Take-home Exercise 2

0. Goals & Objectives.

Note

“A map is not interesting; the patterns and factors revealed by the map is interesting. Can we explain things by building a spatial model?” -- Prof Kam

In this study, we construct a Spatial Interaction Model to determine factors affecting urban mobility patterns, specifically public bus transit. This helps us demonstrate the potential value of Geospatial Data Science & Analysis, by harnessing the explosive growth of data from computing technologies like SMART cards for public transport.

More specifically, we study public bus mobility patterns during Weekday Evening peak periods.

In this study, we build a Generalised Linear Regression Model (GLM) to study a Modifible Areal Unit Problem (MAUP). Singapore’s Master Plan Subzone (MPSZ) is too large and coarse for study; instead, we create analytical hexagons to approximate a traffic/transportation analysis zone (TAZ).

More detail about the task from: https://isss624-ay2023-24nov.netlify.app/take-home_ex02

Important Note

Due to the nature of EDA and Data Analysis, parts of this page have been Collapsed or placed behind tabs, to avoid excessive scrolling.

For easier reading, this study is also presented in point-form.

0.1 Datasets used

0.1.1 Aspatial Dataset

  • Two aspatial datasets were used in this study, as described below:
Table 1: Aspatial Datasets used. |
Dataset, Purpose & Source: Key columns

hdb.csv : HDB Property information data with geocoding

Via data.gov
  • lat, long: coordinates |
  • max_floors, total_dwelling_units : idea of how many units each HDB holds

origin_destination_bus_202310 : Volume of bus passenger trips, by origin/destination, data prepared for 2023 October

Via LTA DataMall
  • ORIGIN_PT_code, DESTINATION_PT_code: O/D information on bus trip
  • TIME_PER_HOUR, DAY_TYPE: Time/Date data on when the trips were taken
  • TOTAL_TRIPS: Bus trip passenger volume

0.1.2 Geospatial Dataset

  • Geospatial datasets were used for two major purposes in this study:

    • To provide context: MPSZ2019 helped give us the outline of Singapore and to provide context for our analytical hexagons/TAZ in the study. Importantly, BusStop also helped trace the location of bus stops to locate the flow of traffic.

    • As explanatory variables: Details such as the location of businesses, F&B outlets, and retail areas.

Table 2: Geospatial Datasets used. |
Filename: Purpose
MPSZ-2019 Shapefile To provide geographical context for analytical hexagons
BusStop Shapefile To identify location of Bus Stops by bus stop number

Shapefiles provided by Prof Kam:

  • Business

  • entertn

  • F&B

  • FinServ

  • Liesure&Recreation

  • Retails

 To provide estimation of density/number for use in spatial interaction modelling

MRT Shapefiles, via LTA Datamall:

  • RapidTransitSystemStation

  • Train_Station_Exit_Layer

 For analysis of MRT stations / MRT station exits in relation to bus flow traffic

1. Geospatial Data Wrangling

This study was performed in R, written in R Studio, and published using Quarto.

1.1 Import Packages

This function calls pacman to load a number of key R packages for use. The following packages are grouped thematically by function.

  • tmap : For thematic mapping; a powerful mapping package for geospatial visualisation
    • leaflet: for custom layer controls over tmap visualisations.
  • sf : For geospatial data handling, but also geoprocessing of buffer zones, point-in-polygon count, etc;
    • sp : An earlier iteration of sf, but loaded here for its high performance spDists() functions
    • sfdep : For useful functions when creating weight matrix, LISA calculations etc;
    • wdpar: For unique function to fix invalid geometry.
  • tidyverse : For non-spatial data handling; commonly used R package and contains dplyr for dataframe manipulation and ggplot for data visualization;
    • reshape2 : For the melt() function, which suits our need better than tidyr’s pivot_longer() alternative
    • patchwork: For arranging subplots created by ggplot with simpler syntax
    • DT: for displaying datatables;
  • stplanar: For creating desire lines to visualize O/D flows
  • performance: For comparing performance and RMSE across models
# NB: Patchwork is still in development, and installed directly from github. Uncomment the following line if you face patchwork errors.
# devtools::install_github("thomasp85/patchwork")

pacman::p_load(tmap, sf, sfdep, tidyverse, DT, leaflet, stplanr, sp, reshape2, wdpar, patchwork, performance)

1.2 Import Geospatial Data I

1.2.1 raw_bus_stop_sf: Load Geospatial Bus Stop Data

  • First, we load BusStop shapefile data from LTA Datamall;
  • st_read() is used to import the ESRI Shapefile data into an sf dataframe.
    • From previous take-home exercise, we know BusStop has the incorrect CRS (coordinate reference system), as EPSG 9001 instead of 3414, so we use st_transform() to correct this
    • We use head() to preview the first 6 rows
show code 
raw_bus_stop_sf <- st_read(dsn = "data/geospatial", 
                 layer = "BusStop") %>%
  st_transform(crs = 3414)
Reading layer `BusStop' from data source 
  `C:\1darren\ISSS624\Take-home_Ex02\data\geospatial' using driver `ESRI Shapefile'
Simple feature collection with 5161 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 3970.122 ymin: 26482.1 xmax: 48284.56 ymax: 52983.82
Projected CRS: SVY21
show code 
head(raw_bus_stop_sf)
Simple feature collection with 6 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 13228.59 ymin: 30391.85 xmax: 41603.76 ymax: 44206.38
Projected CRS: SVY21 / Singapore TM
  BUS_STOP_N BUS_ROOF_N             LOC_DESC                  geometry
1      22069        B06   OPP CEVA LOGISTICS POINT (13576.31 32883.65)
2      32071        B23         AFT TRACK 13 POINT (13228.59 44206.38)
3      44331        B01              BLK 239  POINT (21045.1 40242.08)
4      96081        B05 GRACE INDEPENDENT CH POINT (41603.76 35413.11)
5      11561        B05              BLK 166 POINT (24568.74 30391.85)
6      66191        B03         AFT CORFE PL POINT (30951.58 38079.61)
  • We check the coordinate reference system with st_crs(); and see that it is now indeed correctly set to 3414:
show code 
st_crs(raw_bus_stop_sf)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
  • We use qtm() to perform a quick visualization of the various bus stops:
show code 
tmap_mode("plot")
tmap mode set to plotting
show code 
qtm(raw_bus_stop_sf)

However, this is hard to visualize without the context of boundaries and details. Let’s load the mpsz shapefile to provide geographical context

1.2.2 mpsz_sf: Visualizing Singapore’s Master Plan 2019 Subzone Boundaries

  • We now load Master Plan 2019 Subzone Boundary to provide geographical context for our bus stops.

  • Next, we load MPSZ-2019 shapefile data from Data.gov.sg, comprising Master Plan 2019 Subzone Boundary (No Sea) data ;

  • st_read() is used to import the ESRI Shapefile data into an sf dataframe;

    • We use st_crs() to check the Coordinate Reference System (CRS);
show code 
mpsz_sf <- st_read(dsn = "data/geospatial", 
                 layer = "MPSZ-2019")
Reading layer `MPSZ-2019' from data source 
  `C:\1darren\ISSS624\Take-home_Ex02\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 84
show code 
st_crs(mpsz_sf)
Coordinate Reference System:
  User input: WGS 84 
  wkt:
GEOGCRS["WGS 84",
    DATUM["World Geodetic System 1984",
        ELLIPSOID["WGS 84",6378137,298.257223563,
            LENGTHUNIT["metre",1]]],
    PRIMEM["Greenwich",0,
        ANGLEUNIT["degree",0.0174532925199433]],
    CS[ellipsoidal,2],
        AXIS["latitude",north,
            ORDER[1],
            ANGLEUNIT["degree",0.0174532925199433]],
        AXIS["longitude",east,
            ORDER[2],
            ANGLEUNIT["degree",0.0174532925199433]],
    ID["EPSG",4326]]
  • We see that MPSZ-2019 is set to WGS 84/EPSG 4326 projection, which is inconsistent with the rest of our dataset;
  • Thus, we use st_transform() to reproject the data to SVY21/EPSG 3414 Coordinate Reference System (CRS) to ensure consistent distance calculation:
show code 
mpsz_sf <- mpsz_sf %>%
  st_transform(crs=3414)
st_crs(mpsz_sf)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
  • Now, let’s visualize the bus stop within the mpsz subzone boundaries;
  • We set tmap_mode("plot") to allow us to scroll;
  • We use tm_shape() + tm_polygons() to map a base layer of the mpsz boundaries;
    • On top of which, we layer tm_shape() + tm_dots() to show the bus stops.
show code 
tmap_mode("plot")
tmap mode set to plotting
show code 
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz_sf) +
  tm_polygons() + 
  tm_shape(raw_bus_stop_sf) + 
  tm_dots()
Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

  • We note there are a number of bus stops outside Singapore’s boundaries; Specifically, three bus stops in a cluster just outside the Causeway, and one further North.
  • We perform several steps to isolate & check the data;
    • we use st_filter() to find bus stops within Singapore’s Administrative National Boundaries, and create sg_bus_stop_sf for future use.
    • to check what bus stops have been dropped, we use anti_join() to compare raw_bus_stop_sf with sg_bus_stop_sf. We use st_drop_geometry on both sf dataframes to only compare the non-geometry columns.
show code 
sg_bus_stop_sf <- st_filter(raw_bus_stop_sf, mpsz_sf)
anti_join(st_drop_geometry(raw_bus_stop_sf), st_drop_geometry(sg_bus_stop_sf))
Joining with `by = join_by(BUS_STOP_N, BUS_ROOF_N, LOC_DESC)`
  BUS_STOP_N BUS_ROOF_N            LOC_DESC
1      47701        NIL          JB SENTRAL
2      46239         NA          LARKIN TER
3      46609         NA     KOTARAYA II TER
4      46211        NIL JOHOR BAHRU CHECKPT
5      46219        NIL JOHOR BAHRU CHECKPT
  • We see there are in fact 5 bus stops outside of Singapore (including the defunct Kotaraya II Terminal) that have been removed, which means our data cleaning was correct.

1.3 Geospatial Data Cleaning

1.3.1 Removing Duplicate Bus Stops

  • From Take-home Exercise 1, we know that there are a number of repeated bus stops. We repeat some steps;
  • We use length() to find the total number of raw values in the $BUS_STOP_N column of sg_bus_stop_sf;
    • We then compare this to length(unique()) to find the unique values;
  • And, indeed, we find there are 16 bus stops that are repeated;
cat("\nResults before removing duplicates: \n=======================================================\n")

Results before removing duplicates: 
=======================================================
cat("Total number of rows in sg_bus_stop_sf\t\t: ", paste0(length(sg_bus_stop_sf$BUS_STOP_N)))
Total number of rows in sg_bus_stop_sf      :  5156
cat("\nTotal unique bus stop IDs in sg_bus_stop_sf\t: ", paste0(length(unique(sg_bus_stop_sf$BUS_STOP_N))))

Total unique bus stop IDs in sg_bus_stop_sf :  5140
cat("\nRepeated bus stops\t\t\t\t:   ", paste0(length(sg_bus_stop_sf$BUS_STOP_N) - length(unique(sg_bus_stop_sf$BUS_STOP_N))))

Repeated bus stops              :    16
  • It appears there are 16 datapoints that are specifically repeated; let’s remove them by deleting the duplicated rows:
    • we use duplicated() to identify rows with repeated values of $BUS_STOP_N; duplicated rows will return TRUE while all other rows will return FALSE
    • We use ! to invert the values, so only the unduplicated rows will return TRUE.
    • We then use square brackets [] to index sg_bus_stop_sf based on the rows, and return only the unduplicated rows;
    • We then assign the output using <- into bus_stop_sf, for use.
show code 
bus_stop_sf <- sg_bus_stop_sf[!duplicated(sg_bus_stop_sf$BUS_STOP_N), ]
head(bus_stop_sf)
Simple feature collection with 6 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 13228.59 ymin: 30391.85 xmax: 41603.76 ymax: 44206.38
Projected CRS: SVY21 / Singapore TM
  BUS_STOP_N BUS_ROOF_N             LOC_DESC                  geometry
1      22069        B06   OPP CEVA LOGISTICS POINT (13576.31 32883.65)
2      32071        B23         AFT TRACK 13 POINT (13228.59 44206.38)
3      44331        B01              BLK 239  POINT (21045.1 40242.08)
4      96081        B05 GRACE INDEPENDENT CH POINT (41603.76 35413.11)
5      11561        B05              BLK 166 POINT (24568.74 30391.85)
6      66191        B03         AFT CORFE PL POINT (30951.58 38079.61)
show code 
cat("\nResults after removing duplicates: \n=======================================================\n")

Results after removing duplicates: 
=======================================================
show code 
cat("Total number of rows in bus_stop_sf\t\t: ", paste0(length(bus_stop_sf$BUS_STOP_N)))
Total number of rows in bus_stop_sf     :  5140
show code 
cat("\nTotal unique bus stop IDs in bus_stop_sf\t: ", paste0(length(unique(bus_stop_sf$BUS_STOP_N))))

Total unique bus stop IDs in bus_stop_sf    :  5140
show code 
cat("\nRepeated bus stops\t\t\t\t:   ", paste0(length(bus_stop_sf$BUS_STOP_N) - length(unique(bus_stop_sf$BUS_STOP_N))))

Repeated bus stops              :    0
  • We can do a quick check to visualize these;
    • We use tmap_mode("view") to allow us to scroll around and check that the bus stops fall within Singapore’s national boundaries, and set zoom limits to focus the attention
    • We combine tm_shape() and tm_polygons() to map the master plan subzones in grey;
    • We combine tm_shape() and tm_dots() to map locations of bus stops; for visual distinction with the grey zones, we use the “Spectral” palette
show code 
tmap_mode("view")
tmap mode set to interactive viewing
show code 
tm_shape(mpsz_sf) +
  tm_polygons() + 
  tm_shape(bus_stop_sf) + 
  tm_dots(col = "BUS_STOP_N", palette = "Spectral", legend.show = FALSE) + 
  tm_view(set.zoom.limits = c(11, 13))
Warning: The shape mpsz_sf is invalid (after reprojection). See sf::st_is_valid
Warning: Number of levels of the variable "BUS_STOP_N" is 5140, which is larger
than max.categories (which is 30), so levels are combined. Set
tmap_options(max.categories = 5140) in the layer function to show all levels.
show code 
tmap_mode("plot")
tmap mode set to plotting
  • Now, we can start preparing the hexagon map.

1.4 Generating Hexagon Map of Analytical Hexagons

  • We generate the hexagon map in three steps:
  1. We use st_make_grid() with square = FALSE to create the hexagon layer as defined in the study, which we name raw_hex_grid;
    • We pass cellsize = 750 to create the hexagons of necessary size. Prof Kam defined the apothem as 375m, as the Traffic Analysis Zone is typically 750m in size.
    • We use st_transform() just in case we need to reproject the coordinate system, just in case.
  2. We use st_sf() to convert raw_hex_grid into an sf dataframe for further manipulation later; - However, trying to visualize this right now just gives us a map full of hexagons, so we need to eliminate the empty hexagons;
    • We use mutate() to create a new column, $n_bus_stops that counts the number of bus stops in each hexagon using lengths(st_intersects())
      • st_intersects() gives us a list of bus stops in each hexagon, so we use lengths() to count the number
  3. We create our final sf dataframe, hexagon_sf in two steps;
    • First, we use filter() to select only hexagons with nonzero number of bus stops;
    • Then, mutate() is used here to create a grid_id column, labelling only the hexagons with nonzero bus stops.
  • Finally, we perform a quick plot to confirm that every bus stop is inside a hexagon;
    • Using hexagon_sf as our base layer, we use tmap_shape() and tm_polygons() to visualizes our hexes. We pass palette = "Spectral" for visual distinguishment against the black dots of the bus stops.
    • We use tmap_shape() and tm_dots() to visualize our bus stop as black dots
show code 
# STEP 1 - Create hexagon map 
raw_hex_grid <- st_make_grid(bus_stop_sf, cellsize =750, square = FALSE) %>%
  st_transform(crs = 3414)

# STEP 2 - Convert to sf object and count the number of bus stops inside;
raw_hex_grid <- st_sf(raw_hex_grid) %>%
  mutate(n_bus_stops = lengths(st_intersects(raw_hex_grid, sg_bus_stop_sf))) 

# Count number of points in each grid, code snippet referenced from: 
# https://gis.stackexchange.com/questions/323698/counting-points-in-polygons-with-sf-package-of-r


# STEP 3 - Filter for nonempty hexes and label:

hexagon_sf <- filter(raw_hex_grid, n_bus_stops > 0) 
hexagon_sf <- hexagon_sf %>%
  mutate(grid_id = 1:nrow(hexagon_sf)) %>%
  select(grid_id, raw_hex_grid, n_bus_stops)

write_rds(hexagon_sf, "data/rds/hexagon_sf.rds")

tmap_mode("plot")
tmap mode set to plotting
show code 
tm_shape(hexagon_sf) +
  tm_polygons(col = "grid_id", palette = "Spectral", legend.show = FALSE) + 
  tm_shape(bus_stop_sf) + 
  tm_dots()

show code 
tmap_mode("plot")
tmap mode set to plotting
  • We can visually confirm that every black dot is within a hexagon.
  • We re-use a bit of code from Take-Home Exercise 1 to plot our analytical hexagons on a map of Singapore and visualize the number of bus stops in each hexagon:
show code 
tmap_mode("view")
tmap mode set to interactive viewing
show code 
tm_basemap(providers$OneMapSG.Grey) + 
  tm_shape(hexagon_sf) +
  tm_fill(
    col = "n_bus_stops",
    palette = "-plasma",
    style = "cont",
    breaks = c(0, 4, 8, 12, 16, 20),
    title = "Number of bus_stops",
    id = "grid_id",
    showNA = FALSE,
    alpha = 0.6,
    popup.vars = c(
      "Number of Bus Stops: " = "n_bus_stops"
    ),
    popup.format = list(
      n_bus_stops = list(format = "f", digits = 0)
    )
  ) +
  tm_borders(col = "grey40", lwd = 0.7)  + 
  tm_view(set.zoom.limits = c(11, 13))
show code 
tmap_mode("plot")
tmap mode set to plotting
  • Note the advantage of using OneMapSG: We can see the faint lines of the MRT system underneath, connecting the darker regions of hexagons with high bus-stop-density. This may be a clue for later on.
  • We perform some simple stats to count the total number of filtered hexagons, and to see the maximum number of bus stops in a hexagon.
    • Since our hexagons cover a larger area, the number of raw and filtered analytical hexagons have decreased compared to Take-Home Exercise 1;
    • However, the maximum number of bus stops per hexagon is higher, with 8 hexagons holding 17-19 bus stops.
show code 
# NB: Code reused from my own take-home exercise 1
cat(paste("Total number of raw hexagons is\t\t\t: ", nrow(raw_hex_grid), "\n"))
cat(paste("Total number of hexagons (n_bus_stop > 1) is\t: ", nrow(hexagon_sf)), "\n")

cat("\nPrinting map_hexagon_sf:\n >> ")
hexagon_sf[hexagon_sf$n_bus_stops > 16, ]
  • For the next step, we’ll need to manage the Aspatial bus trips dataset, which is what we’ll work on now.

1.5 Aspatial Data Wrangling: Bus Trip Dataset

1.5.1 Import Bus O/D Dataset

  • For our purposes, we will focus only on 2023-October Passenger Volume by Origin Destination Bus Stops, downloaded from LTA DataMall;

  • We use read_csv() to load the data from the .csv file;

  • We use select() with a - sign to remove two columns redundant for our analysis:

    • $PT_TYPE column indicates the type of public transport, however, every value is “BUS”
    • $YEAR_MONTH column similarly has “2023-10” for every value, which we are aware of
    • With this in mind, we drop these two columns to save space.

  • Finally, we use mutate_at() to convert two columns ($ORIGIN_PT_CODE and $DESTINATION_PT_CODE)from character to factor, for easier analysis.

  • We use str() to check the columns, datatypes, and number of rows:

show code 
odbus_2310 <- read_csv("data/aspatial/origin_destination_bus_202310.csv") %>%
  select( -PT_TYPE, -YEAR_MONTH) %>%
  mutate_at(c("ORIGIN_PT_CODE", "DESTINATION_PT_CODE"), as.factor)

str(odbus_2310)
  • This is a huge tibble dataframe with over 5 million rows, so we will filter this now by peaks;
  • For this study, we focus on Weekday afternoon peak

1.5.2 Filter For Peaks – Weekday Afternoon

  • We now perform a multi-step filter process;
    1. We combine mutate() with case_when() to create a new column, $PEAK, based on the study criteria:
      1. We set the value to “WEEKDAY_AFTERNOON_PEAK” if $DAY_TYPE is “WEEKDAY” and bus tap-on time (e.g. $TIME_PER_HOUR) is between 5 pm and 8pm, inclusive;
        • Note that we convert the values for $TIME_PER_HOUR to 24-hour clock, e.g. “5pm” is “17” hundred hours, “8pm” is “20” hundred hours.
      2. For all remaining values, we assign an “Unknown” value.
    2. We then use filter() to eliminate those with “Unknown” $PEAK values, i.e. rows outside the period of interest for the study
    3. We use group_by() to group the values by $ORIGIN_PT_CODE and $DESTINATION_PT_CODE, and use summarise() to aggregate the sum of $TOTAL_TRIPS as a new column, $TRIPS.
    4. We use write_rds() to save the output dataframe, odbus_filtered, as an RDS object for future reference/load.
show code 
odbus_filtered <- odbus_2310 %>%
  mutate(PEAK = case_when(
    DAY_TYPE == "WEEKDAY" & TIME_PER_HOUR >= 17 &  TIME_PER_HOUR <= 20 ~ "WEEKDAY_AFTERNOON_PEAK",
    TRUE ~ "Unknown"
  )) %>%
  filter(
    case_when(
      PEAK == "Unknown" ~ FALSE,
      TRUE ~ TRUE
    )) %>%
  group_by(ORIGIN_PT_CODE, DESTINATION_PT_CODE) %>%
  summarise(TRIPS = sum(TOTAL_TRIPS))


write_rds(odbus_filtered, "data/rds/odbus_filtered_weekday.rds")
head(odbus_filtered)

1.6 od_data: Creating bus trip flow data between hexagons

  • For our study purposes, we need to have the number of bus trips originating from each hexagon. In order to achieve this, we must combine our three current dataframes:
    • hexagon_sf, an sf dataframe with $grid_id column (primary key) and the specific polygon geometry of each hexagon;
    • bus_stop_sf, an sf dataframe with the $BUS_STOP_N (primary key) and the point geometry of each bus stop;
    • odbus_filtered, a tibble dataframe with the $ORIGIN_PT_CODE (primary key) column and the trip details for each of the four peak periods of interest.

1.6.1 bus_stop_hexgrid_id: Identify Hexagon grid_id For Each Bus Stop

  • First, we combine hexagon_sf with sg_bus_stop_sf ;
    • We use st_intersection to combine the dataframes such that each row of sg_bus_stop_sf has an associated grid_id;
    • We use select() to filter the resultant bus_stop_hexgrid_id dataframe to only $grid_id and $BUS_STOP_N columns, and use st_drop_geometry() to convert into a simple dataframe with just two columns:
show code 
bus_stop_hexgrid_id <- st_intersection(bus_stop_sf, hexagon_sf) %>%
  select(BUS_STOP_N, grid_id) %>%
  st_drop_geometry()

cat("\nNumber of bus stops\t:", length(unique(bus_stop_hexgrid_id$BUS_STOP_N)))
cat("\nNumber of hexgrids\t:", length(unique(bus_stop_hexgrid_id$grid_id)))

head(bus_stop_hexgrid_id)
  • Let’s check if there’s any duplicates:
show code 
cat("\nNumber of unique bus stops\t\t:", length(unique(bus_stop_hexgrid_id$BUS_STOP_N)))
cat("\nNumber of unique hexgrids\t\t: ", length(unique(bus_stop_hexgrid_id$grid_id)))
cat("\nNumber of hexgrids in hexagon_sf\t: ", length(unique(hexagon_sf$grid_id)))

cat("\n\nPrinting rows with duplicated bus stop values :", bus_stop_hexgrid_id$BUS_STOP_N[duplicated(bus_stop_hexgrid_id$BUS_STOP_N)])
cat("\n\n(If the above rows are empty, there are no duplicates!)")
  • We have confirmed there are no duplicates in bus_stop_hexgrid_id.

1.6.2 od_data: Creating flow data by $ORIGIN_HEX, $DESTIN_HEX

  • Now we append hexagon code onto odbus_filtered. We do this in two steps; first adding the origin hexagon, then destination hexagon.
  • First, we use left_join() to add the hexagon $grid_id by BUS_STOP_N number;
    • We use rename() to rename columns, and specify the origin bus stop and origin hexagon grid_id as ORIGIN_BS and ORIGIN_HEX respectively;
    • We create a duplicate tibble data.frame to check for duplicate results, and luckily we see an empty tibble
show code 
od_data <- left_join(odbus_filtered , bus_stop_hexgrid_id,
            by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
  rename(ORIGIN_BS = ORIGIN_PT_CODE,
         ORIGIN_HEX = grid_id)
duplicate <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()
duplicate
  • duplicate returns an empty tibble dataframe, confirming we have no duplicate results.
  • Now we repeat the step, appending the destination hexagon grid_id as $DESTIN_HEX and once again checking for duplicates:
show code 
od_data <- left_join(od_data , bus_stop_hexgrid_id,
            by = c("DESTINATION_PT_CODE" = "BUS_STOP_N")) %>%
  rename(DESTIN_BS = DESTINATION_PT_CODE,
         DESTIN_HEX = grid_id)
duplicate <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()
duplicate
  • Once again, we have an empty tibble.
  • Finally, we now create the final version of our flow dataset.
    • Just to be safe, we perform a step to remove duplicates using unique()
    • drop_na() removes bus stops for which we have no info. It turns out there are bus stop numbers outside our bus stop dataset, like 03361, 03549, 03579, 59009;
      • Some of these may be new bus stops, like 03361, Gardens by the Bay Stn Exit 2, and 03549
    • We use group_by() to combine rows with the same $ORIGIN_HEX and $DESTIN_HEX, and aggregate the number of trips with summarise()
show code 
od_data <- od_data %>%
  unique() %>%
  drop_na() %>%
  group_by(ORIGIN_HEX, DESTIN_HEX) %>%
  summarise(SUM_TRIPS = sum(TRIPS))
head(od_data)
  • Now we write the output to RDS
show code 
write_rds(od_data, "data/rds/od_data.rds")

1.7 flowLine: Creating desire lines to visualize O/D of commuter flows

  • From previous, we load od_data:
show code 
od_data <- read_rds("data/rds/od_data.rds")
hexagon_sf <- read_rds("data/rds/hexagon_sf.rds")
  • In this study, our focus is on interzonal flow, so we remove intrazonal flows with the below;
    • We use square bracket indexing [] to select only specific rows, and leave the columns blank after the ,
    • We select only rows where the $ORIGIN_HEX is equival to $DESTIN_HEX, i.e. intrazonal flows:
  • We use summary() to take a quick peek at the resultant interzonal flow dataset:
show code 
od_flow_data <- od_data[od_data$ORIGIN_HEX!=od_data$DESTIN_HEX,]
summary(od_flow_data$SUM_TRIPS)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
      1       8      35     343     159   77350
  • We see there is tremendous right skew in our dataset, going from 1 trip to 77350 trips during the peak period!
    • The median (35) and the third quartile (159) are 2 orders of magnitude smaller than the maximum!
  • We perform a series of quick visualizations to observe the disparity, using ggplot. We give a quick explanation, as this is not ISSS608 Visual Analytics & Applications;
    • We use geom_point() to create a scatterplot to visualize the distribution of $SUM_TRIPS
    • We use geom_histogram() to create a histogram, using seq() to customize the bins for the histogram
    • To allow comparison between the three plots, we use geom_vline() with the argument “xintercept = 1000” to draw a red vertical line. Even though the graphs are on three different scales, we can use the red line as a visual ‘threshold’ reference for 1000 trips.
  • This is where we use the patchwork package, as it allows us to position the subplots without writing too much syntax. This is the beauty of R packages, indeed.
show code 
lplot <-  ggplot(data = od_flow_data, aes(x=SUM_TRIPS, y=ORIGIN_HEX)) +
          geom_point() +
          labs(title = "Scatterplot: Distribution of Bus Trips by Origin Hex",
               x = "ORIGIN_HEX",
               y = "SUM_TRIPS") + 
          geom_vline(xintercept = 1000, colour="red")

rplot1 <- ggplot(data = od_flow_data, 
                aes(x=SUM_TRIPS)) +
          labs(title = "Histogram of Trips [0-20,000]",
               x = "ORIGIN_HEX",
               y = "(truncated) SUM_TRIPS") +
          geom_histogram(breaks=seq(0, 20000, by = 1000)) + 
          geom_vline(xintercept = 1000, colour="red")

rplot2 <- ggplot(data = od_flow_data, 
                aes(x=SUM_TRIPS)) +
          labs(title = "Histogram of Trips [0-2,000]",
               x = "ORIGIN_HEX",
               y = "(truncated) SUM_TRIPS") +
          geom_histogram(breaks=seq(0, 2000, by = 250)) + 
          geom_vline(xintercept = 1000, colour="red")

# Here is where we use the patchwork syntax
# As opposed to fiddling around with ggarrange
lplot / (rplot1 + rplot2)

  • Now, we convert the flow data to SpatialLinesDataFrame from stplanr
show code 
flowLine <- od2line(flow = od_flow_data, 
                    zones = hexagon_sf,
                    zone_code = "grid_id")
Creating centroids representing desire line start and end points.
show code 
flowLine
Simple feature collection with 67737 features and 3 fields
Geometry type: LINESTRING
Dimension:     XY
Bounding box:  xmin: 3970.122 ymin: 26482.1 xmax: 48220.12 ymax: 49864.79
Projected CRS: SVY21 / Singapore TM
First 10 features:
   ORIGIN_HEX DESTIN_HEX SUM_TRIPS                       geometry
1           1          7         3 LINESTRING (3970.122 27781....
2           1          9        34 LINESTRING (3970.122 27781....
3           1         16       182 LINESTRING (3970.122 27781....
4           1         20        18 LINESTRING (3970.122 27781....
5           1         22         6 LINESTRING (3970.122 27781....
6           1         23         1 LINESTRING (3970.122 27781....
7           1         28         1 LINESTRING (3970.122 27781....
8           1         32       145 LINESTRING (3970.122 27781....
9           2          5         2 LINESTRING (4345.122 28430....
10          2          9         4 LINESTRING (4345.122 28430....

2. Geospatial Visualization / Geospatial Data Science

Q: Display the O-D flows of the passenger trips by using appropriate geovisualisation methods (not more than 5 maps).

2.1 Map 1: O-D Flows Over 1,000 trips

  • From Section 1.7, we know that most of the flow lines have 1000 or fewer trips (63,342 out of 67,737, in fact);
  • Therefore, we will avoid plotting flowLine directly, as it is extremely visually noisy;
    • With 67,737 flow lines, the map will simply be covered in overlapping black lines and have no visual information value.
  • Instead, we choose to focus on the high-traffic flow lines with >1000 trips;
    • With mpsz_sf and hexagon_sf as base, we use tm_lines() to plot flowLine
    • We define custom breaks and use both “palette” and “scale” arguments to add colour and thickness to flow lines for visual scale
custom_palette <- c('#dec060','#d73027','#72001a', '#313695')
tmap_mode("view")
tmap mode set to interactive viewing
tm_basemap(providers$OneMapSG.Grey) +
tm_shape(hexagon_sf) +
  tm_polygons(alpha = 0.5) +
flowLine %>%  
  filter(SUM_TRIPS >= 1000) %>%  
  tm_shape() +
  tm_lines(col = "SUM_TRIPS",
           lwd = "SUM_TRIPS",
           palette = custom_palette,
           style = "fixed",
           breaks = c(1000, 10000, 20000, 50000, 80000),
           scale = c(0.1, 1, 2, 4, 8, 12),
           n = 6,
           alpha = 0.8) + 
tm_view(set.zoom.limits = c(11, 13))
Legend for line widths not available in view mode.
tmap_mode("plot")
tmap mode set to plotting

2.1.1 Map 1 Commentary of O-D Flows Over 1,000 trips

  • Major Trips We see three thick purple lines;
    • Two are in the west, around Jurong West/Choa Chu Kang areas, which may reflect key transport nodes for residential and industrial zones around that part of the island.
    • In the north, the purple line points towards Woodlands Checkpoint/Causeawy, for commuters crossing into Malaysia. On that note,
  • Longest Trips There are some exceptionally long lines from the East (Changi, Tampines, Pasir Ris) and Northeast (Punggol, Sengkang) areas towards the Woodlands Area.
  • Most Trips Note the pattern of thin yellow-orange lines; they approximate the underlying MRT lines. Although we have filtered ~93% of the trips, we see that most of the flow lines between 1000-10,000 trips reflect connections made by MRT lines.
    • Indeed, most of the dark orange/red lines connect to MRT stations like Ang Mo Kio, Bishan, and Toa Payoh (in the North) and Boon Lay, Choa Chu Kang and Clementi in the East.

2.4 Map 4 Comparing Top Origin/Destination Hexagons:

  • We perform our leaflet trick one last time, overlapping ORI_HEX and DES_HEX from the last 2 maps to compare the top hexes by origin/destination:
show code 
tmap_mode("plot")
tmap mode set to plotting
show code 
tm_ori_des <- tm_shape(orig_hexagon_sf, group="ORI_HEX") +
  tm_polygons(col="SUM_ORIG_TRIPS", palette="YlGnBu", style = "fixed", alpha = 0.5, breaks = custom_origin_breaks, group="ORI_HEX") +
  
  tm_shape(dest_hexagon_sf, group="DES_HEX") +
  tm_polygons(col="SUM_DEST_TRIPS", palette="YlOrRd", style = "fixed", alpha = 0.5, breaks = custom_destin_breaks, group="DES_HEX") +
  
  tm_layout(legend.position = c("right", "bottom"), title= 'Comparing Trip Density by ORI/DES Hex', title.position = c("left", "top")) +
  tm_view(set.zoom.limits = c(11, 12))

tm_ori_des %>%
  tmap_leaflet() %>%
  addLayersControl(
    overlayGroups = c("ORI_HEX", "DES_HEX"),
    options = layersControlOptions(collapsed = FALSE),
    position = "topleft"
  )
legend.postion is used for plot mode. Use view.legend.position in tm_view to set the legend position in view mode.

3. Geospatial Data Science II: Data Preparation for Spatial Interaction Models

Q: Compute a distance matrix by using the analytical hexagon data derived earlier.

3.1 Computing Distance Matrix

  • To compute a distance matrix, we first start with our trusty hexagon_sf
    • We use spDists() of sp package to calculate centroid distances, passing “longlat=FALSE” to generate Euclidean distance (since we are not using WGS84 projection)
      • However, this requires an sp dataframe, so we create hexagon_sp first using as(..., "Spatial) to convert types
  • The output distance_matrix is an 831x831 matrix (as we have 831 unique hexagons), so we preview only the first 10 rows and columns using head()
show code 
hexagon_sf <- read_rds("data/rds/hexagon_sf.rds")

hexagon_sp <- as(hexagon_sf, "Spatial")
distance_matrix <- spDists(hexagon_sp, 
                longlat = FALSE)
head(distance_matrix, n=c(10, 10))
          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
 [1,]    0.000  750.000 3269.174 1500.000 2704.163 3968.627 1299.038 2250.000
 [2,]  750.000    0.000 2598.076  750.000 1984.313 3269.174  750.000 1500.000
 [3,] 3269.174 2598.076    0.000 1984.313  750.000  750.000 2704.163 1500.000
 [4,] 1500.000  750.000 1984.313    0.000 1299.038 2598.076  750.000  750.000
 [5,] 2704.163 1984.313  750.000 1299.038    0.000 1299.038 1984.313  750.000
 [6,] 3968.627 3269.174  750.000 2598.076 1299.038    0.000 3269.174 1984.313
 [7,] 1299.038  750.000 2704.163  750.000 1984.313 3269.174    0.000 1299.038
 [8,] 2250.000 1500.000 1500.000  750.000  750.000 1984.313 1299.038    0.000
 [9,] 3436.932 2704.163  750.000 1984.313  750.000  750.000 2598.076 1299.038
[10,] 4683.748 3968.627 1500.000 3269.174 1984.313  750.000 3897.114 2598.076
          [,9]    [,10]
 [1,] 3436.932 4683.748
 [2,] 2704.163 3968.627
 [3,]  750.000 1500.000
 [4,] 1984.313 3269.174
 [5,]  750.000 1984.313
 [6,]  750.000  750.000
 [7,] 2598.076 3897.114
 [8,] 1299.038 2598.076
 [9,]    0.000 1299.038
[10,] 1299.038    0.000
show code 
# dim(distance_matrix)
  • We note two details here that suggest we’re on the right track;
    • Diagonals equal zero, which make sense, as the distance between a hexagon’s centroid and itself is zero;
    • 750m between hexagons 1 & 2, which are adjacent.
  • We now use melt() to convert our distance matrix into dist_pair, a long data table of distance pairs between hexagon centroids. This is needed for spatial interaction modelling later;
    • We use rename() to name our column headers
show code 
distPair <- melt(distance_matrix) %>%
  rename(dist = value
         , grid_id_from = Var1
         , grid_id_to = Var2)
head(distPair, 10)
   grid_id_from grid_id_to     dist
1             1          1    0.000
2             2          1  750.000
3             3          1 3269.174
4             4          1 1500.000
5             5          1 2704.163
6             6          1 3968.627
7             7          1 1299.038
8             8          1 2250.000
9             9          1 3436.932
10           10          1 4683.748
  • Note that we have intra-zonal distances/zero-distances, which may cause issues later. Let’s check the minimum distances:
show code 
distPair %>%
  filter(dist > 0) %>%
  summary()
  grid_id_from   grid_id_to       dist      
 Min.   :  1   Min.   :  1   Min.   :  750  
 1st Qu.:208   1st Qu.:208   1st Qu.: 8250  
 Median :416   Median :416   Median :13269  
 Mean   :416   Mean   :416   Mean   :14135  
 3rd Qu.:624   3rd Qu.:624   3rd Qu.:18929  
 Max.   :831   Max.   :831   Max.   :44680
  • The minimum distance between hexagons is still 750, which is correct; the apothem distance is 375m, which means double that is centroid-to-centroid distance of 750m.
  • To avoid issues with zero-value distances below, we will arbritrarily convert intrazonal distance to 50m. However, we note that having removed intrazonal flows, we should not encounter this error later on.
distPair$dist <- ifelse(distPair$dist == 0,
                        50, distPair$dist)
distPair %>%
  summary()
  grid_id_from   grid_id_to       dist      
 Min.   :  1   Min.   :  1   Min.   :   50  
 1st Qu.:208   1st Qu.:208   1st Qu.: 8250  
 Median :416   Median :416   Median :13269  
 Mean   :416   Mean   :416   Mean   :14118  
 3rd Qu.:624   3rd Qu.:624   3rd Qu.:18929  
 Max.   :831   Max.   :831   Max.   :44680
  • Having convinced ourselves that the minimum distance is nonzero (50m), we write this to RDS and continue our data preparation work:
write_rds(distPair, "data/rds/distPair.rds")

3.2 Prepare Intrazonal OD flow data

  • Our od_data comprises $ORIGIN_HEX, $DESTIN_HEX, and $SUM_TRIPS columns; we now want to add distance information by merging with distPair;
    • First, we create a column $od_no_intra using ifelse() to output 0 for intrazonal flows (e.g. $ORIGIN_HEX == $DESTIN_HEX) and $SUM_TRIPS otherwise;
    • We then join distPair to od_data by matching origin and destination
  • Finally, we perform a quick glimpse using $od_no_intra to view that our filter for intrazonal flows is correct:
od_data$od_no_intra <- ifelse(
  od_data$ORIGIN_HEX == od_data$DESTIN_HEX, 
  0, od_data$SUM_TRIPS)
# od_data$offset <- ifelse(
#   od_data$ORIGIN_HEX == od_data$DESTIN_HEX, 
#   0.000001, 1)

# od_data$ORIGIN_HEX <- as.factor(od_data$ORIGIN_HEX)
# od_data$DESTIN_HEX <- as.factor(od_data$DESTIN_HEX)
# 
od_data_distpair <- od_data %>%
  left_join (distPair,
             by = c("ORIGIN_HEX" = "grid_id_from",
                    "DESTIN_HEX" = "grid_id_to"))
od_data_distpair[od_data_distpair$od_no_intra == 0, ]
# A tibble: 628 × 5
# Groups:   ORIGIN_HEX [628]
   ORIGIN_HEX DESTIN_HEX SUM_TRIPS od_no_intra  dist
        <int>      <int>     <dbl>       <dbl> <dbl>
 1          9          9         1           0    50
 2         14         14         9           0    50
 3         21         21        12           0    50
 4         26         26         2           0    50
 5         27         27        32           0    50
 6         28         28         2           0    50
 7         32         32       517           0    50
 8         33         33        26           0    50
 9         35         35         1           0    50
10         38         38        37           0    50
# ℹ 618 more rows
  • Now, we create inter_zonal_flow by filtering out the intrazonal flows we have seen, and perform a quick histogram visualization usingggplot:
inter_zonal_flow <- od_data_distpair %>%
  filter(od_no_intra > 0) %>%
  select(ORIGIN_HEX, DESTIN_HEX, SUM_TRIPS, dist)

ggplot(data = inter_zonal_flow,
       aes(x = dist,
           y = SUM_TRIPS)) +
  geom_point() +
  ggtitle("Scatter Plot of Number of Trips by Trip Distance") +
  xlab("Distance of Trips") +
  ylab("Number of Trips")

  • We see that once again, the data is extremely right-skewed and exhibits no visible patter. Taking a cue from earlier visualizations however, we can use the log scale;
    • We use geom_smooth() to draw a smoothed line to observe the pattern, and indeed we see a negative correlation between the length (distance) of the trips and the number of trips.
ggplot(data = inter_zonal_flow,
       aes(x = log(dist),
           y = log(SUM_TRIPS))) +
  geom_point() +
  geom_smooth(method = lm) +
  ggtitle("Scatter Plot Number of Trips by Trip Distance, log scale") +
  xlab("log(Distance of Trips)") +
  ylab("log(Number of Trips)")
  • We perform a quick check to ensure there are no zero values before writing to RDS.
write_rds(inter_zonal_flow, "data/rds/inter_zonal_flow.rds")
summary(inter_zonal_flow)

3.4 Preparing three propulsive and three attractiveness variables

Q: Assemble at least three propulsive and three attractiveness variables by using aspatial and geospatial from publicly available sources.

  • Over the next few sections, we will assemble the following explanatory variables for our spatial interaction model. We also note which section they will be handled in (if not stated, they will be addressed in Section 3.4A):

  • Propulsive variables:

    • business_count, finserv_count: We assume in the weekday evenings, people will be leaving their offices or have concluded their businesses from financial services, which are often also closed in the evenings.
    • MRT_EXIT_COUNT: (Section 3.4C) Based on above Map 2 (Section 2.2, 2.3) we see that most trips appear to originate from MRT stations. In all likelihood, MRT Stations can be both propulsive and attractive, but we choose to class it here, explaining as people using MRTs to transit to the desired leisure are.

  • Attractive variables:

    • leisure_count, fnb_count, retail_count, entertainment_count: Using data from Prof Kam, we assume people will leave their workplace to seek out food, entertainment, leisure, or retail shops.
    • hdb_count (Section 3.4B) Alternatively, people may be heading home after work.

3.4A Assembling Various Explanatory Variables

  • Many of the below geospatial datasets have been prepared by Prof Kam, so the data is already cleaned, and the steps are largely uniform;
    1. Use st_read() to read in the geospatial dataset, and use st_transform() to ensure it uses SVY21/CRS3414
    2. Create a new column using lengths(st_intersects()) to count the number of such points in each hexagon grid.
  • Here are the data preparation steps:
show code 
hexagon_sf <- read_rds("data/rds/hexagon_sf.rds")
business_sf <- st_read(dsn = "data/geospatial",
                      layer = "Business") %>%
  st_transform(crs = 3414)
Reading layer `Business' from data source 
  `C:\1darren\ISSS624\Take-home_Ex02\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
show code 
hexagon_sf$`BUSINESS_COUNT`<- lengths(
  st_intersects(
    hexagon_sf, business_sf))
summary(hexagon_sf$BUSINESS_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    0.0     0.0     1.0     7.3     7.0    97.0
  • Quick Visualization:
tmap_mode("plot")
tmap mode set to plotting
tm_shape(mpsz_sf) + tm_polygons() +
 tm_shape(hexagon_sf) +
 tm_borders() + 
 tm_fill(col = "BUSINESS_COUNT", 
         palette = "Greys",
         style = "jenks") 
Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

show code 
entertn_sf <- st_read(dsn = "data/geospatial",
                      layer = "entertn") %>%
  st_transform(crs = 3414)
Reading layer `entertn' from data source 
  `C:\1darren\ISSS624\Take-home_Ex02\data\geospatial' using driver `ESRI Shapefile'
Simple feature collection with 114 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 10809.34 ymin: 26528.63 xmax: 41600.62 ymax: 46375.77
Projected CRS: SVY21 / Singapore TM
show code 
# st_crs(entertn_sf)

hexagon_sf$`ENTERTAIN_COUNT`<- lengths(
  st_intersects(
    hexagon_sf, entertn_sf))
summary(hexagon_sf$ENTERTAIN_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0000  0.0000  0.1336  0.0000  9.0000
  • Quick Visualization:
tmap_mode("plot")
tmap mode set to plotting
tm_shape(mpsz_sf) + tm_polygons() +
 tm_shape(hexagon_sf) +
 tm_borders() + 
 tm_fill(col = "ENTERTAIN_COUNT", 
         palette = "Blues",
         style = "jenks") 
Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

show code 
finserv_sf <- st_read(dsn = "data/geospatial",
                      layer = "FinServ") %>%
  st_transform(crs = 3414)
Reading layer `FinServ' from data source 
  `C:\1darren\ISSS624\Take-home_Ex02\data\geospatial' using driver `ESRI Shapefile'
Simple feature collection with 3320 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 4881.527 ymin: 25171.88 xmax: 46526.16 ymax: 49338.02
Projected CRS: SVY21 / Singapore TM
show code 
# st_crs(finserv_sf)


hexagon_sf$`FINSERV_COUNT`<- lengths(
  st_intersects(
    hexagon_sf, finserv_sf))
summary(hexagon_sf$FINSERV_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.000   1.000   3.936   4.000 139.000
  • Quick Visualization:
tmap_mode("plot")
tmap mode set to plotting
tm_shape(mpsz_sf) + tm_polygons() +
 tm_shape(hexagon_sf) +
 tm_borders() + 
 tm_fill(col = "FINSERV_COUNT", 
         palette = "Greens",
         style = "jenks") 
Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

show code 
fnb_sf <- st_read(dsn = "data/geospatial",
                      layer = "F&B") %>%
  st_transform(crs = 3414)
Reading layer `F&B' from data source 
  `C:\1darren\ISSS624\Take-home_Ex02\data\geospatial' using driver `ESRI Shapefile'
Simple feature collection with 1919 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 6010.495 ymin: 25343.27 xmax: 45462.43 ymax: 48796.21
Projected CRS: SVY21 / Singapore TM
show code 
# st_crs(fnb_sf)

hexagon_sf$`FNB_COUNT`<- lengths(
  st_intersects(
    hexagon_sf, fnb_sf))
summary(hexagon_sf$FNB_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.000   0.000   2.212   1.000 133.000
  • Quick Visualization:
tmap_mode("plot")
tmap mode set to plotting
tm_shape(mpsz_sf) + tm_polygons() +
 tm_shape(hexagon_sf) +
 tm_borders() + 
 tm_fill(col = "FNB_COUNT", 
         palette = "Reds",
         style = "jenks") 
Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

show code 
leisure_sf <- st_read(dsn = "data/geospatial",
                      layer = "Liesure&Recreation") %>%
  st_transform(crs = 3414)
Reading layer `Liesure&Recreation' from data source 
  `C:\1darren\ISSS624\Take-home_Ex02\data\geospatial' using driver `ESRI Shapefile'
Simple feature collection with 1217 features and 30 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 6010.495 ymin: 25134.28 xmax: 48439.77 ymax: 50078.88
Projected CRS: SVY21 / Singapore TM
show code 
# st_crs(leisure_sf)


hexagon_sf$`LEISURE_COUNT`<- lengths(
  st_intersects(
    hexagon_sf, leisure_sf))
summary(hexagon_sf$LEISURE_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.000   0.000   1.312   1.000  41.000
  • Quick Visualization:
tmap_mode("plot")
tmap mode set to plotting
tm_shape(mpsz_sf) + tm_polygons() +
 tm_shape(hexagon_sf) +
 tm_borders() + 
 tm_fill(col = "LEISURE_COUNT", 
         palette = "Purples",
         style = "jenks") 
Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

show code 
retail_sf <- st_read(dsn = "data/geospatial",
                      layer = "Retails") %>%
  st_transform(crs = 3414)
Reading layer `Retails' from data source 
  `C:\1darren\ISSS624\Take-home_Ex02\data\geospatial' using driver `ESRI Shapefile'
Simple feature collection with 37635 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 4737.982 ymin: 25171.88 xmax: 48265.04 ymax: 50135.28
Projected CRS: SVY21 / Singapore TM
show code 
# st_crs(retail_sf)


hexagon_sf$`RETAIL_COUNT`<- lengths(
  st_intersects(
    hexagon_sf, retail_sf))
summary(hexagon_sf$RETAIL_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    0.0     1.0     8.0    44.2    37.0  1678.0
  • Quick Visualization:
tmap_mode("plot")
tmap mode set to plotting
tm_shape(mpsz_sf) + tm_polygons() +
 tm_shape(hexagon_sf) +
 tm_borders() + 
 tm_fill(col = "RETAIL_COUNT", 
         palette = "Oranges",
         style = "jenks") 
Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

  • Originally, I had prepared a leaflet plot with multiple layers that combined all six preceding plots that you could thumb through. However, R/Quarto took too long to render and often crashed, so below is the code snippet to render the plot for your gratification, if you so enjoy.
show code 
# tmap_mode("view")
# 
# tm <- tm_shape(hexagon_sf, group="BUSINESS_COUNT") +
#  tm_borders(group="BUSINESS_COUNT") + 
#  tm_fill(col = "BUSINESS_COUNT", 
#          palette = "Greys",
#          style = "jenks",
#          group="BUSINESS_COUNT") + 
#   
#  tm_shape(hexagon_sf, group="ENTERTAIN_COUNT") +
#  tm_borders(group="ENTERTAIN_COUNT") + 
#  tm_fill(col = "ENTERTAIN_COUNT", 
#          palette = "Blues",
#          style = "jenks",
#          group="ENTERTAIN_COUNT") + 
#   
#  tm_shape(hexagon_sf, group="FINSERV_COUNT") +
#  tm_borders(group="FINSERV_COUNT") + 
#  tm_fill(col = "FINSERV_COUNT", 
#          palette = "Greens",
#          style = "jenks",
#          group="FINSERV_COUNT") + 
#   
#  tm_shape(hexagon_sf, group="FNB_COUNT") +
#  tm_borders(group="FNB_COUNT") + 
#  tm_fill(col = "FNB_COUNT", 
#          palette = "Reds",
#          style = "jenks",
#          group="FNB_COUNT") + 
#   
#  tm_shape(hexagon_sf, group="LEISURE_COUNT") +
#  tm_borders(group="LEISURE_COUNT") + 
#  tm_fill(col = "LEISURE_COUNT", 
#          palette = "Purples",
#          style = "jenks",
#          group="LEISURE_COUNT") + 
# 
#    tm_shape(hexagon_sf, group="RETAIL_COUNT ") +
#  tm_borders(group="RETAIL_COUNT ") + 
#  tm_fill(col = "RETAIL_COUNT", 
#          palette = "Oranges",
#          style = "jenks",
#          group="RETAIL_COUNT")
# 
# 
# tm %>% 
#   tmap_leaflet() %>%
#   hideGroup(c("FINSERV_COUNT", "FNB_COUNT",
#                       "ENTERTAIN_COUNT", "LEISURE_COUNT", "RETAIL_COUNT")) %>%
#   addLayersControl(
#     overlayGroups = c("BUSINESS_COUNT", "ENTERTAIN_COUNT", "FINSERV_COUNT", 
#                       "FNB_COUNT", "LEISURE_COUNT", "RETAIL_COUNT"),
#     options = layersControlOptions(collapsed = FALSE),
#     position = "topleft"
#   )

3.4B MRT Exit Data

  • Here, we have a choice whether to use the geospatial dataset of MRT Train Station Exits data or the dataset of actual MRT Train Station Locations from LTA DataMall.
  • Loading Train Station Exit Data is relatively straightfoward:
show code 
mrt_exit_sf <- st_read(dsn = "data/geospatial",
                      layer = "Train_Station_Exit_Layer")  %>%
  st_transform(crs=3414)
Reading layer `Train_Station_Exit_Layer' from data source 
  `C:\1darren\ISSS624\Take-home_Ex02\data\geospatial' using driver `ESRI Shapefile'
Simple feature collection with 565 features and 2 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 6134.086 ymin: 27499.7 xmax: 45356.36 ymax: 47865.92
Projected CRS: SVY21
show code 
# st_crs(mrt_exit_sf)


hexagon_sf$`MRT_EXIT_COUNT`<- lengths(
  st_intersects(
    hexagon_sf, mrt_exit_sf))
summary(hexagon_sf$MRT_EXIT_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0000  0.0000  0.6739  0.0000 13.0000
  • However, attempting to read from LTA’s RapidTransitSystemStation fails somewhat;
    • There is incomplete or broken geometry in LTA’s original source file
    • use st_make_valid() does not work, so I sourced wdpar::st_repair_geometry wdpar source, based on prepr package to repair geometries
    • thereafter we need to coerce from EPSG9001 to SVY21 using st_transform()
  • Even so, we can compare the difference in the two datasets:
show code 
library(wdpar)

raw_mrt_sf <- st_read(dsn = "data/geospatial",
                      layer = "RapidTransitSystemStation")
Reading layer `RapidTransitSystemStation' from data source 
  `C:\1darren\ISSS624\Take-home_Ex02\data\geospatial' using driver `ESRI Shapefile'
Warning in CPL_read_ogr(dsn, layer, query, as.character(options), quiet, : GDAL
Message 1: Non closed ring detected. To avoid accepting it, set the
OGR_GEOMETRY_ACCEPT_UNCLOSED_RING configuration option to NO
Simple feature collection with 220 features and 4 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: 6068.209 ymin: 27478.44 xmax: 45377.5 ymax: 47913.58
Projected CRS: SVY21
show code 
mrt_sf <- st_repair_geometry(raw_mrt_sf) %>%
  st_transform(crs=3414)
st_crs(mrt_sf)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
show code 
tmap_mode("plot")
tmap mode set to plotting
show code 
# tmap_options(check.and.fix = TRUE)
tm_shape(mpsz_sf) +
  tm_polygons() +
tm_shape(hexagon_sf) +
  tm_polygons(col = "MRT_EXIT_COUNT", palette = "-Spectral") +
tm_shape(mrt_sf) +
  tm_dots(col='red')
Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

  • We can see that the MRT Stations (red dots) appear largely to correspond with the MRT Exits (coloured, non-blue hexes.) We thus choose to use the MRT_EXIT_COUNT dataset, as it is a more logical interpretation of data flow

3.4C HDB Dataset

  • We now draw from the “aspatial” HDB dataset, and use colnames() to examine the columns:
show code 
raw_hdb <- read_csv("data/aspatial/hdb.csv")
New names:
Rows: 12442 Columns: 37
── Column specification
──────────────────────────────────────────────────────── Delimiter: "," chr
(18): blk_no, street, residential, commercial, market_hawker, miscellane... dbl
(19): ...1, max_floor_lvl, year_completed, total_dwelling_units, 1room_s...
ℹ Use `spec()` to retrieve the full column specification for this data. ℹ
Specify the column types or set `show_col_types = FALSE` to quiet this message.
• `` -> `...1`
show code 
colnames(raw_hdb)
 [1] "...1"                  "blk_no"                "street"               
 [4] "max_floor_lvl"         "year_completed"        "residential"          
 [7] "commercial"            "market_hawker"         "miscellaneous"        
[10] "multistorey_carpark"   "precinct_pavilion"     "bldg_contract_town"   
[13] "total_dwelling_units"  "1room_sold"            "2room_sold"           
[16] "3room_sold"            "4room_sold"            "5room_sold"           
[19] "exec_sold"             "multigen_sold"         "studio_apartment_sold"
[22] "1room_rental"          "2room_rental"          "3room_rental"         
[25] "other_room_rental"     "lat"                   "lng"                  
[28] "building"              "addr"                  "postal"               
[31] "SUBZONE_NO"            "SUBZONE_N"             "SUBZONE_C"            
[34] "PLN_AREA_N"            "PLN_AREA_C"            "REGION_N"             
[37] "REGION_C"
  • For our purposes, we need to use $lat and $lng as geocordinates, and to filter by “$residential = Y”
show code 
raw_hdb <- raw_hdb %>% 
  filter(residential == "Y") %>%
  select(
    lat,
    lng  )
hdb_sf <- st_as_sf(raw_hdb,
                   coords = c("lng", "lat"),
                   crs = 4326) %>%
  st_transform(crs = 3414)


hexagon_sf$`hdb_COUNT`<- lengths(
  st_intersects(
    hexagon_sf, hdb_sf))
summary(hexagon_sf$hdb_COUNT)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   0.00    0.00    0.00   12.19   22.00   82.00
  • Now we perform a quick visualization:
show code 
tmap_mode("plot")
tmap mode set to plotting
show code 
tm_shape(mpsz_sf) +
  tm_polygons() +
tm_shape(hexagon_sf) +
  tm_polygons(col = "hdb_COUNT", palette = "-Spectral")
Warning: The shape mpsz_sf is invalid. See sf::st_is_valid

  • Finally, let’s write hexagon_sf to rds
show code 
write_rds(hexagon_sf, "data/rds/hexagon_features.rds")

4. Spatial Interactive Models

  • To distinguish our hexagon_sf with added variables from the previous hexagon_sf used above, we will load and call this one hex_variables_sf
  • We read this from rds first:
inter_zonal_flow <- read_rds("data/rds/inter_zonal_flow.rds")
hex_variables_sf <- read_rds("data/rds/hexagon_features.rds")

4.1.P Propulsive Variables Count

  • Now, we will need to combine our flow data with the origin/destination hexagons as in inter_zonal_flow;
    1. First, we create prop_df, an aspatial dataframe with only propulsiveness variables;
      • We select() only the $grid_id identifier columns with counts for $BUSINESS_COUNT, $FINSERV_COUNT and $MRT_EXIT_COUNT,
      • We use st_drop_geometry() to remove the geospatial data
    2. Next, we left_join() this to our inter_zonal_flow dataset
      • Since these are propulsive variables, we join this to the $ORIGIN_HEX
      • For ease of reading later, we rename these columns by adding a prefix P_ for propulsive variables:
show code 
prop_sf <- hex_variables_sf %>%
  select(grid_id, BUSINESS_COUNT, FINSERV_COUNT, MRT_EXIT_COUNT) %>%
  st_drop_geometry()
inter_zonal_flow_prop <- inter_zonal_flow %>%
  left_join(prop_sf,
            by = c("ORIGIN_HEX" = "grid_id")) %>%
  rename(P_MRT_EXIT_COUNT = MRT_EXIT_COUNT,
         P_FINSERV_COUNT = FINSERV_COUNT, 
         P_BUSINESS_COUNT = BUSINESS_COUNT)
inter_zonal_flow_prop
# A tibble: 67,737 × 7
# Groups:   ORIGIN_HEX [813]
   ORIGIN_HEX DESTIN_HEX SUM_TRIPS  dist P_BUSINESS_COUNT P_FINSERV_COUNT
        <int>      <int>     <dbl> <dbl>            <int>           <int>
 1          1          7         3 1299.                0               0
 2          1          9        34 3437.                0               0
 3          1         16       182 1984.                0               0
 4          1         20        18 6139.                0               0
 5          1         22         6 8649.                0               0
 6          1         23         1 2598.                0               0
 7          1         28         1 8112.                0               0
 8          1         32       145 7612.                0               0
 9          2          5         2 1984.                5               0
10          2          9         4 2704.                5               0
# ℹ 67,727 more rows
# ℹ 1 more variable: P_MRT_EXIT_COUNT <int>

4.1.A Attractiveness Variables Count

  • Similar to the above, we repeat the step for attractiveness variables by creating attr_df; - Repeat to select() only the $grid_id identifier columns with counts for $ENTERTAIN_COUNT, $FNB_COUNT, $LEISURE_COUNT, $RETAIL_COUNT, and $hdb_COUNT, - We use st_drop_geometry() to remove the geospatial data
    1. Next, we left_join() this to our inter_zonal_flow_prop dataset from the previous step
      • Since these are attractiveness variables, we join this to the $DESTIN_HEX
      • For ease of reading later, we rename these columns by adding a prefix A_ for attractive variables:
show code 
attr_sf <- hex_variables_sf %>%
  select(grid_id, ENTERTAIN_COUNT , FNB_COUNT, LEISURE_COUNT, RETAIL_COUNT, hdb_COUNT) %>%
  st_drop_geometry()
SIM_data <- inter_zonal_flow_prop %>%
  left_join(attr_sf,
            by = c("DESTIN_HEX" = "grid_id")) %>%
  rename(A_FNB_COUNT = FNB_COUNT, 
         A_ENTERTAIN_COUNT = ENTERTAIN_COUNT, 
         A_LEISURE_COUNT = LEISURE_COUNT, 
         A_RETAIL_COUNT = RETAIL_COUNT, 
         A_HDB_COUNT = hdb_COUNT)
SIM_data
# A tibble: 67,737 × 12
# Groups:   ORIGIN_HEX [813]
   ORIGIN_HEX DESTIN_HEX SUM_TRIPS  dist P_BUSINESS_COUNT P_FINSERV_COUNT
        <int>      <int>     <dbl> <dbl>            <int>           <int>
 1          1          7         3 1299.                0               0
 2          1          9        34 3437.                0               0
 3          1         16       182 1984.                0               0
 4          1         20        18 6139.                0               0
 5          1         22         6 8649.                0               0
 6          1         23         1 2598.                0               0
 7          1         28         1 8112.                0               0
 8          1         32       145 7612.                0               0
 9          2          5         2 1984.                5               0
10          2          9         4 2704.                5               0
# ℹ 67,727 more rows
# ℹ 6 more variables: P_MRT_EXIT_COUNT <int>, A_ENTERTAIN_COUNT <int>,
#   A_FNB_COUNT <int>, A_LEISURE_COUNT <int>, A_RETAIL_COUNT <int>,
#   A_HDB_COUNT <int>
  • Let’s perform a quick check to ensure no intra-zonal flow:
show code 
SIM_data[SIM_data$ORIGIN_HEX==SIM_data$DESTIN_HEX,]
# A tibble: 0 × 12
# Groups:   ORIGIN_HEX [0]
# ℹ 12 variables: ORIGIN_HEX <int>, DESTIN_HEX <int>, SUM_TRIPS <dbl>,
#   dist <dbl>, P_BUSINESS_COUNT <int>, P_FINSERV_COUNT <int>,
#   P_MRT_EXIT_COUNT <int>, A_ENTERTAIN_COUNT <int>, A_FNB_COUNT <int>,
#   A_LEISURE_COUNT <int>, A_RETAIL_COUNT <int>, A_HDB_COUNT <int>
  • Now, let’s examine the summary of our SIM_data:
show code 
summary(SIM_data)
   ORIGIN_HEX      DESTIN_HEX      SUM_TRIPS          dist      
 Min.   :  1.0   Min.   :  1.0   Min.   :    1   Min.   :  750  
 1st Qu.:326.0   1st Qu.:322.0   1st Qu.:    8   1st Qu.: 3000  
 Median :489.0   Median :489.0   Median :   35   Median : 5662  
 Mean   :476.2   Mean   :476.8   Mean   :  343   Mean   : 6487  
 3rd Qu.:632.0   3rd Qu.:638.0   3rd Qu.:  159   3rd Qu.: 9124  
 Max.   :831.0   Max.   :831.0   Max.   :77350   Max.   :24784  
 P_BUSINESS_COUNT P_FINSERV_COUNT   P_MRT_EXIT_COUNT A_ENTERTAIN_COUNT
 Min.   : 0.000   Min.   :  0.000   Min.   : 0.000   Min.   :0.0000   
 1st Qu.: 0.000   1st Qu.:  1.000   1st Qu.: 0.000   1st Qu.:0.0000   
 Median : 1.000   Median :  3.000   Median : 0.000   Median :0.0000   
 Mean   : 7.084   Mean   :  8.518   Mean   : 1.345   Mean   :0.3151   
 3rd Qu.: 6.000   3rd Qu.:  9.000   3rd Qu.: 2.000   3rd Qu.:0.0000   
 Max.   :97.000   Max.   :139.000   Max.   :13.000   Max.   :9.0000   
  A_FNB_COUNT      A_LEISURE_COUNT  A_RETAIL_COUNT     A_HDB_COUNT   
 Min.   :  0.000   Min.   : 0.000   Min.   :   0.00   Min.   : 0.00  
 1st Qu.:  0.000   1st Qu.: 0.000   1st Qu.:   7.00   1st Qu.: 0.00  
 Median :  0.000   Median : 1.000   Median :  28.00   Median : 8.00  
 Mean   :  5.274   Mean   : 2.229   Mean   :  91.54   Mean   :16.66  
 3rd Qu.:  2.000   3rd Qu.: 3.000   3rd Qu.:  99.00   3rd Qu.:29.00  
 Max.   :133.000   Max.   :41.000   Max.   :1678.00   Max.   :82.00
  • There are hexagons with 0 values for counts, e.g. they contain 0 businesses, or 0 HDB blocks within.
  • We will coerce all 0 values to 0.99 to avoid affecting the log values later.
show code 
replace_zeroes_columns <-  c("P_BUSINESS_COUNT", "P_FINSERV_COUNT", "P_MRT_EXIT_COUNT", "A_ENTERTAIN_COUNT", "A_FNB_COUNT", "A_LEISURE_COUNT", "A_RETAIL_COUNT", "A_HDB_COUNT")

# Apply a function to replace 0 with 1 in specified columns
SIM_data[, replace_zeroes_columns] <- apply(SIM_data[, replace_zeroes_columns], 2, function(x) replace(x, x == 0, 0.99))

summary(SIM_data)
   ORIGIN_HEX      DESTIN_HEX      SUM_TRIPS          dist      
 Min.   :  1.0   Min.   :  1.0   Min.   :    1   Min.   :  750  
 1st Qu.:326.0   1st Qu.:322.0   1st Qu.:    8   1st Qu.: 3000  
 Median :489.0   Median :489.0   Median :   35   Median : 5662  
 Mean   :476.2   Mean   :476.8   Mean   :  343   Mean   : 6487  
 3rd Qu.:632.0   3rd Qu.:638.0   3rd Qu.:  159   3rd Qu.: 9124  
 Max.   :831.0   Max.   :831.0   Max.   :77350   Max.   :24784  
 P_BUSINESS_COUNT P_FINSERV_COUNT   P_MRT_EXIT_COUNT A_ENTERTAIN_COUNT
 Min.   : 0.990   Min.   :  0.990   Min.   : 0.990   Min.   :0.990    
 1st Qu.: 0.990   1st Qu.:  1.000   1st Qu.: 0.990   1st Qu.:0.990    
 Median : 1.000   Median :  3.000   Median : 0.990   Median :0.990    
 Mean   : 7.514   Mean   :  8.754   Mean   : 1.966   Mean   :1.168    
 3rd Qu.: 6.000   3rd Qu.:  9.000   3rd Qu.: 2.000   3rd Qu.:0.990    
 Max.   :97.000   Max.   :139.000   Max.   :13.000   Max.   :9.000    
  A_FNB_COUNT      A_LEISURE_COUNT  A_RETAIL_COUNT     A_HDB_COUNT   
 Min.   :  0.990   Min.   : 0.990   Min.   :   0.99   Min.   : 0.99  
 1st Qu.:  0.990   1st Qu.: 0.990   1st Qu.:   7.00   1st Qu.: 0.99  
 Median :  0.990   Median : 1.000   Median :  28.00   Median : 8.00  
 Mean   :  5.809   Mean   : 2.629   Mean   :  91.61   Mean   :17.02  
 3rd Qu.:  2.000   3rd Qu.: 3.000   3rd Qu.:  99.00   3rd Qu.:29.00  
 Max.   :133.000   Max.   :41.000   Max.   :1678.00   Max.   :82.00
  • Finally, we convert $ORIGIN_HEX and $DESTIN_HEX to factor, also for our modelling purposes later.
  • We write to RDS
show code 
SIM_data$ORIGIN_HEX <- as.factor(SIM_data$ORIGIN_HEX)
SIM_data$DESTIN_HEX <- as.factor(SIM_data$DESTIN_HEX)

write_rds(SIM_data,
          "data/rds/SIM_data_tidy.rds")

4.2 Define R-Squared Function

  • For estimating model goodness-of-fit later, we need to define CalcRSquared() to estimate the goodness-of-fit for our 4 models later:
show code 
CalcRSquared <- function(observed,estimated){
  r <- cor(observed,estimated)
  R2 <- r^2
  R2
}
  • We’re finally ready to create our models.
Q: Present the modelling results by using appropriate geovisualisation and graphical visualisation methods. (Not more than 5 visuals)

4.3 uncSIM: Unconstrained Spatial Interaction Model

  • We use glm() to construct a general linear regression model with all our attractiveness and propulsiveness factors;
show code 
SIM_data <- readRDS("data/rds/SIM_data_tidy.rds")


uncSIM <- glm(formula = SUM_TRIPS ~ 
                log(P_BUSINESS_COUNT) + 
                log(P_MRT_EXIT_COUNT) +
                log(P_FINSERV_COUNT) + 
                log(A_ENTERTAIN_COUNT) + 
                log(A_FNB_COUNT) +
                log(A_LEISURE_COUNT) + 
                log(A_RETAIL_COUNT) + 
                log(A_HDB_COUNT) + 
                log(dist),
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
write_rds(uncSIM, "data/rds/uncSIM.rds")
  • For memory reasons, we write- and read- the model to RDS to save space and time while rendering.
show code 
uncSIM <- read_rds("data/rds/uncSIM.rds")
summary(uncSIM)

Call:
glm(formula = SUM_TRIPS ~ log(P_BUSINESS_COUNT) + log(P_MRT_EXIT_COUNT) + 
    log(P_FINSERV_COUNT) + log(A_ENTERTAIN_COUNT) + log(A_FNB_COUNT) + 
    log(A_LEISURE_COUNT) + log(A_RETAIL_COUNT) + log(A_HDB_COUNT) + 
    log(dist), family = poisson(link = "log"), data = SIM_data, 
    na.action = na.exclude)

Coefficients:
                         Estimate Std. Error  z value Pr(>|z|)    
(Intercept)            16.0445992  0.0019755  8121.94   <2e-16 ***
log(P_BUSINESS_COUNT)  -0.0573406  0.0001767  -324.58   <2e-16 ***
log(P_MRT_EXIT_COUNT)   0.4522680  0.0003732  1212.02   <2e-16 ***
log(P_FINSERV_COUNT)    0.2345601  0.0002307  1016.84   <2e-16 ***
log(A_ENTERTAIN_COUNT)  0.1206693  0.0008320   145.04   <2e-16 ***
log(A_FNB_COUNT)       -0.0178054  0.0003058   -58.23   <2e-16 ***
log(A_LEISURE_COUNT)   -0.1029335  0.0003684  -279.43   <2e-16 ***
log(A_RETAIL_COUNT)     0.0876191  0.0001654   529.85   <2e-16 ***
log(A_HDB_COUNT)        0.3807339  0.0001680  2266.02   <2e-16 ***
log(dist)              -1.4755033  0.0002538 -5813.31   <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: 92488055  on 67736  degrees of freedom
Residual deviance: 42931265  on 67727  degrees of freedom
AIC: 43301678

Number of Fisher Scoring iterations: 6
Q: With reference to the Spatial Interaction Model output tables, maps and data visualisation prepared, describe the modelling results. (not more than 100 words per visual).

4.3c Commentary on uncSIM

  • We can compare the size of the coefficients to assess the impact of the explanatory factors;
    • The decay factor, log(dist), is clearly a strong determinant of the number of trips, with -1.47 as a coefficient. This also reiterates some patterns seen earlier in some visualizations, namely, that greater distance results in fewer trips.
    • MRT_EXIT_COUNT and HDB_COUNT have the highest coefficients (0.45, 0.38) among propulsiveness/attractiveness features, with the next closest being FINSERV_COUNT, validating some parts of our hypothesis.
    • However, BUSINESS_COUNT and FNB_COUNT show extremely small (absolute value <0.06), negative values. It may be that they are outweighed by other factors, or perhaps are wrongly attributed.
show code 
CalcRSquared(uncSIM$data$SUM_TRIPS, uncSIM$fitted.values)
[1] 0.3007902
  • This R-squared of 0.30 is quite low, indicating the model doesn’t perform super great.
  • With more time, I would have enjoyed testing this model for multicollinearity, or doing PCA and eliminating unimportant variables.

4.4 orcSIM: Origin Constrained Spatial Interaction Model

  • In the origin-constrained SIM, we regard each $ORIGIN_HEX as a unique factor (dummy variable), and only consider attractiveness variables;
    • The formula defined is similar to uncSIM above;
    • We add a constant (-1) to remove the intercept.
    • Here, we have to set max.print() to 10,000 in order to allow for us to view the entire variable set.
show code 
orcSIM <- glm(formula = SUM_TRIPS ~ 
                ORIGIN_HEX +
                log(A_ENTERTAIN_COUNT) + 
                log(A_FNB_COUNT) +
                log(A_LEISURE_COUNT) + 
                log(A_RETAIL_COUNT) + 
                log(A_HDB_COUNT) + 
                log(dist) - 1,
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
write_rds(orcSIM, "data/rds/orcSIM.rds")
show code 
options(max.print = 10000)  
orcSIM <- read_rds("data/rds/orcSIM.rds")
summary(orcSIM)

Call:
glm(formula = SUM_TRIPS ~ ORIGIN_HEX + log(A_ENTERTAIN_COUNT) + 
    log(A_FNB_COUNT) + log(A_LEISURE_COUNT) + log(A_RETAIL_COUNT) + 
    log(A_HDB_COUNT) + log(dist) - 1, family = poisson(link = "log"), 
    data = SIM_data, na.action = na.exclude)

Coefficients:
                         Estimate Std. Error  z value Pr(>|z|)    
ORIGIN_HEX1            15.5541813  0.0506773   306.93   <2e-16 ***
ORIGIN_HEX2            14.4152814  0.0936807   153.88   <2e-16 ***
ORIGIN_HEX3            14.7983388  0.0433942   341.02   <2e-16 ***
ORIGIN_HEX4            14.7171088  0.0581541   253.07   <2e-16 ***
ORIGIN_HEX5            16.5546043  0.0164325  1007.43   <2e-16 ***
ORIGIN_HEX6            14.6322293  0.0521621   280.51   <2e-16 ***
ORIGIN_HEX7            16.3164264  0.0229902   709.71   <2e-16 ***
ORIGIN_HEX8            15.3915638  0.0414567   371.27   <2e-16 ***
ORIGIN_HEX9            16.6421522  0.0138469  1201.87   <2e-16 ***
ORIGIN_HEX10           13.0900443  0.0808658   161.87   <2e-16 ***
ORIGIN_HEX11           15.3929914  0.0408011   377.27   <2e-16 ***
ORIGIN_HEX12           15.4431873  0.0350806   440.22   <2e-16 ***
ORIGIN_HEX13           16.1827566  0.0269469   600.54   <2e-16 ***
ORIGIN_HEX14           17.0960062  0.0114904  1487.86   <2e-16 ***
ORIGIN_HEX15           14.9782382  0.0321865   465.36   <2e-16 ***
ORIGIN_HEX16           16.1103990  0.0257452   625.76   <2e-16 ***
ORIGIN_HEX17           15.3528695  0.0769495   199.52   <2e-16 ***
ORIGIN_HEX18           16.3221851  0.0214934   759.40   <2e-16 ***
ORIGIN_HEX19           15.7767030  0.0201777   781.89   <2e-16 ***
ORIGIN_HEX20           16.0088339  0.0189615   844.28   <2e-16 ***
ORIGIN_HEX21           16.2522398  0.0148651  1093.31   <2e-16 ***
ORIGIN_HEX22           14.7963423  0.0458711   322.56   <2e-16 ***
ORIGIN_HEX23           16.6073174  0.0209833   791.45   <2e-16 ***
ORIGIN_HEX24           16.1720466  0.0323049   500.61   <2e-16 ***
ORIGIN_HEX25           16.0026335  0.0279370   572.81   <2e-16 ***
ORIGIN_HEX26           16.2967130  0.0152579  1068.08   <2e-16 ***
ORIGIN_HEX27           16.5059588  0.0109711  1504.50   <2e-16 ***
ORIGIN_HEX28           13.8307155  0.0415673   332.73   <2e-16 ***
ORIGIN_HEX29           16.4627856  0.0252271   652.58   <2e-16 ***
ORIGIN_HEX30           16.4295452  0.0403786   406.89   <2e-16 ***
ORIGIN_HEX31           16.0076482  0.0207283   772.26   <2e-16 ***
ORIGIN_HEX32           15.4489266  0.0175922   878.17   <2e-16 ***
ORIGIN_HEX33           16.7595516  0.0095522  1754.52   <2e-16 ***
ORIGIN_HEX34           16.4825701  0.0188600   873.95   <2e-16 ***
ORIGIN_HEX35           16.2563668  0.0137822  1179.52   <2e-16 ***
ORIGIN_HEX36           14.7074397  0.0521605   281.96   <2e-16 ***
ORIGIN_HEX37           16.1642421  0.0229443   704.50   <2e-16 ***
ORIGIN_HEX38           15.8300751  0.0148313  1067.35   <2e-16 ***
ORIGIN_HEX39           16.8962167  0.0100972  1673.35   <2e-16 ***
ORIGIN_HEX40           14.9744073  0.0465615   321.61   <2e-16 ***
ORIGIN_HEX41           15.4869932  0.0215622   718.25   <2e-16 ***
ORIGIN_HEX42           14.9234132  0.0427224   349.31   <2e-16 ***
ORIGIN_HEX43           16.3350777  0.0175764   929.38   <2e-16 ***
ORIGIN_HEX44           15.6157530  0.0181467   860.53   <2e-16 ***
ORIGIN_HEX45           16.4623630  0.0141788  1161.06   <2e-16 ***
ORIGIN_HEX46           16.8971467  0.0126554  1335.17   <2e-16 ***
ORIGIN_HEX47           16.0141794  0.0146997  1089.42   <2e-16 ***
ORIGIN_HEX48           16.3732383  0.0144622  1132.14   <2e-16 ***
ORIGIN_HEX49           12.8399695  0.1825829    70.32   <2e-16 ***
ORIGIN_HEX50           15.5343809  0.0200863   773.38   <2e-16 ***
ORIGIN_HEX51           15.2236925  0.0197126   772.28   <2e-16 ***
ORIGIN_HEX52           16.8454354  0.0169576   993.38   <2e-16 ***
ORIGIN_HEX53           16.1467796  0.0265825   607.42   <2e-16 ***
ORIGIN_HEX54           16.5648495  0.0164886  1004.62   <2e-16 ***
ORIGIN_HEX55           17.4065104  0.0150508  1156.52   <2e-16 ***
ORIGIN_HEX56           15.9962776  0.0163069   980.95   <2e-16 ***
ORIGIN_HEX57           16.3188213  0.0162374  1005.01   <2e-16 ***
ORIGIN_HEX58           17.0259822  0.0137856  1235.06   <2e-16 ***
ORIGIN_HEX59           17.0553971  0.0097067  1757.07   <2e-16 ***
ORIGIN_HEX60           16.9236819  0.0101670  1664.57   <2e-16 ***
ORIGIN_HEX61           16.0781618  0.0158938  1011.60   <2e-16 ***
ORIGIN_HEX62           17.2828485  0.0137558  1256.40   <2e-16 ***
ORIGIN_HEX63           16.7323040  0.0179349   932.94   <2e-16 ***
ORIGIN_HEX64           17.4036876  0.0126165  1379.44   <2e-16 ***
ORIGIN_HEX65           17.2645476  0.0046925  3679.15   <2e-16 ***
ORIGIN_HEX66           17.2635434  0.0086226  2002.12   <2e-16 ***
ORIGIN_HEX67           18.1112804  0.0049933  3627.09   <2e-16 ***
ORIGIN_HEX68           14.3550746  0.0435206   329.85   <2e-16 ***
ORIGIN_HEX69           16.8294953  0.0093489  1800.15   <2e-16 ***
ORIGIN_HEX70           14.4779777  0.0195089   742.12   <2e-16 ***
ORIGIN_HEX71           17.1121679  0.0079540  2151.39   <2e-16 ***
ORIGIN_HEX72           15.7987046  0.0196474   804.11   <2e-16 ***
ORIGIN_HEX73           15.6406753  0.0273198   572.50   <2e-16 ***
ORIGIN_HEX74           15.2263834  0.0206199   738.43   <2e-16 ***
ORIGIN_HEX75           16.2067296  0.0116207  1394.64   <2e-16 ***
ORIGIN_HEX76           15.5726980  0.0103593  1503.27   <2e-16 ***
ORIGIN_HEX77           15.9269946  0.0109498  1454.55   <2e-16 ***
ORIGIN_HEX79           16.5565089  0.0115202  1437.17   <2e-16 ***
ORIGIN_HEX80           15.7381901  0.0096167  1636.55   <2e-16 ***
ORIGIN_HEX81           16.2276217  0.0068261  2377.28   <2e-16 ***
ORIGIN_HEX82           16.7499141  0.0112506  1488.80   <2e-16 ***
ORIGIN_HEX84           15.7349926  0.0262743   598.87   <2e-16 ***
ORIGIN_HEX85           12.6612722  0.1250153   101.28   <2e-16 ***
ORIGIN_HEX86           16.3775167  0.0090894  1801.83   <2e-16 ***
ORIGIN_HEX87           15.1122473  0.0106365  1420.79   <2e-16 ***
ORIGIN_HEX88           14.4368204  0.0380441   379.48   <2e-16 ***
ORIGIN_HEX89           15.4119762  0.0262374   587.40   <2e-16 ***
ORIGIN_HEX90           16.4553721  0.0130142  1264.42   <2e-16 ***
ORIGIN_HEX91           17.2155019  0.0091965  1871.95   <2e-16 ***
ORIGIN_HEX92           15.7139307  0.0088165  1782.34   <2e-16 ***
ORIGIN_HEX93           16.4103143  0.0054315  3021.32   <2e-16 ***
ORIGIN_HEX94           16.7061363  0.0089930  1857.69   <2e-16 ***
ORIGIN_HEX95           16.3342743  0.0132933  1228.77   <2e-16 ***
ORIGIN_HEX96           13.4001073  0.0725754   184.64   <2e-16 ***
ORIGIN_HEX97           15.2972997  0.0324687   471.14   <2e-16 ***
ORIGIN_HEX98           16.9418398  0.0081697  2073.74   <2e-16 ***
ORIGIN_HEX99           15.9347339  0.0100851  1580.04   <2e-16 ***
ORIGIN_HEX100          17.1373414  0.0039043  4389.40   <2e-16 ***
ORIGIN_HEX101          16.4539018  0.0057850  2844.24   <2e-16 ***
ORIGIN_HEX102          15.7625202  0.0158634   993.64   <2e-16 ***
ORIGIN_HEX103          14.0748809  0.0516794   272.35   <2e-16 ***
ORIGIN_HEX104          14.4217069  0.0516819   279.05   <2e-16 ***
ORIGIN_HEX105          12.1259400  1.0000024    12.13   <2e-16 ***
ORIGIN_HEX106          15.4307461  0.0239294   644.85   <2e-16 ***
ORIGIN_HEX107          16.8948648  0.0129723  1302.38   <2e-16 ***
ORIGIN_HEX108          15.2516382  0.0105118  1450.91   <2e-16 ***
ORIGIN_HEX109          15.8870710  0.0064983  2444.79   <2e-16 ***
ORIGIN_HEX110          16.6404421  0.0085771  1940.10   <2e-16 ***
ORIGIN_HEX111          14.5453734  0.0562075   258.78   <2e-16 ***
ORIGIN_HEX112          16.4412044  0.0167068   984.10   <2e-16 ***
ORIGIN_HEX114          14.9636514  0.0394225   379.57   <2e-16 ***
ORIGIN_HEX115          16.1102321  0.0155802  1034.02   <2e-16 ***
ORIGIN_HEX116          14.7656183  0.0334277   441.72   <2e-16 ***
ORIGIN_HEX117          18.6283320  0.0024498  7603.94   <2e-16 ***
ORIGIN_HEX118          16.0488744  0.0064538  2486.74   <2e-16 ***
ORIGIN_HEX119          12.7656725  0.1015589   125.70   <2e-16 ***
ORIGIN_HEX120          16.0382112  0.0307583   521.43   <2e-16 ***
ORIGIN_HEX121          13.7343146  0.1740932    78.89   <2e-16 ***
ORIGIN_HEX122          15.4422561  0.0373776   413.14   <2e-16 ***
ORIGIN_HEX123          14.8881483  0.0277391   536.72   <2e-16 ***
ORIGIN_HEX124          15.9417817  0.0166317   958.52   <2e-16 ***
ORIGIN_HEX125          16.6526066  0.0062593  2660.47   <2e-16 ***
ORIGIN_HEX126          15.8849571  0.0060543  2623.76   <2e-16 ***
ORIGIN_HEX127          14.8259643  0.0257583   575.58   <2e-16 ***
ORIGIN_HEX128          14.8290452  0.0568428   260.88   <2e-16 ***
ORIGIN_HEX129          14.9314984  0.0494306   302.07   <2e-16 ***
ORIGIN_HEX130          15.0750365  0.0183878   819.84   <2e-16 ***
ORIGIN_HEX131          16.1518732  0.0100977  1599.57   <2e-16 ***
ORIGIN_HEX132          15.1827832  0.0126047  1204.53   <2e-16 ***
ORIGIN_HEX133          16.1970378  0.0056168  2883.70   <2e-16 ***
ORIGIN_HEX134          15.7461644  0.0158447   993.78   <2e-16 ***
ORIGIN_HEX135          15.7931274  0.0119752  1318.82   <2e-16 ***
ORIGIN_HEX136          16.0968373  0.0054484  2954.43   <2e-16 ***
ORIGIN_HEX137          16.6375807  0.0078933  2107.80   <2e-16 ***
ORIGIN_HEX138          16.2195277  0.0063195  2566.57   <2e-16 ***
ORIGIN_HEX139          15.8528940  0.0069213  2290.46   <2e-16 ***
ORIGIN_HEX140          16.6124403  0.0044431  3738.90   <2e-16 ***
ORIGIN_HEX141          16.5809452  0.0098503  1683.30   <2e-16 ***
ORIGIN_HEX142          16.5029380  0.0116145  1420.89   <2e-16 ***
ORIGIN_HEX143          14.4408746  0.0219819   656.94   <2e-16 ***
ORIGIN_HEX144          16.5096568  0.0051475  3207.30   <2e-16 ***
ORIGIN_HEX145          17.6650237  0.0030455  5800.29   <2e-16 ***
ORIGIN_HEX146          14.7273351  0.0155592   946.53   <2e-16 ***
ORIGIN_HEX147          16.1502746  0.0100954  1599.77   <2e-16 ***
ORIGIN_HEX148          15.9580362  0.0071866  2220.51   <2e-16 ***
ORIGIN_HEX149          15.0226016  0.0117241  1281.34   <2e-16 ***
ORIGIN_HEX150          16.3985093  0.0048579  3375.64   <2e-16 ***
ORIGIN_HEX151          16.2447573  0.0109133  1488.53   <2e-16 ***
ORIGIN_HEX152          14.7299007  0.0145270  1013.96   <2e-16 ***
ORIGIN_HEX154          14.1443987  0.0277105   510.43   <2e-16 ***
ORIGIN_HEX156          16.4090801  0.0087251  1880.67   <2e-16 ***
ORIGIN_HEX157          13.5279652  0.0211531   639.53   <2e-16 ***
ORIGIN_HEX158          15.8566940  0.0063350  2503.02   <2e-16 ***
ORIGIN_HEX160          16.6611196  0.0095871  1737.86   <2e-16 ***
ORIGIN_HEX161          16.0918711  0.0090374  1780.58   <2e-16 ***
ORIGIN_HEX162          14.0621388  0.0193899   725.23   <2e-16 ***
ORIGIN_HEX163          16.6751328  0.0040766  4090.44   <2e-16 ***
ORIGIN_HEX164          16.0828240  0.0086590  1857.35   <2e-16 ***
ORIGIN_HEX165          16.5553963  0.0061112  2709.01   <2e-16 ***
ORIGIN_HEX166          14.3025294  0.0429222   333.22   <2e-16 ***
ORIGIN_HEX167          13.6399294  0.0225060   606.06   <2e-16 ***
ORIGIN_HEX168          15.9347478  0.0055123  2890.76   <2e-16 ***
ORIGIN_HEX169          15.5267200  0.0067390  2303.99   <2e-16 ***
ORIGIN_HEX170          16.1091428  0.0089040  1809.21   <2e-16 ***
ORIGIN_HEX171          15.5044881  0.0097673  1587.39   <2e-16 ***
ORIGIN_HEX172          14.9740414  0.0146234  1023.98   <2e-16 ***
ORIGIN_HEX173          15.1860137  0.0182278   833.12   <2e-16 ***
ORIGIN_HEX174          16.3407298  0.0068400  2389.01   <2e-16 ***
ORIGIN_HEX175          17.3719739  0.0032711  5310.78   <2e-16 ***
ORIGIN_HEX176          15.6408706  0.0063864  2449.08   <2e-16 ***
ORIGIN_HEX177          16.1967710  0.0064114  2526.25   <2e-16 ***
ORIGIN_HEX178          14.4125069  0.0202212   712.74   <2e-16 ***
ORIGIN_HEX179          16.2021927  0.0054978  2947.03   <2e-16 ***
ORIGIN_HEX180          15.8863729  0.0084228  1886.12   <2e-16 ***
ORIGIN_HEX181          14.8716602  0.0264506   562.24   <2e-16 ***
ORIGIN_HEX182          15.9183098  0.0136606  1165.27   <2e-16 ***
ORIGIN_HEX183          15.7052645  0.0069874  2247.64   <2e-16 ***
ORIGIN_HEX184          16.2620225  0.0052389  3104.10   <2e-16 ***
ORIGIN_HEX185          16.0906294  0.0051426  3128.91   <2e-16 ***
ORIGIN_HEX186          15.6056819  0.0080656  1934.84   <2e-16 ***
ORIGIN_HEX187          15.3934819  0.0097186  1583.92   <2e-16 ***
ORIGIN_HEX188          18.0331799  0.0027620  6528.98   <2e-16 ***
ORIGIN_HEX189          17.7719854  0.0038100  4664.59   <2e-16 ***
ORIGIN_HEX190          15.0703976  0.0225383   668.66   <2e-16 ***
ORIGIN_HEX191          15.1833530  0.0231482   655.92   <2e-16 ***
ORIGIN_HEX192          15.7393932  0.0075655  2080.42   <2e-16 ***
ORIGIN_HEX193          16.8026092  0.0045708  3676.09   <2e-16 ***
ORIGIN_HEX194          15.7416754  0.0062035  2537.56   <2e-16 ***
ORIGIN_HEX195          14.7242605  0.0104550  1408.35   <2e-16 ***
ORIGIN_HEX196          15.9471387  0.0061337  2599.92   <2e-16 ***
ORIGIN_HEX197          15.9838319  0.0059010  2708.68   <2e-16 ***
ORIGIN_HEX198          15.5919480  0.0086084  1811.26   <2e-16 ***
ORIGIN_HEX199          16.9481921  0.0066582  2545.46   <2e-16 ***
ORIGIN_HEX200          15.7044625  0.0167019   940.28   <2e-16 ***
ORIGIN_HEX201          15.3115577  0.0191075   801.34   <2e-16 ***
ORIGIN_HEX202          14.9158114  0.0248054   601.31   <2e-16 ***
ORIGIN_HEX203          16.4531336  0.0111650  1473.64   <2e-16 ***
ORIGIN_HEX204          16.8156943  0.0054331  3095.02   <2e-16 ***
ORIGIN_HEX205          16.6713256  0.0058194  2864.80   <2e-16 ***
ORIGIN_HEX206          17.3329987  0.0055328  3132.79   <2e-16 ***
ORIGIN_HEX207          17.4048002  0.0030699  5669.49   <2e-16 ***
ORIGIN_HEX208          17.2795221  0.0044945  3844.57   <2e-16 ***
ORIGIN_HEX209          15.2957158  0.0086681  1764.60   <2e-16 ***
ORIGIN_HEX210          14.5368612  0.0139419  1042.67   <2e-16 ***
ORIGIN_HEX211          14.9525123  0.0111643  1339.31   <2e-16 ***
ORIGIN_HEX212          14.3272890  0.0341752   419.23   <2e-16 ***
ORIGIN_HEX213          14.3477752  0.0298678   480.38   <2e-16 ***
ORIGIN_HEX214          14.3533110  0.0281667   509.58   <2e-16 ***
ORIGIN_HEX215          15.5972534  0.0096120  1622.68   <2e-16 ***
ORIGIN_HEX216          15.2541788  0.0104752  1456.22   <2e-16 ***
ORIGIN_HEX217          15.3612838  0.0120720  1272.48   <2e-16 ***
ORIGIN_HEX218          16.2977024  0.0050966  3197.76   <2e-16 ***
ORIGIN_HEX219          15.0371910  0.0151186   994.62   <2e-16 ***
ORIGIN_HEX220          16.4730278  0.0049257  3344.27   <2e-16 ***
ORIGIN_HEX221          14.7992558  0.0123155  1201.68   <2e-16 ***
ORIGIN_HEX222          15.7167943  0.0102811  1528.71   <2e-16 ***
ORIGIN_HEX223          13.5842141  0.0412575   329.25   <2e-16 ***
ORIGIN_HEX224          15.0393035  0.0208746   720.46   <2e-16 ***
ORIGIN_HEX225          16.1580349  0.0143329  1127.34   <2e-16 ***
ORIGIN_HEX226          16.5087197  0.0105822  1560.04   <2e-16 ***
ORIGIN_HEX227          15.9085433  0.0064964  2448.84   <2e-16 ***
ORIGIN_HEX228          14.3728228  0.0148037   970.90   <2e-16 ***
ORIGIN_HEX229          17.1300554  0.0043238  3961.82   <2e-16 ***
ORIGIN_HEX230          15.6811958  0.0068588  2286.28   <2e-16 ***
ORIGIN_HEX231          15.7992542  0.0067074  2355.50   <2e-16 ***
ORIGIN_HEX232          17.1188234  0.0057187  2993.47   <2e-16 ***
ORIGIN_HEX233          14.2430809  0.0264766   537.95   <2e-16 ***
ORIGIN_HEX234          15.1104825  0.0170686   885.28   <2e-16 ***
ORIGIN_HEX235          14.5406249  0.0190856   761.87   <2e-16 ***
ORIGIN_HEX236          15.9008631  0.0064385  2469.65   <2e-16 ***
ORIGIN_HEX237          17.2353180  0.0034448  5003.22   <2e-16 ***
ORIGIN_HEX238          15.2464970  0.0117870  1293.50   <2e-16 ***
ORIGIN_HEX239          14.0234436  0.0321575   436.09   <2e-16 ***
ORIGIN_HEX240          15.9212865  0.0076289  2086.97   <2e-16 ***
ORIGIN_HEX241          14.5588075  0.0139355  1044.72   <2e-16 ***
ORIGIN_HEX242          17.9469778  0.0027812  6452.96   <2e-16 ***
ORIGIN_HEX243          11.9835454  0.1961254    61.10   <2e-16 ***
ORIGIN_HEX244          17.7955907  0.0040792  4362.49   <2e-16 ***
ORIGIN_HEX245          15.0434922  0.0260940   576.51   <2e-16 ***
ORIGIN_HEX246          15.1985112  0.0124232  1223.40   <2e-16 ***
ORIGIN_HEX247          16.9286629  0.0051114  3311.91   <2e-16 ***
ORIGIN_HEX248          17.7794787  0.0029521  6022.60   <2e-16 ***
ORIGIN_HEX249          16.3597697  0.0087453  1870.70   <2e-16 ***
ORIGIN_HEX250          15.5139980  0.0106626  1454.99   <2e-16 ***
ORIGIN_HEX251          13.7785751  0.0197690   696.98   <2e-16 ***
ORIGIN_HEX252          16.6918911  0.0050533  3303.16   <2e-16 ***
ORIGIN_HEX253          14.9366056  0.0108223  1380.17   <2e-16 ***
ORIGIN_HEX254          15.6939017  0.0084998  1846.39   <2e-16 ***
ORIGIN_HEX255          15.8500973  0.0198090   800.15   <2e-16 ***
ORIGIN_HEX256          15.1334605  0.0135641  1115.70   <2e-16 ***
ORIGIN_HEX258          16.4858315  0.0056861  2899.33   <2e-16 ***
ORIGIN_HEX259          16.3347597  0.0048365  3377.38   <2e-16 ***
ORIGIN_HEX260          15.9055279  0.0065485  2428.90   <2e-16 ***
ORIGIN_HEX262          15.3271464  0.0101199  1514.55   <2e-16 ***
ORIGIN_HEX263          14.5237437  0.0152257   953.90   <2e-16 ***
ORIGIN_HEX264          14.3353301  0.0156685   914.92   <2e-16 ***
ORIGIN_HEX265          16.0760566  0.0058979  2725.72   <2e-16 ***
ORIGIN_HEX266          15.7054360  0.0099580  1577.17   <2e-16 ***
ORIGIN_HEX267          14.9702487  0.0120663  1240.67   <2e-16 ***
ORIGIN_HEX268          18.1507003  0.0047696  3805.50   <2e-16 ***
ORIGIN_HEX269          16.5620478  0.0060813  2723.42   <2e-16 ***
ORIGIN_HEX270          16.6063753  0.0052984  3134.20   <2e-16 ***
ORIGIN_HEX271          15.1251673  0.0093186  1623.12   <2e-16 ***
ORIGIN_HEX272          15.1861459  0.0099704  1523.12   <2e-16 ***
ORIGIN_HEX273          17.0694974  0.0045309  3767.32   <2e-16 ***
ORIGIN_HEX274          15.1718132  0.0113464  1337.15   <2e-16 ***
ORIGIN_HEX275          14.9221729  0.0253003   589.80   <2e-16 ***
ORIGIN_HEX276          16.5946660  0.0051247  3238.16   <2e-16 ***
ORIGIN_HEX277          15.9748520  0.0082534  1935.55   <2e-16 ***
ORIGIN_HEX278          15.4252730  0.0202918   760.17   <2e-16 ***
ORIGIN_HEX279          17.4484640  0.0037393  4666.20   <2e-16 ***
ORIGIN_HEX280          17.0244984  0.0047615  3575.46   <2e-16 ***
ORIGIN_HEX281          15.5313429  0.0146568  1059.67   <2e-16 ***
ORIGIN_HEX282          17.5017105  0.0056207  3113.80   <2e-16 ***
ORIGIN_HEX283          15.4309372  0.0093665  1647.46   <2e-16 ***
ORIGIN_HEX284          14.4919124  0.0142577  1016.43   <2e-16 ***
ORIGIN_HEX285          16.4358869  0.0057941  2836.65   <2e-16 ***
ORIGIN_HEX286          16.6109489  0.0053568  3100.94   <2e-16 ***
ORIGIN_HEX287          15.5283494  0.0130189  1192.75   <2e-16 ***
ORIGIN_HEX288          16.4389108  0.0068305  2406.70   <2e-16 ***
ORIGIN_HEX289          15.2928365  0.0124671  1226.66   <2e-16 ***
ORIGIN_HEX290          16.1778267  0.0065697  2462.48   <2e-16 ***
ORIGIN_HEX291          13.6603089  0.0327958   416.53   <2e-16 ***
ORIGIN_HEX292          16.3651226  0.0068911  2374.82   <2e-16 ***
ORIGIN_HEX293          16.5582623  0.0054392  3044.26   <2e-16 ***
ORIGIN_HEX294          16.6605118  0.0049233  3384.00   <2e-16 ***
ORIGIN_HEX295          17.2500106  0.0041320  4174.73   <2e-16 ***
ORIGIN_HEX296          16.1700042  0.0059102  2735.95   <2e-16 ***
ORIGIN_HEX297          16.4823894  0.0111973  1471.99   <2e-16 ***
ORIGIN_HEX298          16.2417105  0.0057103  2844.27   <2e-16 ***
ORIGIN_HEX299          16.0935013  0.0069107  2328.79   <2e-16 ***
ORIGIN_HEX300          16.7682381  0.0053653  3125.31   <2e-16 ***
ORIGIN_HEX301          16.6113104  0.0054451  3050.67   <2e-16 ***
ORIGIN_HEX302          15.8640562  0.0074325  2134.40   <2e-16 ***
ORIGIN_HEX303          15.2782171  0.0101354  1507.41   <2e-16 ***
ORIGIN_HEX304          14.4689932  0.0630367   229.53   <2e-16 ***
ORIGIN_HEX305          17.3883477  0.0036591  4752.03   <2e-16 ***
ORIGIN_HEX306          16.5502860  0.0082083  2016.29   <2e-16 ***
ORIGIN_HEX307          15.3500325  0.0106983  1434.82   <2e-16 ***
ORIGIN_HEX308          16.5322136  0.0062185  2658.55   <2e-16 ***
ORIGIN_HEX309          15.6119410  0.0076365  2044.39   <2e-16 ***
ORIGIN_HEX310          14.9724860  0.0123506  1212.29   <2e-16 ***
ORIGIN_HEX311          16.5018459  0.0057168  2886.57   <2e-16 ***
ORIGIN_HEX312          13.3870298  0.0793291   168.75   <2e-16 ***
ORIGIN_HEX313          16.0647449  0.0072979  2201.28   <2e-16 ***
ORIGIN_HEX314          15.6175668  0.0090225  1730.96   <2e-16 ***
ORIGIN_HEX315          13.8315352  0.0462270   299.21   <2e-16 ***
ORIGIN_HEX316          16.0867004  0.0136553  1178.05   <2e-16 ***
ORIGIN_HEX317          16.0201196  0.0121206  1321.73   <2e-16 ***
ORIGIN_HEX318          16.8493901  0.0041672  4043.34   <2e-16 ***
ORIGIN_HEX319          14.1980663  0.0210978   672.96   <2e-16 ***
ORIGIN_HEX320          15.7359000  0.0078947  1993.23   <2e-16 ***
ORIGIN_HEX321          17.4564810  0.0089775  1944.48   <2e-16 ***
ORIGIN_HEX322          12.0279048  0.1543173    77.94   <2e-16 ***
ORIGIN_HEX323          15.1218709  0.0154458   979.03   <2e-16 ***
ORIGIN_HEX324          18.4790494  0.0024812  7447.67   <2e-16 ***
ORIGIN_HEX325          14.9245355  0.0201145   741.98   <2e-16 ***
ORIGIN_HEX326          15.8252744  0.0082207  1925.06   <2e-16 ***
ORIGIN_HEX327          16.0574478  0.0075785  2118.81   <2e-16 ***
ORIGIN_HEX328          14.2298178  0.0189773   749.83   <2e-16 ***
ORIGIN_HEX329          15.6623835  0.0077821  2012.61   <2e-16 ***
ORIGIN_HEX330          14.7721624  0.0165261   893.87   <2e-16 ***
ORIGIN_HEX331          15.8876519  0.0072972  2177.21   <2e-16 ***
ORIGIN_HEX332          16.2833935  0.0057892  2812.70   <2e-16 ***
ORIGIN_HEX333          17.6512881  0.0058056  3040.38   <2e-16 ***
ORIGIN_HEX334          16.8939033  0.0051028  3310.72   <2e-16 ***
ORIGIN_HEX335          14.4928443  0.0182251   795.22   <2e-16 ***
ORIGIN_HEX336          15.7178333  0.0067320  2334.80   <2e-16 ***
ORIGIN_HEX337          16.1779026  0.0064267  2517.29   <2e-16 ***
ORIGIN_HEX338          15.0281265  0.0258884   580.50   <2e-16 ***
ORIGIN_HEX339          16.1849317  0.0085269  1898.09   <2e-16 ***
ORIGIN_HEX340          16.0273290  0.0057849  2770.53   <2e-16 ***
ORIGIN_HEX341          16.0378811  0.0070722  2267.75   <2e-16 ***
ORIGIN_HEX343          14.9026152  0.0111196  1340.21   <2e-16 ***
ORIGIN_HEX344          15.5481516  0.0070682  2199.72   <2e-16 ***
ORIGIN_HEX345          16.5537622  0.0044361  3731.59   <2e-16 ***
ORIGIN_HEX346          16.4418448  0.0056371  2916.70   <2e-16 ***
ORIGIN_HEX347          17.3933692  0.0035378  4916.40   <2e-16 ***
ORIGIN_HEX348          16.5927676  0.0065306  2540.77   <2e-16 ***
ORIGIN_HEX349          13.6723049  0.0587539   232.71   <2e-16 ***
ORIGIN_HEX350          17.0737902  0.0040051  4263.02   <2e-16 ***
ORIGIN_HEX351          16.1517124  0.0053107  3041.35   <2e-16 ***
ORIGIN_HEX352          16.1932086  0.0051059  3171.45   <2e-16 ***
ORIGIN_HEX353          15.2014367  0.0086298  1761.50   <2e-16 ***
ORIGIN_HEX354          15.8681711  0.0077521  2046.96   <2e-16 ***
ORIGIN_HEX355          14.4824864  0.0350712   412.94   <2e-16 ***
ORIGIN_HEX356          16.5111571  0.0055557  2971.95   <2e-16 ***
ORIGIN_HEX357          16.3704877  0.0057359  2854.06   <2e-16 ***
ORIGIN_HEX358          16.9575625  0.0060793  2789.40   <2e-16 ***
ORIGIN_HEX360          15.5755303  0.0075829  2054.02   <2e-16 ***
ORIGIN_HEX361          15.8228627  0.0063119  2506.84   <2e-16 ***
ORIGIN_HEX362          15.7609339  0.0074674  2110.62   <2e-16 ***
ORIGIN_HEX363          15.4190914  0.0092249  1671.47   <2e-16 ***
ORIGIN_HEX364          14.3485060  0.0506786   283.13   <2e-16 ***
ORIGIN_HEX365          15.9965066  0.0066402  2409.03   <2e-16 ***
ORIGIN_HEX366          16.8026626  0.0096421  1742.64   <2e-16 ***
ORIGIN_HEX367          16.4138034  0.0104514  1570.48   <2e-16 ***
ORIGIN_HEX368          16.0003388  0.0061547  2599.69   <2e-16 ***
ORIGIN_HEX369          16.4825078  0.0044096  3737.84   <2e-16 ***
ORIGIN_HEX370          15.3244336  0.0130355  1175.60   <2e-16 ***
ORIGIN_HEX371          14.8299428  0.0123593  1199.90   <2e-16 ***
ORIGIN_HEX372          15.5102881  0.0088262  1757.31   <2e-16 ***
ORIGIN_HEX373          13.9132710  0.0525228   264.90   <2e-16 ***
ORIGIN_HEX374          14.8357034  0.0357342   415.17   <2e-16 ***
ORIGIN_HEX375          15.9129732  0.0069062  2304.15   <2e-16 ***
ORIGIN_HEX376          15.9075860  0.0088916  1789.05   <2e-16 ***
ORIGIN_HEX377          14.6046717  0.0127367  1146.66   <2e-16 ***
ORIGIN_HEX378          15.1978607  0.0083380  1822.72   <2e-16 ***
ORIGIN_HEX379          16.0065779  0.0054993  2910.68   <2e-16 ***
ORIGIN_HEX380          15.6997304  0.0077028  2038.18   <2e-16 ***
ORIGIN_HEX381          15.4259134  0.0088888  1735.42   <2e-16 ***
ORIGIN_HEX382          16.4043779  0.0064020  2562.37   <2e-16 ***
ORIGIN_HEX383          17.0241358  0.0061702  2759.10   <2e-16 ***
ORIGIN_HEX384          14.5322458  0.0127648  1138.46   <2e-16 ***
ORIGIN_HEX385          16.6919621  0.0038977  4282.50   <2e-16 ***
ORIGIN_HEX386          15.5185181  0.0085208  1821.24   <2e-16 ***
ORIGIN_HEX387          15.1211574  0.0110189  1372.29   <2e-16 ***
ORIGIN_HEX388          15.9563809  0.0074616  2138.46   <2e-16 ***
ORIGIN_HEX389          14.5979671  0.0175279   832.84   <2e-16 ***
ORIGIN_HEX390          11.9348824  0.1026198   116.30   <2e-16 ***
ORIGIN_HEX391          16.3887152  0.0078489  2088.03   <2e-16 ***
ORIGIN_HEX392          16.8192975  0.0045755  3675.92   <2e-16 ***
ORIGIN_HEX393          16.0987449  0.0071041  2266.13   <2e-16 ***
ORIGIN_HEX394          17.5665345  0.0034047  5159.42   <2e-16 ***
ORIGIN_HEX395          16.5487520  0.0043898  3769.78   <2e-16 ***
ORIGIN_HEX396          16.3615368  0.0046004  3556.53   <2e-16 ***
ORIGIN_HEX397          15.8083823  0.0084078  1880.21   <2e-16 ***
ORIGIN_HEX398          13.8888243  0.0312512   444.43   <2e-16 ***
ORIGIN_HEX399          13.9772953  0.0319811   437.05   <2e-16 ***
ORIGIN_HEX400          16.4681443  0.0077074  2136.66   <2e-16 ***
ORIGIN_HEX401          14.4006555  0.0207217   694.96   <2e-16 ***
ORIGIN_HEX402          15.5803439  0.0081593  1909.51   <2e-16 ***
ORIGIN_HEX403          15.8621509  0.0093550  1695.58   <2e-16 ***
ORIGIN_HEX404          16.1438131  0.0057323  2816.28   <2e-16 ***
ORIGIN_HEX405          16.1741578  0.0045944  3520.44   <2e-16 ***
ORIGIN_HEX406          14.0395548  0.0244894   573.29   <2e-16 ***
ORIGIN_HEX407          16.5940911  0.0051150  3244.22   <2e-16 ***
ORIGIN_HEX408          11.5413222  0.1581269    72.99   <2e-16 ***
ORIGIN_HEX409          14.4625498  0.0179506   805.69   <2e-16 ***
ORIGIN_HEX410          14.7749874  0.0122656  1204.59   <2e-16 ***
ORIGIN_HEX411          14.0179131  0.0188239   744.69   <2e-16 ***
ORIGIN_HEX412          17.3373226  0.0036778  4714.08   <2e-16 ***
ORIGIN_HEX413          15.4659464  0.0112238  1377.96   <2e-16 ***
ORIGIN_HEX415          14.8361267  0.0113256  1309.96   <2e-16 ***
ORIGIN_HEX416          16.1265669  0.0049874  3233.44   <2e-16 ***
ORIGIN_HEX417          15.9932214  0.0054154  2953.31   <2e-16 ***
ORIGIN_HEX418          16.0623352  0.0062261  2579.86   <2e-16 ***
ORIGIN_HEX419          16.0028466  0.0089805  1781.95   <2e-16 ***
ORIGIN_HEX420          15.2538526  0.0131849  1156.92   <2e-16 ***
ORIGIN_HEX421          11.3023703  0.2085256    54.20   <2e-16 ***
ORIGIN_HEX422          14.4603841  0.0164441   879.37   <2e-16 ***
ORIGIN_HEX423          15.0929873  0.0128946  1170.49   <2e-16 ***
ORIGIN_HEX424          16.7837427  0.0062986  2664.70   <2e-16 ***
ORIGIN_HEX425          12.5812207  0.0814086   154.54   <2e-16 ***
ORIGIN_HEX426          13.3194880  0.0326378   408.10   <2e-16 ***
ORIGIN_HEX427          13.5054424  0.0237269   569.20   <2e-16 ***
ORIGIN_HEX428          16.7707074  0.0043987  3812.69   <2e-16 ***
ORIGIN_HEX429          15.8666807  0.0079902  1985.77   <2e-16 ***
ORIGIN_HEX430          11.8845263  0.2500098    47.54   <2e-16 ***
ORIGIN_HEX431          15.7872735  0.0075333  2095.68   <2e-16 ***
ORIGIN_HEX432          17.0332450  0.0036482  4668.97   <2e-16 ***
ORIGIN_HEX433          15.7531213  0.0061004  2582.30   <2e-16 ***
ORIGIN_HEX434          17.0599424  0.0043106  3957.71   <2e-16 ***
ORIGIN_HEX435          15.2098114  0.0148364  1025.17   <2e-16 ***
ORIGIN_HEX436          15.1203427  0.0098130  1540.85   <2e-16 ***
ORIGIN_HEX437          14.5471874  0.0138085  1053.50   <2e-16 ***
ORIGIN_HEX438          15.2977245  0.0102127  1497.91   <2e-16 ***
ORIGIN_HEX439          14.5366794  0.0193059   752.97   <2e-16 ***
ORIGIN_HEX440          15.7449143  0.0071911  2189.51   <2e-16 ***
ORIGIN_HEX441          15.6724039  0.0071328  2197.24   <2e-16 ***
ORIGIN_HEX442          15.4918107  0.0076146  2034.48   <2e-16 ***
ORIGIN_HEX443          16.3081409  0.0070536  2312.03   <2e-16 ***
ORIGIN_HEX444          14.0609583  0.0330688   425.20   <2e-16 ***
ORIGIN_HEX445          14.8922677  0.0086596  1719.74   <2e-16 ***
ORIGIN_HEX446          14.9169048  0.0084832  1758.41   <2e-16 ***
ORIGIN_HEX447          17.0021319  0.0036981  4597.48   <2e-16 ***
ORIGIN_HEX448          15.7831198  0.0091397  1726.87   <2e-16 ***
ORIGIN_HEX449          15.2267216  0.0097798  1556.96   <2e-16 ***
ORIGIN_HEX450          12.9458170  0.0366282   353.44   <2e-16 ***
ORIGIN_HEX451          14.3547024  0.0134736  1065.39   <2e-16 ***
ORIGIN_HEX452          15.8314091  0.0089562  1767.65   <2e-16 ***
ORIGIN_HEX453          14.5110740  0.0166874   869.59   <2e-16 ***
ORIGIN_HEX455          12.9099476  0.0430792   299.68   <2e-16 ***
ORIGIN_HEX456          17.5539582  0.0030724  5713.41   <2e-16 ***
ORIGIN_HEX457          17.2506164  0.0033565  5139.44   <2e-16 ***
ORIGIN_HEX458          16.8053415  0.0053378  3148.36   <2e-16 ***
ORIGIN_HEX459          13.8564286  0.0271189   510.95   <2e-16 ***
ORIGIN_HEX460          15.6985739  0.0063520  2471.44   <2e-16 ***
ORIGIN_HEX461          15.1848382  0.0075504  2011.14   <2e-16 ***
ORIGIN_HEX462          15.7251840  0.0064905  2422.80   <2e-16 ***
ORIGIN_HEX463          16.1033157  0.0063763  2525.49   <2e-16 ***
ORIGIN_HEX464          15.5190961  0.0142835  1086.51   <2e-16 ***
ORIGIN_HEX465          14.6470409  0.0119288  1227.88   <2e-16 ***
ORIGIN_HEX466          15.6625031  0.0066036  2371.81   <2e-16 ***
ORIGIN_HEX467          15.5909967  0.0067096  2323.69   <2e-16 ***
ORIGIN_HEX468          16.0948361  0.0057475  2800.32   <2e-16 ***
ORIGIN_HEX469          15.4565568  0.0085751  1802.50   <2e-16 ***
ORIGIN_HEX470          15.1663622  0.0134158  1130.49   <2e-16 ***
ORIGIN_HEX471          14.9511824  0.0122955  1215.99   <2e-16 ***
ORIGIN_HEX472          16.5628593  0.0041168  4023.25   <2e-16 ***
ORIGIN_HEX473          16.0457716  0.0059000  2719.60   <2e-16 ***
ORIGIN_HEX474          16.0956397  0.0189424   849.72   <2e-16 ***
ORIGIN_HEX475          16.4088005  0.0043506  3771.64   <2e-16 ***
ORIGIN_HEX476          15.5910687  0.0068637  2271.53   <2e-16 ***
ORIGIN_HEX477          16.9917513  0.0036733  4625.77   <2e-16 ***
ORIGIN_HEX478          16.4638883  0.0049936  3296.98   <2e-16 ***
ORIGIN_HEX479          15.5403222  0.0064945  2392.84   <2e-16 ***
ORIGIN_HEX480          15.7823055  0.0063874  2470.84   <2e-16 ***
ORIGIN_HEX481          15.6315115  0.0071775  2177.85   <2e-16 ***
ORIGIN_HEX482          15.7063598  0.0060593  2592.09   <2e-16 ***
ORIGIN_HEX483          15.6958298  0.0065511  2395.92   <2e-16 ***
ORIGIN_HEX484          15.6558850  0.0075941  2061.57   <2e-16 ***
ORIGIN_HEX485          15.6299563  0.0075821  2061.42   <2e-16 ***
ORIGIN_HEX486          16.7525109  0.0044971  3725.18   <2e-16 ***
ORIGIN_HEX487          16.3609347  0.0050914  3213.47   <2e-16 ***
ORIGIN_HEX488          17.1306976  0.0034329  4990.20   <2e-16 ***
ORIGIN_HEX489          16.4269469  0.0042756  3841.98   <2e-16 ***
ORIGIN_HEX490          16.0313987  0.0081825  1959.24   <2e-16 ***
ORIGIN_HEX491          16.6644236  0.0043405  3839.28   <2e-16 ***
ORIGIN_HEX492          16.0981646  0.0051483  3126.88   <2e-16 ***
ORIGIN_HEX493          14.1998669  0.0155085   915.62   <2e-16 ***
ORIGIN_HEX494          15.7850193  0.0062378  2530.53   <2e-16 ***
ORIGIN_HEX495          16.2914543  0.0044115  3692.97   <2e-16 ***
ORIGIN_HEX496          16.7901643  0.0040586  4136.91   <2e-16 ***
ORIGIN_HEX497          16.5360042  0.0058455  2828.84   <2e-16 ***
ORIGIN_HEX498          14.9147522  0.0119179  1251.46   <2e-16 ***
ORIGIN_HEX499          16.1522407  0.0057597  2804.34   <2e-16 ***
ORIGIN_HEX500          16.8111021  0.0060277  2788.99   <2e-16 ***
ORIGIN_HEX501          16.8321577  0.0038182  4408.36   <2e-16 ***
ORIGIN_HEX502          16.2259837  0.0047603  3408.62   <2e-16 ***
ORIGIN_HEX503          15.7201840  0.0083501  1882.62   <2e-16 ***
ORIGIN_HEX504          15.4969049  0.0079433  1950.93   <2e-16 ***
ORIGIN_HEX505          16.1316683  0.0054283  2971.75   <2e-16 ***
ORIGIN_HEX506          16.1518938  0.0049914  3235.91   <2e-16 ***
ORIGIN_HEX507          17.3574278  0.0031085  5583.84   <2e-16 ***
ORIGIN_HEX508          15.3005638  0.0072185  2119.62   <2e-16 ***
ORIGIN_HEX509          15.8386726  0.0056730  2791.94   <2e-16 ***
ORIGIN_HEX510          15.9169428  0.0074707  2130.58   <2e-16 ***
ORIGIN_HEX511          16.1566398  0.0060823  2656.36   <2e-16 ***
ORIGIN_HEX512          15.8023698  0.0081090  1948.75   <2e-16 ***
ORIGIN_HEX513          15.1495673  0.0092491  1637.95   <2e-16 ***
ORIGIN_HEX514          16.4582150  0.0045086  3650.40   <2e-16 ***
ORIGIN_HEX515          16.8195667  0.0036057  4664.74   <2e-16 ***
ORIGIN_HEX516          16.9188466  0.0038019  4450.11   <2e-16 ***
ORIGIN_HEX517          15.7559291  0.0066885  2355.69   <2e-16 ***
ORIGIN_HEX518          17.5593801  0.0028119  6244.66   <2e-16 ***
ORIGIN_HEX519          15.4486861  0.0065237  2368.07   <2e-16 ***
ORIGIN_HEX520          15.0585622  0.0078366  1921.58   <2e-16 ***
ORIGIN_HEX521          17.7486173  0.0027253  6512.60   <2e-16 ***
ORIGIN_HEX522          15.6767754  0.0069154  2266.93   <2e-16 ***
ORIGIN_HEX523          16.7487374  0.0058803  2848.29   <2e-16 ***
ORIGIN_HEX524          15.6367899  0.0085329  1832.53   <2e-16 ***
ORIGIN_HEX525          16.3401560  0.0061294  2665.87   <2e-16 ***
ORIGIN_HEX526          16.0219799  0.0051789  3093.69   <2e-16 ***
ORIGIN_HEX527          16.9037720  0.0034483  4902.03   <2e-16 ***
ORIGIN_HEX528          16.3365568  0.0050167  3256.43   <2e-16 ***
ORIGIN_HEX529          16.0586205  0.0052742  3044.75   <2e-16 ***
ORIGIN_HEX530          15.9532182  0.0050699  3146.65   <2e-16 ***
ORIGIN_HEX531          15.7235804  0.0084702  1856.34   <2e-16 ***
ORIGIN_HEX532          16.2084340  0.0046699  3470.86   <2e-16 ***
ORIGIN_HEX533          16.2662309  0.0048068  3383.99   <2e-16 ***
ORIGIN_HEX534          11.6058345  0.0880681   131.78   <2e-16 ***
ORIGIN_HEX536          16.3211669  0.0064574  2527.50   <2e-16 ***
ORIGIN_HEX537          16.7181988  0.0039863  4193.90   <2e-16 ***
ORIGIN_HEX538          15.7785507  0.0064922  2430.38   <2e-16 ***
ORIGIN_HEX539          15.3045777  0.0081376  1880.71   <2e-16 ***
ORIGIN_HEX540          15.8559028  0.0075173  2109.24   <2e-16 ***
ORIGIN_HEX541          15.4385878  0.0066237  2330.82   <2e-16 ***
ORIGIN_HEX542          15.2436712  0.0080572  1891.94   <2e-16 ***
ORIGIN_HEX543          15.9728959  0.0054285  2942.40   <2e-16 ***
ORIGIN_HEX544          16.4993174  0.0079819  2067.10   <2e-16 ***
ORIGIN_HEX545          15.2990665  0.0115217  1327.85   <2e-16 ***
ORIGIN_HEX546          13.5971384  0.0296864   458.03   <2e-16 ***
ORIGIN_HEX547          15.3091712  0.0351457   435.59   <2e-16 ***
ORIGIN_HEX548          15.6059918  0.0116293  1341.95   <2e-16 ***
ORIGIN_HEX549          16.0290407  0.0060821  2635.45   <2e-16 ***
ORIGIN_HEX550          16.2239797  0.0045259  3584.69   <2e-16 ***
ORIGIN_HEX551          16.1308134  0.0045636  3534.70   <2e-16 ***
ORIGIN_HEX552          15.5541163  0.0063338  2455.74   <2e-16 ***
ORIGIN_HEX553          16.5652692  0.0064681  2561.08   <2e-16 ***
ORIGIN_HEX554          14.9544014  0.0116978  1278.40   <2e-16 ***
ORIGIN_HEX555          15.1177377  0.0258066   585.81   <2e-16 ***
ORIGIN_HEX556          15.7079361  0.0078392  2003.76   <2e-16 ***
ORIGIN_HEX557          15.2438079  0.0148773  1024.64   <2e-16 ***
ORIGIN_HEX558          14.1640399  0.0484852   292.13   <2e-16 ***
ORIGIN_HEX559          15.8405900  0.0101893  1554.63   <2e-16 ***
ORIGIN_HEX560          14.7177950  0.0179538   819.76   <2e-16 ***
ORIGIN_HEX561          16.3524833  0.0042113  3883.01   <2e-16 ***
ORIGIN_HEX562          16.5136806  0.0040777  4049.74   <2e-16 ***
ORIGIN_HEX563          15.9961069  0.0067826  2358.42   <2e-16 ***
ORIGIN_HEX564          13.6997011  0.0198052   691.72   <2e-16 ***
ORIGIN_HEX565          14.9710200  0.0087458  1711.80   <2e-16 ***
ORIGIN_HEX566          15.1112231  0.0093772  1611.48   <2e-16 ***
ORIGIN_HEX567          15.7100945  0.0071414  2199.88   <2e-16 ***
ORIGIN_HEX568          14.4739968  0.0166141   871.18   <2e-16 ***
ORIGIN_HEX569          14.4241766  0.0232658   619.97   <2e-16 ***
ORIGIN_HEX570          15.5177086  0.0135507  1145.16   <2e-16 ***
ORIGIN_HEX571          11.8536159  0.2000093    59.27   <2e-16 ***
ORIGIN_HEX572          14.8529517  0.0149921   990.72   <2e-16 ***
ORIGIN_HEX573          15.9155227  0.0054632  2913.24   <2e-16 ***
ORIGIN_HEX574          16.3125708  0.0042682  3821.84   <2e-16 ***
ORIGIN_HEX575          14.4790881  0.0262208   552.20   <2e-16 ***
ORIGIN_HEX576          14.5207439  0.0130209  1115.19   <2e-16 ***
ORIGIN_HEX577          15.7948562  0.0071395  2212.33   <2e-16 ***
ORIGIN_HEX578          16.1800033  0.0054591  2963.86   <2e-16 ***
ORIGIN_HEX579          14.0314746  0.0304185   461.28   <2e-16 ***
ORIGIN_HEX580          15.5114030  0.0139740  1110.02   <2e-16 ***
ORIGIN_HEX581          16.0923153  0.0122509  1313.56   <2e-16 ***
ORIGIN_HEX582          15.8136951  0.0054436  2904.99   <2e-16 ***
ORIGIN_HEX583          15.8893957  0.0063825  2489.51   <2e-16 ***
ORIGIN_HEX584          16.4677802  0.0044237  3722.59   <2e-16 ***
ORIGIN_HEX585          14.8604636  0.0093462  1590.00   <2e-16 ***
ORIGIN_HEX586          15.9919101  0.0054130  2954.34   <2e-16 ***
ORIGIN_HEX587          15.2964011  0.0134411  1138.03   <2e-16 ***
ORIGIN_HEX588          16.4318200  0.0046739  3515.65   <2e-16 ***
ORIGIN_HEX589          16.1320482  0.0059068  2731.12   <2e-16 ***
ORIGIN_HEX590          16.5941660  0.0054705  3033.38   <2e-16 ***
ORIGIN_HEX591          14.7899024  0.0288712   512.27   <2e-16 ***
ORIGIN_HEX592          16.5147506  0.0111219  1484.88   <2e-16 ***
ORIGIN_HEX593          16.2288499  0.0045335  3579.80   <2e-16 ***
ORIGIN_HEX594          16.7535633  0.0041883  4000.12   <2e-16 ***
ORIGIN_HEX595          16.3100540  0.0052361  3114.93   <2e-16 ***
ORIGIN_HEX596          17.9506856  0.0027283  6579.35   <2e-16 ***
ORIGIN_HEX597          14.8206703  0.0091507  1619.62   <2e-16 ***
ORIGIN_HEX598          16.8951250  0.0037360  4522.26   <2e-16 ***
ORIGIN_HEX599          14.7430710  0.0118265  1246.61   <2e-16 ***
ORIGIN_HEX600          15.1916318  0.0103187  1472.24   <2e-16 ***
ORIGIN_HEX601          14.4747531  0.0211755   683.56   <2e-16 ***
ORIGIN_HEX602          14.2916256  0.0262991   543.43   <2e-16 ***
ORIGIN_HEX603          15.9655263  0.0052388  3047.57   <2e-16 ***
ORIGIN_HEX604          15.0277578  0.0113215  1327.37   <2e-16 ***
ORIGIN_HEX605          15.7324675  0.0063002  2497.13   <2e-16 ***
ORIGIN_HEX606          15.7984737  0.0084466  1870.40   <2e-16 ***
ORIGIN_HEX607          15.6573169  0.0059843  2616.41   <2e-16 ***
ORIGIN_HEX608          15.6206291  0.0060485  2582.58   <2e-16 ***
ORIGIN_HEX609          16.5029032  0.0042560  3877.57   <2e-16 ***
ORIGIN_HEX610          16.0366304  0.0067957  2359.82   <2e-16 ***
ORIGIN_HEX611          13.3706097  0.0604415   221.22   <2e-16 ***
ORIGIN_HEX612          16.4634685  0.0041257  3990.48   <2e-16 ***
ORIGIN_HEX613          16.1981010  0.0046400  3490.95   <2e-16 ***
ORIGIN_HEX614          16.1334046  0.0117064  1378.16   <2e-16 ***
ORIGIN_HEX615          15.6041798  0.0065014  2400.14   <2e-16 ***
ORIGIN_HEX616          16.1916549  0.0047424  3414.20   <2e-16 ***
ORIGIN_HEX617          16.3030695  0.0082111  1985.50   <2e-16 ***
ORIGIN_HEX618          15.5533496  0.0096083  1618.74   <2e-16 ***
ORIGIN_HEX619          15.6442833  0.0122455  1277.56   <2e-16 ***
ORIGIN_HEX620          15.9063166  0.0062216  2556.64   <2e-16 ***
ORIGIN_HEX621          15.5062331  0.0065995  2349.61   <2e-16 ***
ORIGIN_HEX622          16.0520677  0.0066215  2424.23   <2e-16 ***
ORIGIN_HEX623          15.6432229  0.0066104  2366.45   <2e-16 ***
ORIGIN_HEX624          14.4321099  0.0130480  1106.08   <2e-16 ***
ORIGIN_HEX625          14.6277912  0.0117624  1243.60   <2e-16 ***
ORIGIN_HEX626          16.0176402  0.0052883  3028.89   <2e-16 ***
ORIGIN_HEX627          14.7150482  0.0127143  1157.36   <2e-16 ***
ORIGIN_HEX628          15.8991773  0.0074845  2124.28   <2e-16 ***
ORIGIN_HEX629          15.3666226  0.0067524  2275.73   <2e-16 ***
ORIGIN_HEX630          16.1452812  0.0051165  3155.54   <2e-16 ***
ORIGIN_HEX631          16.3876800  0.0047494  3450.48   <2e-16 ***
ORIGIN_HEX632          16.1812881  0.0053167  3043.47   <2e-16 ***
ORIGIN_HEX633          16.9287188  0.0037966  4458.96   <2e-16 ***
ORIGIN_HEX634          16.1506621  0.0045890  3519.41   <2e-16 ***
ORIGIN_HEX635          13.8156433  0.0159966   863.66   <2e-16 ***
ORIGIN_HEX636          16.0310971  0.0066155  2423.27   <2e-16 ***
ORIGIN_HEX638          16.0450584  0.0060866  2636.15   <2e-16 ***
ORIGIN_HEX639          16.7873205  0.0037470  4480.18   <2e-16 ***
ORIGIN_HEX640          16.3194559  0.0046207  3531.79   <2e-16 ***
ORIGIN_HEX641          14.8484975  0.0114999  1291.18   <2e-16 ***
ORIGIN_HEX642          16.0875553  0.0055326  2907.76   <2e-16 ***
ORIGIN_HEX643          16.0074352  0.0048690  3287.62   <2e-16 ***
ORIGIN_HEX644          15.3692563  0.0069027  2226.57   <2e-16 ***
ORIGIN_HEX645          16.0452651  0.0053962  2973.43   <2e-16 ***
ORIGIN_HEX646          16.1618854  0.0112554  1435.92   <2e-16 ***
ORIGIN_HEX647          15.4009106  0.0087963  1750.84   <2e-16 ***
ORIGIN_HEX648          16.5445362  0.0041853  3953.01   <2e-16 ***
ORIGIN_HEX649          15.9464270  0.0050482  3158.84   <2e-16 ***
ORIGIN_HEX650          15.7769567  0.0068907  2289.62   <2e-16 ***
ORIGIN_HEX651          16.4022426  0.0046034  3563.08   <2e-16 ***
ORIGIN_HEX652          17.3424163  0.0030222  5738.30   <2e-16 ***
ORIGIN_HEX653          16.6975661  0.0038314  4358.11   <2e-16 ***
ORIGIN_HEX654          15.9565703  0.0059114  2699.27   <2e-16 ***
ORIGIN_HEX655          13.4448440  0.0349068   385.16   <2e-16 ***
ORIGIN_HEX657          15.6646542  0.0069036  2269.06   <2e-16 ***
ORIGIN_HEX658          15.7720631  0.0091720  1719.59   <2e-16 ***
ORIGIN_HEX659          16.1780690  0.0053325  3033.84   <2e-16 ***
ORIGIN_HEX660          16.6031324  0.0089711  1850.74   <2e-16 ***
ORIGIN_HEX661          15.7328967  0.0058719  2679.38   <2e-16 ***
ORIGIN_HEX662          15.0587502  0.0080155  1878.71   <2e-16 ***
ORIGIN_HEX663          17.6124784  0.0028804  6114.49   <2e-16 ***
ORIGIN_HEX664          15.9792962  0.0061813  2585.12   <2e-16 ***
ORIGIN_HEX665          15.2069160  0.0170608   891.34   <2e-16 ***
ORIGIN_HEX666          16.7785892  0.0047662  3520.36   <2e-16 ***
ORIGIN_HEX667          15.8493113  0.0068013  2330.33   <2e-16 ***
ORIGIN_HEX668          15.8615502  0.0072751  2180.26   <2e-16 ***
ORIGIN_HEX669          16.1514860  0.0055852  2891.82   <2e-16 ***
ORIGIN_HEX670          17.3317145  0.0078908  2196.45   <2e-16 ***
ORIGIN_HEX671          13.9549284  0.0223954   623.12   <2e-16 ***
ORIGIN_HEX672          15.8167886  0.0061379  2576.93   <2e-16 ***
ORIGIN_HEX673          15.7524309  0.0058047  2713.74   <2e-16 ***
ORIGIN_HEX674          16.2640419  0.0050760  3204.10   <2e-16 ***
ORIGIN_HEX675          15.1132013  0.0106781  1415.35   <2e-16 ***
ORIGIN_HEX676          14.5363518  0.0319661   454.74   <2e-16 ***
ORIGIN_HEX677          15.8599921  0.0070817  2239.57   <2e-16 ***
ORIGIN_HEX678          17.0077181  0.0035197  4832.12   <2e-16 ***
ORIGIN_HEX679          16.9136953  0.0036775  4599.19   <2e-16 ***
ORIGIN_HEX680          15.2151758  0.0090237  1686.14   <2e-16 ***
ORIGIN_HEX681          15.6757075  0.0062475  2509.12   <2e-16 ***
ORIGIN_HEX682          17.5048198  0.0030706  5700.79   <2e-16 ***
ORIGIN_HEX683          14.1411959  0.0315349   448.43   <2e-16 ***
ORIGIN_HEX684          17.2800406  0.0039853  4335.90   <2e-16 ***
ORIGIN_HEX685          15.5655450  0.0070951  2193.83   <2e-16 ***
ORIGIN_HEX686          15.5528996  0.0063469  2450.49   <2e-16 ***
ORIGIN_HEX687          15.4729101  0.0074230  2084.46   <2e-16 ***
ORIGIN_HEX688          15.5533812  0.0175355   886.97   <2e-16 ***
ORIGIN_HEX689          15.2533186  0.0091092  1674.50   <2e-16 ***
ORIGIN_HEX690          17.3388044  0.0032880  5273.38   <2e-16 ***
ORIGIN_HEX691          15.1372999  0.0158805   953.20   <2e-16 ***
ORIGIN_HEX692          16.4638077  0.0132438  1243.13   <2e-16 ***
ORIGIN_HEX693          15.8526381  0.0061698  2569.38   <2e-16 ***
ORIGIN_HEX694          16.6765716  0.0045140  3694.42   <2e-16 ***
ORIGIN_HEX695          16.1733677  0.0053509  3022.53   <2e-16 ***
ORIGIN_HEX696          16.4683280  0.0096711  1702.85   <2e-16 ***
ORIGIN_HEX697          15.8738142  0.0137478  1154.64   <2e-16 ***
ORIGIN_HEX698          15.9281977  0.0065531  2430.63   <2e-16 ***
ORIGIN_HEX700          15.8632349  0.0088355  1795.41   <2e-16 ***
ORIGIN_HEX701          14.2479526  0.0177170   804.20   <2e-16 ***
ORIGIN_HEX702          15.9961922  0.0174834   914.93   <2e-16 ***
ORIGIN_HEX703          16.1258640  0.0052849  3051.28   <2e-16 ***
ORIGIN_HEX704          15.8741586  0.0131945  1203.09   <2e-16 ***
ORIGIN_HEX705          16.0468034  0.0064152  2501.39   <2e-16 ***
ORIGIN_HEX706          15.3322811  0.0157502   973.47   <2e-16 ***
ORIGIN_HEX707          16.0081998  0.0062754  2550.96   <2e-16 ***
ORIGIN_HEX708          14.8748274  0.0102363  1453.15   <2e-16 ***
ORIGIN_HEX709          16.0674244  0.0067022  2397.35   <2e-16 ***
ORIGIN_HEX710          13.5518176  0.0314976   430.25   <2e-16 ***
ORIGIN_HEX711          15.1354082  0.0226759   667.47   <2e-16 ***
ORIGIN_HEX712          15.0522649  0.0139847  1076.34   <2e-16 ***
ORIGIN_HEX714          15.5443777  0.0085245  1823.49   <2e-16 ***
ORIGIN_HEX715          16.5176499  0.0067972  2430.06   <2e-16 ***
ORIGIN_HEX716          15.9650982  0.0058986  2706.61   <2e-16 ***
ORIGIN_HEX717          16.2499756  0.0116174  1398.76   <2e-16 ***
ORIGIN_HEX718          14.8766527  0.0152699   974.25   <2e-16 ***
ORIGIN_HEX719          15.7796694  0.0078493  2010.32   <2e-16 ***
ORIGIN_HEX720          16.7647971  0.0043610  3844.25   <2e-16 ***
ORIGIN_HEX721          15.9133491  0.0067953  2341.80   <2e-16 ***
ORIGIN_HEX722          15.1412250  0.0190571   794.52   <2e-16 ***
ORIGIN_HEX724          15.4988272  0.0092571  1674.27   <2e-16 ***
ORIGIN_HEX725          17.9483458  0.0026763  6706.33   <2e-16 ***
ORIGIN_HEX726          15.0960881  0.0104541  1444.04   <2e-16 ***
ORIGIN_HEX727          15.9954613  0.0062278  2568.40   <2e-16 ***
ORIGIN_HEX728          15.8495545  0.0164296   964.70   <2e-16 ***
ORIGIN_HEX729          15.4753286  0.0098431  1572.20   <2e-16 ***
ORIGIN_HEX730          15.1635727  0.0088125  1720.69   <2e-16 ***
ORIGIN_HEX731          15.7013788  0.0062905  2496.04   <2e-16 ***
ORIGIN_HEX732          16.1462707  0.0068537  2355.86   <2e-16 ***
ORIGIN_HEX733          16.1208076  0.0059129  2726.36   <2e-16 ***
ORIGIN_HEX734          15.9851282  0.0064771  2467.95   <2e-16 ***
ORIGIN_HEX735          16.1484825  0.0061655  2619.18   <2e-16 ***
ORIGIN_HEX736          15.9971213  0.0062366  2565.03   <2e-16 ***
ORIGIN_HEX737          15.9261245  0.0054299  2933.05   <2e-16 ***
ORIGIN_HEX738          16.4316129  0.0046452  3537.30   <2e-16 ***
ORIGIN_HEX739          16.6775419  0.0046187  3610.91   <2e-16 ***
ORIGIN_HEX740          16.0617300  0.0057464  2795.07   <2e-16 ***
ORIGIN_HEX741          16.7517304  0.0049004  3418.45   <2e-16 ***
ORIGIN_HEX742          13.6155569  0.0261624   520.42   <2e-16 ***
ORIGIN_HEX743          16.1923891  0.0077883  2079.06   <2e-16 ***
ORIGIN_HEX744          16.0789772  0.0052294  3074.74   <2e-16 ***
ORIGIN_HEX745          16.6413743  0.0040875  4071.32   <2e-16 ***
ORIGIN_HEX746          15.7209684  0.0062758  2505.02   <2e-16 ***
ORIGIN_HEX747          14.2684287  0.0157538   905.71   <2e-16 ***
ORIGIN_HEX748          16.6297121  0.0047747  3482.89   <2e-16 ***
ORIGIN_HEX749          15.1936616  0.0105982  1433.61   <2e-16 ***
ORIGIN_HEX750          15.7849502  0.0063597  2482.03   <2e-16 ***
ORIGIN_HEX751          14.6705966  0.0254183   577.17   <2e-16 ***
ORIGIN_HEX752          16.8060561  0.0036245  4636.85   <2e-16 ***
ORIGIN_HEX753          15.4828185  0.0082476  1877.26   <2e-16 ***
ORIGIN_HEX754          15.6146508  0.0071249  2191.57   <2e-16 ***
ORIGIN_HEX755          14.3485810  0.0213622   671.68   <2e-16 ***
ORIGIN_HEX756          15.8375779  0.0071391  2218.44   <2e-16 ***
ORIGIN_HEX757          15.1632393  0.0088993  1703.87   <2e-16 ***
ORIGIN_HEX758          15.2312430  0.0218371   697.50   <2e-16 ***
ORIGIN_HEX759          18.1156078  0.0025308  7157.96   <2e-16 ***
ORIGIN_HEX760          15.6229497  0.0108638  1438.08   <2e-16 ***
ORIGIN_HEX761          15.7513291  0.0072722  2165.95   <2e-16 ***
ORIGIN_HEX762          15.3340021  0.0098733  1553.08   <2e-16 ***
ORIGIN_HEX763          16.9791120  0.0040689  4172.91   <2e-16 ***
ORIGIN_HEX764          16.5072512  0.0048485  3404.63   <2e-16 ***
ORIGIN_HEX765          15.5562128  0.0061220  2541.02   <2e-16 ***
ORIGIN_HEX766          14.9536473  0.0100610  1486.30   <2e-16 ***
ORIGIN_HEX767          17.7881265  0.0029059  6121.43   <2e-16 ***
ORIGIN_HEX768          13.6339912  0.0459226   296.89   <2e-16 ***
ORIGIN_HEX769          15.0829802  0.0533502   282.72   <2e-16 ***
ORIGIN_HEX770          14.8424085  0.0124908  1188.26   <2e-16 ***
ORIGIN_HEX771          16.5894260  0.0048607  3413.00   <2e-16 ***
ORIGIN_HEX772          16.6897125  0.0045271  3686.61   <2e-16 ***
ORIGIN_HEX773          15.9195556  0.0053511  2975.02   <2e-16 ***
ORIGIN_HEX774          14.8354777  0.0117247  1265.32   <2e-16 ***
ORIGIN_HEX775          13.2899714  0.0422601   314.48   <2e-16 ***
ORIGIN_HEX776          14.9241836  0.0161185   925.90   <2e-16 ***
ORIGIN_HEX777          15.5949911  0.0081470  1914.19   <2e-16 ***
ORIGIN_HEX778          16.1127234  0.0048516  3321.11   <2e-16 ***
ORIGIN_HEX779          15.9211152  0.0067108  2372.46   <2e-16 ***
ORIGIN_HEX780          15.9763576  0.0062331  2563.16   <2e-16 ***
ORIGIN_HEX781          15.9101536  0.0114539  1389.06   <2e-16 ***
ORIGIN_HEX782          15.2796255  0.0107441  1422.14   <2e-16 ***
ORIGIN_HEX783          15.8567223  0.0067617  2345.07   <2e-16 ***
ORIGIN_HEX784          16.8615733  0.0035966  4688.24   <2e-16 ***
ORIGIN_HEX785          16.2037328  0.0054026  2999.27   <2e-16 ***
ORIGIN_HEX786          15.4577135  0.0092187  1676.78   <2e-16 ***
ORIGIN_HEX787          16.3060887  0.0058346  2794.70   <2e-16 ***
ORIGIN_HEX788          15.2959826  0.0096635  1582.86   <2e-16 ***
ORIGIN_HEX789          15.3756935  0.0071566  2148.47   <2e-16 ***
ORIGIN_HEX790          15.7280326  0.0075081  2094.82   <2e-16 ***
ORIGIN_HEX791          16.8510182  0.0064620  2607.70   <2e-16 ***
ORIGIN_HEX792          15.3150214  0.0105104  1457.14   <2e-16 ***
ORIGIN_HEX793          15.9744874  0.0064437  2479.10   <2e-16 ***
ORIGIN_HEX794          16.1439897  0.0056080  2878.76   <2e-16 ***
ORIGIN_HEX795          14.9709328  0.0323008   463.49   <2e-16 ***
ORIGIN_HEX796          16.9179992  0.0159344  1061.73   <2e-16 ***
ORIGIN_HEX797          16.5282875  0.0081208  2035.31   <2e-16 ***
ORIGIN_HEX798          16.7842726  0.0083424  2011.92   <2e-16 ***
ORIGIN_HEX799          15.7338981  0.0078687  1999.56   <2e-16 ***
ORIGIN_HEX800          15.5094201  0.0087009  1782.50   <2e-16 ***
ORIGIN_HEX801          16.2392235  0.0131812  1232.00   <2e-16 ***
ORIGIN_HEX802          16.8137094  0.0108277  1552.85   <2e-16 ***
ORIGIN_HEX803          15.6780800  0.0116388  1347.05   <2e-16 ***
ORIGIN_HEX804          13.8189188  0.0218002   633.89   <2e-16 ***
ORIGIN_HEX805          15.7791629  0.0141022  1118.92   <2e-16 ***
ORIGIN_HEX806          15.8497954  0.0165873   955.53   <2e-16 ***
ORIGIN_HEX807          14.5509838  0.0224644   647.74   <2e-16 ***
ORIGIN_HEX808          16.4084085  0.0060369  2718.03   <2e-16 ***
ORIGIN_HEX809          16.2721738  0.0132687  1226.36   <2e-16 ***
ORIGIN_HEX810          15.7827309  0.0221210   713.47   <2e-16 ***
ORIGIN_HEX811          14.9404033  0.0194242   769.16   <2e-16 ***
ORIGIN_HEX812          15.1416778  0.0122307  1238.01   <2e-16 ***
ORIGIN_HEX813          13.9506352  0.0488351   285.67   <2e-16 ***
ORIGIN_HEX814          17.1176104  0.0070398  2431.56   <2e-16 ***
ORIGIN_HEX815          14.7964780  0.0243848   606.79   <2e-16 ***
ORIGIN_HEX816          15.4740922  0.0114649  1349.69   <2e-16 ***
ORIGIN_HEX817          15.8603261  0.0119717  1324.82   <2e-16 ***
ORIGIN_HEX818          17.0952230  0.0062551  2733.02   <2e-16 ***
ORIGIN_HEX819          16.4138039  0.0086289  1902.18   <2e-16 ***
ORIGIN_HEX820          17.0274479  0.0159329  1068.70   <2e-16 ***
ORIGIN_HEX821          17.7145983  0.0052424  3379.08   <2e-16 ***
ORIGIN_HEX822          15.3963800  0.0130352  1181.14   <2e-16 ***
ORIGIN_HEX823          17.0122543  0.0073230  2323.12   <2e-16 ***
ORIGIN_HEX824          14.4492388  0.0277319   521.03   <2e-16 ***
ORIGIN_HEX825          16.5445292  0.0214830   770.12   <2e-16 ***
ORIGIN_HEX826          17.1605775  0.0071785  2390.56   <2e-16 ***
ORIGIN_HEX827          17.6695805  0.0054847  3221.64   <2e-16 ***
ORIGIN_HEX828          15.9249363  0.0143596  1109.01   <2e-16 ***
ORIGIN_HEX829          16.9658848  0.0133918  1266.89   <2e-16 ***
ORIGIN_HEX830          17.0590856  0.0084727  2013.42   <2e-16 ***
ORIGIN_HEX831          16.9471228  0.0258786   654.87   <2e-16 ***
log(A_ENTERTAIN_COUNT)  0.1353021  0.0008526   158.70   <2e-16 ***
log(A_FNB_COUNT)        0.0564351  0.0003153   178.98   <2e-16 ***
log(A_LEISURE_COUNT)   -0.0512839  0.0003726  -137.63   <2e-16 ***
log(A_RETAIL_COUNT)     0.1188308  0.0001777   668.88   <2e-16 ***
log(A_HDB_COUNT)        0.3676924  0.0001778  2067.77   <2e-16 ***
log(dist)              -1.4658504  0.0002628 -5577.59   <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: 317392316  on 67737  degrees of freedom
Residual deviance:  32603657  on 66918  degrees of freedom
AIC: 32975688

Number of Fisher Scoring iterations: 8
  • In case R/Quarto crashes, we add a copy of relevant coefficient readouts here:
Coefficients:
                         Estimate Std. Error  z value Pr(>|z|)    
log(A_ENTERTAIN_COUNT)  0.1353021  0.0008526   158.70   <2e-16 ***
log(A_FNB_COUNT)        0.0564351  0.0003153   178.98   <2e-16 ***
log(A_LEISURE_COUNT)   -0.0512839  0.0003726  -137.63   <2e-16 ***
log(A_RETAIL_COUNT)     0.1188308  0.0001777   668.88   <2e-16 ***
log(A_HDB_COUNT)        0.3676924  0.0001778  2067.77   <2e-16 ***
log(dist)              -1.4658504  0.0002628 -5577.59   <2e-16 ***

4.4c Commentary on orcSIM

  • Once again, we compare the size of the coefficients to assess the impact of the explanatory factors;
    • The decay factor, log(dist), is clearly a strong determinant of the number of trips, with -1.47 as a coefficient. This also reiterates some patterns seen earlier in some visualizations, namely, that greater distance results in fewer trips.
    • MRT_EXIT_COUNT and HDB_COUNT have the highest coefficients (0.45, 0.38) among propulsiveness/attractiveness features, with the next closest being FINSERV_COUNT, validating some parts of our hypothesis.
    • However, BUSINESS_COUNT and FNB_COUNT show extremely small (absolute value <0.06), negative values. It may be that they are outweighed by other factors, or perhaps are wrongly attributed.
show code 
CalcRSquared(orcSIM$data$SUM_TRIPS, orcSIM$fitted.values)
[1] 0.4566753
  • This R-squared of 0.45 is higher than for our unconstrained uncSIM model, however it is still relatively low.

4.5 decSIM Destination Constrained Spatial Interaction Model

  • In the destination-constrained SIM, we regard each $DESTIN_HEX as a unique factor (dummy variable), and only consider propulsiveness variables;
    • The formula defined is similar to decSIM above;
    • We add a constant (-1) to remove the intercept.
show code 
decSIM <- glm(formula = SUM_TRIPS ~ 
                  DESTIN_HEX +
                  log(P_BUSINESS_COUNT) + 
                  log(P_MRT_EXIT_COUNT) +
                  log(P_FINSERV_COUNT) +
                  log(dist) - 1,
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
write_rds(decSIM, "data/rds/decSIM.rds")
  • As before, we read/write to RDS to save space/time.
show code 
options(max.print = 10000)  
decSIM <- read_rds("data/rds/decSIM.rds")
summary(decSIM)

Call:
glm(formula = SUM_TRIPS ~ DESTIN_HEX + log(P_BUSINESS_COUNT) + 
    log(P_MRT_EXIT_COUNT) + log(P_FINSERV_COUNT) + log(dist) - 
    1, family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)

Coefficients:
                        Estimate Std. Error  z value Pr(>|z|)    
DESTIN_HEX1           16.6212048  0.0864150   192.34   <2e-16 ***
DESTIN_HEX2           16.1842671  0.0754079   214.62   <2e-16 ***
DESTIN_HEX3           16.6626085  0.0381554   436.70   <2e-16 ***
DESTIN_HEX4           15.4752075  0.0860897   179.76   <2e-16 ***
DESTIN_HEX5           16.0593283  0.0241106   666.07   <2e-16 ***
DESTIN_HEX6           16.8459566  0.0260748   646.06   <2e-16 ***
DESTIN_HEX7           15.1817025  0.0602218   252.10   <2e-16 ***
DESTIN_HEX8           13.6413784  0.1961257    69.55   <2e-16 ***
DESTIN_HEX9           15.9505329  0.0198014   805.52   <2e-16 ***
DESTIN_HEX10          15.9281536  0.0506721   314.34   <2e-16 ***
DESTIN_HEX11          11.0994169  0.5773533    19.23   <2e-16 ***
DESTIN_HEX12          14.7317025  0.0864105   170.49   <2e-16 ***
DESTIN_HEX13          12.5472911  0.2672680    46.95   <2e-16 ***
DESTIN_HEX14          17.7243359  0.0097923  1810.03   <2e-16 ***
DESTIN_HEX15          13.5096996  0.0873915   154.59   <2e-16 ***
DESTIN_HEX16          17.8417500  0.0141882  1257.51   <2e-16 ***
DESTIN_HEX17          11.2543339  0.4082524    27.57   <2e-16 ***
DESTIN_HEX18          15.2478829  0.0700447   217.69   <2e-16 ***
DESTIN_HEX19          15.1465397  0.0327549   462.42   <2e-16 ***
DESTIN_HEX20          15.4641199  0.0436455   354.31   <2e-16 ***
DESTIN_HEX21          14.4769826  0.0423746   341.64   <2e-16 ***
DESTIN_HEX22          18.3129458  0.0069046  2652.30   <2e-16 ***
DESTIN_HEX23          16.2636053  0.0338007   481.16   <2e-16 ***
DESTIN_HEX24          15.6098294  0.0483244   323.02   <2e-16 ***
DESTIN_HEX25          15.1873461  0.0541058   280.70   <2e-16 ***
DESTIN_HEX26          15.2936182  0.0388820   393.33   <2e-16 ***
DESTIN_HEX27          14.3662260  0.0499736   287.48   <2e-16 ***
DESTIN_HEX28          15.0253778  0.0301156   498.92   <2e-16 ***
DESTIN_HEX29          15.4204172  0.0432311   356.70   <2e-16 ***
DESTIN_HEX30          15.3897102  0.1111299   138.48   <2e-16 ***
DESTIN_HEX31          15.3675222  0.0452563   339.57   <2e-16 ***
DESTIN_HEX32          17.7146846  0.0076344  2320.36   <2e-16 ***
DESTIN_HEX33          15.0550310  0.0319812   470.75   <2e-16 ***
DESTIN_HEX34          12.0271775  0.2182250    55.11   <2e-16 ***
DESTIN_HEX35          14.7736517  0.0356054   414.93   <2e-16 ***
DESTIN_HEX36          13.8922043  0.1020795   136.09   <2e-16 ***
DESTIN_HEX37          15.4146157  0.0731542   210.71   <2e-16 ***
DESTIN_HEX38          18.2318696  0.0064401  2830.99   <2e-16 ***
DESTIN_HEX39          16.0731584  0.0199828   804.35   <2e-16 ***
DESTIN_HEX40          12.9403789  0.1507664    85.83   <2e-16 ***
DESTIN_HEX41          14.3190473  0.0456356   313.77   <2e-16 ***
DESTIN_HEX42          14.5588776  0.1091267   133.41   <2e-16 ***
DESTIN_HEX43          14.7095828  0.0511967   287.31   <2e-16 ***
DESTIN_HEX44          15.5866433  0.0270340   576.56   <2e-16 ***
DESTIN_HEX45          15.8242928  0.0305442   518.08   <2e-16 ***
DESTIN_HEX46          15.4685493  0.0424854   364.09   <2e-16 ***
DESTIN_HEX47          14.7210738  0.0357619   411.64   <2e-16 ***
DESTIN_HEX48          15.0972895  0.0410049   368.18   <2e-16 ***
DESTIN_HEX49          11.9112255  1.0000023    11.91   <2e-16 ***
DESTIN_HEX50          14.7598223  0.0478190   308.66   <2e-16 ***
DESTIN_HEX51          17.8545751  0.0087071  2050.57   <2e-16 ***
DESTIN_HEX52          14.6069138  0.0588493   248.21   <2e-16 ***
DESTIN_HEX53          15.7886177  0.0880677   179.28   <2e-16 ***
DESTIN_HEX54          15.9118331  0.0464667   342.44   <2e-16 ***
DESTIN_HEX55          16.8918570  0.0249471   677.11   <2e-16 ***
DESTIN_HEX56          15.3641609  0.0349933   439.06   <2e-16 ***
DESTIN_HEX57          16.0018120  0.0296675   539.37   <2e-16 ***
DESTIN_HEX58          15.0012087  0.0375212   399.81   <2e-16 ***
DESTIN_HEX59          16.0039445  0.0247169   647.49   <2e-16 ***
DESTIN_HEX60          15.3467719  0.0270910   566.49   <2e-16 ***
DESTIN_HEX61          15.1553990  0.0349284   433.90   <2e-16 ***
DESTIN_HEX62          15.3506485  0.0377311   406.84   <2e-16 ***
DESTIN_HEX63          16.0843892  0.0381697   421.39   <2e-16 ***
DESTIN_HEX64          14.8485648  0.0502228   295.65   <2e-16 ***
DESTIN_HEX65          19.0693394  0.0034429  5538.76   <2e-16 ***
DESTIN_HEX66          17.2440732  0.0173605   993.30   <2e-16 ***
DESTIN_HEX67          17.7483657  0.0104980  1690.65   <2e-16 ***
DESTIN_HEX68          13.9438552  0.0848384   164.36   <2e-16 ***
DESTIN_HEX69          14.5945759  0.0347800   419.63   <2e-16 ***
DESTIN_HEX70          15.5293107  0.0207773   747.42   <2e-16 ***
DESTIN_HEX71          15.7783862  0.0239390   659.11   <2e-16 ***
DESTIN_HEX72          17.5710236  0.0166978  1052.29   <2e-16 ***
DESTIN_HEX73          15.5028253  0.0578665   267.91   <2e-16 ***
DESTIN_HEX74          14.5148219  0.0535613   271.00   <2e-16 ***
DESTIN_HEX75          15.4188189  0.0283689   543.51   <2e-16 ***
DESTIN_HEX76          17.9382147  0.0070426  2547.10   <2e-16 ***
DESTIN_HEX77          16.8997632  0.0130441  1295.59   <2e-16 ***
DESTIN_HEX79          15.7617602  0.0270995   581.62   <2e-16 ***
DESTIN_HEX80          15.9492496  0.0168821   944.74   <2e-16 ***
DESTIN_HEX81          18.5467785  0.0045276  4096.42   <2e-16 ***
DESTIN_HEX82          17.3153478  0.0123827  1398.36   <2e-16 ***
DESTIN_HEX84          14.8070960  0.0596850   248.09   <2e-16 ***
DESTIN_HEX85          15.0350465  0.0962465   156.21   <2e-16 ***
DESTIN_HEX86          16.9606778  0.0124873  1358.23   <2e-16 ***
DESTIN_HEX87          17.2060058  0.0086911  1979.72   <2e-16 ***
DESTIN_HEX88          12.5393359  0.2041334    61.43   <2e-16 ***
DESTIN_HEX89          14.6777065  0.0620486   236.55   <2e-16 ***
DESTIN_HEX90          14.9495515  0.0357388   418.30   <2e-16 ***
DESTIN_HEX91          15.2109747  0.0304857   498.95   <2e-16 ***
DESTIN_HEX92          16.4120221  0.0109179  1503.22   <2e-16 ***
DESTIN_HEX93          18.8644945  0.0036052  5232.53   <2e-16 ***
DESTIN_HEX94          15.4373294  0.0287526   536.90   <2e-16 ***
DESTIN_HEX95          15.3624826  0.0437714   350.97   <2e-16 ***
DESTIN_HEX96          14.0367081  0.0806048   174.14   <2e-16 ***
DESTIN_HEX97          14.7267698  0.0645775   228.05   <2e-16 ***
DESTIN_HEX98          16.0102538  0.0195739   817.94   <2e-16 ***
DESTIN_HEX99          15.3031954  0.0212661   719.60   <2e-16 ***
DESTIN_HEX100         18.9077367  0.0033250  5686.51   <2e-16 ***
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DESTIN_HEX102         15.8543460  0.0226134   701.11   <2e-16 ***
DESTIN_HEX103         13.0134769  0.1543154    84.33   <2e-16 ***
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DESTIN_HEX108         15.3202141  0.0194840   786.30   <2e-16 ***
DESTIN_HEX109         18.3252092  0.0042535  4308.30   <2e-16 ***
DESTIN_HEX110         17.8140865  0.0080560  2211.28   <2e-16 ***
DESTIN_HEX111         14.8219266  0.0570150   259.96   <2e-16 ***
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DESTIN_HEX113         12.5101894  0.4472179    27.97   <2e-16 ***
DESTIN_HEX114         13.0094515  0.2672687    48.68   <2e-16 ***
DESTIN_HEX115         15.2121352  0.0321919   472.55   <2e-16 ***
DESTIN_HEX116         15.6882019  0.0354011   443.16   <2e-16 ***
DESTIN_HEX117         19.6516524  0.0026088  7532.96   <2e-16 ***
DESTIN_HEX118         18.0946734  0.0049821  3631.92   <2e-16 ***
DESTIN_HEX119         13.7999081  0.0710935   194.11   <2e-16 ***
DESTIN_HEX120         14.3933321  0.0887577   162.16   <2e-16 ***
DESTIN_HEX121         14.0360846  0.2357134    59.55   <2e-16 ***
DESTIN_HEX122         15.5223457  0.0508052   305.53   <2e-16 ***
DESTIN_HEX123         14.5795313  0.0693684   210.18   <2e-16 ***
DESTIN_HEX124         15.5017301  0.0264053   587.07   <2e-16 ***
DESTIN_HEX125         15.0229791  0.0221767   677.42   <2e-16 ***
DESTIN_HEX126         17.8579667  0.0046600  3832.20   <2e-16 ***
DESTIN_HEX127         14.1483042  0.0682271   207.37   <2e-16 ***
DESTIN_HEX128         14.8073102  0.0990383   149.51   <2e-16 ***
DESTIN_HEX129         13.6056981  0.1443508    94.25   <2e-16 ***
DESTIN_HEX130         14.4238059  0.0405989   355.28   <2e-16 ***
DESTIN_HEX131         15.0658638  0.0306564   491.44   <2e-16 ***
DESTIN_HEX132         15.8461890  0.0130149  1217.55   <2e-16 ***
DESTIN_HEX133         18.5309866  0.0040753  4547.15   <2e-16 ***
DESTIN_HEX134         14.2812583  0.0572951   249.26   <2e-16 ***
DESTIN_HEX135         14.5131557  0.0395084   367.34   <2e-16 ***
DESTIN_HEX136         18.2831038  0.0040495  4514.93   <2e-16 ***
DESTIN_HEX137         15.6710022  0.0205216   763.63   <2e-16 ***
DESTIN_HEX138         17.2427809  0.0070044  2461.69   <2e-16 ***
DESTIN_HEX139         17.7782149  0.0054905  3238.02   <2e-16 ***
DESTIN_HEX140         18.7541343  0.0034994  5359.24   <2e-16 ***
DESTIN_HEX141         18.5271398  0.0063472  2918.96   <2e-16 ***
DESTIN_HEX142         16.0840554  0.0240330   669.25   <2e-16 ***
DESTIN_HEX143         14.7318543  0.0309181   476.48   <2e-16 ***
DESTIN_HEX144         18.4917159  0.0039383  4695.40   <2e-16 ***
DESTIN_HEX145         18.5530001  0.0037789  4909.66   <2e-16 ***
DESTIN_HEX146         17.5863991  0.0088687  1982.96   <2e-16 ***
DESTIN_HEX147         15.6672676  0.0220411   710.82   <2e-16 ***
DESTIN_HEX148         18.0385204  0.0054814  3290.85   <2e-16 ***
DESTIN_HEX149         17.0771286  0.0082651  2066.18   <2e-16 ***
DESTIN_HEX150         18.5087652  0.0037917  4881.41   <2e-16 ***
DESTIN_HEX151         15.4044265  0.0294507   523.06   <2e-16 ***
DESTIN_HEX152         15.6716999  0.0167139   937.64   <2e-16 ***
DESTIN_HEX154         14.6789280  0.0407683   360.06   <2e-16 ***
DESTIN_HEX156         17.1450230  0.0104970  1633.33   <2e-16 ***
DESTIN_HEX157         15.6399459  0.0144419  1082.96   <2e-16 ***
DESTIN_HEX158         17.7354171  0.0052332  3389.01   <2e-16 ***
DESTIN_HEX160         15.5310632  0.0283033   548.74   <2e-16 ***
DESTIN_HEX161         17.4446378  0.0076911  2268.15   <2e-16 ***
DESTIN_HEX162         14.3004892  0.0283803   503.89   <2e-16 ***
DESTIN_HEX163         18.4203411  0.0036888  4993.52   <2e-16 ***
DESTIN_HEX164         16.9825424  0.0107069  1586.13   <2e-16 ***
DESTIN_HEX165         18.5499185  0.0045648  4063.70   <2e-16 ***
DESTIN_HEX166         14.0968004  0.0745613   189.06   <2e-16 ***
DESTIN_HEX167         15.4541774  0.0169782   910.24   <2e-16 ***
DESTIN_HEX168         17.3437292  0.0052133  3326.81   <2e-16 ***
DESTIN_HEX169         16.9519855  0.0069685  2432.66   <2e-16 ***
DESTIN_HEX170         17.4682090  0.0085600  2040.67   <2e-16 ***
DESTIN_HEX171         18.2192934  0.0055136  3304.43   <2e-16 ***
DESTIN_HEX172         16.3546545  0.0130127  1256.83   <2e-16 ***
DESTIN_HEX173         13.6991074  0.0690323   198.44   <2e-16 ***
DESTIN_HEX174         18.3200728  0.0045712  4007.75   <2e-16 ***
DESTIN_HEX175         18.5585150  0.0033958  5465.20   <2e-16 ***
DESTIN_HEX176         17.6558863  0.0048849  3614.40   <2e-16 ***
DESTIN_HEX177         18.6361104  0.0042481  4386.93   <2e-16 ***
DESTIN_HEX178         16.5101472  0.0141111  1170.01   <2e-16 ***
DESTIN_HEX179         18.4238024  0.0037285  4941.33   <2e-16 ***
DESTIN_HEX180         17.8115136  0.0057171  3115.47   <2e-16 ***
DESTIN_HEX181         16.2034499  0.0215225   752.86   <2e-16 ***
DESTIN_HEX182         14.5250137  0.0441481   329.01   <2e-16 ***
DESTIN_HEX183         16.1284420  0.0099791  1616.22   <2e-16 ***
DESTIN_HEX184         17.9384129  0.0043673  4107.44   <2e-16 ***
DESTIN_HEX185         18.0661138  0.0041195  4385.47   <2e-16 ***
DESTIN_HEX186         18.0084733  0.0051021  3529.65   <2e-16 ***
DESTIN_HEX187         17.9711471  0.0055960  3211.43   <2e-16 ***
DESTIN_HEX188         18.9503687  0.0032278  5870.97   <2e-16 ***
DESTIN_HEX189         18.4479155  0.0052859  3490.01   <2e-16 ***
DESTIN_HEX190         14.8153072  0.0357398   414.53   <2e-16 ***
DESTIN_HEX191         14.2512092  0.0776419   183.55   <2e-16 ***
DESTIN_HEX192         17.3946745  0.0059982  2899.98   <2e-16 ***
DESTIN_HEX193         17.3536082  0.0060238  2880.86   <2e-16 ***
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DESTIN_HEX196         17.6044971  0.0055019  3199.70   <2e-16 ***
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DESTIN_HEX198         17.4641409  0.0061395  2844.55   <2e-16 ***
DESTIN_HEX199         19.3231962  0.0038752  4986.33   <2e-16 ***
DESTIN_HEX200         15.7561393  0.0267298   589.46   <2e-16 ***
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DESTIN_HEX202         16.0441213  0.0203108   789.93   <2e-16 ***
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DESTIN_HEX205         16.1817086  0.0131798  1227.77   <2e-16 ***
DESTIN_HEX206         18.0237415  0.0065341  2758.41   <2e-16 ***
DESTIN_HEX207         18.7103143  0.0032356  5782.56   <2e-16 ***
DESTIN_HEX208         18.3365616  0.0057487  3189.71   <2e-16 ***
DESTIN_HEX209         16.1569102  0.0112960  1430.33   <2e-16 ***
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DESTIN_HEX211         16.5505937  0.0093875  1763.05   <2e-16 ***
DESTIN_HEX212         13.7722001  0.0691976   199.03   <2e-16 ***
DESTIN_HEX213         15.2489815  0.0297055   513.34   <2e-16 ***
DESTIN_HEX214         14.8643513  0.0340502   436.54   <2e-16 ***
DESTIN_HEX215         16.0012437  0.0145357  1100.82   <2e-16 ***
DESTIN_HEX216         17.4164525  0.0067386  2584.60   <2e-16 ***
DESTIN_HEX217         15.2671004  0.0224662   679.56   <2e-16 ***
DESTIN_HEX218         18.2417039  0.0039169  4657.13   <2e-16 ***
DESTIN_HEX219         16.9752643  0.0107550  1578.36   <2e-16 ***
DESTIN_HEX220         18.0877437  0.0040682  4446.12   <2e-16 ***
DESTIN_HEX221         16.1134306  0.0117213  1374.72   <2e-16 ***
DESTIN_HEX222         16.1023747  0.0145788  1104.51   <2e-16 ***
DESTIN_HEX223         15.3280225  0.0284797   538.21   <2e-16 ***
DESTIN_HEX224         15.1655767  0.0225042   673.90   <2e-16 ***
DESTIN_HEX225         14.7050298  0.0368328   399.24   <2e-16 ***
DESTIN_HEX226         16.7671835  0.0160216  1046.54   <2e-16 ***
DESTIN_HEX227         17.3098244  0.0057185  3026.99   <2e-16 ***
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DESTIN_HEX230         17.7195638  0.0048386  3662.16   <2e-16 ***
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DESTIN_HEX237         18.0601512  0.0038043  4747.31   <2e-16 ***
DESTIN_HEX238         15.1485565  0.0213273   710.29   <2e-16 ***
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DESTIN_HEX240         17.5239056  0.0062799  2790.49   <2e-16 ***
DESTIN_HEX241         14.3466388  0.0299718   478.67   <2e-16 ***
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DESTIN_HEX245         14.6590747  0.0425307   344.67   <2e-16 ***
DESTIN_HEX246         16.4397368  0.0108982  1508.48   <2e-16 ***
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DESTIN_HEX249         15.9125275  0.0216251   735.84   <2e-16 ***
DESTIN_HEX250         16.9495969  0.0089623  1891.22   <2e-16 ***
DESTIN_HEX251         15.0138385  0.0192990   777.96   <2e-16 ***
DESTIN_HEX252         17.6379435  0.0055215  3194.41   <2e-16 ***
DESTIN_HEX253         16.0397675  0.0111615  1437.06   <2e-16 ***
DESTIN_HEX254         18.2707152  0.0049977  3655.83   <2e-16 ***
DESTIN_HEX255         15.7894072  0.0293697   537.61   <2e-16 ***
DESTIN_HEX256         15.2177741  0.0242945   626.39   <2e-16 ***
DESTIN_HEX257         19.3670942  0.0039877  4856.70   <2e-16 ***
DESTIN_HEX258         17.0886336  0.0068581  2491.76   <2e-16 ***
DESTIN_HEX259         17.8499773  0.0040316  4427.53   <2e-16 ***
DESTIN_HEX260         17.7404060  0.0046621  3805.24   <2e-16 ***
DESTIN_HEX262         17.2289604  0.0075076  2294.87   <2e-16 ***
DESTIN_HEX263         16.5270279  0.0094030  1757.64   <2e-16 ***
DESTIN_HEX264         15.3535841  0.0176409   870.34   <2e-16 ***
DESTIN_HEX265         18.1298409  0.0040954  4426.85   <2e-16 ***
DESTIN_HEX266         18.1759578  0.0062052  2929.13   <2e-16 ***
DESTIN_HEX267         15.7842642  0.0153055  1031.28   <2e-16 ***
DESTIN_HEX269         17.0265663  0.0074998  2270.26   <2e-16 ***
DESTIN_HEX270         17.3505269  0.0059291  2926.32   <2e-16 ***
DESTIN_HEX271         16.5022412  0.0081568  2023.12   <2e-16 ***
DESTIN_HEX272         16.2371202  0.0100074  1622.52   <2e-16 ***
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DESTIN_HEX274         16.6633676  0.0089922  1853.10   <2e-16 ***
DESTIN_HEX275         16.0424306  0.0204325   785.14   <2e-16 ***
DESTIN_HEX276         18.7188713  0.0037021  5056.32   <2e-16 ***
DESTIN_HEX277         18.1864457  0.0056997  3190.79   <2e-16 ***
DESTIN_HEX278         15.3791962  0.0296819   518.13   <2e-16 ***
DESTIN_HEX279         18.4989168  0.0041892  4415.89   <2e-16 ***
DESTIN_HEX280         19.5265024  0.0029818  6548.56   <2e-16 ***
DESTIN_HEX281         15.7121508  0.0243902   644.20   <2e-16 ***
DESTIN_HEX282         16.6899425  0.0124569  1339.81   <2e-16 ***
DESTIN_HEX283         16.0202909  0.0120027  1334.72   <2e-16 ***
DESTIN_HEX284         16.1589542  0.0103855  1555.92   <2e-16 ***
DESTIN_HEX285         16.2869762  0.0100644  1618.28   <2e-16 ***
DESTIN_HEX286         17.8971268  0.0049322  3628.63   <2e-16 ***
DESTIN_HEX287         17.0672941  0.0108239  1576.81   <2e-16 ***
DESTIN_HEX288         17.7764056  0.0062268  2854.84   <2e-16 ***
DESTIN_HEX289         17.4451022  0.0087805  1986.80   <2e-16 ***
DESTIN_HEX290         18.2751177  0.0047355  3859.21   <2e-16 ***
DESTIN_HEX291         14.9890050  0.0316924   472.95   <2e-16 ***
DESTIN_HEX292         16.3236663  0.0105694  1544.43   <2e-16 ***
DESTIN_HEX293         17.2273419  0.0061759  2789.44   <2e-16 ***
DESTIN_HEX294         17.3201592  0.0057996  2986.44   <2e-16 ***
DESTIN_HEX295         16.9383688  0.0071377  2373.08   <2e-16 ***
DESTIN_HEX296         17.0914977  0.0060825  2809.96   <2e-16 ***
DESTIN_HEX297         15.5240004  0.0282086   550.33   <2e-16 ***
DESTIN_HEX298         18.2614119  0.0042408  4306.17   <2e-16 ***
DESTIN_HEX299         18.1501766  0.0051538  3521.74   <2e-16 ***
DESTIN_HEX300         17.6271227  0.0054787  3217.38   <2e-16 ***
DESTIN_HEX301         16.6733935  0.0077800  2143.10   <2e-16 ***
DESTIN_HEX302         17.4512273  0.0054183  3220.82   <2e-16 ***
DESTIN_HEX303         16.3982670  0.0091461  1792.92   <2e-16 ***
DESTIN_HEX304         12.0091268  0.2582060    46.51   <2e-16 ***
DESTIN_HEX305         17.8155481  0.0054827  3249.42   <2e-16 ***
DESTIN_HEX306         18.1227351  0.0066983  2705.58   <2e-16 ***
DESTIN_HEX307         17.0262185  0.0074540  2284.19   <2e-16 ***
DESTIN_HEX308         15.8655705  0.0128868  1231.15   <2e-16 ***
DESTIN_HEX309         15.7525753  0.0107552  1464.64   <2e-16 ***
DESTIN_HEX310         16.2112451  0.0094148  1721.88   <2e-16 ***
DESTIN_HEX311         17.7572931  0.0050707  3501.92   <2e-16 ***
DESTIN_HEX312         13.2578518  0.2773589    47.80   <2e-16 ***
DESTIN_HEX313         17.6990977  0.0062883  2814.60   <2e-16 ***
DESTIN_HEX314         16.5752119  0.0118705  1396.33   <2e-16 ***
DESTIN_HEX315         14.4982498  0.0342208   423.67   <2e-16 ***
DESTIN_HEX316         15.6806410  0.0214406   731.35   <2e-16 ***
DESTIN_HEX317         15.4148626  0.0255197   604.04   <2e-16 ***
DESTIN_HEX318         17.9586157  0.0039626  4532.09   <2e-16 ***
DESTIN_HEX319         15.4545995  0.0175339   881.41   <2e-16 ***
DESTIN_HEX320         16.8632001  0.0072658  2320.89   <2e-16 ***
DESTIN_HEX321         16.5413649  0.0195391   846.58   <2e-16 ***
DESTIN_HEX322         12.9641518  0.1525128    85.00   <2e-16 ***
DESTIN_HEX323         16.5277939  0.0149418  1106.15   <2e-16 ***
DESTIN_HEX324         19.5897664  0.0026960  7266.10   <2e-16 ***
DESTIN_HEX325         17.1107096  0.0109811  1558.19   <2e-16 ***
DESTIN_HEX326         16.9159648  0.0083106  2035.48   <2e-16 ***
DESTIN_HEX327         15.5146447  0.0149705  1036.35   <2e-16 ***
DESTIN_HEX328         16.3363486  0.0108888  1500.29   <2e-16 ***
DESTIN_HEX329         16.2082407  0.0090886  1783.37   <2e-16 ***
DESTIN_HEX330         16.0217793  0.0127201  1259.57   <2e-16 ***
DESTIN_HEX331         18.3004615  0.0047897  3820.78   <2e-16 ***
DESTIN_HEX332         18.4558361  0.0041932  4401.32   <2e-16 ***
DESTIN_HEX333         17.6793388  0.0098580  1793.40   <2e-16 ***
DESTIN_HEX334         15.5893111  0.0155114  1005.02   <2e-16 ***
DESTIN_HEX335         14.5783453  0.0279267   522.02   <2e-16 ***
DESTIN_HEX336         17.1552016  0.0054195  3165.45   <2e-16 ***
DESTIN_HEX337         16.7446931  0.0078012  2146.41   <2e-16 ***
DESTIN_HEX338         14.1660584  0.0778756   181.91   <2e-16 ***
DESTIN_HEX339         16.3606594  0.0199918   818.37   <2e-16 ***
DESTIN_HEX340         18.6317235  0.0037012  5033.98   <2e-16 ***
DESTIN_HEX341         17.3932965  0.0076804  2264.65   <2e-16 ***
DESTIN_HEX343         15.6261177  0.0126046  1239.72   <2e-16 ***
DESTIN_HEX344         17.0102611  0.0059888  2840.36   <2e-16 ***
DESTIN_HEX345         17.8511647  0.0041193  4333.55   <2e-16 ***
DESTIN_HEX346         18.7430773  0.0041107  4559.64   <2e-16 ***
DESTIN_HEX347         19.1101363  0.0033974  5624.99   <2e-16 ***
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DESTIN_HEX391         16.6323400  0.0110856  1500.36   <2e-16 ***
DESTIN_HEX392         18.2409117  0.0044272  4120.22   <2e-16 ***
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DESTIN_HEX403         18.0408021  0.0056715  3180.94   <2e-16 ***
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DESTIN_HEX421         12.1533865  0.2425438    50.11   <2e-16 ***
DESTIN_HEX422         15.5010622  0.0158472   978.16   <2e-16 ***
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DESTIN_HEX428         18.4134250  0.0040052  4597.35   <2e-16 ***
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DESTIN_HEX430         13.8699044  0.1000178   138.67   <2e-16 ***
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DESTIN_HEX438         16.5891985  0.0092851  1786.64   <2e-16 ***
DESTIN_HEX439         15.6803072  0.0204794   765.66   <2e-16 ***
DESTIN_HEX440         18.5999986  0.0039086  4758.75   <2e-16 ***
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DESTIN_HEX511         18.3871506  0.0045394  4050.60   <2e-16 ***
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DESTIN_HEX526         16.0658728  0.0060084  2673.91   <2e-16 ***
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DESTIN_HEX528         16.9340710  0.0051485  3289.14   <2e-16 ***
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DESTIN_HEX537         16.8012672  0.0045607  3683.92   <2e-16 ***
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DESTIN_HEX539         17.0094896  0.0051993  3271.48   <2e-16 ***
DESTIN_HEX540         18.0412218  0.0049830  3620.57   <2e-16 ***
DESTIN_HEX541         16.5701700  0.0075864  2184.20   <2e-16 ***
DESTIN_HEX542         15.6385039  0.0124844  1252.64   <2e-16 ***
DESTIN_HEX543         18.3142974  0.0036243  5053.25   <2e-16 ***
DESTIN_HEX544         16.8129574  0.0117408  1432.01   <2e-16 ***
DESTIN_HEX545         17.0146465  0.0090282  1884.60   <2e-16 ***
DESTIN_HEX546         16.6332790  0.0148558  1119.65   <2e-16 ***
DESTIN_HEX547         13.9618461  0.0473879   294.63   <2e-16 ***
DESTIN_HEX548         15.3337037  0.0137837  1112.45   <2e-16 ***
DESTIN_HEX549         16.0962078  0.0069410  2318.99   <2e-16 ***
DESTIN_HEX550         16.9432535  0.0046514  3642.63   <2e-16 ***
DESTIN_HEX551         16.9569418  0.0047502  3569.70   <2e-16 ***
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DESTIN_HEX554         15.5574505  0.0168067   925.67   <2e-16 ***
DESTIN_HEX555         16.3840160  0.0210366   778.83   <2e-16 ***
DESTIN_HEX556         17.0853923  0.0084012  2033.69   <2e-16 ***
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DESTIN_HEX560         16.6824358  0.0188010   887.32   <2e-16 ***
DESTIN_HEX561         17.0600578  0.0046766  3647.97   <2e-16 ***
DESTIN_HEX562         17.9724555  0.0035775  5023.68   <2e-16 ***
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DESTIN_HEX564         14.6618001  0.0211910   691.89   <2e-16 ***
DESTIN_HEX565         16.6448912  0.0071082  2341.64   <2e-16 ***
DESTIN_HEX566         15.5379154  0.0145696  1066.46   <2e-16 ***
DESTIN_HEX567         15.9634131  0.0129009  1237.39   <2e-16 ***
DESTIN_HEX568         15.7276258  0.0172070   914.02   <2e-16 ***
DESTIN_HEX569         13.4229453  0.0894634   150.04   <2e-16 ***
DESTIN_HEX570         13.9557433  0.0630227   221.44   <2e-16 ***
DESTIN_HEX571         13.3448011  0.0562834   237.10   <2e-16 ***
DESTIN_HEX572         15.5598080  0.0134534  1156.57   <2e-16 ***
DESTIN_HEX573         14.8631349  0.0150008   990.82   <2e-16 ***
DESTIN_HEX574         17.6736886  0.0039490  4475.47   <2e-16 ***
DESTIN_HEX575         16.9480623  0.0143438  1181.56   <2e-16 ***
DESTIN_HEX576         16.3879541  0.0095864  1709.50   <2e-16 ***
DESTIN_HEX577         17.5087118  0.0060412  2898.19   <2e-16 ***
DESTIN_HEX578         15.6445676  0.0140651  1112.29   <2e-16 ***
DESTIN_HEX579         13.5700919  0.0695319   195.16   <2e-16 ***
DESTIN_HEX580         13.9724842  0.0687095   203.36   <2e-16 ***
DESTIN_HEX581         17.4113431  0.0096148  1810.89   <2e-16 ***
DESTIN_HEX582         16.4521468  0.0063771  2579.89   <2e-16 ***
DESTIN_HEX583         17.2053121  0.0056052  3069.50   <2e-16 ***
DESTIN_HEX584         17.7717456  0.0045904  3871.49   <2e-16 ***
DESTIN_HEX585         16.5005274  0.0073552  2243.38   <2e-16 ***
DESTIN_HEX586         17.2844099  0.0051069  3384.52   <2e-16 ***
DESTIN_HEX587         17.7931494  0.0075308  2362.72   <2e-16 ***
DESTIN_HEX588         16.3155936  0.0101391  1609.17   <2e-16 ***
DESTIN_HEX589         18.0638120  0.0045798  3944.20   <2e-16 ***
DESTIN_HEX590         17.7886140  0.0057361  3101.14   <2e-16 ***
DESTIN_HEX591         14.5824494  0.0695351   209.71   <2e-16 ***
DESTIN_HEX592         16.8471021  0.0148401  1135.24   <2e-16 ***
DESTIN_HEX593         17.7349753  0.0038316  4628.65   <2e-16 ***
DESTIN_HEX594         16.6048869  0.0073313  2264.92   <2e-16 ***
DESTIN_HEX595         17.7198423  0.0045859  3863.95   <2e-16 ***
DESTIN_HEX596         18.6586240  0.0030705  6076.81   <2e-16 ***
DESTIN_HEX597         16.5921785  0.0072460  2289.84   <2e-16 ***
DESTIN_HEX598         18.5437223  0.0035641  5202.98   <2e-16 ***
DESTIN_HEX599         17.2398427  0.0069988  2463.27   <2e-16 ***
DESTIN_HEX600         17.0415794  0.0082093  2075.90   <2e-16 ***
DESTIN_HEX601         13.9376226  0.0541884   257.21   <2e-16 ***
DESTIN_HEX602         15.1102073  0.0270206   559.21   <2e-16 ***
DESTIN_HEX603         17.4505763  0.0045481  3836.86   <2e-16 ***
DESTIN_HEX604         16.1669426  0.0109437  1477.29   <2e-16 ***
DESTIN_HEX605         17.1501575  0.0054993  3118.59   <2e-16 ***
DESTIN_HEX606         16.7281705  0.0091920  1819.86   <2e-16 ***
DESTIN_HEX607         17.3140799  0.0049478  3499.32   <2e-16 ***
DESTIN_HEX608         17.5375405  0.0048846  3590.39   <2e-16 ***
DESTIN_HEX609         18.1444524  0.0040287  4503.84   <2e-16 ***
DESTIN_HEX610         18.0293737  0.0051433  3505.41   <2e-16 ***
DESTIN_HEX611         13.2703601  0.0854540   155.29   <2e-16 ***
DESTIN_HEX612         17.8295083  0.0038602  4618.75   <2e-16 ***
DESTIN_HEX613         16.7505731  0.0060206  2782.19   <2e-16 ***
DESTIN_HEX614         15.7892482  0.0190876   827.20   <2e-16 ***
DESTIN_HEX615         17.5823601  0.0046872  3751.17   <2e-16 ***
DESTIN_HEX616         18.4519715  0.0035611  5181.51   <2e-16 ***
DESTIN_HEX617         18.7746887  0.0055729  3368.90   <2e-16 ***
DESTIN_HEX618         18.0211440  0.0059477  3029.94   <2e-16 ***
DESTIN_HEX619         16.8832712  0.0115741  1458.72   <2e-16 ***
DESTIN_HEX620         17.3300345  0.0052006  3332.34   <2e-16 ***
DESTIN_HEX621         16.8650411  0.0057899  2912.86   <2e-16 ***
DESTIN_HEX622         17.1740785  0.0076213  2253.43   <2e-16 ***
DESTIN_HEX623         16.3589843  0.0084044  1946.47   <2e-16 ***
DESTIN_HEX624         15.8763566  0.0114006  1392.59   <2e-16 ***
DESTIN_HEX625         17.1049357  0.0072511  2358.96   <2e-16 ***
DESTIN_HEX626         17.9018418  0.0046090  3884.09   <2e-16 ***
DESTIN_HEX627         17.1257354  0.0080110  2137.78   <2e-16 ***
DESTIN_HEX628         17.1827736  0.0063054  2725.07   <2e-16 ***
DESTIN_HEX629         17.1472670  0.0049632  3454.91   <2e-16 ***
DESTIN_HEX630         17.4461651  0.0046753  3731.59   <2e-16 ***
DESTIN_HEX631         17.0897892  0.0059230  2885.34   <2e-16 ***
DESTIN_HEX632         17.9420987  0.0045236  3966.33   <2e-16 ***
DESTIN_HEX633         17.9422419  0.0045073  3980.66   <2e-16 ***
DESTIN_HEX634         18.2298386  0.0036480  4997.24   <2e-16 ***
DESTIN_HEX635         15.6507804  0.0137927  1134.71   <2e-16 ***
DESTIN_HEX636         18.0445455  0.0050561  3568.83   <2e-16 ***
DESTIN_HEX638         17.3252733  0.0053149  3259.74   <2e-16 ***
DESTIN_HEX639         17.3917021  0.0046514  3739.05   <2e-16 ***
DESTIN_HEX640         16.9652808  0.0057278  2961.94   <2e-16 ***
DESTIN_HEX641         14.8879360  0.0228987   650.17   <2e-16 ***
DESTIN_HEX642         17.5930315  0.0052730  3336.44   <2e-16 ***
DESTIN_HEX643         17.9327884  0.0039819  4503.59   <2e-16 ***
DESTIN_HEX644         17.5815623  0.0048390  3633.28   <2e-16 ***
DESTIN_HEX645         17.9970757  0.0040956  4394.20   <2e-16 ***
DESTIN_HEX646         18.6337588  0.0065118  2861.53   <2e-16 ***
DESTIN_HEX647         16.5698378  0.0082204  2015.70   <2e-16 ***
DESTIN_HEX648         17.8498815  0.0038299  4660.71   <2e-16 ***
DESTIN_HEX649         16.6441743  0.0064217  2591.88   <2e-16 ***
DESTIN_HEX650         15.9159023  0.0119479  1332.11   <2e-16 ***
DESTIN_HEX651         18.0851267  0.0040582  4456.46   <2e-16 ***
DESTIN_HEX652         18.5779532  0.0032695  5682.18   <2e-16 ***
DESTIN_HEX653         17.8722029  0.0042510  4204.25   <2e-16 ***
DESTIN_HEX654         17.3374228  0.0057095  3036.58   <2e-16 ***
DESTIN_HEX655         14.9735014  0.0317189   472.07   <2e-16 ***
DESTIN_HEX657         17.1256871  0.0056863  3011.74   <2e-16 ***
DESTIN_HEX658         16.5369167  0.0083478  1980.99   <2e-16 ***
DESTIN_HEX659         16.5016812  0.0087125  1894.03   <2e-16 ***
DESTIN_HEX660         15.9778918  0.0220922   723.24   <2e-16 ***
DESTIN_HEX661         17.5208325  0.0053751  3259.64   <2e-16 ***
DESTIN_HEX662         17.0252197  0.0062626  2718.55   <2e-16 ***
DESTIN_HEX663         18.4719661  0.0033767  5470.39   <2e-16 ***
DESTIN_HEX664         18.0834707  0.0043205  4185.51   <2e-16 ***
DESTIN_HEX665         16.6419298  0.0149512  1113.08   <2e-16 ***
DESTIN_HEX666         17.8903941  0.0045547  3927.90   <2e-16 ***
DESTIN_HEX667         16.7041605  0.0076164  2193.19   <2e-16 ***
DESTIN_HEX668         17.3462151  0.0066994  2589.22   <2e-16 ***
DESTIN_HEX669         16.4268604  0.0091029  1804.58   <2e-16 ***
DESTIN_HEX670         15.7948684  0.0310110   509.33   <2e-16 ***
DESTIN_HEX671         14.8893238  0.0283072   525.99   <2e-16 ***
DESTIN_HEX672         17.9939213  0.0045395  3963.89   <2e-16 ***
DESTIN_HEX673         17.9191414  0.0042010  4265.42   <2e-16 ***
DESTIN_HEX674         18.0286245  0.0041818  4311.22   <2e-16 ***
DESTIN_HEX675         17.2497618  0.0071820  2401.82   <2e-16 ***
DESTIN_HEX676         16.5723949  0.0221849   747.01   <2e-16 ***
DESTIN_HEX677         16.9263002  0.0067840  2495.02   <2e-16 ***
DESTIN_HEX678         17.9863195  0.0037902  4745.54   <2e-16 ***
DESTIN_HEX679         17.8254355  0.0042104  4233.64   <2e-16 ***
DESTIN_HEX680         17.8058586  0.0053636  3319.73   <2e-16 ***
DESTIN_HEX681         17.7862228  0.0045042  3948.82   <2e-16 ***
DESTIN_HEX682         18.3671649  0.0034908  5261.66   <2e-16 ***
DESTIN_HEX683         15.4236393  0.0229296   672.65   <2e-16 ***
DESTIN_HEX684         18.0640783  0.0043184  4183.07   <2e-16 ***
DESTIN_HEX685         16.8926246  0.0064844  2605.12   <2e-16 ***
DESTIN_HEX686         17.1973031  0.0054354  3163.96   <2e-16 ***
DESTIN_HEX687         16.4338751  0.0098355  1670.87   <2e-16 ***
DESTIN_HEX688         14.2778152  0.0618107   230.99   <2e-16 ***
DESTIN_HEX689         17.2012100  0.0069721  2467.16   <2e-16 ***
DESTIN_HEX690         18.9974732  0.0029367  6468.99   <2e-16 ***
DESTIN_HEX691         15.4727879  0.0212014   729.80   <2e-16 ***
DESTIN_HEX692         17.7507207  0.0094703  1874.36   <2e-16 ***
DESTIN_HEX693         17.3478538  0.0052550  3301.21   <2e-16 ***
DESTIN_HEX694         17.4242288  0.0051811  3363.06   <2e-16 ***
DESTIN_HEX695         18.0693059  0.0041680  4335.28   <2e-16 ***
DESTIN_HEX696         14.8941070  0.0364204   408.95   <2e-16 ***
DESTIN_HEX697         18.2320354  0.0081587  2234.67   <2e-16 ***
DESTIN_HEX698         17.8109334  0.0050194  3548.44   <2e-16 ***
DESTIN_HEX700         17.8294430  0.0055799  3195.28   <2e-16 ***
DESTIN_HEX701         15.9866967  0.0140421  1138.49   <2e-16 ***
DESTIN_HEX702         17.8700153  0.0100747  1773.75   <2e-16 ***
DESTIN_HEX703         17.5241624  0.0052160  3359.66   <2e-16 ***
DESTIN_HEX704         14.2904149  0.0513341   278.38   <2e-16 ***
DESTIN_HEX705         17.9191878  0.0050317  3561.24   <2e-16 ***
DESTIN_HEX706         17.6580535  0.0091208  1936.01   <2e-16 ***
DESTIN_HEX707         17.3313544  0.0056342  3076.09   <2e-16 ***
DESTIN_HEX708         16.3575142  0.0090337  1810.72   <2e-16 ***
DESTIN_HEX709         16.6342789  0.0096625  1721.54   <2e-16 ***
DESTIN_HEX710         13.4085713  0.0803439   166.89   <2e-16 ***
DESTIN_HEX711         13.7643453  0.0887579   155.08   <2e-16 ***
DESTIN_HEX712         17.1865895  0.0084045  2044.94   <2e-16 ***
DESTIN_HEX714         16.5793289  0.0083703  1980.74   <2e-16 ***
DESTIN_HEX715         18.1667434  0.0054805  3314.77   <2e-16 ***
DESTIN_HEX716         17.7817714  0.0048420  3672.43   <2e-16 ***
DESTIN_HEX717         15.6400735  0.0252616   619.12   <2e-16 ***
DESTIN_HEX718         17.2478387  0.0088517  1948.53   <2e-16 ***
DESTIN_HEX719         17.1384350  0.0068073  2517.67   <2e-16 ***
DESTIN_HEX720         17.8609977  0.0046206  3865.55   <2e-16 ***
DESTIN_HEX721         18.3509133  0.0042053  4363.74   <2e-16 ***
DESTIN_HEX722         14.7061868  0.0386510   380.49   <2e-16 ***
DESTIN_HEX724         16.7752674  0.0086448  1940.51   <2e-16 ***
DESTIN_HEX725         19.0181583  0.0028236  6735.40   <2e-16 ***
DESTIN_HEX726         17.1378291  0.0072573  2361.45   <2e-16 ***
DESTIN_HEX727         18.1750987  0.0045881  3961.32   <2e-16 ***
DESTIN_HEX728         14.6815072  0.0625288   234.80   <2e-16 ***
DESTIN_HEX729         16.9025292  0.0085358  1980.19   <2e-16 ***
DESTIN_HEX730         15.5135828  0.0133796  1159.50   <2e-16 ***
DESTIN_HEX731         17.8132688  0.0050010  3561.95   <2e-16 ***
DESTIN_HEX732         16.6902550  0.0111211  1500.78   <2e-16 ***
DESTIN_HEX733         18.1674551  0.0047307  3840.31   <2e-16 ***
DESTIN_HEX734         17.0615572  0.0076860  2219.82   <2e-16 ***
DESTIN_HEX735         17.4034878  0.0070428  2471.10   <2e-16 ***
DESTIN_HEX736         17.2888522  0.0060146  2874.50   <2e-16 ***
DESTIN_HEX737         17.7864306  0.0043223  4115.05   <2e-16 ***
DESTIN_HEX738         17.6212366  0.0052292  3369.80   <2e-16 ***
DESTIN_HEX739         18.3552334  0.0041306  4443.69   <2e-16 ***
DESTIN_HEX740         18.0654174  0.0045738  3949.80   <2e-16 ***
DESTIN_HEX741         17.2897893  0.0076139  2270.83   <2e-16 ***
DESTIN_HEX742         16.1681214  0.0173855   929.98   <2e-16 ***
DESTIN_HEX743         17.7950927  0.0061809  2879.05   <2e-16 ***
DESTIN_HEX744         18.4499546  0.0037097  4973.41   <2e-16 ***
DESTIN_HEX745         17.7261455  0.0047408  3739.05   <2e-16 ***
DESTIN_HEX746         17.6928960  0.0049495  3574.69   <2e-16 ***
DESTIN_HEX747         17.1201259  0.0084003  2038.04   <2e-16 ***
DESTIN_HEX748         18.4584079  0.0041125  4488.40   <2e-16 ***
DESTIN_HEX749         17.1218449  0.0074184  2308.02   <2e-16 ***
DESTIN_HEX750         18.0281833  0.0042414  4250.50   <2e-16 ***
DESTIN_HEX751         15.0792835  0.0285140   528.84   <2e-16 ***
DESTIN_HEX752         18.0618497  0.0037623  4800.76   <2e-16 ***
DESTIN_HEX753         17.7193090  0.0050646  3498.63   <2e-16 ***
DESTIN_HEX754         17.8768318  0.0049715  3595.89   <2e-16 ***
DESTIN_HEX755         15.3444765  0.0231352   663.25   <2e-16 ***
DESTIN_HEX756         17.8226796  0.0051009  3494.05   <2e-16 ***
DESTIN_HEX757         16.8252872  0.0074912  2246.01   <2e-16 ***
DESTIN_HEX758         15.3207120  0.0260994   587.01   <2e-16 ***
DESTIN_HEX759         19.2014620  0.0027689  6934.70   <2e-16 ***
DESTIN_HEX760         18.0241219  0.0061580  2926.93   <2e-16 ***
DESTIN_HEX761         18.0400302  0.0051223  3521.86   <2e-16 ***
DESTIN_HEX762         16.7818543  0.0088920  1887.31   <2e-16 ***
DESTIN_HEX763         18.2069764  0.0041187  4420.54   <2e-16 ***
DESTIN_HEX764         16.7738573  0.0075805  2212.76   <2e-16 ***
DESTIN_HEX765         17.6228846  0.0046733  3770.99   <2e-16 ***
DESTIN_HEX766         17.0728869  0.0074296  2297.94   <2e-16 ***
DESTIN_HEX767         18.7639700  0.0033531  5596.06   <2e-16 ***
DESTIN_HEX768         14.4192340  0.0548290   262.99   <2e-16 ***
DESTIN_HEX769         16.2872464  0.0848505   191.95   <2e-16 ***
DESTIN_HEX770         15.5011483  0.0162312   955.02   <2e-16 ***
DESTIN_HEX771         16.4410413  0.0086542  1899.77   <2e-16 ***
DESTIN_HEX772         17.8779183  0.0050208  3560.75   <2e-16 ***
DESTIN_HEX773         17.5221984  0.0050004  3504.13   <2e-16 ***
DESTIN_HEX774         17.0281957  0.0082105  2073.95   <2e-16 ***
DESTIN_HEX775         14.4440626  0.0528813   273.14   <2e-16 ***
DESTIN_HEX776         16.3997601  0.0124583  1316.38   <2e-16 ***
DESTIN_HEX777         16.2312640  0.0119991  1352.71   <2e-16 ***
DESTIN_HEX778         18.0867680  0.0039594  4568.11   <2e-16 ***
DESTIN_HEX779         18.3257141  0.0045889  3993.52   <2e-16 ***
DESTIN_HEX780         17.7365564  0.0054887  3231.45   <2e-16 ***
DESTIN_HEX781         17.0479474  0.0107156  1590.95   <2e-16 ***
DESTIN_HEX782         15.4671639  0.0163315   947.08   <2e-16 ***
DESTIN_HEX783         17.9005977  0.0048122  3719.81   <2e-16 ***
DESTIN_HEX784         18.5756188  0.0034263  5421.41   <2e-16 ***
DESTIN_HEX785         18.5590507  0.0038816  4781.28   <2e-16 ***
DESTIN_HEX786         17.9595365  0.0059097  3039.01   <2e-16 ***
DESTIN_HEX787         17.4141220  0.0058996  2951.76   <2e-16 ***
DESTIN_HEX788         17.0127868  0.0077372  2198.82   <2e-16 ***
DESTIN_HEX789         17.4811416  0.0054369  3215.30   <2e-16 ***
DESTIN_HEX790         18.0097605  0.0052707  3416.93   <2e-16 ***
DESTIN_HEX791         16.6792757  0.0118055  1412.84   <2e-16 ***
DESTIN_HEX792         16.1146570  0.0129021  1248.99   <2e-16 ***
DESTIN_HEX793         17.4208903  0.0062570  2784.21   <2e-16 ***
DESTIN_HEX794         17.8729150  0.0049489  3611.46   <2e-16 ***
DESTIN_HEX795         17.1511605  0.0199545   859.51   <2e-16 ***
DESTIN_HEX796         15.3087383  0.0571102   268.06   <2e-16 ***
DESTIN_HEX797         15.1858746  0.0233322   650.86   <2e-16 ***
DESTIN_HEX798         15.6608980  0.0245811   637.11   <2e-16 ***
DESTIN_HEX799         17.6972872  0.0060791  2911.17   <2e-16 ***
DESTIN_HEX800         15.6291930  0.0176263   886.70   <2e-16 ***
DESTIN_HEX801         14.9924839  0.0365358   410.35   <2e-16 ***
DESTIN_HEX802         16.0333039  0.0271306   590.97   <2e-16 ***
DESTIN_HEX803         16.8286804  0.0119235  1411.39   <2e-16 ***
DESTIN_HEX804         15.8055324  0.0175342   901.41   <2e-16 ***
DESTIN_HEX805         14.5210416  0.0462114   314.23   <2e-16 ***
DESTIN_HEX806         15.3145394  0.0337219   454.14   <2e-16 ***
DESTIN_HEX807         15.6811975  0.0204857   765.47   <2e-16 ***
DESTIN_HEX808         16.2782440  0.0129588  1256.15   <2e-16 ***
DESTIN_HEX809         15.0393501  0.0520926   288.70   <2e-16 ***
DESTIN_HEX810         15.5958950  0.0376038   414.74   <2e-16 ***
DESTIN_HEX811         16.8717499  0.0124359  1356.69   <2e-16 ***
DESTIN_HEX812         15.1512605  0.0228004   664.52   <2e-16 ***
DESTIN_HEX813         14.4701481  0.0596851   242.44   <2e-16 ***
DESTIN_HEX814         15.9814772  0.0210272   760.04   <2e-16 ***
DESTIN_HEX815         14.1562782  0.0566460   249.91   <2e-16 ***
DESTIN_HEX816         15.6793168  0.0190771   821.89   <2e-16 ***
DESTIN_HEX817         17.5091871  0.0097394  1797.77   <2e-16 ***
DESTIN_HEX818         18.3430542  0.0072231  2539.51   <2e-16 ***
DESTIN_HEX819         17.0916111  0.0109127  1566.21   <2e-16 ***
DESTIN_HEX820         18.2838035  0.0120162  1521.60   <2e-16 ***
DESTIN_HEX821         18.1349525  0.0066914  2710.20   <2e-16 ***
DESTIN_HEX822         16.8588567  0.0112941  1492.72   <2e-16 ***
DESTIN_HEX823         16.7019827  0.0133743  1248.81   <2e-16 ***
DESTIN_HEX824         16.2252957  0.0185038   876.86   <2e-16 ***
DESTIN_HEX825         17.2824657  0.0179612   962.21   <2e-16 ***
DESTIN_HEX826         16.7618739  0.0162685  1030.33   <2e-16 ***
DESTIN_HEX827         16.3371900  0.0173212   943.19   <2e-16 ***
DESTIN_HEX828         14.6582391  0.0453565   323.18   <2e-16 ***
DESTIN_HEX829         16.6844285  0.0316196   527.66   <2e-16 ***
DESTIN_HEX830         17.1776462  0.0131462  1306.66   <2e-16 ***
DESTIN_HEX831         16.0641959  0.0589668   272.43   <2e-16 ***
log(P_BUSINESS_COUNT) -0.0072523  0.0001856   -39.08   <2e-16 ***
log(P_MRT_EXIT_COUNT)  0.4958807  0.0003921  1264.79   <2e-16 ***
log(P_FINSERV_COUNT)   0.2948417  0.0002426  1215.21   <2e-16 ***
log(dist)             -1.5435141  0.0002644 -5837.79   <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: 317392316  on 67737  degrees of freedom
Residual deviance:  32204254  on 66917  degrees of freedom
AIC: 32576287

Number of Fisher Scoring iterations: 7
  • In case R/Quarto crashes, we add a copy of relevant coefficient readouts here for decSIM:
Coefficients:
                         Estimate Std. Error  z value Pr(>|z|)    
log(P_BUSINESS_COUNT) -0.0072523  0.0001856   -39.08   <2e-16 ***
log(P_MRT_EXIT_COUNT)  0.4958807  0.0003921  1264.79   <2e-16 ***
log(P_FINSERV_COUNT)   0.2948417  0.0002426  1215.21   <2e-16 ***
log(dist)             -1.5435141  0.0002644 -5837.79   <2e-16 ***

4.5c Commentary on decSIM

  • Once again, we compare the size of the coefficients to assess the impact of the explanatory factors;
    • As above, the decay factor, log(dist), is clearly a strong determinant of the number of trips, with -1.54
    • Similar to the above, we see MRT_EXIT_COUNT followed by FINSERV_COUNT having high coefficient values.
    • BUSINESS_COUNT shows an extremely small (<0.01) value, again suggesting that it not relevant or misaligned.
show code 
CalcRSquared(decSIM$data$SUM_TRIPS, decSIM$fitted.values)
[1] 0.4157096
  • The R-squared value of 0.4157 is not great, but performs better than the unconstrained model.

4.6 Doubly Constrained Spatial Interaction Modelling

  • In the Doubly-Constrained SIM, we eliminate all variables and focus only on the identities of the origin and destination hexagons.
show code 
dbcSIM <- glm(formula = SUM_TRIPS ~ 
                ORIGIN_HEX +
                DESTIN_HEX+ 
                log(dist),
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
write_rds(dbcSIM, "data/rds/dbcSIM.rds")
  • As before, we read/write to RDS to save space/time.
show code 
options(max.print = 10000)  
dbcSIM <- read_rds("data/rds/dbcSIM.rds")
summary(dbcSIM)

Call:
glm(formula = SUM_TRIPS ~ ORIGIN_HEX + DESTIN_HEX + log(dist), 
    family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)

Coefficients:
                Estimate Std. Error   z value Pr(>|z|)    
(Intercept)   15.7559003  0.1016735   154.966  < 2e-16 ***
ORIGIN_HEX2   -1.5409200  0.1066568   -14.447  < 2e-16 ***
ORIGIN_HEX3   -0.0397336  0.0688980    -0.577 0.564141    
ORIGIN_HEX4   -0.9158894  0.0771161   -11.877  < 2e-16 ***
ORIGIN_HEX5    1.5678416  0.0543126    28.867  < 2e-16 ***
ORIGIN_HEX6    0.0941121  0.0748847     1.257 0.208840    
ORIGIN_HEX7    0.2610398  0.0559956     4.662 3.13e-06 ***
ORIGIN_HEX8    1.0100360  0.0682648    14.796  < 2e-16 ***
ORIGIN_HEX9    1.9064689  0.0539424    35.343  < 2e-16 ***
ORIGIN_HEX10  -2.4801722  0.0971078   -25.540  < 2e-16 ***
ORIGIN_HEX11   0.6000142  0.0674092     8.901  < 2e-16 ***
ORIGIN_HEX12   0.3737291  0.0639781     5.842 5.17e-09 ***
ORIGIN_HEX13   0.6167145  0.0600953    10.262  < 2e-16 ***
ORIGIN_HEX14   2.8641853  0.0550780    52.002  < 2e-16 ***
ORIGIN_HEX15  -0.5687051  0.0623855    -9.116  < 2e-16 ***
ORIGIN_HEX16   2.2178248  0.0613028    36.178  < 2e-16 ***
ORIGIN_HEX17   0.3561286  0.0937947     3.797 0.000147 ***
ORIGIN_HEX18   1.0332597  0.0575943    17.940  < 2e-16 ***
ORIGIN_HEX19   0.2600845  0.0573756     4.533 5.81e-06 ***
ORIGIN_HEX20   0.2080053  0.0566356     3.673 0.000240 ***
ORIGIN_HEX21   0.6627568  0.0554093    11.961  < 2e-16 ***
ORIGIN_HEX22   0.5840346  0.0723249     8.075 6.74e-16 ***
ORIGIN_HEX23   3.0048113  0.0575199    52.240  < 2e-16 ***
ORIGIN_HEX24   0.6656195  0.0624490    10.659  < 2e-16 ***
ORIGIN_HEX25   1.1576190  0.0607937    19.042  < 2e-16 ***
ORIGIN_HEX26   1.4280834  0.0559183    25.539  < 2e-16 ***
ORIGIN_HEX27   1.2677056  0.0545427    23.242  < 2e-16 ***
ORIGIN_HEX28  -1.7146630  0.0677083   -25.324  < 2e-16 ***
ORIGIN_HEX29   2.1617054  0.0600784    35.981  < 2e-16 ***
ORIGIN_HEX30   0.6753658  0.0671990    10.050  < 2e-16 ***
ORIGIN_HEX31   0.4030453  0.0577948     6.974 3.09e-12 ***
ORIGIN_HEX32   0.4887417  0.0564501     8.658  < 2e-16 ***
ORIGIN_HEX33   1.3244119  0.0543231    24.380  < 2e-16 ***
ORIGIN_HEX34   0.6414546  0.0571552    11.223  < 2e-16 ***
ORIGIN_HEX35   0.5258511  0.0553930     9.493  < 2e-16 ***
ORIGIN_HEX36  -0.1688267  0.0748898    -2.254 0.024175 *  
ORIGIN_HEX37   0.9113126  0.0585606    15.562  < 2e-16 ***
ORIGIN_HEX38   1.5561843  0.0557161    27.931  < 2e-16 ***
ORIGIN_HEX39   1.3476696  0.0545521    24.704  < 2e-16 ***
ORIGIN_HEX40   0.4095428  0.0712645     5.747 9.09e-09 ***
ORIGIN_HEX41   0.0827913  0.0578444     1.431 0.152351    
ORIGIN_HEX42   0.1671422  0.0685756     2.437 0.014796 *  
ORIGIN_HEX43   1.4120828  0.0566585    24.923  < 2e-16 ***
ORIGIN_HEX44  -0.1258324  0.0567162    -2.219 0.026512 *  
ORIGIN_HEX45   0.9514420  0.0554612    17.155  < 2e-16 ***
ORIGIN_HEX46   3.0989903  0.0553826    55.956  < 2e-16 ***
ORIGIN_HEX47   1.0479735  0.0556963    18.816  < 2e-16 ***
ORIGIN_HEX48   0.6443477  0.0556356    11.582  < 2e-16 ***
ORIGIN_HEX49  -2.0980578  0.1904592   -11.016  < 2e-16 ***
ORIGIN_HEX50   1.1826579  0.0574452    20.588  < 2e-16 ***
ORIGIN_HEX51   0.3812825  0.0572193     6.664 2.67e-11 ***
ORIGIN_HEX52   2.1215576  0.0568046    37.348  < 2e-16 ***
ORIGIN_HEX53   0.8083594  0.0600630    13.459  < 2e-16 ***
ORIGIN_HEX54   0.9240026  0.0561966    16.442  < 2e-16 ***
ORIGIN_HEX55   2.7865749  0.0559360    49.817  < 2e-16 ***
ORIGIN_HEX56   1.5333368  0.0562319    27.268  < 2e-16 ***
ORIGIN_HEX57   0.4781298  0.0562072     8.507  < 2e-16 ***
ORIGIN_HEX58   1.7275205  0.0555553    31.096  < 2e-16 ***
ORIGIN_HEX59   1.0531071  0.0546338    19.276  < 2e-16 ***
ORIGIN_HEX60   2.4640579  0.0547369    45.016  < 2e-16 ***
ORIGIN_HEX61   0.1828847  0.0560806     3.261 0.001110 ** 
ORIGIN_HEX62   0.6239314  0.0555143    11.239  < 2e-16 ***
ORIGIN_HEX63   2.0160311  0.0567892    35.500  < 2e-16 ***
ORIGIN_HEX64   1.6899114  0.0552734    30.574  < 2e-16 ***
ORIGIN_HEX65   2.5242097  0.0539528    46.785  < 2e-16 ***
ORIGIN_HEX66   1.8675626  0.0545127    34.259  < 2e-16 ***
ORIGIN_HEX67   2.8515397  0.0540694    52.738  < 2e-16 ***
ORIGIN_HEX68  -1.0058494  0.0694400   -14.485  < 2e-16 ***
ORIGIN_HEX69   1.0089396  0.0545735    18.488  < 2e-16 ***
ORIGIN_HEX70  -1.1404847  0.0571822   -19.945  < 2e-16 ***
ORIGIN_HEX71   1.5639980  0.0544281    28.735  < 2e-16 ***
ORIGIN_HEX72   0.1182659  0.0574716     2.058 0.039608 *  
ORIGIN_HEX73   0.8323854  0.0604422    13.772  < 2e-16 ***
ORIGIN_HEX74   0.1565215  0.0576213     2.716 0.006600 ** 
ORIGIN_HEX75   0.3768821  0.0549924     6.853 7.21e-12 ***
ORIGIN_HEX76   0.2461855  0.0547842     4.494 7.00e-06 ***
ORIGIN_HEX77   0.4392799  0.0549619     7.992 1.32e-15 ***
ORIGIN_HEX79   1.2201596  0.0549892    22.189  < 2e-16 ***
ORIGIN_HEX80   0.2837113  0.0546371     5.193 2.07e-07 ***
ORIGIN_HEX81   0.8656610  0.0542401    15.960  < 2e-16 ***
ORIGIN_HEX82   1.2238815  0.0551106    22.208  < 2e-16 ***
ORIGIN_HEX84   0.8079114  0.0599259    13.482  < 2e-16 ***
ORIGIN_HEX85  -2.5170172  0.1361200   -18.491  < 2e-16 ***
ORIGIN_HEX86   1.0446819  0.0545286    19.158  < 2e-16 ***
ORIGIN_HEX87  -0.3640572  0.0548467    -6.638 3.19e-11 ***
ORIGIN_HEX88  -1.1058765  0.0659227   -16.775  < 2e-16 ***
ORIGIN_HEX89  -0.1346777  0.0599373    -2.247 0.024642 *  
ORIGIN_HEX90   1.8223675  0.0554342    32.874  < 2e-16 ***
ORIGIN_HEX91   1.7111944  0.0545603    31.363  < 2e-16 ***
ORIGIN_HEX92   0.3780403  0.0545118     6.935 4.06e-12 ***
ORIGIN_HEX93   0.9859947  0.0540790    18.232  < 2e-16 ***
ORIGIN_HEX94   1.1943208  0.0546044    21.872  < 2e-16 ***
ORIGIN_HEX95   0.9780519  0.0554962    17.624  < 2e-16 ***
ORIGIN_HEX96  -1.9087480  0.0904698   -21.098  < 2e-16 ***
ORIGIN_HEX97   0.5285691  0.0629227     8.400  < 2e-16 ***
ORIGIN_HEX98   2.4504994  0.0544691    44.989  < 2e-16 ***
ORIGIN_HEX99   0.6435635  0.0547315    11.759  < 2e-16 ***
ORIGIN_HEX100  1.6797948  0.0539442    31.139  < 2e-16 ***
ORIGIN_HEX101  1.1200200  0.0541175    20.696  < 2e-16 ***
ORIGIN_HEX102  0.5698782  0.0561676    10.146  < 2e-16 ***
ORIGIN_HEX103 -1.2202911  0.0747230   -16.331  < 2e-16 ***
ORIGIN_HEX104 -1.0041655  0.0747640   -13.431  < 2e-16 ***
ORIGIN_HEX105 -2.5475852  1.0017118    -2.543 0.010983 *  
ORIGIN_HEX106  0.7480838  0.0590086    12.678  < 2e-16 ***
ORIGIN_HEX107  1.4274940  0.0553827    25.775  < 2e-16 ***
ORIGIN_HEX108 -0.3135901  0.0548244    -5.720 1.07e-08 ***
ORIGIN_HEX109  0.2897064  0.0541981     5.345 9.03e-08 ***
ORIGIN_HEX110  1.0833579  0.0544991    19.878  < 2e-16 ***
ORIGIN_HEX111 -1.2677977  0.0782016   -16.212  < 2e-16 ***
ORIGIN_HEX112  1.5208536  0.0565107    26.913  < 2e-16 ***
ORIGIN_HEX114  0.1728181  0.0667586     2.589 0.009634 ** 
ORIGIN_HEX115  1.3225161  0.0561016    23.574  < 2e-16 ***
ORIGIN_HEX116 -1.2484215  0.0633468   -19.708  < 2e-16 ***
ORIGIN_HEX117  3.5908254  0.0538574    66.673  < 2e-16 ***
ORIGIN_HEX118  0.5823691  0.0541994    10.745  < 2e-16 ***
ORIGIN_HEX119 -3.2426653  0.1149623   -28.206  < 2e-16 ***
ORIGIN_HEX120  0.4038417  0.0620514     6.508 7.61e-11 ***
ORIGIN_HEX121 -2.2911622  0.1822376   -12.572  < 2e-16 ***
ORIGIN_HEX122  0.4664261  0.0658299     7.085 1.39e-12 ***
ORIGIN_HEX123  0.0935258  0.0605722     1.544 0.122579    
ORIGIN_HEX124  0.8480768  0.0563720    15.044  < 2e-16 ***
ORIGIN_HEX125  1.0400150  0.0541792    19.196  < 2e-16 ***
ORIGIN_HEX126  0.3577313  0.0541486     6.606 3.94e-11 ***
ORIGIN_HEX127 -0.7494307  0.0596910   -12.555  < 2e-16 ***
ORIGIN_HEX128 -0.7831237  0.0783809    -9.991  < 2e-16 ***
ORIGIN_HEX129 -0.5536653  0.0749793    -7.384 1.53e-13 ***
ORIGIN_HEX130  0.1114559  0.0568868     1.959 0.050083 .  
ORIGIN_HEX131  0.7676071  0.0547653    14.016  < 2e-16 ***
ORIGIN_HEX132 -0.5486683  0.0552788    -9.925  < 2e-16 ***
ORIGIN_HEX133  0.8850516  0.0541048    16.358  < 2e-16 ***
ORIGIN_HEX134 -0.2254220  0.0562229    -4.009 6.09e-05 ***
ORIGIN_HEX135  0.2123270  0.0551506     3.850 0.000118 ***
ORIGIN_HEX136  0.7893713  0.0540906    14.594  < 2e-16 ***
ORIGIN_HEX137  1.6652037  0.0544164    30.601  < 2e-16 ***
ORIGIN_HEX138  1.0698700  0.0541931    19.742  < 2e-16 ***
ORIGIN_HEX139  0.4759447  0.0542659     8.771  < 2e-16 ***
ORIGIN_HEX140  1.3549069  0.0540014    25.090  < 2e-16 ***
ORIGIN_HEX141  1.3243451  0.0547420    24.192  < 2e-16 ***
ORIGIN_HEX142  1.6386169  0.0550970    29.741  < 2e-16 ***
ORIGIN_HEX143 -0.7869679  0.0581462   -13.534  < 2e-16 ***
ORIGIN_HEX144  1.4242145  0.0540683    26.341  < 2e-16 ***
ORIGIN_HEX145  2.5393018  0.0539109    47.102  < 2e-16 ***
ORIGIN_HEX146 -0.5931103  0.0560413   -10.583  < 2e-16 ***
ORIGIN_HEX147  1.0635640  0.0547780    19.416  < 2e-16 ***
ORIGIN_HEX148  0.8424963  0.0543000    15.516  < 2e-16 ***
ORIGIN_HEX149 -0.3863547  0.0550897    -7.013 2.33e-12 ***
ORIGIN_HEX150  1.1933134  0.0540392    22.082  < 2e-16 ***
ORIGIN_HEX151  0.2683940  0.0549971     4.880 1.06e-06 ***
ORIGIN_HEX152 -0.7737403  0.0557602   -13.876  < 2e-16 ***
ORIGIN_HEX154 -1.7484790  0.0605824   -28.861  < 2e-16 ***
ORIGIN_HEX156  1.4500581  0.0545576    26.578  < 2e-16 ***
ORIGIN_HEX157 -1.6484617  0.0578324   -28.504  < 2e-16 ***
ORIGIN_HEX158  0.6668361  0.0541913    12.305  < 2e-16 ***
ORIGIN_HEX160  1.7068362  0.0547318    31.185  < 2e-16 ***
ORIGIN_HEX161  0.8706913  0.0545982    15.947  < 2e-16 ***
ORIGIN_HEX162 -1.1850043  0.0572101   -20.713  < 2e-16 ***
ORIGIN_HEX163  1.6391136  0.0539757    30.368  < 2e-16 ***
ORIGIN_HEX164  0.4205912  0.0545428     7.711 1.25e-14 ***
ORIGIN_HEX165  0.9566107  0.0542003    17.650  < 2e-16 ***
ORIGIN_HEX166 -0.9823996  0.0691708   -14.203  < 2e-16 ***
ORIGIN_HEX167 -1.6194795  0.0583471   -27.756  < 2e-16 ***
ORIGIN_HEX168  0.8137326  0.0541046    15.040  < 2e-16 ***
ORIGIN_HEX169  0.2473506  0.0542524     4.559 5.13e-06 ***
ORIGIN_HEX170  0.4712530  0.0545865     8.633  < 2e-16 ***
ORIGIN_HEX171 -0.1561789  0.0547364    -2.853 0.004327 ** 
ORIGIN_HEX172 -0.9857145  0.0558144   -17.661  < 2e-16 ***
ORIGIN_HEX173  0.2520185  0.0568685     4.432 9.35e-06 ***
ORIGIN_HEX174  1.3517378  0.0542657    24.910  < 2e-16 ***
ORIGIN_HEX175  2.4635121  0.0539234    45.685  < 2e-16 ***
ORIGIN_HEX176  0.4790719  0.0542050     8.838  < 2e-16 ***
ORIGIN_HEX177  0.9916155  0.0542279    18.286  < 2e-16 ***
ORIGIN_HEX178 -1.0378052  0.0575237   -18.041  < 2e-16 ***
ORIGIN_HEX179  0.5722746  0.0541271    10.573  < 2e-16 ***
ORIGIN_HEX180  0.0803225  0.0545237     1.473 0.140706    
ORIGIN_HEX181 -0.1621574  0.0602223    -2.693 0.007089 ** 
ORIGIN_HEX182  1.0896311  0.0555709    19.608  < 2e-16 ***
ORIGIN_HEX183  0.6025186  0.0542789    11.100  < 2e-16 ***
ORIGIN_HEX184  1.1230365  0.0540822    20.765  < 2e-16 ***
ORIGIN_HEX185  0.8338447  0.0540782    15.419  < 2e-16 ***
ORIGIN_HEX186  0.3428850  0.0544452     6.298 3.02e-10 ***
ORIGIN_HEX187 -0.2838555  0.0547229    -5.187 2.14e-07 ***
ORIGIN_HEX188  2.6462044  0.0539154    49.081  < 2e-16 ***
ORIGIN_HEX189  1.9148302  0.0540316    35.439  < 2e-16 ***
ORIGIN_HEX190 -0.1236346  0.0585769    -2.111 0.034803 *  
ORIGIN_HEX191  0.3127081  0.0586153     5.335 9.56e-08 ***
ORIGIN_HEX192  0.7422158  0.0543572    13.654  < 2e-16 ***
ORIGIN_HEX193  1.7533305  0.0540176    32.459  < 2e-16 ***
ORIGIN_HEX194  0.5686533  0.0541878    10.494  < 2e-16 ***
ORIGIN_HEX195 -0.7013357  0.0548483   -12.787  < 2e-16 ***
ORIGIN_HEX196  0.5084124  0.0541899     9.382  < 2e-16 ***
ORIGIN_HEX197  0.3860394  0.0541648     7.127 1.02e-12 ***
ORIGIN_HEX198 -0.1222092  0.0545517    -2.240 0.025075 *  
ORIGIN_HEX199  1.4976895  0.0543255    27.569  < 2e-16 ***
ORIGIN_HEX200  0.5317521  0.0564366     9.422  < 2e-16 ***
ORIGIN_HEX201 -0.0303418  0.0572309    -0.530 0.595998    
ORIGIN_HEX202 -0.1649111  0.0594043    -2.776 0.005502 ** 
ORIGIN_HEX203  1.4325722  0.0549935    26.050  < 2e-16 ***
ORIGIN_HEX204  1.7953233  0.0541055    33.182  < 2e-16 ***
ORIGIN_HEX205  1.6352252  0.0541353    30.206  < 2e-16 ***
ORIGIN_HEX206  2.3671826  0.0541386    43.725  < 2e-16 ***
ORIGIN_HEX207  2.3450642  0.0539179    43.493  < 2e-16 ***
ORIGIN_HEX208  1.9010542  0.0540415    35.178  < 2e-16 ***
ORIGIN_HEX209 -0.1908176  0.0545316    -3.499 0.000467 ***
ORIGIN_HEX210 -1.0527908  0.0556263   -18.926  < 2e-16 ***
ORIGIN_HEX211 -0.8287908  0.0550139   -15.065  < 2e-16 ***
ORIGIN_HEX212 -1.0085835  0.0638561   -15.795  < 2e-16 ***
ORIGIN_HEX213 -1.4610903  0.0616040   -23.717  < 2e-16 ***
ORIGIN_HEX214 -1.0196868  0.0608762   -16.750  < 2e-16 ***
ORIGIN_HEX215  0.6202197  0.0546955    11.339  < 2e-16 ***
ORIGIN_HEX216  0.2087047  0.0548400     3.806 0.000141 ***
ORIGIN_HEX217  0.0812283  0.0551795     1.472 0.141001    
ORIGIN_HEX218  1.2601771  0.0540711    23.306  < 2e-16 ***
ORIGIN_HEX219 -0.3911915  0.0559731    -6.989 2.77e-12 ***
ORIGIN_HEX220  0.8927373  0.0540609    16.514  < 2e-16 ***
ORIGIN_HEX221 -0.7741322  0.0552370   -14.015  < 2e-16 ***
ORIGIN_HEX222  0.2963917  0.0548202     5.407 6.42e-08 ***
ORIGIN_HEX223 -2.3734654  0.0678458   -34.983  < 2e-16 ***
ORIGIN_HEX224 -1.2451153  0.0577994   -21.542  < 2e-16 ***
ORIGIN_HEX225  0.5466840  0.0558243     9.793  < 2e-16 ***
ORIGIN_HEX226  1.7542897  0.0548914    31.959  < 2e-16 ***
ORIGIN_HEX227  0.8051852  0.0542204    14.850  < 2e-16 ***
ORIGIN_HEX228 -0.6742056  0.0558257   -12.077  < 2e-16 ***
ORIGIN_HEX229  1.9920943  0.0540107    36.883  < 2e-16 ***
ORIGIN_HEX230  0.5146432  0.0542653     9.484  < 2e-16 ***
ORIGIN_HEX231  0.1554827  0.0542578     2.866 0.004162 ** 
ORIGIN_HEX232  1.7586037  0.0541433    32.481  < 2e-16 ***
ORIGIN_HEX233 -1.8322352  0.0600326   -30.521  < 2e-16 ***
ORIGIN_HEX234 -1.0814652  0.0565257   -19.132  < 2e-16 ***
ORIGIN_HEX235 -0.3868867  0.0571436    -6.770 1.28e-11 ***
ORIGIN_HEX236  0.8724881  0.0542160    16.093  < 2e-16 ***
ORIGIN_HEX237  2.2724387  0.0539353    42.133  < 2e-16 ***
ORIGIN_HEX238  0.1250946  0.0551107     2.270 0.023215 *  
ORIGIN_HEX239 -0.9797614  0.0627274   -15.619  < 2e-16 ***
ORIGIN_HEX240  0.7774071  0.0543763    14.297  < 2e-16 ***
ORIGIN_HEX241 -0.8396563  0.0556064   -15.100  < 2e-16 ***
ORIGIN_HEX242  2.5960893  0.0539091    48.157  < 2e-16 ***
ORIGIN_HEX243 -4.0828742  0.2034499   -20.068  < 2e-16 ***
ORIGIN_HEX244  2.3867985  0.0540095    44.192  < 2e-16 ***
ORIGIN_HEX245 -2.1291171  0.0598941   -35.548  < 2e-16 ***
ORIGIN_HEX246  0.3250465  0.0552480     5.883 4.02e-09 ***
ORIGIN_HEX247  2.0170351  0.0540785    37.298  < 2e-16 ***
ORIGIN_HEX248  2.9930875  0.0539086    55.522  < 2e-16 ***
ORIGIN_HEX249  1.1242953  0.0545393    20.614  < 2e-16 ***
ORIGIN_HEX250  0.4487152  0.0548861     8.175 2.95e-16 ***
ORIGIN_HEX251 -1.4073073  0.0573474   -24.540  < 2e-16 ***
ORIGIN_HEX252  1.4660599  0.0540686    27.115  < 2e-16 ***
ORIGIN_HEX253 -0.6818614  0.0549166   -12.416  < 2e-16 ***
ORIGIN_HEX254 -0.1172161  0.0545264    -2.150 0.031578 *  
ORIGIN_HEX255  0.2916461  0.0575504     5.068 4.03e-07 ***
ORIGIN_HEX256 -0.9923803  0.0555537   -17.863  < 2e-16 ***
ORIGIN_HEX258  1.6143579  0.0541353    29.821  < 2e-16 ***
ORIGIN_HEX259  1.3734596  0.0540467    25.412  < 2e-16 ***
ORIGIN_HEX260  0.8459007  0.0542287    15.599  < 2e-16 ***
ORIGIN_HEX262  0.2976836  0.0547735     5.435 5.49e-08 ***
ORIGIN_HEX263 -0.8160052  0.0559473   -14.585  < 2e-16 ***
ORIGIN_HEX264 -1.2093903  0.0560767   -21.567  < 2e-16 ***
ORIGIN_HEX265  0.4351736  0.0541697     8.034 9.47e-16 ***
ORIGIN_HEX266  0.0631437  0.0547802     1.153 0.249045    
ORIGIN_HEX267 -1.1941104  0.0552107   -21.628  < 2e-16 ***
ORIGIN_HEX268  1.9566521  0.0540973    36.169  < 2e-16 ***
ORIGIN_HEX269  1.7898203  0.0541722    33.039  < 2e-16 ***
ORIGIN_HEX270  1.7147656  0.0540909    31.702  < 2e-16 ***
ORIGIN_HEX271  0.0546795  0.0546346     1.001 0.316913    
ORIGIN_HEX272  0.2303945  0.0547455     4.208 2.57e-05 ***
ORIGIN_HEX273  1.9605261  0.0540221    36.291  < 2e-16 ***
ORIGIN_HEX274 -0.0413274  0.0550121    -0.751 0.452507    
ORIGIN_HEX275 -1.1123448  0.0595298   -18.686  < 2e-16 ***
ORIGIN_HEX276  1.2396413  0.0540867    22.920  < 2e-16 ***
ORIGIN_HEX277  0.2169651  0.0544970     3.981 6.86e-05 ***
ORIGIN_HEX278  0.1501129  0.0575858     2.607 0.009140 ** 
ORIGIN_HEX279  1.8113697  0.0539889    33.551  < 2e-16 ***
ORIGIN_HEX280  1.1091283  0.0540931    20.504  < 2e-16 ***
ORIGIN_HEX281  0.5244886  0.0558136     9.397  < 2e-16 ***
ORIGIN_HEX282  2.5678070  0.0541437    47.426  < 2e-16 ***
ORIGIN_HEX283  0.5507625  0.0546430    10.079  < 2e-16 ***
ORIGIN_HEX284 -0.3736047  0.0556944    -6.708 1.97e-11 ***
ORIGIN_HEX285  1.4687864  0.0541414    27.129  < 2e-16 ***
ORIGIN_HEX286  1.6528527  0.0540942    30.555  < 2e-16 ***
ORIGIN_HEX287 -0.3130961  0.0554153    -5.650 1.60e-08 ***
ORIGIN_HEX288  0.6675604  0.0542971    12.295  < 2e-16 ***
ORIGIN_HEX289 -0.2535375  0.0552960    -4.585 4.54e-06 ***
ORIGIN_HEX290  0.4168582  0.0542689     7.681 1.57e-14 ***
ORIGIN_HEX291 -2.4703308  0.0630788   -39.163  < 2e-16 ***
ORIGIN_HEX292  1.5342950  0.0542753    28.269  < 2e-16 ***
ORIGIN_HEX293  1.7721482  0.0541066    32.753  < 2e-16 ***
ORIGIN_HEX294  1.9259441  0.0540587    35.627  < 2e-16 ***
ORIGIN_HEX295  2.3873629  0.0539873    44.221  < 2e-16 ***
ORIGIN_HEX296  1.1560498  0.0541499    21.349  < 2e-16 ***
ORIGIN_HEX297  1.3889334  0.0550345    25.238  < 2e-16 ***
ORIGIN_HEX298  0.6790914  0.0541606    12.538  < 2e-16 ***
ORIGIN_HEX299  0.3198846  0.0543112     5.890 3.87e-09 ***
ORIGIN_HEX300  2.1979741  0.0541003    40.628  < 2e-16 ***
ORIGIN_HEX301  1.8569562  0.0541098    34.318  < 2e-16 ***
ORIGIN_HEX302  1.0514104  0.0543454    19.347  < 2e-16 ***
ORIGIN_HEX303  0.4736636  0.0547823     8.646  < 2e-16 ***
ORIGIN_HEX304 -0.5293926  0.0829150    -6.385 1.72e-10 ***
ORIGIN_HEX305  1.6934850  0.0539911    31.366  < 2e-16 ***
ORIGIN_HEX306  0.7143813  0.0544964    13.109  < 2e-16 ***
ORIGIN_HEX307  0.7257183  0.0548886    13.222  < 2e-16 ***
ORIGIN_HEX308  1.8081454  0.0541982    33.362  < 2e-16 ***
ORIGIN_HEX309  0.8887842  0.0543773    16.345  < 2e-16 ***
ORIGIN_HEX310  0.1345031  0.0552391     2.435 0.014895 *  
ORIGIN_HEX311  1.5954883  0.0541258    29.477  < 2e-16 ***
ORIGIN_HEX312 -2.0962427  0.0961136   -21.810  < 2e-16 ***
ORIGIN_HEX313  0.3266505  0.0543616     6.009 1.87e-09 ***
ORIGIN_HEX314 -0.1040014  0.0546212    -1.904 0.056904 .  
ORIGIN_HEX315 -1.2103393  0.0709727   -17.054  < 2e-16 ***
ORIGIN_HEX316  1.1538862  0.0556120    20.749  < 2e-16 ***
ORIGIN_HEX317  2.0986328  0.0552829    37.962  < 2e-16 ***
ORIGIN_HEX318  2.2920786  0.0539939    42.451  < 2e-16 ***
ORIGIN_HEX319 -0.5595526  0.0578300    -9.676  < 2e-16 ***
ORIGIN_HEX320  0.8148614  0.0544024    14.978  < 2e-16 ***
ORIGIN_HEX321  2.7703892  0.0546298    50.712  < 2e-16 ***
ORIGIN_HEX322 -3.1810337  0.1634823   -19.458  < 2e-16 ***
ORIGIN_HEX323 -0.2457767  0.0560551    -4.385 1.16e-05 ***
ORIGIN_HEX324  3.3165303  0.0539169    61.512  < 2e-16 ***
ORIGIN_HEX325 -1.0335034  0.0575067   -17.972  < 2e-16 ***
ORIGIN_HEX326  1.2893117  0.0544578    23.675  < 2e-16 ***
ORIGIN_HEX327  1.5730987  0.0543700    28.933  < 2e-16 ***
ORIGIN_HEX328 -0.4935902  0.0570936    -8.645  < 2e-16 ***
ORIGIN_HEX329  1.0354126  0.0543978    19.034  < 2e-16 ***
ORIGIN_HEX330 -0.0561596  0.0563219    -0.997 0.318707    
ORIGIN_HEX331  0.2179473  0.0543673     4.009 6.10e-05 ***
ORIGIN_HEX332  0.6394973  0.0541783    11.804  < 2e-16 ***
ORIGIN_HEX333  2.0029705  0.0541846    36.966  < 2e-16 ***
ORIGIN_HEX334  2.3818988  0.0540756    44.048  < 2e-16 ***
ORIGIN_HEX335 -0.0276055  0.0568678    -0.485 0.627369    
ORIGIN_HEX336  1.0762395  0.0542547    19.837  < 2e-16 ***
ORIGIN_HEX337  1.3729375  0.0542072    25.328  < 2e-16 ***
ORIGIN_HEX338  0.0330126  0.0598152     0.552 0.581010    
ORIGIN_HEX339  0.5595861  0.0545575    10.257  < 2e-16 ***
ORIGIN_HEX340  0.4469649  0.0541798     8.250  < 2e-16 ***
ORIGIN_HEX341  0.6408002  0.0543354    11.793  < 2e-16 ***
ORIGIN_HEX343  0.4435320  0.0549750     8.068 7.15e-16 ***
ORIGIN_HEX344  1.0788303  0.0542957    19.870  < 2e-16 ***
ORIGIN_HEX345  2.0960717  0.0540171    38.804  < 2e-16 ***
ORIGIN_HEX346  1.1610644  0.0541677    21.435  < 2e-16 ***
ORIGIN_HEX347  2.0909333  0.0539867    38.731  < 2e-16 ***
ORIGIN_HEX348  1.2947523  0.0542676    23.859  < 2e-16 ***
ORIGIN_HEX349 -1.0395230  0.0798134   -13.024  < 2e-16 ***
ORIGIN_HEX350  2.6442736  0.0539815    48.985  < 2e-16 ***
ORIGIN_HEX351  1.7743698  0.0540994    32.798  < 2e-16 ***
ORIGIN_HEX352  1.6974122  0.0540775    31.388  < 2e-16 ***
ORIGIN_HEX353  0.6048145  0.0545212    11.093  < 2e-16 ***
ORIGIN_HEX354  1.0832182  0.0543801    19.919  < 2e-16 ***
ORIGIN_HEX355 -0.5664280  0.0642923    -8.810  < 2e-16 ***
ORIGIN_HEX356  0.9379921  0.0541633    17.318  < 2e-16 ***
ORIGIN_HEX357  1.0885466  0.0541795    20.091  < 2e-16 ***
ORIGIN_HEX358  1.8171440  0.0542081    33.522  < 2e-16 ***
ORIGIN_HEX360  1.1741360  0.0543770    21.593  < 2e-16 ***
ORIGIN_HEX361  1.3576027  0.0542094    25.044  < 2e-16 ***
ORIGIN_HEX362  1.2244892  0.0543485    22.530  < 2e-16 ***
ORIGIN_HEX363  0.6958626  0.0546125    12.742  < 2e-16 ***
ORIGIN_HEX364 -0.6158302  0.0740306    -8.319  < 2e-16 ***
ORIGIN_HEX365  0.6821482  0.0542817    12.567  < 2e-16 ***
ORIGIN_HEX366  1.2201225  0.0547487    22.286  < 2e-16 ***
ORIGIN_HEX367  1.1411144  0.0548869    20.790  < 2e-16 ***
ORIGIN_HEX368  1.4942588  0.0541847    27.577  < 2e-16 ***
ORIGIN_HEX369  2.0677811  0.0540172    38.280  < 2e-16 ***
ORIGIN_HEX370  0.7188407  0.0554090    12.973  < 2e-16 ***
ORIGIN_HEX371  0.2300126  0.0552359     4.164 3.12e-05 ***
ORIGIN_HEX372  0.9104675  0.0545530    16.690  < 2e-16 ***
ORIGIN_HEX373 -1.2597330  0.0753403   -16.721  < 2e-16 ***
ORIGIN_HEX374 -0.2960239  0.0646327    -4.580 4.65e-06 ***
ORIGIN_HEX375  0.6828273  0.0543181    12.571  < 2e-16 ***
ORIGIN_HEX376  0.9083857  0.0546136    16.633  < 2e-16 ***
ORIGIN_HEX377 -0.0999099  0.0553243    -1.806 0.070934 .  
ORIGIN_HEX378  0.7813761  0.0544870    14.341  < 2e-16 ***
ORIGIN_HEX379  1.6049624  0.0541196    29.656  < 2e-16 ***
ORIGIN_HEX380  1.0434770  0.0543769    19.190  < 2e-16 ***
ORIGIN_HEX381  0.2249769  0.0546012     4.120 3.78e-05 ***
ORIGIN_HEX382  1.2854408  0.0542657    23.688  < 2e-16 ***
ORIGIN_HEX383  1.9264901  0.0542243    35.528  < 2e-16 ***
ORIGIN_HEX384 -0.1327029  0.0553412    -2.398 0.016489 *  
ORIGIN_HEX385  2.2250455  0.0539773    41.222  < 2e-16 ***
ORIGIN_HEX386  1.0947102  0.0545209    20.079  < 2e-16 ***
ORIGIN_HEX387  0.5884097  0.0549481    10.708  < 2e-16 ***
ORIGIN_HEX388  1.3002595  0.0543466    23.925  < 2e-16 ***
ORIGIN_HEX389 -0.0297500  0.0566134    -0.525 0.599240    
ORIGIN_HEX390 -3.3854043  0.1159240   -29.204  < 2e-16 ***
ORIGIN_HEX391  1.3758544  0.0544459    25.270  < 2e-16 ***
ORIGIN_HEX392  1.6249279  0.0540705    30.052  < 2e-16 ***
ORIGIN_HEX393  0.9584140  0.0543458    17.635  < 2e-16 ***
ORIGIN_HEX394  3.1559305  0.0539403    58.508  < 2e-16 ***
ORIGIN_HEX395  2.0938594  0.0540212    38.760  < 2e-16 ***
ORIGIN_HEX396  2.0391211  0.0540356    37.737  < 2e-16 ***
ORIGIN_HEX397  1.2080873  0.0544883    22.172  < 2e-16 ***
ORIGIN_HEX398 -0.7653271  0.0622449   -12.295  < 2e-16 ***
ORIGIN_HEX399 -0.9510339  0.0626550   -15.179  < 2e-16 ***
ORIGIN_HEX400  1.7234481  0.0544083    31.676  < 2e-16 ***
ORIGIN_HEX401 -0.6211507  0.0577103   -10.763  < 2e-16 ***
ORIGIN_HEX402  0.3665753  0.0544876     6.728 1.72e-11 ***
ORIGIN_HEX403  0.5660641  0.0546970    10.349  < 2e-16 ***
ORIGIN_HEX404  1.5968688  0.0541526    29.488  < 2e-16 ***
ORIGIN_HEX405  1.7364034  0.0540349    32.135  < 2e-16 ***
ORIGIN_HEX406 -0.5075736  0.0591567    -8.580  < 2e-16 ***
ORIGIN_HEX407  1.9839171  0.0540717    36.690  < 2e-16 ***
ORIGIN_HEX408 -3.0399522  0.1670545   -18.197  < 2e-16 ***
ORIGIN_HEX409 -0.5753611  0.0567686   -10.135  < 2e-16 ***
ORIGIN_HEX410 -0.2813244  0.0552442    -5.092 3.54e-07 ***
ORIGIN_HEX411 -1.2151141  0.0570630   -21.294  < 2e-16 ***
ORIGIN_HEX412  2.1653222  0.0540027    40.097  < 2e-16 ***
ORIGIN_HEX413  0.3031483  0.0550350     5.508 3.62e-08 ***
ORIGIN_HEX415  0.0942339  0.0550199     1.713 0.086763 .  
ORIGIN_HEX416  1.6873176  0.0540711    31.206  < 2e-16 ***
ORIGIN_HEX417  1.5387215  0.0541113    28.436  < 2e-16 ***
ORIGIN_HEX418  1.4956226  0.0541925    27.598  < 2e-16 ***
ORIGIN_HEX419  1.2858544  0.0545812    23.559  < 2e-16 ***
ORIGIN_HEX420  0.5768164  0.0554320    10.406  < 2e-16 ***
ORIGIN_HEX421 -3.5484828  0.2153678   -16.476  < 2e-16 ***
ORIGIN_HEX422 -0.1072006  0.0562997    -1.904 0.056896 .  
ORIGIN_HEX423  0.3891511  0.0553714     7.028 2.09e-12 ***
ORIGIN_HEX424  1.9638135  0.0542200    36.219  < 2e-16 ***
ORIGIN_HEX425 -2.7192682  0.0976123   -27.858  < 2e-16 ***
ORIGIN_HEX426 -1.9548209  0.0629729   -31.042  < 2e-16 ***
ORIGIN_HEX427 -1.5675154  0.0588603   -26.631  < 2e-16 ***
ORIGIN_HEX428  1.7041885  0.0540433    31.534  < 2e-16 ***
ORIGIN_HEX429  0.6435584  0.0544599    11.817  < 2e-16 ***
ORIGIN_HEX430 -3.6437285  0.2557484   -14.247  < 2e-16 ***
ORIGIN_HEX431  1.2793841  0.0543641    23.534  < 2e-16 ***
ORIGIN_HEX432  2.7673433  0.0539668    51.279  < 2e-16 ***
ORIGIN_HEX433  1.3315074  0.0541808    24.575  < 2e-16 ***
ORIGIN_HEX434  2.4943708  0.0540048    46.188  < 2e-16 ***
ORIGIN_HEX435  0.3569232  0.0558675     6.389 1.67e-10 ***
ORIGIN_HEX436  0.5232042  0.0547335     9.559  < 2e-16 ***
ORIGIN_HEX437 -0.1121980  0.0555895    -2.018 0.043557 *  
ORIGIN_HEX438  0.5331057  0.0548116     9.726  < 2e-16 ***
ORIGIN_HEX439 -0.5579350  0.0572034    -9.754  < 2e-16 ***
ORIGIN_HEX440  0.8342024  0.0543346    15.353  < 2e-16 ***
ORIGIN_HEX441  0.4969960  0.0543399     9.146  < 2e-16 ***
ORIGIN_HEX442  0.2997355  0.0544062     5.509 3.60e-08 ***
ORIGIN_HEX443  1.0301778  0.0543495    18.955  < 2e-16 ***
ORIGIN_HEX444 -1.1995533  0.0632354   -18.970  < 2e-16 ***
ORIGIN_HEX445  0.5265164  0.0545310     9.655  < 2e-16 ***
ORIGIN_HEX446  0.5438264  0.0545037     9.978  < 2e-16 ***
ORIGIN_HEX447  2.5087415  0.0539582    46.494  < 2e-16 ***
ORIGIN_HEX448  1.0885654  0.0546055    19.935  < 2e-16 ***
ORIGIN_HEX449  0.5490340  0.0547192    10.034  < 2e-16 ***
ORIGIN_HEX450 -1.6303420  0.0651132   -25.039  < 2e-16 ***
ORIGIN_HEX451 -0.1867237  0.0555033    -3.364 0.000768 ***
ORIGIN_HEX452  1.2684516  0.0545972    23.233  < 2e-16 ***
ORIGIN_HEX453 -0.1334606  0.0564010    -2.366 0.017968 *  
ORIGIN_HEX455 -2.3819096  0.0689882   -34.526  < 2e-16 ***
ORIGIN_HEX456  2.5814661  0.0539480    47.851  < 2e-16 ***
ORIGIN_HEX457  2.2679416  0.0539711    42.021  < 2e-16 ***
ORIGIN_HEX458  1.5970535  0.0541425    29.497  < 2e-16 ***
ORIGIN_HEX459 -1.6756871  0.0604010   -27.743  < 2e-16 ***
ORIGIN_HEX460  1.2933015  0.0542079    23.858  < 2e-16 ***
ORIGIN_HEX461  0.8317864  0.0543681    15.299  < 2e-16 ***
ORIGIN_HEX462  1.2162690  0.0542266    22.429  < 2e-16 ***
ORIGIN_HEX463  1.4396789  0.0542131    26.556  < 2e-16 ***
ORIGIN_HEX464  0.9346550  0.0557091    16.777  < 2e-16 ***
ORIGIN_HEX465  0.0433802  0.0551456     0.787 0.431487    
ORIGIN_HEX466  1.1663129  0.0542396    21.503  < 2e-16 ***
ORIGIN_HEX467  1.0092184  0.0542632    18.599  < 2e-16 ***
ORIGIN_HEX468  1.4415826  0.0541560    26.619  < 2e-16 ***
ORIGIN_HEX469  0.6463047  0.0545366    11.851  < 2e-16 ***
ORIGIN_HEX470  0.3577836  0.0554957     6.447 1.14e-10 ***
ORIGIN_HEX471 -0.2856664  0.0552653    -5.169 2.35e-07 ***
ORIGIN_HEX472  1.5472149  0.0540206    28.641  < 2e-16 ***
ORIGIN_HEX473  0.9196528  0.0541956    16.969  < 2e-16 ***
ORIGIN_HEX474  0.6338854  0.0571773    11.086  < 2e-16 ***
ORIGIN_HEX475  2.0715935  0.0540108    38.355  < 2e-16 ***
ORIGIN_HEX476  1.1730026  0.0542748    21.612  < 2e-16 ***
ORIGIN_HEX477  2.5002137  0.0539568    46.337  < 2e-16 ***
ORIGIN_HEX478  1.8949510  0.0540644    35.050  < 2e-16 ***
ORIGIN_HEX479  1.0023166  0.0542266    18.484  < 2e-16 ***
ORIGIN_HEX480  1.1998655  0.0542200    22.130  < 2e-16 ***
ORIGIN_HEX481  0.9602275  0.0543210    17.677  < 2e-16 ***
ORIGIN_HEX482  1.0187323  0.0541874    18.800  < 2e-16 ***
ORIGIN_HEX483  0.9074964  0.0542504    16.728  < 2e-16 ***
ORIGIN_HEX484  0.8623485  0.0543836    15.857  < 2e-16 ***
ORIGIN_HEX485  0.5687003  0.0544175    10.451  < 2e-16 ***
ORIGIN_HEX486  1.6947123  0.0540736    31.341  < 2e-16 ***
ORIGIN_HEX487  1.9516424  0.0540724    36.093  < 2e-16 ***
ORIGIN_HEX488  2.7715237  0.0539433    51.378  < 2e-16 ***
ORIGIN_HEX489  1.9731824  0.0540016    36.539  < 2e-16 ***
ORIGIN_HEX490  1.4059409  0.0544586    25.817  < 2e-16 ***
ORIGIN_HEX491  2.1722119  0.0540127    40.217  < 2e-16 ***
ORIGIN_HEX492  1.4564058  0.0540832    26.929  < 2e-16 ***
ORIGIN_HEX493 -0.4290115  0.0560367    -7.656 1.92e-14 ***
ORIGIN_HEX494  1.1120903  0.0542058    20.516  < 2e-16 ***
ORIGIN_HEX495  1.5931077  0.0540251    29.488  < 2e-16 ***
ORIGIN_HEX496  2.1473927  0.0539988    39.767  < 2e-16 ***
ORIGIN_HEX497  1.7766505  0.0541651    32.801  < 2e-16 ***
ORIGIN_HEX498 -0.1752863  0.0551833    -3.176 0.001491 ** 
ORIGIN_HEX499  1.1902205  0.0541934    21.962  < 2e-16 ***
ORIGIN_HEX500  1.9426299  0.0542298    35.822  < 2e-16 ***
ORIGIN_HEX501  2.4484861  0.0539682    45.369  < 2e-16 ***
ORIGIN_HEX502  1.7980256  0.0540436    33.270  < 2e-16 ***
ORIGIN_HEX503  1.2486453  0.0544872    22.916  < 2e-16 ***
ORIGIN_HEX504  1.0369700  0.0544240    19.054  < 2e-16 ***
ORIGIN_HEX505  1.5429791  0.0541176    28.512  < 2e-16 ***
ORIGIN_HEX506  1.4959847  0.0540738    27.666  < 2e-16 ***
ORIGIN_HEX507  2.8469697  0.0539322    52.788  < 2e-16 ***
ORIGIN_HEX508  0.5126847  0.0543289     9.437  < 2e-16 ***
ORIGIN_HEX509  1.0027774  0.0541463    18.520  < 2e-16 ***
ORIGIN_HEX510  1.1089776  0.0543743    20.395  < 2e-16 ***
ORIGIN_HEX511  1.2665111  0.0542208    23.358  < 2e-16 ***
ORIGIN_HEX512  0.8817749  0.0544965    16.180  < 2e-16 ***
ORIGIN_HEX513  0.8165638  0.0546224    14.949  < 2e-16 ***
ORIGIN_HEX514  2.0593149  0.0540222    38.120  < 2e-16 ***
ORIGIN_HEX515  2.3918912  0.0539524    44.333  < 2e-16 ***
ORIGIN_HEX516  2.4966152  0.0539692    46.260  < 2e-16 ***
ORIGIN_HEX517  1.2606466  0.0542562    23.235  < 2e-16 ***
ORIGIN_HEX518  3.0133974  0.0539133    55.893  < 2e-16 ***
ORIGIN_HEX519  0.7762722  0.0542380    14.312  < 2e-16 ***
ORIGIN_HEX520  0.3494054  0.0544123     6.421 1.35e-10 ***
ORIGIN_HEX521  3.1037324  0.0539124    57.570  < 2e-16 ***
ORIGIN_HEX522  0.8693452  0.0542933    16.012  < 2e-16 ***
ORIGIN_HEX523  1.9051467  0.0541681    35.171  < 2e-16 ***
ORIGIN_HEX524  0.5177267  0.0545600     9.489  < 2e-16 ***
ORIGIN_HEX525  1.9481755  0.0541831    35.955  < 2e-16 ***
ORIGIN_HEX526  1.5942155  0.0540818    29.478  < 2e-16 ***
ORIGIN_HEX527  2.4858492  0.0539456    46.081  < 2e-16 ***
ORIGIN_HEX528  1.8617003  0.0540759    34.428  < 2e-16 ***
ORIGIN_HEX529  1.4986793  0.0541004    27.702  < 2e-16 ***
ORIGIN_HEX530  1.2595467  0.0540852    23.288  < 2e-16 ***
ORIGIN_HEX531  1.1250708  0.0545187    20.636  < 2e-16 ***
ORIGIN_HEX532  1.4701635  0.0540462    27.202  < 2e-16 ***
ORIGIN_HEX533  1.4623829  0.0540621    27.050  < 2e-16 ***
ORIGIN_HEX534 -3.6389615  0.1032524   -35.243  < 2e-16 ***
ORIGIN_HEX536  1.8760853  0.0542197    34.602  < 2e-16 ***
ORIGIN_HEX537  2.2916461  0.0539808    42.453  < 2e-16 ***
ORIGIN_HEX538  1.3413458  0.0542303    24.734  < 2e-16 ***
ORIGIN_HEX539  0.7935098  0.0544570    14.571  < 2e-16 ***
ORIGIN_HEX540  0.9959408  0.0543929    18.310  < 2e-16 ***
ORIGIN_HEX541  0.7276307  0.0542545    13.411  < 2e-16 ***
ORIGIN_HEX542  0.5290738  0.0544414     9.718  < 2e-16 ***
ORIGIN_HEX543  1.2509968  0.0541195    23.115  < 2e-16 ***
ORIGIN_HEX544  1.6230094  0.0544355    29.815  < 2e-16 ***
ORIGIN_HEX545  0.4824413  0.0550650     8.761  < 2e-16 ***
ORIGIN_HEX546 -1.2981126  0.0615196   -21.101  < 2e-16 ***
ORIGIN_HEX547  1.2260598  0.0657169    18.657  < 2e-16 ***
ORIGIN_HEX548  1.1354720  0.0550921    20.610  < 2e-16 ***
ORIGIN_HEX549  1.5846472  0.0541752    29.250  < 2e-16 ***
ORIGIN_HEX550  1.8549807  0.0540258    34.335  < 2e-16 ***
ORIGIN_HEX551  1.7066821  0.0540317    31.587  < 2e-16 ***
ORIGIN_HEX552  0.9672554  0.0542157    17.841  < 2e-16 ***
ORIGIN_HEX553  1.9968107  0.0542611    36.800  < 2e-16 ***
ORIGIN_HEX554  0.3081377  0.0551044     5.592 2.25e-08 ***
ORIGIN_HEX555  0.0215785  0.0597883     0.361 0.718163    
ORIGIN_HEX556  1.0656496  0.0544230    19.581  < 2e-16 ***
ORIGIN_HEX557  0.2454067  0.0558793     4.392 1.12e-05 ***
ORIGIN_HEX558  0.5181032  0.0739238     7.009 2.41e-12 ***
ORIGIN_HEX559  1.4244799  0.0547956    25.996  < 2e-16 ***
ORIGIN_HEX560  0.4007888  0.0567635     7.061 1.66e-12 ***
ORIGIN_HEX561  1.9715720  0.0540006    36.510  < 2e-16 ***
ORIGIN_HEX562  2.0713285  0.0539940    38.362  < 2e-16 ***
ORIGIN_HEX563  1.2262357  0.0542692    22.595  < 2e-16 ***
ORIGIN_HEX564 -0.9225192  0.0573685   -16.081  < 2e-16 ***
ORIGIN_HEX565  0.3038971  0.0545483     5.571 2.53e-08 ***
ORIGIN_HEX566  0.2880001  0.0546587     5.269 1.37e-07 ***
ORIGIN_HEX567  0.9406782  0.0543180    17.318  < 2e-16 ***
ORIGIN_HEX568 -0.5516477  0.0563606    -9.788  < 2e-16 ***
ORIGIN_HEX569 -0.7759178  0.0586885   -13.221  < 2e-16 ***
ORIGIN_HEX570  0.5800211  0.0555466    10.442  < 2e-16 ***
ORIGIN_HEX571 -2.1849695  0.2076723   -10.521  < 2e-16 ***
ORIGIN_HEX572  0.4891397  0.0559027     8.750  < 2e-16 ***
ORIGIN_HEX573  1.3633474  0.0541172    25.192  < 2e-16 ***
ORIGIN_HEX574  1.7932727  0.0540079    33.204  < 2e-16 ***
ORIGIN_HEX575 -0.4398635  0.0599317    -7.339 2.15e-13 ***
ORIGIN_HEX576 -0.2353662  0.0554002    -4.248 2.15e-05 ***
ORIGIN_HEX577  1.1147843  0.0543317    20.518  < 2e-16 ***
ORIGIN_HEX578  1.4258316  0.0541271    26.342  < 2e-16 ***
ORIGIN_HEX579 -1.2630723  0.0618733   -20.414  < 2e-16 ***
ORIGIN_HEX580  0.5709000  0.0556462    10.259  < 2e-16 ***
ORIGIN_HEX581  1.4245012  0.0553227    25.749  < 2e-16 ***
ORIGIN_HEX582  1.3170126  0.0541142    24.338  < 2e-16 ***
ORIGIN_HEX583  1.2532735  0.0542211    23.114  < 2e-16 ***
ORIGIN_HEX584  1.9175801  0.0540248    35.494  < 2e-16 ***
ORIGIN_HEX585  0.1866799  0.0546476     3.416 0.000635 ***
ORIGIN_HEX586  1.1817542  0.0541141    21.838  < 2e-16 ***
ORIGIN_HEX587  0.2571022  0.0555332     4.630 3.66e-06 ***
ORIGIN_HEX588  1.5531992  0.0540518    28.735  < 2e-16 ***
ORIGIN_HEX589  1.2306564  0.0541782    22.715  < 2e-16 ***
ORIGIN_HEX590  1.6752693  0.0541272    30.951  < 2e-16 ***
ORIGIN_HEX591 -0.4805896  0.0611308    -7.862 3.79e-15 ***
ORIGIN_HEX592  1.3433079  0.0551410    24.361  < 2e-16 ***
ORIGIN_HEX593  1.7153165  0.0540279    31.749  < 2e-16 ***
ORIGIN_HEX594  2.3515355  0.0540044    43.543  < 2e-16 ***
ORIGIN_HEX595  1.7067962  0.0540938    31.553  < 2e-16 ***
ORIGIN_HEX596  3.3511340  0.0539091    62.163  < 2e-16 ***
ORIGIN_HEX597  0.0235209  0.0546180     0.431 0.666727    
ORIGIN_HEX598  2.0815677  0.0539767    38.564  < 2e-16 ***
ORIGIN_HEX599 -0.2372495  0.0551412    -4.303 1.69e-05 ***
ORIGIN_HEX600 -0.0421622  0.0548478    -0.769 0.442064    
ORIGIN_HEX601 -0.8480446  0.0578783   -14.652  < 2e-16 ***
ORIGIN_HEX602 -0.6697885  0.0600371   -11.156  < 2e-16 ***
ORIGIN_HEX603  1.4162987  0.0540954    26.182  < 2e-16 ***
ORIGIN_HEX604  0.5466374  0.0550286     9.934  < 2e-16 ***
ORIGIN_HEX605  1.2620514  0.0542097    23.281  < 2e-16 ***
ORIGIN_HEX606  1.0506117  0.0545086    19.274  < 2e-16 ***
ORIGIN_HEX607  0.8804998  0.0541740    16.253  < 2e-16 ***
ORIGIN_HEX608  0.7871909  0.0541848    14.528  < 2e-16 ***
ORIGIN_HEX609  1.6029020  0.0540153    29.675  < 2e-16 ***
ORIGIN_HEX610  0.9036601  0.0542962    16.643  < 2e-16 ***
ORIGIN_HEX611 -1.8734458  0.0810430   -23.117  < 2e-16 ***
ORIGIN_HEX612  1.9818314  0.0539979    36.702  < 2e-16 ***
ORIGIN_HEX613  1.7662810  0.0540404    32.684  < 2e-16 ***
ORIGIN_HEX614  1.1587980  0.0551253    21.021  < 2e-16 ***
ORIGIN_HEX615  0.8919313  0.0542354    16.446  < 2e-16 ***
ORIGIN_HEX616  1.2903755  0.0540572    23.871  < 2e-16 ***
ORIGIN_HEX617  1.4267212  0.0544867    26.185  < 2e-16 ***
ORIGIN_HEX618  0.4032026  0.0547233     7.368 1.73e-13 ***
ORIGIN_HEX619  0.8554411  0.0552397    15.486  < 2e-16 ***
ORIGIN_HEX620  1.1712947  0.0542014    21.610  < 2e-16 ***
ORIGIN_HEX621  0.9908038  0.0542467    18.265  < 2e-16 ***
ORIGIN_HEX622  1.5647875  0.0542550    28.841  < 2e-16 ***
ORIGIN_HEX623  0.9682889  0.0542463    17.850  < 2e-16 ***
ORIGIN_HEX624 -0.4102225  0.0554043    -7.404 1.32e-13 ***
ORIGIN_HEX625 -0.3534166  0.0551231    -6.411 1.44e-10 ***
ORIGIN_HEX626  1.0163502  0.0541158    18.781  < 2e-16 ***
ORIGIN_HEX627 -0.3263927  0.0553475    -5.897 3.70e-09 ***
ORIGIN_HEX628  1.1308363  0.0543662    20.800  < 2e-16 ***
ORIGIN_HEX629  0.7940477  0.0542632    14.633  < 2e-16 ***
ORIGIN_HEX630  1.6576411  0.0540834    30.650  < 2e-16 ***
ORIGIN_HEX631  1.8636241  0.0540489    34.480  < 2e-16 ***
ORIGIN_HEX632  1.5542350  0.0541050    28.726  < 2e-16 ***
ORIGIN_HEX633  2.1801872  0.0539815    40.388  < 2e-16 ***
ORIGIN_HEX634  1.2725911  0.0540433    23.548  < 2e-16 ***
ORIGIN_HEX635 -1.1150125  0.0561806   -19.847  < 2e-16 ***
ORIGIN_HEX636  0.8857903  0.0542697    16.322  < 2e-16 ***
ORIGIN_HEX638  1.3407869  0.0541890    24.743  < 2e-16 ***
ORIGIN_HEX639  2.2897568  0.0539726    42.424  < 2e-16 ***
ORIGIN_HEX640  1.8109424  0.0540386    33.512  < 2e-16 ***
ORIGIN_HEX641  0.2323038  0.0550574     4.219 2.45e-05 ***
ORIGIN_HEX642  1.3334769  0.0541295    24.635  < 2e-16 ***
ORIGIN_HEX643  1.1736132  0.0540667    21.707  < 2e-16 ***
ORIGIN_HEX644  0.3890157  0.0542911     7.165 7.76e-13 ***
ORIGIN_HEX645  0.9721927  0.0541251    17.962  < 2e-16 ***
ORIGIN_HEX646  1.0144990  0.0551029    18.411  < 2e-16 ***
ORIGIN_HEX647  0.5946901  0.0545585    10.900  < 2e-16 ***
ORIGIN_HEX648  1.9556178  0.0540012    36.214  < 2e-16 ***
ORIGIN_HEX649  1.5145147  0.0540775    28.006  < 2e-16 ***
ORIGIN_HEX650  1.2533590  0.0542808    23.090  < 2e-16 ***
ORIGIN_HEX651  1.6614731  0.0540425    30.744  < 2e-16 ***
ORIGIN_HEX652  2.5328029  0.0539315    46.963  < 2e-16 ***
ORIGIN_HEX653  1.7046983  0.0539879    31.576  < 2e-16 ***
ORIGIN_HEX654  0.7590416  0.0541824    14.009  < 2e-16 ***
ORIGIN_HEX655 -2.3320123  0.0643196   -36.257  < 2e-16 ***
ORIGIN_HEX657  0.9359905  0.0542865    17.242  < 2e-16 ***
ORIGIN_HEX658  1.0876120  0.0546236    19.911  < 2e-16 ***
ORIGIN_HEX659  1.8036758  0.0541098    33.334  < 2e-16 ***
ORIGIN_HEX660  2.4377883  0.0546337    44.621  < 2e-16 ***
ORIGIN_HEX661  0.8647365  0.0541658    15.965  < 2e-16 ***
ORIGIN_HEX662  0.0743805  0.0544457     1.366 0.171894    
ORIGIN_HEX663  2.5827640  0.0539298    47.891  < 2e-16 ***
ORIGIN_HEX664  0.6383398  0.0542491    11.767  < 2e-16 ***
ORIGIN_HEX665 -0.0444679  0.0568371    -0.782 0.433995    
ORIGIN_HEX666  2.0428892  0.0540549    37.793  < 2e-16 ***
ORIGIN_HEX667  1.1642894  0.0542707    21.453  < 2e-16 ***
ORIGIN_HEX668  1.3956551  0.0543438    25.682  < 2e-16 ***
ORIGIN_HEX669  1.7016484  0.0541330    31.435  < 2e-16 ***
ORIGIN_HEX670  3.1569263  0.0544551    57.973  < 2e-16 ***
ORIGIN_HEX671 -0.8919988  0.0583233   -15.294  < 2e-16 ***
ORIGIN_HEX672  0.9106754  0.0541997    16.802  < 2e-16 ***
ORIGIN_HEX673  0.7363735  0.0541646    13.595  < 2e-16 ***
ORIGIN_HEX674  1.0042399  0.0540963    18.564  < 2e-16 ***
ORIGIN_HEX675 -0.2816270  0.0549478    -5.125 2.97e-07 ***
ORIGIN_HEX676 -1.4762389  0.0631857   -23.364  < 2e-16 ***
ORIGIN_HEX677  1.0308022  0.0543149    18.978  < 2e-16 ***
ORIGIN_HEX678  2.4889294  0.0539545    46.130  < 2e-16 ***
ORIGIN_HEX679  2.4397587  0.0539674    45.208  < 2e-16 ***
ORIGIN_HEX680  0.2379031  0.0546069     4.357 1.32e-05 ***
ORIGIN_HEX681  0.3958446  0.0542262     7.300 2.88e-13 ***
ORIGIN_HEX682  2.2848738  0.0539500    42.352  < 2e-16 ***
ORIGIN_HEX683 -1.6296765  0.0628115   -25.945  < 2e-16 ***
ORIGIN_HEX684  2.4631655  0.0539936    45.620  < 2e-16 ***
ORIGIN_HEX685  0.8844537  0.0543096    16.285  < 2e-16 ***
ORIGIN_HEX686  1.0147510  0.0542171    18.716  < 2e-16 ***
ORIGIN_HEX687  0.9616715  0.0543567    17.692  < 2e-16 ***
ORIGIN_HEX688  0.8367489  0.0566519    14.770  < 2e-16 ***
ORIGIN_HEX689  0.1469250  0.0546212     2.690 0.007148 ** 
ORIGIN_HEX690  2.3336208  0.0539557    43.251  < 2e-16 ***
ORIGIN_HEX691 -0.4179951  0.0562456    -7.432 1.07e-13 ***
ORIGIN_HEX692  1.8668524  0.0556823    33.527  < 2e-16 ***
ORIGIN_HEX693  1.1149880  0.0541974    20.573  < 2e-16 ***
ORIGIN_HEX694  1.9252292  0.0540407    35.626  < 2e-16 ***
ORIGIN_HEX695  1.6666248  0.0541108    30.800  < 2e-16 ***
ORIGIN_HEX696  1.8209057  0.0547209    33.276  < 2e-16 ***
ORIGIN_HEX697  0.8945694  0.0556275    16.081  < 2e-16 ***
ORIGIN_HEX698  0.5314385  0.0542698     9.793  < 2e-16 ***
ORIGIN_HEX700  0.9614495  0.0545746    17.617  < 2e-16 ***
ORIGIN_HEX701 -0.5894914  0.0566952   -10.398  < 2e-16 ***
ORIGIN_HEX702  1.1165322  0.0567016    19.691  < 2e-16 ***
ORIGIN_HEX703  1.6128973  0.0541046    29.811  < 2e-16 ***
ORIGIN_HEX704  1.2879081  0.0554688    23.219  < 2e-16 ***
ORIGIN_HEX705  0.6944217  0.0542452    12.802  < 2e-16 ***
ORIGIN_HEX706  0.1976439  0.0561867     3.518 0.000435 ***
ORIGIN_HEX707  1.2431947  0.0542092    22.933  < 2e-16 ***
ORIGIN_HEX708  0.0380684  0.0548177     0.694 0.487397    
ORIGIN_HEX709  1.3033402  0.0542763    24.013  < 2e-16 ***
ORIGIN_HEX710 -1.0589971  0.0624066   -16.969  < 2e-16 ***
ORIGIN_HEX711  0.4504306  0.0584350     7.708 1.28e-14 ***
ORIGIN_HEX712 -0.2900228  0.0557174    -5.205 1.94e-07 ***
ORIGIN_HEX714  0.6334662  0.0545212    11.619  < 2e-16 ***
ORIGIN_HEX715  1.4306109  0.0542881    26.352  < 2e-16 ***
ORIGIN_HEX716  1.3678883  0.0541712    25.251  < 2e-16 ***
ORIGIN_HEX717  1.6262794  0.0551005    29.515  < 2e-16 ***
ORIGIN_HEX718 -0.2742676  0.0560021    -4.897 9.71e-07 ***
ORIGIN_HEX719  1.0082177  0.0544154    18.528  < 2e-16 ***
ORIGIN_HEX720  1.9496583  0.0540250    36.088  < 2e-16 ***
ORIGIN_HEX721  1.1767005  0.0542839    21.677  < 2e-16 ***
ORIGIN_HEX722  0.3502329  0.0571464     6.129 8.86e-10 ***
ORIGIN_HEX724  0.6362266  0.0546393    11.644  < 2e-16 ***
ORIGIN_HEX725  3.3251287  0.0539122    61.677  < 2e-16 ***
ORIGIN_HEX726  0.3831040  0.0548550     6.984 2.87e-12 ***
ORIGIN_HEX727  1.3489478  0.0542093    24.884  < 2e-16 ***
ORIGIN_HEX728  1.1138511  0.0563737    19.758  < 2e-16 ***
ORIGIN_HEX729  0.6753298  0.0547380    12.338  < 2e-16 ***
ORIGIN_HEX730  0.2352329  0.0545698     4.311 1.63e-05 ***
ORIGIN_HEX731  0.8576355  0.0542198    15.818  < 2e-16 ***
ORIGIN_HEX732  1.4190728  0.0542933    26.137  < 2e-16 ***
ORIGIN_HEX733  1.3679675  0.0541800    25.249  < 2e-16 ***
ORIGIN_HEX734  1.2667406  0.0542419    23.354  < 2e-16 ***
ORIGIN_HEX735  1.4163134  0.0542039    26.129  < 2e-16 ***
ORIGIN_HEX736  1.2703619  0.0542081    23.435  < 2e-16 ***
ORIGIN_HEX737  1.0947255  0.0541219    20.227  < 2e-16 ***
ORIGIN_HEX738  1.7822146  0.0540497    32.974  < 2e-16 ***
ORIGIN_HEX739  1.9016215  0.0540558    35.179  < 2e-16 ***
ORIGIN_HEX740  1.3538157  0.0541591    24.997  < 2e-16 ***
ORIGIN_HEX741  1.8594080  0.0540808    34.382  < 2e-16 ***
ORIGIN_HEX742 -1.2163981  0.0598812   -20.314  < 2e-16 ***
ORIGIN_HEX743  1.2035515  0.0544192    22.116  < 2e-16 ***
ORIGIN_HEX744  1.3932858  0.0541035    25.752  < 2e-16 ***
ORIGIN_HEX745  2.0010119  0.0540044    37.053  < 2e-16 ***
ORIGIN_HEX746  0.8422461  0.0542204    15.534  < 2e-16 ***
ORIGIN_HEX747 -0.5763992  0.0561222   -10.270  < 2e-16 ***
ORIGIN_HEX748  1.9178289  0.0540651    35.473  < 2e-16 ***
ORIGIN_HEX749  0.3776034  0.0548843     6.880 5.99e-12 ***
ORIGIN_HEX750  0.9744238  0.0542265    17.970  < 2e-16 ***
ORIGIN_HEX751  0.1400666  0.0595725     2.351 0.018713 *  
ORIGIN_HEX752  2.1096904  0.0539724    39.088  < 2e-16 ***
ORIGIN_HEX753  0.5077205  0.0544862     9.318  < 2e-16 ***
ORIGIN_HEX754  0.7936353  0.0543274    14.608  < 2e-16 ***
ORIGIN_HEX755 -0.4498133  0.0579721    -7.759 8.55e-15 ***
ORIGIN_HEX756  0.9862052  0.0543276    18.153  < 2e-16 ***
ORIGIN_HEX757  0.3402150  0.0545849     6.233 4.58e-10 ***
ORIGIN_HEX758  0.0075076  0.0581373     0.129 0.897250    
ORIGIN_HEX759  3.5898051  0.0539085    66.591  < 2e-16 ***
ORIGIN_HEX760  0.5389202  0.0549509     9.807  < 2e-16 ***
ORIGIN_HEX761  0.9616455  0.0543505    17.693  < 2e-16 ***
ORIGIN_HEX762  0.5522441  0.0547488    10.087  < 2e-16 ***
ORIGIN_HEX763  2.3158121  0.0540072    42.880  < 2e-16 ***
ORIGIN_HEX764  1.8050027  0.0540700    33.383  < 2e-16 ***
ORIGIN_HEX765  0.8787163  0.0542008    16.212  < 2e-16 ***
ORIGIN_HEX766  0.1809147  0.0547933     3.302 0.000961 ***
ORIGIN_HEX767  3.1448005  0.0539300    58.313  < 2e-16 ***
ORIGIN_HEX768 -1.3627426  0.0708190   -19.243  < 2e-16 ***
ORIGIN_HEX769  0.0993480  0.0758211     1.310 0.190096    
ORIGIN_HEX770 -0.0595369  0.0552857    -1.077 0.281527    
ORIGIN_HEX771  1.8164800  0.0540712    33.594  < 2e-16 ***
ORIGIN_HEX772  2.1135723  0.0540485    39.105  < 2e-16 ***
ORIGIN_HEX773  1.1691353  0.0541226    21.602  < 2e-16 ***
ORIGIN_HEX774 -0.0899512  0.0551196    -1.632 0.102695    
ORIGIN_HEX775 -1.7407720  0.0684952   -25.415  < 2e-16 ***
ORIGIN_HEX776 -0.1091029  0.0562282    -1.940 0.052336 .  
ORIGIN_HEX777  0.8817606  0.0544710    16.188  < 2e-16 ***
ORIGIN_HEX778  1.5172911  0.0540720    28.061  < 2e-16 ***
ORIGIN_HEX779  1.3161798  0.0542783    24.249  < 2e-16 ***
ORIGIN_HEX780  1.1003543  0.0542189    20.295  < 2e-16 ***
ORIGIN_HEX781  1.0427983  0.0550622    18.939  < 2e-16 ***
ORIGIN_HEX782  0.4998765  0.0549172     9.102  < 2e-16 ***
ORIGIN_HEX783  1.2426528  0.0542817    22.893  < 2e-16 ***
ORIGIN_HEX784  2.2962151  0.0539743    42.543  < 2e-16 ***
ORIGIN_HEX785  1.5509766  0.0541262    28.655  < 2e-16 ***
ORIGIN_HEX786  0.7237506  0.0546515    13.243  < 2e-16 ***
ORIGIN_HEX787  1.7274545  0.0541717    31.888  < 2e-16 ***
ORIGIN_HEX788  0.5811003  0.0547232    10.619  < 2e-16 ***
ORIGIN_HEX789  0.6363683  0.0543293    11.713  < 2e-16 ***
ORIGIN_HEX790  0.9488388  0.0543830    17.447  < 2e-16 ***
ORIGIN_HEX791  2.1116602  0.0542526    38.923  < 2e-16 ***
ORIGIN_HEX792  0.6319172  0.0548761    11.515  < 2e-16 ***
ORIGIN_HEX793  1.3026944  0.0542461    24.015  < 2e-16 ***
ORIGIN_HEX794  1.4384936  0.0541478    26.566  < 2e-16 ***
ORIGIN_HEX795 -0.3534023  0.0628780    -5.620 1.90e-08 ***
ORIGIN_HEX796  1.7264292  0.0562538    30.690  < 2e-16 ***
ORIGIN_HEX797  1.7603621  0.0544818    32.311  < 2e-16 ***
ORIGIN_HEX798  2.0737491  0.0545521    38.014  < 2e-16 ***
ORIGIN_HEX799  1.1406663  0.0544395    20.953  < 2e-16 ***
ORIGIN_HEX800  0.9055267  0.0545595    16.597  < 2e-16 ***
ORIGIN_HEX801  1.6684891  0.0555142    30.055  < 2e-16 ***
ORIGIN_HEX802  2.3190750  0.0549924    42.171  < 2e-16 ***
ORIGIN_HEX803  0.9596436  0.0551370    17.405  < 2e-16 ***
ORIGIN_HEX804 -0.7464113  0.0581045   -12.846  < 2e-16 ***
ORIGIN_HEX805  1.2790482  0.0557265    22.952  < 2e-16 ***
ORIGIN_HEX806  1.1863378  0.0564242    21.025  < 2e-16 ***
ORIGIN_HEX807 -0.3526594  0.0583942    -6.039 1.55e-09 ***
ORIGIN_HEX808  1.8944464  0.0541961    34.955  < 2e-16 ***
ORIGIN_HEX809  1.9244597  0.0555222    34.661  < 2e-16 ***
ORIGIN_HEX810  0.8788912  0.0582875    15.079  < 2e-16 ***
ORIGIN_HEX811  0.3808781  0.0572786     6.650 2.94e-11 ***
ORIGIN_HEX812  0.6761898  0.0552332    12.242  < 2e-16 ***
ORIGIN_HEX813 -0.8197960  0.0728906   -11.247  < 2e-16 ***
ORIGIN_HEX814  2.4007082  0.0542930    44.218  < 2e-16 ***
ORIGIN_HEX815  0.1185399  0.0591769     2.003 0.045162 *  
ORIGIN_HEX816  0.9634898  0.0550840    17.491  < 2e-16 ***
ORIGIN_HEX817  0.9583000  0.0551755    17.368  < 2e-16 ***
ORIGIN_HEX818  2.1952517  0.0542343    40.477  < 2e-16 ***
ORIGIN_HEX819  2.0284259  0.0545563    37.180  < 2e-16 ***
ORIGIN_HEX820  2.0789044  0.0572741    36.297  < 2e-16 ***
ORIGIN_HEX821  3.0373857  0.0540993    56.145  < 2e-16 ***
ORIGIN_HEX822  0.8751260  0.0554397    15.785  < 2e-16 ***
ORIGIN_HEX823  2.0379001  0.0543727    37.480  < 2e-16 ***
ORIGIN_HEX824 -0.0146057  0.0605944    -0.241 0.809524    
ORIGIN_HEX825  0.5399484  0.0592151     9.118  < 2e-16 ***
ORIGIN_HEX826  2.6860053  0.0543303    49.438  < 2e-16 ***
ORIGIN_HEX827  3.2474888  0.0541609    59.960  < 2e-16 ***
ORIGIN_HEX828  1.4556216  0.0557722    26.099  < 2e-16 ***
ORIGIN_HEX829  2.5860186  0.0555659    46.540  < 2e-16 ***
ORIGIN_HEX830  2.6912638  0.0545337    49.350  < 2e-16 ***
ORIGIN_HEX831  1.7077490  0.0601664    28.384  < 2e-16 ***
DESTIN_HEX2   -0.6931436  0.1149077    -6.032 1.62e-09 ***
DESTIN_HEX3   -0.0031759  0.0960276    -0.033 0.973616    
DESTIN_HEX4   -1.5214829  0.1221358   -12.457  < 2e-16 ***
DESTIN_HEX5   -0.6867929  0.0912111    -7.530 5.09e-14 ***
DESTIN_HEX6    0.2304863  0.0920459     2.504 0.012279 *  
DESTIN_HEX7   -0.6151609  0.1062040    -5.792 6.94e-09 ***
DESTIN_HEX8   -4.3335805  0.2154756   -20.112  < 2e-16 ***
DESTIN_HEX9   -0.4449630  0.0894742    -4.973 6.59e-07 ***
DESTIN_HEX10  -2.0716120  0.1019734   -20.315  < 2e-16 ***
DESTIN_HEX11  -6.9568076  0.5840876   -11.911  < 2e-16 ***
DESTIN_HEX12  -1.9386380  0.1233564   -15.716  < 2e-16 ***
DESTIN_HEX13  -4.5066952  0.2814726   -16.011  < 2e-16 ***
DESTIN_HEX14   1.9560484  0.0880556    22.214  < 2e-16 ***
DESTIN_HEX15  -3.1537826  0.1238650   -25.461  < 2e-16 ***
DESTIN_HEX16   2.0678657  0.0887367    23.303  < 2e-16 ***
DESTIN_HEX17  -6.6311785  0.4178626   -15.869  < 2e-16 ***
DESTIN_HEX18  -0.8046113  0.1123855    -7.159 8.10e-13 ***
DESTIN_HEX19  -1.1372232  0.0938202   -12.121  < 2e-16 ***
DESTIN_HEX20  -1.0588796  0.0977980   -10.827  < 2e-16 ***
DESTIN_HEX21  -1.7108923  0.0973173   -17.581  < 2e-16 ***
DESTIN_HEX22   2.1611391  0.0878582    24.598  < 2e-16 ***
DESTIN_HEX23  -0.8708340  0.0963666    -9.037  < 2e-16 ***
DESTIN_HEX24  -0.9156919  0.0996108    -9.193  < 2e-16 ***
DESTIN_HEX25  -0.9374162  0.1033454    -9.071  < 2e-16 ***
DESTIN_HEX26  -0.7848025  0.0961900    -8.159 3.38e-16 ***
DESTIN_HEX27  -1.8050522  0.1008671   -17.895  < 2e-16 ***
DESTIN_HEX28  -1.2066752  0.0926530   -13.024  < 2e-16 ***
DESTIN_HEX29  -0.7238597  0.0987694    -7.329 2.32e-13 ***
DESTIN_HEX30  -1.2395925  0.1419056    -8.735  < 2e-16 ***
DESTIN_HEX31  -1.2287657  0.0991603   -12.392  < 2e-16 ***
DESTIN_HEX32   1.5334800  0.0879433    17.437  < 2e-16 ***
DESTIN_HEX33  -1.2986326  0.0940981   -13.801  < 2e-16 ***
DESTIN_HEX34  -4.4466673  0.2353872   -18.891  < 2e-16 ***
DESTIN_HEX35  -1.5041404  0.0946925   -15.884  < 2e-16 ***
DESTIN_HEX36  -2.7172748  0.1350400   -20.122  < 2e-16 ***
DESTIN_HEX37  -1.3868866  0.1144451   -12.118  < 2e-16 ***
DESTIN_HEX38   2.0058316  0.0879994    22.794  < 2e-16 ***
DESTIN_HEX39   0.0398311  0.0900124     0.443 0.658122    
DESTIN_HEX40  -3.4930904  0.1747364   -19.991  < 2e-16 ***
DESTIN_HEX41  -1.8291152  0.0989398   -18.487  < 2e-16 ***
DESTIN_HEX42  -2.2987276  0.1404117   -16.371  < 2e-16 ***
DESTIN_HEX43  -2.8738075  0.1019141   -28.198  < 2e-16 ***
DESTIN_HEX44  -0.7104156  0.0919022    -7.730 1.07e-14 ***
DESTIN_HEX45  -0.5569371  0.0929570    -5.991 2.08e-09 ***
DESTIN_HEX46  -1.5064735  0.0979018   -15.388  < 2e-16 ***
DESTIN_HEX47  -1.5766458  0.0949361   -16.607  < 2e-16 ***
DESTIN_HEX48  -1.1400733  0.0969154   -11.764  < 2e-16 ***
DESTIN_HEX49  -5.0754358  1.0038545    -5.056 4.28e-07 ***
DESTIN_HEX50  -2.5791141  0.1003177   -25.709  < 2e-16 ***
DESTIN_HEX51   1.7618901  0.0881925    19.978  < 2e-16 ***
DESTIN_HEX52  -3.0587607  0.1060219   -28.850  < 2e-16 ***
DESTIN_HEX53  -1.2368928  0.1244021    -9.943  < 2e-16 ***
DESTIN_HEX54  -0.8718591  0.0993483    -8.776  < 2e-16 ***
DESTIN_HEX55  -0.4874087  0.0918389    -5.307 1.11e-07 ***
DESTIN_HEX56  -2.0400676  0.0946517   -21.553  < 2e-16 ***
DESTIN_HEX57  -0.4194940  0.0926853    -4.526 6.01e-06 ***
DESTIN_HEX58  -1.3804821  0.0956496   -14.433  < 2e-16 ***
DESTIN_HEX59  -0.6911711  0.0912363    -7.576 3.57e-14 ***
DESTIN_HEX60  -1.7230887  0.0919904   -18.731  < 2e-16 ***
DESTIN_HEX61  -1.7109348  0.0944943   -18.106  < 2e-16 ***
DESTIN_HEX62  -1.2988552  0.0955912   -13.588  < 2e-16 ***
DESTIN_HEX63   0.2910747  0.0959407     3.034 0.002414 ** 
DESTIN_HEX64  -2.5484039  0.1012491   -25.170  < 2e-16 ***
DESTIN_HEX65   2.7810249  0.0878118    31.670  < 2e-16 ***
DESTIN_HEX66   0.3422451  0.0895331     3.823 0.000132 ***
DESTIN_HEX67   1.5990023  0.0884806    18.072  < 2e-16 ***
DESTIN_HEX68  -2.8210968  0.1224783   -23.033  < 2e-16 ***
DESTIN_HEX69  -2.2074288  0.0944347   -23.375  < 2e-16 ***
DESTIN_HEX70  -0.8488244  0.0901827    -9.412  < 2e-16 ***
DESTIN_HEX71  -1.2001661  0.0910569   -13.180  < 2e-16 ***
DESTIN_HEX72   0.8928010  0.0894992     9.976  < 2e-16 ***
DESTIN_HEX73  -1.1626966  0.1052206   -11.050  < 2e-16 ***
DESTIN_HEX74  -2.4136619  0.1028795   -23.461  < 2e-16 ***
DESTIN_HEX75  -1.2537880  0.0922664   -13.589  < 2e-16 ***
DESTIN_HEX76   1.7994187  0.0880790    20.430  < 2e-16 ***
DESTIN_HEX77   0.0425011  0.0888127     0.479 0.632260    
DESTIN_HEX79  -0.5843715  0.0919076    -6.358 2.04e-10 ***
DESTIN_HEX80  -0.2030584  0.0893932    -2.272 0.023116 *  
DESTIN_HEX81   2.2122873  0.0879282    25.160  < 2e-16 ***
DESTIN_HEX82   0.7098987  0.0887174     8.002 1.23e-15 ***
DESTIN_HEX84  -1.7425691  0.1064302   -16.373  < 2e-16 ***
DESTIN_HEX85  -1.8931805  0.1302793   -14.532  < 2e-16 ***
DESTIN_HEX86   0.6031936  0.0886762     6.802 1.03e-11 ***
DESTIN_HEX87   0.8913258  0.0882202    10.103  < 2e-16 ***
DESTIN_HEX88  -4.0832788  0.2222432   -18.373  < 2e-16 ***
DESTIN_HEX89  -1.6115777  0.1076210   -14.975  < 2e-16 ***
DESTIN_HEX90  -1.6686921  0.0949697   -17.571  < 2e-16 ***
DESTIN_HEX91  -1.4292436  0.0930236   -15.364  < 2e-16 ***
DESTIN_HEX92   0.0841042  0.0884675     0.951 0.341768    
DESTIN_HEX93   2.5835880  0.0878662    29.404  < 2e-16 ***
DESTIN_HEX94  -1.0823013  0.0924233   -11.710  < 2e-16 ***
DESTIN_HEX95  -0.9296775  0.0981809    -9.469  < 2e-16 ***
DESTIN_HEX96  -1.5441160  0.1194592   -12.926  < 2e-16 ***
DESTIN_HEX97  -2.3762989  0.1091645   -21.768  < 2e-16 ***
DESTIN_HEX98  -0.4227185  0.0901057    -4.691 2.71e-06 ***
DESTIN_HEX99  -1.2334866  0.0903476   -13.653  < 2e-16 ***
DESTIN_HEX100  2.4433974  0.0878560    27.811  < 2e-16 ***
DESTIN_HEX101  2.8852682  0.0878789    32.832  < 2e-16 ***
DESTIN_HEX102  0.0581031  0.0907707     0.640 0.522102    
DESTIN_HEX103 -2.4237523  0.1776811   -13.641  < 2e-16 ***
DESTIN_HEX104 -1.2341627  0.1317105    -9.370  < 2e-16 ***
DESTIN_HEX105 -2.4078723  1.0038639    -2.399 0.016458 *  
DESTIN_HEX106 -2.5059003  0.1062755   -23.579  < 2e-16 ***
DESTIN_HEX107 -1.0695921  0.0972366   -11.000  < 2e-16 ***
DESTIN_HEX108 -1.3813463  0.0899349   -15.359  < 2e-16 ***
DESTIN_HEX109  1.8537528  0.0878980    21.090  < 2e-16 ***
DESTIN_HEX110  1.4449038  0.0881830    16.385  < 2e-16 ***
DESTIN_HEX111 -0.8448234  0.1050930    -8.039 9.07e-16 ***
DESTIN_HEX112  1.2991437  0.0937497    13.858  < 2e-16 ***
DESTIN_HEX113 -4.2612198  0.4560215    -9.344  < 2e-16 ***
DESTIN_HEX114 -4.1315624  0.2813960   -14.682  < 2e-16 ***
DESTIN_HEX115 -1.5391829  0.0936347   -16.438  < 2e-16 ***
DESTIN_HEX116 -1.2059829  0.0946757   -12.738  < 2e-16 ***
DESTIN_HEX117  3.6381703  0.0878304    41.423  < 2e-16 ***
DESTIN_HEX118  1.8849355  0.0879435    21.433  < 2e-16 ***
DESTIN_HEX119 -2.2112689  0.1130341   -19.563  < 2e-16 ***
DESTIN_HEX120 -2.0855125  0.1255369   -16.613  < 2e-16 ***
DESTIN_HEX121 -1.8167255  0.2515509    -7.222 5.12e-13 ***
DESTIN_HEX122  0.2662948  0.1030238     2.585 0.009744 ** 
DESTIN_HEX123 -1.6687752  0.1119355   -14.908  < 2e-16 ***
DESTIN_HEX124 -1.1490180  0.0917599   -12.522  < 2e-16 ***
DESTIN_HEX125 -1.5856067  0.0905606   -17.509  < 2e-16 ***
DESTIN_HEX126  1.4665469  0.0879224    16.680  < 2e-16 ***
DESTIN_HEX127 -1.6588446  0.1112154   -14.916  < 2e-16 ***
DESTIN_HEX128 -1.4717895  0.1327251   -11.089  < 2e-16 ***
DESTIN_HEX129 -2.2154827  0.1705574   -12.990  < 2e-16 ***
DESTIN_HEX130 -2.1177488  0.0967916   -21.879  < 2e-16 ***
DESTIN_HEX131 -1.5266395  0.0930095   -16.414  < 2e-16 ***
DESTIN_HEX132 -0.6781618  0.0887618    -7.640 2.17e-14 ***
DESTIN_HEX133  2.3430453  0.0878937    26.658  < 2e-16 ***
DESTIN_HEX134 -1.8874795  0.1048981   -17.993  < 2e-16 ***
DESTIN_HEX135 -2.0500354  0.0962885   -21.291  < 2e-16 ***
DESTIN_HEX136  2.0724241  0.0878959    23.578  < 2e-16 ***
DESTIN_HEX137 -0.5303064  0.0902230    -5.878 4.16e-09 ***
DESTIN_HEX138  1.0955043  0.0880869    12.437  < 2e-16 ***
DESTIN_HEX139  1.4862518  0.0879771    16.894  < 2e-16 ***
DESTIN_HEX140  2.6535867  0.0878729    30.198  < 2e-16 ***
DESTIN_HEX141  2.8069890  0.0880654    31.874  < 2e-16 ***
DESTIN_HEX142 -0.0931520  0.0911172    -1.022 0.306624    
DESTIN_HEX143 -1.6510843  0.0931107   -17.732  < 2e-16 ***
DESTIN_HEX144  2.3879423  0.0878939    27.168  < 2e-16 ***
DESTIN_HEX145  2.6369158  0.0878867    30.004  < 2e-16 ***
DESTIN_HEX146  1.4909445  0.0882636    16.892  < 2e-16 ***
DESTIN_HEX147 -0.8263644  0.0905786    -9.123  < 2e-16 ***
DESTIN_HEX148  1.8676154  0.0879766    21.229  < 2e-16 ***
DESTIN_HEX149  0.7997643  0.0881964     9.068  < 2e-16 ***
DESTIN_HEX150  2.4513512  0.0878864    27.892  < 2e-16 ***
DESTIN_HEX151 -0.5885050  0.0926670    -6.351 2.14e-10 ***
DESTIN_HEX152 -0.4649100  0.0893891    -5.201 1.98e-07 ***
DESTIN_HEX154 -1.3126048  0.0968348   -13.555  < 2e-16 ***
DESTIN_HEX156  0.7604731  0.0884743     8.595  < 2e-16 ***
DESTIN_HEX157 -0.2754523  0.0889883    -3.095 0.001966 ** 
DESTIN_HEX158  1.7648912  0.0879601    20.065  < 2e-16 ***
DESTIN_HEX160 -0.7264631  0.0923199    -7.869 3.58e-15 ***
DESTIN_HEX161  1.1550862  0.0881594    13.102  < 2e-16 ***
DESTIN_HEX162 -1.6009054  0.0922837   -17.348  < 2e-16 ***
DESTIN_HEX163  2.5135370  0.0878824    28.601  < 2e-16 ***
DESTIN_HEX164  0.9792248  0.0884654    11.069  < 2e-16 ***
DESTIN_HEX165  2.9066257  0.0879384    33.053  < 2e-16 ***
DESTIN_HEX166 -1.4073002  0.1153745   -12.198  < 2e-16 ***
DESTIN_HEX167 -0.5961595  0.0894380    -6.666 2.64e-11 ***
DESTIN_HEX168  1.2849449  0.0879625    14.608  < 2e-16 ***
DESTIN_HEX169  1.0747930  0.0880857    12.202  < 2e-16 ***
DESTIN_HEX170  1.5650759  0.0882330    17.738  < 2e-16 ***
DESTIN_HEX171  2.5282447  0.0879986    28.731  < 2e-16 ***
DESTIN_HEX172  0.4956005  0.0887923     5.582 2.38e-08 ***
DESTIN_HEX173 -2.7393306  0.1117622   -24.510  < 2e-16 ***
DESTIN_HEX174  2.1442246  0.0879331    24.385  < 2e-16 ***
DESTIN_HEX175  2.4705431  0.0878736    28.115  < 2e-16 ***
DESTIN_HEX176  1.7113988  0.0879445    19.460  < 2e-16 ***
DESTIN_HEX177  2.8964752  0.0879252    32.943  < 2e-16 ***
DESTIN_HEX178  0.6543143  0.0889447     7.356 1.89e-13 ***
DESTIN_HEX179  2.6730207  0.0878964    30.411  < 2e-16 ***
DESTIN_HEX180  1.9821336  0.0880217    22.519  < 2e-16 ***
DESTIN_HEX181  0.8425240  0.0905875     9.301  < 2e-16 ***
DESTIN_HEX182 -1.7642912  0.0983594   -17.937  < 2e-16 ***
DESTIN_HEX183 -0.0236566  0.0883759    -0.268 0.788944    
DESTIN_HEX184  1.7335462  0.0879229    19.717  < 2e-16 ***
DESTIN_HEX185  2.1022283  0.0879068    23.914  < 2e-16 ***
DESTIN_HEX186  2.1436380  0.0879634    24.370  < 2e-16 ***
DESTIN_HEX187  2.2550355  0.0880020    25.625  < 2e-16 ***
DESTIN_HEX188  3.3294776  0.0878730    37.890  < 2e-16 ***
DESTIN_HEX189  2.7029543  0.0880093    30.712  < 2e-16 ***
DESTIN_HEX190 -0.5253846  0.0949649    -5.532 3.16e-08 ***
DESTIN_HEX191 -2.0845937  0.1172281   -17.782  < 2e-16 ***
DESTIN_HEX192  1.1844740  0.0880152    13.458  < 2e-16 ***
DESTIN_HEX193  1.2970765  0.0880177    14.737  < 2e-16 ***
DESTIN_HEX194  1.4803674  0.0879674    16.829  < 2e-16 ***
DESTIN_HEX195  0.7811705  0.0881837     8.858  < 2e-16 ***
DESTIN_HEX196  1.8100557  0.0879869    20.572  < 2e-16 ***
DESTIN_HEX197  2.2142183  0.0879197    25.185  < 2e-16 ***
DESTIN_HEX198  1.7253951  0.0880490    19.596  < 2e-16 ***
DESTIN_HEX199  3.6823508  0.0879378    41.874  < 2e-16 ***
DESTIN_HEX200  0.2525505  0.0918464     2.750 0.005965 ** 
DESTIN_HEX201 -0.9947189  0.0972505   -10.228  < 2e-16 ***
DESTIN_HEX202  0.5870269  0.0902780     6.502 7.90e-11 ***
DESTIN_HEX203 -0.5603551  0.0913412    -6.135 8.53e-10 ***
DESTIN_HEX204  0.0838698  0.0886963     0.946 0.344361    
DESTIN_HEX205 -0.0232959  0.0887940    -0.262 0.793045    
DESTIN_HEX206  1.7593319  0.0880666    19.977  < 2e-16 ***
DESTIN_HEX207  2.8148900  0.0878680    32.035  < 2e-16 ***
DESTIN_HEX208  2.6617219  0.0880181    30.241  < 2e-16 ***
DESTIN_HEX209  0.3815665  0.0885365     4.310 1.63e-05 ***
DESTIN_HEX210  1.1459785  0.0882422    12.987  < 2e-16 ***
DESTIN_HEX211  0.7115570  0.0883281     8.056 7.89e-16 ***
DESTIN_HEX212 -1.9105547  0.1118781   -17.077  < 2e-16 ***
DESTIN_HEX213 -0.5537588  0.0927718    -5.969 2.39e-09 ***
DESTIN_HEX214 -0.6169708  0.0942773    -6.544 5.98e-11 ***
DESTIN_HEX215 -0.4703063  0.0890202    -5.283 1.27e-07 ***
DESTIN_HEX216  1.1034168  0.0880693    12.529  < 2e-16 ***
DESTIN_HEX217 -1.2657880  0.0906535   -13.963  < 2e-16 ***
DESTIN_HEX218  2.1860654  0.0878977    24.871  < 2e-16 ***
DESTIN_HEX219  1.0262039  0.0884962    11.596  < 2e-16 ***
DESTIN_HEX220  2.3557257  0.0879083    26.798  < 2e-16 ***
DESTIN_HEX221  0.3336024  0.0885965     3.765 0.000166 ***
DESTIN_HEX222  0.1797950  0.0890294     2.020 0.043435 *  
DESTIN_HEX223 -0.8362467  0.0923399    -9.056  < 2e-16 ***
DESTIN_HEX224 -0.5713462  0.0906939    -6.300 2.98e-10 ***
DESTIN_HEX225 -0.7156123  0.0953043    -7.509 5.97e-14 ***
DESTIN_HEX226  0.6086033  0.0892842     6.816 9.33e-12 ***
DESTIN_HEX227  0.9136869  0.0879990    10.383  < 2e-16 ***
DESTIN_HEX228 -1.7822132  0.0912648   -19.528  < 2e-16 ***
DESTIN_HEX229  0.6766162  0.0881816     7.673 1.68e-14 ***
DESTIN_HEX230  1.7258739  0.0879429    19.625  < 2e-16 ***
DESTIN_HEX231  2.1010080  0.0879350    23.893  < 2e-16 ***
DESTIN_HEX232  1.9153529  0.0881111    21.738  < 2e-16 ***
DESTIN_HEX233 -2.4372803  0.1054065   -23.123  < 2e-16 ***
DESTIN_HEX234 -0.4442826  0.0898462    -4.945 7.62e-07 ***
DESTIN_HEX235 -0.0274619  0.0888612    -0.309 0.757290    
DESTIN_HEX236  1.4626406  0.0879351    16.633  < 2e-16 ***
DESTIN_HEX237  1.8592576  0.0878926    21.154  < 2e-16 ***
DESTIN_HEX238 -1.1898787  0.0903695   -13.167  < 2e-16 ***
DESTIN_HEX239 -0.2676435  0.0904930    -2.958 0.003100 ** 
DESTIN_HEX240  1.6380204  0.0880382    18.606  < 2e-16 ***
DESTIN_HEX241 -1.5437357  0.0927871   -16.637  < 2e-16 ***
DESTIN_HEX242  3.3333804  0.0878633    37.938  < 2e-16 ***
DESTIN_HEX243 -5.4670478  0.4176104   -13.091  < 2e-16 ***
DESTIN_HEX244  3.1978009  0.0879245    36.370  < 2e-16 ***
DESTIN_HEX245 -1.5174500  0.0975900   -15.549  < 2e-16 ***
DESTIN_HEX246  0.1020013  0.0884902     1.153 0.249040    
DESTIN_HEX247  1.8746444  0.0879545    21.314  < 2e-16 ***
DESTIN_HEX248  3.0095201  0.0878535    34.256  < 2e-16 ***
DESTIN_HEX249 -0.7648325  0.0904409    -8.457  < 2e-16 ***
DESTIN_HEX250  0.6611049  0.0882764     7.489 6.94e-14 ***
DESTIN_HEX251 -0.8505438  0.0899075    -9.460  < 2e-16 ***
DESTIN_HEX252  1.8450467  0.0879829    20.971  < 2e-16 ***
DESTIN_HEX253  0.1495044  0.0885203     1.689 0.091233 .  
DESTIN_HEX254  2.5281357  0.0879748    28.737  < 2e-16 ***
DESTIN_HEX255 -0.5849912  0.0926756    -6.312 2.75e-10 ***
DESTIN_HEX256 -0.8982007  0.0911405    -9.855  < 2e-16 ***
DESTIN_HEX257  3.8128299  0.0879310    43.362  < 2e-16 ***
DESTIN_HEX258  0.5861347  0.0880859     6.654 2.85e-11 ***
DESTIN_HEX259  1.5486648  0.0879045    17.618  < 2e-16 ***
DESTIN_HEX260  1.4481463  0.0879359    16.468  < 2e-16 ***
DESTIN_HEX262  1.2155630  0.0881322    13.792  < 2e-16 ***
DESTIN_HEX263  0.6600299  0.0883147     7.474 7.80e-14 ***
DESTIN_HEX264 -0.5705617  0.0895669    -6.370 1.89e-10 ***
DESTIN_HEX265  2.3664760  0.0879113    26.919  < 2e-16 ***
DESTIN_HEX266  2.5806785  0.0880451    29.311  < 2e-16 ***
DESTIN_HEX267 -0.2094433  0.0891565    -2.349 0.018816 *  
DESTIN_HEX269  0.7363001  0.0881364     8.354  < 2e-16 ***
DESTIN_HEX270  0.9132457  0.0880176    10.376  < 2e-16 ***
DESTIN_HEX271  0.1745425  0.0881927     1.979 0.047804 *  
DESTIN_HEX272 -0.0415394  0.0883809    -0.470 0.638352    
DESTIN_HEX273  1.1140783  0.0880515    12.653  < 2e-16 ***
DESTIN_HEX274  0.7636898  0.0882720     8.652  < 2e-16 ***
DESTIN_HEX275  0.3669057  0.0901980     4.068 4.75e-05 ***
DESTIN_HEX276  3.0842155  0.0878939    35.090  < 2e-16 ***
DESTIN_HEX277  2.5129437  0.0880145    28.551  < 2e-16 ***
DESTIN_HEX278 -0.7730188  0.0927974    -8.330  < 2e-16 ***
DESTIN_HEX279  2.5433154  0.0879228    28.927  < 2e-16 ***
DESTIN_HEX280  3.5207814  0.0878825    40.062  < 2e-16 ***
DESTIN_HEX281 -0.8951825  0.0911557    -9.820  < 2e-16 ***
DESTIN_HEX282  0.2315316  0.0887078     2.610 0.009053 ** 
DESTIN_HEX283 -0.3428433  0.0886342    -3.868 0.000110 ***
DESTIN_HEX284 -0.0611690  0.0884282    -0.692 0.489103    
DESTIN_HEX285  0.0227121  0.0883882     0.257 0.797211    
DESTIN_HEX286  1.8252686  0.0879502    20.753  < 2e-16 ***
DESTIN_HEX287  1.3367154  0.0884937    15.105  < 2e-16 ***
DESTIN_HEX288  1.9706336  0.0880372    22.384  < 2e-16 ***
DESTIN_HEX289  1.4098970  0.0882764    15.971  < 2e-16 ***
DESTIN_HEX290  2.1970797  0.0879608    24.978  < 2e-16 ***
DESTIN_HEX291 -1.1293058  0.0933839   -12.093  < 2e-16 ***
DESTIN_HEX292 -0.0844379  0.0884550    -0.955 0.339787    
DESTIN_HEX293  1.0268411  0.0880326    11.664  < 2e-16 ***
DESTIN_HEX294  1.2432979  0.0880044    14.128  < 2e-16 ***
DESTIN_HEX295  0.8909620  0.0881016    10.113  < 2e-16 ***
DESTIN_HEX296  0.9646053  0.0880214    10.959  < 2e-16 ***
DESTIN_HEX297 -0.6499599  0.0923536    -7.038 1.95e-12 ***
DESTIN_HEX298  2.2069002  0.0879286    25.099  < 2e-16 ***
DESTIN_HEX299  1.9844720  0.0879863    22.554  < 2e-16 ***
DESTIN_HEX300  1.3860605  0.0879930    15.752  < 2e-16 ***
DESTIN_HEX301  0.2820230  0.0881652     3.199 0.001380 ** 
DESTIN_HEX302  1.2764398  0.0879831    14.508  < 2e-16 ***
DESTIN_HEX303  0.2762202  0.0882914     3.129 0.001757 ** 
DESTIN_HEX304 -4.8156438  0.2727999   -17.653  < 2e-16 ***
DESTIN_HEX305  1.5668836  0.0880052    17.804  < 2e-16 ***
DESTIN_HEX306  1.9303769  0.0880930    21.913  < 2e-16 ***
DESTIN_HEX307  0.6822018  0.0881368     7.740 9.92e-15 ***
DESTIN_HEX308 -0.5316591  0.0887636    -5.990 2.10e-09 ***
DESTIN_HEX309 -0.5080804  0.0884811    -5.742 9.34e-09 ***
DESTIN_HEX310  0.1581768  0.0883207     1.791 0.073304 .  
DESTIN_HEX311  1.7396466  0.0879560    19.779  < 2e-16 ***
DESTIN_HEX312 -3.0790259  0.2909416   -10.583  < 2e-16 ***
DESTIN_HEX313  1.2640776  0.0880614    14.355  < 2e-16 ***
DESTIN_HEX314 -0.0434398  0.0886348    -0.490 0.624065    
DESTIN_HEX315 -1.9639346  0.0942607   -20.835  < 2e-16 ***
DESTIN_HEX316 -0.8722755  0.0904283    -9.646  < 2e-16 ***
DESTIN_HEX317 -0.4240861  0.0915162    -4.634 3.59e-06 ***
DESTIN_HEX318  1.8958078  0.0879053    21.566  < 2e-16 ***
DESTIN_HEX319 -0.3961535  0.0895521    -4.424 9.70e-06 ***
DESTIN_HEX320  0.8061370  0.0881116     9.149  < 2e-16 ***
DESTIN_HEX321  0.8971125  0.0900513     9.962  < 2e-16 ***
DESTIN_HEX322 -3.8572959  0.1760662   -21.908  < 2e-16 ***
DESTIN_HEX323  0.3679339  0.0891039     4.129 3.64e-05 ***
DESTIN_HEX324  3.7017165  0.0878672    42.129  < 2e-16 ***
DESTIN_HEX325  0.5478415  0.0885290     6.188 6.08e-10 ***
DESTIN_HEX326  0.4741535  0.0882110     5.375 7.65e-08 ***
DESTIN_HEX327 -0.6687310  0.0891040    -7.505 6.14e-14 ***
DESTIN_HEX328  0.3376735  0.0884935     3.816 0.000136 ***
DESTIN_HEX329  0.3577549  0.0882862     4.052 5.07e-05 ***
DESTIN_HEX330  0.2064962  0.0887355     2.327 0.019960 *  
DESTIN_HEX331  1.9482861  0.0879712    22.147  < 2e-16 ***
DESTIN_HEX332  1.9864921  0.0879339    22.591  < 2e-16 ***
DESTIN_HEX333  1.2437197  0.0883954    14.070  < 2e-16 ***
DESTIN_HEX334 -0.7726718  0.0891784    -8.664  < 2e-16 ***
DESTIN_HEX335 -1.5416991  0.0922017   -16.721  < 2e-16 ***
DESTIN_HEX336  1.0651497  0.0879830    12.106  < 2e-16 ***
DESTIN_HEX337  0.7394756  0.0881562     8.388  < 2e-16 ***
DESTIN_HEX338 -2.3352221  0.1174756   -19.878  < 2e-16 ***
DESTIN_HEX339  0.0278111  0.0900916     0.309 0.757551    
DESTIN_HEX340  2.2666466  0.0879129    25.783  < 2e-16 ***
DESTIN_HEX341  0.9705154  0.0881714    11.007  < 2e-16 ***
DESTIN_HEX343 -0.8004897  0.0887190    -9.023  < 2e-16 ***
DESTIN_HEX344  0.8994791  0.0880186    10.219  < 2e-16 ***
DESTIN_HEX345  1.8887959  0.0879098    21.486  < 2e-16 ***
DESTIN_HEX346  2.7365173  0.0879345    31.120  < 2e-16 ***
DESTIN_HEX347  3.0011123  0.0879026    34.141  < 2e-16 ***
DESTIN_HEX348 -0.0340302  0.0888502    -0.383 0.701715    
DESTIN_HEX349 -4.1175827  0.2580213   -15.958  < 2e-16 ***
DESTIN_HEX350  0.3091786  0.0881896     3.506 0.000455 ***
DESTIN_HEX351  0.8242141  0.0880041     9.366  < 2e-16 ***
DESTIN_HEX352  1.5477292  0.0879234    17.603  < 2e-16 ***
DESTIN_HEX353  0.8465333  0.0880484     9.614  < 2e-16 ***
DESTIN_HEX354  0.0495250  0.0885642     0.559 0.576026    
DESTIN_HEX355 -0.5763181  0.0935369    -6.161 7.21e-10 ***
DESTIN_HEX356  1.6562601  0.0880634    18.808  < 2e-16 ***
DESTIN_HEX357  1.6075217  0.0880098    18.265  < 2e-16 ***
DESTIN_HEX358 -0.0752164  0.0891618    -0.844 0.398896    
DESTIN_HEX360  0.6030682  0.0880645     6.848 7.49e-12 ***
DESTIN_HEX361  0.7840606  0.0880237     8.907  < 2e-16 ***
DESTIN_HEX362  0.6368001  0.0881766     7.222 5.13e-13 ***
DESTIN_HEX363  0.4185727  0.0882696     4.742 2.12e-06 ***
DESTIN_HEX364 -4.4397116  0.3448068   -12.876  < 2e-16 ***
DESTIN_HEX365  2.1895610  0.0879576    24.893  < 2e-16 ***
DESTIN_HEX366 -1.9589052  0.1018225   -19.238  < 2e-16 ***
DESTIN_HEX367 -1.2423989  0.0928268   -13.384  < 2e-16 ***
DESTIN_HEX368  1.3028007  0.0879461    14.814  < 2e-16 ***
DESTIN_HEX369  1.2266787  0.0879412    13.949  < 2e-16 ***
DESTIN_HEX370  0.7835522  0.0884219     8.862  < 2e-16 ***
DESTIN_HEX371 -0.3737552  0.0888183    -4.208 2.58e-05 ***
DESTIN_HEX372  0.6157159  0.0881892     6.982 2.92e-12 ***
DESTIN_HEX373 -2.3154939  0.1109963   -20.861  < 2e-16 ***
DESTIN_HEX374 -2.2175180  0.1439915   -15.400  < 2e-16 ***
DESTIN_HEX375 -0.3791574  0.0892881    -4.246 2.17e-05 ***
DESTIN_HEX376  0.2802852  0.0888132     3.156 0.001600 ** 
DESTIN_HEX377 -0.5371712  0.0885783    -6.064 1.32e-09 ***
DESTIN_HEX378  0.5427949  0.0880566     6.164 7.09e-10 ***
DESTIN_HEX379  0.9679272  0.0879749    11.002  < 2e-16 ***
DESTIN_HEX380  0.4716136  0.0882048     5.347 8.95e-08 ***
DESTIN_HEX381  1.0911846  0.0882113    12.370  < 2e-16 ***
DESTIN_HEX382  1.7228108  0.0880880    19.558  < 2e-16 ***
DESTIN_HEX383  0.3274899  0.0889372     3.682 0.000231 ***
DESTIN_HEX384 -0.6582987  0.0886334    -7.427 1.11e-13 ***
DESTIN_HEX385  0.9379089  0.0879602    10.663  < 2e-16 ***
DESTIN_HEX386 -0.2086430  0.0885793    -2.355 0.018501 *  
DESTIN_HEX387 -0.2009080  0.0886978    -2.265 0.023508 *  
DESTIN_HEX388  0.4238751  0.0883029     4.800 1.58e-06 ***
DESTIN_HEX389 -0.9349120  0.0909857   -10.275  < 2e-16 ***
DESTIN_HEX390 -3.8360678  0.1544498   -24.837  < 2e-16 ***
DESTIN_HEX391  0.7064756  0.0885407     7.979 1.47e-15 ***
DESTIN_HEX392  2.1703495  0.0879496    24.677  < 2e-16 ***
DESTIN_HEX393  0.1306293  0.0886569     1.473 0.140636    
DESTIN_HEX394  2.4875122  0.0878815    28.305  < 2e-16 ***
DESTIN_HEX395  1.2243399  0.0879475    13.921  < 2e-16 ***
DESTIN_HEX396  1.6372310  0.0879091    18.624  < 2e-16 ***
DESTIN_HEX397 -0.9342093  0.0895187   -10.436  < 2e-16 ***
DESTIN_HEX398 -1.8658788  0.1007198   -18.525  < 2e-16 ***
DESTIN_HEX399 -3.7443793  0.1483565   -25.239  < 2e-16 ***
DESTIN_HEX400  2.0200268  0.0880541    22.941  < 2e-16 ***
DESTIN_HEX401 -0.3599157  0.0898676    -4.005 6.20e-05 ***
DESTIN_HEX402  1.0687706  0.0881690    12.122  < 2e-16 ***
DESTIN_HEX403  1.8008603  0.0880299    20.457  < 2e-16 ***
DESTIN_HEX404  1.5682132  0.0879238    17.836  < 2e-16 ***
DESTIN_HEX405  1.0747596  0.0879320    12.223  < 2e-16 ***
DESTIN_HEX406 -1.1625529  0.0945806   -12.292  < 2e-16 ***
DESTIN_HEX407  0.9117490  0.0880428    10.356  < 2e-16 ***
DESTIN_HEX408 -3.4573427  0.1791873   -19.295  < 2e-16 ***
DESTIN_HEX409 -1.5876806  0.0951305   -16.690  < 2e-16 ***
DESTIN_HEX410  0.3301668  0.0885202     3.730 0.000192 ***
DESTIN_HEX411 -0.3178060  0.0892188    -3.562 0.000368 ***
DESTIN_HEX412  2.5594956  0.0879281    29.109  < 2e-16 ***
DESTIN_HEX413  0.7950811  0.0884992     8.984  < 2e-16 ***
DESTIN_HEX414  0.5893947  0.0904757     6.514 7.30e-11 ***
DESTIN_HEX415 -0.8696571  0.0888282    -9.790  < 2e-16 ***
DESTIN_HEX416  1.2364328  0.0879318    14.061  < 2e-16 ***
DESTIN_HEX417  1.0168879  0.0879599    11.561  < 2e-16 ***
DESTIN_HEX418 -0.0916495  0.0883062    -1.038 0.299335    
DESTIN_HEX419 -0.0622166  0.0885066    -0.703 0.482081    
DESTIN_HEX420  1.4298391  0.0882153    16.209  < 2e-16 ***
DESTIN_HEX421 -3.5263411  0.2579689   -13.670  < 2e-16 ***
DESTIN_HEX422 -0.2355504  0.0892377    -2.640 0.008301 ** 
DESTIN_HEX423  0.1883583  0.0888075     2.121 0.033924 *  
DESTIN_HEX424  0.0660939  0.0892598     0.740 0.459017    
DESTIN_HEX425 -1.3613958  0.1056239   -12.889  < 2e-16 ***
DESTIN_HEX426 -1.2282403  0.0926230   -13.261  < 2e-16 ***
DESTIN_HEX427 -3.3684026  0.1152143   -29.236  < 2e-16 ***
DESTIN_HEX428  2.4141228  0.0879221    27.458  < 2e-16 ***
DESTIN_HEX429  1.4044631  0.0881091    15.940  < 2e-16 ***
DESTIN_HEX430 -1.8853021  0.1331379   -14.161  < 2e-16 ***
DESTIN_HEX431  0.6716521  0.0881168     7.622 2.49e-14 ***
DESTIN_HEX432  2.0377412  0.0878922    23.185  < 2e-16 ***
DESTIN_HEX433  0.6912903  0.0880065     7.855 4.00e-15 ***
DESTIN_HEX434  0.8294036  0.0880504     9.420  < 2e-16 ***
DESTIN_HEX435 -0.4872275  0.0891434    -5.466 4.61e-08 ***
DESTIN_HEX436  0.5529779  0.0882422     6.267 3.69e-10 ***
DESTIN_HEX437 -0.5758040  0.0893545    -6.444 1.16e-10 ***
DESTIN_HEX438  0.5932564  0.0883173     6.717 1.85e-11 ***
DESTIN_HEX439 -0.2931676  0.0901766    -3.251 0.001150 ** 
DESTIN_HEX440  2.5974968  0.0879103    29.547  < 2e-16 ***
DESTIN_HEX441  1.3515868  0.0880113    15.357  < 2e-16 ***
DESTIN_HEX442  1.2415795  0.0880555    14.100  < 2e-16 ***
DESTIN_HEX443  2.4842145  0.0879575    28.243  < 2e-16 ***
DESTIN_HEX444 -1.9299923  0.1056858   -18.262  < 2e-16 ***
DESTIN_HEX445 -0.1342030  0.0882325    -1.521 0.128256    
DESTIN_HEX446 -0.1791398  0.0882153    -2.031 0.042284 *  
DESTIN_HEX447  1.2764558  0.0879190    14.519  < 2e-16 ***
DESTIN_HEX448  0.0873081  0.0882486     0.989 0.322496    
DESTIN_HEX449 -0.8923136  0.0894632    -9.974  < 2e-16 ***
DESTIN_HEX450 -1.6986344  0.0939133   -18.087  < 2e-16 ***
DESTIN_HEX451 -0.2063059  0.0886043    -2.328 0.019891 *  
DESTIN_HEX452  1.4106792  0.0881095    16.011  < 2e-16 ***
DESTIN_HEX453  0.4782152  0.0888418     5.383 7.33e-08 ***
DESTIN_HEX455 -0.6707424  0.0921803    -7.276 3.43e-13 ***
DESTIN_HEX456  2.3612405  0.0879160    26.858  < 2e-16 ***
DESTIN_HEX457  2.8177471  0.0878941    32.058  < 2e-16 ***
DESTIN_HEX458  2.0141497  0.0880305    22.880  < 2e-16 ***
DESTIN_HEX459 -0.0380114  0.0894872    -0.425 0.671005    
DESTIN_HEX460  0.6077920  0.0880352     6.904 5.06e-12 ***
DESTIN_HEX461  0.0509946  0.0881189     0.579 0.562790    
DESTIN_HEX462  0.2073864  0.0881047     2.354 0.018580 *  
DESTIN_HEX463 -0.0221162  0.0882047    -0.251 0.802017    
DESTIN_HEX464  0.4106141  0.0903419     4.545 5.49e-06 ***
DESTIN_HEX465 -1.4440924  0.0900809   -16.031  < 2e-16 ***
DESTIN_HEX466  0.4681889  0.0881507     5.311 1.09e-07 ***
DESTIN_HEX467  0.8574709  0.0880655     9.737  < 2e-16 ***
DESTIN_HEX468  1.5975643  0.0879725    18.160  < 2e-16 ***
DESTIN_HEX469  1.5477322  0.0879810    17.592  < 2e-16 ***
DESTIN_HEX470  0.3249797  0.0886461     3.666 0.000246 ***
DESTIN_HEX471  1.5154594  0.0881049    17.201  < 2e-16 ***
DESTIN_HEX472  1.9357713  0.0879237    22.016  < 2e-16 ***
DESTIN_HEX473  1.5958469  0.0879937    18.136  < 2e-16 ***
DESTIN_HEX474  2.2768433  0.0888472    25.626  < 2e-16 ***
DESTIN_HEX475  1.3369642  0.0879156    15.207  < 2e-16 ***
DESTIN_HEX476  0.0573096  0.0881573     0.650 0.515638    
DESTIN_HEX477  1.2589465  0.0879225    14.319  < 2e-16 ***
DESTIN_HEX478  0.8770672  0.0879933     9.967  < 2e-16 ***
DESTIN_HEX479  0.3251623  0.0881028     3.691 0.000224 ***
DESTIN_HEX480  0.0540216  0.0883043     0.612 0.540693    
DESTIN_HEX481  0.6400107  0.0881381     7.261 3.83e-13 ***
DESTIN_HEX482  0.4945379  0.0881365     5.611 2.01e-08 ***
DESTIN_HEX483  1.3094059  0.0879898    14.881  < 2e-16 ***
DESTIN_HEX484  0.8380798  0.0881209     9.511  < 2e-16 ***
DESTIN_HEX485  1.7593703  0.0879937    19.994  < 2e-16 ***
DESTIN_HEX486  1.5589143  0.0880346    17.708  < 2e-16 ***
DESTIN_HEX487  0.7731121  0.0880506     8.780  < 2e-16 ***
DESTIN_HEX488  1.6250076  0.0878981    18.487  < 2e-16 ***
DESTIN_HEX489  1.2710633  0.0879121    14.458  < 2e-16 ***
DESTIN_HEX490 -0.9761085  0.0897489   -10.876  < 2e-16 ***
DESTIN_HEX491  1.1352358  0.0879642    12.906  < 2e-16 ***
DESTIN_HEX492  1.2316156  0.0879362    14.006  < 2e-16 ***
DESTIN_HEX493 -1.7422344  0.0912385   -19.095  < 2e-16 ***
DESTIN_HEX494  1.5725693  0.0879373    17.883  < 2e-16 ***
DESTIN_HEX495  1.9556679  0.0878937    22.250  < 2e-16 ***
DESTIN_HEX496  2.4354780  0.0878890    27.711  < 2e-16 ***
DESTIN_HEX497 -0.7163338  0.0897584    -7.981 1.46e-15 ***
DESTIN_HEX498  0.9852001  0.0884202    11.142  < 2e-16 ***
DESTIN_HEX499  1.9998773  0.0879825    22.730  < 2e-16 ***
DESTIN_HEX500  1.1675669  0.0884492    13.200  < 2e-16 ***
DESTIN_HEX501  0.6213566  0.0880124     7.060 1.67e-12 ***
DESTIN_HEX502  0.7821266  0.0879747     8.890  < 2e-16 ***
DESTIN_HEX503  0.0596591  0.0882154     0.676 0.498857    
DESTIN_HEX504 -0.0715229  0.0883387    -0.810 0.418145    
DESTIN_HEX505  0.9758399  0.0879942    11.090  < 2e-16 ***
DESTIN_HEX506  1.7304299  0.0879324    19.679  < 2e-16 ***
DESTIN_HEX507  2.1594816  0.0878935    24.569  < 2e-16 ***
DESTIN_HEX508  0.9316428  0.0879980    10.587  < 2e-16 ***
DESTIN_HEX509  1.2075521  0.0879576    13.729  < 2e-16 ***
DESTIN_HEX510 -0.4901156  0.0889899    -5.508 3.64e-08 ***
DESTIN_HEX511  2.4914422  0.0879543    28.327  < 2e-16 ***
DESTIN_HEX512  1.6399737  0.0881558    18.603  < 2e-16 ***
DESTIN_HEX513 -0.3772844  0.0886254    -4.257 2.07e-05 ***
DESTIN_HEX514  0.3814140  0.0880669     4.331 1.48e-05 ***
DESTIN_HEX515  1.3084177  0.0879037    14.885  < 2e-16 ***
DESTIN_HEX516  1.6531137  0.0878976    18.807  < 2e-16 ***
DESTIN_HEX517  0.8904663  0.0879969    10.119  < 2e-16 ***
DESTIN_HEX518  2.4637955  0.0878652    28.041  < 2e-16 ***
DESTIN_HEX519  0.5057624  0.0880846     5.742 9.37e-09 ***
DESTIN_HEX520  0.4255643  0.0880910     4.831 1.36e-06 ***
DESTIN_HEX521  2.6207519  0.0878699    29.825  < 2e-16 ***
DESTIN_HEX522 -0.1137050  0.0885971    -1.283 0.199354    
DESTIN_HEX523 -0.2196928  0.0891088    -2.465 0.013684 *  
DESTIN_HEX524  1.1028766  0.0883065    12.489  < 2e-16 ***
DESTIN_HEX525 -0.2535406  0.0883693    -2.869 0.004116 ** 
DESTIN_HEX526  0.3506575  0.0880247     3.984 6.79e-05 ***
DESTIN_HEX527  1.3468760  0.0879041    15.322  < 2e-16 ***
DESTIN_HEX528  0.9962681  0.0879699    11.325  < 2e-16 ***
DESTIN_HEX529  1.1273638  0.0879602    12.817  < 2e-16 ***
DESTIN_HEX530  1.6852529  0.0879051    19.171  < 2e-16 ***
DESTIN_HEX531  1.4946194  0.0880078    16.983  < 2e-16 ***
DESTIN_HEX532  1.7187839  0.0879111    19.551  < 2e-16 ***
DESTIN_HEX533  1.4566056  0.0879505    16.562  < 2e-16 ***
DESTIN_HEX534 -1.8267377  0.1152549   -15.850  < 2e-16 ***
DESTIN_HEX535 -4.8957885  0.4562997   -10.729  < 2e-16 ***
DESTIN_HEX536 -0.1938636  0.0893826    -2.169 0.030089 *  
DESTIN_HEX537  1.0397111  0.0879368    11.823  < 2e-16 ***
DESTIN_HEX538  1.3126742  0.0879697    14.922  < 2e-16 ***
DESTIN_HEX539  0.9918384  0.0879739    11.274  < 2e-16 ***
DESTIN_HEX540  1.6730771  0.0879707    19.019  < 2e-16 ***
DESTIN_HEX541  0.3312893  0.0881469     3.758 0.000171 ***
DESTIN_HEX542 -0.5519947  0.0887016    -6.223 4.88e-10 ***
DESTIN_HEX543  2.0785660  0.0878959    23.648  < 2e-16 ***
DESTIN_HEX544  0.5181814  0.0886102     5.848 4.98e-09 ***
DESTIN_HEX545  0.8287482  0.0882885     9.387  < 2e-16 ***
DESTIN_HEX546  0.6237584  0.0890881     7.002 2.53e-12 ***
DESTIN_HEX547 -1.0332957  0.1004886   -10.283  < 2e-16 ***
DESTIN_HEX548 -0.2258301  0.0889054    -2.540 0.011081 *  
DESTIN_HEX549  0.3809958  0.0880945     4.325 1.53e-05 ***
DESTIN_HEX550  1.0648754  0.0879403    12.109  < 2e-16 ***
DESTIN_HEX551  0.9964427  0.0879463    11.330  < 2e-16 ***
DESTIN_HEX552  1.2532724  0.0879313    14.253  < 2e-16 ***
DESTIN_HEX553  2.3933523  0.0880107    27.194  < 2e-16 ***
DESTIN_HEX554 -0.6569994  0.0894154    -7.348 2.02e-13 ***
DESTIN_HEX555  0.3067695  0.0903383     3.396 0.000684 ***
DESTIN_HEX556  0.8114298  0.0882304     9.197  < 2e-16 ***
DESTIN_HEX557 -2.0279943  0.1059775   -19.136  < 2e-16 ***
DESTIN_HEX558 -0.7450299  0.0959202    -7.767 8.03e-15 ***
DESTIN_HEX559  0.5366765  0.0883326     6.076 1.23e-09 ***
DESTIN_HEX560  0.5055513  0.0898064     5.629 1.81e-08 ***
DESTIN_HEX561  1.0954183  0.0879407    12.456  < 2e-16 ***
DESTIN_HEX562  1.8910384  0.0878905    21.516  < 2e-16 ***
DESTIN_HEX563  1.3451100  0.0879765    15.289  < 2e-16 ***
DESTIN_HEX564 -1.5530217  0.0903402   -17.191  < 2e-16 ***
DESTIN_HEX565  0.5302734  0.0881061     6.019 1.76e-09 ***
DESTIN_HEX566 -0.7291116  0.0890243    -8.190 2.61e-16 ***
DESTIN_HEX567 -0.3436286  0.0887691    -3.871 0.000108 ***
DESTIN_HEX568 -0.4016526  0.0894942    -4.488 7.19e-06 ***
DESTIN_HEX569 -2.9269982  0.1253905   -23.343  < 2e-16 ***
DESTIN_HEX570 -1.9483035  0.1081485   -18.015  < 2e-16 ***
DESTIN_HEX571 -1.6353584  0.1047729   -15.609  < 2e-16 ***
DESTIN_HEX572 -0.4001678  0.0888458    -4.504 6.67e-06 ***
DESTIN_HEX573 -1.2278739  0.0890913   -13.782  < 2e-16 ***
DESTIN_HEX574  1.5150023  0.0879063    17.234  < 2e-16 ***
DESTIN_HEX575  0.5389445  0.0890122     6.055 1.41e-09 ***
DESTIN_HEX576  0.0293208  0.0883440     0.332 0.739970    
DESTIN_HEX577  1.4137084  0.0880352    16.058  < 2e-16 ***
DESTIN_HEX578 -0.6144089  0.0889424    -6.908 4.92e-12 ***
DESTIN_HEX579 -2.5647277  0.1120437   -22.890  < 2e-16 ***
DESTIN_HEX580 -2.0667975  0.1115394   -18.530  < 2e-16 ***
DESTIN_HEX581  1.5093406  0.0884145    17.071  < 2e-16 ***
DESTIN_HEX582  0.4518240  0.0880495     5.131 2.87e-07 ***
DESTIN_HEX583  0.9241536  0.0879985    10.502  < 2e-16 ***
DESTIN_HEX584  1.6469322  0.0879367    18.729  < 2e-16 ***
DESTIN_HEX585  0.2441421  0.0881269     2.770 0.005600 ** 
DESTIN_HEX586  1.0960835  0.0879685    12.460  < 2e-16 ***
DESTIN_HEX587  1.3791710  0.0881610    15.644  < 2e-16 ***
DESTIN_HEX588  0.0522528  0.0884072     0.591 0.554489    
DESTIN_HEX589  2.1386034  0.0879416    24.318  < 2e-16 ***
DESTIN_HEX590  2.0058528  0.0880118    22.791  < 2e-16 ***
DESTIN_HEX591 -1.5372098  0.1120381   -13.720  < 2e-16 ***
DESTIN_HEX592  0.5946884  0.0891689     6.669 2.57e-11 ***
DESTIN_HEX593  1.6612206  0.0879001    18.899  < 2e-16 ***
DESTIN_HEX594  0.4046162  0.0881260     4.591 4.40e-06 ***
DESTIN_HEX595  1.5904388  0.0879393    18.086  < 2e-16 ***
DESTIN_HEX596  2.6336654  0.0878708    29.972  < 2e-16 ***
DESTIN_HEX597  0.5149555  0.0881182     5.844 5.10e-09 ***
DESTIN_HEX598  2.3740406  0.0878928    27.011  < 2e-16 ***
DESTIN_HEX599  1.0600103  0.0881028    12.032  < 2e-16 ***
DESTIN_HEX600  1.0736860  0.0882153    12.171  < 2e-16 ***
DESTIN_HEX601 -2.1325665  0.1032158   -20.661  < 2e-16 ***
DESTIN_HEX602 -0.9510371  0.0919620   -10.342  < 2e-16 ***
DESTIN_HEX603  1.4015066  0.0879372    15.938  < 2e-16 ***
DESTIN_HEX604 -0.1191270  0.0885039    -1.346 0.178300    
DESTIN_HEX605  0.8318082  0.0879916     9.453  < 2e-16 ***
DESTIN_HEX606  0.2417718  0.0883043     2.738 0.006183 ** 
DESTIN_HEX607  1.1224524  0.0879588    12.761  < 2e-16 ***
DESTIN_HEX608  1.4008862  0.0879540    15.927  < 2e-16 ***
DESTIN_HEX609  1.9991423  0.0879126    22.740  < 2e-16 ***
DESTIN_HEX610  2.1397365  0.0879795    24.321  < 2e-16 ***
DESTIN_HEX611 -2.8208288  0.1226118   -23.006  < 2e-16 ***
DESTIN_HEX612  1.7160958  0.0879023    19.523  < 2e-16 ***
DESTIN_HEX613  0.5660487  0.0880254     6.431 1.27e-10 ***
DESTIN_HEX614 -0.2758336  0.0898748    -3.069 0.002147 ** 
DESTIN_HEX615  1.3111121  0.0879460    14.908  < 2e-16 ***
DESTIN_HEX616  2.2531376  0.0878926    25.635  < 2e-16 ***
DESTIN_HEX617  2.7035272  0.0880080    30.719  < 2e-16 ***
DESTIN_HEX618  2.2155092  0.0880389    25.165  < 2e-16 ***
DESTIN_HEX619  0.7360361  0.0885911     8.308  < 2e-16 ***
DESTIN_HEX620  1.2111883  0.0879726    13.768  < 2e-16 ***
DESTIN_HEX621  0.7023382  0.0880111     7.980 1.46e-15 ***
DESTIN_HEX622  0.5899490  0.0881555     6.692 2.20e-11 ***
DESTIN_HEX623  0.0931361  0.0882202     1.056 0.291095    
DESTIN_HEX624 -0.3402434  0.0885594    -3.842 0.000122 ***
DESTIN_HEX625  0.8646298  0.0881241     9.811  < 2e-16 ***
DESTIN_HEX626  1.7515476  0.0879445    19.917  < 2e-16 ***
DESTIN_HEX627  1.2653200  0.0881946    14.347  < 2e-16 ***
DESTIN_HEX628  1.1374997  0.0880470    12.919  < 2e-16 ***
DESTIN_HEX629  1.0374850  0.0879593    11.795  < 2e-16 ***
DESTIN_HEX630  1.1653026  0.0879437    13.251  < 2e-16 ***
DESTIN_HEX631  0.8319460  0.0880182     9.452  < 2e-16 ***
DESTIN_HEX632  1.6503478  0.0879353    18.768  < 2e-16 ***
DESTIN_HEX633  1.8353801  0.0879361    20.872  < 2e-16 ***
DESTIN_HEX634  2.0876681  0.0878966    23.751  < 2e-16 ***
DESTIN_HEX635 -0.3885432  0.0889016    -4.370 1.24e-05 ***
DESTIN_HEX636  2.1535700  0.0879739    24.480  < 2e-16 ***
DESTIN_HEX638  1.2693584  0.0879810    14.428  < 2e-16 ***
DESTIN_HEX639  1.2691436  0.0879415    14.432  < 2e-16 ***
DESTIN_HEX640  0.6305637  0.0880072     7.165 7.78e-13 ***
DESTIN_HEX641 -1.5137527  0.0907567   -16.679  < 2e-16 ***
DESTIN_HEX642  1.2948800  0.0879782    14.718  < 2e-16 ***
DESTIN_HEX643  1.7592438  0.0879109    20.012  < 2e-16 ***
DESTIN_HEX644  1.4636212  0.0879555    16.640  < 2e-16 ***
DESTIN_HEX645  2.0682825  0.0879207    23.524  < 2e-16 ***
DESTIN_HEX646  3.2803269  0.0881160    37.227  < 2e-16 ***
DESTIN_HEX647  0.4185678  0.0882043     4.745 2.08e-06 ***
DESTIN_HEX648  1.7020289  0.0879012    19.363  < 2e-16 ***
DESTIN_HEX649  0.4014402  0.0880543     4.559 5.14e-06 ***
DESTIN_HEX650 -0.7091344  0.0886402    -8.000 1.24e-15 ***
DESTIN_HEX651  1.8819840  0.0879143    21.407  < 2e-16 ***
DESTIN_HEX652  2.4840109  0.0878793    28.266  < 2e-16 ***
DESTIN_HEX653  1.8373860  0.0879259    20.897  < 2e-16 ***
DESTIN_HEX654  1.3653560  0.0880122    15.513  < 2e-16 ***
DESTIN_HEX655 -0.5001731  0.0934634    -5.352 8.72e-08 ***
DESTIN_HEX657  0.9860145  0.0880051    11.204  < 2e-16 ***
DESTIN_HEX658  0.4389410  0.0882163     4.976 6.50e-07 ***
DESTIN_HEX659  0.0470323  0.0882537     0.533 0.594088    
DESTIN_HEX660 -1.3059391  0.0906564   -14.405  < 2e-16 ***
DESTIN_HEX661  1.3384522  0.0879861    15.212  < 2e-16 ***
DESTIN_HEX662  0.9707073  0.0880472    11.025  < 2e-16 ***
DESTIN_HEX663  2.5751392  0.0878880    29.300  < 2e-16 ***
DESTIN_HEX664  2.2013561  0.0879362    25.034  < 2e-16 ***
DESTIN_HEX665  1.5330965  0.0891455    17.198  < 2e-16 ***
DESTIN_HEX666  1.7619045  0.0879381    20.036  < 2e-16 ***
DESTIN_HEX667  0.4144965  0.0881507     4.702 2.57e-06 ***
DESTIN_HEX668  0.8879625  0.0880836    10.081  < 2e-16 ***
DESTIN_HEX669 -0.1911760  0.0883036    -2.165 0.030389 *  
DESTIN_HEX670 -1.3133929  0.0932470   -14.085  < 2e-16 ***
DESTIN_HEX671 -1.5368679  0.0922772   -16.655  < 2e-16 ***
DESTIN_HEX672  1.9638403  0.0879398    22.332  < 2e-16 ***
DESTIN_HEX673  1.9005968  0.0879242    21.616  < 2e-16 ***
DESTIN_HEX674  1.9182943  0.0879268    21.817  < 2e-16 ***
DESTIN_HEX675  1.3489325  0.0881336    15.306  < 2e-16 ***
DESTIN_HEX676  1.2866775  0.0907633    14.176  < 2e-16 ***
DESTIN_HEX677  0.7496206  0.0880857     8.510  < 2e-16 ***
DESTIN_HEX678  1.7379488  0.0879007    19.772  < 2e-16 ***
DESTIN_HEX679  1.4278541  0.0879219    16.240  < 2e-16 ***
DESTIN_HEX680  1.9285211  0.0879907    21.917  < 2e-16 ***
DESTIN_HEX681  1.7692435  0.0879445    20.118  < 2e-16 ***
DESTIN_HEX682  2.5992035  0.0878965    29.571  < 2e-16 ***
DESTIN_HEX683 -0.1525183  0.0910689    -1.675 0.093982 .  
DESTIN_HEX684  1.9265491  0.0879262    21.911  < 2e-16 ***
DESTIN_HEX685  0.6592447  0.0880615     7.486 7.09e-14 ***
DESTIN_HEX686  0.7743237  0.0879894     8.800  < 2e-16 ***
DESTIN_HEX687 -0.0993826  0.0883720    -1.125 0.260761    
DESTIN_HEX688 -2.3494172  0.1074618   -21.863  < 2e-16 ***
DESTIN_HEX689  1.3786731  0.0881031    15.648  < 2e-16 ***
DESTIN_HEX690  3.1337722  0.0878739    35.662  < 2e-16 ***
DESTIN_HEX691 -0.1436909  0.0904116    -1.589 0.111993    
DESTIN_HEX692  2.9985519  0.0884578    33.898  < 2e-16 ***
DESTIN_HEX693  1.1318562  0.0879770    12.865  < 2e-16 ***
DESTIN_HEX694  1.1530930  0.0879746    13.107  < 2e-16 ***
DESTIN_HEX695  1.7130901  0.0879206    19.485  < 2e-16 ***
DESTIN_HEX696 -1.4809999  0.0951414   -15.566  < 2e-16 ***
DESTIN_HEX697  2.5921398  0.0882286    29.380  < 2e-16 ***
DESTIN_HEX698  1.8696226  0.0879751    21.252  < 2e-16 ***
DESTIN_HEX700  1.6173205  0.0880033    18.378  < 2e-16 ***
DESTIN_HEX701 -0.3491520  0.0889421    -3.926 8.65e-05 ***
DESTIN_HEX702  1.6570153  0.0884487    18.734  < 2e-16 ***
DESTIN_HEX703  1.2643522  0.0879766    14.371  < 2e-16 ***
DESTIN_HEX704 -2.3191259  0.1018057   -22.780  < 2e-16 ***
DESTIN_HEX705  1.9495746  0.0879722    22.161  < 2e-16 ***
DESTIN_HEX706  2.3051829  0.0883426    26.094  < 2e-16 ***
DESTIN_HEX707  1.1815826  0.0879998    13.427  < 2e-16 ***
DESTIN_HEX708 -0.0501890  0.0882865    -0.568 0.569710    
DESTIN_HEX709  0.1301192  0.0883565     1.473 0.140842    
DESTIN_HEX710 -3.0775355  0.1190434   -25.852  < 2e-16 ***
DESTIN_HEX711 -2.7247715  0.1249346   -21.810  < 2e-16 ***
DESTIN_HEX712  1.5734281  0.0882459    17.830  < 2e-16 ***
DESTIN_HEX714  0.3431603  0.0882205     3.890 0.000100 ***
DESTIN_HEX715  1.5110054  0.0880018    17.170  < 2e-16 ***
DESTIN_HEX716  1.5122329  0.0879560    17.193  < 2e-16 ***
DESTIN_HEX717 -0.8208677  0.0914639    -8.975  < 2e-16 ***
DESTIN_HEX718  1.7241108  0.0882825    19.529  < 2e-16 ***
DESTIN_HEX719  1.0095631  0.0880834    11.461  < 2e-16 ***
DESTIN_HEX720  1.4704413  0.0879437    16.720  < 2e-16 ***
DESTIN_HEX721  1.9286410  0.0879295    21.934  < 2e-16 ***
DESTIN_HEX722 -1.8967741  0.0960103   -19.756  < 2e-16 ***
DESTIN_HEX724  0.5300645  0.0882469     6.007 1.89e-09 ***
DESTIN_HEX725  2.8423217  0.0878650    32.349  < 2e-16 ***
DESTIN_HEX726  0.7094654  0.0881223     8.051 8.22e-16 ***
DESTIN_HEX727  1.6951903  0.0879428    19.276  < 2e-16 ***
DESTIN_HEX728 -1.9105767  0.1078364   -17.717  < 2e-16 ***
DESTIN_HEX729  0.6948527  0.0882339     7.875 3.40e-15 ***
DESTIN_HEX730 -0.8738753  0.0888387    -9.837  < 2e-16 ***
DESTIN_HEX731  1.3908114  0.0879679    15.810  < 2e-16 ***
DESTIN_HEX732  0.1116368  0.0885293     1.261 0.207304    
DESTIN_HEX733  1.5837595  0.0879539    18.007  < 2e-16 ***
DESTIN_HEX734  0.5541490  0.0881667     6.285 3.27e-10 ***
DESTIN_HEX735  0.9969602  0.0881074    11.315  < 2e-16 ***
DESTIN_HEX736  1.1491394  0.0880270    13.054  < 2e-16 ***
DESTIN_HEX737  1.3890419  0.0879283    15.797  < 2e-16 ***
DESTIN_HEX738  1.2517923  0.0879779    14.228  < 2e-16 ***
DESTIN_HEX739  1.8203862  0.0879238    20.704  < 2e-16 ***
DESTIN_HEX740  1.5523927  0.0879448    17.652  < 2e-16 ***
DESTIN_HEX741  0.7402090  0.0881575     8.396  < 2e-16 ***
DESTIN_HEX742 -0.4199443  0.0895365    -4.690 2.73e-06 ***
DESTIN_HEX743  1.3811840  0.0880442    15.687  < 2e-16 ***
DESTIN_HEX744  2.1078700  0.0879017    23.980  < 2e-16 ***
DESTIN_HEX745  1.2570267  0.0879506    14.292  < 2e-16 ***
DESTIN_HEX746  1.0391141  0.0879676    11.812  < 2e-16 ***
DESTIN_HEX747  0.5018865  0.0882331     5.688 1.28e-08 ***
DESTIN_HEX748  2.0883652  0.0879224    23.752  < 2e-16 ***
DESTIN_HEX749  0.9417070  0.0881346    10.685  < 2e-16 ***
DESTIN_HEX750  1.6628614  0.0879257    18.912  < 2e-16 ***
DESTIN_HEX751 -1.4178058  0.0923501   -15.353  < 2e-16 ***
DESTIN_HEX752  1.6175448  0.0879056    18.401  < 2e-16 ***
DESTIN_HEX753  1.1186394  0.0879754    12.715  < 2e-16 ***
DESTIN_HEX754  1.3302132  0.0879688    15.121  < 2e-16 ***
DESTIN_HEX755 -1.0871955  0.0908274   -11.970  < 2e-16 ***
DESTIN_HEX756  1.5400395  0.0879755    17.505  < 2e-16 ***
DESTIN_HEX757  0.4079682  0.0881449     4.628 3.69e-06 ***
DESTIN_HEX758 -1.4158974  0.0916340   -15.452  < 2e-16 ***
DESTIN_HEX759  2.8731069  0.0878655    32.699  < 2e-16 ***
DESTIN_HEX760  1.2267140  0.0880477    13.932  < 2e-16 ***
DESTIN_HEX761  1.5099247  0.0879805    17.162  < 2e-16 ***
DESTIN_HEX762  0.5842448  0.0882705     6.619 3.62e-11 ***
DESTIN_HEX763  1.9403842  0.0879213    22.070  < 2e-16 ***
DESTIN_HEX764  0.3635454  0.0881534     4.124 3.72e-05 ***
DESTIN_HEX765  1.0555442  0.0879511    12.001  < 2e-16 ***
DESTIN_HEX766  0.5091809  0.0881450     5.777 7.62e-09 ***
DESTIN_HEX767  2.5242183  0.0878871    28.721  < 2e-16 ***
DESTIN_HEX768 -1.9481585  0.1035636   -18.811  < 2e-16 ***
DESTIN_HEX769 -0.8101981  0.1221455    -6.633 3.29e-11 ***
DESTIN_HEX770 -0.7831749  0.0893151    -8.769  < 2e-16 ***
DESTIN_HEX771  0.0881406  0.0882512     0.999 0.317918    
DESTIN_HEX772  1.3686571  0.0879720    15.558  < 2e-16 ***
DESTIN_HEX773  0.9490131  0.0879706    10.788  < 2e-16 ***
DESTIN_HEX774  0.3517773  0.0882109     3.988 6.67e-05 ***
DESTIN_HEX775 -2.5493702  0.1025387   -24.863  < 2e-16 ***
DESTIN_HEX776  0.0038488  0.0887140     0.043 0.965395    
DESTIN_HEX777 -0.0566971  0.0886505    -0.640 0.522460    
DESTIN_HEX778  1.6409201  0.0879150    18.665  < 2e-16 ***
DESTIN_HEX779  1.9017919  0.0879503    21.623  < 2e-16 ***
DESTIN_HEX780  1.1613767  0.0879992    13.198  < 2e-16 ***
DESTIN_HEX781  0.8358506  0.0884779     9.447  < 2e-16 ***
DESTIN_HEX782 -1.0220237  0.0893401   -11.440  < 2e-16 ***
DESTIN_HEX783  1.4560067  0.0879619    16.553  < 2e-16 ***
DESTIN_HEX784  2.1312868  0.0878925    24.249  < 2e-16 ***
DESTIN_HEX785  2.1374621  0.0879105    24.314  < 2e-16 ***
DESTIN_HEX786  1.4187898  0.0880289    16.117  < 2e-16 ***
DESTIN_HEX787  0.9830730  0.0880304    11.167  < 2e-16 ***
DESTIN_HEX788  0.6300195  0.0881705     7.145 8.97e-13 ***
DESTIN_HEX789  1.0635991  0.0879937    12.087  < 2e-16 ***
DESTIN_HEX790  1.4932132  0.0879897    16.970  < 2e-16 ***
DESTIN_HEX791  0.1659247  0.0886554     1.872 0.061266 .  
DESTIN_HEX792 -0.3595857  0.0887758    -4.050 5.11e-05 ***
DESTIN_HEX793  0.9223970  0.0880610    10.475  < 2e-16 ***
DESTIN_HEX794  1.4369345  0.0879654    16.335  < 2e-16 ***
DESTIN_HEX795  0.6018619  0.0901082     6.679 2.40e-11 ***
DESTIN_HEX796 -1.2390513  0.1048366   -11.819  < 2e-16 ***
DESTIN_HEX797 -1.1479273  0.0909191   -12.626  < 2e-16 ***
DESTIN_HEX798 -1.1326337  0.0913088   -12.404  < 2e-16 ***
DESTIN_HEX799  1.2913075  0.0880467    14.666  < 2e-16 ***
DESTIN_HEX800 -0.9680251  0.0895917   -10.805  < 2e-16 ***
DESTIN_HEX801 -1.3060344  0.0951811   -13.722  < 2e-16 ***
DESTIN_HEX802 -0.8258131  0.0920506    -8.971  < 2e-16 ***
DESTIN_HEX803  0.5149852  0.0886453     5.810 6.27e-09 ***
DESTIN_HEX804 -0.8520010  0.0895682    -9.512  < 2e-16 ***
DESTIN_HEX805 -2.1965570  0.0993366   -22.112  < 2e-16 ***
DESTIN_HEX806 -1.7163672  0.0942002   -18.220  < 2e-16 ***
DESTIN_HEX807 -0.7421391  0.0902234    -8.226  < 2e-16 ***
DESTIN_HEX808 -0.2414295  0.0887973    -2.719 0.006550 ** 
DESTIN_HEX809 -1.4620128  0.1021651   -14.310  < 2e-16 ***
DESTIN_HEX810 -1.0541116  0.0956078   -11.025  < 2e-16 ***
DESTIN_HEX811  0.5238931  0.0887321     5.904 3.54e-09 ***
DESTIN_HEX812 -1.5603437  0.0907689   -17.190  < 2e-16 ***
DESTIN_HEX813 -2.2510314  0.1062897   -21.178  < 2e-16 ***
DESTIN_HEX814 -0.4784424  0.0903161    -5.297 1.17e-07 ***
DESTIN_HEX815 -2.3646424  0.1045509   -22.617  < 2e-16 ***
DESTIN_HEX816 -0.9334291  0.0899004   -10.383  < 2e-16 ***
DESTIN_HEX817  0.9381132  0.0883660    10.616  < 2e-16 ***
DESTIN_HEX818  2.0229084  0.0881149    22.958  < 2e-16 ***
DESTIN_HEX819  0.9417704  0.0885320    10.638  < 2e-16 ***
DESTIN_HEX820  1.8503207  0.0889758    20.796  < 2e-16 ***
DESTIN_HEX821  1.5497210  0.0881127    17.588  < 2e-16 ***
DESTIN_HEX822 -0.0125229  0.0885791    -0.141 0.887573    
DESTIN_HEX823 -0.2401522  0.0888730    -2.702 0.006888 ** 
DESTIN_HEX824 -0.8947610  0.0898045    -9.963  < 2e-16 ***
DESTIN_HEX825  0.3891188  0.0905514     4.297 1.73e-05 ***
DESTIN_HEX826 -0.6397907  0.0893847    -7.158 8.20e-13 ***
DESTIN_HEX827 -1.0178978  0.0896316   -11.356  < 2e-16 ***
DESTIN_HEX828 -2.6135883  0.0989159   -26.422  < 2e-16 ***
DESTIN_HEX829 -1.5356793  0.0934829   -16.427  < 2e-16 ***
DESTIN_HEX830 -0.2394955  0.0888773    -2.695 0.007046 ** 
DESTIN_HEX831 -0.4668885  0.1060244    -4.404 1.06e-05 ***
log(dist)     -1.6045515  0.0002857 -5615.262  < 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: 92488055  on 67736  degrees of freedom
Residual deviance: 22253173  on 66108  degrees of freedom
AIC: 22626824

Number of Fisher Scoring iterations: 8
  • In case R/Quarto crashes, we add a copy of relevant coefficient readouts here for dbcSIM:
Coefficients:
                         Estimate Std. Error  z value Pr(>|z|)    
log(dist)     -1.6045515  0.0002857 -5615.262  < 2e-16 ***

4.6c Commentary on dbcSIM

  • Once again, we compare the size of the coefficients to assess the impact of the explanatory factors;
    • As above, the decay factor, log(dist), is clearly a strong determinant of the number of trips, with coefficient of -1.60 and a low z-value, indicating strong statistical significance.
show code 
CalcRSquared(dbcSIM$data$SUM_TRIPS, dbcSIM$fitted.values)
  • The R-squared value of 0.586 is also higher than for other models, suggesting it performs better. Now it is approaching good performance.

4.7RMSE Model Comparison by RMSE

  • Aggregating all 4 models by RMSE, we perform the following printout:
show code 
model_list <- list(
  Unconstrained = uncSIM,
  Origin_Constrained = orcSIM,
  Destination_Constrained = decSIM,
  Doubly_Constrained = dbcSIM)
compare_performance(model_list,
                    metrics = "RMSE")
  • It appears that the doubly-constrained model performs best, with the lowest error;
    • dbcSIM relies only on the identity of the origin and destination hexes, without any of the attractiveness/propulsiveness variables we have selected for analysis. Another way to say it is that the identity of each hexagon is unique, and thus encodes some variety of specific attractiveness/propulsiveness variables beyond our analysis.
    • It is possible, if we gather more data and more variables, to build a better model and thus approach the performance/RMSE of our doubly-constrained SIM model.
  • The slight edge on Origin-Constrained model (i.e. RMSE slightly lower than for Destination_Constrained) suggests our choice of propulsiveness variables outperform our choices on attractiveness variables.
    • However, my intuition is simply that the MRT Station Exits are simply too strong a factor for bus trip origin. Given more time, we should repeat with MRT Stations on both Origin and Destination models.

4.7g Model Comparison by Goodness-of-Fit

  • Finally, we can perform a quick scatterplot to show the goodness-of-fit of our fitted values, across all 4 models.
show code 
uncSIM_df <- as.data.frame(uncSIM$fitted.values) %>%
  round(digits = 0) 
orcSIM_df <- as.data.frame(orcSIM$fitted.values) %>%
  round(digits = 0)
decSIM_df <- as.data.frame(decSIM$fitted.values) %>%
  round(digits = 0)
dbcSIM_df <- as.data.frame(dbcSIM$fitted.values) %>%
  round(digits = 0)



model_comparison <- SIM_data %>%
  cbind(
    uncSIM_df,
    orcSIM_df,
    decSIM_df,
    dbcSIM_df 
  ) %>%
  rename(
    uncTRIPS = "uncSIM$fitted.values",
    orcTRIPS = "orcSIM$fitted.values",
    decTRIPS = "decSIM$fitted.values",
    dbcTRIPS = "dbcSIM$fitted.values" 
  )


write_rds(model_comparison, "data/rds/model_comparison.rds")
model_comparison
  • Here we again use the read/write RDS trick.
show code 
model_comparison <- read_rds("data/rds/model_comparison.rds")
orc_p <- ggplot(data = model_comparison,
                aes(x = orcTRIPS,
                    y = SUM_TRIPS)) +
  geom_point() +
  geom_smooth(method = lm) +
  coord_cartesian(xlim=c(0,100000),
                  ylim=c(0,100000))

dbc_p <- ggplot(data = model_comparison,
                aes(x = dbcTRIPS,
                    y = SUM_TRIPS)) +
  geom_point() +
  geom_smooth(method = lm) +
  coord_cartesian(xlim=c(0,100000),
                  ylim=c(0,100000))


unc_p <- ggplot(data = model_comparison,
                aes(x = uncTRIPS,
                    y = SUM_TRIPS)) +
  geom_point() +
  geom_smooth(method = lm) +
  coord_cartesian(xlim=c(0,100000),
                  ylim=c(0,100000))


dec_p <- ggplot(data = model_comparison,
                aes(x = decTRIPS,
                    y = SUM_TRIPS)) +
  geom_point() +
  geom_smooth(method = lm) +
  coord_cartesian(xlim=c(0,100000),
                  ylim=c(0,100000))

(unc_p + orc_p) / (dec_p + dbc_p)
`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'

  • Overall, it looks like the doubly-constrained model (dbcTRIPS) shows better fit for most points and outliers compared to the other models;
  • It reiterates what was said in Section 4.7RMSE, that the doubly-constrained model performs best.

5. Summary and Future Work

  • Overall, we can observe that the flow patterns of public transportation are highly complex.
  • Existing Transportation Systems Work. It appears the current flow of bus traffic on weekday evenings does cater to the expected regions (from CBD areas, towards residential areas, with transit hubs near MRT Stations). However, we must be careful not to fall for a logical fallacy of only looking at data that is there.
    • Most commuters have no alternatives but to take public transport, so it makes sense that our data shows that existing public transport is utilised and popular.
    • However, this does not include untracked travel, including people who walk between stations/stops, or use alternative transports like shuttle buses, (rental) bicycles, and so on.
    • It’s also possible that routes that have not been catered for result in people relying on taxi or ride-hailing services.
    • However, it must be acknowledged that the interplay of bus-and-MRT Stations do work.
  • More Data Is Needed. It’s clear that of our four Spatial Interaction Models, the best-performing model disregards the propulsiveness/attractiveness variables we have selected, in favour of dummy-encoding each analytical hexagon as its own dummy variables. As mentioned, this suggests that there are hidden variables that are not fully described by our analysis.
    • It must be acknowledged that we did not do any data cleaning or feature selection, but this module is not focused on that.
  • More Time Is Needed. Unfortunately we must also acknowledge our lack of time for analysis. In particular, our HDB dataset analysis leaves much to be desired; we only counted the number of HDB buildings and not the relative population living there. Indeed, we can envisage an entire study based on the HDB.csv, making use of the number of dwelling units or even the resident age groups, and fitting the best predictor to the dataset.