Code
pacman::p_load(tmap, sf, sp, DT, performance, reshape2, units, tidyverse, patchwork)In-class Exercise 3 - Calibrating Spatial Interaction Models with R
1 Overview
Spatial Interaction Models (SIMs), developed by Alan Wilson in the late 1960s, estimate flows between spatial entities. Traditionally, there are four types: Unconstrained, Production-constrained, Attraction-constrained, and Doubly-constrained. This chapter explores hands-on calibration of SIM using Ordinary Least Square (OLS), log-normal, Poisson, and negative binomial regression methods. Calibration involves adjusting parameters to align model estimates with observed data, facilitated by computer iterative processes. The exercise focuses on calibrating SIM to understand factors influencing public bus passenger flows during the morning peak in Singapore.
In this exercise, we are going to calibrate SIM to determine factors affecting the public bus passenger flows during the morning peak in Singapore.
2 Preparation
tmapfor creating thematic maps.sffor importing, integrating, processing and transforming geospatial data.spis for storing special polygon dataframe in which the processes will be more efficient withtidyversefor importing, integrating, wrangling and visualising data.performancefor checking model performance.reshape2for doing certain processes in which it’s more efficient compared to tidyverse (it’s an old package).patchworkfor arranging several charts in one display.
Continuing from the Hands-on Exercise 3, this exercise utilizes two key datasets:
- od_data.rds: Weekday morning peak passenger flows at the planning subzone level.
- mpsz.rds: URA Master Plan 2019 Planning Subzone boundaries in simple feature tibble data frame format.
Additionally, an attribute data file named pop.csv will be used as well.
Code
mpsz <- read_rds("../data/rds/mpsz.rds")
mpszSimple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21 / Singapore TM
First 10 features:
SUBZONE_N SUBZONE_C PLN_AREA_N PLN_AREA_C REGION_N
1 MARINA EAST MESZ01 MARINA EAST ME CENTRAL REGION
2 INSTITUTION HILL RVSZ05 RIVER VALLEY RV CENTRAL REGION
3 ROBERTSON QUAY SRSZ01 SINGAPORE RIVER SR CENTRAL REGION
4 JURONG ISLAND AND BUKOM WISZ01 WESTERN ISLANDS WI WEST REGION
5 FORT CANNING MUSZ02 MUSEUM MU CENTRAL REGION
6 MARINA EAST (MP) MPSZ05 MARINE PARADE MP CENTRAL REGION
7 SUDONG WISZ03 WESTERN ISLANDS WI WEST REGION
8 SEMAKAU WISZ02 WESTERN ISLANDS WI WEST REGION
9 SOUTHERN GROUP SISZ02 SOUTHERN ISLANDS SI CENTRAL REGION
10 SENTOSA SISZ01 SOUTHERN ISLANDS SI CENTRAL REGION
REGION_C geometry
1 CR MULTIPOLYGON (((33222.98 29...
2 CR MULTIPOLYGON (((28481.45 30...
3 CR MULTIPOLYGON (((28087.34 30...
4 WR MULTIPOLYGON (((14557.7 304...
5 CR MULTIPOLYGON (((29542.53 31...
6 CR MULTIPOLYGON (((35279.55 30...
7 WR MULTIPOLYGON (((15772.59 21...
8 WR MULTIPOLYGON (((19843.41 21...
9 CR MULTIPOLYGON (((30870.53 22...
10 CR MULTIPOLYGON (((26879.04 26...3 Data Wrangling
3.1 Distance Matrix Computation
Notice that the previous imported data is a sf tibble dataframe object class. Computing distance can take longer with the sf based data. To make it faster, use Spatial Polygons Dataframe. Conver the data using as.Spatial().
Code
mpsz_sp <- as(mpsz, "Spatial")
mpsz_spclass : SpatialPolygonsDataFrame
features : 332
extent : 2667.538, 56396.44, 15748.72, 50256.33 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 6
names : SUBZONE_N, SUBZONE_C, PLN_AREA_N, PLN_AREA_C, REGION_N, REGION_C
min values : ADMIRALTY, AMSZ01, ANG MO KIO, AM, CENTRAL REGION, CR
max values : YUNNAN, YSSZ09, YISHUN, YS, WEST REGION, WR Next, spDists() of sp package will be used to compute the Euclidean distance between the centroids of the planning subzones.
Do you know why the distance is calculated between two centroids of a pair of spatial polygons? The distance between two centroids of spatial polygons is commonly calculated as a measure of proximity or spatial relationship between the polygons. This approach simplifies spatial analysis by representing each polygon as a single point (centroid), providing a straightforward measure of the overall spatial separation or closeness between the features.
Code
# generate generic R Matrix object
dist <- spDists(mpsz_sp,
longlat = FALSE)
# show the output
head(dist, n=c(10, 10)) [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.000 3926.0025 3939.108 20252.964 2989.9839 1431.330 19211.836
[2,] 3926.003 0.0000 305.737 16513.865 951.8314 5254.066 16242.523
[3,] 3939.108 305.7370 0.000 16412.062 1045.9088 5299.849 16026.146
[4,] 20252.964 16513.8648 16412.062 0.000 17450.3044 21665.795 7229.017
[5,] 2989.984 951.8314 1045.909 17450.304 0.0000 4303.232 17020.916
[6,] 1431.330 5254.0664 5299.849 21665.795 4303.2323 0.000 20617.082
[7,] 19211.836 16242.5230 16026.146 7229.017 17020.9161 20617.082 0.000
[8,] 14960.942 12749.4101 12477.871 11284.279 13336.0421 16281.453 5606.082
[9,] 7515.256 7934.8082 7649.776 18427.503 7801.6163 8403.896 14810.930
[10,] 6391.342 4975.0021 4669.295 15469.566 5226.8731 7707.091 13111.391
[,8] [,9] [,10]
[1,] 14960.942 7515.256 6391.342
[2,] 12749.410 7934.808 4975.002
[3,] 12477.871 7649.776 4669.295
[4,] 11284.279 18427.503 15469.566
[5,] 13336.042 7801.616 5226.873
[6,] 16281.453 8403.896 7707.091
[7,] 5606.082 14810.930 13111.391
[8,] 0.000 9472.024 8575.490
[9,] 9472.024 0.000 3780.800
[10,] 8575.490 3780.800 0.000Output of dist is a matrix object class of R that does not have any column headers and row headers are not labeled with the planning subzone codes. Therefore the next step is to label it.
3.2 Labelling column and row heanders of a distance matrix
Create list of the headers
Code
sz_names <- mpsz$SUBZONE_C
# check the output
sz_names [1] "MESZ01" "RVSZ05" "SRSZ01" "WISZ01" "MUSZ02" "MPSZ05" "WISZ03" "WISZ02"
[9] "SISZ02" "SISZ01" "BMSZ17" "DTSZ10" "SVSZ01" "BMSZ01" "BMSZ15" "DTSZ09"
[17] "BMSZ16" "BMSZ14" "DTSZ07" "DTSZ08" "BMSZ11" "BMSZ13" "QTSZ14" "DTSZ11"
[25] "BMSZ05" "BMSZ12" "BMSZ02" "OTSZ03" "DTSZ04" "DTSZ05" "OTSZ04" "BMSZ10"
[33] "DTSZ12" "BMSZ04" "DTSZ06" "MSSZ01" "OTSZ01" "SRSZ03" "BMSZ08" "BMSZ03"
[41] "BMSZ07" "BMSZ09" "SRSZ02" "QTSZ13" "QTSZ07" "QTSZ12" "BMSZ06" "QTSZ04"
[49] "RCSZ06" "RCSZ03" "QTSZ08" "KLSZ05" "QTSZ03" "QTSZ10" "TNSZ03" "NTSZ04"
[57] "CLSZ08" "NTSZ05" "BDSZ07" "CLSZ07" "PNSZ05" "JESZ11" "NTSZ01" "KLSZ04"
[65] "MPSZ02" "ORSZ02" "NTSZ06" "RCSZ02" "PNSZ04" "DTSZ03" "MUSZ03" "RVSZ04"
[73] "DTSZ02" "QTSZ06" "RVSZ03" "QTSZ15" "MUSZ01" "DTSZ01" "RCSZ10" "RVSZ02"
[81] "MPSZ04" "QTSZ11" "RVSZ01" "ORSZ03" "RCSZ09" "TNSZ02" "RCSZ05" "RCSZ08"
[89] "RCSZ07" "RCSZ04" "DTSZ13" "QTSZ05" "ORSZ01" "MPSZ03" "PNSZ01" "GLSZ01"
[97] "JESZ07" "BLSZ01" "BTSZ06" "BDSZ03" "NVSZ04" "CLSZ02" "GLSZ02" "TPSZ07"
[105] "BDSZ04" "TPSZ02" "JESZ06" "BTSZ03" "GLSZ03" "TPSZ11" "TPSZ09" "TSSZ03"
[113] "TPSZ06" "TPSZ04" "JWSZ06" "JWSZ07" "RCSZ01" "NTSZ03" "JESZ10" "BLSZ03"
[121] "BLSZ04" "QTSZ01" "KLSZ06" "NTSZ02" "CLSZ09" "QTSZ09" "CLSZ06" "KLSZ07"
[129] "KLSZ03" "KLSZ08" "BTSZ04" "BTSZ08" "TNSZ01" "CLSZ05" "BDSZ08" "PNSZ03"
[137] "PNSZ02" "TNSZ04" "NVSZ02" "BLSZ02" "BDSZ05" "CLSZ04" "BTSZ07" "GLSZ05"
[145] "JESZ09" "JESZ08" "KLSZ02" "CLSZ03" "NVSZ03" "BDSZ06" "KLSZ01" "NVSZ01"
[153] "TSSZ02" "SGSZ06" "BSSZ03" "TMSZ03" "BKSZ03" "HGSZ09" "CBSZ01" "PLSZ02"
[161] "BKSZ02" "HGSZ06" "AMSZ03" "SGSZ04" "HGSZ01" "PRSZ07" "BPSZ06" "PRSZ05"
[169] "TMSZ01" "AMSZ02" "AMSZ01" "AMSZ06" "SGSZ02" "THSZ02" "SGSZ03" "BKSZ04"
[177] "JWSZ01" "BPSZ07" "TMSZ02" "HGSZ07" "PRSZ08" "BKSZ05" "CLSZ01" "NVSZ05"
[185] "BTSZ05" "TPSZ12" "JWSZ05" "TPSZ05" "JESZ03" "TPSZ03" "TPSZ10" "TPSZ08"
[193] "JWSZ04" "JESZ04" "TPSZ01" "BDSZ01" "JESZ02" "BKSZ09" "JWSZ09" "BDSZ02"
[201] "BTSZ01" "BTSZ02" "TMSZ05" "TMSZ04" "JWSZ02" "BKSZ08" "BKSZ06" "BKSZ07"
[209] "SGSZ07" "HGSZ08" "TSSZ01" "JESZ01" "JWSZ08" "SGSZ05" "JWSZ03" "SLSZ04"
[217] "SKSZ04" "SLSZ01" "YSSZ08" "MDSZ01" "PGSZ07" "YSSZ04" "YSSZ05" "PGSZ01"
[225] "MDSZ03" "YSSZ01" "PRSZ03" "BKSZ01" "PLSZ01" "HGSZ03" "HGSZ10" "HGSZ02"
[233] "AMSZ07" "BPSZ05" "CKSZ02" "HGSZ04" "PLSZ03" "BPSZ04" "SESZ01" "CKSZ04"
[241] "PRSZ02" "AMSZ09" "HGSZ05" "CKSZ01" "CKSZ03" "BPSZ03" "BPSZ01" "BPSZ02"
[249] "SGSZ01" "SESZ05" "AMSZ12" "AMSZ10" "PRSZ06" "AMSZ08" "PRSZ04" "CKSZ05"
[257] "SESZ02" "AMSZ11" "CHSZ01" "SESZ03" "SESZ04" "SESZ07" "SESZ06" "PGSZ04"
[265] "CKSZ06" "PRSZ01" "PGSZ03" "PGSZ05" "SKSZ03" "YSSZ06" "PGSZ02" "PGSZ06"
[273] "CCSZ01" "SBSZ06" "SBSZ07" "SBSZ08" "KLSZ09" "TSSZ04" "TSSZ05" "WCSZ03"
[281] "WCSZ02" "JESZ05" "THSZ03" "THSZ04" "THSZ01" "THSZ06" "THSZ05" "PLSZ04"
[289] "CHSZ02" "QTSZ02" "CHSZ03" "OTSZ02" "MPSZ01" "GLSZ04" "SLSZ03" "SKSZ02"
[297] "WDSZ04" "WDSZ05" "YSSZ03" "WCSZ01" "SLSZ02" "YSSZ09" "WDSZ01" "NESZ01"
[305] "SMSZ03" "YSSZ02" "WDSZ02" "WDSZ06" "SBSZ02" "SKSZ01" "SKSZ05" "WDSZ03"
[313] "SBSZ03" "WDSZ07" "SBSZ01" "WDSZ08" "SMSZ04" "SBSZ05" "LKSZ01" "SMSZ01"
[321] "SBSZ09" "SBSZ04" "SMSZ02" "WDSZ09" "PLSZ05" "MDSZ02" "YSSZ07" "BSSZ01"
[329] "AMSZ05" "AMSZ04" "BSSZ02" "TSSZ06"attach SUBZONE_C to row and column for distance matrix matching ahead
Code
colnames(dist) <- paste0(sz_names)
rownames(dist) <- paste0(sz_names)3.3 Pivoting distance value by SUBZONE_C
Next, pivot the distance matrix into a long table by using the row and column subzone codes using this code.
Code
distPair <- melt(dist) %>%
rename(dist = value)
head(distPair, 10) Var1 Var2 dist
1 MESZ01 MESZ01 0.000
2 RVSZ05 MESZ01 3926.003
3 SRSZ01 MESZ01 3939.108
4 WISZ01 MESZ01 20252.964
5 MUSZ02 MESZ01 2989.984
6 MPSZ05 MESZ01 1431.330
7 WISZ03 MESZ01 19211.836
8 WISZ02 MESZ01 14960.942
9 SISZ02 MESZ01 7515.256
10 SISZ01 MESZ01 6391.342
Warning!
do not sort the data because the sequence will be broken
3.4 Updating intra-zonal distances
In this section, we are going to append a constant value to replace the intra-zonal distance of 0.
First, we will select and find out the minimum value of the distance by using summary().
Code
distPair %>%
filter(dist > 0) %>%
summary() Var1 Var2 dist
MESZ01 : 331 MESZ01 : 331 Min. : 173.8
RVSZ05 : 331 RVSZ05 : 331 1st Qu.: 7149.5
SRSZ01 : 331 SRSZ01 : 331 Median :11890.0
WISZ01 : 331 WISZ01 : 331 Mean :12229.4
MUSZ02 : 331 MUSZ02 : 331 3rd Qu.:16401.7
MPSZ05 : 331 MPSZ05 : 331 Max. :49894.4
(Other):107906 (Other):107906 The constant distant selected for intra-zones must be below the minimum distance (173.8). 50m is picked as the fix distance to be put into intra-zones distance.
Code
distPair$dist <- ifelse(distPair$dist == 0,
50, distPair$dist)
# check the output
summary(distPair) Var1 Var2 dist
MESZ01 : 332 MESZ01 : 332 Min. : 50
RVSZ05 : 332 RVSZ05 : 332 1st Qu.: 7097
SRSZ01 : 332 SRSZ01 : 332 Median :11864
WISZ01 : 332 WISZ01 : 332 Mean :12193
MUSZ02 : 332 MUSZ02 : 332 3rd Qu.:16388
MPSZ05 : 332 MPSZ05 : 332 Max. :49894
(Other):108232 (Other):108232 notice that the minimum value has change (i.e. 0 within-distance has changed to 50)
alternative method to calculate the within-distance!
- calculate the parameter
- calculate the distance
The code chunk below is used to rename the origin and destination fields.
Code
distPair <- distPair %>%
rename(orig = Var1,
dest = Var2)Lastly, the code chunk below is used to save the dataframe for future use.
Code
write_rds(distPair, "../data/rds/distPair.rds") 4 Feature Engineering - Preparing flow data
The code chunk below is used import od_data save in Chapter 15 into R environment.
Code
od_data <- read_rds("../data/rds/od_data.rds")Next, we will compute the total passenger trip between and within planning subzones by using the code chunk below. The output is all flow_data.
Code
flow_data <- od_data %>%
group_by(ORIGIN_SZ, DESTIN_SZ) %>%
summarize(TRIPS = sum(MORNING_PEAK)) Use the code chunk below to display flow_data dataframe.
Code
head(flow_data, 10)# A tibble: 10 × 3
# Groups: ORIGIN_SZ [1]
ORIGIN_SZ DESTIN_SZ TRIPS
<chr> <chr> <dbl>
1 AMSZ01 AMSZ01 1866
2 AMSZ01 AMSZ02 8726
3 AMSZ01 AMSZ03 12598
4 AMSZ01 AMSZ04 2098
5 AMSZ01 AMSZ05 7718
6 AMSZ01 AMSZ06 1631
7 AMSZ01 AMSZ07 1308
8 AMSZ01 AMSZ08 2261
9 AMSZ01 AMSZ09 1526
10 AMSZ01 AMSZ10 1414.1 Separating intra-flow from passenger volume df
Code chunk below is used to add three new fields in flow_data dataframe.
Code
flow_data$FlowNoIntra <- ifelse(
flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ,
0, flow_data$TRIPS)
flow_data$offset <- ifelse(
flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ,
0.000001, 1)4.2 Combining passenger volume data with distance value
Before we can join flow_data and distPair, we need to convert data value type of ORIGIN_SZ and DESTIN_SZ fields of flow_data dataframe into factor data type.
Code
flow_data$ORIGIN_SZ <- as.factor(flow_data$ORIGIN_SZ)
flow_data$DESTIN_SZ <- as.factor(flow_data$DESTIN_SZ)Now, left_join() of dplyr will be used to flow_data dataframe and distPair dataframe. The output is called flow_data1.
Code
flow_data1 <- flow_data %>%
left_join (distPair,
by = c("ORIGIN_SZ" = "orig",
"DESTIN_SZ" = "dest"))
# check the output
print(flow_data1)# A tibble: 20,595 × 6
# Groups: ORIGIN_SZ [309]
ORIGIN_SZ DESTIN_SZ TRIPS FlowNoIntra offset dist
<fct> <fct> <dbl> <dbl> <dbl> <dbl>
1 AMSZ01 AMSZ01 1866 0 0.000001 50
2 AMSZ01 AMSZ02 8726 8726 1 810.
3 AMSZ01 AMSZ03 12598 12598 1 1361.
4 AMSZ01 AMSZ04 2098 2098 1 840.
5 AMSZ01 AMSZ05 7718 7718 1 1077.
6 AMSZ01 AMSZ06 1631 1631 1 805.
7 AMSZ01 AMSZ07 1308 1308 1 1799.
8 AMSZ01 AMSZ08 2261 2261 1 2576.
9 AMSZ01 AMSZ09 1526 1526 1 1204.
10 AMSZ01 AMSZ10 141 141 1 1418.
# ℹ 20,585 more rows5 Feature Engineering - Preparing Origin and Destination Attributes
5.1 Importing population data
Code
pop <- read_csv("../data/aspatial/pop.csv")
# check the output
pop# A tibble: 332 × 5
PA SZ AGE7_12 AGE13_24 AGE25_64
<chr> <chr> <dbl> <dbl> <dbl>
1 ANG MO KIO ANG MO KIO TOWN CENTRE 310 710 2780
2 ANG MO KIO CHENG SAN 1140 2770 15700
3 ANG MO KIO CHONG BOON 1010 2650 14240
4 ANG MO KIO KEBUN BAHRU 1050 2390 12460
5 ANG MO KIO SEMBAWANG HILLS 420 1120 3620
6 ANG MO KIO SHANGRI-LA 810 1920 9650
7 ANG MO KIO TAGORE 390 1150 4350
8 ANG MO KIO TOWNSVILLE 980 2000 11320
9 ANG MO KIO YIO CHU KANG 0 0 0
10 ANG MO KIO YIO CHU KANG EAST 260 650 2500
# ℹ 322 more rows5.2 Geospatial data wrangling
Code
pop <- pop %>%
left_join(mpsz,
by = c("PA" = "PLN_AREA_N",
"SZ" = "SUBZONE_N")) %>%
select(1:6) %>%
rename(SZ_NAME = SZ,
SZ = SUBZONE_C)
# check the output
glimpse(pop)Rows: 332
Columns: 6
$ PA <chr> "ANG MO KIO", "ANG MO KIO", "ANG MO KIO", "ANG MO KIO", "ANG …
$ SZ_NAME <chr> "ANG MO KIO TOWN CENTRE", "CHENG SAN", "CHONG BOON", "KEBUN B…
$ AGE7_12 <dbl> 310, 1140, 1010, 1050, 420, 810, 390, 980, 0, 260, 0, 1190, 6…
$ AGE13_24 <dbl> 710, 2770, 2650, 2390, 1120, 1920, 1150, 2000, 0, 650, 0, 326…
$ AGE25_64 <dbl> 2780, 15700, 14240, 12460, 3620, 9650, 4350, 11320, 0, 2500, …
$ SZ <chr> "AMSZ01", "AMSZ02", "AMSZ03", "AMSZ06", "AMSZ07", "AMSZ05", "…this is the useful trick of how to merge two table that has different reference column.
5.3 Preparing origin & destination attribute
Code
# Preparing origin attribute
flow_data1 <- flow_data1 %>%
left_join(pop,
by = c(ORIGIN_SZ = "SZ")) %>%
rename(ORIGIN_AGE7_12 = AGE7_12,
ORIGIN_AGE13_24 = AGE13_24,
ORIGIN_AGE25_64 = AGE25_64) %>%
select(-c(PA, SZ_NAME))
# Preparing destination attribute
flow_data1 <- flow_data1 %>%
left_join(pop,
# use a subzone code
by = c(DESTIN_SZ = "SZ")) %>%
rename(DESTIN_AGE7_12 = AGE7_12,
DESTIN_AGE13_24 = AGE13_24,
DESTIN_AGE25_64 = AGE25_64) %>%
select(-c(PA, SZ_NAME))
# check the output
glimpse(flow_data1)Rows: 20,595
Columns: 12
Groups: ORIGIN_SZ [309]
$ ORIGIN_SZ <chr> "AMSZ01", "AMSZ01", "AMSZ01", "AMSZ01", "AMSZ01", "AMS…
$ DESTIN_SZ <chr> "AMSZ01", "AMSZ02", "AMSZ03", "AMSZ04", "AMSZ05", "AMS…
$ TRIPS <dbl> 1866, 8726, 12598, 2098, 7718, 1631, 1308, 2261, 1526,…
$ FlowNoIntra <dbl> 0, 8726, 12598, 2098, 7718, 1631, 1308, 2261, 1526, 14…
$ offset <dbl> 1e-06, 1e+00, 1e+00, 1e+00, 1e+00, 1e+00, 1e+00, 1e+00…
$ dist <dbl> 50.0000, 810.4491, 1360.9294, 840.4432, 1076.7916, 805…
$ ORIGIN_AGE7_12 <dbl> 310, 310, 310, 310, 310, 310, 310, 310, 310, 310, 310,…
$ ORIGIN_AGE13_24 <dbl> 710, 710, 710, 710, 710, 710, 710, 710, 710, 710, 710,…
$ ORIGIN_AGE25_64 <dbl> 2780, 2780, 2780, 2780, 2780, 2780, 2780, 2780, 2780, …
$ DESTIN_AGE7_12 <dbl> 310, 1140, 1010, 980, 810, 1050, 420, 390, 1190, 0, 0,…
$ DESTIN_AGE13_24 <dbl> 710, 2770, 2650, 2000, 1920, 2390, 1120, 1150, 3260, 0…
$ DESTIN_AGE25_64 <dbl> 2780, 15700, 14240, 11320, 9650, 12460, 3620, 4350, 13…Instead of doing simple join, this join use origin subzone code and destination subzone code. Having population for both is useful for the transport planning analysis as depending on the case, you might need to look at either the origin or destination population. It also conform with the general factors of geospatial flow analysis which consists of push and pull factors
We will called the output data file SIM_data. it is in rds data file format.
Code
glimpse(flow_data1)Rows: 20,595
Columns: 12
Groups: ORIGIN_SZ [309]
$ ORIGIN_SZ <chr> "AMSZ01", "AMSZ01", "AMSZ01", "AMSZ01", "AMSZ01", "AMS…
$ DESTIN_SZ <chr> "AMSZ01", "AMSZ02", "AMSZ03", "AMSZ04", "AMSZ05", "AMS…
$ TRIPS <dbl> 1866, 8726, 12598, 2098, 7718, 1631, 1308, 2261, 1526,…
$ FlowNoIntra <dbl> 0, 8726, 12598, 2098, 7718, 1631, 1308, 2261, 1526, 14…
$ offset <dbl> 1e-06, 1e+00, 1e+00, 1e+00, 1e+00, 1e+00, 1e+00, 1e+00…
$ dist <dbl> 50.0000, 810.4491, 1360.9294, 840.4432, 1076.7916, 805…
$ ORIGIN_AGE7_12 <dbl> 310, 310, 310, 310, 310, 310, 310, 310, 310, 310, 310,…
$ ORIGIN_AGE13_24 <dbl> 710, 710, 710, 710, 710, 710, 710, 710, 710, 710, 710,…
$ ORIGIN_AGE25_64 <dbl> 2780, 2780, 2780, 2780, 2780, 2780, 2780, 2780, 2780, …
$ DESTIN_AGE7_12 <dbl> 310, 1140, 1010, 980, 810, 1050, 420, 390, 1190, 0, 0,…
$ DESTIN_AGE13_24 <dbl> 710, 2770, 2650, 2000, 1920, 2390, 1120, 1150, 3260, 0…
$ DESTIN_AGE25_64 <dbl> 2780, 15700, 14240, 11320, 9650, 12460, 3620, 4350, 13…Code
write_rds(flow_data1, "../data/rds/SIM_data.rds")6 Calibrating Spatial Interaction Models
In this section, you will learn how to calibrate Spatial Interaction Models by using Poisson Regression method.
6.1 Importing the modelling data
Firstly, let us import the modelling data by using the code chunk below.
Code
SIM_data <- read_rds("../data/rds/SIM_data.rds")
# check the output
glimpse(SIM_data)Rows: 20,595
Columns: 12
Groups: ORIGIN_SZ [309]
$ ORIGIN_SZ <chr> "AMSZ01", "AMSZ01", "AMSZ01", "AMSZ01", "AMSZ01", "AMS…
$ DESTIN_SZ <chr> "AMSZ01", "AMSZ02", "AMSZ03", "AMSZ04", "AMSZ05", "AMS…
$ TRIPS <dbl> 1866, 8726, 12598, 2098, 7718, 1631, 1308, 2261, 1526,…
$ FlowNoIntra <dbl> 0, 8726, 12598, 2098, 7718, 1631, 1308, 2261, 1526, 14…
$ offset <dbl> 1e-06, 1e+00, 1e+00, 1e+00, 1e+00, 1e+00, 1e+00, 1e+00…
$ dist <dbl> 50.0000, 810.4491, 1360.9294, 840.4432, 1076.7916, 805…
$ ORIGIN_AGE7_12 <dbl> 310, 310, 310, 310, 310, 310, 310, 310, 310, 310, 310,…
$ ORIGIN_AGE13_24 <dbl> 710, 710, 710, 710, 710, 710, 710, 710, 710, 710, 710,…
$ ORIGIN_AGE25_64 <dbl> 2780, 2780, 2780, 2780, 2780, 2780, 2780, 2780, 2780, …
$ DESTIN_AGE7_12 <dbl> 310, 1140, 1010, 980, 810, 1050, 420, 390, 1190, 0, 0,…
$ DESTIN_AGE13_24 <dbl> 710, 2770, 2650, 2000, 1920, 2390, 1120, 1150, 3260, 0…
$ DESTIN_AGE25_64 <dbl> 2780, 15700, 14240, 11320, 9650, 12460, 3620, 4350, 13…6.2 Visualising the dependent variable
Firstly, let us plot the distribution of the dependent variable (i.e. TRIPS) by using histogram method by using the code chunk below.
Code
ggplot(data = SIM_data,
aes(x = TRIPS)) +
geom_histogram()
Notice that the distribution is highly skewed and not resemble bell shape or also known as normal distribution.
Next, let us visualise the relation between the dependent variable and one of the key independent variable in Spatial Interaction Model, namely distance.
Code
ggplot(data = SIM_data,
aes(x = dist,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
Notice that their relationship hardly resemble linear relationship.
On the other hand, if we plot the scatter plot by using the log transformed version of both variables, we can see that their relationship is more resemble linear relationship.
Code
ggplot(data = SIM_data,
aes(x = log(dist),
y = log(TRIPS))) +
geom_point() +
geom_smooth(method = lm)
6.3 Checking for variables with zero values
Since Poisson Regression is based of log and log 0 is undefined, it is important for us to ensure that no 0 values in the explanatory variables.
In the code chunk below, summary() of Base R is used to compute the summary statistics of all variables in SIM_data data frame.
Code
summary(SIM_data) ORIGIN_SZ DESTIN_SZ TRIPS FlowNoIntra
Length:20595 Length:20595 Min. : 1 Min. : 0.0
Class :character Class :character 1st Qu.: 17 1st Qu.: 15.0
Mode :character Mode :character Median : 82 Median : 77.0
Mean : 1035 Mean : 867.4
3rd Qu.: 418 3rd Qu.: 382.0
Max. :294318 Max. :193431.0
offset dist ORIGIN_AGE7_12 ORIGIN_AGE13_24
Min. :0.000001 Min. : 50 Min. : 0.0 Min. : 0
1st Qu.:1.000000 1st Qu.: 3351 1st Qu.: 50.0 1st Qu.: 100
Median :1.000000 Median : 6108 Median : 510.0 Median : 1140
Mean :0.985870 Mean : 6952 Mean : 890.6 Mean : 1958
3rd Qu.:1.000000 3rd Qu.: 9849 3rd Qu.:1360.0 3rd Qu.: 3010
Max. :1.000000 Max. :26136 Max. :6340.0 Max. :16380
ORIGIN_AGE25_64 DESTIN_AGE7_12 DESTIN_AGE13_24 DESTIN_AGE25_64
Min. : 0 Min. : 0.0 Min. : 0 Min. : 0
1st Qu.: 730 1st Qu.: 10.0 1st Qu.: 60 1st Qu.: 630
Median : 5730 Median : 510.0 Median : 1090 Median : 5640
Mean : 9111 Mean : 847.9 Mean : 1879 Mean : 8753
3rd Qu.:14200 3rd Qu.:1200.0 3rd Qu.: 2920 3rd Qu.:13650
Max. :74610 Max. :6340.0 Max. :16380 Max. :74610 The print report above reveals that variables ORIGIN_AGE7_12, ORIGIN_AGE13_24, ORIGIN_AGE25_64,DESTIN_AGE7_12, DESTIN_AGE13_24, DESTIN_AGE25_64 consist of 0 values.
In view of this, code chunk below will be used to replace zero values to 0.99.
Code
SIM_data$DESTIN_AGE7_12 <- ifelse(
SIM_data$DESTIN_AGE7_12 == 0,
0.99, SIM_data$DESTIN_AGE7_12)
SIM_data$DESTIN_AGE13_24 <- ifelse(
SIM_data$DESTIN_AGE13_24 == 0,
0.99, SIM_data$DESTIN_AGE13_24)
SIM_data$DESTIN_AGE25_64 <- ifelse(
SIM_data$DESTIN_AGE25_64 == 0,
0.99, SIM_data$DESTIN_AGE25_64)
SIM_data$ORIGIN_AGE7_12 <- ifelse(
SIM_data$ORIGIN_AGE7_12 == 0,
0.99, SIM_data$ORIGIN_AGE7_12)
SIM_data$ORIGIN_AGE13_24 <- ifelse(
SIM_data$ORIGIN_AGE13_24 == 0,
0.99, SIM_data$ORIGIN_AGE13_24)
SIM_data$ORIGIN_AGE25_64 <- ifelse(
SIM_data$ORIGIN_AGE25_64 == 0,
0.99, SIM_data$ORIGIN_AGE25_64)
# check the summary again
summary(SIM_data) ORIGIN_SZ DESTIN_SZ TRIPS FlowNoIntra
Length:20595 Length:20595 Min. : 1 Min. : 0.0
Class :character Class :character 1st Qu.: 17 1st Qu.: 15.0
Mode :character Mode :character Median : 82 Median : 77.0
Mean : 1035 Mean : 867.4
3rd Qu.: 418 3rd Qu.: 382.0
Max. :294318 Max. :193431.0
offset dist ORIGIN_AGE7_12 ORIGIN_AGE13_24
Min. :0.000001 Min. : 50 Min. : 0.99 Min. : 0.99
1st Qu.:1.000000 1st Qu.: 3351 1st Qu.: 50.00 1st Qu.: 100.00
Median :1.000000 Median : 6108 Median : 510.00 Median : 1140.00
Mean :0.985870 Mean : 6952 Mean : 890.79 Mean : 1958.29
3rd Qu.:1.000000 3rd Qu.: 9849 3rd Qu.:1360.00 3rd Qu.: 3010.00
Max. :1.000000 Max. :26136 Max. :6340.00 Max. :16380.00
ORIGIN_AGE25_64 DESTIN_AGE7_12 DESTIN_AGE13_24 DESTIN_AGE25_64
Min. : 0.99 Min. : 0.99 Min. : 0.99 Min. : 0.99
1st Qu.: 730.00 1st Qu.: 10.00 1st Qu.: 60.00 1st Qu.: 630.00
Median : 5730.00 Median : 510.00 Median : 1090.00 Median : 5640.00
Mean : 9111.14 Mean : 848.09 Mean : 1878.77 Mean : 8752.82
3rd Qu.:14200.00 3rd Qu.:1200.00 3rd Qu.: 2920.00 3rd Qu.:13650.00
Max. :74610.00 Max. :6340.00 Max. :16380.00 Max. :74610.00 Notice that all the 0 values have been replaced by 0.99.
6.4 Unconstrained Spatial Interaction Model
In this section, you will learn how to calibrate an unconstrained spatial interaction model by using glm() of Base Stats. The explanatory variables are origin population by different age cohort, destination population by different age cohort (i.e. ORIGIN_AGE25_64) and distance between origin and destination in km (i.e. dist).
The code chunk used to calibrate to model is shown below:
Code
uncSIM <- glm(formula = TRIPS ~
log(ORIGIN_AGE25_64) +
log(DESTIN_AGE25_64) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
uncSIM
Call: glm(formula = TRIPS ~ log(ORIGIN_AGE25_64) + log(DESTIN_AGE25_64) +
log(dist), family = poisson(link = "log"), data = SIM_data,
na.action = na.exclude)
Coefficients:
(Intercept) log(ORIGIN_AGE25_64) log(DESTIN_AGE25_64)
10.22832 0.27718 0.02411
log(dist)
-0.71469
Degrees of Freedom: 20594 Total (i.e. Null); 20591 Residual
Null Deviance: 88880000
Residual Deviance: 53020000 AIC: 531500006.5 R-squared function
The model by default doesn’t calculate the R-Squared. In order to measure how much variation of the trips can be accounted by the model we will write a function to calculate R-Squared value as shown below.
Code
CalcRSquared <- function(observed,estimated){
r <- cor(observed,estimated)
R2 <- r^2
R2
}Next, we will compute the R-squared of the unconstrained SIM by using the code chunk below.
Code
CalcRSquared(uncSIM$data$TRIPS, uncSIM$fitted.values)[1] 0.1967139Code
r2_mcfadden(uncSIM)# R2 for Generalized Linear Regression
R2: 0.403
adj. R2: 0.4036.6 Origin (Production) constrained SIM
In this section, we will fit an origin constrained SIM by using the code chunk below.
Code
orcSIM <- glm(formula = TRIPS ~
ORIGIN_SZ +
log(DESTIN_AGE25_64) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
summary(orcSIM)
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + log(DESTIN_AGE25_64) + log(dist),
family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 12.2572696 0.0033923 3613.272 < 2e-16 ***
ORIGIN_SZAMSZ02 1.1212940 0.0039607 283.101 < 2e-16 ***
ORIGIN_SZAMSZ03 0.6787221 0.0040298 168.427 < 2e-16 ***
ORIGIN_SZAMSZ04 0.0636727 0.0045251 14.071 < 2e-16 ***
ORIGIN_SZAMSZ05 -0.1296956 0.0051665 -25.103 < 2e-16 ***
ORIGIN_SZAMSZ06 0.4646209 0.0046414 100.103 < 2e-16 ***
ORIGIN_SZAMSZ07 -1.2315871 0.0081619 -150.895 < 2e-16 ***
ORIGIN_SZAMSZ08 -0.8741408 0.0075459 -115.843 < 2e-16 ***
ORIGIN_SZAMSZ09 0.2398512 0.0048975 48.975 < 2e-16 ***
ORIGIN_SZAMSZ10 0.2244468 0.0045595 49.226 < 2e-16 ***
ORIGIN_SZAMSZ11 -1.4593622 0.0098202 -148.608 < 2e-16 ***
ORIGIN_SZAMSZ12 -1.4677469 0.0095357 -153.921 < 2e-16 ***
ORIGIN_SZBDSZ01 1.1106031 0.0038840 285.940 < 2e-16 ***
ORIGIN_SZBDSZ02 0.5793879 0.0044817 129.279 < 2e-16 ***
ORIGIN_SZBDSZ03 1.0615203 0.0040366 262.976 < 2e-16 ***
ORIGIN_SZBDSZ04 1.8081125 0.0034995 516.672 < 2e-16 ***
ORIGIN_SZBDSZ05 0.8010218 0.0039584 202.362 < 2e-16 ***
ORIGIN_SZBDSZ06 0.9819301 0.0040389 243.116 < 2e-16 ***
ORIGIN_SZBDSZ07 -0.7462355 0.0068016 -109.715 < 2e-16 ***
ORIGIN_SZBDSZ08 -0.6166486 0.0064772 -95.203 < 2e-16 ***
ORIGIN_SZBKSZ01 -0.1949723 0.0055333 -35.236 < 2e-16 ***
ORIGIN_SZBKSZ02 0.5449125 0.0044864 121.459 < 2e-16 ***
ORIGIN_SZBKSZ03 0.8673677 0.0042071 206.167 < 2e-16 ***
ORIGIN_SZBKSZ04 0.0297416 0.0051862 5.735 9.77e-09 ***
ORIGIN_SZBKSZ05 0.0432635 0.0049218 8.790 < 2e-16 ***
ORIGIN_SZBKSZ06 0.1661698 0.0051314 32.383 < 2e-16 ***
ORIGIN_SZBKSZ07 0.8341305 0.0039471 211.330 < 2e-16 ***
ORIGIN_SZBKSZ08 0.1716913 0.0045799 37.488 < 2e-16 ***
ORIGIN_SZBKSZ09 0.1324636 0.0048567 27.274 < 2e-16 ***
ORIGIN_SZBLSZ01 -1.1815847 0.0105831 -111.648 < 2e-16 ***
ORIGIN_SZBLSZ02 -1.9027359 0.0157452 -120.845 < 2e-16 ***
ORIGIN_SZBLSZ03 -3.1794436 0.0356395 -89.211 < 2e-16 ***
ORIGIN_SZBLSZ04 -1.9390262 0.0190190 -101.952 < 2e-16 ***
ORIGIN_SZBMSZ01 0.0422565 0.0044140 9.573 < 2e-16 ***
ORIGIN_SZBMSZ02 -1.1557535 0.0061561 -187.741 < 2e-16 ***
ORIGIN_SZBMSZ03 -0.4645261 0.0050813 -91.420 < 2e-16 ***
ORIGIN_SZBMSZ04 -0.0188526 0.0044369 -4.249 2.15e-05 ***
ORIGIN_SZBMSZ05 -1.2949324 0.0067112 -192.951 < 2e-16 ***
ORIGIN_SZBMSZ06 -1.8316625 0.0106920 -171.311 < 2e-16 ***
ORIGIN_SZBMSZ07 -0.3965595 0.0048890 -81.112 < 2e-16 ***
ORIGIN_SZBMSZ08 -0.4426364 0.0048874 -90.568 < 2e-16 ***
ORIGIN_SZBMSZ09 -1.1520773 0.0064126 -179.659 < 2e-16 ***
ORIGIN_SZBMSZ10 -1.3498102 0.0071277 -189.375 < 2e-16 ***
ORIGIN_SZBMSZ11 -0.7587589 0.0056716 -133.781 < 2e-16 ***
ORIGIN_SZBMSZ12 -1.0123456 0.0075871 -133.430 < 2e-16 ***
ORIGIN_SZBMSZ13 -0.0326386 0.0048100 -6.786 1.16e-11 ***
ORIGIN_SZBMSZ14 -0.5068184 0.0056570 -89.592 < 2e-16 ***
ORIGIN_SZBMSZ15 -0.2700839 0.0051562 -52.381 < 2e-16 ***
ORIGIN_SZBMSZ16 -1.3018102 0.0066844 -194.754 < 2e-16 ***
ORIGIN_SZBMSZ17 -1.7002849 0.0099997 -170.034 < 2e-16 ***
ORIGIN_SZBPSZ01 0.2670882 0.0048127 55.496 < 2e-16 ***
ORIGIN_SZBPSZ02 0.3029033 0.0052799 57.369 < 2e-16 ***
ORIGIN_SZBPSZ03 0.5460184 0.0049083 111.245 < 2e-16 ***
ORIGIN_SZBPSZ04 0.6201988 0.0043235 143.448 < 2e-16 ***
ORIGIN_SZBPSZ05 0.7093808 0.0040011 177.298 < 2e-16 ***
ORIGIN_SZBPSZ06 -1.0264891 0.0074092 -138.543 < 2e-16 ***
ORIGIN_SZBPSZ07 -0.7883103 0.0071685 -109.969 < 2e-16 ***
ORIGIN_SZBSSZ01 -0.0579461 0.0047779 -12.128 < 2e-16 ***
ORIGIN_SZBSSZ02 0.2422283 0.0043752 55.363 < 2e-16 ***
ORIGIN_SZBSSZ03 0.2542201 0.0042320 60.070 < 2e-16 ***
ORIGIN_SZBTSZ01 0.0436110 0.0046547 9.369 < 2e-16 ***
ORIGIN_SZBTSZ02 -1.0024374 0.0067691 -148.091 < 2e-16 ***
ORIGIN_SZBTSZ03 -0.2061598 0.0050780 -40.598 < 2e-16 ***
ORIGIN_SZBTSZ04 -0.9023295 0.0087625 -102.976 < 2e-16 ***
ORIGIN_SZBTSZ05 -1.6251914 0.0096449 -168.503 < 2e-16 ***
ORIGIN_SZBTSZ06 -0.8480543 0.0065978 -128.537 < 2e-16 ***
ORIGIN_SZBTSZ07 -2.0292996 0.0104316 -194.534 < 2e-16 ***
ORIGIN_SZBTSZ08 -1.2640422 0.0079299 -159.401 < 2e-16 ***
ORIGIN_SZCCSZ01 -1.6771075 0.0118019 -142.105 < 2e-16 ***
ORIGIN_SZCHSZ01 -1.0912676 0.0099165 -110.045 < 2e-16 ***
ORIGIN_SZCHSZ02 -0.4514736 0.0068723 -65.695 < 2e-16 ***
ORIGIN_SZCHSZ03 0.5201937 0.0051526 100.957 < 2e-16 ***
ORIGIN_SZCKSZ01 0.4643065 0.0043433 106.901 < 2e-16 ***
ORIGIN_SZCKSZ02 0.9712995 0.0043842 221.545 < 2e-16 ***
ORIGIN_SZCKSZ03 0.9651436 0.0039914 241.809 < 2e-16 ***
ORIGIN_SZCKSZ04 1.3776079 0.0041025 335.799 < 2e-16 ***
ORIGIN_SZCKSZ05 1.1403408 0.0046546 244.994 < 2e-16 ***
ORIGIN_SZCKSZ06 1.1814517 0.0047394 249.284 < 2e-16 ***
ORIGIN_SZCLSZ01 -0.2625408 0.0060463 -43.421 < 2e-16 ***
ORIGIN_SZCLSZ02 -1.5833035 0.0111998 -141.369 < 2e-16 ***
ORIGIN_SZCLSZ03 -0.6651994 0.0063921 -104.066 < 2e-16 ***
ORIGIN_SZCLSZ04 0.7306030 0.0040000 182.652 < 2e-16 ***
ORIGIN_SZCLSZ05 -1.7395269 0.0113461 -153.316 < 2e-16 ***
ORIGIN_SZCLSZ06 0.9151166 0.0037622 243.237 < 2e-16 ***
ORIGIN_SZCLSZ07 -0.1290062 0.0047742 -27.022 < 2e-16 ***
ORIGIN_SZCLSZ08 0.2831183 0.0053130 53.288 < 2e-16 ***
ORIGIN_SZCLSZ09 -1.7014889 0.0141617 -120.147 < 2e-16 ***
ORIGIN_SZDTSZ01 -1.8145219 0.0079086 -229.438 < 2e-16 ***
ORIGIN_SZDTSZ02 -1.7116162 0.0074074 -231.068 < 2e-16 ***
ORIGIN_SZDTSZ03 -2.7281355 0.0134862 -202.291 < 2e-16 ***
ORIGIN_SZDTSZ04 -4.8770124 0.1768059 -27.584 < 2e-16 ***
ORIGIN_SZDTSZ05 -3.1783516 0.0248945 -127.673 < 2e-16 ***
ORIGIN_SZDTSZ06 -2.9790538 0.0184580 -161.397 < 2e-16 ***
ORIGIN_SZDTSZ07 -2.0587311 0.0234708 -87.715 < 2e-16 ***
ORIGIN_SZDTSZ08 -2.6020132 0.0120040 -216.761 < 2e-16 ***
ORIGIN_SZDTSZ09 -3.1137420 0.0238669 -130.463 < 2e-16 ***
ORIGIN_SZDTSZ10 -2.4198270 0.0126801 -190.837 < 2e-16 ***
ORIGIN_SZDTSZ11 -2.4192801 0.0124179 -194.822 < 2e-16 ***
ORIGIN_SZDTSZ12 -3.4779254 0.0258344 -134.624 < 2e-16 ***
ORIGIN_SZDTSZ13 -2.4434777 0.0138218 -176.784 < 2e-16 ***
ORIGIN_SZGLSZ01 -1.3115899 0.0077081 -170.158 < 2e-16 ***
ORIGIN_SZGLSZ02 0.2730786 0.0043545 62.712 < 2e-16 ***
ORIGIN_SZGLSZ03 0.2478516 0.0043346 57.179 < 2e-16 ***
ORIGIN_SZGLSZ04 1.0058548 0.0036748 273.720 < 2e-16 ***
ORIGIN_SZGLSZ05 0.7072126 0.0038732 182.591 < 2e-16 ***
ORIGIN_SZHGSZ01 0.3007989 0.0042707 70.434 < 2e-16 ***
ORIGIN_SZHGSZ02 0.6581956 0.0041215 159.696 < 2e-16 ***
ORIGIN_SZHGSZ03 0.3816820 0.0044541 85.692 < 2e-16 ***
ORIGIN_SZHGSZ04 1.0312270 0.0038239 269.679 < 2e-16 ***
ORIGIN_SZHGSZ05 1.3474590 0.0037638 358.002 < 2e-16 ***
ORIGIN_SZHGSZ06 -0.0008560 0.0047716 -0.179 0.858
ORIGIN_SZHGSZ07 0.6783256 0.0040470 167.613 < 2e-16 ***
ORIGIN_SZHGSZ08 0.2694945 0.0046363 58.127 < 2e-16 ***
ORIGIN_SZHGSZ09 -0.3546400 0.0059699 -59.405 < 2e-16 ***
ORIGIN_SZHGSZ10 -3.5666964 0.0406525 -87.736 < 2e-16 ***
ORIGIN_SZJESZ01 0.4529442 0.0044005 102.930 < 2e-16 ***
ORIGIN_SZJESZ02 0.3211377 0.0044029 72.938 < 2e-16 ***
ORIGIN_SZJESZ03 0.3064323 0.0046509 65.887 < 2e-16 ***
ORIGIN_SZJESZ04 -0.7940371 0.0072484 -109.547 < 2e-16 ***
ORIGIN_SZJESZ05 -2.0200755 0.0124785 -161.885 < 2e-16 ***
ORIGIN_SZJESZ06 0.3574364 0.0042945 83.232 < 2e-16 ***
ORIGIN_SZJESZ07 -1.6623511 0.0097460 -170.567 < 2e-16 ***
ORIGIN_SZJESZ08 -0.5936736 0.0084664 -70.122 < 2e-16 ***
ORIGIN_SZJESZ09 0.5925988 0.0043747 135.460 < 2e-16 ***
ORIGIN_SZJESZ10 -1.8928884 0.0174179 -108.675 < 2e-16 ***
ORIGIN_SZJESZ11 -1.9498962 0.0176831 -110.269 < 2e-16 ***
ORIGIN_SZJWSZ01 0.3397470 0.0055918 60.758 < 2e-16 ***
ORIGIN_SZJWSZ02 0.9872669 0.0040137 245.972 < 2e-16 ***
ORIGIN_SZJWSZ03 1.3117797 0.0037866 346.426 < 2e-16 ***
ORIGIN_SZJWSZ04 1.4410492 0.0038105 378.182 < 2e-16 ***
ORIGIN_SZJWSZ05 -1.2965989 0.0110930 -116.885 < 2e-16 ***
ORIGIN_SZJWSZ06 -0.6945608 0.0086716 -80.096 < 2e-16 ***
ORIGIN_SZJWSZ07 -2.0864854 0.0190587 -109.477 < 2e-16 ***
ORIGIN_SZJWSZ08 2.0611243 0.0036751 560.841 < 2e-16 ***
ORIGIN_SZJWSZ09 1.9210266 0.0035021 548.532 < 2e-16 ***
ORIGIN_SZKLSZ01 0.1862217 0.0042349 43.973 < 2e-16 ***
ORIGIN_SZKLSZ02 -0.4125654 0.0052719 -78.258 < 2e-16 ***
ORIGIN_SZKLSZ03 -0.4641146 0.0053630 -86.540 < 2e-16 ***
ORIGIN_SZKLSZ04 -1.6469790 0.0075243 -218.888 < 2e-16 ***
ORIGIN_SZKLSZ05 -0.5708516 0.0062612 -91.173 < 2e-16 ***
ORIGIN_SZKLSZ06 -0.6135703 0.0050199 -122.229 < 2e-16 ***
ORIGIN_SZKLSZ07 -0.9243953 0.0065292 -141.580 < 2e-16 ***
ORIGIN_SZKLSZ08 -0.8402631 0.0057370 -146.463 < 2e-16 ***
ORIGIN_SZKLSZ09 -1.5443628 0.0071835 -214.989 < 2e-16 ***
ORIGIN_SZLKSZ01 -3.0498721 0.0325902 -93.582 < 2e-16 ***
ORIGIN_SZMDSZ01 -2.2872480 0.0220629 -103.670 < 2e-16 ***
ORIGIN_SZMDSZ02 -0.9139494 0.0097760 -93.490 < 2e-16 ***
ORIGIN_SZMDSZ03 -1.7584031 0.0142443 -123.446 < 2e-16 ***
ORIGIN_SZMPSZ01 -0.7418280 0.0063752 -116.361 < 2e-16 ***
ORIGIN_SZMPSZ02 -0.4049433 0.0056898 -71.170 < 2e-16 ***
ORIGIN_SZMPSZ03 0.4293520 0.0042584 100.826 < 2e-16 ***
ORIGIN_SZMSSZ01 -5.2500139 0.2582191 -20.332 < 2e-16 ***
ORIGIN_SZMUSZ01 -1.2678739 0.0063126 -200.850 < 2e-16 ***
ORIGIN_SZMUSZ02 -3.3942329 0.0181446 -187.066 < 2e-16 ***
ORIGIN_SZMUSZ03 -1.8581351 0.0074767 -248.523 < 2e-16 ***
ORIGIN_SZNTSZ01 -2.4562075 0.0264752 -92.774 < 2e-16 ***
ORIGIN_SZNTSZ02 -2.6884420 0.0153396 -175.261 < 2e-16 ***
ORIGIN_SZNTSZ03 -1.0303438 0.0068334 -150.781 < 2e-16 ***
ORIGIN_SZNTSZ05 -2.9962455 0.0381225 -78.595 < 2e-16 ***
ORIGIN_SZNTSZ06 -3.3552120 0.0417904 -80.287 < 2e-16 ***
ORIGIN_SZNVSZ01 0.6548716 0.0038396 170.557 < 2e-16 ***
ORIGIN_SZNVSZ02 -0.5361448 0.0053627 -99.976 < 2e-16 ***
ORIGIN_SZNVSZ03 -1.0528433 0.0064538 -163.134 < 2e-16 ***
ORIGIN_SZNVSZ04 -1.3381785 0.0079171 -169.024 < 2e-16 ***
ORIGIN_SZNVSZ05 -2.5754839 0.0143828 -179.067 < 2e-16 ***
ORIGIN_SZORSZ01 -3.4040375 0.0362979 -93.781 < 2e-16 ***
ORIGIN_SZORSZ02 -1.3352978 0.0065131 -205.018 < 2e-16 ***
ORIGIN_SZORSZ03 -1.7229476 0.0075332 -228.713 < 2e-16 ***
ORIGIN_SZOTSZ01 -1.8245855 0.0081594 -223.619 < 2e-16 ***
ORIGIN_SZOTSZ02 -1.9273604 0.0094606 -203.725 < 2e-16 ***
ORIGIN_SZOTSZ03 -0.8069204 0.0057452 -140.452 < 2e-16 ***
ORIGIN_SZOTSZ04 -0.7940269 0.0094023 -84.451 < 2e-16 ***
ORIGIN_SZPGSZ01 -0.5446157 0.0094909 -57.383 < 2e-16 ***
ORIGIN_SZPGSZ02 -0.2397058 0.0059692 -40.157 < 2e-16 ***
ORIGIN_SZPGSZ03 1.1783844 0.0038896 302.957 < 2e-16 ***
ORIGIN_SZPGSZ04 1.3000300 0.0038964 333.647 < 2e-16 ***
ORIGIN_SZPGSZ05 0.5408202 0.0048536 111.427 < 2e-16 ***
ORIGIN_SZPLSZ01 -0.4449592 0.0083124 -53.530 < 2e-16 ***
ORIGIN_SZPLSZ02 -1.3633297 0.0119902 -113.704 < 2e-16 ***
ORIGIN_SZPLSZ03 -2.9115692 0.0335677 -86.737 < 2e-16 ***
ORIGIN_SZPLSZ04 -2.9023724 0.0287202 -101.057 < 2e-16 ***
ORIGIN_SZPLSZ05 -2.1073402 0.0177182 -118.937 < 2e-16 ***
ORIGIN_SZPNSZ01 1.7040086 0.0039994 426.071 < 2e-16 ***
ORIGIN_SZPNSZ02 -0.4002217 0.0098818 -40.501 < 2e-16 ***
ORIGIN_SZPNSZ03 -1.8693822 0.0176894 -105.678 < 2e-16 ***
ORIGIN_SZPNSZ04 -2.4096607 0.0245671 -98.085 < 2e-16 ***
ORIGIN_SZPNSZ05 -1.8960264 0.0204403 -92.759 < 2e-16 ***
ORIGIN_SZPRSZ01 -0.5425870 0.0095462 -56.838 < 2e-16 ***
ORIGIN_SZPRSZ02 1.1920907 0.0040336 295.540 < 2e-16 ***
ORIGIN_SZPRSZ03 0.9184264 0.0040785 225.187 < 2e-16 ***
ORIGIN_SZPRSZ04 -0.0751974 0.0062876 -11.960 < 2e-16 ***
ORIGIN_SZPRSZ05 1.3805921 0.0038601 357.658 < 2e-16 ***
ORIGIN_SZPRSZ06 -0.3837116 0.0070846 -54.161 < 2e-16 ***
ORIGIN_SZPRSZ07 -2.4584271 0.0177702 -138.345 < 2e-16 ***
ORIGIN_SZPRSZ08 0.2235210 0.0053221 41.999 < 2e-16 ***
ORIGIN_SZQTSZ01 -0.3595589 0.0058016 -61.976 < 2e-16 ***
ORIGIN_SZQTSZ02 -0.7358763 0.0055570 -132.424 < 2e-16 ***
ORIGIN_SZQTSZ03 -0.2046825 0.0049273 -41.541 < 2e-16 ***
ORIGIN_SZQTSZ04 -1.1088186 0.0067100 -165.250 < 2e-16 ***
ORIGIN_SZQTSZ05 -0.2193014 0.0049742 -44.088 < 2e-16 ***
ORIGIN_SZQTSZ06 -0.5989010 0.0057359 -104.413 < 2e-16 ***
ORIGIN_SZQTSZ07 -1.4949944 0.0082826 -180.498 < 2e-16 ***
ORIGIN_SZQTSZ08 -0.2099139 0.0051293 -40.924 < 2e-16 ***
ORIGIN_SZQTSZ09 -0.5306478 0.0058251 -91.097 < 2e-16 ***
ORIGIN_SZQTSZ10 -0.4512726 0.0057866 -77.986 < 2e-16 ***
ORIGIN_SZQTSZ11 -1.4759004 0.0090242 -163.549 < 2e-16 ***
ORIGIN_SZQTSZ12 -1.1911006 0.0085137 -139.904 < 2e-16 ***
ORIGIN_SZQTSZ13 -0.2161536 0.0053915 -40.091 < 2e-16 ***
ORIGIN_SZQTSZ14 -1.4897181 0.0083117 -179.232 < 2e-16 ***
ORIGIN_SZQTSZ15 -0.7477987 0.0090161 -82.941 < 2e-16 ***
ORIGIN_SZRCSZ01 -0.6762835 0.0058785 -115.044 < 2e-16 ***
ORIGIN_SZRCSZ02 -2.1258129 0.0156784 -135.589 < 2e-16 ***
ORIGIN_SZRCSZ03 -1.4399103 0.0078671 -183.030 < 2e-16 ***
ORIGIN_SZRCSZ04 -2.3099870 0.0123228 -187.456 < 2e-16 ***
ORIGIN_SZRCSZ05 -2.6222453 0.0136375 -192.281 < 2e-16 ***
ORIGIN_SZRCSZ06 -0.5427707 0.0077544 -69.995 < 2e-16 ***
ORIGIN_SZRCSZ08 -2.6176399 0.0179817 -145.572 < 2e-16 ***
ORIGIN_SZRCSZ09 -1.9918704 0.0131464 -151.515 < 2e-16 ***
ORIGIN_SZRCSZ10 -1.8807519 0.0078372 -239.977 < 2e-16 ***
ORIGIN_SZRVSZ01 -2.7768113 0.0139448 -199.129 < 2e-16 ***
ORIGIN_SZRVSZ02 -1.2333052 0.0074671 -165.164 < 2e-16 ***
ORIGIN_SZRVSZ03 -2.0800925 0.0113273 -183.636 < 2e-16 ***
ORIGIN_SZRVSZ04 -2.2042043 0.0173312 -127.181 < 2e-16 ***
ORIGIN_SZRVSZ05 -2.2883530 0.0135606 -168.750 < 2e-16 ***
ORIGIN_SZSBSZ01 0.8761288 0.0047107 185.987 < 2e-16 ***
ORIGIN_SZSBSZ02 -0.5335854 0.0068864 -77.484 < 2e-16 ***
ORIGIN_SZSBSZ03 1.0956192 0.0040819 268.409 < 2e-16 ***
ORIGIN_SZSBSZ04 0.8241213 0.0047312 174.189 < 2e-16 ***
ORIGIN_SZSBSZ05 0.0023653 0.0057903 0.408 0.683
ORIGIN_SZSBSZ06 -1.4914450 0.0137999 -108.077 < 2e-16 ***
ORIGIN_SZSBSZ07 -0.6571146 0.0094394 -69.614 < 2e-16 ***
ORIGIN_SZSBSZ08 -0.8442772 0.0096352 -87.625 < 2e-16 ***
ORIGIN_SZSBSZ09 -0.3064340 0.0072204 -42.440 < 2e-16 ***
ORIGIN_SZSESZ02 1.1589509 0.0038964 297.442 < 2e-16 ***
ORIGIN_SZSESZ03 1.3881796 0.0036936 375.831 < 2e-16 ***
ORIGIN_SZSESZ04 1.0524974 0.0042260 249.052 < 2e-16 ***
ORIGIN_SZSESZ05 -0.0564228 0.0051174 -11.026 < 2e-16 ***
ORIGIN_SZSESZ06 1.0440818 0.0040293 259.121 < 2e-16 ***
ORIGIN_SZSESZ07 -2.1820069 0.0150605 -144.882 < 2e-16 ***
ORIGIN_SZSGSZ01 -0.8092938 0.0073395 -110.266 < 2e-16 ***
ORIGIN_SZSGSZ02 -1.0735865 0.0086924 -123.508 < 2e-16 ***
ORIGIN_SZSGSZ03 0.4033899 0.0045448 88.758 < 2e-16 ***
ORIGIN_SZSGSZ04 0.3064766 0.0042752 71.688 < 2e-16 ***
ORIGIN_SZSGSZ05 -1.6035741 0.0089939 -178.295 < 2e-16 ***
ORIGIN_SZSGSZ06 0.4487510 0.0040601 110.526 < 2e-16 ***
ORIGIN_SZSGSZ07 -0.4956594 0.0053568 -92.529 < 2e-16 ***
ORIGIN_SZSKSZ01 -0.1479711 0.0070814 -20.896 < 2e-16 ***
ORIGIN_SZSKSZ02 0.3170221 0.0052617 60.251 < 2e-16 ***
ORIGIN_SZSKSZ03 -0.3532955 0.0064310 -54.936 < 2e-16 ***
ORIGIN_SZSKSZ04 -2.0951054 0.0205180 -102.110 < 2e-16 ***
ORIGIN_SZSKSZ05 -1.1107362 0.0128652 -86.337 < 2e-16 ***
ORIGIN_SZSLSZ01 -3.0575264 0.0267883 -114.137 < 2e-16 ***
ORIGIN_SZSLSZ04 -0.2971794 0.0062148 -47.818 < 2e-16 ***
ORIGIN_SZSRSZ01 -1.6849961 0.0080872 -208.354 < 2e-16 ***
ORIGIN_SZSRSZ02 -1.7795845 0.0078321 -227.218 < 2e-16 ***
ORIGIN_SZSRSZ03 -2.9319335 0.0175878 -166.703 < 2e-16 ***
ORIGIN_SZSVSZ01 -4.0241271 0.0567990 -70.849 < 2e-16 ***
ORIGIN_SZTHSZ01 -1.7036328 0.0363923 -46.813 < 2e-16 ***
ORIGIN_SZTHSZ03 -1.8017255 0.0161459 -111.590 < 2e-16 ***
ORIGIN_SZTHSZ04 -2.6751882 0.0251165 -106.511 < 2e-16 ***
ORIGIN_SZTHSZ06 -2.1120029 0.0149976 -140.823 < 2e-16 ***
ORIGIN_SZTMSZ01 0.9092740 0.0044891 202.550 < 2e-16 ***
ORIGIN_SZTMSZ02 2.2887849 0.0034150 670.215 < 2e-16 ***
ORIGIN_SZTMSZ03 1.5450987 0.0036606 422.093 < 2e-16 ***
ORIGIN_SZTMSZ04 0.9778404 0.0042052 232.532 < 2e-16 ***
ORIGIN_SZTMSZ05 -0.2336931 0.0065677 -35.582 < 2e-16 ***
ORIGIN_SZTNSZ01 -1.2750543 0.0069423 -183.665 < 2e-16 ***
ORIGIN_SZTNSZ02 -1.1577323 0.0065583 -176.529 < 2e-16 ***
ORIGIN_SZTNSZ03 -1.6369087 0.0087512 -187.050 < 2e-16 ***
ORIGIN_SZTNSZ04 -0.7124980 0.0060485 -117.797 < 2e-16 ***
ORIGIN_SZTPSZ01 -0.6310450 0.0055166 -114.391 < 2e-16 ***
ORIGIN_SZTPSZ02 0.4834635 0.0038861 124.408 < 2e-16 ***
ORIGIN_SZTPSZ03 -0.3603214 0.0053561 -67.274 < 2e-16 ***
ORIGIN_SZTPSZ04 -0.1342562 0.0050550 -26.559 < 2e-16 ***
ORIGIN_SZTPSZ05 -0.1562347 0.0053099 -29.424 < 2e-16 ***
ORIGIN_SZTPSZ06 0.3199803 0.0052927 60.457 < 2e-16 ***
ORIGIN_SZTPSZ07 -0.2968771 0.0057224 -51.880 < 2e-16 ***
ORIGIN_SZTPSZ08 -0.7926332 0.0075233 -105.356 < 2e-16 ***
ORIGIN_SZTPSZ09 -0.4045617 0.0056964 -71.021 < 2e-16 ***
ORIGIN_SZTPSZ10 -0.5376511 0.0061383 -87.589 < 2e-16 ***
ORIGIN_SZTPSZ11 0.2588880 0.0045921 56.377 < 2e-16 ***
ORIGIN_SZTPSZ12 -0.4225728 0.0055988 -75.476 < 2e-16 ***
ORIGIN_SZTSSZ01 -3.7467870 0.0498600 -75.146 < 2e-16 ***
ORIGIN_SZTSSZ02 0.5058653 0.0063176 80.072 < 2e-16 ***
ORIGIN_SZTSSZ03 0.6462577 0.0061046 105.864 < 2e-16 ***
ORIGIN_SZTSSZ04 0.5993265 0.0063391 94.544 < 2e-16 ***
ORIGIN_SZTSSZ05 -0.8641353 0.0117636 -73.458 < 2e-16 ***
ORIGIN_SZTSSZ06 -1.0589688 0.0142616 -74.253 < 2e-16 ***
ORIGIN_SZWCSZ01 0.4621239 0.0058731 78.685 < 2e-16 ***
ORIGIN_SZWCSZ02 -2.6525127 0.0266061 -99.696 < 2e-16 ***
ORIGIN_SZWCSZ03 -4.3369080 0.1291395 -33.583 < 2e-16 ***
ORIGIN_SZWDSZ01 1.4189977 0.0037443 378.974 < 2e-16 ***
ORIGIN_SZWDSZ02 1.2245458 0.0041590 294.432 < 2e-16 ***
ORIGIN_SZWDSZ03 2.2497227 0.0036310 619.591 < 2e-16 ***
ORIGIN_SZWDSZ04 1.2932832 0.0043466 297.541 < 2e-16 ***
ORIGIN_SZWDSZ05 0.7227242 0.0043728 165.279 < 2e-16 ***
ORIGIN_SZWDSZ06 1.2863430 0.0041281 311.603 < 2e-16 ***
ORIGIN_SZWDSZ07 -0.0704585 0.0067853 -10.384 < 2e-16 ***
ORIGIN_SZWDSZ08 -0.0999039 0.0064851 -15.405 < 2e-16 ***
ORIGIN_SZWDSZ09 1.4918246 0.0039823 374.609 < 2e-16 ***
ORIGIN_SZYSSZ01 0.0491501 0.0048620 10.109 < 2e-16 ***
ORIGIN_SZYSSZ02 1.0569803 0.0044148 239.416 < 2e-16 ***
ORIGIN_SZYSSZ03 1.9680202 0.0037549 524.125 < 2e-16 ***
ORIGIN_SZYSSZ04 0.9772633 0.0039924 244.778 < 2e-16 ***
ORIGIN_SZYSSZ05 0.2284194 0.0049481 46.163 < 2e-16 ***
ORIGIN_SZYSSZ06 -0.9728595 0.0088031 -110.513 < 2e-16 ***
ORIGIN_SZYSSZ07 -0.7317909 0.0083972 -87.147 < 2e-16 ***
ORIGIN_SZYSSZ08 0.0293379 0.0054995 5.335 9.57e-08 ***
ORIGIN_SZYSSZ09 1.4941665 0.0038008 393.122 < 2e-16 ***
log(DESTIN_AGE25_64) 0.0233376 0.0000707 330.078 < 2e-16 ***
log(dist) -0.6992470 0.0001103 -6341.237 < 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: 88883132 on 20594 degrees of freedom
Residual deviance: 38641306 on 20284 degrees of freedom
AIC: 38771033
Number of Fisher Scoring iterations: 7We can examine how the constraints hold for destinations this time.
Code
CalcRSquared(orcSIM$data$TRIPS, orcSIM$fitted.values)[1] 0.39171516.7 Destination constrained
In this section, we will fit a destination constrained SIM by using the code chunk below.
Code
decSIM <- glm(formula = TRIPS ~
DESTIN_SZ +
log(ORIGIN_AGE25_64) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
summary(decSIM)
Call:
glm(formula = TRIPS ~ DESTIN_SZ + log(ORIGIN_AGE25_64) + log(dist),
family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 10.7544783 0.0030778 3494.224 < 2e-16 ***
DESTIN_SZAMSZ02 0.2842784 0.0038567 73.710 < 2e-16 ***
DESTIN_SZAMSZ03 0.4311221 0.0036823 117.079 < 2e-16 ***
DESTIN_SZAMSZ04 -0.8007388 0.0054756 -146.237 < 2e-16 ***
DESTIN_SZAMSZ05 -0.8581992 0.0052691 -162.875 < 2e-16 ***
DESTIN_SZAMSZ06 -0.6858516 0.0052062 -131.737 < 2e-16 ***
DESTIN_SZAMSZ07 -1.7152759 0.0089336 -192.002 < 2e-16 ***
DESTIN_SZAMSZ08 -0.8492781 0.0058007 -146.409 < 2e-16 ***
DESTIN_SZAMSZ09 -0.8315432 0.0054654 -152.147 < 2e-16 ***
DESTIN_SZAMSZ10 0.5098596 0.0038774 131.496 < 2e-16 ***
DESTIN_SZAMSZ11 0.1428305 0.0066949 21.334 < 2e-16 ***
DESTIN_SZAMSZ12 -0.6776163 0.0061136 -110.838 < 2e-16 ***
DESTIN_SZBDSZ01 0.6859492 0.0034558 198.491 < 2e-16 ***
DESTIN_SZBDSZ02 -0.0650460 0.0044247 -14.701 < 2e-16 ***
DESTIN_SZBDSZ03 0.1535219 0.0038934 39.432 < 2e-16 ***
DESTIN_SZBDSZ04 1.1610114 0.0031908 363.861 < 2e-16 ***
DESTIN_SZBDSZ05 0.5402216 0.0035351 152.817 < 2e-16 ***
DESTIN_SZBDSZ06 0.3405709 0.0038462 88.547 < 2e-16 ***
DESTIN_SZBDSZ07 -0.7850130 0.0077583 -101.184 < 2e-16 ***
DESTIN_SZBDSZ08 -1.5454694 0.0090502 -170.766 < 2e-16 ***
DESTIN_SZBKSZ01 -0.8865585 0.0056112 -157.997 < 2e-16 ***
DESTIN_SZBKSZ02 -0.0322555 0.0046131 -6.992 2.71e-12 ***
DESTIN_SZBKSZ03 -0.3163073 0.0048345 -65.427 < 2e-16 ***
DESTIN_SZBKSZ04 0.2299458 0.0042654 53.910 < 2e-16 ***
DESTIN_SZBKSZ05 -0.5607967 0.0049507 -113.275 < 2e-16 ***
DESTIN_SZBKSZ06 -0.7635426 0.0055115 -138.536 < 2e-16 ***
DESTIN_SZBKSZ07 0.4333388 0.0036382 119.110 < 2e-16 ***
DESTIN_SZBKSZ08 -1.0067557 0.0062984 -159.844 < 2e-16 ***
DESTIN_SZBKSZ09 -0.2171145 0.0045109 -48.131 < 2e-16 ***
DESTIN_SZBLSZ01 -0.0916339 0.0058702 -15.610 < 2e-16 ***
DESTIN_SZBLSZ02 0.8721431 0.0057725 151.086 < 2e-16 ***
DESTIN_SZBLSZ03 1.7192914 0.0063042 272.722 < 2e-16 ***
DESTIN_SZBLSZ04 0.4513896 0.0103799 43.487 < 2e-16 ***
DESTIN_SZBMSZ01 -0.0938854 0.0040617 -23.115 < 2e-16 ***
DESTIN_SZBMSZ02 -0.4640402 0.0043367 -107.003 < 2e-16 ***
DESTIN_SZBMSZ03 -0.8431024 0.0052166 -161.619 < 2e-16 ***
DESTIN_SZBMSZ04 -0.5076804 0.0044859 -113.172 < 2e-16 ***
DESTIN_SZBMSZ05 -0.5560107 0.0053786 -103.375 < 2e-16 ***
DESTIN_SZBMSZ06 -1.6557020 0.0091469 -181.012 < 2e-16 ***
DESTIN_SZBMSZ07 -0.0433223 0.0039372 -11.003 < 2e-16 ***
DESTIN_SZBMSZ08 -1.0924453 0.0053523 -204.108 < 2e-16 ***
DESTIN_SZBMSZ09 -1.9925313 0.0084765 -235.065 < 2e-16 ***
DESTIN_SZBMSZ10 -1.6125983 0.0070600 -228.413 < 2e-16 ***
DESTIN_SZBMSZ11 -1.4951070 0.0065271 -229.062 < 2e-16 ***
DESTIN_SZBMSZ12 -1.0089277 0.0067882 -148.629 < 2e-16 ***
DESTIN_SZBMSZ13 -0.2564068 0.0043203 -59.349 < 2e-16 ***
DESTIN_SZBMSZ14 -1.0339214 0.0068113 -151.796 < 2e-16 ***
DESTIN_SZBMSZ15 -1.1402099 0.0061096 -186.625 < 2e-16 ***
DESTIN_SZBMSZ16 -1.4639092 0.0064083 -228.439 < 2e-16 ***
DESTIN_SZBMSZ17 -1.3756233 0.0075163 -183.019 < 2e-16 ***
DESTIN_SZBPSZ01 -0.4144672 0.0048362 -85.702 < 2e-16 ***
DESTIN_SZBPSZ02 -1.3855434 0.0077314 -179.210 < 2e-16 ***
DESTIN_SZBPSZ03 -1.0821948 0.0071960 -150.388 < 2e-16 ***
DESTIN_SZBPSZ04 -0.5978653 0.0053735 -111.263 < 2e-16 ***
DESTIN_SZBPSZ05 0.6144057 0.0035375 173.686 < 2e-16 ***
DESTIN_SZBPSZ06 -0.6599947 0.0065643 -100.543 < 2e-16 ***
DESTIN_SZBPSZ07 -0.3935038 0.0066280 -59.370 < 2e-16 ***
DESTIN_SZBSSZ01 -0.1330548 0.0040959 -32.485 < 2e-16 ***
DESTIN_SZBSSZ02 -0.6723597 0.0046826 -143.587 < 2e-16 ***
DESTIN_SZBSSZ03 0.2323470 0.0035879 64.759 < 2e-16 ***
DESTIN_SZBTSZ01 0.2201042 0.0037721 58.351 < 2e-16 ***
DESTIN_SZBTSZ02 -0.5616989 0.0056783 -98.919 < 2e-16 ***
DESTIN_SZBTSZ03 -0.1094260 0.0044112 -24.807 < 2e-16 ***
DESTIN_SZBTSZ04 -1.5480721 0.0088248 -175.424 < 2e-16 ***
DESTIN_SZBTSZ05 -0.6457278 0.0060380 -106.945 < 2e-16 ***
DESTIN_SZBTSZ06 -0.8461376 0.0055675 -151.979 < 2e-16 ***
DESTIN_SZBTSZ07 -1.8056009 0.0084486 -213.717 < 2e-16 ***
DESTIN_SZBTSZ08 -1.1684703 0.0073421 -159.147 < 2e-16 ***
DESTIN_SZCCSZ01 -0.5873222 0.0062887 -93.393 < 2e-16 ***
DESTIN_SZCHSZ01 -0.8919204 0.0076306 -116.887 < 2e-16 ***
DESTIN_SZCHSZ02 0.1715306 0.0047410 36.180 < 2e-16 ***
DESTIN_SZCHSZ03 1.8317483 0.0034465 531.484 < 2e-16 ***
DESTIN_SZCKSZ01 -0.1736070 0.0045215 -38.396 < 2e-16 ***
DESTIN_SZCKSZ02 -0.4057962 0.0048588 -83.517 < 2e-16 ***
DESTIN_SZCKSZ03 0.8039981 0.0035410 227.055 < 2e-16 ***
DESTIN_SZCKSZ04 -0.6234057 0.0056195 -110.937 < 2e-16 ***
DESTIN_SZCKSZ05 -0.2374672 0.0058197 -40.804 < 2e-16 ***
DESTIN_SZCKSZ06 0.6855188 0.0043127 158.955 < 2e-16 ***
DESTIN_SZCLSZ01 0.5971829 0.0042068 141.958 < 2e-16 ***
DESTIN_SZCLSZ02 -2.1086874 0.0116870 -180.431 < 2e-16 ***
DESTIN_SZCLSZ03 -0.9473942 0.0065915 -143.730 < 2e-16 ***
DESTIN_SZCLSZ04 0.1727454 0.0039508 43.724 < 2e-16 ***
DESTIN_SZCLSZ05 -0.9604930 0.0068922 -139.359 < 2e-16 ***
DESTIN_SZCLSZ06 0.1958679 0.0037619 52.066 < 2e-16 ***
DESTIN_SZCLSZ07 -0.5245235 0.0047575 -110.253 < 2e-16 ***
DESTIN_SZCLSZ08 -0.3842019 0.0052616 -73.020 < 2e-16 ***
DESTIN_SZCLSZ09 0.3507891 0.0056529 62.055 < 2e-16 ***
DESTIN_SZDTSZ01 -0.8139268 0.0048763 -166.915 < 2e-16 ***
DESTIN_SZDTSZ02 -0.8764834 0.0048218 -181.775 < 2e-16 ***
DESTIN_SZDTSZ03 -1.0713079 0.0056029 -191.205 < 2e-16 ***
DESTIN_SZDTSZ04 -1.1612049 0.0125653 -92.414 < 2e-16 ***
DESTIN_SZDTSZ05 -1.1554964 0.0088096 -131.164 < 2e-16 ***
DESTIN_SZDTSZ06 -0.9495244 0.0056955 -166.715 < 2e-16 ***
DESTIN_SZDTSZ07 -2.0195022 0.0209759 -96.277 < 2e-16 ***
DESTIN_SZDTSZ08 -0.5385311 0.0043871 -122.754 < 2e-16 ***
DESTIN_SZDTSZ09 -1.3557589 0.0096701 -140.201 < 2e-16 ***
DESTIN_SZDTSZ10 -1.5547723 0.0088951 -174.790 < 2e-16 ***
DESTIN_SZDTSZ11 -0.6096089 0.0047472 -128.414 < 2e-16 ***
DESTIN_SZDTSZ12 -2.5528352 0.0171936 -148.476 < 2e-16 ***
DESTIN_SZDTSZ13 -1.8700821 0.0097461 -191.880 < 2e-16 ***
DESTIN_SZGLSZ01 0.1395801 0.0045185 30.891 < 2e-16 ***
DESTIN_SZGLSZ02 -0.2215239 0.0041878 -52.897 < 2e-16 ***
DESTIN_SZGLSZ03 0.5305704 0.0035148 150.953 < 2e-16 ***
DESTIN_SZGLSZ04 0.4909619 0.0034415 142.658 < 2e-16 ***
DESTIN_SZGLSZ05 0.2789833 0.0035946 77.611 < 2e-16 ***
DESTIN_SZHGSZ01 0.4828098 0.0035262 136.921 < 2e-16 ***
DESTIN_SZHGSZ02 -0.4108850 0.0046526 -88.313 < 2e-16 ***
DESTIN_SZHGSZ03 -1.0120680 0.0057393 -176.340 < 2e-16 ***
DESTIN_SZHGSZ04 -0.1510585 0.0040498 -37.300 < 2e-16 ***
DESTIN_SZHGSZ05 -0.0317293 0.0040499 -7.834 4.71e-15 ***
DESTIN_SZHGSZ06 -0.7387780 0.0050170 -147.255 < 2e-16 ***
DESTIN_SZHGSZ07 0.2848829 0.0037586 75.794 < 2e-16 ***
DESTIN_SZHGSZ08 -0.1747518 0.0042881 -40.753 < 2e-16 ***
DESTIN_SZHGSZ09 0.4955605 0.0043403 114.177 < 2e-16 ***
DESTIN_SZHGSZ10 -2.7988711 0.0247620 -113.031 < 2e-16 ***
DESTIN_SZJESZ01 -0.0758996 0.0045726 -16.599 < 2e-16 ***
DESTIN_SZJESZ02 -0.4300445 0.0047711 -90.135 < 2e-16 ***
DESTIN_SZJESZ03 -0.4320075 0.0050294 -85.897 < 2e-16 ***
DESTIN_SZJESZ04 0.1591352 0.0051327 31.004 < 2e-16 ***
DESTIN_SZJESZ05 -0.7026679 0.0079778 -88.078 < 2e-16 ***
DESTIN_SZJESZ06 0.6240016 0.0036527 170.832 < 2e-16 ***
DESTIN_SZJESZ07 -0.7797674 0.0065106 -119.769 < 2e-16 ***
DESTIN_SZJESZ08 -0.3112521 0.0065040 -47.856 < 2e-16 ***
DESTIN_SZJESZ09 -0.2554206 0.0049023 -52.102 < 2e-16 ***
DESTIN_SZJESZ10 0.8982130 0.0060479 148.517 < 2e-16 ***
DESTIN_SZJESZ11 1.1158030 0.0056855 196.254 < 2e-16 ***
DESTIN_SZJWSZ01 -0.1421579 0.0054897 -25.896 < 2e-16 ***
DESTIN_SZJWSZ02 -0.1998764 0.0047858 -41.764 < 2e-16 ***
DESTIN_SZJWSZ03 0.7305091 0.0036739 198.837 < 2e-16 ***
DESTIN_SZJWSZ04 1.1620904 0.0034094 340.844 < 2e-16 ***
DESTIN_SZJWSZ05 0.0798337 0.0051584 15.476 < 2e-16 ***
DESTIN_SZJWSZ06 0.6143926 0.0047591 129.099 < 2e-16 ***
DESTIN_SZJWSZ07 -0.6933967 0.0215336 -32.201 < 2e-16 ***
DESTIN_SZJWSZ08 0.5692668 0.0041424 137.425 < 2e-16 ***
DESTIN_SZJWSZ09 1.5977471 0.0031439 508.206 < 2e-16 ***
DESTIN_SZKLSZ01 -0.5100828 0.0044070 -115.744 < 2e-16 ***
DESTIN_SZKLSZ02 -0.7448952 0.0051360 -145.034 < 2e-16 ***
DESTIN_SZKLSZ03 -1.1356547 0.0054828 -207.131 < 2e-16 ***
DESTIN_SZKLSZ04 -1.5526978 0.0069498 -223.417 < 2e-16 ***
DESTIN_SZKLSZ05 -0.6954976 0.0061482 -113.122 < 2e-16 ***
DESTIN_SZKLSZ06 -0.9305524 0.0049534 -187.861 < 2e-16 ***
DESTIN_SZKLSZ07 -0.9602322 0.0054427 -176.425 < 2e-16 ***
DESTIN_SZKLSZ08 -0.0682538 0.0040067 -17.035 < 2e-16 ***
DESTIN_SZKLSZ09 -1.8633662 0.0074100 -251.467 < 2e-16 ***
DESTIN_SZLKSZ01 -1.4555600 0.0194246 -74.934 < 2e-16 ***
DESTIN_SZMDSZ01 -0.9205158 0.0151847 -60.621 < 2e-16 ***
DESTIN_SZMDSZ02 -0.8530309 0.0093758 -90.982 < 2e-16 ***
DESTIN_SZMDSZ03 -2.6279135 0.0214513 -122.506 < 2e-16 ***
DESTIN_SZMPSZ01 -0.9379614 0.0063215 -148.375 < 2e-16 ***
DESTIN_SZMPSZ02 -0.7981221 0.0053387 -149.498 < 2e-16 ***
DESTIN_SZMPSZ03 -0.1189503 0.0042521 -27.974 < 2e-16 ***
DESTIN_SZMSSZ01 -2.9742837 0.0754302 -39.431 < 2e-16 ***
DESTIN_SZMUSZ01 -1.0789767 0.0052588 -205.176 < 2e-16 ***
DESTIN_SZMUSZ02 -1.4883519 0.0081593 -182.412 < 2e-16 ***
DESTIN_SZMUSZ03 -1.0844740 0.0051780 -209.439 < 2e-16 ***
DESTIN_SZNTSZ01 -2.5081050 0.0218327 -114.878 < 2e-16 ***
DESTIN_SZNTSZ02 -1.8745053 0.0091064 -205.844 < 2e-16 ***
DESTIN_SZNTSZ03 -1.3526210 0.0071449 -189.314 < 2e-16 ***
DESTIN_SZNTSZ05 -1.5799884 0.0168031 -94.030 < 2e-16 ***
DESTIN_SZNTSZ06 -2.7007796 0.0268534 -100.575 < 2e-16 ***
DESTIN_SZNVSZ01 -0.2170594 0.0039180 -55.400 < 2e-16 ***
DESTIN_SZNVSZ02 -0.4885292 0.0045283 -107.883 < 2e-16 ***
DESTIN_SZNVSZ03 -0.4266774 0.0045732 -93.300 < 2e-16 ***
DESTIN_SZNVSZ04 -2.1083372 0.0096520 -218.435 < 2e-16 ***
DESTIN_SZNVSZ05 -1.6998039 0.0076754 -221.462 < 2e-16 ***
DESTIN_SZORSZ01 -1.8517320 0.0180727 -102.460 < 2e-16 ***
DESTIN_SZORSZ02 -0.1337264 0.0040315 -33.170 < 2e-16 ***
DESTIN_SZORSZ03 -0.8867178 0.0051682 -171.570 < 2e-16 ***
DESTIN_SZOTSZ01 -1.5251540 0.0066856 -228.125 < 2e-16 ***
DESTIN_SZOTSZ02 -0.8898234 0.0060551 -146.955 < 2e-16 ***
DESTIN_SZOTSZ03 -1.5830128 0.0066076 -239.575 < 2e-16 ***
DESTIN_SZOTSZ04 -1.6713218 0.0095654 -174.727 < 2e-16 ***
DESTIN_SZPGSZ01 -1.7557523 0.0139239 -126.096 < 2e-16 ***
DESTIN_SZPGSZ02 -0.6203081 0.0056497 -109.796 < 2e-16 ***
DESTIN_SZPGSZ03 0.5839537 0.0036165 161.467 < 2e-16 ***
DESTIN_SZPGSZ04 0.2932457 0.0039200 74.807 < 2e-16 ***
DESTIN_SZPGSZ05 -0.7680694 0.0064170 -119.692 < 2e-16 ***
DESTIN_SZPLSZ01 0.2996748 0.0055417 54.077 < 2e-16 ***
DESTIN_SZPLSZ02 -1.0304855 0.0105925 -97.285 < 2e-16 ***
DESTIN_SZPLSZ03 0.2810055 0.0079192 35.484 < 2e-16 ***
DESTIN_SZPLSZ04 0.0979554 0.0077745 12.600 < 2e-16 ***
DESTIN_SZPLSZ05 -0.2631702 0.0092023 -28.598 < 2e-16 ***
DESTIN_SZPNSZ01 1.3763953 0.0043673 315.160 < 2e-16 ***
DESTIN_SZPNSZ02 1.9495227 0.0056086 347.593 < 2e-16 ***
DESTIN_SZPNSZ03 1.2682898 0.0063574 199.498 < 2e-16 ***
DESTIN_SZPNSZ04 2.2043895 0.0062029 355.382 < 2e-16 ***
DESTIN_SZPNSZ05 1.4510981 0.0085470 169.779 < 2e-16 ***
DESTIN_SZPRSZ01 -0.5227217 0.0064447 -81.109 < 2e-16 ***
DESTIN_SZPRSZ02 0.0071364 0.0044295 1.611 0.10716
DESTIN_SZPRSZ03 0.8826983 0.0034383 256.728 < 2e-16 ***
DESTIN_SZPRSZ04 -0.6916099 0.0076043 -90.949 < 2e-16 ***
DESTIN_SZPRSZ05 0.0514085 0.0042404 12.123 < 2e-16 ***
DESTIN_SZPRSZ06 0.6308976 0.0043312 145.663 < 2e-16 ***
DESTIN_SZPRSZ07 -1.2823462 0.0101052 -126.900 < 2e-16 ***
DESTIN_SZPRSZ08 -0.6839480 0.0059022 -115.880 < 2e-16 ***
DESTIN_SZQTSZ01 -1.2525761 0.0081381 -153.915 < 2e-16 ***
DESTIN_SZQTSZ02 -1.5688066 0.0069717 -225.023 < 2e-16 ***
DESTIN_SZQTSZ03 -0.7788391 0.0057643 -135.115 < 2e-16 ***
DESTIN_SZQTSZ04 -1.0494929 0.0060113 -174.586 < 2e-16 ***
DESTIN_SZQTSZ05 -0.8787358 0.0052678 -166.812 < 2e-16 ***
DESTIN_SZQTSZ06 -1.1509624 0.0057286 -200.916 < 2e-16 ***
DESTIN_SZQTSZ07 -1.5545926 0.0092974 -167.208 < 2e-16 ***
DESTIN_SZQTSZ08 0.0925594 0.0041608 22.246 < 2e-16 ***
DESTIN_SZQTSZ09 -0.3361120 0.0050421 -66.661 < 2e-16 ***
DESTIN_SZQTSZ10 -0.3992278 0.0046792 -85.319 < 2e-16 ***
DESTIN_SZQTSZ11 -0.0812029 0.0049649 -16.355 < 2e-16 ***
DESTIN_SZQTSZ12 -0.4611852 0.0060190 -76.622 < 2e-16 ***
DESTIN_SZQTSZ13 0.1938269 0.0042970 45.107 < 2e-16 ***
DESTIN_SZQTSZ14 -0.1786807 0.0050797 -35.175 < 2e-16 ***
DESTIN_SZQTSZ15 0.1077121 0.0059041 18.244 < 2e-16 ***
DESTIN_SZRCSZ01 -1.1748182 0.0061019 -192.533 < 2e-16 ***
DESTIN_SZRCSZ02 -2.2155688 0.0150485 -147.228 < 2e-16 ***
DESTIN_SZRCSZ03 -1.1411216 0.0079271 -143.951 < 2e-16 ***
DESTIN_SZRCSZ04 -2.3802643 0.0110853 -214.723 < 2e-16 ***
DESTIN_SZRCSZ05 -2.4902964 0.0115138 -216.288 < 2e-16 ***
DESTIN_SZRCSZ06 -2.0403985 0.0131477 -155.190 < 2e-16 ***
DESTIN_SZRCSZ08 -2.2575983 0.0126788 -178.061 < 2e-16 ***
DESTIN_SZRCSZ09 -1.4314909 0.0099334 -144.109 < 2e-16 ***
DESTIN_SZRCSZ10 -1.2087170 0.0057812 -209.079 < 2e-16 ***
DESTIN_SZRVSZ01 -2.0913677 0.0094462 -221.399 < 2e-16 ***
DESTIN_SZRVSZ02 -2.2172184 0.0123002 -180.259 < 2e-16 ***
DESTIN_SZRVSZ03 -2.4430526 0.0109800 -222.500 < 2e-16 ***
DESTIN_SZRVSZ04 -2.1093568 0.0151723 -139.026 < 2e-16 ***
DESTIN_SZRVSZ05 -1.8205586 0.0113968 -159.743 < 2e-16 ***
DESTIN_SZSBSZ01 0.0341079 0.0051219 6.659 2.75e-11 ***
DESTIN_SZSBSZ02 -0.9434174 0.0066889 -141.042 < 2e-16 ***
DESTIN_SZSBSZ03 0.7580848 0.0037726 200.946 < 2e-16 ***
DESTIN_SZSBSZ04 0.3681192 0.0045548 80.820 < 2e-16 ***
DESTIN_SZSBSZ05 -0.6636922 0.0062550 -106.105 < 2e-16 ***
DESTIN_SZSBSZ06 -2.3085673 0.0211679 -109.060 < 2e-16 ***
DESTIN_SZSBSZ07 -0.1535895 0.0132984 -11.549 < 2e-16 ***
DESTIN_SZSBSZ08 1.8331070 0.0042436 431.966 < 2e-16 ***
DESTIN_SZSBSZ09 1.1019346 0.0043139 255.436 < 2e-16 ***
DESTIN_SZSESZ02 -0.0331664 0.0041744 -7.945 1.94e-15 ***
DESTIN_SZSESZ03 0.7795130 0.0033616 231.891 < 2e-16 ***
DESTIN_SZSESZ04 -0.5233151 0.0049127 -106.522 < 2e-16 ***
DESTIN_SZSESZ05 -0.0680997 0.0041639 -16.355 < 2e-16 ***
DESTIN_SZSESZ06 -0.4259112 0.0050952 -83.591 < 2e-16 ***
DESTIN_SZSESZ07 -2.7408513 0.0200848 -136.464 < 2e-16 ***
DESTIN_SZSGSZ01 -0.2220681 0.0050154 -44.277 < 2e-16 ***
DESTIN_SZSGSZ02 0.1571425 0.0045272 34.711 < 2e-16 ***
DESTIN_SZSGSZ03 -0.2261526 0.0042946 -52.660 < 2e-16 ***
DESTIN_SZSGSZ04 -0.2248776 0.0043414 -51.799 < 2e-16 ***
DESTIN_SZSGSZ05 -1.8169721 0.0076843 -236.454 < 2e-16 ***
DESTIN_SZSGSZ06 0.5056863 0.0034431 146.868 < 2e-16 ***
DESTIN_SZSGSZ07 -0.3125875 0.0044256 -70.632 < 2e-16 ***
DESTIN_SZSISZ01 -1.4108241 0.0200736 -70.282 < 2e-16 ***
DESTIN_SZSKSZ01 0.1519040 0.0058959 25.764 < 2e-16 ***
DESTIN_SZSKSZ02 0.1206667 0.0059173 20.392 < 2e-16 ***
DESTIN_SZSKSZ03 0.2271475 0.0050553 44.933 < 2e-16 ***
DESTIN_SZSKSZ04 -0.3226828 0.0122955 -26.244 < 2e-16 ***
DESTIN_SZSKSZ05 0.3828177 0.0093083 41.127 < 2e-16 ***
DESTIN_SZSLSZ01 -0.1437078 0.0066352 -21.658 < 2e-16 ***
DESTIN_SZSLSZ04 -0.3148252 0.0055407 -56.821 < 2e-16 ***
DESTIN_SZSRSZ01 -1.5337059 0.0067560 -227.014 < 2e-16 ***
DESTIN_SZSRSZ02 -1.6868178 0.0084825 -198.859 < 2e-16 ***
DESTIN_SZSRSZ03 -1.6154544 0.0077337 -208.886 < 2e-16 ***
DESTIN_SZSVSZ01 -3.2208870 0.0556290 -57.899 < 2e-16 ***
DESTIN_SZTHSZ01 -2.6968053 0.0331414 -81.373 < 2e-16 ***
DESTIN_SZTHSZ03 -1.5397800 0.0185714 -82.911 < 2e-16 ***
DESTIN_SZTHSZ04 -2.1028004 0.0189657 -110.874 < 2e-16 ***
DESTIN_SZTHSZ06 -0.8463339 0.0105837 -79.966 < 2e-16 ***
DESTIN_SZTMSZ01 0.1408655 0.0045968 30.644 < 2e-16 ***
DESTIN_SZTMSZ02 1.7840540 0.0030328 588.257 < 2e-16 ***
DESTIN_SZTMSZ03 0.8761093 0.0034123 256.753 < 2e-16 ***
DESTIN_SZTMSZ04 0.9279782 0.0034956 265.467 < 2e-16 ***
DESTIN_SZTMSZ05 0.7251426 0.0043728 165.831 < 2e-16 ***
DESTIN_SZTNSZ01 -0.6461319 0.0048962 -131.967 < 2e-16 ***
DESTIN_SZTNSZ02 -1.4175346 0.0063417 -223.527 < 2e-16 ***
DESTIN_SZTNSZ03 -1.4387860 0.0078047 -184.348 < 2e-16 ***
DESTIN_SZTNSZ04 -0.9596368 0.0058085 -165.212 < 2e-16 ***
DESTIN_SZTPSZ01 -0.4308093 0.0047748 -90.225 < 2e-16 ***
DESTIN_SZTPSZ02 0.2298095 0.0034491 66.629 < 2e-16 ***
DESTIN_SZTPSZ03 -0.3633392 0.0048621 -74.728 < 2e-16 ***
DESTIN_SZTPSZ04 -1.5435318 0.0068323 -225.916 < 2e-16 ***
DESTIN_SZTPSZ05 -0.7878038 0.0051291 -153.596 < 2e-16 ***
DESTIN_SZTPSZ06 -0.2302491 0.0059194 -38.898 < 2e-16 ***
DESTIN_SZTPSZ07 -1.6384615 0.0093336 -175.544 < 2e-16 ***
DESTIN_SZTPSZ08 -1.3106964 0.0072787 -180.072 < 2e-16 ***
DESTIN_SZTPSZ09 -0.5340740 0.0053383 -100.046 < 2e-16 ***
DESTIN_SZTPSZ10 -0.6923468 0.0067313 -102.855 < 2e-16 ***
DESTIN_SZTPSZ11 -0.3157414 0.0044419 -71.083 < 2e-16 ***
DESTIN_SZTPSZ12 -0.7150679 0.0054086 -132.209 < 2e-16 ***
DESTIN_SZTSSZ01 -0.1925873 0.0187108 -10.293 < 2e-16 ***
DESTIN_SZTSSZ02 1.2687738 0.0077142 164.473 < 2e-16 ***
DESTIN_SZTSSZ03 2.0454651 0.0055935 365.683 < 2e-16 ***
DESTIN_SZTSSZ04 1.9140305 0.0058153 329.139 < 2e-16 ***
DESTIN_SZTSSZ05 2.0435564 0.0064391 317.368 < 2e-16 ***
DESTIN_SZTSSZ06 0.9954141 0.0109280 91.088 < 2e-16 ***
DESTIN_SZWCSZ01 1.6560834 0.0040593 407.975 < 2e-16 ***
DESTIN_SZWCSZ02 -0.1341972 0.0102862 -13.046 < 2e-16 ***
DESTIN_SZWCSZ03 -1.5152439 0.0236971 -63.942 < 2e-16 ***
DESTIN_SZWDSZ01 1.6938261 0.0032123 527.292 < 2e-16 ***
DESTIN_SZWDSZ02 -0.1398727 0.0050461 -27.719 < 2e-16 ***
DESTIN_SZWDSZ03 1.3486310 0.0033673 400.508 < 2e-16 ***
DESTIN_SZWDSZ04 0.2678174 0.0048596 55.111 < 2e-16 ***
DESTIN_SZWDSZ05 0.3375247 0.0045944 73.464 < 2e-16 ***
DESTIN_SZWDSZ06 0.6686614 0.0036977 180.829 < 2e-16 ***
DESTIN_SZWDSZ07 0.7000912 0.0057454 121.853 < 2e-16 ***
DESTIN_SZWDSZ08 0.9491777 0.0052819 179.703 < 2e-16 ***
DESTIN_SZWDSZ09 0.5929994 0.0042996 137.919 < 2e-16 ***
DESTIN_SZYSSZ01 1.3385552 0.0034421 388.881 < 2e-16 ***
DESTIN_SZYSSZ02 0.3976804 0.0043811 90.771 < 2e-16 ***
DESTIN_SZYSSZ03 -0.0163261 0.0047699 -3.423 0.00062 ***
DESTIN_SZYSSZ04 0.1898015 0.0043696 43.437 < 2e-16 ***
DESTIN_SZYSSZ05 -1.4769782 0.0091390 -161.613 < 2e-16 ***
DESTIN_SZYSSZ06 -1.1722255 0.0071348 -164.297 < 2e-16 ***
DESTIN_SZYSSZ07 -0.7645400 0.0086822 -88.059 < 2e-16 ***
DESTIN_SZYSSZ08 0.7420003 0.0035755 207.525 < 2e-16 ***
DESTIN_SZYSSZ09 0.5275341 0.0036041 146.370 < 2e-16 ***
log(ORIGIN_AGE25_64) 0.2386409 0.0001137 2098.153 < 2e-16 ***
log(dist) -0.6978605 0.0001106 -6307.089 < 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: 88883132 on 20594 degrees of freedom
Residual deviance: 37371399 on 20283 degrees of freedom
AIC: 37501128
Number of Fisher Scoring iterations: 7We can examine how the constraints hold for destinations this time.
Code
CalcRSquared(decSIM$data$TRIPS, decSIM$fitted.values)[1] 0.4938856.8 Doubly constrained
In this section, we will fit a doubly constrained SIM by using the code chunk below.
Code
dbcSIM <- glm(formula = TRIPS ~
ORIGIN_SZ +
DESTIN_SZ +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
summary(dbcSIM)
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(dist), family = poisson(link = "log"),
data = SIM_data, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 12.4969974 0.0040560 3081.143 < 2e-16 ***
ORIGIN_SZAMSZ02 1.0585352 0.0040651 260.394 < 2e-16 ***
ORIGIN_SZAMSZ03 0.6135064 0.0041129 149.165 < 2e-16 ***
ORIGIN_SZAMSZ04 0.2234400 0.0045742 48.848 < 2e-16 ***
ORIGIN_SZAMSZ05 0.0805773 0.0052347 15.393 < 2e-16 ***
ORIGIN_SZAMSZ06 0.6097174 0.0047523 128.298 < 2e-16 ***
ORIGIN_SZAMSZ07 -0.9071313 0.0082206 -110.349 < 2e-16 ***
ORIGIN_SZAMSZ08 -0.7119432 0.0076480 -93.089 < 2e-16 ***
ORIGIN_SZAMSZ09 0.4215134 0.0049866 84.529 < 2e-16 ***
ORIGIN_SZAMSZ10 0.1528793 0.0046441 32.919 < 2e-16 ***
ORIGIN_SZAMSZ11 -1.5725619 0.0100603 -156.313 < 2e-16 ***
ORIGIN_SZAMSZ12 -1.4789510 0.0096129 -153.851 < 2e-16 ***
ORIGIN_SZBDSZ01 0.8347089 0.0040177 207.758 < 2e-16 ***
ORIGIN_SZBDSZ02 0.4469370 0.0046180 96.782 < 2e-16 ***
ORIGIN_SZBDSZ03 0.8343885 0.0041582 200.662 < 2e-16 ***
ORIGIN_SZBDSZ04 1.4640644 0.0036149 405.008 < 2e-16 ***
ORIGIN_SZBDSZ05 0.5923638 0.0040717 145.483 < 2e-16 ***
ORIGIN_SZBDSZ06 0.8072327 0.0041885 192.727 < 2e-16 ***
ORIGIN_SZBDSZ07 -0.6448177 0.0070077 -92.016 < 2e-16 ***
ORIGIN_SZBDSZ08 -0.4406728 0.0065497 -67.281 < 2e-16 ***
ORIGIN_SZBKSZ01 -0.0658852 0.0056722 -11.615 < 2e-16 ***
ORIGIN_SZBKSZ02 0.6191879 0.0047239 131.075 < 2e-16 ***
ORIGIN_SZBKSZ03 1.0465666 0.0044145 237.072 < 2e-16 ***
ORIGIN_SZBKSZ04 -0.0295930 0.0053939 -5.486 4.10e-08 ***
ORIGIN_SZBKSZ05 0.2000655 0.0050727 39.440 < 2e-16 ***
ORIGIN_SZBKSZ06 0.3291624 0.0053213 61.857 < 2e-16 ***
ORIGIN_SZBKSZ07 0.8013047 0.0041211 194.440 < 2e-16 ***
ORIGIN_SZBKSZ08 0.3492390 0.0047076 74.187 < 2e-16 ***
ORIGIN_SZBKSZ09 0.1382536 0.0050302 27.485 < 2e-16 ***
ORIGIN_SZBLSZ01 -1.7064146 0.0107886 -158.168 < 2e-16 ***
ORIGIN_SZBLSZ02 -2.7844825 0.0160509 -173.478 < 2e-16 ***
ORIGIN_SZBLSZ03 -5.0982841 0.0360710 -141.340 < 2e-16 ***
ORIGIN_SZBLSZ04 -2.7782971 0.0197491 -140.680 < 2e-16 ***
ORIGIN_SZBMSZ01 0.1189019 0.0045203 26.304 < 2e-16 ***
ORIGIN_SZBMSZ02 -0.9645711 0.0062329 -154.756 < 2e-16 ***
ORIGIN_SZBMSZ03 -0.1832371 0.0051937 -35.281 < 2e-16 ***
ORIGIN_SZBMSZ04 0.2762267 0.0045627 60.540 < 2e-16 ***
ORIGIN_SZBMSZ05 -1.0171637 0.0067988 -149.608 < 2e-16 ***
ORIGIN_SZBMSZ06 -1.3103122 0.0108482 -120.786 < 2e-16 ***
ORIGIN_SZBMSZ07 -0.3034128 0.0050059 -60.612 < 2e-16 ***
ORIGIN_SZBMSZ08 -0.1440184 0.0049756 -28.945 < 2e-16 ***
ORIGIN_SZBMSZ09 -0.7416821 0.0064917 -114.250 < 2e-16 ***
ORIGIN_SZBMSZ10 -0.9403180 0.0072095 -130.428 < 2e-16 ***
ORIGIN_SZBMSZ11 -0.3870364 0.0057654 -67.131 < 2e-16 ***
ORIGIN_SZBMSZ12 -0.6539074 0.0078371 -83.438 < 2e-16 ***
ORIGIN_SZBMSZ13 0.0637862 0.0049636 12.851 < 2e-16 ***
ORIGIN_SZBMSZ14 -0.1466269 0.0058604 -25.020 < 2e-16 ***
ORIGIN_SZBMSZ15 0.1335255 0.0053046 25.172 < 2e-16 ***
ORIGIN_SZBMSZ16 -0.9840092 0.0067507 -145.765 < 2e-16 ***
ORIGIN_SZBMSZ17 -1.3928312 0.0100778 -138.207 < 2e-16 ***
ORIGIN_SZBPSZ01 0.5543538 0.0049891 111.113 < 2e-16 ***
ORIGIN_SZBPSZ02 0.8631047 0.0055229 156.277 < 2e-16 ***
ORIGIN_SZBPSZ03 1.0974914 0.0051871 211.580 < 2e-16 ***
ORIGIN_SZBPSZ04 0.8279752 0.0044952 184.190 < 2e-16 ***
ORIGIN_SZBPSZ05 0.6829984 0.0041756 163.567 < 2e-16 ***
ORIGIN_SZBPSZ06 -0.8675522 0.0075597 -114.761 < 2e-16 ***
ORIGIN_SZBPSZ07 -0.6910822 0.0074107 -93.255 < 2e-16 ***
ORIGIN_SZBSSZ01 0.0379090 0.0048734 7.779 7.33e-15 ***
ORIGIN_SZBSSZ02 0.3650074 0.0044337 82.326 < 2e-16 ***
ORIGIN_SZBSSZ03 0.2151802 0.0043036 50.000 < 2e-16 ***
ORIGIN_SZBTSZ01 0.0193421 0.0047842 4.043 5.28e-05 ***
ORIGIN_SZBTSZ02 -0.8627500 0.0068646 -125.682 < 2e-16 ***
ORIGIN_SZBTSZ03 -0.1632234 0.0052269 -31.227 < 2e-16 ***
ORIGIN_SZBTSZ04 -0.5694261 0.0090629 -62.830 < 2e-16 ***
ORIGIN_SZBTSZ05 -1.4629727 0.0097759 -149.652 < 2e-16 ***
ORIGIN_SZBTSZ06 -0.6595061 0.0067083 -98.312 < 2e-16 ***
ORIGIN_SZBTSZ07 -1.6934731 0.0104883 -161.463 < 2e-16 ***
ORIGIN_SZBTSZ08 -1.0536365 0.0080677 -130.599 < 2e-16 ***
ORIGIN_SZCCSZ01 -1.5992805 0.0119339 -134.012 < 2e-16 ***
ORIGIN_SZCHSZ01 -1.1701468 0.0100471 -116.467 < 2e-16 ***
ORIGIN_SZCHSZ02 -0.7770700 0.0070575 -110.105 < 2e-16 ***
ORIGIN_SZCHSZ03 -0.6149688 0.0054235 -113.390 < 2e-16 ***
ORIGIN_SZCKSZ01 0.5649842 0.0045198 125.002 < 2e-16 ***
ORIGIN_SZCKSZ02 1.2687266 0.0046708 271.632 < 2e-16 ***
ORIGIN_SZCKSZ03 0.9259840 0.0042289 218.968 < 2e-16 ***
ORIGIN_SZCKSZ04 1.8273092 0.0044373 411.810 < 2e-16 ***
ORIGIN_SZCKSZ05 1.6304834 0.0054119 301.276 < 2e-16 ***
ORIGIN_SZCKSZ06 1.1141202 0.0060601 183.846 < 2e-16 ***
ORIGIN_SZCLSZ01 -0.5063730 0.0062711 -80.747 < 2e-16 ***
ORIGIN_SZCLSZ02 -1.2071079 0.0112862 -106.954 < 2e-16 ***
ORIGIN_SZCLSZ03 -0.5135109 0.0065376 -78.547 < 2e-16 ***
ORIGIN_SZCLSZ04 0.7781677 0.0041424 187.855 < 2e-16 ***
ORIGIN_SZCLSZ05 -1.6265795 0.0114806 -141.681 < 2e-16 ***
ORIGIN_SZCLSZ06 0.9038801 0.0038966 231.966 < 2e-16 ***
ORIGIN_SZCLSZ07 -0.0696302 0.0049005 -14.209 < 2e-16 ***
ORIGIN_SZCLSZ08 0.2472209 0.0056402 43.832 < 2e-16 ***
ORIGIN_SZCLSZ09 -2.1290439 0.0145332 -146.495 < 2e-16 ***
ORIGIN_SZDTSZ01 -1.4448077 0.0079621 -181.461 < 2e-16 ***
ORIGIN_SZDTSZ02 -1.3905811 0.0074516 -186.616 < 2e-16 ***
ORIGIN_SZDTSZ03 -2.4388315 0.0135161 -180.440 < 2e-16 ***
ORIGIN_SZDTSZ04 -4.6567555 0.1768256 -26.335 < 2e-16 ***
ORIGIN_SZDTSZ05 -2.8937655 0.0249101 -116.168 < 2e-16 ***
ORIGIN_SZDTSZ06 -2.7736191 0.0184754 -150.125 < 2e-16 ***
ORIGIN_SZDTSZ07 -1.5431077 0.0235495 -65.526 < 2e-16 ***
ORIGIN_SZDTSZ08 -2.3597869 0.0120595 -195.678 < 2e-16 ***
ORIGIN_SZDTSZ09 -2.6807399 0.0239658 -111.857 < 2e-16 ***
ORIGIN_SZDTSZ10 -2.0497135 0.0127305 -161.008 < 2e-16 ***
ORIGIN_SZDTSZ11 -2.0960362 0.0125222 -167.385 < 2e-16 ***
ORIGIN_SZDTSZ12 -3.0478200 0.0258594 -117.861 < 2e-16 ***
ORIGIN_SZDTSZ13 -2.0650275 0.0138674 -148.913 < 2e-16 ***
ORIGIN_SZGLSZ01 -1.3667829 0.0078027 -175.168 < 2e-16 ***
ORIGIN_SZGLSZ02 0.2837204 0.0044427 63.863 < 2e-16 ***
ORIGIN_SZGLSZ03 0.0617651 0.0044254 13.957 < 2e-16 ***
ORIGIN_SZGLSZ04 0.9877879 0.0037691 262.076 < 2e-16 ***
ORIGIN_SZGLSZ05 0.6022436 0.0039570 152.196 < 2e-16 ***
ORIGIN_SZHGSZ01 0.1991867 0.0043549 45.739 < 2e-16 ***
ORIGIN_SZHGSZ02 0.6822466 0.0042133 161.929 < 2e-16 ***
ORIGIN_SZHGSZ03 0.5240765 0.0045300 115.689 < 2e-16 ***
ORIGIN_SZHGSZ04 1.0093933 0.0039061 258.414 < 2e-16 ***
ORIGIN_SZHGSZ05 1.3344098 0.0038616 345.556 < 2e-16 ***
ORIGIN_SZHGSZ06 0.1114608 0.0048345 23.055 < 2e-16 ***
ORIGIN_SZHGSZ07 0.5728434 0.0041369 138.472 < 2e-16 ***
ORIGIN_SZHGSZ08 0.1603633 0.0047329 33.883 < 2e-16 ***
ORIGIN_SZHGSZ09 -0.6404905 0.0061647 -103.897 < 2e-16 ***
ORIGIN_SZHGSZ10 -3.2186440 0.0407330 -79.018 < 2e-16 ***
ORIGIN_SZJESZ01 0.4865136 0.0045985 105.799 < 2e-16 ***
ORIGIN_SZJESZ02 0.3896517 0.0045631 85.392 < 2e-16 ***
ORIGIN_SZJESZ03 0.3699308 0.0048219 76.719 < 2e-16 ***
ORIGIN_SZJESZ04 -0.9600960 0.0074627 -128.653 < 2e-16 ***
ORIGIN_SZJESZ05 -2.0530997 0.0125837 -163.155 < 2e-16 ***
ORIGIN_SZJESZ06 0.2250878 0.0044617 50.448 < 2e-16 ***
ORIGIN_SZJESZ07 -1.6329910 0.0098352 -166.036 < 2e-16 ***
ORIGIN_SZJESZ08 -0.8496068 0.0087262 -97.363 < 2e-16 ***
ORIGIN_SZJESZ09 0.5250890 0.0045997 114.157 < 2e-16 ***
ORIGIN_SZJESZ10 -2.6979788 0.0178824 -150.874 < 2e-16 ***
ORIGIN_SZJESZ11 -2.9343236 0.0181710 -161.484 < 2e-16 ***
ORIGIN_SZJWSZ01 0.5050356 0.0059817 84.429 < 2e-16 ***
ORIGIN_SZJWSZ02 1.0284036 0.0042065 244.480 < 2e-16 ***
ORIGIN_SZJWSZ03 1.1767024 0.0040388 291.349 < 2e-16 ***
ORIGIN_SZJWSZ04 0.9879552 0.0041159 240.034 < 2e-16 ***
ORIGIN_SZJWSZ05 -1.7689426 0.0112643 -157.040 < 2e-16 ***
ORIGIN_SZJWSZ06 -1.1128041 0.0089465 -124.384 < 2e-16 ***
ORIGIN_SZJWSZ07 -1.8271393 0.0196741 -92.870 < 2e-16 ***
ORIGIN_SZJWSZ08 2.0485221 0.0040451 506.417 < 2e-16 ***
ORIGIN_SZJWSZ09 1.4092915 0.0037779 373.039 < 2e-16 ***
ORIGIN_SZKLSZ01 0.3013119 0.0043140 69.844 < 2e-16 ***
ORIGIN_SZKLSZ02 -0.2604935 0.0053520 -48.672 < 2e-16 ***
ORIGIN_SZKLSZ03 -0.3381835 0.0054299 -62.281 < 2e-16 ***
ORIGIN_SZKLSZ04 -1.3123255 0.0075688 -173.386 < 2e-16 ***
ORIGIN_SZKLSZ05 -0.2874114 0.0064393 -44.634 < 2e-16 ***
ORIGIN_SZKLSZ06 -0.3292034 0.0050852 -64.738 < 2e-16 ***
ORIGIN_SZKLSZ07 -0.6745380 0.0066048 -102.128 < 2e-16 ***
ORIGIN_SZKLSZ08 -0.7463159 0.0058127 -128.393 < 2e-16 ***
ORIGIN_SZKLSZ09 -1.2047347 0.0072276 -166.686 < 2e-16 ***
ORIGIN_SZLKSZ01 -2.4757562 0.0330011 -75.020 < 2e-16 ***
ORIGIN_SZMDSZ01 -1.6719701 0.0233312 -71.662 < 2e-16 ***
ORIGIN_SZMDSZ02 -0.9907626 0.0100552 -98.532 < 2e-16 ***
ORIGIN_SZMDSZ03 -1.3852942 0.0145185 -95.416 < 2e-16 ***
ORIGIN_SZMPSZ01 -0.6401960 0.0064785 -98.818 < 2e-16 ***
ORIGIN_SZMPSZ02 -0.4100916 0.0057738 -71.026 < 2e-16 ***
ORIGIN_SZMPSZ03 0.4045439 0.0043620 92.742 < 2e-16 ***
ORIGIN_SZMSSZ01 -4.6281771 0.2589989 -17.869 < 2e-16 ***
ORIGIN_SZMUSZ01 -0.9259692 0.0063669 -145.435 < 2e-16 ***
ORIGIN_SZMUSZ02 -2.9035388 0.0181864 -159.655 < 2e-16 ***
ORIGIN_SZMUSZ03 -1.5266527 0.0075187 -203.048 < 2e-16 ***
ORIGIN_SZNTSZ01 -2.4591778 0.0264981 -92.806 < 2e-16 ***
ORIGIN_SZNTSZ02 -2.2829191 0.0153859 -148.377 < 2e-16 ***
ORIGIN_SZNTSZ03 -0.6895668 0.0069140 -99.734 < 2e-16 ***
ORIGIN_SZNTSZ05 -2.6608966 0.0381505 -69.747 < 2e-16 ***
ORIGIN_SZNTSZ06 -2.9170745 0.0418365 -69.726 < 2e-16 ***
ORIGIN_SZNVSZ01 0.8294000 0.0039285 211.125 < 2e-16 ***
ORIGIN_SZNVSZ02 -0.3623933 0.0054461 -66.542 < 2e-16 ***
ORIGIN_SZNVSZ03 -0.9534548 0.0065276 -146.065 < 2e-16 ***
ORIGIN_SZNVSZ04 -1.1185507 0.0079621 -140.484 < 2e-16 ***
ORIGIN_SZNVSZ05 -2.3846251 0.0144101 -165.483 < 2e-16 ***
ORIGIN_SZORSZ01 -3.0416618 0.0363234 -83.738 < 2e-16 ***
ORIGIN_SZORSZ02 -1.1396769 0.0065822 -173.146 < 2e-16 ***
ORIGIN_SZORSZ03 -1.4183029 0.0075866 -186.948 < 2e-16 ***
ORIGIN_SZOTSZ01 -1.4248909 0.0082256 -173.227 < 2e-16 ***
ORIGIN_SZOTSZ02 -1.6613037 0.0095479 -173.997 < 2e-16 ***
ORIGIN_SZOTSZ03 -0.4208618 0.0058305 -72.182 < 2e-16 ***
ORIGIN_SZOTSZ04 -0.4992767 0.0094839 -52.645 < 2e-16 ***
ORIGIN_SZPGSZ01 0.7068700 0.0114505 61.733 < 2e-16 ***
ORIGIN_SZPGSZ02 -0.2125532 0.0060915 -34.894 < 2e-16 ***
ORIGIN_SZPGSZ03 1.0452900 0.0040272 259.556 < 2e-16 ***
ORIGIN_SZPGSZ04 1.1928688 0.0040335 295.741 < 2e-16 ***
ORIGIN_SZPGSZ05 0.6360577 0.0050326 126.388 < 2e-16 ***
ORIGIN_SZPLSZ01 -0.7134222 0.0086869 -82.126 < 2e-16 ***
ORIGIN_SZPLSZ02 -1.1549832 0.0121921 -94.732 < 2e-16 ***
ORIGIN_SZPLSZ03 -3.4626403 0.0341188 -101.488 < 2e-16 ***
ORIGIN_SZPLSZ04 -3.3319503 0.0291243 -114.405 < 2e-16 ***
ORIGIN_SZPLSZ05 -2.2494482 0.0180739 -124.458 < 2e-16 ***
ORIGIN_SZPNSZ01 0.9408740 0.0049059 191.784 < 2e-16 ***
ORIGIN_SZPNSZ02 -1.8458038 0.0112962 -163.400 < 2e-16 ***
ORIGIN_SZPNSZ03 -2.9084875 0.0180972 -160.715 < 2e-16 ***
ORIGIN_SZPNSZ04 -4.7294338 0.0253115 -186.849 < 2e-16 ***
ORIGIN_SZPNSZ05 -3.6917514 0.0221409 -166.739 < 2e-16 ***
ORIGIN_SZPRSZ01 -0.5249244 0.0098223 -53.442 < 2e-16 ***
ORIGIN_SZPRSZ02 1.0782251 0.0041892 257.385 < 2e-16 ***
ORIGIN_SZPRSZ03 0.4979912 0.0042288 117.761 < 2e-16 ***
ORIGIN_SZPRSZ04 -0.2698254 0.0065625 -41.116 < 2e-16 ***
ORIGIN_SZPRSZ05 1.1813902 0.0040044 295.020 < 2e-16 ***
ORIGIN_SZPRSZ06 -0.8899822 0.0072810 -122.234 < 2e-16 ***
ORIGIN_SZPRSZ07 -2.5601915 0.0178807 -143.182 < 2e-16 ***
ORIGIN_SZPRSZ08 0.0891621 0.0054741 16.288 < 2e-16 ***
ORIGIN_SZQTSZ01 0.1053491 0.0059887 17.591 < 2e-16 ***
ORIGIN_SZQTSZ02 -0.4509932 0.0056347 -80.038 < 2e-16 ***
ORIGIN_SZQTSZ03 0.1074403 0.0050690 21.195 < 2e-16 ***
ORIGIN_SZQTSZ04 -0.9488308 0.0068053 -139.425 < 2e-16 ***
ORIGIN_SZQTSZ05 0.0816099 0.0051045 15.988 < 2e-16 ***
ORIGIN_SZQTSZ06 -0.3183846 0.0058467 -54.455 < 2e-16 ***
ORIGIN_SZQTSZ07 -1.2162553 0.0083632 -145.430 < 2e-16 ***
ORIGIN_SZQTSZ08 -0.2116394 0.0052931 -39.984 < 2e-16 ***
ORIGIN_SZQTSZ09 -0.4600715 0.0059520 -77.297 < 2e-16 ***
ORIGIN_SZQTSZ10 -0.3870119 0.0059269 -65.297 < 2e-16 ***
ORIGIN_SZQTSZ11 -1.5551482 0.0091487 -169.986 < 2e-16 ***
ORIGIN_SZQTSZ12 -1.1249732 0.0087131 -129.112 < 2e-16 ***
ORIGIN_SZQTSZ13 -0.3368401 0.0055854 -60.307 < 2e-16 ***
ORIGIN_SZQTSZ14 -1.4603472 0.0084380 -173.068 < 2e-16 ***
ORIGIN_SZQTSZ15 -1.0770799 0.0095415 -112.884 < 2e-16 ***
ORIGIN_SZRCSZ01 -0.3990011 0.0059609 -66.936 < 2e-16 ***
ORIGIN_SZRCSZ02 -1.7209712 0.0157109 -109.540 < 2e-16 ***
ORIGIN_SZRCSZ03 -0.9157002 0.0079829 -114.708 < 2e-16 ***
ORIGIN_SZRCSZ04 -2.0999136 0.0123473 -170.070 < 2e-16 ***
ORIGIN_SZRCSZ05 -2.1120232 0.0136706 -154.493 < 2e-16 ***
ORIGIN_SZRCSZ06 -0.2396834 0.0078165 -30.664 < 2e-16 ***
ORIGIN_SZRCSZ08 -2.3205294 0.0180477 -128.578 < 2e-16 ***
ORIGIN_SZRCSZ09 -1.6751682 0.0131884 -127.018 < 2e-16 ***
ORIGIN_SZRCSZ10 -1.5468207 0.0078843 -196.191 < 2e-16 ***
ORIGIN_SZRVSZ01 -2.4370886 0.0139860 -174.252 < 2e-16 ***
ORIGIN_SZRVSZ02 -0.6962962 0.0075705 -91.975 < 2e-16 ***
ORIGIN_SZRVSZ03 -1.4729227 0.0113978 -129.229 < 2e-16 ***
ORIGIN_SZRVSZ04 -1.7851931 0.0173663 -102.796 < 2e-16 ***
ORIGIN_SZRVSZ05 -1.6959294 0.0137815 -123.058 < 2e-16 ***
ORIGIN_SZSBSZ01 0.9346035 0.0052711 177.305 < 2e-16 ***
ORIGIN_SZSBSZ02 -0.6345971 0.0070356 -90.198 < 2e-16 ***
ORIGIN_SZSBSZ03 0.6466352 0.0043863 147.421 < 2e-16 ***
ORIGIN_SZSBSZ04 0.2844137 0.0051901 54.799 < 2e-16 ***
ORIGIN_SZSBSZ05 -0.0315396 0.0060369 -5.224 1.75e-07 ***
ORIGIN_SZSBSZ06 -0.9467078 0.0144656 -65.445 < 2e-16 ***
ORIGIN_SZSBSZ07 -0.1393199 0.0104412 -13.343 < 2e-16 ***
ORIGIN_SZSBSZ08 -2.0852218 0.0100783 -206.901 < 2e-16 ***
ORIGIN_SZSBSZ09 -1.0766873 0.0075667 -142.293 < 2e-16 ***
ORIGIN_SZSESZ02 1.1929837 0.0039976 298.428 < 2e-16 ***
ORIGIN_SZSESZ03 1.2050114 0.0037979 317.281 < 2e-16 ***
ORIGIN_SZSESZ04 1.1772849 0.0043782 268.900 < 2e-16 ***
ORIGIN_SZSESZ05 -0.0832362 0.0052039 -15.995 < 2e-16 ***
ORIGIN_SZSESZ06 1.1906711 0.0041427 287.415 < 2e-16 ***
ORIGIN_SZSESZ07 -1.9365539 0.0150835 -128.389 < 2e-16 ***
ORIGIN_SZSGSZ01 -0.8164219 0.0075108 -108.699 < 2e-16 ***
ORIGIN_SZSGSZ02 -1.2122141 0.0087858 -137.975 < 2e-16 ***
ORIGIN_SZSGSZ03 0.3942694 0.0046328 85.104 < 2e-16 ***
ORIGIN_SZSGSZ04 0.3471163 0.0043489 79.817 < 2e-16 ***
ORIGIN_SZSGSZ05 -1.4932087 0.0090230 -165.489 < 2e-16 ***
ORIGIN_SZSGSZ06 0.3553651 0.0041347 85.946 < 2e-16 ***
ORIGIN_SZSGSZ07 -0.4461572 0.0054205 -82.309 < 2e-16 ***
ORIGIN_SZSKSZ01 -0.1754109 0.0075712 -23.168 < 2e-16 ***
ORIGIN_SZSKSZ02 0.3778613 0.0056560 66.807 < 2e-16 ***
ORIGIN_SZSKSZ03 -0.3211144 0.0066773 -48.090 < 2e-16 ***
ORIGIN_SZSKSZ04 -1.8579156 0.0218864 -84.889 < 2e-16 ***
ORIGIN_SZSKSZ05 -1.1791036 0.0150172 -78.517 < 2e-16 ***
ORIGIN_SZSLSZ01 -2.9386230 0.0269159 -109.178 < 2e-16 ***
ORIGIN_SZSLSZ04 -0.3162287 0.0063166 -50.063 < 2e-16 ***
ORIGIN_SZSRSZ01 -1.2357537 0.0081725 -151.208 < 2e-16 ***
ORIGIN_SZSRSZ02 -1.4119003 0.0078902 -178.944 < 2e-16 ***
ORIGIN_SZSRSZ03 -2.4401744 0.0176796 -138.022 < 2e-16 ***
ORIGIN_SZSVSZ01 -3.1123828 0.0690011 -45.106 < 2e-16 ***
ORIGIN_SZTHSZ01 -2.1288324 0.0364590 -58.390 < 2e-16 ***
ORIGIN_SZTHSZ03 -1.0800575 0.0166298 -64.947 < 2e-16 ***
ORIGIN_SZTHSZ04 -1.8515092 0.0253268 -73.105 < 2e-16 ***
ORIGIN_SZTHSZ06 -1.7602926 0.0151912 -115.876 < 2e-16 ***
ORIGIN_SZTMSZ01 0.5636227 0.0046859 120.280 < 2e-16 ***
ORIGIN_SZTMSZ02 1.6637870 0.0035614 467.174 < 2e-16 ***
ORIGIN_SZTMSZ03 1.1602498 0.0038039 305.014 < 2e-16 ***
ORIGIN_SZTMSZ04 0.3914037 0.0044252 88.448 < 2e-16 ***
ORIGIN_SZTMSZ05 -0.8440109 0.0068916 -122.469 < 2e-16 ***
ORIGIN_SZTNSZ01 -1.0098810 0.0070227 -143.802 < 2e-16 ***
ORIGIN_SZTNSZ02 -0.8202286 0.0066367 -123.589 < 2e-16 ***
ORIGIN_SZTNSZ03 -1.2654603 0.0088505 -142.982 < 2e-16 ***
ORIGIN_SZTNSZ04 -0.3634416 0.0061635 -58.966 < 2e-16 ***
ORIGIN_SZTPSZ01 -0.4368116 0.0056105 -77.856 < 2e-16 ***
ORIGIN_SZTPSZ02 0.5475521 0.0039618 138.209 < 2e-16 ***
ORIGIN_SZTPSZ03 -0.3623128 0.0054592 -66.367 < 2e-16 ***
ORIGIN_SZTPSZ04 0.0472206 0.0051346 9.196 < 2e-16 ***
ORIGIN_SZTPSZ05 0.0839462 0.0054103 15.516 < 2e-16 ***
ORIGIN_SZTPSZ06 0.7233657 0.0060194 120.171 < 2e-16 ***
ORIGIN_SZTPSZ07 -0.1165915 0.0058183 -20.039 < 2e-16 ***
ORIGIN_SZTPSZ08 -0.4935634 0.0076322 -64.669 < 2e-16 ***
ORIGIN_SZTPSZ09 -0.4433213 0.0058146 -76.243 < 2e-16 ***
ORIGIN_SZTPSZ10 -0.3389133 0.0062514 -54.214 < 2e-16 ***
ORIGIN_SZTPSZ11 0.2873925 0.0047071 61.055 < 2e-16 ***
ORIGIN_SZTPSZ12 -0.4040528 0.0056796 -71.141 < 2e-16 ***
ORIGIN_SZTSSZ01 -3.9404955 0.0511551 -77.030 < 2e-16 ***
ORIGIN_SZTSSZ02 -0.0018479 0.0082813 -0.223 0.82343
ORIGIN_SZTSSZ03 -0.2699457 0.0082589 -32.685 < 2e-16 ***
ORIGIN_SZTSSZ04 -0.5500880 0.0085283 -64.501 < 2e-16 ***
ORIGIN_SZTSSZ05 -2.5923354 0.0136981 -189.248 < 2e-16 ***
ORIGIN_SZTSSZ06 -2.7750672 0.0207483 -133.749 < 2e-16 ***
ORIGIN_SZWCSZ01 -0.5072529 0.0067650 -74.982 < 2e-16 ***
ORIGIN_SZWCSZ02 -2.5295897 0.0269185 -93.972 < 2e-16 ***
ORIGIN_SZWCSZ03 -4.6345070 0.1291550 -35.883 < 2e-16 ***
ORIGIN_SZWDSZ01 0.8534772 0.0039216 217.634 < 2e-16 ***
ORIGIN_SZWDSZ02 1.0317707 0.0043850 235.293 < 2e-16 ***
ORIGIN_SZWDSZ03 1.6509819 0.0040202 410.668 < 2e-16 ***
ORIGIN_SZWDSZ04 1.2229578 0.0047770 256.008 < 2e-16 ***
ORIGIN_SZWDSZ05 0.5691316 0.0046162 123.291 < 2e-16 ***
ORIGIN_SZWDSZ06 0.9562165 0.0044186 216.408 < 2e-16 ***
ORIGIN_SZWDSZ07 -0.3917521 0.0072004 -54.407 < 2e-16 ***
ORIGIN_SZWDSZ08 -0.6830954 0.0068347 -99.945 < 2e-16 ***
ORIGIN_SZWDSZ09 1.3693027 0.0043386 315.608 < 2e-16 ***
ORIGIN_SZYSSZ01 -0.3751982 0.0050361 -74.502 < 2e-16 ***
ORIGIN_SZYSSZ02 1.0075483 0.0047931 210.210 < 2e-16 ***
ORIGIN_SZYSSZ03 2.2177900 0.0040349 549.658 < 2e-16 ***
ORIGIN_SZYSSZ04 0.9548457 0.0041373 230.787 < 2e-16 ***
ORIGIN_SZYSSZ05 0.4236718 0.0050438 83.998 < 2e-16 ***
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DESTIN_SZAMSZ11 0.0370421 0.0069016 5.367 8.00e-08 ***
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DESTIN_SZBDSZ05 0.5055376 0.0036518 138.436 < 2e-16 ***
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DESTIN_SZSRSZ02 -1.3648802 0.0085433 -159.759 < 2e-16 ***
DESTIN_SZSRSZ03 -1.4232536 0.0077757 -183.039 < 2e-16 ***
DESTIN_SZSVSZ01 -1.5450264 0.0678568 -22.769 < 2e-16 ***
DESTIN_SZTHSZ01 -3.4849698 0.0332037 -104.957 < 2e-16 ***
DESTIN_SZTHSZ03 -2.0915968 0.0191235 -109.373 < 2e-16 ***
DESTIN_SZTHSZ04 -2.4816319 0.0191469 -129.610 < 2e-16 ***
DESTIN_SZTHSZ06 -1.2146563 0.0107822 -112.654 < 2e-16 ***
DESTIN_SZTMSZ01 -0.1795562 0.0048237 -37.224 < 2e-16 ***
DESTIN_SZTMSZ02 1.3459495 0.0031928 421.557 < 2e-16 ***
DESTIN_SZTMSZ03 0.6155716 0.0035825 171.825 < 2e-16 ***
DESTIN_SZTMSZ04 0.8812566 0.0036848 239.160 < 2e-16 ***
DESTIN_SZTMSZ05 0.7011240 0.0046012 152.378 < 2e-16 ***
DESTIN_SZTNSZ01 -0.3870757 0.0049760 -77.788 < 2e-16 ***
DESTIN_SZTNSZ02 -0.9949268 0.0064182 -155.016 < 2e-16 ***
DESTIN_SZTNSZ03 -0.9978034 0.0079010 -126.288 < 2e-16 ***
DESTIN_SZTNSZ04 -0.8085834 0.0059076 -136.872 < 2e-16 ***
DESTIN_SZTPSZ01 -0.2290991 0.0048608 -47.132 < 2e-16 ***
DESTIN_SZTPSZ02 0.2932592 0.0035262 83.166 < 2e-16 ***
DESTIN_SZTPSZ03 -0.1524046 0.0049960 -30.506 < 2e-16 ***
DESTIN_SZTPSZ04 -1.5546156 0.0068975 -225.390 < 2e-16 ***
DESTIN_SZTPSZ05 -0.8451520 0.0052213 -161.867 < 2e-16 ***
DESTIN_SZTPSZ06 -0.4801699 0.0068484 -70.114 < 2e-16 ***
DESTIN_SZTPSZ07 -1.6202115 0.0094773 -170.958 < 2e-16 ***
DESTIN_SZTPSZ08 -1.2079178 0.0073927 -163.393 < 2e-16 ***
DESTIN_SZTPSZ09 -0.2848465 0.0054706 -52.068 < 2e-16 ***
DESTIN_SZTPSZ10 -0.9056787 0.0068525 -132.167 < 2e-16 ***
DESTIN_SZTPSZ11 -0.2396166 0.0045591 -52.557 < 2e-16 ***
DESTIN_SZTPSZ12 -0.5960675 0.0054969 -108.438 < 2e-16 ***
DESTIN_SZTSSZ01 -0.4670670 0.0195128 -23.936 < 2e-16 ***
DESTIN_SZTSSZ02 -0.2880986 0.0096690 -29.796 < 2e-16 ***
DESTIN_SZTSSZ03 0.6128605 0.0075844 80.805 < 2e-16 ***
DESTIN_SZTSSZ04 0.7145093 0.0077311 92.420 < 2e-16 ***
DESTIN_SZTSSZ05 1.5840051 0.0081297 194.841 < 2e-16 ***
DESTIN_SZTSSZ06 1.4119631 0.0162860 86.698 < 2e-16 ***
DESTIN_SZWCSZ01 1.1481065 0.0046985 244.356 < 2e-16 ***
DESTIN_SZWCSZ02 -1.0364062 0.0105727 -98.027 < 2e-16 ***
DESTIN_SZWCSZ03 -2.2979112 0.0237591 -96.717 < 2e-16 ***
DESTIN_SZWDSZ01 0.9778749 0.0034042 287.257 < 2e-16 ***
DESTIN_SZWDSZ02 -0.6843440 0.0053440 -128.059 < 2e-16 ***
DESTIN_SZWDSZ03 0.6697853 0.0038300 174.877 < 2e-16 ***
DESTIN_SZWDSZ04 -0.4215144 0.0054825 -76.883 < 2e-16 ***
DESTIN_SZWDSZ05 -0.0626035 0.0048976 -12.782 < 2e-16 ***
DESTIN_SZWDSZ06 0.2330792 0.0039807 58.552 < 2e-16 ***
DESTIN_SZWDSZ07 -0.2057066 0.0061765 -33.305 < 2e-16 ***
DESTIN_SZWDSZ08 0.1936142 0.0056566 34.228 < 2e-16 ***
DESTIN_SZWDSZ09 -0.2671763 0.0047455 -56.301 < 2e-16 ***
DESTIN_SZYSSZ01 0.9919868 0.0036639 270.743 < 2e-16 ***
DESTIN_SZYSSZ02 -0.1925947 0.0048104 -40.037 < 2e-16 ***
DESTIN_SZYSSZ03 -1.1480259 0.0052039 -220.610 < 2e-16 ***
DESTIN_SZYSSZ04 -0.2304262 0.0045926 -50.173 < 2e-16 ***
DESTIN_SZYSSZ05 -1.7879632 0.0092881 -192.501 < 2e-16 ***
DESTIN_SZYSSZ06 -1.2562397 0.0072268 -173.830 < 2e-16 ***
DESTIN_SZYSSZ07 -0.5439553 0.0092673 -58.696 < 2e-16 ***
DESTIN_SZYSSZ08 0.6465839 0.0037045 174.540 < 2e-16 ***
DESTIN_SZYSSZ09 0.1198061 0.0037926 31.589 < 2e-16 ***
log(dist) -0.6771805 0.0001165 -5810.772 < 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: 88883132 on 20594 degrees of freedom
Residual deviance: 29961664 on 19976 degrees of freedom
AIC: 30092008
Number of Fisher Scoring iterations: 7We can examine how the constraints hold for destinations this time.
Code
CalcRSquared(dbcSIM$data$TRIPS, dbcSIM$fitted.values)[1] 0.5726181Notice that there is a relatively greater improvement in the R^2 value.
6.9 Model comparison
Another useful model performance measure for continuous dependent variable is Root Mean Squared Error. In this sub-section, you will learn how to use compare_performance() of performance package
First of all, let us create a list called model_list by using the code chunk below.
Code
model_list <- list(unconstrained=uncSIM,
originConstrained=orcSIM,
destinationConstrained=decSIM,
doublyConstrained=dbcSIM)Next, we will compute the RMSE of all the models in model_list file by using the code chunk below.
Code
compare_performance(model_list,
metrics = "RMSE")# Comparison of Model Performance Indices
Name | Model | RMSE
-----------------------------------------
unconstrained | glm | 4653.362
originConstrained | glm | 4091.480
destinationConstrained | glm | 3717.931
doublyConstrained | glm | 3548.660The print above reveals that doubly constrained SIM is the best model among all the four SIMs because it has the smallest RMSE value of 1487.111.
6.10 Visualising fitted
In this section, you will learn how to visualise the observed values and the fitted values.
Firstly we will extract the fitted values from each model by using the code chunk below.
Code
df <- as.data.frame(uncSIM$fitted.values) %>%
round(digits = 0)Next, we will join the values to SIM_data data frame.
Code
SIM_data <- SIM_data %>%
cbind(df) %>%
rename(uncTRIPS = "uncSIM$fitted.values")Repeat the same step by for Origin Constrained SIM (i.e. orcSIM)
Code
df <- as.data.frame(orcSIM$fitted.values) %>%
round(digits = 0)Code
SIM_data <- SIM_data %>%
cbind(df) %>%
rename(orcTRIPS = "orcSIM$fitted.values")Repeat the same step by for Destination Constrained SIM (i.e. decSIM)
Code
df <- as.data.frame(decSIM$fitted.values) %>%
round(digits = 0)Code
SIM_data <- SIM_data %>%
cbind(df) %>%
rename(decTRIPS = "decSIM$fitted.values")Repeat the same step by for Doubly Constrained SIM (i.e. dbcSIM)
Code
df <- as.data.frame(dbcSIM$fitted.values) %>%
round(digits = 0)Code
SIM_data <- SIM_data %>%
cbind(df) %>%
rename(dbcTRIPS = "dbcSIM$fitted.values")Code
unc_p <- ggplot(data = SIM_data,
aes(x = uncTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
orc_p <- ggplot(data = SIM_data,
aes(x = orcTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
dec_p <- ggplot(data = SIM_data,
aes(x = decTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
dbc_p <- ggplot(data = SIM_data,
aes(x = dbcTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
# Use patchwork to arrange the plots
(unc_p | orc_p) / (dec_p | dbc_p)