN_AGE25_64 SCHOOL_COUNT.x RETAIL_COUNT
Min. : 0.99 Min. : 0.99 Min. : 0.990 Min. : 0.99
1st Qu.: 460.00 1st Qu.: 2200.00 1st Qu.: 0.990 1st Qu.: 0.99
Median : 1420.00 Median : 7030.00 Median : 1.000 Median : 3.00
Mean : 2290.35 Mean :10574.46 Mean : 1.987 Mean : 16.47
3rd Qu.: 3260.00 3rd Qu.:15830.00 3rd Qu.: 2.000 3rd Qu.: 12.00
Max. :16380.00 Max. :74610.00 Max. :12.000 Max. :307.00
SCHOOL_COUNT.y BUSINESS_COUNT geometry
Min. : 0.000 Min. : 0.99 LINESTRING :14734
1st Qu.: 0.000 1st Qu.: 0.99 epsg:3414 : 0
Median : 1.000 Median : 3.00 +proj=tmer...: 0
Mean : 1.583 Mean : 16.47
3rd Qu.: 2.000 3rd Qu.: 12.00
Max. :12.000 Max. :307.00
Functions
- any from base R checks if any of the values in a given vector meet a specified condition, here checking for zero values in
SCHOOL_COUNTandBUSINESS_COUNT. - ifelse from base R applies a conditional test to each element of a vector, returning one value if the condition is true and another if it’s false. In this code, it’s used to replace zero values in
SCHOOL_COUNTandBUSINESS_COUNTwith 0.99. - summary from base R provides a summary of an object’s contents, typically offering minimum, maximum, median, mean, and other useful statistics. Here, it’s used to check the updated values in
flow_data.
export the data as rds for future usage.
Code
write_rds(flow_data, "../data/rds/flow_data_tidy_update.rds")2 Calibrating Spatial Interaction Models with R
2.1 Overview
We will continue our journey of calibrating Spatial Interaction Models by using propulsiveness and attractiveness variables prepared in earlier in-class exercise.
2.2 Getting Started
firstly, import the libraries
Code
pacman::p_load(tmap, sf, performance, AER, MASS, ggpubr, tidyverse, DT, knitr)
Packages Explanations
tmap: This package is used for creating thematic maps in R. It allows for the visualization of spatial data and supports both static and interactive mapping.
sf: Stands for “simple features” and is an R package that provides standardized support for spatial data manipulation. It integrates well with the
tidyversesuite of data science tools.performance: Provides tools for checking and assessing the quality and performance of statistical models, including regression models and mixed-effect models.
AER: Short for “Applied Econometrics with R”, this package includes functions and data sets for the book of the same name, which is useful for econometric analysis.
MASS: The package supplies functions and datasets to support the book “Modern Applied Statistics with S” by Venables and Ripley, including a variety of statistical methods such as linear and quadratic discriminant function analysis, and robust multivariate statistics.
ggpubr: Provides a simple interface for creating publication-ready plots using an extension of
ggplot2, with additional functions for commonly needed statistics and plots.tidyverse: A collection of R packages designed for data science tasks that make it easy to import, tidy, transform, and visualize data in a coherent data analysis workflow.
knitr for creating html tables
2.3 The Data
import the data from previous processes.
Code
flow_data <- read_rds("../data/rds/flow_data_tidy_update.rds")
# check the output
glimpse(flow_data)Rows: 14,734
Columns: 15
$ ORIGIN_SZ <chr> "AMSZ01", "AMSZ01", "AMSZ01", "AMSZ01", "AMSZ01", "AMS…
$ DESTIN_SZ <chr> "AMSZ01", "AMSZ02", "AMSZ03", "AMSZ04", "AMSZ05", "AMS…
$ TRIPS <dbl> 1998, 8289, 8971, 2252, 6136, 2148, 1620, 1925, 1773, …
$ DIST <dbl> 50.0000, 810.4491, 1360.9294, 840.4432, 1076.7916, 805…
$ ORIGIN_AGE7_12 <dbl> 310, 310, 310, 310, 310, 310, 310, 310, 310, 310, 310,…
$ ORIGIN_AGE13_24 <dbl> 710, 710, 710, 710, 710, 710, 710, 710, 710, 710, 710,…
$ ORIGIN_AGE25_64 <dbl> 2780, 2780, 2780, 2780, 2780, 2780, 2780, 2780, 2780, …
$ DESTIN_AGE7_12 <dbl> 310.00, 1140.00, 1010.00, 980.00, 810.00, 1050.00, 420…
$ DESTIN_AGE13_24 <dbl> 710.00, 2770.00, 2650.00, 2000.00, 1920.00, 2390.00, 1…
$ DESTIN_AGE25_64 <dbl> 2780.00, 15700.00, 14240.00, 11320.00, 9650.00, 12460.…
$ SCHOOL_COUNT.x <dbl> 0.99, 2.00, 2.00, 1.00, 3.00, 2.00, 0.99, 0.99, 3.00, …
$ RETAIL_COUNT <dbl> 1.00, 0.99, 6.00, 0.99, 0.99, 0.99, 1.00, 117.00, 0.99…
$ SCHOOL_COUNT.y <int> 0, 2, 2, 1, 3, 2, 0, 0, 3, 1, 0, 0, 1, 1, 7, 4, 5, 1, …
$ BUSINESS_COUNT <dbl> 1.00, 0.99, 6.00, 0.99, 0.99, 0.99, 1.00, 117.00, 0.99…
$ geometry <LINESTRING [m]> LINESTRING (29501.77 39419...., LINESTRING …this sf tibble data.frame includes two additional fields namely: SCHOOL_COUNT and BUSINESS_COUNT. Both of them will be used as attractiveness variables when calibrating origin constrained SIM.
check first five columns and rows of flow_data
Code
kable(head(flow_data[, 1:5], n = 5))| ORIGIN_SZ | DESTIN_SZ | TRIPS | DIST | ORIGIN_AGE7_12 | geometry |
|---|---|---|---|---|---|
| AMSZ01 | AMSZ01 | 1998 | 50.0000 | 310 | LINESTRING (29501.77 39419…. |
| AMSZ01 | AMSZ02 | 8289 | 810.4491 | 310 | LINESTRING (29501.77 39419…. |
| AMSZ01 | AMSZ03 | 8971 | 1360.9294 | 310 | LINESTRING (29501.77 39419…. |
| AMSZ01 | AMSZ04 | 2252 | 840.4432 | 310 | LINESTRING (29501.77 39419…. |
| AMSZ01 | AMSZ05 | 6136 | 1076.7916 | 310 | LINESTRING (29501.77 39419…. |
Functions
- head from base R retrieves the first
nrows of a data frame or matrix. Here, it’s used to get the first 5 rows offlow_data, considering only the first 5 columns. - kable from the knitr package creates a simple table from a data frame or matrix. This function is used to display the selected subset of
flow_dataas a markdown table.
Notice that this data.frame include intra-zonal flow. The next part will remove it
2.3.1 Preparing inter-zonal flow data
In general, we will calibrate separate Spatial Interaction Models for inter- and intra-zonal flows. In this hands-on exercise, we will focus our attention on inter-zonal flow. Hence, we need to exclude the intra-zonal flow from flow_data.
First, two new columns called FlowNoIntra and offset will be created by using the code chunk below. All intra-zonal flow will be given a value of 0 or else the original flow values will be inserted. Then, inter-zonal flow will be selected from flow_data and save into a new output data.frame called inter_zonal_flow
Code
flow_data$FlowNoIntra <- ifelse(
flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ,
0, flow_data$TRIPS)
flow_data$offset <- ifelse(
flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ,
0.000001, 1)
inter_zonal_flow <- flow_data %>%
filter(FlowNoIntra > 0)
Functions
- ifelse from base R applies a conditional test to each element of a vector. In this code, it is used twice: firstly, to create the
FlowNoIntracolumn inflow_data, where the value is set to 0 if the origin and destination subzones are the same, otherwise it’s set to the value ofTRIPS; secondly, to create theoffsetcolumn, assigning a very small number (0.000001) if the origin and destination subzones are the same, otherwise 1. - filter from dplyr package is used to retain rows based on a specified condition. Here, it filters
flow_datato keep rows whereFlowNoIntrais greater than 0, effectively selecting rows where the flow is not within the same subzone (inter-zonal flow).
2.4 Calibrating Spatial Interaction Models
In this section, we will focus on calibrating an origin constrained SIM and a doubly constrained by using flow_data prepared. It will complement materials from Hands-on Exercise 3.
2.4.1 Origin- (Production-) constrained Model
Code chunk below shows the calibration of the model by using glm() of R and flow_data.
Code
orcSIM_Poisson <- glm(formula = TRIPS ~
ORIGIN_SZ +
log(SCHOOL_COUNT.x) +
log(BUSINESS_COUNT) +
log(DIST) - 1,
family = poisson(link = "log"),
data = inter_zonal_flow,
na.action = na.exclude)
summary(orcSIM_Poisson)
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + log(SCHOOL_COUNT.x) + log(BUSINESS_COUNT) +
log(DIST) - 1, family = poisson(link = "log"), data = inter_zonal_flow,
na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
ORIGIN_SZAMSZ01 19.8739840 0.0047627 4172.84 <2e-16 ***
ORIGIN_SZAMSZ02 20.5902203 0.0042786 4812.33 <2e-16 ***
ORIGIN_SZAMSZ03 20.2327026 0.0045531 4443.70 <2e-16 ***
ORIGIN_SZAMSZ04 19.7744438 0.0049837 3967.79 <2e-16 ***
ORIGIN_SZAMSZ05 19.6574529 0.0056396 3485.61 <2e-16 ***
ORIGIN_SZAMSZ06 19.9659115 0.0048946 4079.16 <2e-16 ***
ORIGIN_SZAMSZ07 18.6746164 0.0096316 1938.90 <2e-16 ***
ORIGIN_SZAMSZ08 19.2701601 0.0090776 2122.82 <2e-16 ***
ORIGIN_SZAMSZ09 19.9889467 0.0052858 3781.64 <2e-16 ***
ORIGIN_SZAMSZ10 20.3422035 0.0045778 4443.62 <2e-16 ***
ORIGIN_SZAMSZ11 18.3944113 0.0129212 1423.58 <2e-16 ***
ORIGIN_SZAMSZ12 18.3484209 0.0109652 1673.33 <2e-16 ***
ORIGIN_SZBDSZ01 20.9668587 0.0043388 4832.36 <2e-16 ***
ORIGIN_SZBDSZ02 20.4059518 0.0050601 4032.75 <2e-16 ***
ORIGIN_SZBDSZ03 20.6725514 0.0045276 4565.93 <2e-16 ***
ORIGIN_SZBDSZ04 21.6703853 0.0038930 5566.44 <2e-16 ***
ORIGIN_SZBDSZ05 20.7497445 0.0046085 4502.46 <2e-16 ***
ORIGIN_SZBDSZ06 20.9119361 0.0046432 4503.77 <2e-16 ***
ORIGIN_SZBDSZ07 18.9749815 0.0097896 1938.28 <2e-16 ***
ORIGIN_SZBDSZ08 19.1933901 0.0091312 2101.95 <2e-16 ***
ORIGIN_SZBKSZ01 19.5422606 0.0064732 3018.96 <2e-16 ***
ORIGIN_SZBKSZ02 20.1748913 0.0050076 4028.89 <2e-16 ***
ORIGIN_SZBKSZ03 20.3984624 0.0047226 4319.35 <2e-16 ***
ORIGIN_SZBKSZ04 19.6182212 0.0059652 3288.76 <2e-16 ***
ORIGIN_SZBKSZ05 19.6033818 0.0063181 3102.74 <2e-16 ***
ORIGIN_SZBKSZ06 19.7145224 0.0056372 3497.20 <2e-16 ***
ORIGIN_SZBKSZ07 20.4237448 0.0041912 4873.03 <2e-16 ***
ORIGIN_SZBKSZ08 19.7992538 0.0050405 3928.02 <2e-16 ***
ORIGIN_SZBKSZ09 19.7821586 0.0055558 3560.66 <2e-16 ***
ORIGIN_SZBLSZ01 17.7977276 0.0149058 1194.01 <2e-16 ***
ORIGIN_SZBLSZ02 17.4287491 0.0192364 906.03 <2e-16 ***
ORIGIN_SZBLSZ03 16.5884288 0.0459848 360.74 <2e-16 ***
ORIGIN_SZBLSZ04 17.7851626 0.0232823 763.89 <2e-16 ***
ORIGIN_SZBMSZ01 20.0751840 0.0052887 3795.89 <2e-16 ***
ORIGIN_SZBMSZ02 18.6956140 0.0066656 2804.80 <2e-16 ***
ORIGIN_SZBMSZ03 19.3204425 0.0054755 3528.56 <2e-16 ***
ORIGIN_SZBMSZ04 19.4724220 0.0049390 3942.59 <2e-16 ***
ORIGIN_SZBMSZ05 16.9581801 0.0168804 1004.61 <2e-16 ***
ORIGIN_SZBMSZ06 16.9898638 0.0181852 934.27 <2e-16 ***
ORIGIN_SZBMSZ07 19.2868403 0.0056231 3429.91 <2e-16 ***
ORIGIN_SZBMSZ08 19.1477543 0.0055918 3424.28 <2e-16 ***
ORIGIN_SZBMSZ09 18.7564539 0.0086298 2173.46 <2e-16 ***
ORIGIN_SZBMSZ10 18.3617854 0.0089250 2057.35 <2e-16 ***
ORIGIN_SZBMSZ11 18.9167941 0.0063340 2986.54 <2e-16 ***
ORIGIN_SZBMSZ12 18.7874661 0.0093024 2019.63 <2e-16 ***
ORIGIN_SZBMSZ13 19.5654046 0.0057517 3401.70 <2e-16 ***
ORIGIN_SZBMSZ14 19.0685619 0.0063346 3010.24 <2e-16 ***
ORIGIN_SZBMSZ15 19.4403124 0.0058147 3343.30 <2e-16 ***
ORIGIN_SZBMSZ16 18.4469203 0.0092638 1991.28 <2e-16 ***
ORIGIN_SZBMSZ17 18.3430175 0.0157692 1163.22 <2e-16 ***
ORIGIN_SZBPSZ01 20.1806714 0.0053660 3760.81 <2e-16 ***
ORIGIN_SZBPSZ02 19.8116707 0.0061485 3222.19 <2e-16 ***
ORIGIN_SZBPSZ03 19.8467602 0.0059769 3320.57 <2e-16 ***
ORIGIN_SZBPSZ04 20.4613200 0.0048398 4227.72 <2e-16 ***
ORIGIN_SZBPSZ05 20.5379711 0.0043769 4692.39 <2e-16 ***
ORIGIN_SZBPSZ06 18.8948034 0.0093668 2017.21 <2e-16 ***
ORIGIN_SZBPSZ07 19.4104568 0.0087961 2206.70 <2e-16 ***
ORIGIN_SZBSSZ01 20.0139503 0.0056561 3538.45 <2e-16 ***
ORIGIN_SZBSSZ02 20.2543885 0.0047198 4291.38 <2e-16 ***
ORIGIN_SZBSSZ03 19.5428803 0.0052713 3707.41 <2e-16 ***
ORIGIN_SZBTSZ01 20.0198045 0.0058541 3419.77 <2e-16 ***
ORIGIN_SZBTSZ02 19.3618525 0.0081472 2376.51 <2e-16 ***
ORIGIN_SZBTSZ03 19.5883853 0.0068935 2841.59 <2e-16 ***
ORIGIN_SZBTSZ04 18.7720238 0.0103909 1806.58 <2e-16 ***
ORIGIN_SZBTSZ05 18.8069026 0.0120628 1559.08 <2e-16 ***
ORIGIN_SZBTSZ06 18.7068633 0.0094575 1978.00 <2e-16 ***
ORIGIN_SZBTSZ07 17.6292257 0.0141551 1245.43 <2e-16 ***
ORIGIN_SZBTSZ08 18.6989374 0.0109610 1705.94 <2e-16 ***
ORIGIN_SZCBSZ01 18.2189868 0.0548317 332.27 <2e-16 ***
ORIGIN_SZCCSZ01 18.9734563 0.0139450 1360.59 <2e-16 ***
ORIGIN_SZCHSZ01 19.5955119 0.0121035 1619.00 <2e-16 ***
ORIGIN_SZCHSZ02 19.3320960 0.0081620 2368.55 <2e-16 ***
ORIGIN_SZCHSZ03 21.2164518 0.0063552 3338.43 <2e-16 ***
ORIGIN_SZCKSZ01 20.1046845 0.0049333 4075.29 <2e-16 ***
ORIGIN_SZCKSZ02 20.5371946 0.0050256 4086.53 <2e-16 ***
ORIGIN_SZCKSZ03 20.7210560 0.0042184 4912.07 <2e-16 ***
ORIGIN_SZCKSZ04 21.4013886 0.0042524 5032.80 <2e-16 ***
ORIGIN_SZCKSZ05 20.9413146 0.0049434 4236.18 <2e-16 ***
ORIGIN_SZCKSZ06 20.2557727 0.0071832 2819.88 <2e-16 ***
ORIGIN_SZCLSZ01 19.3383703 0.0076634 2523.46 <2e-16 ***
ORIGIN_SZCLSZ02 18.5226956 0.0135522 1366.77 <2e-16 ***
ORIGIN_SZCLSZ03 19.0225512 0.0080145 2373.51 <2e-16 ***
ORIGIN_SZCLSZ04 20.7981505 0.0042400 4905.22 <2e-16 ***
ORIGIN_SZCLSZ05 18.3015625 0.0146815 1246.58 <2e-16 ***
ORIGIN_SZCLSZ06 20.8207386 0.0039567 5262.09 <2e-16 ***
ORIGIN_SZCLSZ07 19.6728958 0.0054199 3629.76 <2e-16 ***
ORIGIN_SZCLSZ08 20.0851929 0.0056956 3526.43 <2e-16 ***
ORIGIN_SZCLSZ09 18.5749589 0.0165415 1122.93 <2e-16 ***
ORIGIN_SZDTSZ02 15.8276209 0.0833992 189.78 <2e-16 ***
ORIGIN_SZDTSZ03 16.2512838 0.0737972 220.22 <2e-16 ***
ORIGIN_SZDTSZ13 16.7744385 0.0312450 536.87 <2e-16 ***
ORIGIN_SZGLSZ01 18.2368248 0.0096104 1897.62 <2e-16 ***
ORIGIN_SZGLSZ02 19.8705255 0.0049014 4054.06 <2e-16 ***
ORIGIN_SZGLSZ03 19.8249435 0.0053109 3732.85 <2e-16 ***
ORIGIN_SZGLSZ04 20.7800335 0.0041261 5036.20 <2e-16 ***
ORIGIN_SZGLSZ05 20.6040494 0.0043049 4786.23 <2e-16 ***
ORIGIN_SZHGSZ01 20.0273475 0.0044824 4468.04 <2e-16 ***
ORIGIN_SZHGSZ02 20.2480656 0.0044575 4542.47 <2e-16 ***
ORIGIN_SZHGSZ03 20.0756442 0.0049003 4096.81 <2e-16 ***
ORIGIN_SZHGSZ04 20.7577748 0.0040465 5129.84 <2e-16 ***
ORIGIN_SZHGSZ05 20.9779992 0.0040123 5228.42 <2e-16 ***
ORIGIN_SZHGSZ06 19.7403058 0.0054229 3640.20 <2e-16 ***
ORIGIN_SZHGSZ07 20.1896268 0.0046051 4384.22 <2e-16 ***
ORIGIN_SZHGSZ08 19.8646492 0.0052403 3790.72 <2e-16 ***
ORIGIN_SZHGSZ09 18.3647736 0.0069196 2654.04 <2e-16 ***
ORIGIN_SZHGSZ10 16.8720475 0.0421046 400.72 <2e-16 ***
ORIGIN_SZJESZ01 20.2673794 0.0046723 4337.79 <2e-16 ***
ORIGIN_SZJESZ02 20.0595982 0.0046503 4313.61 <2e-16 ***
ORIGIN_SZJESZ03 19.9128778 0.0049848 3994.75 <2e-16 ***
ORIGIN_SZJESZ04 18.5053667 0.0099227 1864.94 <2e-16 ***
ORIGIN_SZJESZ05 17.8172930 0.0138840 1283.29 <2e-16 ***
ORIGIN_SZJESZ06 20.0124157 0.0045009 4446.36 <2e-16 ***
ORIGIN_SZJESZ07 18.1821423 0.0117267 1550.49 <2e-16 ***
ORIGIN_SZJESZ08 18.8713046 0.0116456 1620.46 <2e-16 ***
ORIGIN_SZJESZ09 20.5535527 0.0048456 4241.72 <2e-16 ***
ORIGIN_SZJESZ10 18.4922322 0.0191243 966.95 <2e-16 ***
ORIGIN_SZJESZ11 18.2891211 0.0197114 927.85 <2e-16 ***
ORIGIN_SZJWSZ01 20.4912737 0.0063102 3247.35 <2e-16 ***
ORIGIN_SZJWSZ02 20.8236694 0.0042249 4928.82 <2e-16 ***
ORIGIN_SZJWSZ03 21.2587613 0.0039733 5350.40 <2e-16 ***
ORIGIN_SZJWSZ04 20.3816464 0.0046199 4411.67 <2e-16 ***
ORIGIN_SZJWSZ05 18.0607448 0.0128857 1401.61 <2e-16 ***
ORIGIN_SZJWSZ06 18.7015202 0.0107614 1737.83 <2e-16 ***
ORIGIN_SZJWSZ07 17.3991822 0.0277096 627.91 <2e-16 ***
ORIGIN_SZJWSZ08 21.8044465 0.0037356 5836.95 <2e-16 ***
ORIGIN_SZJWSZ09 21.5414930 0.0036033 5978.19 <2e-16 ***
ORIGIN_SZKLSZ01 20.0307712 0.0047868 4184.59 <2e-16 ***
ORIGIN_SZKLSZ02 19.0634769 0.0062318 3059.05 <2e-16 ***
ORIGIN_SZKLSZ03 19.2685700 0.0057172 3370.25 <2e-16 ***
ORIGIN_SZKLSZ04 17.7085067 0.0119809 1478.06 <2e-16 ***
ORIGIN_SZKLSZ05 18.6384471 0.0107596 1732.26 <2e-16 ***
ORIGIN_SZKLSZ06 13.7280296 0.1857160 73.92 <2e-16 ***
ORIGIN_SZKLSZ07 18.6425146 0.0084952 2194.47 <2e-16 ***
ORIGIN_SZKLSZ08 18.0928506 0.0101567 1781.37 <2e-16 ***
ORIGIN_SZLKSZ01 17.8907138 0.0397083 450.55 <2e-16 ***
ORIGIN_SZMDSZ01 18.7605188 0.0285455 657.22 <2e-16 ***
ORIGIN_SZMDSZ02 19.1533927 0.0102815 1862.90 <2e-16 ***
ORIGIN_SZMDSZ03 17.8404982 0.0169690 1051.36 <2e-16 ***
ORIGIN_SZMPSZ01 19.0765941 0.0083937 2272.74 <2e-16 ***
ORIGIN_SZMPSZ02 19.2162527 0.0068331 2812.24 <2e-16 ***
ORIGIN_SZMPSZ03 19.9965344 0.0054569 3664.44 <2e-16 ***
ORIGIN_SZMUSZ02 15.9130765 0.1037472 153.38 <2e-16 ***
ORIGIN_SZNTSZ01 17.0840999 0.0352513 484.64 <2e-16 ***
ORIGIN_SZNTSZ02 16.5792122 0.0233186 710.99 <2e-16 ***
ORIGIN_SZNTSZ03 18.9506415 0.0075957 2494.93 <2e-16 ***
ORIGIN_SZNTSZ05 15.8770261 0.0495825 320.21 <2e-16 ***
ORIGIN_SZNTSZ06 15.3997415 0.0557029 276.46 <2e-16 ***
ORIGIN_SZNVSZ01 20.2241694 0.0043487 4650.65 <2e-16 ***
ORIGIN_SZNVSZ02 19.1897826 0.0065383 2934.97 <2e-16 ***
ORIGIN_SZNVSZ03 18.8854268 0.0080459 2347.22 <2e-16 ***
ORIGIN_SZNVSZ04 18.8940191 0.0090985 2076.61 <2e-16 ***
ORIGIN_SZNVSZ05 17.6278585 0.0168107 1048.61 <2e-16 ***
ORIGIN_SZPGSZ01 19.4825220 0.0122960 1584.46 <2e-16 ***
ORIGIN_SZPGSZ02 19.4726761 0.0073116 2663.25 <2e-16 ***
ORIGIN_SZPGSZ03 20.5515713 0.0045631 4503.86 <2e-16 ***
ORIGIN_SZPGSZ04 21.0527131 0.0041500 5072.89 <2e-16 ***
ORIGIN_SZPGSZ05 20.1436604 0.0057267 3517.48 <2e-16 ***
ORIGIN_SZPLSZ01 19.1832002 0.0120006 1598.53 <2e-16 ***
ORIGIN_SZPLSZ02 18.8752206 0.0149740 1260.53 <2e-16 ***
ORIGIN_SZPLSZ03 18.1000818 0.0371769 486.86 <2e-16 ***
ORIGIN_SZPLSZ04 17.1730559 0.0370280 463.79 <2e-16 ***
ORIGIN_SZPLSZ05 17.9084439 0.0225031 795.82 <2e-16 ***
ORIGIN_SZPNSZ01 21.0804425 0.0044829 4702.41 <2e-16 ***
ORIGIN_SZPNSZ02 19.8822123 0.0111507 1783.05 <2e-16 ***
ORIGIN_SZPNSZ03 17.9293289 0.0193571 926.24 <2e-16 ***
ORIGIN_SZPNSZ04 17.1039594 0.0334954 510.64 <2e-16 ***
ORIGIN_SZPNSZ05 18.2543864 0.0275554 662.46 <2e-16 ***
ORIGIN_SZPRSZ01 19.8777935 0.0117586 1690.49 <2e-16 ***
ORIGIN_SZPRSZ02 21.0751780 0.0044832 4700.88 <2e-16 ***
ORIGIN_SZPRSZ03 20.6717019 0.0045577 4535.55 <2e-16 ***
ORIGIN_SZPRSZ04 19.6365125 0.0074923 2620.90 <2e-16 ***
ORIGIN_SZPRSZ05 21.3132151 0.0042119 5060.24 <2e-16 ***
ORIGIN_SZPRSZ06 18.9314574 0.0117278 1614.24 <2e-16 ***
ORIGIN_SZPRSZ07 17.2822918 0.0162430 1063.98 <2e-16 ***
ORIGIN_SZPRSZ08 19.9267642 0.0062298 3198.62 <2e-16 ***
ORIGIN_SZQTSZ01 19.7357175 0.0066359 2974.08 <2e-16 ***
ORIGIN_SZQTSZ02 19.2082141 0.0061402 3128.26 <2e-16 ***
ORIGIN_SZQTSZ03 19.7771883 0.0056220 3517.83 <2e-16 ***
ORIGIN_SZQTSZ04 18.7114421 0.0072842 2568.76 <2e-16 ***
ORIGIN_SZQTSZ05 19.3049324 0.0062401 3093.69 <2e-16 ***
ORIGIN_SZQTSZ06 19.2643228 0.0065590 2937.09 <2e-16 ***
ORIGIN_SZQTSZ07 18.5697347 0.0095373 1947.06 <2e-16 ***
ORIGIN_SZQTSZ08 19.6147001 0.0061330 3198.21 <2e-16 ***
ORIGIN_SZQTSZ09 19.2550793 0.0069947 2752.82 <2e-16 ***
ORIGIN_SZQTSZ10 19.5801866 0.0064513 3035.07 <2e-16 ***
ORIGIN_SZQTSZ11 17.7398366 0.0143648 1234.95 <2e-16 ***
ORIGIN_SZQTSZ12 17.2420354 0.0186736 923.34 <2e-16 ***
ORIGIN_SZQTSZ13 19.3857418 0.0078878 2457.69 <2e-16 ***
ORIGIN_SZQTSZ14 18.1300753 0.0122096 1484.90 <2e-16 ***
ORIGIN_SZQTSZ15 19.4222283 0.0120871 1606.86 <2e-16 ***
ORIGIN_SZRCSZ01 18.1549045 0.0125108 1451.13 <2e-16 ***
ORIGIN_SZRCSZ06 18.8836400 0.0082161 2298.38 <2e-16 ***
ORIGIN_SZRVSZ01 16.7864438 0.0323796 518.43 <2e-16 ***
ORIGIN_SZRVSZ02 16.4203244 0.0276836 593.14 <2e-16 ***
ORIGIN_SZRVSZ03 16.6453738 0.0244992 679.42 <2e-16 ***
ORIGIN_SZRVSZ04 15.9559213 0.0556344 286.80 <2e-16 ***
ORIGIN_SZRVSZ05 17.0476331 0.0164122 1038.71 <2e-16 ***
ORIGIN_SZSBSZ01 20.0417968 0.0062488 3207.29 <2e-16 ***
ORIGIN_SZSBSZ02 19.1869565 0.0081051 2367.26 <2e-16 ***
ORIGIN_SZSBSZ03 20.5769861 0.0045108 4561.70 <2e-16 ***
ORIGIN_SZSBSZ04 20.5154199 0.0050548 4058.57 <2e-16 ***
ORIGIN_SZSBSZ05 19.6250669 0.0065562 2993.35 <2e-16 ***
ORIGIN_SZSBSZ06 18.8419757 0.0171135 1101.00 <2e-16 ***
ORIGIN_SZSBSZ07 19.4897259 0.0124528 1565.09 <2e-16 ***
ORIGIN_SZSBSZ08 18.7027917 0.0140545 1330.73 <2e-16 ***
ORIGIN_SZSBSZ09 18.8893480 0.0088571 2132.67 <2e-16 ***
ORIGIN_SZSESZ02 20.8962192 0.0041665 5015.34 <2e-16 ***
ORIGIN_SZSESZ03 20.9452771 0.0039737 5270.94 <2e-16 ***
ORIGIN_SZSESZ04 20.6576142 0.0046364 4455.55 <2e-16 ***
ORIGIN_SZSESZ05 19.5170732 0.0058912 3312.92 <2e-16 ***
ORIGIN_SZSESZ06 20.7595824 0.0045747 4537.89 <2e-16 ***
ORIGIN_SZSESZ07 17.6888256 0.0195787 903.47 <2e-16 ***
ORIGIN_SZSGSZ01 19.1359250 0.0085781 2230.79 <2e-16 ***
ORIGIN_SZSGSZ02 18.5614369 0.0102037 1819.10 <2e-16 ***
ORIGIN_SZSGSZ03 19.9933176 0.0050434 3964.23 <2e-16 ***
ORIGIN_SZSGSZ04 20.2426871 0.0047211 4287.71 <2e-16 ***
ORIGIN_SZSGSZ05 18.0114965 0.0107743 1671.70 <2e-16 ***
ORIGIN_SZSGSZ06 20.2593194 0.0044538 4548.76 <2e-16 ***
ORIGIN_SZSGSZ07 19.0763664 0.0062968 3029.54 <2e-16 ***
ORIGIN_SZSKSZ01 19.9222451 0.0085136 2340.04 <2e-16 ***
ORIGIN_SZSKSZ02 20.8633383 0.0055248 3776.33 <2e-16 ***
ORIGIN_SZSKSZ03 19.6528148 0.0080534 2440.33 <2e-16 ***
ORIGIN_SZSKSZ04 18.0754470 0.0275771 655.45 <2e-16 ***
ORIGIN_SZSKSZ05 19.1192521 0.0155579 1228.91 <2e-16 ***
ORIGIN_SZSLSZ01 17.1501034 0.0329384 520.67 <2e-16 ***
ORIGIN_SZSLSZ04 19.5949774 0.0076753 2552.98 <2e-16 ***
ORIGIN_SZSRSZ01 16.9761403 0.0162020 1047.78 <2e-16 ***
ORIGIN_SZTHSZ01 17.9695687 0.0488559 367.81 <2e-16 ***
ORIGIN_SZTHSZ03 18.5427522 0.0223617 829.22 <2e-16 ***
ORIGIN_SZTHSZ04 17.4760374 0.0286247 610.52 <2e-16 ***
ORIGIN_SZTHSZ06 17.8401186 0.0183322 973.16 <2e-16 ***
ORIGIN_SZTMSZ01 20.3406361 0.0056607 3593.33 <2e-16 ***
ORIGIN_SZTMSZ02 22.0307026 0.0037386 5892.85 <2e-16 ***
ORIGIN_SZTMSZ03 21.3451920 0.0040606 5256.65 <2e-16 ***
ORIGIN_SZTMSZ04 20.6611593 0.0049896 4140.87 <2e-16 ***
ORIGIN_SZTMSZ05 19.3323133 0.0112868 1712.82 <2e-16 ***
ORIGIN_SZTNSZ01 17.9513571 0.0128266 1399.54 <2e-16 ***
ORIGIN_SZTNSZ02 18.0267387 0.0098372 1832.51 <2e-16 ***
ORIGIN_SZTNSZ03 17.7253700 0.0134668 1316.23 <2e-16 ***
ORIGIN_SZTNSZ04 19.4474075 0.0073760 2636.59 <2e-16 ***
ORIGIN_SZTPSZ01 19.1078631 0.0065635 2911.25 <2e-16 ***
ORIGIN_SZTPSZ02 20.2837634 0.0041411 4898.18 <2e-16 ***
ORIGIN_SZTPSZ03 19.1838238 0.0059552 3221.37 <2e-16 ***
ORIGIN_SZTPSZ04 19.1805388 0.0054778 3501.53 <2e-16 ***
ORIGIN_SZTPSZ05 19.3718076 0.0058610 3305.18 <2e-16 ***
ORIGIN_SZTPSZ06 19.6605723 0.0054968 3576.70 <2e-16 ***
ORIGIN_SZTPSZ07 19.4499807 0.0060491 3215.36 <2e-16 ***
ORIGIN_SZTPSZ08 18.7996538 0.0095757 1963.28 <2e-16 ***
ORIGIN_SZTPSZ09 19.0025110 0.0067068 2833.31 <2e-16 ***
ORIGIN_SZTPSZ10 18.8899657 0.0076094 2482.46 <2e-16 ***
ORIGIN_SZTPSZ11 19.6277780 0.0053983 3635.93 <2e-16 ***
ORIGIN_SZTPSZ12 19.1471104 0.0065742 2912.45 <2e-16 ***
ORIGIN_SZTSSZ01 17.4901113 0.0478954 365.17 <2e-16 ***
ORIGIN_SZTSSZ02 20.4997466 0.0081850 2504.55 <2e-16 ***
ORIGIN_SZTSSZ03 20.1076553 0.0084728 2373.19 <2e-16 ***
ORIGIN_SZTSSZ04 20.0646610 0.0089008 2254.26 <2e-16 ***
ORIGIN_SZTSSZ05 19.3962067 0.0151392 1281.19 <2e-16 ***
ORIGIN_SZTSSZ06 20.9235857 0.0178278 1173.65 <2e-16 ***
ORIGIN_SZWCSZ01 20.8411600 0.0086519 2408.86 <2e-16 ***
ORIGIN_SZWCSZ02 17.7355404 0.0328889 539.26 <2e-16 ***
ORIGIN_SZWCSZ03 14.9380886 0.1240699 120.40 <2e-16 ***
ORIGIN_SZWDSZ01 21.1969012 0.0037830 5603.23 <2e-16 ***
ORIGIN_SZWDSZ02 20.5930001 0.0044572 4620.13 <2e-16 ***
ORIGIN_SZWDSZ03 21.2521867 0.0041672 5099.85 <2e-16 ***
ORIGIN_SZWDSZ04 21.0702687 0.0048648 4331.13 <2e-16 ***
ORIGIN_SZWDSZ05 20.4008998 0.0051801 3938.35 <2e-16 ***
ORIGIN_SZWDSZ06 20.6669176 0.0049280 4193.78 <2e-16 ***
ORIGIN_SZWDSZ07 19.0500370 0.0082729 2302.71 <2e-16 ***
ORIGIN_SZWDSZ08 19.0816252 0.0080667 2365.49 <2e-16 ***
ORIGIN_SZWDSZ09 21.4182096 0.0040391 5302.73 <2e-16 ***
ORIGIN_SZYSSZ01 19.5355157 0.0057540 3395.14 <2e-16 ***
ORIGIN_SZYSSZ02 20.8737972 0.0048278 4323.64 <2e-16 ***
ORIGIN_SZYSSZ03 21.6614437 0.0040011 5413.81 <2e-16 ***
ORIGIN_SZYSSZ04 20.9305289 0.0043595 4801.10 <2e-16 ***
ORIGIN_SZYSSZ05 20.1727678 0.0058466 3450.34 <2e-16 ***
ORIGIN_SZYSSZ06 19.1481507 0.0116724 1640.47 <2e-16 ***
ORIGIN_SZYSSZ07 18.7919074 0.0141636 1326.78 <2e-16 ***
ORIGIN_SZYSSZ08 19.9733515 0.0061229 3262.07 <2e-16 ***
ORIGIN_SZYSSZ09 20.9366181 0.0040347 5189.15 <2e-16 ***
log(SCHOOL_COUNT.x) 0.4755516 0.0004701 1011.55 <2e-16 ***
log(BUSINESS_COUNT) 0.1796905 0.0001856 968.12 <2e-16 ***
log(DIST) -1.6929522 0.0004093 -4136.01 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 189463537 on 14471 degrees of freedom
Residual deviance: 15526121 on 14189 degrees of freedom
AIC: 15615824
Number of Fisher Scoring iterations: 6
Tip
- For origin-constrained model, only explanatory variables representing the attractiveness at the destinations will be used.
- All the explanatory variables including distance will be log transformed.
- ORIGIN_SZ is used to model 𝜇𝑖 . It must be in categorical data type.
- It is important to note that -1 is added in the equation after the distance variable. The -1 serves the purpose of removing the intercept that by default, glm will insert into the model.
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + log(SCHOOL_COUNT.x) + log(BUSINESS_COUNT) +
log(DIST) - 1, family = poisson(link = "log"), data = inter_zonal_flow,
na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
ORIGIN_SZAMSZ01 19.8739840 0.0047627 4172.84 <2e-16 ***
ORIGIN_SZAMSZ02 20.5902203 0.0042786 4812.33 <2e-16 ***
ORIGIN_SZAMSZ03 20.2327026 0.0045531 4443.70 <2e-16 ***
ORIGIN_SZAMSZ04 19.7744438 0.0049837 3967.79 <2e-16 ***
ORIGIN_SZAMSZ05 19.6574529 0.0056396 3485.61 <2e-16 ***
ORIGIN_SZAMSZ06 19.9659115 0.0048946 4079.16 <2e-16 ***
ORIGIN_SZAMSZ07 18.6746164 0.0096316 1938.90 <2e-16 ***
ORIGIN_SZAMSZ08 19.2701601 0.0090776 2122.82 <2e-16 ***
ORIGIN_SZAMSZ09 19.9889467 0.0052858 3781.64 <2e-16 ***
ORIGIN_SZAMSZ10 20.3422035 0.0045778 4443.62 <2e-16 ***
ORIGIN_SZAMSZ11 18.3944113 0.0129212 1423.58 <2e-16 ***
ORIGIN_SZAMSZ12 18.3484209 0.0109652 1673.33 <2e-16 ***
ORIGIN_SZBDSZ01 20.9668587 0.0043388 4832.36 <2e-16 ***
ORIGIN_SZBDSZ02 20.4059518 0.0050601 4032.75 <2e-16 ***
ORIGIN_SZBDSZ03 20.6725514 0.0045276 4565.93 <2e-16 ***
ORIGIN_SZBDSZ04 21.6703853 0.0038930 5566.44 <2e-16 ***
ORIGIN_SZBDSZ05 20.7497445 0.0046085 4502.46 <2e-16 ***
ORIGIN_SZBDSZ06 20.9119361 0.0046432 4503.77 <2e-16 ***
ORIGIN_SZBDSZ07 18.9749815 0.0097896 1938.28 <2e-16 ***
ORIGIN_SZBDSZ08 19.1933901 0.0091312 2101.95 <2e-16 ***
ORIGIN_SZBKSZ01 19.5422606 0.0064732 3018.96 <2e-16 ***
ORIGIN_SZBKSZ02 20.1748913 0.0050076 4028.89 <2e-16 ***
ORIGIN_SZBKSZ03 20.3984624 0.0047226 4319.35 <2e-16 ***
ORIGIN_SZBKSZ04 19.6182212 0.0059652 3288.76 <2e-16 ***
ORIGIN_SZBKSZ05 19.6033818 0.0063181 3102.74 <2e-16 ***
ORIGIN_SZBKSZ06 19.7145224 0.0056372 3497.20 <2e-16 ***
ORIGIN_SZBKSZ07 20.4237448 0.0041912 4873.03 <2e-16 ***
ORIGIN_SZBKSZ08 19.7992538 0.0050405 3928.02 <2e-16 ***
ORIGIN_SZBKSZ09 19.7821586 0.0055558 3560.66 <2e-16 ***
ORIGIN_SZBLSZ01 17.7977276 0.0149058 1194.01 <2e-16 ***
ORIGIN_SZBLSZ02 17.4287491 0.0192364 906.03 <2e-16 ***
ORIGIN_SZBLSZ03 16.5884288 0.0459848 360.74 <2e-16 ***
ORIGIN_SZBLSZ04 17.7851626 0.0232823 763.89 <2e-16 ***
ORIGIN_SZBMSZ01 20.0751840 0.0052887 3795.89 <2e-16 ***
ORIGIN_SZBMSZ02 18.6956140 0.0066656 2804.80 <2e-16 ***
ORIGIN_SZBMSZ03 19.3204425 0.0054755 3528.56 <2e-16 ***
ORIGIN_SZBMSZ04 19.4724220 0.0049390 3942.59 <2e-16 ***
ORIGIN_SZBMSZ05 16.9581801 0.0168804 1004.61 <2e-16 ***
ORIGIN_SZBMSZ06 16.9898638 0.0181852 934.27 <2e-16 ***
ORIGIN_SZBMSZ07 19.2868403 0.0056231 3429.91 <2e-16 ***
ORIGIN_SZBMSZ08 19.1477543 0.0055918 3424.28 <2e-16 ***
ORIGIN_SZBMSZ09 18.7564539 0.0086298 2173.46 <2e-16 ***
ORIGIN_SZBMSZ10 18.3617854 0.0089250 2057.35 <2e-16 ***
ORIGIN_SZBMSZ11 18.9167941 0.0063340 2986.54 <2e-16 ***
ORIGIN_SZBMSZ12 18.7874661 0.0093024 2019.63 <2e-16 ***
ORIGIN_SZBMSZ13 19.5654046 0.0057517 3401.70 <2e-16 ***
ORIGIN_SZBMSZ14 19.0685619 0.0063346 3010.24 <2e-16 ***
ORIGIN_SZBMSZ15 19.4403124 0.0058147 3343.30 <2e-16 ***
ORIGIN_SZBMSZ16 18.4469203 0.0092638 1991.28 <2e-16 ***
ORIGIN_SZBMSZ17 18.3430175 0.0157692 1163.22 <2e-16 ***
ORIGIN_SZBPSZ01 20.1806714 0.0053660 3760.81 <2e-16 ***
ORIGIN_SZBPSZ02 19.8116707 0.0061485 3222.19 <2e-16 ***
ORIGIN_SZBPSZ03 19.8467602 0.0059769 3320.57 <2e-16 ***
ORIGIN_SZBPSZ04 20.4613200 0.0048398 4227.72 <2e-16 ***
ORIGIN_SZBPSZ05 20.5379711 0.0043769 4692.39 <2e-16 ***
ORIGIN_SZBPSZ06 18.8948034 0.0093668 2017.21 <2e-16 ***
ORIGIN_SZBPSZ07 19.4104568 0.0087961 2206.70 <2e-16 ***
ORIGIN_SZBSSZ01 20.0139503 0.0056561 3538.45 <2e-16 ***
ORIGIN_SZBSSZ02 20.2543885 0.0047198 4291.38 <2e-16 ***
ORIGIN_SZBSSZ03 19.5428803 0.0052713 3707.41 <2e-16 ***
ORIGIN_SZBTSZ01 20.0198045 0.0058541 3419.77 <2e-16 ***
ORIGIN_SZBTSZ02 19.3618525 0.0081472 2376.51 <2e-16 ***
ORIGIN_SZBTSZ03 19.5883853 0.0068935 2841.59 <2e-16 ***
ORIGIN_SZBTSZ04 18.7720238 0.0103909 1806.58 <2e-16 ***
ORIGIN_SZBTSZ05 18.8069026 0.0120628 1559.08 <2e-16 ***
ORIGIN_SZBTSZ06 18.7068633 0.0094575 1978.00 <2e-16 ***
ORIGIN_SZBTSZ07 17.6292257 0.0141551 1245.43 <2e-16 ***
ORIGIN_SZBTSZ08 18.6989374 0.0109610 1705.94 <2e-16 ***
ORIGIN_SZCBSZ01 18.2189868 0.0548317 332.27 <2e-16 ***
ORIGIN_SZCCSZ01 18.9734563 0.0139450 1360.59 <2e-16 ***
ORIGIN_SZCHSZ01 19.5955119 0.0121035 1619.00 <2e-16 ***
ORIGIN_SZCHSZ02 19.3320960 0.0081620 2368.55 <2e-16 ***
ORIGIN_SZCHSZ03 21.2164518 0.0063552 3338.43 <2e-16 ***
ORIGIN_SZCKSZ01 20.1046845 0.0049333 4075.29 <2e-16 ***
ORIGIN_SZCKSZ02 20.5371946 0.0050256 4086.53 <2e-16 ***
ORIGIN_SZCKSZ03 20.7210560 0.0042184 4912.07 <2e-16 ***
ORIGIN_SZCKSZ04 21.4013886 0.0042524 5032.80 <2e-16 ***
ORIGIN_SZCKSZ05 20.9413146 0.0049434 4236.18 <2e-16 ***
ORIGIN_SZCKSZ06 20.2557727 0.0071832 2819.88 <2e-16 ***
ORIGIN_SZCLSZ01 19.3383703 0.0076634 2523.46 <2e-16 ***
ORIGIN_SZCLSZ02 18.5226956 0.0135522 1366.77 <2e-16 ***
ORIGIN_SZCLSZ03 19.0225512 0.0080145 2373.51 <2e-16 ***
ORIGIN_SZCLSZ04 20.7981505 0.0042400 4905.22 <2e-16 ***
ORIGIN_SZCLSZ05 18.3015625 0.0146815 1246.58 <2e-16 ***
ORIGIN_SZCLSZ06 20.8207386 0.0039567 5262.09 <2e-16 ***
ORIGIN_SZCLSZ07 19.6728958 0.0054199 3629.76 <2e-16 ***
ORIGIN_SZCLSZ08 20.0851929 0.0056956 3526.43 <2e-16 ***
ORIGIN_SZCLSZ09 18.5749589 0.0165415 1122.93 <2e-16 ***
ORIGIN_SZDTSZ02 15.8276209 0.0833992 189.78 <2e-16 ***
ORIGIN_SZDTSZ03 16.2512838 0.0737972 220.22 <2e-16 ***
ORIGIN_SZDTSZ13 16.7744385 0.0312450 536.87 <2e-16 ***
ORIGIN_SZGLSZ01 18.2368248 0.0096104 1897.62 <2e-16 ***
ORIGIN_SZGLSZ02 19.8705255 0.0049014 4054.06 <2e-16 ***
ORIGIN_SZGLSZ03 19.8249435 0.0053109 3732.85 <2e-16 ***
ORIGIN_SZGLSZ04 20.7800335 0.0041261 5036.20 <2e-16 ***
ORIGIN_SZGLSZ05 20.6040494 0.0043049 4786.23 <2e-16 ***
ORIGIN_SZHGSZ01 20.0273475 0.0044824 4468.04 <2e-16 ***
ORIGIN_SZHGSZ02 20.2480656 0.0044575 4542.47 <2e-16 ***
ORIGIN_SZHGSZ03 20.0756442 0.0049003 4096.81 <2e-16 ***
ORIGIN_SZHGSZ04 20.7577748 0.0040465 5129.84 <2e-16 ***
ORIGIN_SZHGSZ05 20.9779992 0.0040123 5228.42 <2e-16 ***
ORIGIN_SZHGSZ06 19.7403058 0.0054229 3640.20 <2e-16 ***
ORIGIN_SZHGSZ07 20.1896268 0.0046051 4384.22 <2e-16 ***
ORIGIN_SZHGSZ08 19.8646492 0.0052403 3790.72 <2e-16 ***
ORIGIN_SZHGSZ09 18.3647736 0.0069196 2654.04 <2e-16 ***
ORIGIN_SZHGSZ10 16.8720475 0.0421046 400.72 <2e-16 ***
ORIGIN_SZJESZ01 20.2673794 0.0046723 4337.79 <2e-16 ***
ORIGIN_SZJESZ02 20.0595982 0.0046503 4313.61 <2e-16 ***
ORIGIN_SZJESZ03 19.9128778 0.0049848 3994.75 <2e-16 ***
ORIGIN_SZJESZ04 18.5053667 0.0099227 1864.94 <2e-16 ***
ORIGIN_SZJESZ05 17.8172930 0.0138840 1283.29 <2e-16 ***
ORIGIN_SZJESZ06 20.0124157 0.0045009 4446.36 <2e-16 ***
ORIGIN_SZJESZ07 18.1821423 0.0117267 1550.49 <2e-16 ***
ORIGIN_SZJESZ08 18.8713046 0.0116456 1620.46 <2e-16 ***
ORIGIN_SZJESZ09 20.5535527 0.0048456 4241.72 <2e-16 ***
ORIGIN_SZJESZ10 18.4922322 0.0191243 966.95 <2e-16 ***
ORIGIN_SZJESZ11 18.2891211 0.0197114 927.85 <2e-16 ***
ORIGIN_SZJWSZ01 20.4912737 0.0063102 3247.35 <2e-16 ***
ORIGIN_SZJWSZ02 20.8236694 0.0042249 4928.82 <2e-16 ***
ORIGIN_SZJWSZ03 21.2587613 0.0039733 5350.40 <2e-16 ***
ORIGIN_SZJWSZ04 20.3816464 0.0046199 4411.67 <2e-16 ***
ORIGIN_SZJWSZ05 18.0607448 0.0128857 1401.61 <2e-16 ***
ORIGIN_SZJWSZ06 18.7015202 0.0107614 1737.83 <2e-16 ***
ORIGIN_SZJWSZ07 17.3991822 0.0277096 627.91 <2e-16 ***
ORIGIN_SZJWSZ08 21.8044465 0.0037356 5836.95 <2e-16 ***
ORIGIN_SZJWSZ09 21.5414930 0.0036033 5978.19 <2e-16 ***
ORIGIN_SZKLSZ01 20.0307712 0.0047868 4184.59 <2e-16 ***
ORIGIN_SZKLSZ02 19.0634769 0.0062318 3059.05 <2e-16 ***
ORIGIN_SZKLSZ03 19.2685700 0.0057172 3370.25 <2e-16 ***
ORIGIN_SZKLSZ04 17.7085067 0.0119809 1478.06 <2e-16 ***
ORIGIN_SZKLSZ05 18.6384471 0.0107596 1732.26 <2e-16 ***
ORIGIN_SZKLSZ06 13.7280296 0.1857160 73.92 <2e-16 ***
ORIGIN_SZKLSZ07 18.6425146 0.0084952 2194.47 <2e-16 ***
ORIGIN_SZKLSZ08 18.0928506 0.0101567 1781.37 <2e-16 ***
ORIGIN_SZLKSZ01 17.8907138 0.0397083 450.55 <2e-16 ***
ORIGIN_SZMDSZ01 18.7605188 0.0285455 657.22 <2e-16 ***
ORIGIN_SZMDSZ02 19.1533927 0.0102815 1862.90 <2e-16 ***
ORIGIN_SZMDSZ03 17.8404982 0.0169690 1051.36 <2e-16 ***
ORIGIN_SZMPSZ01 19.0765941 0.0083937 2272.74 <2e-16 ***
ORIGIN_SZMPSZ02 19.2162527 0.0068331 2812.24 <2e-16 ***
ORIGIN_SZMPSZ03 19.9965344 0.0054569 3664.44 <2e-16 ***
ORIGIN_SZMUSZ02 15.9130765 0.1037472 153.38 <2e-16 ***
ORIGIN_SZNTSZ01 17.0840999 0.0352513 484.64 <2e-16 ***
ORIGIN_SZNTSZ02 16.5792122 0.0233186 710.99 <2e-16 ***
ORIGIN_SZNTSZ03 18.9506415 0.0075957 2494.93 <2e-16 ***
ORIGIN_SZNTSZ05 15.8770261 0.0495825 320.21 <2e-16 ***
ORIGIN_SZNTSZ06 15.3997415 0.0557029 276.46 <2e-16 ***
ORIGIN_SZNVSZ01 20.2241694 0.0043487 4650.65 <2e-16 ***
ORIGIN_SZNVSZ02 19.1897826 0.0065383 2934.97 <2e-16 ***
ORIGIN_SZNVSZ03 18.8854268 0.0080459 2347.22 <2e-16 ***
ORIGIN_SZNVSZ04 18.8940191 0.0090985 2076.61 <2e-16 ***
ORIGIN_SZNVSZ05 17.6278585 0.0168107 1048.61 <2e-16 ***
ORIGIN_SZPGSZ01 19.4825220 0.0122960 1584.46 <2e-16 ***
ORIGIN_SZPGSZ02 19.4726761 0.0073116 2663.25 <2e-16 ***
ORIGIN_SZPGSZ03 20.5515713 0.0045631 4503.86 <2e-16 ***
ORIGIN_SZPGSZ04 21.0527131 0.0041500 5072.89 <2e-16 ***
ORIGIN_SZPGSZ05 20.1436604 0.0057267 3517.48 <2e-16 ***
ORIGIN_SZPLSZ01 19.1832002 0.0120006 1598.53 <2e-16 ***
ORIGIN_SZPLSZ02 18.8752206 0.0149740 1260.53 <2e-16 ***
ORIGIN_SZPLSZ03 18.1000818 0.0371769 486.86 <2e-16 ***
ORIGIN_SZPLSZ04 17.1730559 0.0370280 463.79 <2e-16 ***
ORIGIN_SZPLSZ05 17.9084439 0.0225031 795.82 <2e-16 ***
ORIGIN_SZPNSZ01 21.0804425 0.0044829 4702.41 <2e-16 ***
ORIGIN_SZPNSZ02 19.8822123 0.0111507 1783.05 <2e-16 ***
ORIGIN_SZPNSZ03 17.9293289 0.0193571 926.24 <2e-16 ***
ORIGIN_SZPNSZ04 17.1039594 0.0334954 510.64 <2e-16 ***
ORIGIN_SZPNSZ05 18.2543864 0.0275554 662.46 <2e-16 ***
ORIGIN_SZPRSZ01 19.8777935 0.0117586 1690.49 <2e-16 ***
ORIGIN_SZPRSZ02 21.0751780 0.0044832 4700.88 <2e-16 ***
ORIGIN_SZPRSZ03 20.6717019 0.0045577 4535.55 <2e-16 ***
ORIGIN_SZPRSZ04 19.6365125 0.0074923 2620.90 <2e-16 ***
ORIGIN_SZPRSZ05 21.3132151 0.0042119 5060.24 <2e-16 ***
ORIGIN_SZPRSZ06 18.9314574 0.0117278 1614.24 <2e-16 ***
ORIGIN_SZPRSZ07 17.2822918 0.0162430 1063.98 <2e-16 ***
ORIGIN_SZPRSZ08 19.9267642 0.0062298 3198.62 <2e-16 ***
ORIGIN_SZQTSZ01 19.7357175 0.0066359 2974.08 <2e-16 ***
ORIGIN_SZQTSZ02 19.2082141 0.0061402 3128.26 <2e-16 ***
ORIGIN_SZQTSZ03 19.7771883 0.0056220 3517.83 <2e-16 ***
ORIGIN_SZQTSZ04 18.7114421 0.0072842 2568.76 <2e-16 ***
ORIGIN_SZQTSZ05 19.3049324 0.0062401 3093.69 <2e-16 ***
ORIGIN_SZQTSZ06 19.2643228 0.0065590 2937.09 <2e-16 ***
ORIGIN_SZQTSZ07 18.5697347 0.0095373 1947.06 <2e-16 ***
ORIGIN_SZQTSZ08 19.6147001 0.0061330 3198.21 <2e-16 ***
ORIGIN_SZQTSZ09 19.2550793 0.0069947 2752.82 <2e-16 ***
ORIGIN_SZQTSZ10 19.5801866 0.0064513 3035.07 <2e-16 ***
ORIGIN_SZQTSZ11 17.7398366 0.0143648 1234.95 <2e-16 ***
ORIGIN_SZQTSZ12 17.2420354 0.0186736 923.34 <2e-16 ***
ORIGIN_SZQTSZ13 19.3857418 0.0078878 2457.69 <2e-16 ***
ORIGIN_SZQTSZ14 18.1300753 0.0122096 1484.90 <2e-16 ***
ORIGIN_SZQTSZ15 19.4222283 0.0120871 1606.86 <2e-16 ***
ORIGIN_SZRCSZ01 18.1549045 0.0125108 1451.13 <2e-16 ***
ORIGIN_SZRCSZ06 18.8836400 0.0082161 2298.38 <2e-16 ***
ORIGIN_SZRVSZ01 16.7864438 0.0323796 518.43 <2e-16 ***
ORIGIN_SZRVSZ02 16.4203244 0.0276836 593.14 <2e-16 ***
ORIGIN_SZRVSZ03 16.6453738 0.0244992 679.42 <2e-16 ***
ORIGIN_SZRVSZ04 15.9559213 0.0556344 286.80 <2e-16 ***
ORIGIN_SZRVSZ05 17.0476331 0.0164122 1038.71 <2e-16 ***
ORIGIN_SZSBSZ01 20.0417968 0.0062488 3207.29 <2e-16 ***
ORIGIN_SZSBSZ02 19.1869565 0.0081051 2367.26 <2e-16 ***
ORIGIN_SZSBSZ03 20.5769861 0.0045108 4561.70 <2e-16 ***
ORIGIN_SZSBSZ04 20.5154199 0.0050548 4058.57 <2e-16 ***
ORIGIN_SZSBSZ05 19.6250669 0.0065562 2993.35 <2e-16 ***
ORIGIN_SZSBSZ06 18.8419757 0.0171135 1101.00 <2e-16 ***
ORIGIN_SZSBSZ07 19.4897259 0.0124528 1565.09 <2e-16 ***
ORIGIN_SZSBSZ08 18.7027917 0.0140545 1330.73 <2e-16 ***
ORIGIN_SZSBSZ09 18.8893480 0.0088571 2132.67 <2e-16 ***
ORIGIN_SZSESZ02 20.8962192 0.0041665 5015.34 <2e-16 ***
ORIGIN_SZSESZ03 20.9452771 0.0039737 5270.94 <2e-16 ***
ORIGIN_SZSESZ04 20.6576142 0.0046364 4455.55 <2e-16 ***
ORIGIN_SZSESZ05 19.5170732 0.0058912 3312.92 <2e-16 ***
ORIGIN_SZSESZ06 20.7595824 0.0045747 4537.89 <2e-16 ***
ORIGIN_SZSESZ07 17.6888256 0.0195787 903.47 <2e-16 ***
ORIGIN_SZSGSZ01 19.1359250 0.0085781 2230.79 <2e-16 ***
ORIGIN_SZSGSZ02 18.5614369 0.0102037 1819.10 <2e-16 ***
ORIGIN_SZSGSZ03 19.9933176 0.0050434 3964.23 <2e-16 ***
ORIGIN_SZSGSZ04 20.2426871 0.0047211 4287.71 <2e-16 ***
ORIGIN_SZSGSZ05 18.0114965 0.0107743 1671.70 <2e-16 ***
ORIGIN_SZSGSZ06 20.2593194 0.0044538 4548.76 <2e-16 ***
ORIGIN_SZSGSZ07 19.0763664 0.0062968 3029.54 <2e-16 ***
ORIGIN_SZSKSZ01 19.9222451 0.0085136 2340.04 <2e-16 ***
ORIGIN_SZSKSZ02 20.8633383 0.0055248 3776.33 <2e-16 ***
ORIGIN_SZSKSZ03 19.6528148 0.0080534 2440.33 <2e-16 ***
ORIGIN_SZSKSZ04 18.0754470 0.0275771 655.45 <2e-16 ***
ORIGIN_SZSKSZ05 19.1192521 0.0155579 1228.91 <2e-16 ***
ORIGIN_SZSLSZ01 17.1501034 0.0329384 520.67 <2e-16 ***
ORIGIN_SZSLSZ04 19.5949774 0.0076753 2552.98 <2e-16 ***
ORIGIN_SZSRSZ01 16.9761403 0.0162020 1047.78 <2e-16 ***
ORIGIN_SZTHSZ01 17.9695687 0.0488559 367.81 <2e-16 ***
ORIGIN_SZTHSZ03 18.5427522 0.0223617 829.22 <2e-16 ***
ORIGIN_SZTHSZ04 17.4760374 0.0286247 610.52 <2e-16 ***
ORIGIN_SZTHSZ06 17.8401186 0.0183322 973.16 <2e-16 ***
ORIGIN_SZTMSZ01 20.3406361 0.0056607 3593.33 <2e-16 ***
ORIGIN_SZTMSZ02 22.0307026 0.0037386 5892.85 <2e-16 ***
ORIGIN_SZTMSZ03 21.3451920 0.0040606 5256.65 <2e-16 ***
ORIGIN_SZTMSZ04 20.6611593 0.0049896 4140.87 <2e-16 ***
ORIGIN_SZTMSZ05 19.3323133 0.0112868 1712.82 <2e-16 ***
ORIGIN_SZTNSZ01 17.9513571 0.0128266 1399.54 <2e-16 ***
ORIGIN_SZTNSZ02 18.0267387 0.0098372 1832.51 <2e-16 ***
ORIGIN_SZTNSZ03 17.7253700 0.0134668 1316.23 <2e-16 ***
ORIGIN_SZTNSZ04 19.4474075 0.0073760 2636.59 <2e-16 ***
ORIGIN_SZTPSZ01 19.1078631 0.0065635 2911.25 <2e-16 ***
ORIGIN_SZTPSZ02 20.2837634 0.0041411 4898.18 <2e-16 ***
ORIGIN_SZTPSZ03 19.1838238 0.0059552 3221.37 <2e-16 ***
ORIGIN_SZTPSZ04 19.1805388 0.0054778 3501.53 <2e-16 ***
ORIGIN_SZTPSZ05 19.3718076 0.0058610 3305.18 <2e-16 ***
ORIGIN_SZTPSZ06 19.6605723 0.0054968 3576.70 <2e-16 ***
ORIGIN_SZTPSZ07 19.4499807 0.0060491 3215.36 <2e-16 ***
ORIGIN_SZTPSZ08 18.7996538 0.0095757 1963.28 <2e-16 ***
ORIGIN_SZTPSZ09 19.0025110 0.0067068 2833.31 <2e-16 ***
ORIGIN_SZTPSZ10 18.8899657 0.0076094 2482.46 <2e-16 ***
ORIGIN_SZTPSZ11 19.6277780 0.0053983 3635.93 <2e-16 ***
ORIGIN_SZTPSZ12 19.1471104 0.0065742 2912.45 <2e-16 ***
ORIGIN_SZTSSZ01 17.4901113 0.0478954 365.17 <2e-16 ***
ORIGIN_SZTSSZ02 20.4997466 0.0081850 2504.55 <2e-16 ***
ORIGIN_SZTSSZ03 20.1076553 0.0084728 2373.19 <2e-16 ***
ORIGIN_SZTSSZ04 20.0646610 0.0089008 2254.26 <2e-16 ***
ORIGIN_SZTSSZ05 19.3962067 0.0151392 1281.19 <2e-16 ***
ORIGIN_SZTSSZ06 20.9235857 0.0178278 1173.65 <2e-16 ***
ORIGIN_SZWCSZ01 20.8411600 0.0086519 2408.86 <2e-16 ***
ORIGIN_SZWCSZ02 17.7355404 0.0328889 539.26 <2e-16 ***
ORIGIN_SZWCSZ03 14.9380886 0.1240699 120.40 <2e-16 ***
ORIGIN_SZWDSZ01 21.1969012 0.0037830 5603.23 <2e-16 ***
ORIGIN_SZWDSZ02 20.5930001 0.0044572 4620.13 <2e-16 ***
ORIGIN_SZWDSZ03 21.2521867 0.0041672 5099.85 <2e-16 ***
ORIGIN_SZWDSZ04 21.0702687 0.0048648 4331.13 <2e-16 ***
ORIGIN_SZWDSZ05 20.4008998 0.0051801 3938.35 <2e-16 ***
ORIGIN_SZWDSZ06 20.6669176 0.0049280 4193.78 <2e-16 ***
ORIGIN_SZWDSZ07 19.0500370 0.0082729 2302.71 <2e-16 ***
ORIGIN_SZWDSZ08 19.0816252 0.0080667 2365.49 <2e-16 ***
ORIGIN_SZWDSZ09 21.4182096 0.0040391 5302.73 <2e-16 ***
ORIGIN_SZYSSZ01 19.5355157 0.0057540 3395.14 <2e-16 ***
ORIGIN_SZYSSZ02 20.8737972 0.0048278 4323.64 <2e-16 ***
ORIGIN_SZYSSZ03 21.6614437 0.0040011 5413.81 <2e-16 ***
ORIGIN_SZYSSZ04 20.9305289 0.0043595 4801.10 <2e-16 ***
ORIGIN_SZYSSZ05 20.1727678 0.0058466 3450.34 <2e-16 ***
ORIGIN_SZYSSZ06 19.1481507 0.0116724 1640.47 <2e-16 ***
ORIGIN_SZYSSZ07 18.7919074 0.0141636 1326.78 <2e-16 ***
ORIGIN_SZYSSZ08 19.9733515 0.0061229 3262.07 <2e-16 ***
ORIGIN_SZYSSZ09 20.9366181 0.0040347 5189.15 <2e-16 ***
log(SCHOOL_COUNT.x) 0.4755516 0.0004701 1011.55 <2e-16 ***
log(BUSINESS_COUNT) 0.1796905 0.0001856 968.12 <2e-16 ***
log(DIST) -1.6929522 0.0004093 -4136.01 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 189463537 on 14471 degrees of freedom
Residual deviance: 15526121 on 14189 degrees of freedom
AIC: 15615824
Number of Fisher Scoring iterations: 6
Functions
- glm from stats package fits generalized linear models. In this code, a Poisson regression model is specified with the
family = poisson(link = "log")argument. The formulaTRIPS ~ ORIGIN_SZ + log(SCHOOL_COUNT.x) + log(BUSINESS_COUNT) + log(DIST) - 1defines the dependent variable (TRIPS) and the independent variables (ORIGIN_SZ, logarithm ofSCHOOL_COUNT.x,BUSINESS_COUNT, andDIST), with-1indicating no intercept in the model. - The
dataargument specifiesinter_zonal_flowas the dataset used for the model. na.action = na.excludespecifies how missing values (NAs) should be treated in the analysis.- summary from base R provides a summary of the fitted model
orcSIM_Poisson, including coefficients, statistical significance, and other diagnostic measures.
Tip
the ⍺1 and ⍺2 of SCHOOL_COUNT and BUSINESS_COUNT are 0.4755516 and 0.1796905 respectively.
𝛽, the distance decay parameter is -1.6929522
there are a series of parameters which are the vector of 𝜇𝑖 values associated with the origin constraints.
2.4.2 Goodness of fit
In statistical modelling, the next question we would like to answer is how well the proportion of variance in the dependent variable (i.e. TRIPS) that can be explained by the explanatory variables.
In order to provide answer to this question, R-squared statistics will be used. However, R-squared is not an output of glm(). Hence we will write a function called CalcRSquared by using the code chunk below.
Code
CalcRSquared <- function(observed, estimated){
r <- cor(observed, estimated)
R2 <- r^2
R2
}
Functions
- cor from stats package calculates the correlation coefficient between two vectors. In this user-defined function
CalcRSquared, it is used to find the correlation (r) betweenobservedandestimatedvalues. - The function
CalcRSquaredcomputes the square of the correlation coefficient (R2), which is a measure of the proportion of variance in the observed data that is predictable from the estimated data. - This custom function is designed to return the value of
R2, providing a simple way to calculate the coefficient of determination (R-squared) for a set of observed and estimated values.
Now, we can examine how the constraints hold for destinations this time.
Code
CalcRSquared(orcSIM_Poisson$data$TRIPS, orcSIM_Poisson$fitted.values)[1] 0.4362208
Functions
- The custom function
CalcRSquared, defined earlier, is used here to calculate the coefficient of determination (R-squared). This statistical measure indicates how well the estimated values (orcSIM_Poisson$fitted.values) approximate the actual, observed values (orcSIM_Poisson$data$TRIPS). - In this code,
orcSIM_Poisson$data$TRIPSrefers to the actual observed values of trips, andorcSIM_Poisson$fitted.valuesrefers to the values estimated by theorcSIM_Poissongeneralized linear model. - The function call
CalcRSquared(orcSIM_Poisson$data$TRIPS, orcSIM_Poisson$fitted.values)computes the R-squared value, which quantifies the proportion of variance in the observed data that can be explained by the model’s estimated values.
With reference to the R-Squared above, we can conclude that the model accounts for about 44% of the variation of flows in the systems. Not bad, but not brilliant either.
2.4.3 Doubly constrained model
In this section, we will fit a doubly constrained SIM
Code
dbcSIM_Poisson <- glm(formula = TRIPS ~
ORIGIN_SZ +
DESTIN_SZ +
log(DIST),
family = poisson(link = "log"),
data = inter_zonal_flow,
na.action = na.exclude)
summary(dbcSIM_Poisson)
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(DIST), family = poisson(link = "log"),
data = inter_zonal_flow, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 21.8312374 0.0059160 3690.190 < 2e-16 ***
ORIGIN_SZAMSZ02 0.5263502 0.0048031 109.585 < 2e-16 ***
ORIGIN_SZAMSZ03 0.3139982 0.0049254 63.751 < 2e-16 ***
ORIGIN_SZAMSZ04 -0.2146257 0.0053639 -40.013 < 2e-16 ***
ORIGIN_SZAMSZ05 -0.1890446 0.0060386 -31.306 < 2e-16 ***
ORIGIN_SZAMSZ06 0.1539201 0.0054401 28.294 < 2e-16 ***
ORIGIN_SZAMSZ07 -0.9826565 0.0098676 -99.584 < 2e-16 ***
ORIGIN_SZAMSZ08 -0.4488417 0.0093070 -48.226 < 2e-16 ***
ORIGIN_SZAMSZ09 0.0713474 0.0057402 12.429 < 2e-16 ***
ORIGIN_SZAMSZ10 0.4313742 0.0050370 85.641 < 2e-16 ***
ORIGIN_SZAMSZ11 -1.4712226 0.0131178 -112.154 < 2e-16 ***
ORIGIN_SZAMSZ12 -1.7250733 0.0111603 -154.573 < 2e-16 ***
ORIGIN_SZBDSZ01 0.8810576 0.0048168 182.914 < 2e-16 ***
ORIGIN_SZBDSZ02 0.1100240 0.0055529 19.814 < 2e-16 ***
ORIGIN_SZBDSZ03 0.3606166 0.0050672 71.167 < 2e-16 ***
ORIGIN_SZBDSZ04 1.4624347 0.0044212 330.781 < 2e-16 ***
ORIGIN_SZBDSZ05 0.6207557 0.0050843 122.092 < 2e-16 ***
ORIGIN_SZBDSZ06 0.6712973 0.0051953 129.214 < 2e-16 ***
ORIGIN_SZBDSZ07 -1.2338669 0.0100775 -122.437 < 2e-16 ***
ORIGIN_SZBDSZ08 -1.0444562 0.0094555 -110.460 < 2e-16 ***
ORIGIN_SZBKSZ01 -0.2838426 0.0071354 -39.780 < 2e-16 ***
ORIGIN_SZBKSZ02 0.5550522 0.0059014 94.054 < 2e-16 ***
ORIGIN_SZBKSZ03 0.7396640 0.0056796 130.231 < 2e-16 ***
ORIGIN_SZBKSZ04 -0.2242451 0.0067482 -33.230 < 2e-16 ***
ORIGIN_SZBKSZ05 -0.2371614 0.0069386 -34.180 < 2e-16 ***
ORIGIN_SZBKSZ06 -0.1413812 0.0065035 -21.739 < 2e-16 ***
ORIGIN_SZBKSZ07 0.7089989 0.0051843 136.758 < 2e-16 ***
ORIGIN_SZBKSZ08 -0.0907065 0.0059157 -15.333 < 2e-16 ***
ORIGIN_SZBKSZ09 -0.1775146 0.0063302 -28.042 < 2e-16 ***
ORIGIN_SZBLSZ01 -2.3684539 0.0154280 -153.516 < 2e-16 ***
ORIGIN_SZBLSZ02 -2.8078475 0.0197839 -141.926 < 2e-16 ***
ORIGIN_SZBLSZ03 -3.3122763 0.0466091 -71.065 < 2e-16 ***
ORIGIN_SZBLSZ04 -2.6770542 0.0241793 -110.717 < 2e-16 ***
ORIGIN_SZBMSZ01 0.0618035 0.0059400 10.405 < 2e-16 ***
ORIGIN_SZBMSZ02 -1.3535767 0.0073741 -183.557 < 2e-16 ***
ORIGIN_SZBMSZ03 -0.7569095 0.0063187 -119.790 < 2e-16 ***
ORIGIN_SZBMSZ04 -0.2949304 0.0059603 -49.483 < 2e-16 ***
ORIGIN_SZBMSZ05 -2.6131992 0.0172376 -151.599 < 2e-16 ***
ORIGIN_SZBMSZ06 -3.0315024 0.0185502 -163.422 < 2e-16 ***
ORIGIN_SZBMSZ07 -0.6962524 0.0064068 -108.674 < 2e-16 ***
ORIGIN_SZBMSZ08 -0.9310730 0.0064541 -144.261 < 2e-16 ***
ORIGIN_SZBMSZ09 -1.2911253 0.0092047 -140.268 < 2e-16 ***
ORIGIN_SZBMSZ10 -1.6687004 0.0095708 -174.353 < 2e-16 ***
ORIGIN_SZBMSZ11 -1.1152794 0.0072027 -154.841 < 2e-16 ***
ORIGIN_SZBMSZ12 -1.5323954 0.0099932 -153.344 < 2e-16 ***
ORIGIN_SZBMSZ13 -0.6267376 0.0065863 -95.158 < 2e-16 ***
ORIGIN_SZBMSZ14 -1.0475467 0.0072472 -144.544 < 2e-16 ***
ORIGIN_SZBMSZ15 -0.5049444 0.0067390 -74.929 < 2e-16 ***
ORIGIN_SZBMSZ16 -1.5282897 0.0099545 -153.527 < 2e-16 ***
ORIGIN_SZBMSZ17 -1.5722349 0.0161533 -97.332 < 2e-16 ***
ORIGIN_SZBPSZ01 0.5814175 0.0062904 92.429 < 2e-16 ***
ORIGIN_SZBPSZ02 0.0875442 0.0072190 12.127 < 2e-16 ***
ORIGIN_SZBPSZ03 0.3358227 0.0070460 47.662 < 2e-16 ***
ORIGIN_SZBPSZ04 0.6507586 0.0057726 112.733 < 2e-16 ***
ORIGIN_SZBPSZ05 0.9502124 0.0052971 179.384 < 2e-16 ***
ORIGIN_SZBPSZ06 -1.0480314 0.0098191 -106.734 < 2e-16 ***
ORIGIN_SZBPSZ07 -0.5467931 0.0091676 -59.644 < 2e-16 ***
ORIGIN_SZBSSZ01 0.2998334 0.0059193 50.654 < 2e-16 ***
ORIGIN_SZBSSZ02 0.2841036 0.0050863 55.856 < 2e-16 ***
ORIGIN_SZBSSZ03 -0.2331505 0.0056565 -41.218 < 2e-16 ***
ORIGIN_SZBTSZ01 0.0987284 0.0063715 15.495 < 2e-16 ***
ORIGIN_SZBTSZ02 -0.6261229 0.0084604 -74.006 < 2e-16 ***
ORIGIN_SZBTSZ03 -0.4326963 0.0073452 -58.909 < 2e-16 ***
ORIGIN_SZBTSZ04 -1.4998668 0.0110013 -136.336 < 2e-16 ***
ORIGIN_SZBTSZ05 -0.9564768 0.0122202 -78.270 < 2e-16 ***
ORIGIN_SZBTSZ06 -1.2853131 0.0099328 -129.401 < 2e-16 ***
ORIGIN_SZBTSZ07 -2.3870991 0.0144589 -165.096 < 2e-16 ***
ORIGIN_SZBTSZ08 -1.3715855 0.0113825 -120.499 < 2e-16 ***
ORIGIN_SZCBSZ01 -3.5940232 0.0548979 -65.467 < 2e-16 ***
ORIGIN_SZCCSZ01 -0.7008220 0.0140373 -49.926 < 2e-16 ***
ORIGIN_SZCHSZ01 -0.9109524 0.0122869 -74.140 < 2e-16 ***
ORIGIN_SZCHSZ02 -0.8566547 0.0088749 -96.526 < 2e-16 ***
ORIGIN_SZCHSZ03 1.1153731 0.0066136 168.650 < 2e-16 ***
ORIGIN_SZCKSZ01 0.3001815 0.0058548 51.271 < 2e-16 ***
ORIGIN_SZCKSZ02 0.7185711 0.0060595 118.585 < 2e-16 ***
ORIGIN_SZCKSZ03 1.1389824 0.0053179 214.178 < 2e-16 ***
ORIGIN_SZCKSZ04 1.6281772 0.0054761 297.324 < 2e-16 ***
ORIGIN_SZCKSZ05 0.8338470 0.0064178 129.927 < 2e-16 ***
ORIGIN_SZCKSZ06 0.6528993 0.0082375 79.259 < 2e-16 ***
ORIGIN_SZCLSZ01 -0.7174758 0.0082123 -87.366 < 2e-16 ***
ORIGIN_SZCLSZ02 -1.7513100 0.0139062 -125.938 < 2e-16 ***
ORIGIN_SZCLSZ03 -1.0362873 0.0085485 -121.224 < 2e-16 ***
ORIGIN_SZCLSZ04 0.6160017 0.0051276 120.136 < 2e-16 ***
ORIGIN_SZCLSZ05 -2.1005122 0.0150228 -139.821 < 2e-16 ***
ORIGIN_SZCLSZ06 0.7252108 0.0049447 146.665 < 2e-16 ***
ORIGIN_SZCLSZ07 -0.5343482 0.0062500 -85.496 < 2e-16 ***
ORIGIN_SZCLSZ08 -0.2153408 0.0067571 -31.869 < 2e-16 ***
ORIGIN_SZCLSZ09 -1.8019961 0.0169078 -106.578 < 2e-16 ***
ORIGIN_SZDTSZ02 -3.9057711 0.0834668 -46.794 < 2e-16 ***
ORIGIN_SZDTSZ03 -3.4152419 0.0738650 -46.236 < 2e-16 ***
ORIGIN_SZDTSZ13 -3.0183438 0.0315257 -95.742 < 2e-16 ***
ORIGIN_SZGLSZ01 -1.7812384 0.0099367 -179.258 < 2e-16 ***
ORIGIN_SZGLSZ02 -0.1074991 0.0054325 -19.788 < 2e-16 ***
ORIGIN_SZGLSZ03 -0.2461106 0.0057176 -43.045 < 2e-16 ***
ORIGIN_SZGLSZ04 0.8657186 0.0046413 186.524 < 2e-16 ***
ORIGIN_SZGLSZ05 0.5871393 0.0047939 122.477 < 2e-16 ***
ORIGIN_SZHGSZ01 0.3543819 0.0050461 70.229 < 2e-16 ***
ORIGIN_SZHGSZ02 0.4218178 0.0050820 83.003 < 2e-16 ***
ORIGIN_SZHGSZ03 0.2411309 0.0054241 44.456 < 2e-16 ***
ORIGIN_SZHGSZ04 0.8180622 0.0046153 177.252 < 2e-16 ***
ORIGIN_SZHGSZ05 1.2173687 0.0045655 266.647 < 2e-16 ***
ORIGIN_SZHGSZ06 -0.1826300 0.0058214 -31.372 < 2e-16 ***
ORIGIN_SZHGSZ07 0.3172839 0.0050733 62.540 < 2e-16 ***
ORIGIN_SZHGSZ08 -0.1151369 0.0057067 -20.176 < 2e-16 ***
ORIGIN_SZHGSZ09 -1.2873441 0.0091690 -140.401 < 2e-16 ***
ORIGIN_SZHGSZ10 -3.3783178 0.0424682 -79.549 < 2e-16 ***
ORIGIN_SZJESZ01 0.4859234 0.0055927 86.885 < 2e-16 ***
ORIGIN_SZJESZ02 0.1766088 0.0055800 31.650 < 2e-16 ***
ORIGIN_SZJESZ03 -0.2177441 0.0059535 -36.574 < 2e-16 ***
ORIGIN_SZJESZ04 -1.5532182 0.0104526 -148.597 < 2e-16 ***
ORIGIN_SZJESZ05 -2.3332926 0.0142701 -163.509 < 2e-16 ***
ORIGIN_SZJESZ06 0.3007382 0.0055019 54.661 < 2e-16 ***
ORIGIN_SZJESZ07 -1.9687994 0.0121092 -162.587 < 2e-16 ***
ORIGIN_SZJESZ08 -1.3032070 0.0122024 -106.800 < 2e-16 ***
ORIGIN_SZJESZ09 0.5762635 0.0058766 98.061 < 2e-16 ***
ORIGIN_SZJESZ10 -1.4423113 0.0194773 -74.051 < 2e-16 ***
ORIGIN_SZJESZ11 -1.9720897 0.0200811 -98.206 < 2e-16 ***
ORIGIN_SZJWSZ01 0.3808627 0.0071357 53.374 < 2e-16 ***
ORIGIN_SZJWSZ02 0.7963999 0.0053150 149.840 < 2e-16 ***
ORIGIN_SZJWSZ03 1.5429636 0.0049961 308.834 < 2e-16 ***
ORIGIN_SZJWSZ04 0.6410760 0.0056711 113.042 < 2e-16 ***
ORIGIN_SZJWSZ05 -2.1571049 0.0133584 -161.479 < 2e-16 ***
ORIGIN_SZJWSZ06 -1.5174532 0.0113384 -133.833 < 2e-16 ***
ORIGIN_SZJWSZ07 -2.7089963 0.0280439 -96.598 < 2e-16 ***
ORIGIN_SZJWSZ08 1.5343415 0.0051711 296.713 < 2e-16 ***
ORIGIN_SZJWSZ09 1.8837410 0.0048845 385.656 < 2e-16 ***
ORIGIN_SZKLSZ01 0.1081286 0.0053307 20.284 < 2e-16 ***
ORIGIN_SZKLSZ02 -0.8844695 0.0067728 -130.591 < 2e-16 ***
ORIGIN_SZKLSZ03 -0.6872640 0.0062857 -109.337 < 2e-16 ***
ORIGIN_SZKLSZ04 -2.2090319 0.0122440 -180.418 < 2e-16 ***
ORIGIN_SZKLSZ05 -1.1728726 0.0110765 -105.888 < 2e-16 ***
ORIGIN_SZKLSZ06 -6.1162315 0.1857789 -32.922 < 2e-16 ***
ORIGIN_SZKLSZ07 -1.4082749 0.0092299 -152.578 < 2e-16 ***
ORIGIN_SZKLSZ08 -1.7781551 0.0104682 -169.862 < 2e-16 ***
ORIGIN_SZLKSZ01 -2.0531568 0.0398803 -51.483 < 2e-16 ***
ORIGIN_SZMDSZ01 -0.8825639 0.0287621 -30.685 < 2e-16 ***
ORIGIN_SZMDSZ02 -0.6219993 0.0107388 -57.921 < 2e-16 ***
ORIGIN_SZMDSZ03 -2.0840156 0.0173117 -120.382 < 2e-16 ***
ORIGIN_SZMPSZ01 -0.9659093 0.0086972 -111.060 < 2e-16 ***
ORIGIN_SZMPSZ02 -1.0411153 0.0073403 -141.836 < 2e-16 ***
ORIGIN_SZMPSZ03 0.0001659 0.0059401 0.028 0.977719
ORIGIN_SZMUSZ02 -3.7599031 0.1037937 -36.225 < 2e-16 ***
ORIGIN_SZNTSZ01 -3.0388366 0.0355325 -85.523 < 2e-16 ***
ORIGIN_SZNTSZ02 -3.4230640 0.0235902 -145.106 < 2e-16 ***
ORIGIN_SZNTSZ03 -0.9094796 0.0082551 -110.172 < 2e-16 ***
ORIGIN_SZNTSZ05 -4.0861681 0.0499630 -81.784 < 2e-16 ***
ORIGIN_SZNTSZ06 -3.9497128 0.0565388 -69.858 < 2e-16 ***
ORIGIN_SZNVSZ01 0.3235636 0.0049439 65.447 < 2e-16 ***
ORIGIN_SZNVSZ02 -0.6946748 0.0070536 -98.485 < 2e-16 ***
ORIGIN_SZNVSZ03 -1.0540196 0.0083781 -125.806 < 2e-16 ***
ORIGIN_SZNVSZ04 -0.9897977 0.0093463 -105.903 < 2e-16 ***
ORIGIN_SZNVSZ05 -2.2578432 0.0169180 -133.458 < 2e-16 ***
ORIGIN_SZPGSZ01 0.2399827 0.0130436 18.398 < 2e-16 ***
ORIGIN_SZPGSZ02 -0.3352342 0.0078451 -42.732 < 2e-16 ***
ORIGIN_SZPGSZ03 0.9515148 0.0051376 185.207 < 2e-16 ***
ORIGIN_SZPGSZ04 1.3998952 0.0047991 291.697 < 2e-16 ***
ORIGIN_SZPGSZ05 0.4451629 0.0063423 70.189 < 2e-16 ***
ORIGIN_SZPLSZ01 -0.9705918 0.0122781 -79.050 < 2e-16 ***
ORIGIN_SZPLSZ02 -1.0670151 0.0153358 -69.577 < 2e-16 ***
ORIGIN_SZPLSZ03 -2.1229124 0.0373527 -56.834 < 2e-16 ***
ORIGIN_SZPLSZ04 -3.0911932 0.0371296 -83.254 < 2e-16 ***
ORIGIN_SZPLSZ05 -2.1705708 0.0226085 -96.007 < 2e-16 ***
ORIGIN_SZPNSZ01 0.9052637 0.0065952 137.262 < 2e-16 ***
ORIGIN_SZPNSZ02 -0.1720425 0.0125658 -13.691 < 2e-16 ***
ORIGIN_SZPNSZ03 -2.3973459 0.0201408 -119.029 < 2e-16 ***
ORIGIN_SZPNSZ04 -3.4483689 0.0343741 -100.319 < 2e-16 ***
ORIGIN_SZPNSZ05 -2.0588530 0.0282328 -72.924 < 2e-16 ***
ORIGIN_SZPRSZ01 -0.6399015 0.0120470 -53.117 < 2e-16 ***
ORIGIN_SZPRSZ02 0.8122270 0.0050886 159.617 < 2e-16 ***
ORIGIN_SZPRSZ03 0.3990960 0.0051810 77.031 < 2e-16 ***
ORIGIN_SZPRSZ04 -0.8485348 0.0079236 -107.089 < 2e-16 ***
ORIGIN_SZPRSZ05 0.8008791 0.0048532 165.021 < 2e-16 ***
ORIGIN_SZPRSZ06 -1.4498806 0.0121422 -119.408 < 2e-16 ***
ORIGIN_SZPRSZ07 -3.2025045 0.0167118 -191.631 < 2e-16 ***
ORIGIN_SZPRSZ08 -0.5862269 0.0067255 -87.165 < 2e-16 ***
ORIGIN_SZQTSZ01 -0.1859270 0.0075531 -24.616 < 2e-16 ***
ORIGIN_SZQTSZ02 -0.8715122 0.0068124 -127.929 < 2e-16 ***
ORIGIN_SZQTSZ03 -0.1259816 0.0064796 -19.443 < 2e-16 ***
ORIGIN_SZQTSZ04 -1.4620032 0.0079848 -183.098 < 2e-16 ***
ORIGIN_SZQTSZ05 -0.6675643 0.0069616 -95.892 < 2e-16 ***
ORIGIN_SZQTSZ06 -0.8190026 0.0072713 -112.634 < 2e-16 ***
ORIGIN_SZQTSZ07 -1.5189403 0.0099864 -152.101 < 2e-16 ***
ORIGIN_SZQTSZ08 -0.4976238 0.0067874 -73.316 < 2e-16 ***
ORIGIN_SZQTSZ09 -0.9006162 0.0075978 -118.536 < 2e-16 ***
ORIGIN_SZQTSZ10 -0.6690184 0.0071574 -93.473 < 2e-16 ***
ORIGIN_SZQTSZ11 -2.5203437 0.0147000 -171.452 < 2e-16 ***
ORIGIN_SZQTSZ12 -3.0461675 0.0190193 -160.162 < 2e-16 ***
ORIGIN_SZQTSZ13 -0.7501068 0.0084481 -88.791 < 2e-16 ***
ORIGIN_SZQTSZ14 -1.9321849 0.0126114 -153.209 < 2e-16 ***
ORIGIN_SZQTSZ15 -0.9576828 0.0127157 -75.315 < 2e-16 ***
ORIGIN_SZRCSZ01 -1.8167951 0.0129234 -140.582 < 2e-16 ***
ORIGIN_SZRCSZ06 -0.5560563 0.0090507 -61.438 < 2e-16 ***
ORIGIN_SZRVSZ01 -2.8862570 0.0325532 -88.663 < 2e-16 ***
ORIGIN_SZRVSZ02 -3.1555662 0.0281279 -112.186 < 2e-16 ***
ORIGIN_SZRVSZ03 -2.9836089 0.0248449 -120.089 < 2e-16 ***
ORIGIN_SZRVSZ04 -3.5520422 0.0561371 -63.274 < 2e-16 ***
ORIGIN_SZRVSZ05 -2.5866584 0.0180382 -143.399 < 2e-16 ***
ORIGIN_SZSBSZ01 0.2867444 0.0071098 40.331 < 2e-16 ***
ORIGIN_SZSBSZ02 -0.9012334 0.0087262 -103.278 < 2e-16 ***
ORIGIN_SZSBSZ03 0.8311038 0.0055422 149.958 < 2e-16 ***
ORIGIN_SZSBSZ04 0.4044170 0.0062047 65.179 < 2e-16 ***
ORIGIN_SZSBSZ05 -0.2661845 0.0074162 -35.892 < 2e-16 ***
ORIGIN_SZSBSZ06 -0.9023075 0.0175046 -51.547 < 2e-16 ***
ORIGIN_SZSBSZ07 0.0505870 0.0131317 3.852 0.000117 ***
ORIGIN_SZSBSZ08 -1.1158011 0.0145416 -76.732 < 2e-16 ***
ORIGIN_SZSBSZ09 -0.9682835 0.0095396 -101.501 < 2e-16 ***
ORIGIN_SZSESZ02 1.1452735 0.0047810 239.548 < 2e-16 ***
ORIGIN_SZSESZ03 1.2815277 0.0045677 280.564 < 2e-16 ***
ORIGIN_SZSESZ04 0.8085857 0.0052756 153.269 < 2e-16 ***
ORIGIN_SZSESZ05 -0.2329413 0.0063113 -36.909 < 2e-16 ***
ORIGIN_SZSESZ06 1.0576879 0.0049909 211.925 < 2e-16 ***
ORIGIN_SZSESZ07 -2.3165908 0.0196831 -117.695 < 2e-16 ***
ORIGIN_SZSGSZ01 -0.6606350 0.0088079 -75.005 < 2e-16 ***
ORIGIN_SZSGSZ02 -1.3638984 0.0104040 -131.094 < 2e-16 ***
ORIGIN_SZSGSZ03 0.1152591 0.0054649 21.091 < 2e-16 ***
ORIGIN_SZSGSZ04 0.2954067 0.0050865 58.077 < 2e-16 ***
ORIGIN_SZSGSZ05 -2.0792678 0.0109882 -189.227 < 2e-16 ***
ORIGIN_SZSGSZ06 0.4563227 0.0048880 93.356 < 2e-16 ***
ORIGIN_SZSGSZ07 -0.8955254 0.0067100 -133.461 < 2e-16 ***
ORIGIN_SZSKSZ01 -0.3184402 0.0093032 -34.229 < 2e-16 ***
ORIGIN_SZSKSZ02 1.1160484 0.0063851 174.790 < 2e-16 ***
ORIGIN_SZSKSZ03 -0.2566692 0.0086021 -29.838 < 2e-16 ***
ORIGIN_SZSKSZ04 -1.5781827 0.0279394 -56.486 < 2e-16 ***
ORIGIN_SZSKSZ05 -0.2724361 0.0163597 -16.653 < 2e-16 ***
ORIGIN_SZSLSZ01 -2.4458625 0.0330301 -74.050 < 2e-16 ***
ORIGIN_SZSLSZ04 -0.0987076 0.0079626 -12.396 < 2e-16 ***
ORIGIN_SZSRSZ01 -2.2584977 0.0176647 -127.854 < 2e-16 ***
ORIGIN_SZTHSZ01 -2.5878524 0.0489998 -52.814 < 2e-16 ***
ORIGIN_SZTHSZ03 -0.8101746 0.0226814 -35.720 < 2e-16 ***
ORIGIN_SZTHSZ04 -2.4186655 0.0288663 -83.789 < 2e-16 ***
ORIGIN_SZTHSZ06 -1.7080541 0.0186353 -91.657 < 2e-16 ***
ORIGIN_SZTMSZ01 -0.2193476 0.0061823 -35.480 < 2e-16 ***
ORIGIN_SZTMSZ02 1.7772464 0.0043394 409.558 < 2e-16 ***
ORIGIN_SZTMSZ03 1.0051343 0.0046055 218.249 < 2e-16 ***
ORIGIN_SZTMSZ04 0.1642370 0.0055078 29.819 < 2e-16 ***
ORIGIN_SZTMSZ05 -1.2878706 0.0114828 -112.157 < 2e-16 ***
ORIGIN_SZTNSZ01 -1.7163504 0.0131268 -130.751 < 2e-16 ***
ORIGIN_SZTNSZ02 -1.6508988 0.0103851 -158.968 < 2e-16 ***
ORIGIN_SZTNSZ03 -2.1545577 0.0137947 -156.187 < 2e-16 ***
ORIGIN_SZTNSZ04 -0.3949120 0.0078496 -50.310 < 2e-16 ***
ORIGIN_SZTPSZ01 -0.8058100 0.0069916 -115.253 < 2e-16 ***
ORIGIN_SZTPSZ02 0.5369060 0.0047272 113.577 < 2e-16 ***
ORIGIN_SZTPSZ03 -0.7779333 0.0064278 -121.027 < 2e-16 ***
ORIGIN_SZTPSZ04 -0.8153581 0.0061387 -132.823 < 2e-16 ***
ORIGIN_SZTPSZ05 -0.5073676 0.0067771 -74.865 < 2e-16 ***
ORIGIN_SZTPSZ06 0.0847301 0.0065717 12.893 < 2e-16 ***
ORIGIN_SZTPSZ07 -0.5839519 0.0066148 -88.280 < 2e-16 ***
ORIGIN_SZTPSZ08 -1.0577941 0.0098480 -107.412 < 2e-16 ***
ORIGIN_SZTPSZ09 -0.9067707 0.0071367 -127.057 < 2e-16 ***
ORIGIN_SZTPSZ10 -1.1362091 0.0080905 -140.438 < 2e-16 ***
ORIGIN_SZTPSZ11 -0.2374621 0.0059472 -39.928 < 2e-16 ***
ORIGIN_SZTPSZ12 -0.8028874 0.0069663 -115.253 < 2e-16 ***
ORIGIN_SZTSSZ01 -2.7809271 0.0482843 -57.595 < 2e-16 ***
ORIGIN_SZTSSZ02 0.0425804 0.0105088 4.052 5.08e-05 ***
ORIGIN_SZTSSZ03 0.1142369 0.0109412 10.441 < 2e-16 ***
ORIGIN_SZTSSZ04 -0.6186261 0.0116324 -53.181 < 2e-16 ***
ORIGIN_SZTSSZ05 -1.0846732 0.0173555 -62.497 < 2e-16 ***
ORIGIN_SZTSSZ06 0.3980173 0.0198100 20.092 < 2e-16 ***
ORIGIN_SZWCSZ01 1.3545143 0.0092002 147.227 < 2e-16 ***
ORIGIN_SZWCSZ02 -2.9863278 0.0330906 -90.247 < 2e-16 ***
ORIGIN_SZWCSZ03 -5.0504916 0.1241385 -40.684 < 2e-16 ***
ORIGIN_SZWDSZ01 1.5238429 0.0049404 308.448 < 2e-16 ***
ORIGIN_SZWDSZ02 0.2832576 0.0056218 50.386 < 2e-16 ***
ORIGIN_SZWDSZ03 1.3702524 0.0053266 257.245 < 2e-16 ***
ORIGIN_SZWDSZ04 1.0248225 0.0059272 172.903 < 2e-16 ***
ORIGIN_SZWDSZ05 0.2356778 0.0060587 38.899 < 2e-16 ***
ORIGIN_SZWDSZ06 0.3146925 0.0059919 52.520 < 2e-16 ***
ORIGIN_SZWDSZ07 -1.4971897 0.0091243 -164.088 < 2e-16 ***
ORIGIN_SZWDSZ08 -0.8894079 0.0087414 -101.747 < 2e-16 ***
ORIGIN_SZWDSZ09 1.4437633 0.0053160 271.590 < 2e-16 ***
ORIGIN_SZYSSZ01 -0.2519398 0.0064443 -39.095 < 2e-16 ***
ORIGIN_SZYSSZ02 0.8726785 0.0057658 151.354 < 2e-16 ***
ORIGIN_SZYSSZ03 1.7868139 0.0050674 352.611 < 2e-16 ***
ORIGIN_SZYSSZ04 0.8418040 0.0051738 162.704 < 2e-16 ***
ORIGIN_SZYSSZ05 0.4292096 0.0062520 68.652 < 2e-16 ***
ORIGIN_SZYSSZ06 -0.7459961 0.0119123 -62.624 < 2e-16 ***
ORIGIN_SZYSSZ07 -0.8422281 0.0144559 -58.262 < 2e-16 ***
ORIGIN_SZYSSZ08 0.1829428 0.0067885 26.949 < 2e-16 ***
ORIGIN_SZYSSZ09 1.1159712 0.0050760 219.853 < 2e-16 ***
DESTIN_SZAMSZ02 0.0694567 0.0045966 15.111 < 2e-16 ***
DESTIN_SZAMSZ03 0.0760100 0.0044639 17.028 < 2e-16 ***
DESTIN_SZAMSZ04 -1.1306391 0.0064373 -175.639 < 2e-16 ***
DESTIN_SZAMSZ05 -1.0751133 0.0065164 -164.985 < 2e-16 ***
DESTIN_SZAMSZ06 -0.9624298 0.0065937 -145.962 < 2e-16 ***
DESTIN_SZAMSZ07 -1.5060319 0.0097616 -154.281 < 2e-16 ***
DESTIN_SZAMSZ08 -0.4813202 0.0069794 -68.963 < 2e-16 ***
DESTIN_SZAMSZ09 -1.0220675 0.0066313 -154.129 < 2e-16 ***
DESTIN_SZAMSZ10 0.1235142 0.0047044 26.255 < 2e-16 ***
DESTIN_SZAMSZ11 -0.8917993 0.0088519 -100.746 < 2e-16 ***
DESTIN_SZAMSZ12 0.0195208 0.0051704 3.775 0.000160 ***
DESTIN_SZBDSZ01 0.9736349 0.0042757 227.713 < 2e-16 ***
DESTIN_SZBDSZ02 -0.1969470 0.0055284 -35.625 < 2e-16 ***
DESTIN_SZBDSZ03 0.1266471 0.0050786 24.938 < 2e-16 ***
DESTIN_SZBDSZ04 1.1608485 0.0041956 276.684 < 2e-16 ***
DESTIN_SZBDSZ05 0.9293840 0.0044412 209.265 < 2e-16 ***
DESTIN_SZBDSZ06 0.4090567 0.0050300 81.323 < 2e-16 ***
DESTIN_SZBDSZ07 -0.8171478 0.0098945 -82.586 < 2e-16 ***
DESTIN_SZBDSZ08 -1.5895287 0.0111632 -142.391 < 2e-16 ***
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DESTIN_SZBKSZ02 -0.5253670 0.0061879 -84.903 < 2e-16 ***
DESTIN_SZBKSZ03 -1.0095362 0.0065426 -154.301 < 2e-16 ***
DESTIN_SZBKSZ04 -0.5662858 0.0056453 -100.311 < 2e-16 ***
DESTIN_SZBKSZ05 -0.9406607 0.0070597 -133.244 < 2e-16 ***
DESTIN_SZBKSZ06 -1.3129276 0.0067414 -194.755 < 2e-16 ***
DESTIN_SZBKSZ07 0.0120605 0.0049284 2.447 0.014400 *
DESTIN_SZBKSZ08 -1.3658471 0.0075109 -181.849 < 2e-16 ***
DESTIN_SZBKSZ09 -0.1771310 0.0055645 -31.832 < 2e-16 ***
DESTIN_SZBLSZ01 -0.8175223 0.0075645 -108.074 < 2e-16 ***
DESTIN_SZBLSZ02 0.1631280 0.0071753 22.735 < 2e-16 ***
DESTIN_SZBLSZ03 1.2598494 0.0081706 154.194 < 2e-16 ***
DESTIN_SZBLSZ04 -0.5642975 0.0137827 -40.943 < 2e-16 ***
DESTIN_SZBMSZ01 0.6921844 0.0054211 127.684 < 2e-16 ***
DESTIN_SZBMSZ02 -0.1209392 0.0055362 -21.845 < 2e-16 ***
DESTIN_SZBMSZ03 -0.2373881 0.0062427 -38.027 < 2e-16 ***
DESTIN_SZBMSZ04 -0.0407117 0.0058001 -7.019 2.23e-12 ***
DESTIN_SZBMSZ05 -0.2363309 0.0075967 -31.110 < 2e-16 ***
DESTIN_SZBMSZ06 -1.1930710 0.0134761 -88.532 < 2e-16 ***
DESTIN_SZBMSZ07 0.4625103 0.0051864 89.178 < 2e-16 ***
DESTIN_SZBMSZ08 -0.8604731 0.0069899 -123.102 < 2e-16 ***
DESTIN_SZBMSZ09 -2.1290239 0.0154841 -137.498 < 2e-16 ***
DESTIN_SZBMSZ10 -1.4617153 0.0094014 -155.478 < 2e-16 ***
DESTIN_SZBMSZ11 -1.3234050 0.0085506 -154.773 < 2e-16 ***
DESTIN_SZBMSZ12 -0.8399230 0.0085361 -98.397 < 2e-16 ***
DESTIN_SZBMSZ13 0.1366529 0.0059697 22.891 < 2e-16 ***
DESTIN_SZBMSZ14 -1.0491968 0.0083021 -126.378 < 2e-16 ***
DESTIN_SZBMSZ15 -0.6726684 0.0076276 -88.189 < 2e-16 ***
DESTIN_SZBMSZ16 -1.4011734 0.0116569 -120.201 < 2e-16 ***
DESTIN_SZBMSZ17 -1.5682752 0.0167333 -93.722 < 2e-16 ***
DESTIN_SZBPSZ01 -1.1120017 0.0063197 -175.959 < 2e-16 ***
DESTIN_SZBPSZ02 -2.0833466 0.0091139 -228.590 < 2e-16 ***
DESTIN_SZBPSZ03 -1.6937265 0.0087437 -193.709 < 2e-16 ***
DESTIN_SZBPSZ04 -0.7964999 0.0066129 -120.447 < 2e-16 ***
DESTIN_SZBPSZ05 0.2109118 0.0048815 43.206 < 2e-16 ***
DESTIN_SZBPSZ06 -1.1808365 0.0083657 -141.152 < 2e-16 ***
DESTIN_SZBPSZ07 -0.2077428 0.0084543 -24.572 < 2e-16 ***
DESTIN_SZBSSZ01 0.3164175 0.0050682 62.431 < 2e-16 ***
DESTIN_SZBSSZ02 -0.4852688 0.0057001 -85.134 < 2e-16 ***
DESTIN_SZBSSZ03 0.4130432 0.0043061 95.921 < 2e-16 ***
DESTIN_SZBTSZ01 0.6215095 0.0048914 127.061 < 2e-16 ***
DESTIN_SZBTSZ02 -0.0145076 0.0071799 -2.021 0.043324 *
DESTIN_SZBTSZ03 0.4919981 0.0058498 84.105 < 2e-16 ***
DESTIN_SZBTSZ04 -0.6957555 0.0114078 -60.989 < 2e-16 ***
DESTIN_SZBTSZ05 0.3329814 0.0073568 45.262 < 2e-16 ***
DESTIN_SZBTSZ06 -0.1333295 0.0073965 -18.026 < 2e-16 ***
DESTIN_SZBTSZ07 -1.4449581 0.0113186 -127.663 < 2e-16 ***
DESTIN_SZBTSZ08 -0.7079056 0.0103797 -68.201 < 2e-16 ***
DESTIN_SZCBSZ01 -5.7344725 0.3162767 -18.131 < 2e-16 ***
DESTIN_SZCCSZ01 -0.0009541 0.0083381 -0.114 0.908900
DESTIN_SZCHSZ01 -0.2083016 0.0099054 -21.029 < 2e-16 ***
DESTIN_SZCHSZ02 0.5369606 0.0057531 93.334 < 2e-16 ***
DESTIN_SZCHSZ03 2.5530638 0.0043945 580.971 < 2e-16 ***
DESTIN_SZCKSZ01 -0.5725975 0.0056507 -101.333 < 2e-16 ***
DESTIN_SZCKSZ02 -1.1181852 0.0063287 -176.685 < 2e-16 ***
DESTIN_SZCKSZ03 0.1156680 0.0049440 23.396 < 2e-16 ***
DESTIN_SZCKSZ04 -0.8647725 0.0071003 -121.794 < 2e-16 ***
DESTIN_SZCKSZ05 -1.1641791 0.0076248 -152.684 < 2e-16 ***
DESTIN_SZCKSZ06 -0.4397612 0.0073040 -60.208 < 2e-16 ***
DESTIN_SZCLSZ01 0.1930552 0.0053752 35.916 < 2e-16 ***
DESTIN_SZCLSZ02 -2.0436501 0.0136039 -150.225 < 2e-16 ***
DESTIN_SZCLSZ03 -0.9338571 0.0082908 -112.638 < 2e-16 ***
DESTIN_SZCLSZ04 0.0532041 0.0053276 9.987 < 2e-16 ***
DESTIN_SZCLSZ05 -1.0782781 0.0088184 -122.276 < 2e-16 ***
DESTIN_SZCLSZ06 0.4068171 0.0049068 82.910 < 2e-16 ***
DESTIN_SZCLSZ07 -0.3579507 0.0060289 -59.373 < 2e-16 ***
DESTIN_SZCLSZ08 -0.2487993 0.0066588 -37.364 < 2e-16 ***
DESTIN_SZCLSZ09 0.1611080 0.0071178 22.635 < 2e-16 ***
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DESTIN_SZDTSZ03 -0.5994253 0.0146230 -40.992 < 2e-16 ***
DESTIN_SZDTSZ13 -1.3685031 0.0162803 -84.059 < 2e-16 ***
DESTIN_SZGLSZ01 -0.0910001 0.0055275 -16.463 < 2e-16 ***
DESTIN_SZGLSZ02 -0.0692224 0.0052840 -13.100 < 2e-16 ***
DESTIN_SZGLSZ03 0.6493421 0.0043446 149.459 < 2e-16 ***
DESTIN_SZGLSZ04 0.9327947 0.0043674 213.583 < 2e-16 ***
DESTIN_SZGLSZ05 0.8161728 0.0043625 187.087 < 2e-16 ***
DESTIN_SZHGSZ01 0.0658625 0.0042516 15.491 < 2e-16 ***
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DESTIN_SZHGSZ03 -1.3546132 0.0066257 -204.448 < 2e-16 ***
DESTIN_SZHGSZ04 -0.4500588 0.0048448 -92.895 < 2e-16 ***
DESTIN_SZHGSZ05 -0.5026431 0.0050996 -98.566 < 2e-16 ***
DESTIN_SZHGSZ06 -0.8673686 0.0059530 -145.704 < 2e-16 ***
DESTIN_SZHGSZ07 0.0560490 0.0047702 11.750 < 2e-16 ***
DESTIN_SZHGSZ08 -0.0443189 0.0052599 -8.426 < 2e-16 ***
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DESTIN_SZJESZ02 -0.7369159 0.0058686 -125.570 < 2e-16 ***
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DESTIN_SZJESZ05 -1.5324974 0.0102612 -149.349 < 2e-16 ***
DESTIN_SZJESZ06 0.3105267 0.0048241 64.370 < 2e-16 ***
DESTIN_SZJESZ07 -1.3234483 0.0085497 -154.795 < 2e-16 ***
DESTIN_SZJESZ08 -0.6559742 0.0083174 -78.867 < 2e-16 ***
DESTIN_SZJESZ09 0.2663752 0.0063370 42.035 < 2e-16 ***
DESTIN_SZJESZ10 0.8529026 0.0076067 112.126 < 2e-16 ***
DESTIN_SZJESZ11 0.5559641 0.0074629 74.497 < 2e-16 ***
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DESTIN_SZJWSZ02 -0.8746590 0.0060179 -145.342 < 2e-16 ***
DESTIN_SZJWSZ03 0.5689062 0.0049105 115.855 < 2e-16 ***
DESTIN_SZJWSZ04 0.4520963 0.0050302 89.876 < 2e-16 ***
DESTIN_SZJWSZ05 -1.0249671 0.0067371 -152.137 < 2e-16 ***
DESTIN_SZJWSZ06 -0.7451483 0.0062189 -119.819 < 2e-16 ***
DESTIN_SZJWSZ07 -2.8453099 0.0287335 -99.024 < 2e-16 ***
DESTIN_SZJWSZ08 -0.3372309 0.0058003 -58.141 < 2e-16 ***
DESTIN_SZJWSZ09 1.0505330 0.0045908 228.832 < 2e-16 ***
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DESTIN_SZKLSZ02 -0.5416148 0.0061432 -88.164 < 2e-16 ***
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DESTIN_SZKLSZ04 -1.2918594 0.0090197 -143.227 < 2e-16 ***
DESTIN_SZKLSZ05 -0.4069101 0.0087812 -46.339 < 2e-16 ***
DESTIN_SZKLSZ06 -2.5333101 0.0363215 -69.747 < 2e-16 ***
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DESTIN_SZMDSZ01 -1.5655800 0.0202787 -77.203 < 2e-16 ***
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DESTIN_SZMDSZ03 -3.3328109 0.0254294 -131.061 < 2e-16 ***
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DESTIN_SZMPSZ02 -0.5386560 0.0064620 -83.358 < 2e-16 ***
DESTIN_SZMPSZ03 0.4952000 0.0052295 94.694 < 2e-16 ***
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DESTIN_SZNVSZ02 -0.0274710 0.0057611 -4.768 1.86e-06 ***
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DESTIN_SZQTSZ10 0.1993449 0.0059923 33.267 < 2e-16 ***
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DESTIN_SZQTSZ13 0.5500978 0.0063091 87.192 < 2e-16 ***
DESTIN_SZQTSZ14 0.5364435 0.0070157 76.463 < 2e-16 ***
DESTIN_SZQTSZ15 1.3611043 0.0081643 166.715 < 2e-16 ***
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DESTIN_SZTMSZ04 1.0222812 0.0043466 235.191 < 2e-16 ***
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DESTIN_SZTSSZ03 0.6525526 0.0092450 70.585 < 2e-16 ***
DESTIN_SZTSSZ04 0.5285464 0.0100182 52.759 < 2e-16 ***
DESTIN_SZTSSZ05 1.4670106 0.0104357 140.577 < 2e-16 ***
DESTIN_SZTSSZ06 2.5043588 0.0167444 149.564 < 2e-16 ***
DESTIN_SZWCSZ01 1.9787931 0.0054306 364.375 < 2e-16 ***
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DESTIN_SZWCSZ03 -3.1897655 0.0326927 -97.568 < 2e-16 ***
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DESTIN_SZWDSZ02 -1.3176990 0.0065894 -199.973 < 2e-16 ***
DESTIN_SZWDSZ03 0.3432057 0.0052496 65.377 < 2e-16 ***
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DESTIN_SZWDSZ08 -0.5124717 0.0069223 -74.032 < 2e-16 ***
DESTIN_SZWDSZ09 0.3813542 0.0054697 69.721 < 2e-16 ***
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DESTIN_SZYSSZ07 -0.7839065 0.0144357 -54.304 < 2e-16 ***
DESTIN_SZYSSZ08 0.6265412 0.0045504 137.691 < 2e-16 ***
DESTIN_SZYSSZ09 0.1520067 0.0048092 31.607 < 2e-16 ***
log(DIST) -1.8468315 0.0004608 -4008.033 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 47094011 on 14470 degrees of freedom
Residual deviance: 10420261 on 13912 degrees of freedom
AIC: 10510518
Number of Fisher Scoring iterations: 7
Functions
- glm from stats package fits generalized linear models. In this code, a Poisson regression model is specified with
family = poisson(link = "log"). The formulaTRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(DIST)defines the dependent variable (TRIPS) and the independent variables (ORIGIN_SZ,DESTIN_SZ, and logarithm ofDIST). - The
dataargument specifiesinter_zonal_flowas the dataset used for the model. na.action = na.excludeindicates how missing values (NAs) should be handled in the model fitting process.- summary from base R provides a comprehensive summary of the fitted model
dbcSIM_Poisson, including the model coefficients, their statistical significance, and other diagnostic measures.
Important
It is important to note that there is a slight change of the code chunk. -1 is removed which means that an intercept will appear in the model again. The -1 for removing the intercept only works with one factor level but in double-constrained model we have two factor levels, namely: origins and destinations.
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(DIST), family = poisson(link = "log"),
data = inter_zonal_flow, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 21.8312374 0.0059160 3690.190 < 2e-16 ***
ORIGIN_SZAMSZ02 0.5263502 0.0048031 109.585 < 2e-16 ***
ORIGIN_SZAMSZ03 0.3139982 0.0049254 63.751 < 2e-16 ***
ORIGIN_SZAMSZ04 -0.2146257 0.0053639 -40.013 < 2e-16 ***
ORIGIN_SZAMSZ05 -0.1890446 0.0060386 -31.306 < 2e-16 ***
ORIGIN_SZAMSZ06 0.1539201 0.0054401 28.294 < 2e-16 ***
ORIGIN_SZAMSZ07 -0.9826565 0.0098676 -99.584 < 2e-16 ***
ORIGIN_SZAMSZ08 -0.4488417 0.0093070 -48.226 < 2e-16 ***
ORIGIN_SZAMSZ09 0.0713474 0.0057402 12.429 < 2e-16 ***
ORIGIN_SZAMSZ10 0.4313742 0.0050370 85.641 < 2e-16 ***
ORIGIN_SZAMSZ11 -1.4712226 0.0131178 -112.154 < 2e-16 ***
ORIGIN_SZAMSZ12 -1.7250733 0.0111603 -154.573 < 2e-16 ***
ORIGIN_SZBDSZ01 0.8810576 0.0048168 182.914 < 2e-16 ***
ORIGIN_SZBDSZ02 0.1100240 0.0055529 19.814 < 2e-16 ***
ORIGIN_SZBDSZ03 0.3606166 0.0050672 71.167 < 2e-16 ***
ORIGIN_SZBDSZ04 1.4624347 0.0044212 330.781 < 2e-16 ***
ORIGIN_SZBDSZ05 0.6207557 0.0050843 122.092 < 2e-16 ***
ORIGIN_SZBDSZ06 0.6712973 0.0051953 129.214 < 2e-16 ***
ORIGIN_SZBDSZ07 -1.2338669 0.0100775 -122.437 < 2e-16 ***
ORIGIN_SZBDSZ08 -1.0444562 0.0094555 -110.460 < 2e-16 ***
ORIGIN_SZBKSZ01 -0.2838426 0.0071354 -39.780 < 2e-16 ***
ORIGIN_SZBKSZ02 0.5550522 0.0059014 94.054 < 2e-16 ***
ORIGIN_SZBKSZ03 0.7396640 0.0056796 130.231 < 2e-16 ***
ORIGIN_SZBKSZ04 -0.2242451 0.0067482 -33.230 < 2e-16 ***
ORIGIN_SZBKSZ05 -0.2371614 0.0069386 -34.180 < 2e-16 ***
ORIGIN_SZBKSZ06 -0.1413812 0.0065035 -21.739 < 2e-16 ***
ORIGIN_SZBKSZ07 0.7089989 0.0051843 136.758 < 2e-16 ***
ORIGIN_SZBKSZ08 -0.0907065 0.0059157 -15.333 < 2e-16 ***
ORIGIN_SZBKSZ09 -0.1775146 0.0063302 -28.042 < 2e-16 ***
ORIGIN_SZBLSZ01 -2.3684539 0.0154280 -153.516 < 2e-16 ***
ORIGIN_SZBLSZ02 -2.8078475 0.0197839 -141.926 < 2e-16 ***
ORIGIN_SZBLSZ03 -3.3122763 0.0466091 -71.065 < 2e-16 ***
ORIGIN_SZBLSZ04 -2.6770542 0.0241793 -110.717 < 2e-16 ***
ORIGIN_SZBMSZ01 0.0618035 0.0059400 10.405 < 2e-16 ***
ORIGIN_SZBMSZ02 -1.3535767 0.0073741 -183.557 < 2e-16 ***
ORIGIN_SZBMSZ03 -0.7569095 0.0063187 -119.790 < 2e-16 ***
ORIGIN_SZBMSZ04 -0.2949304 0.0059603 -49.483 < 2e-16 ***
ORIGIN_SZBMSZ05 -2.6131992 0.0172376 -151.599 < 2e-16 ***
ORIGIN_SZBMSZ06 -3.0315024 0.0185502 -163.422 < 2e-16 ***
ORIGIN_SZBMSZ07 -0.6962524 0.0064068 -108.674 < 2e-16 ***
ORIGIN_SZBMSZ08 -0.9310730 0.0064541 -144.261 < 2e-16 ***
ORIGIN_SZBMSZ09 -1.2911253 0.0092047 -140.268 < 2e-16 ***
ORIGIN_SZBMSZ10 -1.6687004 0.0095708 -174.353 < 2e-16 ***
ORIGIN_SZBMSZ11 -1.1152794 0.0072027 -154.841 < 2e-16 ***
ORIGIN_SZBMSZ12 -1.5323954 0.0099932 -153.344 < 2e-16 ***
ORIGIN_SZBMSZ13 -0.6267376 0.0065863 -95.158 < 2e-16 ***
ORIGIN_SZBMSZ14 -1.0475467 0.0072472 -144.544 < 2e-16 ***
ORIGIN_SZBMSZ15 -0.5049444 0.0067390 -74.929 < 2e-16 ***
ORIGIN_SZBMSZ16 -1.5282897 0.0099545 -153.527 < 2e-16 ***
ORIGIN_SZBMSZ17 -1.5722349 0.0161533 -97.332 < 2e-16 ***
ORIGIN_SZBPSZ01 0.5814175 0.0062904 92.429 < 2e-16 ***
ORIGIN_SZBPSZ02 0.0875442 0.0072190 12.127 < 2e-16 ***
ORIGIN_SZBPSZ03 0.3358227 0.0070460 47.662 < 2e-16 ***
ORIGIN_SZBPSZ04 0.6507586 0.0057726 112.733 < 2e-16 ***
ORIGIN_SZBPSZ05 0.9502124 0.0052971 179.384 < 2e-16 ***
ORIGIN_SZBPSZ06 -1.0480314 0.0098191 -106.734 < 2e-16 ***
ORIGIN_SZBPSZ07 -0.5467931 0.0091676 -59.644 < 2e-16 ***
ORIGIN_SZBSSZ01 0.2998334 0.0059193 50.654 < 2e-16 ***
ORIGIN_SZBSSZ02 0.2841036 0.0050863 55.856 < 2e-16 ***
ORIGIN_SZBSSZ03 -0.2331505 0.0056565 -41.218 < 2e-16 ***
ORIGIN_SZBTSZ01 0.0987284 0.0063715 15.495 < 2e-16 ***
ORIGIN_SZBTSZ02 -0.6261229 0.0084604 -74.006 < 2e-16 ***
ORIGIN_SZBTSZ03 -0.4326963 0.0073452 -58.909 < 2e-16 ***
ORIGIN_SZBTSZ04 -1.4998668 0.0110013 -136.336 < 2e-16 ***
ORIGIN_SZBTSZ05 -0.9564768 0.0122202 -78.270 < 2e-16 ***
ORIGIN_SZBTSZ06 -1.2853131 0.0099328 -129.401 < 2e-16 ***
ORIGIN_SZBTSZ07 -2.3870991 0.0144589 -165.096 < 2e-16 ***
ORIGIN_SZBTSZ08 -1.3715855 0.0113825 -120.499 < 2e-16 ***
ORIGIN_SZCBSZ01 -3.5940232 0.0548979 -65.467 < 2e-16 ***
ORIGIN_SZCCSZ01 -0.7008220 0.0140373 -49.926 < 2e-16 ***
ORIGIN_SZCHSZ01 -0.9109524 0.0122869 -74.140 < 2e-16 ***
ORIGIN_SZCHSZ02 -0.8566547 0.0088749 -96.526 < 2e-16 ***
ORIGIN_SZCHSZ03 1.1153731 0.0066136 168.650 < 2e-16 ***
ORIGIN_SZCKSZ01 0.3001815 0.0058548 51.271 < 2e-16 ***
ORIGIN_SZCKSZ02 0.7185711 0.0060595 118.585 < 2e-16 ***
ORIGIN_SZCKSZ03 1.1389824 0.0053179 214.178 < 2e-16 ***
ORIGIN_SZCKSZ04 1.6281772 0.0054761 297.324 < 2e-16 ***
ORIGIN_SZCKSZ05 0.8338470 0.0064178 129.927 < 2e-16 ***
ORIGIN_SZCKSZ06 0.6528993 0.0082375 79.259 < 2e-16 ***
ORIGIN_SZCLSZ01 -0.7174758 0.0082123 -87.366 < 2e-16 ***
ORIGIN_SZCLSZ02 -1.7513100 0.0139062 -125.938 < 2e-16 ***
ORIGIN_SZCLSZ03 -1.0362873 0.0085485 -121.224 < 2e-16 ***
ORIGIN_SZCLSZ04 0.6160017 0.0051276 120.136 < 2e-16 ***
ORIGIN_SZCLSZ05 -2.1005122 0.0150228 -139.821 < 2e-16 ***
ORIGIN_SZCLSZ06 0.7252108 0.0049447 146.665 < 2e-16 ***
ORIGIN_SZCLSZ07 -0.5343482 0.0062500 -85.496 < 2e-16 ***
ORIGIN_SZCLSZ08 -0.2153408 0.0067571 -31.869 < 2e-16 ***
ORIGIN_SZCLSZ09 -1.8019961 0.0169078 -106.578 < 2e-16 ***
ORIGIN_SZDTSZ02 -3.9057711 0.0834668 -46.794 < 2e-16 ***
ORIGIN_SZDTSZ03 -3.4152419 0.0738650 -46.236 < 2e-16 ***
ORIGIN_SZDTSZ13 -3.0183438 0.0315257 -95.742 < 2e-16 ***
ORIGIN_SZGLSZ01 -1.7812384 0.0099367 -179.258 < 2e-16 ***
ORIGIN_SZGLSZ02 -0.1074991 0.0054325 -19.788 < 2e-16 ***
ORIGIN_SZGLSZ03 -0.2461106 0.0057176 -43.045 < 2e-16 ***
ORIGIN_SZGLSZ04 0.8657186 0.0046413 186.524 < 2e-16 ***
ORIGIN_SZGLSZ05 0.5871393 0.0047939 122.477 < 2e-16 ***
ORIGIN_SZHGSZ01 0.3543819 0.0050461 70.229 < 2e-16 ***
ORIGIN_SZHGSZ02 0.4218178 0.0050820 83.003 < 2e-16 ***
ORIGIN_SZHGSZ03 0.2411309 0.0054241 44.456 < 2e-16 ***
ORIGIN_SZHGSZ04 0.8180622 0.0046153 177.252 < 2e-16 ***
ORIGIN_SZHGSZ05 1.2173687 0.0045655 266.647 < 2e-16 ***
ORIGIN_SZHGSZ06 -0.1826300 0.0058214 -31.372 < 2e-16 ***
ORIGIN_SZHGSZ07 0.3172839 0.0050733 62.540 < 2e-16 ***
ORIGIN_SZHGSZ08 -0.1151369 0.0057067 -20.176 < 2e-16 ***
ORIGIN_SZHGSZ09 -1.2873441 0.0091690 -140.401 < 2e-16 ***
ORIGIN_SZHGSZ10 -3.3783178 0.0424682 -79.549 < 2e-16 ***
ORIGIN_SZJESZ01 0.4859234 0.0055927 86.885 < 2e-16 ***
ORIGIN_SZJESZ02 0.1766088 0.0055800 31.650 < 2e-16 ***
ORIGIN_SZJESZ03 -0.2177441 0.0059535 -36.574 < 2e-16 ***
ORIGIN_SZJESZ04 -1.5532182 0.0104526 -148.597 < 2e-16 ***
ORIGIN_SZJESZ05 -2.3332926 0.0142701 -163.509 < 2e-16 ***
ORIGIN_SZJESZ06 0.3007382 0.0055019 54.661 < 2e-16 ***
ORIGIN_SZJESZ07 -1.9687994 0.0121092 -162.587 < 2e-16 ***
ORIGIN_SZJESZ08 -1.3032070 0.0122024 -106.800 < 2e-16 ***
ORIGIN_SZJESZ09 0.5762635 0.0058766 98.061 < 2e-16 ***
ORIGIN_SZJESZ10 -1.4423113 0.0194773 -74.051 < 2e-16 ***
ORIGIN_SZJESZ11 -1.9720897 0.0200811 -98.206 < 2e-16 ***
ORIGIN_SZJWSZ01 0.3808627 0.0071357 53.374 < 2e-16 ***
ORIGIN_SZJWSZ02 0.7963999 0.0053150 149.840 < 2e-16 ***
ORIGIN_SZJWSZ03 1.5429636 0.0049961 308.834 < 2e-16 ***
ORIGIN_SZJWSZ04 0.6410760 0.0056711 113.042 < 2e-16 ***
ORIGIN_SZJWSZ05 -2.1571049 0.0133584 -161.479 < 2e-16 ***
ORIGIN_SZJWSZ06 -1.5174532 0.0113384 -133.833 < 2e-16 ***
ORIGIN_SZJWSZ07 -2.7089963 0.0280439 -96.598 < 2e-16 ***
ORIGIN_SZJWSZ08 1.5343415 0.0051711 296.713 < 2e-16 ***
ORIGIN_SZJWSZ09 1.8837410 0.0048845 385.656 < 2e-16 ***
ORIGIN_SZKLSZ01 0.1081286 0.0053307 20.284 < 2e-16 ***
ORIGIN_SZKLSZ02 -0.8844695 0.0067728 -130.591 < 2e-16 ***
ORIGIN_SZKLSZ03 -0.6872640 0.0062857 -109.337 < 2e-16 ***
ORIGIN_SZKLSZ04 -2.2090319 0.0122440 -180.418 < 2e-16 ***
ORIGIN_SZKLSZ05 -1.1728726 0.0110765 -105.888 < 2e-16 ***
ORIGIN_SZKLSZ06 -6.1162315 0.1857789 -32.922 < 2e-16 ***
ORIGIN_SZKLSZ07 -1.4082749 0.0092299 -152.578 < 2e-16 ***
ORIGIN_SZKLSZ08 -1.7781551 0.0104682 -169.862 < 2e-16 ***
ORIGIN_SZLKSZ01 -2.0531568 0.0398803 -51.483 < 2e-16 ***
ORIGIN_SZMDSZ01 -0.8825639 0.0287621 -30.685 < 2e-16 ***
ORIGIN_SZMDSZ02 -0.6219993 0.0107388 -57.921 < 2e-16 ***
ORIGIN_SZMDSZ03 -2.0840156 0.0173117 -120.382 < 2e-16 ***
ORIGIN_SZMPSZ01 -0.9659093 0.0086972 -111.060 < 2e-16 ***
ORIGIN_SZMPSZ02 -1.0411153 0.0073403 -141.836 < 2e-16 ***
ORIGIN_SZMPSZ03 0.0001659 0.0059401 0.028 0.977719
ORIGIN_SZMUSZ02 -3.7599031 0.1037937 -36.225 < 2e-16 ***
ORIGIN_SZNTSZ01 -3.0388366 0.0355325 -85.523 < 2e-16 ***
ORIGIN_SZNTSZ02 -3.4230640 0.0235902 -145.106 < 2e-16 ***
ORIGIN_SZNTSZ03 -0.9094796 0.0082551 -110.172 < 2e-16 ***
ORIGIN_SZNTSZ05 -4.0861681 0.0499630 -81.784 < 2e-16 ***
ORIGIN_SZNTSZ06 -3.9497128 0.0565388 -69.858 < 2e-16 ***
ORIGIN_SZNVSZ01 0.3235636 0.0049439 65.447 < 2e-16 ***
ORIGIN_SZNVSZ02 -0.6946748 0.0070536 -98.485 < 2e-16 ***
ORIGIN_SZNVSZ03 -1.0540196 0.0083781 -125.806 < 2e-16 ***
ORIGIN_SZNVSZ04 -0.9897977 0.0093463 -105.903 < 2e-16 ***
ORIGIN_SZNVSZ05 -2.2578432 0.0169180 -133.458 < 2e-16 ***
ORIGIN_SZPGSZ01 0.2399827 0.0130436 18.398 < 2e-16 ***
ORIGIN_SZPGSZ02 -0.3352342 0.0078451 -42.732 < 2e-16 ***
ORIGIN_SZPGSZ03 0.9515148 0.0051376 185.207 < 2e-16 ***
ORIGIN_SZPGSZ04 1.3998952 0.0047991 291.697 < 2e-16 ***
ORIGIN_SZPGSZ05 0.4451629 0.0063423 70.189 < 2e-16 ***
ORIGIN_SZPLSZ01 -0.9705918 0.0122781 -79.050 < 2e-16 ***
ORIGIN_SZPLSZ02 -1.0670151 0.0153358 -69.577 < 2e-16 ***
ORIGIN_SZPLSZ03 -2.1229124 0.0373527 -56.834 < 2e-16 ***
ORIGIN_SZPLSZ04 -3.0911932 0.0371296 -83.254 < 2e-16 ***
ORIGIN_SZPLSZ05 -2.1705708 0.0226085 -96.007 < 2e-16 ***
ORIGIN_SZPNSZ01 0.9052637 0.0065952 137.262 < 2e-16 ***
ORIGIN_SZPNSZ02 -0.1720425 0.0125658 -13.691 < 2e-16 ***
ORIGIN_SZPNSZ03 -2.3973459 0.0201408 -119.029 < 2e-16 ***
ORIGIN_SZPNSZ04 -3.4483689 0.0343741 -100.319 < 2e-16 ***
ORIGIN_SZPNSZ05 -2.0588530 0.0282328 -72.924 < 2e-16 ***
ORIGIN_SZPRSZ01 -0.6399015 0.0120470 -53.117 < 2e-16 ***
ORIGIN_SZPRSZ02 0.8122270 0.0050886 159.617 < 2e-16 ***
ORIGIN_SZPRSZ03 0.3990960 0.0051810 77.031 < 2e-16 ***
ORIGIN_SZPRSZ04 -0.8485348 0.0079236 -107.089 < 2e-16 ***
ORIGIN_SZPRSZ05 0.8008791 0.0048532 165.021 < 2e-16 ***
ORIGIN_SZPRSZ06 -1.4498806 0.0121422 -119.408 < 2e-16 ***
ORIGIN_SZPRSZ07 -3.2025045 0.0167118 -191.631 < 2e-16 ***
ORIGIN_SZPRSZ08 -0.5862269 0.0067255 -87.165 < 2e-16 ***
ORIGIN_SZQTSZ01 -0.1859270 0.0075531 -24.616 < 2e-16 ***
ORIGIN_SZQTSZ02 -0.8715122 0.0068124 -127.929 < 2e-16 ***
ORIGIN_SZQTSZ03 -0.1259816 0.0064796 -19.443 < 2e-16 ***
ORIGIN_SZQTSZ04 -1.4620032 0.0079848 -183.098 < 2e-16 ***
ORIGIN_SZQTSZ05 -0.6675643 0.0069616 -95.892 < 2e-16 ***
ORIGIN_SZQTSZ06 -0.8190026 0.0072713 -112.634 < 2e-16 ***
ORIGIN_SZQTSZ07 -1.5189403 0.0099864 -152.101 < 2e-16 ***
ORIGIN_SZQTSZ08 -0.4976238 0.0067874 -73.316 < 2e-16 ***
ORIGIN_SZQTSZ09 -0.9006162 0.0075978 -118.536 < 2e-16 ***
ORIGIN_SZQTSZ10 -0.6690184 0.0071574 -93.473 < 2e-16 ***
ORIGIN_SZQTSZ11 -2.5203437 0.0147000 -171.452 < 2e-16 ***
ORIGIN_SZQTSZ12 -3.0461675 0.0190193 -160.162 < 2e-16 ***
ORIGIN_SZQTSZ13 -0.7501068 0.0084481 -88.791 < 2e-16 ***
ORIGIN_SZQTSZ14 -1.9321849 0.0126114 -153.209 < 2e-16 ***
ORIGIN_SZQTSZ15 -0.9576828 0.0127157 -75.315 < 2e-16 ***
ORIGIN_SZRCSZ01 -1.8167951 0.0129234 -140.582 < 2e-16 ***
ORIGIN_SZRCSZ06 -0.5560563 0.0090507 -61.438 < 2e-16 ***
ORIGIN_SZRVSZ01 -2.8862570 0.0325532 -88.663 < 2e-16 ***
ORIGIN_SZRVSZ02 -3.1555662 0.0281279 -112.186 < 2e-16 ***
ORIGIN_SZRVSZ03 -2.9836089 0.0248449 -120.089 < 2e-16 ***
ORIGIN_SZRVSZ04 -3.5520422 0.0561371 -63.274 < 2e-16 ***
ORIGIN_SZRVSZ05 -2.5866584 0.0180382 -143.399 < 2e-16 ***
ORIGIN_SZSBSZ01 0.2867444 0.0071098 40.331 < 2e-16 ***
ORIGIN_SZSBSZ02 -0.9012334 0.0087262 -103.278 < 2e-16 ***
ORIGIN_SZSBSZ03 0.8311038 0.0055422 149.958 < 2e-16 ***
ORIGIN_SZSBSZ04 0.4044170 0.0062047 65.179 < 2e-16 ***
ORIGIN_SZSBSZ05 -0.2661845 0.0074162 -35.892 < 2e-16 ***
ORIGIN_SZSBSZ06 -0.9023075 0.0175046 -51.547 < 2e-16 ***
ORIGIN_SZSBSZ07 0.0505870 0.0131317 3.852 0.000117 ***
ORIGIN_SZSBSZ08 -1.1158011 0.0145416 -76.732 < 2e-16 ***
ORIGIN_SZSBSZ09 -0.9682835 0.0095396 -101.501 < 2e-16 ***
ORIGIN_SZSESZ02 1.1452735 0.0047810 239.548 < 2e-16 ***
ORIGIN_SZSESZ03 1.2815277 0.0045677 280.564 < 2e-16 ***
ORIGIN_SZSESZ04 0.8085857 0.0052756 153.269 < 2e-16 ***
ORIGIN_SZSESZ05 -0.2329413 0.0063113 -36.909 < 2e-16 ***
ORIGIN_SZSESZ06 1.0576879 0.0049909 211.925 < 2e-16 ***
ORIGIN_SZSESZ07 -2.3165908 0.0196831 -117.695 < 2e-16 ***
ORIGIN_SZSGSZ01 -0.6606350 0.0088079 -75.005 < 2e-16 ***
ORIGIN_SZSGSZ02 -1.3638984 0.0104040 -131.094 < 2e-16 ***
ORIGIN_SZSGSZ03 0.1152591 0.0054649 21.091 < 2e-16 ***
ORIGIN_SZSGSZ04 0.2954067 0.0050865 58.077 < 2e-16 ***
ORIGIN_SZSGSZ05 -2.0792678 0.0109882 -189.227 < 2e-16 ***
ORIGIN_SZSGSZ06 0.4563227 0.0048880 93.356 < 2e-16 ***
ORIGIN_SZSGSZ07 -0.8955254 0.0067100 -133.461 < 2e-16 ***
ORIGIN_SZSKSZ01 -0.3184402 0.0093032 -34.229 < 2e-16 ***
ORIGIN_SZSKSZ02 1.1160484 0.0063851 174.790 < 2e-16 ***
ORIGIN_SZSKSZ03 -0.2566692 0.0086021 -29.838 < 2e-16 ***
ORIGIN_SZSKSZ04 -1.5781827 0.0279394 -56.486 < 2e-16 ***
ORIGIN_SZSKSZ05 -0.2724361 0.0163597 -16.653 < 2e-16 ***
ORIGIN_SZSLSZ01 -2.4458625 0.0330301 -74.050 < 2e-16 ***
ORIGIN_SZSLSZ04 -0.0987076 0.0079626 -12.396 < 2e-16 ***
ORIGIN_SZSRSZ01 -2.2584977 0.0176647 -127.854 < 2e-16 ***
ORIGIN_SZTHSZ01 -2.5878524 0.0489998 -52.814 < 2e-16 ***
ORIGIN_SZTHSZ03 -0.8101746 0.0226814 -35.720 < 2e-16 ***
ORIGIN_SZTHSZ04 -2.4186655 0.0288663 -83.789 < 2e-16 ***
ORIGIN_SZTHSZ06 -1.7080541 0.0186353 -91.657 < 2e-16 ***
ORIGIN_SZTMSZ01 -0.2193476 0.0061823 -35.480 < 2e-16 ***
ORIGIN_SZTMSZ02 1.7772464 0.0043394 409.558 < 2e-16 ***
ORIGIN_SZTMSZ03 1.0051343 0.0046055 218.249 < 2e-16 ***
ORIGIN_SZTMSZ04 0.1642370 0.0055078 29.819 < 2e-16 ***
ORIGIN_SZTMSZ05 -1.2878706 0.0114828 -112.157 < 2e-16 ***
ORIGIN_SZTNSZ01 -1.7163504 0.0131268 -130.751 < 2e-16 ***
ORIGIN_SZTNSZ02 -1.6508988 0.0103851 -158.968 < 2e-16 ***
ORIGIN_SZTNSZ03 -2.1545577 0.0137947 -156.187 < 2e-16 ***
ORIGIN_SZTNSZ04 -0.3949120 0.0078496 -50.310 < 2e-16 ***
ORIGIN_SZTPSZ01 -0.8058100 0.0069916 -115.253 < 2e-16 ***
ORIGIN_SZTPSZ02 0.5369060 0.0047272 113.577 < 2e-16 ***
ORIGIN_SZTPSZ03 -0.7779333 0.0064278 -121.027 < 2e-16 ***
ORIGIN_SZTPSZ04 -0.8153581 0.0061387 -132.823 < 2e-16 ***
ORIGIN_SZTPSZ05 -0.5073676 0.0067771 -74.865 < 2e-16 ***
ORIGIN_SZTPSZ06 0.0847301 0.0065717 12.893 < 2e-16 ***
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ORIGIN_SZTSSZ02 0.0425804 0.0105088 4.052 5.08e-05 ***
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ORIGIN_SZTSSZ05 -1.0846732 0.0173555 -62.497 < 2e-16 ***
ORIGIN_SZTSSZ06 0.3980173 0.0198100 20.092 < 2e-16 ***
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ORIGIN_SZWCSZ02 -2.9863278 0.0330906 -90.247 < 2e-16 ***
ORIGIN_SZWCSZ03 -5.0504916 0.1241385 -40.684 < 2e-16 ***
ORIGIN_SZWDSZ01 1.5238429 0.0049404 308.448 < 2e-16 ***
ORIGIN_SZWDSZ02 0.2832576 0.0056218 50.386 < 2e-16 ***
ORIGIN_SZWDSZ03 1.3702524 0.0053266 257.245 < 2e-16 ***
ORIGIN_SZWDSZ04 1.0248225 0.0059272 172.903 < 2e-16 ***
ORIGIN_SZWDSZ05 0.2356778 0.0060587 38.899 < 2e-16 ***
ORIGIN_SZWDSZ06 0.3146925 0.0059919 52.520 < 2e-16 ***
ORIGIN_SZWDSZ07 -1.4971897 0.0091243 -164.088 < 2e-16 ***
ORIGIN_SZWDSZ08 -0.8894079 0.0087414 -101.747 < 2e-16 ***
ORIGIN_SZWDSZ09 1.4437633 0.0053160 271.590 < 2e-16 ***
ORIGIN_SZYSSZ01 -0.2519398 0.0064443 -39.095 < 2e-16 ***
ORIGIN_SZYSSZ02 0.8726785 0.0057658 151.354 < 2e-16 ***
ORIGIN_SZYSSZ03 1.7868139 0.0050674 352.611 < 2e-16 ***
ORIGIN_SZYSSZ04 0.8418040 0.0051738 162.704 < 2e-16 ***
ORIGIN_SZYSSZ05 0.4292096 0.0062520 68.652 < 2e-16 ***
ORIGIN_SZYSSZ06 -0.7459961 0.0119123 -62.624 < 2e-16 ***
ORIGIN_SZYSSZ07 -0.8422281 0.0144559 -58.262 < 2e-16 ***
ORIGIN_SZYSSZ08 0.1829428 0.0067885 26.949 < 2e-16 ***
ORIGIN_SZYSSZ09 1.1159712 0.0050760 219.853 < 2e-16 ***
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DESTIN_SZAMSZ03 0.0760100 0.0044639 17.028 < 2e-16 ***
DESTIN_SZAMSZ04 -1.1306391 0.0064373 -175.639 < 2e-16 ***
DESTIN_SZAMSZ05 -1.0751133 0.0065164 -164.985 < 2e-16 ***
DESTIN_SZAMSZ06 -0.9624298 0.0065937 -145.962 < 2e-16 ***
DESTIN_SZAMSZ07 -1.5060319 0.0097616 -154.281 < 2e-16 ***
DESTIN_SZAMSZ08 -0.4813202 0.0069794 -68.963 < 2e-16 ***
DESTIN_SZAMSZ09 -1.0220675 0.0066313 -154.129 < 2e-16 ***
DESTIN_SZAMSZ10 0.1235142 0.0047044 26.255 < 2e-16 ***
DESTIN_SZAMSZ11 -0.8917993 0.0088519 -100.746 < 2e-16 ***
DESTIN_SZAMSZ12 0.0195208 0.0051704 3.775 0.000160 ***
DESTIN_SZBDSZ01 0.9736349 0.0042757 227.713 < 2e-16 ***
DESTIN_SZBDSZ02 -0.1969470 0.0055284 -35.625 < 2e-16 ***
DESTIN_SZBDSZ03 0.1266471 0.0050786 24.938 < 2e-16 ***
DESTIN_SZBDSZ04 1.1608485 0.0041956 276.684 < 2e-16 ***
DESTIN_SZBDSZ05 0.9293840 0.0044412 209.265 < 2e-16 ***
DESTIN_SZBDSZ06 0.4090567 0.0050300 81.323 < 2e-16 ***
DESTIN_SZBDSZ07 -0.8171478 0.0098945 -82.586 < 2e-16 ***
DESTIN_SZBDSZ08 -1.5895287 0.0111632 -142.391 < 2e-16 ***
DESTIN_SZBKSZ01 -1.3793311 0.0072145 -191.189 < 2e-16 ***
DESTIN_SZBKSZ02 -0.5253670 0.0061879 -84.903 < 2e-16 ***
DESTIN_SZBKSZ03 -1.0095362 0.0065426 -154.301 < 2e-16 ***
DESTIN_SZBKSZ04 -0.5662858 0.0056453 -100.311 < 2e-16 ***
DESTIN_SZBKSZ05 -0.9406607 0.0070597 -133.244 < 2e-16 ***
DESTIN_SZBKSZ06 -1.3129276 0.0067414 -194.755 < 2e-16 ***
DESTIN_SZBKSZ07 0.0120605 0.0049284 2.447 0.014400 *
DESTIN_SZBKSZ08 -1.3658471 0.0075109 -181.849 < 2e-16 ***
DESTIN_SZBKSZ09 -0.1771310 0.0055645 -31.832 < 2e-16 ***
DESTIN_SZBLSZ01 -0.8175223 0.0075645 -108.074 < 2e-16 ***
DESTIN_SZBLSZ02 0.1631280 0.0071753 22.735 < 2e-16 ***
DESTIN_SZBLSZ03 1.2598494 0.0081706 154.194 < 2e-16 ***
DESTIN_SZBLSZ04 -0.5642975 0.0137827 -40.943 < 2e-16 ***
DESTIN_SZBMSZ01 0.6921844 0.0054211 127.684 < 2e-16 ***
DESTIN_SZBMSZ02 -0.1209392 0.0055362 -21.845 < 2e-16 ***
DESTIN_SZBMSZ03 -0.2373881 0.0062427 -38.027 < 2e-16 ***
DESTIN_SZBMSZ04 -0.0407117 0.0058001 -7.019 2.23e-12 ***
DESTIN_SZBMSZ05 -0.2363309 0.0075967 -31.110 < 2e-16 ***
DESTIN_SZBMSZ06 -1.1930710 0.0134761 -88.532 < 2e-16 ***
DESTIN_SZBMSZ07 0.4625103 0.0051864 89.178 < 2e-16 ***
DESTIN_SZBMSZ08 -0.8604731 0.0069899 -123.102 < 2e-16 ***
DESTIN_SZBMSZ09 -2.1290239 0.0154841 -137.498 < 2e-16 ***
DESTIN_SZBMSZ10 -1.4617153 0.0094014 -155.478 < 2e-16 ***
DESTIN_SZBMSZ11 -1.3234050 0.0085506 -154.773 < 2e-16 ***
DESTIN_SZBMSZ12 -0.8399230 0.0085361 -98.397 < 2e-16 ***
DESTIN_SZBMSZ13 0.1366529 0.0059697 22.891 < 2e-16 ***
DESTIN_SZBMSZ14 -1.0491968 0.0083021 -126.378 < 2e-16 ***
DESTIN_SZBMSZ15 -0.6726684 0.0076276 -88.189 < 2e-16 ***
DESTIN_SZBMSZ16 -1.4011734 0.0116569 -120.201 < 2e-16 ***
DESTIN_SZBMSZ17 -1.5682752 0.0167333 -93.722 < 2e-16 ***
DESTIN_SZBPSZ01 -1.1120017 0.0063197 -175.959 < 2e-16 ***
DESTIN_SZBPSZ02 -2.0833466 0.0091139 -228.590 < 2e-16 ***
DESTIN_SZBPSZ03 -1.6937265 0.0087437 -193.709 < 2e-16 ***
DESTIN_SZBPSZ04 -0.7964999 0.0066129 -120.447 < 2e-16 ***
DESTIN_SZBPSZ05 0.2109118 0.0048815 43.206 < 2e-16 ***
DESTIN_SZBPSZ06 -1.1808365 0.0083657 -141.152 < 2e-16 ***
DESTIN_SZBPSZ07 -0.2077428 0.0084543 -24.572 < 2e-16 ***
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DESTIN_SZBSSZ02 -0.4852688 0.0057001 -85.134 < 2e-16 ***
DESTIN_SZBSSZ03 0.4130432 0.0043061 95.921 < 2e-16 ***
DESTIN_SZBTSZ01 0.6215095 0.0048914 127.061 < 2e-16 ***
DESTIN_SZBTSZ02 -0.0145076 0.0071799 -2.021 0.043324 *
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DESTIN_SZBTSZ04 -0.6957555 0.0114078 -60.989 < 2e-16 ***
DESTIN_SZBTSZ05 0.3329814 0.0073568 45.262 < 2e-16 ***
DESTIN_SZBTSZ06 -0.1333295 0.0073965 -18.026 < 2e-16 ***
DESTIN_SZBTSZ07 -1.4449581 0.0113186 -127.663 < 2e-16 ***
DESTIN_SZBTSZ08 -0.7079056 0.0103797 -68.201 < 2e-16 ***
DESTIN_SZCBSZ01 -5.7344725 0.3162767 -18.131 < 2e-16 ***
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DESTIN_SZCHSZ02 0.5369606 0.0057531 93.334 < 2e-16 ***
DESTIN_SZCHSZ03 2.5530638 0.0043945 580.971 < 2e-16 ***
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DESTIN_SZCKSZ02 -1.1181852 0.0063287 -176.685 < 2e-16 ***
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DESTIN_SZCKSZ05 -1.1641791 0.0076248 -152.684 < 2e-16 ***
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DESTIN_SZCLSZ02 -2.0436501 0.0136039 -150.225 < 2e-16 ***
DESTIN_SZCLSZ03 -0.9338571 0.0082908 -112.638 < 2e-16 ***
DESTIN_SZCLSZ04 0.0532041 0.0053276 9.987 < 2e-16 ***
DESTIN_SZCLSZ05 -1.0782781 0.0088184 -122.276 < 2e-16 ***
DESTIN_SZCLSZ06 0.4068171 0.0049068 82.910 < 2e-16 ***
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DESTIN_SZCLSZ08 -0.2487993 0.0066588 -37.364 < 2e-16 ***
DESTIN_SZCLSZ09 0.1611080 0.0071178 22.635 < 2e-16 ***
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DESTIN_SZDTSZ13 -1.3685031 0.0162803 -84.059 < 2e-16 ***
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DESTIN_SZGLSZ02 -0.0692224 0.0052840 -13.100 < 2e-16 ***
DESTIN_SZGLSZ03 0.6493421 0.0043446 149.459 < 2e-16 ***
DESTIN_SZGLSZ04 0.9327947 0.0043674 213.583 < 2e-16 ***
DESTIN_SZGLSZ05 0.8161728 0.0043625 187.087 < 2e-16 ***
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DESTIN_SZHGSZ02 -0.8134329 0.0056721 -143.409 < 2e-16 ***
DESTIN_SZHGSZ03 -1.3546132 0.0066257 -204.448 < 2e-16 ***
DESTIN_SZHGSZ04 -0.4500588 0.0048448 -92.895 < 2e-16 ***
DESTIN_SZHGSZ05 -0.5026431 0.0050996 -98.566 < 2e-16 ***
DESTIN_SZHGSZ06 -0.8673686 0.0059530 -145.704 < 2e-16 ***
DESTIN_SZHGSZ07 0.0560490 0.0047702 11.750 < 2e-16 ***
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DESTIN_SZJESZ05 -1.5324974 0.0102612 -149.349 < 2e-16 ***
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DESTIN_SZJESZ07 -1.3234483 0.0085497 -154.795 < 2e-16 ***
DESTIN_SZJESZ08 -0.6559742 0.0083174 -78.867 < 2e-16 ***
DESTIN_SZJESZ09 0.2663752 0.0063370 42.035 < 2e-16 ***
DESTIN_SZJESZ10 0.8529026 0.0076067 112.126 < 2e-16 ***
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DESTIN_SZJWSZ02 -0.8746590 0.0060179 -145.342 < 2e-16 ***
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DESTIN_SZJWSZ09 1.0505330 0.0045908 228.832 < 2e-16 ***
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DESTIN_SZSLSZ04 -0.8586515 0.0073142 -117.396 < 2e-16 ***
DESTIN_SZSRSZ01 -1.1370887 0.0142148 -79.993 < 2e-16 ***
DESTIN_SZTHSZ01 -4.3259988 0.0368554 -117.378 < 2e-16 ***
DESTIN_SZTHSZ03 -2.6632914 0.0252720 -105.385 < 2e-16 ***
DESTIN_SZTHSZ04 -3.1000906 0.0216372 -143.276 < 2e-16 ***
DESTIN_SZTHSZ06 -2.5952642 0.0156340 -166.001 < 2e-16 ***
DESTIN_SZTMSZ01 -0.2092828 0.0059257 -35.318 < 2e-16 ***
DESTIN_SZTMSZ02 1.8238139 0.0039155 465.798 < 2e-16 ***
DESTIN_SZTMSZ03 0.8518259 0.0043636 195.210 < 2e-16 ***
DESTIN_SZTMSZ04 1.0222812 0.0043466 235.191 < 2e-16 ***
DESTIN_SZTMSZ05 0.6323777 0.0060058 105.294 < 2e-16 ***
DESTIN_SZTNSZ01 -0.3336078 0.0074388 -44.847 < 2e-16 ***
DESTIN_SZTNSZ02 -1.0820469 0.0101689 -106.408 < 2e-16 ***
DESTIN_SZTNSZ03 -1.4186505 0.0119906 -118.313 < 2e-16 ***
DESTIN_SZTNSZ04 -0.3058199 0.0074743 -40.916 < 2e-16 ***
DESTIN_SZTPSZ01 -0.4872299 0.0061571 -79.133 < 2e-16 ***
DESTIN_SZTPSZ02 0.7158441 0.0041312 173.278 < 2e-16 ***
DESTIN_SZTPSZ03 -0.4314229 0.0059917 -72.004 < 2e-16 ***
DESTIN_SZTPSZ04 -1.5898245 0.0076083 -208.959 < 2e-16 ***
DESTIN_SZTPSZ05 -1.0445550 0.0062363 -167.497 < 2e-16 ***
DESTIN_SZTPSZ06 -0.4319582 0.0070100 -61.621 < 2e-16 ***
DESTIN_SZTPSZ07 -2.1602303 0.0120352 -179.493 < 2e-16 ***
DESTIN_SZTPSZ08 -1.1920493 0.0093083 -128.063 < 2e-16 ***
DESTIN_SZTPSZ09 -0.2022481 0.0071137 -28.431 < 2e-16 ***
DESTIN_SZTPSZ10 -1.2464793 0.0090124 -138.308 < 2e-16 ***
DESTIN_SZTPSZ11 -0.0808445 0.0056019 -14.432 < 2e-16 ***
DESTIN_SZTPSZ12 -0.6784376 0.0066340 -102.267 < 2e-16 ***
DESTIN_SZTSSZ01 -1.5845062 0.0222086 -71.346 < 2e-16 ***
DESTIN_SZTSSZ02 -0.1886010 0.0146338 -12.888 < 2e-16 ***
DESTIN_SZTSSZ03 0.6525526 0.0092450 70.585 < 2e-16 ***
DESTIN_SZTSSZ04 0.5285464 0.0100182 52.759 < 2e-16 ***
DESTIN_SZTSSZ05 1.4670106 0.0104357 140.577 < 2e-16 ***
DESTIN_SZTSSZ06 2.5043588 0.0167444 149.564 < 2e-16 ***
DESTIN_SZWCSZ01 1.9787931 0.0054306 364.375 < 2e-16 ***
DESTIN_SZWCSZ02 -2.2593108 0.0127916 -176.624 < 2e-16 ***
DESTIN_SZWCSZ03 -3.1897655 0.0326927 -97.568 < 2e-16 ***
DESTIN_SZWDSZ01 1.0476108 0.0044629 234.738 < 2e-16 ***
DESTIN_SZWDSZ02 -1.3176990 0.0065894 -199.973 < 2e-16 ***
DESTIN_SZWDSZ03 0.3432057 0.0052496 65.377 < 2e-16 ***
DESTIN_SZWDSZ04 -0.7895927 0.0073392 -107.586 < 2e-16 ***
DESTIN_SZWDSZ05 -0.8751665 0.0072946 -119.975 < 2e-16 ***
DESTIN_SZWDSZ06 -0.2106221 0.0053027 -39.720 < 2e-16 ***
DESTIN_SZWDSZ07 -1.6050834 0.0071754 -223.692 < 2e-16 ***
DESTIN_SZWDSZ08 -0.5124717 0.0069223 -74.032 < 2e-16 ***
DESTIN_SZWDSZ09 0.3813542 0.0054697 69.721 < 2e-16 ***
DESTIN_SZYSSZ01 0.0853753 0.0046572 18.332 < 2e-16 ***
DESTIN_SZYSSZ02 -0.3227172 0.0057351 -56.271 < 2e-16 ***
DESTIN_SZYSSZ03 -0.4151283 0.0066299 -62.615 < 2e-16 ***
DESTIN_SZYSSZ04 -0.4637327 0.0058206 -79.671 < 2e-16 ***
DESTIN_SZYSSZ05 -1.5888242 0.0111001 -143.136 < 2e-16 ***
DESTIN_SZYSSZ06 -1.4606209 0.0107759 -135.545 < 2e-16 ***
DESTIN_SZYSSZ07 -0.7839065 0.0144357 -54.304 < 2e-16 ***
DESTIN_SZYSSZ08 0.6265412 0.0045504 137.691 < 2e-16 ***
DESTIN_SZYSSZ09 0.1520067 0.0048092 31.607 < 2e-16 ***
log(DIST) -1.8468315 0.0004608 -4008.033 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 47094011 on 14470 degrees of freedom
Residual deviance: 10420261 on 13912 degrees of freedom
AIC: 10510518
Number of Fisher Scoring iterations: 7
Functions
- glm from stats package is used to fit generalized linear models. In this code, a Poisson regression model is specified using the formula
TRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(DIST), withfamily = poisson(link = "log"). This sets up a model whereTRIPSis the dependent variable, andORIGIN_SZ,DESTIN_SZ, and the logarithm ofDISTare independent variables. data = inter_zonal_flowspecifies that the model should be fitted using theinter_zonal_flowdataset.na.action = na.excludeinstructs the model to exclude cases with missing values (NAs) in the model fitting process.- summary from base R provides a detailed summary of the fitted model
dbcSIM_Poisson. This includes information about the model coefficients, their statistical significance, residuals, and other diagnostic measures. - The
#| echo: falsedirective at the start indicates that this code chunk is executed but not displayed in the output when rendered in a document like an R Markdown report.
Next, let us examine how well the proportion of variance in the dependent variable (i.e. TRIPS) that can be explained by the explanatory variables. Using the R-Squared function written earlier, compute the R-Squared of the Doubly-constrined Model.
Code
CalcRSquared(dbcSIM_Poisson$data$TRIPS,
dbcSIM_Poisson$fitted.values)[1] 0.7001882
Functions
- The custom function
CalcRSquared, defined earlier, is used here to calculate the coefficient of determination (R-squared). This statistical measure indicates how well the estimated values (dbcSIM_Poisson$fitted.values) approximate the actual, observed values (dbcSIM_Poisson$data$TRIPS). - In this code,
dbcSIM_Poisson$data$TRIPSrefers to the actual observed values of trips, anddbcSIM_Poisson$fitted.valuesrefers to the values estimated by thedbcSIM_Poissongeneralized linear model. - The function call
CalcRSquared(dbcSIM_Poisson$data$TRIPS, dbcSIM_Poisson$fitted.values)computes the R-squared value, which quantifies the proportion of variance in the observed data that can be explained by the model’s estimated values.
Notice that there is a relatively greater improvement in the R-Squared value.
2.5 Model comparison
2.5.1 Statistical measures
Another useful model performance measure for continuous dependent variable is Root Mean Squared Error. In this sub-section, you will learn how to use compare_performance() of performance package
First of all, create a list called model_list by using the code chunk below.
Code
model_list <- list(
Origin_Constrained = orcSIM_Poisson,
Doubly_Constrained = dbcSIM_Poisson)
Functions
list from base R is a generic function to create lists. In this code, model_list is created to store different model objects: Origin_Constrained stores the orcSIM_Poisson model, and Doubly_Constrained stores the dbcSIM_Poisson model.
Next, compute the RMSE of all the models in model_list file by using the code chunk below.
Code
compare_performance(model_list,
metrics = "RMSE")# Comparison of Model Performance Indices
Name | Model | RMSE
-------------------------------------
Origin_Constrained | glm | 2613.236
Doubly_Constrained | glm | 1906.694The print above reveals that doubly constrained SIM is the best model among the two SIMs because it has the smallest RMSE value of 1906.694.
2.5.2 Visualising fitted values
In this section, visualise the observed values and the fitted values.
Firstly we will extract the fitted values from Origin-constrained Model by using the code chunk below.
Code
df <- as.data.frame(orcSIM_Poisson$fitted.values) %>%
round(digits = 0)Next, append the fitted values into inter_zonal_flow data frame by using the code chunk below.
Code
inter_zonal_flow <- inter_zonal_flow %>%
cbind(df) %>%
rename(orcTRIPS = "orcSIM_Poisson.fitted.values")
Functions
- cbind from base R combines data frames or matrices by columns. In this code, it’s used to add the columns from
dftointer_zonal_flow. - rename from dplyr package changes the name of a specific column in a data frame. Here, the column named
orcSIM_Poisson.fitted.valuesin the merged data frame is renamed toorcTRIPS. Notice thatrename()is used to rename the field name and the$in the original field name has been replaced with an.. This is because R replaced$with.during thecbind().
Repeat the same step for Doubly Constrained Model (i.e. dbcSIM_Poisson)
Code
df <- as.data.frame(dbcSIM_Poisson$fitted.values) %>%
round(digits = 0)Code
inter_zonal_flow <- inter_zonal_flow %>%
cbind(df) %>%
rename(dbcTRIPS = "dbcSIM_Poisson.fitted.values")Next, two scatterplots will be created by using geom_point() and other appropriate functions of ggplot2 package. And be put into a single visual for better comparison.
Code
orc_p <- ggplot(data = inter_zonal_flow,
aes(x = orcTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm) +
coord_cartesian(xlim=c(0,150000),
ylim=c(0,150000))
dbc_p <- ggplot(data = inter_zonal_flow,
aes(x = dbcTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm) +
coord_cartesian(xlim=c(0,150000),
ylim=c(0,150000))
ggarrange(orc_p, dbc_p,
ncol = 2,
nrow = 1)
Functions
- ggplot from ggplot2 package creates a new ggplot graph, specifying its aesthetic mappings. In this code,
ggplotis used twice to create two plots (orc_panddbc_p), each with different x-axis variables (orcTRIPSfororc_p,dbcTRIPSfordbc_p) but the same y-axis variable (TRIPS). - geom_point from ggplot2 package adds a scatterplot layer to the ggplot.
- geom_smooth from ggplot2 package adds a smoothed line to the plot, here using a linear model (
lmmethod) for fitting. - coord_cartesian from ggplot2 package sets the limits for the x and y axes without changing the scale. Both plots have their axes limited to the range of 0 to 150,000.
- The code snippets create two plots comparing the fitted values from two different models (
orcSIM_PoissonanddbcSIM_Poisson) against observed trips (TRIPS), with scatter plots and linear regression lines.
Quiz Answer
From the figure, the left graph shows the relationship between the observed trips (TRIPS) and the estimated trips from the Origin constrained model (orcTRIPS). The dispersion of points and the less pronounced trend line suggest that the model does not predict the observed trips as accurately. The right graph, showing the relationship between observed trips (TRIPS) and the estimated trips from the Doubly Constrained Model (dbcTRIPS), displays a much tighter alignment of points along the trend line, indicating a more accurate prediction of the observed trips.
The follow-up action would be to further investigate the Doubly Constrained Model since it appears to be more effective at predicting trip patterns. This could involve examining the underlying assumptions of the model, the parameters used, and possibly applying it to another set of data for validation purposes. It would also be prudent to look into the reasons why the Origin constrained model performs less accurately to understand the limitations or potential areas for model improvement.