pacman::p_load(tmap, sf, sp, DT, stplanr, performance, reshape2,
ggpubr, units, tidyverse)3: Spatial Interaction Models
Spatial interaction represents the flow of people, material, or information between locations in geographical space.
Getting started
The code chunk below uses p_load() of pacman package to check if the required packages have been installed on the computer. If they are, the packages will be launched. The packages used are:
- tmap: for thematic mapping
- sf: for geospatial data wrangling
- tidyverse: for non-spatial data wrangling
Computing Distance Matrix
In spatial interaction, a distance matrix is a table that shows the distance between pairs of locations. A location’s distance from itself, which is shown in the main diagonal of a distance matrix table, is 0.
First, import mpsz.rds into the R environment by using the code chunk below.
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...Notice that it is a sf tibble dataframe object class.
Converting from sf data.table to SpatialPolygonsDataFrame
There are at least two ways to compute the required distance matrix. One is based on sf and the other is based on sp. Past experience shown that computing distance matrix by using sf function took relatively longer time that sp method especially the data set is large. In view of this, sp method is used in the code chunks below.
First as.Spatial() is used to convert mpsz from sf tibble data frame to SpatialPolygonsDataFrame of sp object as shown in the code chunk below.
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, the distance is calculated between the centroids of each pair of spatial polygons. This is a common approach as it simplifies the computation while providing a reasonable approximation of the spatial relationship between the polygons. Computing the distance between centroids is computationally less intensive as compared to calculating distances between all points along the edges of polygons, especially when dealing with complex polygons with many vertices. Additionally, centroids represent a single point that encapsulates the entire polygon. While edges provide more detailed information about the shape, centroids offer a generalized representation that can be useful in many cases, especially when the exact shape or details of the edges are less relevant.
dist <- spDists(mpsz_sp,
longlat = FALSE)
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 0.000Notice that the output dist is a matrix object class of R. Also notice that the column heanders and row headers are not labeled with the planning subzone codes.
Labelling column and row headers of a distance matrix.
First, create a list sorted according to the the distance matrix by planning sub-zone code.
sz_names <- mpsz$SUBZONE_CNext, attach SUBZONE_C to row and column for distance matrix matching.
colnames(dist) <- paste0(sz_names)
rownames(dist) <- paste0(sz_names)Pivoting distance value by SUBZONE_C
Next, pivot the distance matrix into a long table by using the row and column subzone codes as show in the code chunk below.
distPair <- melt(dist) %>%
rename(dist = value)
head(distPair, 10) Var1 Var2 dist
1 MESZ01 MESZ01 0.000
2 RVSZ05 MESZ01 3926.003
3 SRSZ01 MESZ01 3939.108
4 WISZ01 MESZ01 20252.964
5 MUSZ02 MESZ01 2989.984
6 MPSZ05 MESZ01 1431.330
7 WISZ03 MESZ01 19211.836
8 WISZ02 MESZ01 14960.942
9 SISZ02 MESZ01 7515.256
10 SISZ01 MESZ01 6391.342Notice that the within zone distance is 0.
Updating intra-zonal distances
Next, append a constant value to replace the intra-zonal distance of 0.To do so, first select and find the minimum value of the distance by using summary().
distPair %>%
filter(dist > 0) %>%
summary() Var1 Var2 dist
MESZ01 : 331 MESZ01 : 331 Min. : 173.8
RVSZ05 : 331 RVSZ05 : 331 1st Qu.: 7149.5
SRSZ01 : 331 SRSZ01 : 331 Median :11890.0
WISZ01 : 331 WISZ01 : 331 Mean :12229.4
MUSZ02 : 331 MUSZ02 : 331 3rd Qu.:16401.7
MPSZ05 : 331 MPSZ05 : 331 Max. :49894.4
(Other):107906 (Other):107906 Next, a constant distance value of 50m is added into intra-zones distance.
distPair$dist <- ifelse(distPair$dist == 0,
50, distPair$dist)The code chunk below will be used to check the result data.frame.
distPair %>%
summary() 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 The code chunk below is used to rename the origin and destination fields.
distPair <- distPair %>%
rename(orig = Var1,
dest = Var2)Lastly, the code chunk below is used to save the dataframe for future use.
write_rds(distPair, "data/rds/distPair.rds") Preparing flow data
The code chunk below is used import od_data rds file that was saved in Hands-on Exercise 3 into the R environment.
od_data <- read_rds("data/rds/od_data.rds")Next, compute the total passenger trip between and within planning subzones by using the code chunk below to get the output flow_data.
flow_data <- od_data %>%
group_by(ORIGIN_SZ, DESTIN_SZ) %>%
summarize(TRIPS = sum(MORNING_PEAK)) Use the code chunk below to display the flow_data dataframe.
head(flow_data, 10)# A tibble: 10 × 3
# Groups: ORIGIN_SZ [1]
ORIGIN_SZ DESTIN_SZ TRIPS
<chr> <chr> <dbl>
1 AMSZ01 AMSZ01 2694
2 AMSZ01 AMSZ02 10591
3 AMSZ01 AMSZ03 14980
4 AMSZ01 AMSZ04 3106
5 AMSZ01 AMSZ05 7734
6 AMSZ01 AMSZ06 2306
7 AMSZ01 AMSZ07 1824
8 AMSZ01 AMSZ08 2734
9 AMSZ01 AMSZ09 2300
10 AMSZ01 AMSZ10 164Separating intra-flow from passenger volume df
The code chunk below is used to add three new fields into the flow_data dataframe.
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$DESTIN_SZ, 0.000001, 1)Combining passenger volume data with distance value
Before joining flow_data and distPair, convert data value type of ORIGIN_SZ and DESTIN_SZ fields of flow_data dataframe into factor data type.
flow_data$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 join flow_data dataframe and distPair dataframe to give an output called flow_data1.
flow_data1 <- flow_data %>%
left_join (distPair,
by = c("ORIGIN_SZ" = "orig",
"DESTIN_SZ" = "dest"))Preparing Origin and Destination Attributes
Importing population data
pop <- read_csv("data/aspatial/pop.csv")Geospatial data wrangling
pop <- pop %>%
left_join(mpsz,
by = c("PA" = "PLN_AREA_N",
"SZ" = "SUBZONE_N")) %>%
select(1:6) %>%
rename(SZ_NAME = SZ,
SZ = SUBZONE_C)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,
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))The output data file is named SIM_data and saved out in rds data file format.
write_rds(flow_data1, "data/rds/SIM_data")Calibrating Spatial Interaction Models
In this section, Spatial Interaction Models are calibrated using Poisson Regression method.
Importing the modelling data
Firstly, import the modelling data using the code chunk below.
SIM_data <- read_rds("data/rds/SIM_data.rds")Visualising the dependent variable
Plot the distribution of the dependent variable (i.e. TRIPS) as a histogram by using the code chunk below.
ggplot(data = SIM_data,
aes(x = TRIPS)) +
geom_histogram()
Notice that the distribution is highly skewed and not resemble a bell shape (also known as a normal distribution).
Next, visualise the relation between the dependent variable and one of the key independent variable in Spatial Interaction Model, namely distance.
ggplot(data = SIM_data,
aes(x = dist,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
Notice that their relationship hardly resembles a linear relationship.
On the other hand, plotting the scatter plot using the log transformed version of both variables reveals a closer resemblance to a linear relationship.
ggplot(data = SIM_data,
aes(x = log(dist),
y = log(TRIPS))) +
geom_point() +
geom_smooth(method = lm)
Checking for variables with zero values
Since Poisson Regression is based of log and log 0 is undefined, it is important to ensure that there are 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.
summary(SIM_data) ORIGIN_SZ DESTIN_SZ TRIPS FlowNoIntra
Length:14274 Length:14274 Min. : 1.0 Min. : 1.0
Class :character Class :character 1st Qu.: 11.0 1st Qu.: 11.0
Mode :character Mode :character Median : 56.0 Median : 56.0
Mean : 664.3 Mean : 664.3
3rd Qu.: 296.0 3rd Qu.: 296.0
Max. :104167.0 Max. :104167.0
offset dist ORIGIN_AGE7_12 ORIGIN_AGE13_24 ORIGIN_AGE25_64
Min. :1 Min. : 173.8 Min. : 0 Min. : 0 Min. : 0
1st Qu.:1 1st Qu.: 3465.4 1st Qu.: 240 1st Qu.: 460 1st Qu.: 2210
Median :1 Median : 6121.0 Median : 710 Median : 1400 Median : 7030
Mean :1 Mean : 6951.8 Mean :1037 Mean : 2278 Mean :10536
3rd Qu.:1 3rd Qu.: 9725.1 3rd Qu.:1500 3rd Qu.: 3282 3rd Qu.:15830
Max. :1 Max. :26135.8 Max. :6340 Max. :16380 Max. :74610
DESTIN_AGE7_12 DESTIN_AGE13_24 DESTIN_AGE25_64
Min. : 0 Min. : 0 Min. : 0
1st Qu.: 250 1st Qu.: 460 1st Qu.: 2210
Median : 720 Median : 1430 Median : 7120
Mean :1040 Mean : 2305 Mean :10648
3rd Qu.:1500 3rd Qu.: 3290 3rd Qu.:15830
Max. :6340 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 all contain 0 values. In view of this, code chunk below will be used to replace zero values to 0.99.
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)Run summary() again to check that the replacement has been done correctly.
summary(SIM_data) ORIGIN_SZ DESTIN_SZ TRIPS FlowNoIntra
Length:14274 Length:14274 Min. : 1.0 Min. : 1.0
Class :character Class :character 1st Qu.: 11.0 1st Qu.: 11.0
Mode :character Mode :character Median : 56.0 Median : 56.0
Mean : 664.3 Mean : 664.3
3rd Qu.: 296.0 3rd Qu.: 296.0
Max. :104167.0 Max. :104167.0
offset dist ORIGIN_AGE7_12 ORIGIN_AGE13_24
Min. :1 Min. : 173.8 Min. : 0.99 Min. : 0.99
1st Qu.:1 1st Qu.: 3465.4 1st Qu.: 240.00 1st Qu.: 460.00
Median :1 Median : 6121.0 Median : 710.00 Median : 1400.00
Mean :1 Mean : 6951.8 Mean :1036.73 Mean : 2278.59
3rd Qu.:1 3rd Qu.: 9725.1 3rd Qu.:1500.00 3rd Qu.: 3282.50
Max. :1 Max. :26135.8 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.: 2210.00 1st Qu.: 250.00 1st Qu.: 460.00 1st Qu.: 2210.00
Median : 7030.00 Median : 720.00 Median : 1430.00 Median : 7120.00
Mean :10535.93 Mean :1039.98 Mean : 2305.33 Mean :10647.95
3rd Qu.:15830.00 3rd Qu.:1500.00 3rd Qu.: 3290.00 3rd Qu.:15830.00
Max. :74610.00 Max. :6340.00 Max. :16380.00 Max. :74610.00 Notice that all 0 values have been replaced by 0.99.
Unconstrained Spatial Interaction Model
Next, 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 general formula of Unconstrained Spatial Interaction Model is:
\[ \lambda_{ij} = exp(k + \mu lnV_i + \alpha lnW_j - \beta lnd_{ij}) \]
The code chunk used to calibrate to model is shown below:
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)
17.00287 0.21001 0.01289
log(dist)
-1.51785
Degrees of Freedom: 14273 Total (i.e. Null); 14270 Residual
Null Deviance: 36120000
Residual Deviance: 19960000 AIC: 20040000R-squared function
To measure how much variation of the trips can be accounted by the model, a function to calculate R-Squared value is written in the code chunk below.
CalcRSquared <- function(observed,estimated){
r <- cor(observed,estimated)
R2 <- r^2
R2
}Next, compute the R-squared of the unconstrained SIM by using the code chunk below.
CalcRSquared(uncSIM$data$TRIPS, uncSIM$fitted.values)[1] 0.1694734r2_mcfadden(uncSIM)# R2 for Generalized Linear Regression
R2: 0.446
adj. R2: 0.446Origin (Production) Constrained Spatial Interaction Model
Next, fit an origin constrained SIM by using the code chunk below.
The general formula of Origin Constrained Spatial Interaction Model is:
\[ \lambda_{ij} = exp(k + \mu_i + \alpha lnW_j - \beta lnd_{ij}) \]
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)
Deviance Residuals:
Min 1Q Median 3Q Max
-241.02 -16.13 -7.46 0.80 418.33
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 19.9309957 0.0054015 3689.887 < 2e-16 ***
ORIGIN_SZAMSZ02 0.6805710 0.0052686 129.175 < 2e-16 ***
ORIGIN_SZAMSZ03 0.3597850 0.0054884 65.554 < 2e-16 ***
ORIGIN_SZAMSZ04 -0.1106566 0.0060027 -18.434 < 2e-16 ***
ORIGIN_SZAMSZ05 -0.3140561 0.0067998 -46.186 < 2e-16 ***
ORIGIN_SZAMSZ06 0.0634425 0.0060258 10.528 < 2e-16 ***
ORIGIN_SZAMSZ07 -1.1301580 0.0110298 -102.464 < 2e-16 ***
ORIGIN_SZAMSZ08 -0.6330394 0.0102949 -61.491 < 2e-16 ***
ORIGIN_SZAMSZ09 0.1064915 0.0063450 16.784 < 2e-16 ***
ORIGIN_SZAMSZ10 0.5061899 0.0053889 93.931 < 2e-16 ***
ORIGIN_SZAMSZ11 -1.3167911 0.0144870 -90.895 < 2e-16 ***
ORIGIN_SZAMSZ12 -1.5103004 0.0127453 -118.499 < 2e-16 ***
ORIGIN_SZBDSZ01 1.3626004 0.0051433 264.929 < 2e-16 ***
ORIGIN_SZBDSZ02 0.9554084 0.0059655 160.156 < 2e-16 ***
ORIGIN_SZBDSZ03 1.1476190 0.0054278 211.433 < 2e-16 ***
ORIGIN_SZBDSZ04 2.0110410 0.0046344 433.940 < 2e-16 ***
ORIGIN_SZBDSZ05 1.0658940 0.0053976 197.477 < 2e-16 ***
ORIGIN_SZBDSZ06 1.2719222 0.0054774 232.213 < 2e-16 ***
ORIGIN_SZBDSZ07 -0.5053039 0.0111553 -45.297 < 2e-16 ***
ORIGIN_SZBDSZ08 -0.3556193 0.0102947 -34.544 < 2e-16 ***
ORIGIN_SZBKSZ01 -0.3606399 0.0075473 -47.784 < 2e-16 ***
ORIGIN_SZBKSZ02 0.1357265 0.0061394 22.107 < 2e-16 ***
ORIGIN_SZBKSZ03 0.4101999 0.0058983 69.545 < 2e-16 ***
ORIGIN_SZBKSZ04 -0.3418645 0.0070764 -48.310 < 2e-16 ***
ORIGIN_SZBKSZ05 -0.2986750 0.0074073 -40.322 < 2e-16 ***
ORIGIN_SZBKSZ06 -0.2637855 0.0068739 -38.375 < 2e-16 ***
ORIGIN_SZBKSZ07 0.5498323 0.0051476 106.813 < 2e-16 ***
ORIGIN_SZBKSZ08 -0.0527393 0.0061457 -8.582 < 2e-16 ***
ORIGIN_SZBKSZ09 -0.1564691 0.0067300 -23.249 < 2e-16 ***
ORIGIN_SZBLSZ01 -1.7551329 0.0176599 -99.385 < 2e-16 ***
ORIGIN_SZBLSZ02 -1.9493637 0.0213859 -91.152 < 2e-16 ***
ORIGIN_SZBLSZ03 -2.9057732 0.0535995 -54.213 < 2e-16 ***
ORIGIN_SZBLSZ04 -1.4672066 0.0254726 -57.599 < 2e-16 ***
ORIGIN_SZBMSZ01 0.1806064 0.0060563 29.821 < 2e-16 ***
ORIGIN_SZBMSZ02 -1.4026549 0.0078244 -179.267 < 2e-16 ***
ORIGIN_SZBMSZ03 -0.5976236 0.0063808 -93.660 < 2e-16 ***
ORIGIN_SZBMSZ04 -0.5456513 0.0059061 -92.388 < 2e-16 ***
ORIGIN_SZBMSZ05 -3.1095195 0.0188118 -165.297 < 2e-16 ***
ORIGIN_SZBMSZ06 -3.0273827 0.0194319 -155.794 < 2e-16 ***
ORIGIN_SZBMSZ07 -0.7378197 0.0066865 -110.345 < 2e-16 ***
ORIGIN_SZBMSZ08 -0.9306150 0.0067188 -138.510 < 2e-16 ***
ORIGIN_SZBMSZ09 -1.4137345 0.0101071 -139.876 < 2e-16 ***
ORIGIN_SZBMSZ10 -1.7054195 0.0101582 -167.886 < 2e-16 ***
ORIGIN_SZBMSZ11 -1.2418380 0.0076792 -161.714 < 2e-16 ***
ORIGIN_SZBMSZ12 -1.3746537 0.0109769 -125.231 < 2e-16 ***
ORIGIN_SZBMSZ13 -0.4339494 0.0069335 -62.587 < 2e-16 ***
ORIGIN_SZBMSZ14 -0.9950458 0.0076302 -130.410 < 2e-16 ***
ORIGIN_SZBMSZ15 -0.6544196 0.0068964 -94.892 < 2e-16 ***
ORIGIN_SZBMSZ16 -1.5193747 0.0105329 -144.250 < 2e-16 ***
ORIGIN_SZBMSZ17 -1.6536771 0.0180672 -91.529 < 2e-16 ***
ORIGIN_SZBPSZ01 0.1484355 0.0064734 22.930 < 2e-16 ***
ORIGIN_SZBPSZ02 -0.3602094 0.0073902 -48.741 < 2e-16 ***
ORIGIN_SZBPSZ03 -0.1567975 0.0072226 -21.709 < 2e-16 ***
ORIGIN_SZBPSZ04 0.4504873 0.0058418 77.115 < 2e-16 ***
ORIGIN_SZBPSZ05 0.5028646 0.0053682 93.675 < 2e-16 ***
ORIGIN_SZBPSZ06 -1.0125668 0.0105638 -95.853 < 2e-16 ***
ORIGIN_SZBPSZ07 -0.3859065 0.0098561 -39.154 < 2e-16 ***
ORIGIN_SZBSSZ01 0.1488497 0.0065504 22.724 < 2e-16 ***
ORIGIN_SZBSSZ02 0.4269498 0.0055893 76.387 < 2e-16 ***
ORIGIN_SZBSSZ03 -0.2437385 0.0062020 -39.300 < 2e-16 ***
ORIGIN_SZBTSZ01 0.1987940 0.0066672 29.817 < 2e-16 ***
ORIGIN_SZBTSZ02 -0.4571546 0.0090784 -50.356 < 2e-16 ***
ORIGIN_SZBTSZ03 -0.2697243 0.0077941 -34.606 < 2e-16 ***
ORIGIN_SZBTSZ04 -1.0997236 0.0115225 -95.441 < 2e-16 ***
ORIGIN_SZBTSZ05 -1.0053122 0.0132594 -75.819 < 2e-16 ***
ORIGIN_SZBTSZ06 -1.0841201 0.0102242 -106.035 < 2e-16 ***
ORIGIN_SZBTSZ07 -2.3134497 0.0158499 -145.960 < 2e-16 ***
ORIGIN_SZBTSZ08 -1.1581618 0.0121161 -95.589 < 2e-16 ***
ORIGIN_SZCBSZ01 -1.0805930 0.0577831 -18.701 < 2e-16 ***
ORIGIN_SZCCSZ01 -0.8145372 0.0152638 -53.364 < 2e-16 ***
ORIGIN_SZCHSZ01 0.0377079 0.0133240 2.830 0.004654 **
ORIGIN_SZCHSZ02 -0.6209553 0.0096388 -64.422 < 2e-16 ***
ORIGIN_SZCHSZ03 1.6790244 0.0069559 241.381 < 2e-16 ***
ORIGIN_SZCKSZ01 0.0839586 0.0059934 14.008 < 2e-16 ***
ORIGIN_SZCKSZ02 0.4379511 0.0062289 70.309 < 2e-16 ***
ORIGIN_SZCKSZ03 0.7956950 0.0051892 153.335 < 2e-16 ***
ORIGIN_SZCKSZ04 1.2740323 0.0053165 239.637 < 2e-16 ***
ORIGIN_SZCKSZ05 0.9326213 0.0061807 150.893 < 2e-16 ***
ORIGIN_SZCKSZ06 0.3976273 0.0085639 46.431 < 2e-16 ***
ORIGIN_SZCLSZ01 -0.7522917 0.0094655 -79.477 < 2e-16 ***
ORIGIN_SZCLSZ02 -1.3937450 0.0153260 -90.940 < 2e-16 ***
ORIGIN_SZCLSZ03 -0.7898683 0.0091016 -86.784 < 2e-16 ***
ORIGIN_SZCLSZ04 0.8451512 0.0051258 164.882 < 2e-16 ***
ORIGIN_SZCLSZ05 -1.6573818 0.0166091 -99.788 < 2e-16 ***
ORIGIN_SZCLSZ06 0.9478181 0.0048182 196.716 < 2e-16 ***
ORIGIN_SZCLSZ07 -0.2499753 0.0064632 -38.677 < 2e-16 ***
ORIGIN_SZCLSZ08 0.1350119 0.0069296 19.483 < 2e-16 ***
ORIGIN_SZCLSZ09 -1.3868782 0.0192743 -71.955 < 2e-16 ***
ORIGIN_SZDTSZ02 -3.7535792 0.0871325 -43.079 < 2e-16 ***
ORIGIN_SZDTSZ03 -3.8462041 0.0840156 -45.780 < 2e-16 ***
ORIGIN_SZDTSZ13 -2.9738127 0.0349241 -85.151 < 2e-16 ***
ORIGIN_SZGLSZ01 -1.5175198 0.0110135 -137.787 < 2e-16 ***
ORIGIN_SZGLSZ02 0.2405712 0.0058742 40.954 < 2e-16 ***
ORIGIN_SZGLSZ03 0.1940241 0.0061989 31.300 < 2e-16 ***
ORIGIN_SZGLSZ04 1.0292572 0.0049028 209.931 < 2e-16 ***
ORIGIN_SZGLSZ05 0.9864552 0.0050898 193.811 < 2e-16 ***
ORIGIN_SZHGSZ01 0.3073609 0.0054307 56.597 < 2e-16 ***
ORIGIN_SZHGSZ02 0.3827293 0.0054555 70.154 < 2e-16 ***
ORIGIN_SZHGSZ03 0.2342580 0.0059240 39.544 < 2e-16 ***
ORIGIN_SZHGSZ04 0.8750090 0.0049639 176.275 < 2e-16 ***
ORIGIN_SZHGSZ05 1.1695280 0.0049468 236.420 < 2e-16 ***
ORIGIN_SZHGSZ06 -0.0462411 0.0063805 -7.247 4.25e-13 ***
ORIGIN_SZHGSZ07 0.4488583 0.0055139 81.404 < 2e-16 ***
ORIGIN_SZHGSZ08 0.2236095 0.0061279 36.490 < 2e-16 ***
ORIGIN_SZHGSZ09 -1.6376674 0.0084442 -193.941 < 2e-16 ***
ORIGIN_SZHGSZ10 -2.9849025 0.0501042 -59.574 < 2e-16 ***
ORIGIN_SZJESZ01 0.3926525 0.0056268 69.783 < 2e-16 ***
ORIGIN_SZJESZ02 0.1230160 0.0056864 21.633 < 2e-16 ***
ORIGIN_SZJESZ03 0.0188276 0.0061020 3.085 0.002032 **
ORIGIN_SZJESZ04 -1.3611618 0.0117184 -116.156 < 2e-16 ***
ORIGIN_SZJESZ05 -2.0643662 0.0157083 -131.419 < 2e-16 ***
ORIGIN_SZJESZ06 0.1556368 0.0055245 28.172 < 2e-16 ***
ORIGIN_SZJESZ07 -1.7664532 0.0133171 -132.646 < 2e-16 ***
ORIGIN_SZJESZ08 -0.9115981 0.0138203 -65.961 < 2e-16 ***
ORIGIN_SZJESZ09 0.6121916 0.0060381 101.388 < 2e-16 ***
ORIGIN_SZJESZ10 -1.1953045 0.0233216 -51.253 < 2e-16 ***
ORIGIN_SZJESZ11 -1.4088748 0.0220921 -63.773 < 2e-16 ***
ORIGIN_SZJWSZ01 0.5759093 0.0077741 74.081 < 2e-16 ***
ORIGIN_SZJWSZ02 0.9769314 0.0053029 184.227 < 2e-16 ***
ORIGIN_SZJWSZ03 1.3242695 0.0049068 269.882 < 2e-16 ***
ORIGIN_SZJWSZ04 0.5621088 0.0057831 97.199 < 2e-16 ***
ORIGIN_SZJWSZ05 -1.5744341 0.0146904 -107.174 < 2e-16 ***
ORIGIN_SZJWSZ06 -0.9113320 0.0126913 -71.807 < 2e-16 ***
ORIGIN_SZJWSZ07 -2.3083419 0.0357843 -64.507 < 2e-16 ***
ORIGIN_SZJWSZ08 2.0114225 0.0047956 419.429 < 2e-16 ***
ORIGIN_SZJWSZ09 1.9086705 0.0045255 421.759 < 2e-16 ***
ORIGIN_SZKLSZ01 0.2743166 0.0056908 48.204 < 2e-16 ***
ORIGIN_SZKLSZ02 -0.6443386 0.0074521 -86.463 < 2e-16 ***
ORIGIN_SZKLSZ03 -0.3990113 0.0067213 -59.366 < 2e-16 ***
ORIGIN_SZKLSZ04 -2.1413876 0.0138405 -154.719 < 2e-16 ***
ORIGIN_SZKLSZ05 -1.0913697 0.0121512 -89.816 < 2e-16 ***
ORIGIN_SZKLSZ06 -5.6240764 0.1857405 -30.279 < 2e-16 ***
ORIGIN_SZKLSZ07 -1.1885897 0.0096830 -122.750 < 2e-16 ***
ORIGIN_SZKLSZ08 -1.7018593 0.0114317 -148.872 < 2e-16 ***
ORIGIN_SZLKSZ01 -1.6659670 0.0446420 -37.318 < 2e-16 ***
ORIGIN_SZMDSZ01 -1.1210505 0.0318834 -35.161 < 2e-16 ***
ORIGIN_SZMDSZ02 -0.5096299 0.0116645 -43.691 < 2e-16 ***
ORIGIN_SZMDSZ03 -1.9187039 0.0198291 -96.762 < 2e-16 ***
ORIGIN_SZMPSZ01 -0.5260512 0.0094201 -55.844 < 2e-16 ***
ORIGIN_SZMPSZ02 -0.2905084 0.0077974 -37.257 < 2e-16 ***
ORIGIN_SZMPSZ03 0.3342293 0.0063715 52.457 < 2e-16 ***
ORIGIN_SZMUSZ02 -3.8337096 0.1105053 -34.693 < 2e-16 ***
ORIGIN_SZNTSZ01 -2.9845040 0.0397028 -75.171 < 2e-16 ***
ORIGIN_SZNTSZ02 -3.1812985 0.0249470 -127.522 < 2e-16 ***
ORIGIN_SZNTSZ03 -0.9742991 0.0085424 -114.054 < 2e-16 ***
ORIGIN_SZNTSZ05 -4.2086932 0.0579737 -72.597 < 2e-16 ***
ORIGIN_SZNTSZ06 -4.5831822 0.0583494 -78.547 < 2e-16 ***
ORIGIN_SZNVSZ01 0.3186962 0.0052944 60.195 < 2e-16 ***
ORIGIN_SZNVSZ02 -0.5321136 0.0073747 -72.154 < 2e-16 ***
ORIGIN_SZNVSZ03 -0.9911852 0.0090560 -109.451 < 2e-16 ***
ORIGIN_SZNVSZ04 -0.8329721 0.0099590 -83.640 < 2e-16 ***
ORIGIN_SZNVSZ05 -2.1460777 0.0182401 -117.657 < 2e-16 ***
ORIGIN_SZPGSZ01 -0.5604078 0.0151515 -36.987 < 2e-16 ***
ORIGIN_SZPGSZ02 -0.4025139 0.0085135 -47.279 < 2e-16 ***
ORIGIN_SZPGSZ03 0.6975483 0.0055534 125.608 < 2e-16 ***
ORIGIN_SZPGSZ04 1.2175486 0.0051080 238.363 < 2e-16 ***
ORIGIN_SZPGSZ05 0.3895354 0.0069851 55.767 < 2e-16 ***
ORIGIN_SZPLSZ01 -0.5572701 0.0134473 -41.441 < 2e-16 ***
ORIGIN_SZPLSZ02 -0.9854214 0.0172337 -57.180 < 2e-16 ***
ORIGIN_SZPLSZ03 -1.6991954 0.0472629 -35.952 < 2e-16 ***
ORIGIN_SZPLSZ04 -2.2000217 0.0373580 -58.890 < 2e-16 ***
ORIGIN_SZPLSZ05 -1.7086663 0.0260920 -65.486 < 2e-16 ***
ORIGIN_SZPNSZ01 1.5292867 0.0055102 277.535 < 2e-16 ***
ORIGIN_SZPNSZ02 0.7457519 0.0127815 58.346 < 2e-16 ***
ORIGIN_SZPNSZ03 -1.3659046 0.0216180 -63.184 < 2e-16 ***
ORIGIN_SZPNSZ04 -2.0025379 0.0360655 -55.525 < 2e-16 ***
ORIGIN_SZPNSZ05 -0.9157959 0.0320955 -28.533 < 2e-16 ***
ORIGIN_SZPRSZ01 0.0522611 0.0139142 3.756 0.000173 ***
ORIGIN_SZPRSZ02 1.3063371 0.0053809 242.774 < 2e-16 ***
ORIGIN_SZPRSZ03 0.9963670 0.0054293 183.516 < 2e-16 ***
ORIGIN_SZPRSZ04 -0.0300950 0.0088010 -3.419 0.000627 ***
ORIGIN_SZPRSZ05 1.6840313 0.0050839 331.245 < 2e-16 ***
ORIGIN_SZPRSZ06 -0.8277202 0.0131296 -63.042 < 2e-16 ***
ORIGIN_SZPRSZ07 -2.1698449 0.0177362 -122.340 < 2e-16 ***
ORIGIN_SZPRSZ08 0.4559353 0.0072609 62.793 < 2e-16 ***
ORIGIN_SZQTSZ01 -0.3517047 0.0078770 -44.650 < 2e-16 ***
ORIGIN_SZQTSZ02 -0.8199353 0.0071544 -114.605 < 2e-16 ***
ORIGIN_SZQTSZ03 -0.2457614 0.0065555 -37.490 < 2e-16 ***
ORIGIN_SZQTSZ04 -1.2216614 0.0084050 -145.349 < 2e-16 ***
ORIGIN_SZQTSZ05 -0.7219952 0.0072360 -99.778 < 2e-16 ***
ORIGIN_SZQTSZ06 -0.6729363 0.0076658 -87.784 < 2e-16 ***
ORIGIN_SZQTSZ07 -1.4497690 0.0109365 -132.563 < 2e-16 ***
ORIGIN_SZQTSZ08 -0.2770151 0.0070193 -39.465 < 2e-16 ***
ORIGIN_SZQTSZ09 -0.6157554 0.0078739 -78.202 < 2e-16 ***
ORIGIN_SZQTSZ10 -0.3091547 0.0075471 -40.963 < 2e-16 ***
ORIGIN_SZQTSZ11 -1.9698881 0.0151247 -130.243 < 2e-16 ***
ORIGIN_SZQTSZ12 -2.6449643 0.0205857 -128.485 < 2e-16 ***
ORIGIN_SZQTSZ13 -0.3754107 0.0088433 -42.452 < 2e-16 ***
ORIGIN_SZQTSZ14 -1.6537473 0.0134378 -123.067 < 2e-16 ***
ORIGIN_SZQTSZ15 -0.3435351 0.0131956 -26.034 < 2e-16 ***
ORIGIN_SZRCSZ01 -1.7104390 0.0141179 -121.154 < 2e-16 ***
ORIGIN_SZRCSZ06 -1.1250727 0.0094909 -118.542 < 2e-16 ***
ORIGIN_SZRVSZ01 -3.0220116 0.0339694 -88.963 < 2e-16 ***
ORIGIN_SZRVSZ02 -3.6040075 0.0297641 -121.086 < 2e-16 ***
ORIGIN_SZRVSZ03 -3.2345594 0.0259149 -124.814 < 2e-16 ***
ORIGIN_SZRVSZ04 -3.6900313 0.0575908 -64.073 < 2e-16 ***
ORIGIN_SZRVSZ05 -2.9527570 0.0178582 -165.344 < 2e-16 ***
ORIGIN_SZSBSZ01 0.0238445 0.0078563 3.035 0.002405 **
ORIGIN_SZSBSZ02 -0.5780602 0.0093054 -62.121 < 2e-16 ***
ORIGIN_SZSBSZ03 0.8961719 0.0054586 164.175 < 2e-16 ***
ORIGIN_SZSBSZ04 0.8421798 0.0061888 136.080 < 2e-16 ***
ORIGIN_SZSBSZ05 -0.1682984 0.0078342 -21.482 < 2e-16 ***
ORIGIN_SZSBSZ06 -1.1482701 0.0196421 -58.460 < 2e-16 ***
ORIGIN_SZSBSZ07 -0.8830317 0.0160709 -54.946 < 2e-16 ***
ORIGIN_SZSBSZ08 -1.1039492 0.0174602 -63.226 < 2e-16 ***
ORIGIN_SZSBSZ09 -0.5946691 0.0101961 -58.323 < 2e-16 ***
ORIGIN_SZSESZ02 1.1144933 0.0050948 218.749 < 2e-16 ***
ORIGIN_SZSESZ03 1.1058963 0.0049026 225.574 < 2e-16 ***
ORIGIN_SZSESZ04 0.7427975 0.0056948 130.433 < 2e-16 ***
ORIGIN_SZSESZ05 -0.2812684 0.0069596 -40.414 < 2e-16 ***
ORIGIN_SZSESZ06 0.8168315 0.0055800 146.387 < 2e-16 ***
ORIGIN_SZSESZ07 -2.2842043 0.0231232 -98.784 < 2e-16 ***
ORIGIN_SZSGSZ01 -0.7313790 0.0098957 -73.909 < 2e-16 ***
ORIGIN_SZSGSZ02 -1.1185406 0.0110919 -100.843 < 2e-16 ***
ORIGIN_SZSGSZ03 0.1752618 0.0060508 28.965 < 2e-16 ***
ORIGIN_SZSGSZ04 0.3764395 0.0056165 67.023 < 2e-16 ***
ORIGIN_SZSGSZ05 -1.7203916 0.0118945 -144.637 < 2e-16 ***
ORIGIN_SZSGSZ06 0.4630857 0.0052886 87.563 < 2e-16 ***
ORIGIN_SZSGSZ07 -0.7051233 0.0073133 -96.417 < 2e-16 ***
ORIGIN_SZSKSZ01 0.2053928 0.0100710 20.395 < 2e-16 ***
ORIGIN_SZSKSZ02 1.2630428 0.0063490 198.935 < 2e-16 ***
ORIGIN_SZSKSZ03 -0.3035297 0.0096788 -31.360 < 2e-16 ***
ORIGIN_SZSKSZ04 -1.7952886 0.0359225 -49.977 < 2e-16 ***
ORIGIN_SZSKSZ05 -0.3836861 0.0176686 -21.716 < 2e-16 ***
ORIGIN_SZSLSZ01 -2.5916326 0.0348001 -74.472 < 2e-16 ***
ORIGIN_SZSLSZ04 -0.2251549 0.0088517 -25.436 < 2e-16 ***
ORIGIN_SZSRSZ01 -2.9590365 0.0173638 -170.414 < 2e-16 ***
ORIGIN_SZTHSZ01 -1.9639893 0.0570321 -34.437 < 2e-16 ***
ORIGIN_SZTHSZ03 -1.7281304 0.0272797 -63.349 < 2e-16 ***
ORIGIN_SZTHSZ04 -2.7837906 0.0343179 -81.118 < 2e-16 ***
ORIGIN_SZTHSZ06 -2.1800693 0.0205491 -106.091 < 2e-16 ***
ORIGIN_SZTMSZ01 0.8228136 0.0066824 123.131 < 2e-16 ***
ORIGIN_SZTMSZ02 2.3174781 0.0044978 515.243 < 2e-16 ***
ORIGIN_SZTMSZ03 1.7061757 0.0048615 350.957 < 2e-16 ***
ORIGIN_SZTMSZ04 1.2407899 0.0058389 212.504 < 2e-16 ***
ORIGIN_SZTMSZ05 -0.1000526 0.0124079 -8.064 7.41e-16 ***
ORIGIN_SZTNSZ01 -2.0347519 0.0139596 -145.760 < 2e-16 ***
ORIGIN_SZTNSZ02 -1.8682671 0.0107901 -173.146 < 2e-16 ***
ORIGIN_SZTNSZ03 -2.1737183 0.0146759 -148.115 < 2e-16 ***
ORIGIN_SZTNSZ04 -0.5006452 0.0081501 -61.428 < 2e-16 ***
ORIGIN_SZTPSZ01 -0.6722487 0.0075606 -88.914 < 2e-16 ***
ORIGIN_SZTPSZ02 0.4552916 0.0050191 90.711 < 2e-16 ***
ORIGIN_SZTPSZ03 -0.7865781 0.0072250 -108.869 < 2e-16 ***
ORIGIN_SZTPSZ04 -0.7049044 0.0066456 -106.071 < 2e-16 ***
ORIGIN_SZTPSZ05 -0.5574925 0.0070366 -79.227 < 2e-16 ***
ORIGIN_SZTPSZ06 -0.4247282 0.0068709 -61.815 < 2e-16 ***
ORIGIN_SZTPSZ07 -0.2846984 0.0071030 -40.081 < 2e-16 ***
ORIGIN_SZTPSZ08 -1.0898051 0.0110046 -99.031 < 2e-16 ***
ORIGIN_SZTPSZ09 -0.8092746 0.0079160 -102.232 < 2e-16 ***
ORIGIN_SZTPSZ10 -0.9332072 0.0086809 -107.502 < 2e-16 ***
ORIGIN_SZTPSZ11 -0.0421981 0.0064343 -6.558 5.44e-11 ***
ORIGIN_SZTPSZ12 -0.6330081 0.0078324 -80.819 < 2e-16 ***
ORIGIN_SZTSSZ01 -1.7650409 0.0517357 -34.116 < 2e-16 ***
ORIGIN_SZTSSZ02 1.1707267 0.0094178 124.310 < 2e-16 ***
ORIGIN_SZTSSZ03 0.6581679 0.0095894 68.635 < 2e-16 ***
ORIGIN_SZTSSZ04 0.8736493 0.0104965 83.233 < 2e-16 ***
ORIGIN_SZTSSZ05 0.0957248 0.0178709 5.356 8.49e-08 ***
ORIGIN_SZTSSZ06 1.7581609 0.0206810 85.013 < 2e-16 ***
ORIGIN_SZWCSZ01 0.8097950 0.0105622 76.669 < 2e-16 ***
ORIGIN_SZWCSZ02 -1.9966163 0.0345747 -57.748 < 2e-16 ***
ORIGIN_SZWCSZ03 -5.0687420 0.1474971 -34.365 < 2e-16 ***
ORIGIN_SZWDSZ01 1.4926003 0.0047216 316.124 < 2e-16 ***
ORIGIN_SZWDSZ02 0.9916597 0.0055755 177.859 < 2e-16 ***
ORIGIN_SZWDSZ03 1.5918065 0.0052180 305.062 < 2e-16 ***
ORIGIN_SZWDSZ04 1.3717152 0.0060516 226.669 < 2e-16 ***
ORIGIN_SZWDSZ05 0.6700111 0.0062287 107.569 < 2e-16 ***
ORIGIN_SZWDSZ06 0.8115996 0.0060947 133.165 < 2e-16 ***
ORIGIN_SZWDSZ07 -0.6488914 0.0093567 -69.351 < 2e-16 ***
ORIGIN_SZWDSZ08 -0.3610234 0.0096440 -37.435 < 2e-16 ***
ORIGIN_SZWDSZ09 1.4445461 0.0052279 276.317 < 2e-16 ***
ORIGIN_SZYSSZ01 -0.2039272 0.0069548 -29.322 < 2e-16 ***
ORIGIN_SZYSSZ02 0.8707707 0.0058957 147.697 < 2e-16 ***
ORIGIN_SZYSSZ03 1.8348842 0.0050377 364.231 < 2e-16 ***
ORIGIN_SZYSSZ04 1.0780641 0.0052960 203.564 < 2e-16 ***
ORIGIN_SZYSSZ05 0.3222765 0.0069700 46.237 < 2e-16 ***
ORIGIN_SZYSSZ06 -0.4424689 0.0124866 -35.435 < 2e-16 ***
ORIGIN_SZYSSZ07 -1.0267883 0.0155821 -65.895 < 2e-16 ***
ORIGIN_SZYSSZ08 0.1833117 0.0070935 25.842 < 2e-16 ***
ORIGIN_SZYSSZ09 1.0766070 0.0050451 213.396 < 2e-16 ***
log(DESTIN_AGE25_64) 0.0295428 0.0001051 280.998 < 2e-16 ***
log(dist) -1.7024691 0.0004625 -3681.042 < 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: 36117615 on 14273 degrees of freedom
Residual deviance: 12983718 on 13993 degrees of freedom
AIC: 13068835
Number of Fisher Scoring iterations: 6Examine how the constraints hold for destinations this time.
CalcRSquared(orcSIM$data$TRIPS, orcSIM$fitted.values)[1] 0.4029115Destination Constrained Spatial Interaction Model
Next, fit a destination constrained SIM by using the code chunk below.
The general formula of Destination Constrained Spatial Interaction Model is:
\[ \lambda_{ij} = exp(k + \mu lnV_i + \alpha_i - \beta lnd_{ij}) \]
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)
Deviance Residuals:
Min 1Q Median 3Q Max
-189.20 -15.64 -7.08 1.55 379.03
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 19.4822997 0.0050784 3836.298 < 2e-16 ***
DESTIN_SZAMSZ02 0.1263056 0.0049743 25.392 < 2e-16 ***
DESTIN_SZAMSZ03 0.0421788 0.0049859 8.460 < 2e-16 ***
DESTIN_SZAMSZ04 -1.1668479 0.0074254 -157.143 < 2e-16 ***
DESTIN_SZAMSZ05 -1.2586639 0.0075854 -165.931 < 2e-16 ***
DESTIN_SZAMSZ06 -1.1414791 0.0073474 -155.359 < 2e-16 ***
DESTIN_SZAMSZ07 -1.5565804 0.0109476 -142.185 < 2e-16 ***
DESTIN_SZAMSZ08 -0.3990754 0.0074159 -53.813 < 2e-16 ***
DESTIN_SZAMSZ09 -1.0109118 0.0076802 -131.626 < 2e-16 ***
DESTIN_SZAMSZ10 0.0159285 0.0051765 3.077 0.00209 **
DESTIN_SZAMSZ11 -0.3653273 0.0094866 -38.510 < 2e-16 ***
DESTIN_SZAMSZ12 0.5297606 0.0053243 99.500 < 2e-16 ***
DESTIN_SZBDSZ01 1.0394822 0.0044226 235.037 < 2e-16 ***
DESTIN_SZBDSZ02 0.1956964 0.0059564 32.855 < 2e-16 ***
DESTIN_SZBDSZ03 0.3209267 0.0053718 59.742 < 2e-16 ***
DESTIN_SZBDSZ04 1.2429874 0.0043104 288.370 < 2e-16 ***
DESTIN_SZBDSZ05 0.8535842 0.0046360 184.122 < 2e-16 ***
DESTIN_SZBDSZ06 0.5181443 0.0053736 96.423 < 2e-16 ***
DESTIN_SZBDSZ07 -0.5849371 0.0110468 -52.951 < 2e-16 ***
DESTIN_SZBDSZ08 -1.2871050 0.0128623 -100.068 < 2e-16 ***
DESTIN_SZBKSZ01 -1.0633560 0.0077771 -136.730 < 2e-16 ***
DESTIN_SZBKSZ02 -0.4065316 0.0066712 -60.938 < 2e-16 ***
DESTIN_SZBKSZ03 -0.6815674 0.0066509 -102.477 < 2e-16 ***
DESTIN_SZBKSZ04 -0.4185485 0.0058306 -71.785 < 2e-16 ***
DESTIN_SZBKSZ05 -0.8887654 0.0073867 -120.319 < 2e-16 ***
DESTIN_SZBKSZ06 -0.9436078 0.0068625 -137.501 < 2e-16 ***
DESTIN_SZBKSZ07 -0.0067325 0.0048408 -1.391 0.16430
DESTIN_SZBKSZ08 -1.2680903 0.0079177 -160.160 < 2e-16 ***
DESTIN_SZBKSZ09 -0.0350151 0.0054287 -6.450 1.12e-10 ***
DESTIN_SZBLSZ01 -0.3045203 0.0081978 -37.146 < 2e-16 ***
DESTIN_SZBLSZ02 0.6432424 0.0074449 86.400 < 2e-16 ***
DESTIN_SZBLSZ03 1.9595113 0.0084705 231.333 < 2e-16 ***
DESTIN_SZBLSZ04 0.0149756 0.0172081 0.870 0.38415
DESTIN_SZBMSZ01 -0.0378127 0.0055294 -6.838 8.00e-12 ***
DESTIN_SZBMSZ02 -0.8458055 0.0054043 -156.505 < 2e-16 ***
DESTIN_SZBMSZ03 -1.1334399 0.0063720 -177.878 < 2e-16 ***
DESTIN_SZBMSZ04 -1.1164759 0.0057743 -193.353 < 2e-16 ***
DESTIN_SZBMSZ05 -1.1078742 0.0078703 -140.766 < 2e-16 ***
DESTIN_SZBMSZ06 -2.2787234 0.0155126 -146.895 < 2e-16 ***
DESTIN_SZBMSZ07 -0.2739089 0.0051924 -52.752 < 2e-16 ***
DESTIN_SZBMSZ08 -1.6825978 0.0071842 -234.209 < 2e-16 ***
DESTIN_SZBMSZ09 -3.0047801 0.0159980 -187.823 < 2e-16 ***
DESTIN_SZBMSZ10 -2.2232689 0.0096907 -229.423 < 2e-16 ***
DESTIN_SZBMSZ11 -1.9657136 0.0086445 -227.394 < 2e-16 ***
DESTIN_SZBMSZ12 -1.5359286 0.0089658 -171.310 < 2e-16 ***
DESTIN_SZBMSZ13 -0.5657561 0.0059960 -94.355 < 2e-16 ***
DESTIN_SZBMSZ14 -1.6904858 0.0084858 -199.214 < 2e-16 ***
DESTIN_SZBMSZ15 -1.5268383 0.0079959 -190.953 < 2e-16 ***
DESTIN_SZBMSZ16 -2.2045600 0.0130872 -168.452 < 2e-16 ***
DESTIN_SZBMSZ17 -2.2992381 0.0184895 -124.353 < 2e-16 ***
DESTIN_SZBPSZ01 -0.8549497 0.0065168 -131.191 < 2e-16 ***
DESTIN_SZBPSZ02 -1.7470549 0.0095751 -182.457 < 2e-16 ***
DESTIN_SZBPSZ03 -1.4015145 0.0090888 -154.203 < 2e-16 ***
DESTIN_SZBPSZ04 -0.5250632 0.0066496 -78.962 < 2e-16 ***
DESTIN_SZBPSZ05 0.3413171 0.0046404 73.553 < 2e-16 ***
DESTIN_SZBPSZ06 -0.8569188 0.0090795 -94.380 < 2e-16 ***
DESTIN_SZBPSZ07 -0.0751284 0.0089704 -8.375 < 2e-16 ***
DESTIN_SZBSSZ01 0.1015228 0.0055735 18.215 < 2e-16 ***
DESTIN_SZBSSZ02 -0.7066412 0.0063845 -110.682 < 2e-16 ***
DESTIN_SZBSSZ03 0.1622730 0.0046689 34.756 < 2e-16 ***
DESTIN_SZBTSZ01 0.5470615 0.0047984 114.009 < 2e-16 ***
DESTIN_SZBTSZ02 -0.1393371 0.0078266 -17.803 < 2e-16 ***
DESTIN_SZBTSZ03 0.1474771 0.0059428 24.816 < 2e-16 ***
DESTIN_SZBTSZ04 -1.2857827 0.0122000 -105.392 < 2e-16 ***
DESTIN_SZBTSZ05 -0.2629188 0.0081769 -32.154 < 2e-16 ***
DESTIN_SZBTSZ06 -0.8319920 0.0081401 -102.209 < 2e-16 ***
DESTIN_SZBTSZ07 -1.8829448 0.0121227 -155.324 < 2e-16 ***
DESTIN_SZBTSZ08 -1.5732123 0.0116752 -134.748 < 2e-16 ***
DESTIN_SZCBSZ01 -3.5334327 0.3333510 -10.600 < 2e-16 ***
DESTIN_SZCCSZ01 -0.2129306 0.0093782 -22.705 < 2e-16 ***
DESTIN_SZCHSZ01 -0.1494972 0.0113078 -13.221 < 2e-16 ***
DESTIN_SZCHSZ02 0.0041774 0.0063195 0.661 0.50860
DESTIN_SZCHSZ03 2.5565450 0.0046495 549.857 < 2e-16 ***
DESTIN_SZCKSZ01 0.0489719 0.0053801 9.102 < 2e-16 ***
DESTIN_SZCKSZ02 -0.3548993 0.0060671 -58.496 < 2e-16 ***
DESTIN_SZCKSZ03 0.5386351 0.0044913 119.928 < 2e-16 ***
DESTIN_SZCKSZ04 -0.4425512 0.0073837 -59.936 < 2e-16 ***
DESTIN_SZCKSZ05 -0.4092591 0.0077267 -52.967 < 2e-16 ***
DESTIN_SZCKSZ06 0.2207041 0.0074252 29.724 < 2e-16 ***
DESTIN_SZCLSZ01 0.2851460 0.0052362 54.457 < 2e-16 ***
DESTIN_SZCLSZ02 -1.9270528 0.0147688 -130.482 < 2e-16 ***
DESTIN_SZCLSZ03 -0.6266521 0.0086780 -72.212 < 2e-16 ***
DESTIN_SZCLSZ04 -0.1335581 0.0054216 -24.634 < 2e-16 ***
DESTIN_SZCLSZ05 -0.8912963 0.0096015 -92.829 < 2e-16 ***
DESTIN_SZCLSZ06 0.1781234 0.0048150 36.993 < 2e-16 ***
DESTIN_SZCLSZ07 -0.5609619 0.0062277 -90.075 < 2e-16 ***
DESTIN_SZCLSZ08 -0.3875308 0.0068390 -56.665 < 2e-16 ***
DESTIN_SZCLSZ09 0.2539453 0.0072623 34.968 < 2e-16 ***
DESTIN_SZDTSZ02 -2.5036295 0.0373421 -67.046 < 2e-16 ***
DESTIN_SZDTSZ03 -0.8956407 0.0149971 -59.721 < 2e-16 ***
DESTIN_SZDTSZ13 -1.6562176 0.0175441 -94.403 < 2e-16 ***
DESTIN_SZGLSZ01 -0.2716152 0.0056553 -48.029 < 2e-16 ***
DESTIN_SZGLSZ02 -0.1735665 0.0055548 -31.246 < 2e-16 ***
DESTIN_SZGLSZ03 0.7029507 0.0044934 156.441 < 2e-16 ***
DESTIN_SZGLSZ04 0.5788027 0.0045449 127.351 < 2e-16 ***
DESTIN_SZGLSZ05 0.6865291 0.0045131 152.118 < 2e-16 ***
DESTIN_SZHGSZ01 0.3275950 0.0043866 74.681 < 2e-16 ***
DESTIN_SZHGSZ02 -0.6326974 0.0063517 -99.610 < 2e-16 ***
DESTIN_SZHGSZ03 -1.0597982 0.0073914 -143.382 < 2e-16 ***
DESTIN_SZHGSZ04 -0.2267013 0.0052178 -43.448 < 2e-16 ***
DESTIN_SZHGSZ05 -0.3063050 0.0055452 -55.238 < 2e-16 ***
DESTIN_SZHGSZ06 -0.7483961 0.0065544 -114.182 < 2e-16 ***
DESTIN_SZHGSZ07 0.1096958 0.0051309 21.379 < 2e-16 ***
DESTIN_SZHGSZ08 -0.1374201 0.0056692 -24.240 < 2e-16 ***
DESTIN_SZHGSZ09 0.0775400 0.0060230 12.874 < 2e-16 ***
DESTIN_SZHGSZ10 -3.3017475 0.0289292 -114.132 < 2e-16 ***
DESTIN_SZJESZ01 -0.0489065 0.0057246 -8.543 < 2e-16 ***
DESTIN_SZJESZ02 -0.5101614 0.0060074 -84.921 < 2e-16 ***
DESTIN_SZJESZ03 -0.5328921 0.0064129 -83.097 < 2e-16 ***
DESTIN_SZJESZ04 -0.7348953 0.0082249 -89.351 < 2e-16 ***
DESTIN_SZJESZ05 -1.0864570 0.0111740 -97.231 < 2e-16 ***
DESTIN_SZJESZ06 0.2407920 0.0046801 51.451 < 2e-16 ***
DESTIN_SZJESZ07 -1.1523093 0.0090103 -127.888 < 2e-16 ***
DESTIN_SZJESZ08 -0.4627356 0.0094529 -48.952 < 2e-16 ***
DESTIN_SZJESZ09 0.0528616 0.0068126 7.759 8.53e-15 ***
DESTIN_SZJESZ10 1.0240660 0.0084045 121.848 < 2e-16 ***
DESTIN_SZJESZ11 0.7875517 0.0076251 103.284 < 2e-16 ***
DESTIN_SZJWSZ01 -0.1533418 0.0076198 -20.124 < 2e-16 ***
DESTIN_SZJWSZ02 -0.0011019 0.0059389 -0.186 0.85280
DESTIN_SZJWSZ03 0.9063789 0.0046747 193.892 < 2e-16 ***
DESTIN_SZJWSZ04 0.7019286 0.0049743 141.112 < 2e-16 ***
DESTIN_SZJWSZ05 -0.5197057 0.0072971 -71.220 < 2e-16 ***
DESTIN_SZJWSZ06 0.3350986 0.0061171 54.780 < 2e-16 ***
DESTIN_SZJWSZ07 -0.5961960 0.0328336 -18.158 < 2e-16 ***
DESTIN_SZJWSZ08 0.8054662 0.0056006 143.819 < 2e-16 ***
DESTIN_SZJWSZ09 1.5860146 0.0040282 393.723 < 2e-16 ***
DESTIN_SZKLSZ01 -0.6500838 0.0063560 -102.279 < 2e-16 ***
DESTIN_SZKLSZ02 -0.7039434 0.0064465 -109.197 < 2e-16 ***
DESTIN_SZKLSZ03 -1.1972384 0.0075577 -158.413 < 2e-16 ***
DESTIN_SZKLSZ04 -1.7172228 0.0097573 -175.993 < 2e-16 ***
DESTIN_SZKLSZ05 -0.6042386 0.0093730 -64.466 < 2e-16 ***
DESTIN_SZKLSZ06 -3.0201496 0.0389503 -77.539 < 2e-16 ***
DESTIN_SZKLSZ07 -1.1522413 0.0076607 -150.409 < 2e-16 ***
DESTIN_SZKLSZ08 -0.6977825 0.0057610 -121.122 < 2e-16 ***
DESTIN_SZLKSZ01 -0.6895952 0.0268661 -25.668 < 2e-16 ***
DESTIN_SZMDSZ01 -0.7155951 0.0228203 -31.358 < 2e-16 ***
DESTIN_SZMDSZ02 -0.8153643 0.0123003 -66.288 < 2e-16 ***
DESTIN_SZMDSZ03 -2.7745226 0.0301326 -92.077 < 2e-16 ***
DESTIN_SZMPSZ01 -0.5492095 0.0087198 -62.984 < 2e-16 ***
DESTIN_SZMPSZ02 -0.6104744 0.0069346 -88.033 < 2e-16 ***
DESTIN_SZMPSZ03 0.2775047 0.0054964 50.489 < 2e-16 ***
DESTIN_SZMUSZ02 -2.6322870 0.0214943 -122.464 < 2e-16 ***
DESTIN_SZNTSZ01 -4.0762008 0.0531046 -76.758 < 2e-16 ***
DESTIN_SZNTSZ02 -1.9765545 0.0125659 -157.296 < 2e-16 ***
DESTIN_SZNTSZ03 -1.4563069 0.0085433 -170.462 < 2e-16 ***
DESTIN_SZNTSZ05 -2.0125598 0.0270737 -74.336 < 2e-16 ***
DESTIN_SZNTSZ06 -3.0145357 0.0504986 -59.695 < 2e-16 ***
DESTIN_SZNVSZ01 -0.4693625 0.0053866 -87.135 < 2e-16 ***
DESTIN_SZNVSZ02 -0.4525631 0.0060428 -74.894 < 2e-16 ***
DESTIN_SZNVSZ03 -0.4821492 0.0064725 -74.492 < 2e-16 ***
DESTIN_SZNVSZ04 -1.8929756 0.0128397 -147.432 < 2e-16 ***
DESTIN_SZNVSZ05 -1.4501752 0.0099737 -145.400 < 2e-16 ***
DESTIN_SZPGSZ01 -1.2305867 0.0174321 -70.593 < 2e-16 ***
DESTIN_SZPGSZ02 -0.8232919 0.0080153 -102.715 < 2e-16 ***
DESTIN_SZPGSZ03 0.2138480 0.0050850 42.054 < 2e-16 ***
DESTIN_SZPGSZ04 0.1045757 0.0053579 19.518 < 2e-16 ***
DESTIN_SZPGSZ05 -0.7542450 0.0088883 -84.858 < 2e-16 ***
DESTIN_SZPLSZ01 -0.0098642 0.0080428 -1.226 0.22003
DESTIN_SZPLSZ02 -1.2630412 0.0152594 -82.771 < 2e-16 ***
DESTIN_SZPLSZ03 -0.1554479 0.0108611 -14.312 < 2e-16 ***
DESTIN_SZPLSZ04 -1.5505819 0.0114768 -135.105 < 2e-16 ***
DESTIN_SZPLSZ05 -0.2417805 0.0130391 -18.543 < 2e-16 ***
DESTIN_SZPNSZ01 0.7926715 0.0073628 107.659 < 2e-16 ***
DESTIN_SZPNSZ02 2.1914920 0.0073537 298.013 < 2e-16 ***
DESTIN_SZPNSZ03 1.0246845 0.0086874 117.951 < 2e-16 ***
DESTIN_SZPNSZ04 2.5522612 0.0091789 278.057 < 2e-16 ***
DESTIN_SZPNSZ05 1.7995301 0.0138562 129.872 < 2e-16 ***
DESTIN_SZPRSZ01 -0.6576686 0.0096037 -68.481 < 2e-16 ***
DESTIN_SZPRSZ02 0.3113532 0.0059851 52.021 < 2e-16 ***
DESTIN_SZPRSZ03 0.9255296 0.0044779 206.687 < 2e-16 ***
DESTIN_SZPRSZ04 -0.0028578 0.0093218 -0.307 0.75917
DESTIN_SZPRSZ05 0.2457863 0.0058261 42.187 < 2e-16 ***
DESTIN_SZPRSZ06 0.3692137 0.0064542 57.205 < 2e-16 ***
DESTIN_SZPRSZ07 -1.6733306 0.0138440 -120.871 < 2e-16 ***
DESTIN_SZPRSZ08 -0.2221048 0.0074846 -29.675 < 2e-16 ***
DESTIN_SZQTSZ01 -1.0185488 0.0093179 -109.311 < 2e-16 ***
DESTIN_SZQTSZ02 -1.2802688 0.0081670 -156.761 < 2e-16 ***
DESTIN_SZQTSZ03 -1.3322708 0.0079106 -168.415 < 2e-16 ***
DESTIN_SZQTSZ04 -1.1803631 0.0077366 -152.568 < 2e-16 ***
DESTIN_SZQTSZ05 -1.2215818 0.0072829 -167.734 < 2e-16 ***
DESTIN_SZQTSZ06 -1.3213145 0.0074858 -176.509 < 2e-16 ***
DESTIN_SZQTSZ07 -1.6426306 0.0123347 -133.171 < 2e-16 ***
DESTIN_SZQTSZ08 -0.2224169 0.0058405 -38.082 < 2e-16 ***
DESTIN_SZQTSZ09 -0.8142678 0.0069796 -116.665 < 2e-16 ***
DESTIN_SZQTSZ10 -0.1090496 0.0062573 -17.428 < 2e-16 ***
DESTIN_SZQTSZ11 -0.0108951 0.0061145 -1.782 0.07477 .
DESTIN_SZQTSZ12 -0.8582515 0.0090243 -95.105 < 2e-16 ***
DESTIN_SZQTSZ13 0.1834409 0.0065231 28.122 < 2e-16 ***
DESTIN_SZQTSZ14 0.1994454 0.0073615 27.093 < 2e-16 ***
DESTIN_SZQTSZ15 0.6740197 0.0088699 75.990 < 2e-16 ***
DESTIN_SZRCSZ01 -0.7746427 0.0079375 -97.593 < 2e-16 ***
DESTIN_SZRCSZ06 -1.4394098 0.0209931 -68.566 < 2e-16 ***
DESTIN_SZRVSZ01 -2.6060495 0.0175759 -148.274 < 2e-16 ***
DESTIN_SZRVSZ02 -2.5823769 0.0354706 -72.803 < 2e-16 ***
DESTIN_SZRVSZ03 -2.5890601 0.0152644 -169.614 < 2e-16 ***
DESTIN_SZRVSZ04 -2.2277482 0.0165661 -134.477 < 2e-16 ***
DESTIN_SZRVSZ05 -3.8610445 0.0298251 -129.456 < 2e-16 ***
DESTIN_SZSBSZ01 -1.2035529 0.0103954 -115.777 < 2e-16 ***
DESTIN_SZSBSZ02 -1.0267199 0.0085239 -120.452 < 2e-16 ***
DESTIN_SZSBSZ03 0.5977382 0.0050336 118.750 < 2e-16 ***
DESTIN_SZSBSZ04 0.5362769 0.0060573 88.534 < 2e-16 ***
DESTIN_SZSBSZ05 -1.0440525 0.0089622 -116.495 < 2e-16 ***
DESTIN_SZSBSZ06 -1.3939595 0.0246679 -56.509 < 2e-16 ***
DESTIN_SZSBSZ07 0.1029116 0.0235414 4.372 1.23e-05 ***
DESTIN_SZSBSZ08 1.3564902 0.0060529 224.105 < 2e-16 ***
DESTIN_SZSBSZ09 0.4573712 0.0056585 80.829 < 2e-16 ***
DESTIN_SZSESZ02 -0.1553609 0.0056716 -27.393 < 2e-16 ***
DESTIN_SZSESZ03 0.5412776 0.0043801 123.576 < 2e-16 ***
DESTIN_SZSESZ04 -0.6382091 0.0065411 -97.568 < 2e-16 ***
DESTIN_SZSESZ05 -0.3332093 0.0055002 -60.581 < 2e-16 ***
DESTIN_SZSESZ06 -0.3085951 0.0072340 -42.659 < 2e-16 ***
DESTIN_SZSESZ07 -2.6237684 0.0245753 -106.764 < 2e-16 ***
DESTIN_SZSGSZ01 -0.1062372 0.0066634 -15.943 < 2e-16 ***
DESTIN_SZSGSZ02 -0.0475568 0.0058908 -8.073 6.85e-16 ***
DESTIN_SZSGSZ03 -0.2118402 0.0055056 -38.477 < 2e-16 ***
DESTIN_SZSGSZ04 -0.1099618 0.0054841 -20.051 < 2e-16 ***
DESTIN_SZSGSZ05 -2.1556963 0.0113821 -189.394 < 2e-16 ***
DESTIN_SZSGSZ06 0.4416352 0.0043842 100.734 < 2e-16 ***
DESTIN_SZSGSZ07 -0.3949335 0.0059250 -66.655 < 2e-16 ***
DESTIN_SZSISZ01 -1.2847094 0.0288610 -44.514 < 2e-16 ***
DESTIN_SZSKSZ01 0.3089834 0.0082924 37.261 < 2e-16 ***
DESTIN_SZSKSZ02 1.4139309 0.0059981 235.729 < 2e-16 ***
DESTIN_SZSKSZ03 0.2427688 0.0067373 36.034 < 2e-16 ***
DESTIN_SZSKSZ04 -0.2527488 0.0161286 -15.671 < 2e-16 ***
DESTIN_SZSKSZ05 0.6046051 0.0122766 49.249 < 2e-16 ***
DESTIN_SZSLSZ01 -0.3927387 0.0099790 -39.356 < 2e-16 ***
DESTIN_SZSLSZ04 -0.5942110 0.0086225 -68.914 < 2e-16 ***
DESTIN_SZSRSZ01 -2.6855766 0.0138707 -193.615 < 2e-16 ***
DESTIN_SZTHSZ01 -3.2750084 0.0402668 -81.333 < 2e-16 ***
DESTIN_SZTHSZ03 -1.7964408 0.0261810 -68.616 < 2e-16 ***
DESTIN_SZTHSZ04 -2.6323994 0.0241831 -108.853 < 2e-16 ***
DESTIN_SZTHSZ06 -1.9444390 0.0166052 -117.098 < 2e-16 ***
DESTIN_SZTMSZ01 0.3856054 0.0063086 61.123 < 2e-16 ***
DESTIN_SZTMSZ02 1.8586526 0.0039229 473.790 < 2e-16 ***
DESTIN_SZTMSZ03 1.2601385 0.0044018 286.278 < 2e-16 ***
DESTIN_SZTMSZ04 1.5884327 0.0043362 366.316 < 2e-16 ***
DESTIN_SZTMSZ05 1.0377553 0.0063271 164.018 < 2e-16 ***
DESTIN_SZTNSZ01 -0.9954275 0.0080345 -123.895 < 2e-16 ***
DESTIN_SZTNSZ02 -2.1032696 0.0109228 -192.557 < 2e-16 ***
DESTIN_SZTNSZ03 -2.0044892 0.0129215 -155.128 < 2e-16 ***
DESTIN_SZTNSZ04 -0.9750326 0.0081677 -119.377 < 2e-16 ***
DESTIN_SZTPSZ01 -0.7788383 0.0068769 -113.254 < 2e-16 ***
DESTIN_SZTPSZ02 0.2866080 0.0042843 66.898 < 2e-16 ***
DESTIN_SZTPSZ03 -0.8749841 0.0065470 -133.646 < 2e-16 ***
DESTIN_SZTPSZ04 -1.6852792 0.0081488 -206.812 < 2e-16 ***
DESTIN_SZTPSZ05 -1.3721346 0.0068230 -201.104 < 2e-16 ***
DESTIN_SZTPSZ06 -0.7832133 0.0069164 -113.239 < 2e-16 ***
DESTIN_SZTPSZ07 -2.3109126 0.0130830 -176.635 < 2e-16 ***
DESTIN_SZTPSZ08 -1.6406531 0.0104897 -156.406 < 2e-16 ***
DESTIN_SZTPSZ09 -0.5636273 0.0076848 -73.343 < 2e-16 ***
DESTIN_SZTPSZ10 -1.5640843 0.0099984 -156.433 < 2e-16 ***
DESTIN_SZTPSZ11 -0.3700482 0.0059834 -61.846 < 2e-16 ***
DESTIN_SZTPSZ12 -0.8828228 0.0072302 -122.102 < 2e-16 ***
DESTIN_SZTSSZ01 0.3529526 0.0221887 15.907 < 2e-16 ***
DESTIN_SZTSSZ02 1.0265792 0.0153515 66.871 < 2e-16 ***
DESTIN_SZTSSZ03 1.9647347 0.0092388 212.662 < 2e-16 ***
DESTIN_SZTSSZ04 1.8649836 0.0089976 207.275 < 2e-16 ***
DESTIN_SZTSSZ05 2.8437058 0.0085738 331.673 < 2e-16 ***
DESTIN_SZTSSZ06 3.4238870 0.0161304 212.263 < 2e-16 ***
DESTIN_SZWCSZ01 2.9550693 0.0051690 571.689 < 2e-16 ***
DESTIN_SZWCSZ02 -0.8214103 0.0129213 -63.570 < 2e-16 ***
DESTIN_SZWCSZ03 -1.7393427 0.0347472 -50.057 < 2e-16 ***
DESTIN_SZWDSZ01 1.3424417 0.0039957 335.972 < 2e-16 ***
DESTIN_SZWDSZ02 -0.2103694 0.0068601 -30.666 < 2e-16 ***
DESTIN_SZWDSZ03 0.8268551 0.0051363 160.983 < 2e-16 ***
DESTIN_SZWDSZ04 -0.0643997 0.0079076 -8.144 3.82e-16 ***
DESTIN_SZWDSZ05 0.0451985 0.0075732 5.968 2.40e-09 ***
DESTIN_SZWDSZ06 0.6981330 0.0051936 134.423 < 2e-16 ***
DESTIN_SZWDSZ07 -0.0403233 0.0067749 -5.952 2.65e-09 ***
DESTIN_SZWDSZ08 0.2850631 0.0069225 41.179 < 2e-16 ***
DESTIN_SZWDSZ09 1.3016106 0.0050365 258.433 < 2e-16 ***
DESTIN_SZYSSZ01 0.7598564 0.0044144 172.133 < 2e-16 ***
DESTIN_SZYSSZ02 0.2648061 0.0058239 45.469 < 2e-16 ***
DESTIN_SZYSSZ03 -0.0412163 0.0068337 -6.031 1.63e-09 ***
DESTIN_SZYSSZ04 -0.0561054 0.0060829 -9.223 < 2e-16 ***
DESTIN_SZYSSZ05 -0.9970159 0.0121827 -81.839 < 2e-16 ***
DESTIN_SZYSSZ06 -1.3808376 0.0125738 -109.819 < 2e-16 ***
DESTIN_SZYSSZ07 -0.7128364 0.0165296 -43.125 < 2e-16 ***
DESTIN_SZYSSZ08 0.9409510 0.0045886 205.064 < 2e-16 ***
DESTIN_SZYSSZ09 0.3738436 0.0047971 77.930 < 2e-16 ***
log(ORIGIN_AGE25_64) 0.1928847 0.0001667 1157.214 < 2e-16 ***
log(dist) -1.7828141 0.0004794 -3718.501 < 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: 36117615 on 14273 degrees of freedom
Residual deviance: 12319763 on 13992 degrees of freedom
AIC: 12404881
Number of Fisher Scoring iterations: 7Examine how the constraints hold for destinations this time.
CalcRSquared(decSIM$data$TRIPS, decSIM$fitted.values)[1] 0.496166Doubly Constrained Spatial Interaction Model
Next, fit a doubly constrained SIM by using the code chunk below.
The general formula of Doubly Constrained Spatial Interaction Model is:
\[ \lambda_{ij} = exp(k + \mu_i + \alpha_i - \beta lnd_{ij}) \]
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)
Deviance Residuals:
Min 1Q Median 3Q Max
-159.373 -12.413 -4.694 2.892 270.252
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 21.9587595 0.0066831 3285.715 < 2e-16 ***
ORIGIN_SZAMSZ02 0.4778050 0.0054127 88.275 < 2e-16 ***
ORIGIN_SZAMSZ03 0.2895973 0.0055517 52.163 < 2e-16 ***
ORIGIN_SZAMSZ04 -0.2628080 0.0060720 -43.282 < 2e-16 ***
ORIGIN_SZAMSZ05 -0.2631404 0.0069008 -38.132 < 2e-16 ***
ORIGIN_SZAMSZ06 0.1722337 0.0062028 27.767 < 2e-16 ***
ORIGIN_SZAMSZ07 -0.9883200 0.0111224 -88.859 < 2e-16 ***
ORIGIN_SZAMSZ08 -0.4052821 0.0104095 -38.934 < 2e-16 ***
ORIGIN_SZAMSZ09 0.0356290 0.0064816 5.497 3.86e-08 ***
ORIGIN_SZAMSZ10 0.4815569 0.0055521 86.735 < 2e-16 ***
ORIGIN_SZAMSZ11 -1.4440079 0.0146079 -98.851 < 2e-16 ***
ORIGIN_SZAMSZ12 -1.7862677 0.0128071 -139.475 < 2e-16 ***
ORIGIN_SZBDSZ01 0.8653749 0.0054381 159.132 < 2e-16 ***
ORIGIN_SZBDSZ02 0.0841000 0.0062834 13.385 < 2e-16 ***
ORIGIN_SZBDSZ03 0.3158343 0.0057510 54.918 < 2e-16 ***
ORIGIN_SZBDSZ04 1.4556701 0.0049986 291.215 < 2e-16 ***
ORIGIN_SZBDSZ05 0.6363125 0.0057193 111.257 < 2e-16 ***
ORIGIN_SZBDSZ06 0.6749341 0.0058650 115.078 < 2e-16 ***
ORIGIN_SZBDSZ07 -1.2176407 0.0113698 -107.095 < 2e-16 ***
ORIGIN_SZBDSZ08 -0.9803580 0.0105604 -92.833 < 2e-16 ***
ORIGIN_SZBKSZ01 -0.2919642 0.0080763 -36.151 < 2e-16 ***
ORIGIN_SZBKSZ02 0.4609570 0.0067997 67.791 < 2e-16 ***
ORIGIN_SZBKSZ03 0.6273448 0.0065989 95.068 < 2e-16 ***
ORIGIN_SZBKSZ04 -0.2499063 0.0076555 -32.644 < 2e-16 ***
ORIGIN_SZBKSZ05 -0.2628428 0.0078905 -33.311 < 2e-16 ***
ORIGIN_SZBKSZ06 -0.2174034 0.0075134 -28.936 < 2e-16 ***
ORIGIN_SZBKSZ07 0.7094093 0.0058574 121.114 < 2e-16 ***
ORIGIN_SZBKSZ08 -0.1614362 0.0067626 -23.872 < 2e-16 ***
ORIGIN_SZBKSZ09 -0.2739085 0.0072969 -37.537 < 2e-16 ***
ORIGIN_SZBLSZ01 -2.4281074 0.0181172 -134.022 < 2e-16 ***
ORIGIN_SZBLSZ02 -2.7305447 0.0219341 -124.489 < 2e-16 ***
ORIGIN_SZBLSZ03 -3.3071431 0.0540398 -61.198 < 2e-16 ***
ORIGIN_SZBLSZ04 -2.4550671 0.0263946 -93.014 < 2e-16 ***
ORIGIN_SZBMSZ01 0.1198976 0.0065964 18.176 < 2e-16 ***
ORIGIN_SZBMSZ02 -1.3908667 0.0083230 -167.112 < 2e-16 ***
ORIGIN_SZBMSZ03 -0.6999122 0.0069754 -100.339 < 2e-16 ***
ORIGIN_SZBMSZ04 -0.2691159 0.0066184 -40.662 < 2e-16 ***
ORIGIN_SZBMSZ05 -2.6163780 0.0190989 -136.991 < 2e-16 ***
ORIGIN_SZBMSZ06 -2.9729956 0.0197182 -150.774 < 2e-16 ***
ORIGIN_SZBMSZ07 -0.7309916 0.0072407 -100.956 < 2e-16 ***
ORIGIN_SZBMSZ08 -1.0019514 0.0073169 -136.936 < 2e-16 ***
ORIGIN_SZBMSZ09 -1.3667460 0.0105325 -129.764 < 2e-16 ***
ORIGIN_SZBMSZ10 -1.6907268 0.0106687 -158.476 < 2e-16 ***
ORIGIN_SZBMSZ11 -1.2288802 0.0082919 -148.202 < 2e-16 ***
ORIGIN_SZBMSZ12 -1.6517767 0.0115101 -143.507 < 2e-16 ***
ORIGIN_SZBMSZ13 -0.7251351 0.0075289 -96.314 < 2e-16 ***
ORIGIN_SZBMSZ14 -1.1534912 0.0082629 -139.599 < 2e-16 ***
ORIGIN_SZBMSZ15 -0.5476774 0.0075710 -72.339 < 2e-16 ***
ORIGIN_SZBMSZ16 -1.5195034 0.0111459 -136.329 < 2e-16 ***
ORIGIN_SZBMSZ17 -1.6026767 0.0184419 -86.904 < 2e-16 ***
ORIGIN_SZBPSZ01 0.5571291 0.0071866 77.523 < 2e-16 ***
ORIGIN_SZBPSZ02 0.0523197 0.0082259 6.360 2.01e-10 ***
ORIGIN_SZBPSZ03 0.2942047 0.0080482 36.555 < 2e-16 ***
ORIGIN_SZBPSZ04 0.6246296 0.0065878 94.816 < 2e-16 ***
ORIGIN_SZBPSZ05 0.8663708 0.0060852 142.372 < 2e-16 ***
ORIGIN_SZBPSZ06 -0.9896182 0.0109551 -90.334 < 2e-16 ***
ORIGIN_SZBPSZ07 -0.5219250 0.0101830 -51.255 < 2e-16 ***
ORIGIN_SZBSSZ01 0.3299588 0.0066440 49.663 < 2e-16 ***
ORIGIN_SZBSSZ02 0.2851357 0.0057077 49.956 < 2e-16 ***
ORIGIN_SZBSSZ03 -0.2084740 0.0063364 -32.901 < 2e-16 ***
ORIGIN_SZBTSZ01 0.1425664 0.0071103 20.051 < 2e-16 ***
ORIGIN_SZBTSZ02 -0.5591999 0.0093616 -59.733 < 2e-16 ***
ORIGIN_SZBTSZ03 -0.3648190 0.0081677 -44.666 < 2e-16 ***
ORIGIN_SZBTSZ04 -1.4555078 0.0120138 -121.152 < 2e-16 ***
ORIGIN_SZBTSZ05 -0.8635510 0.0133848 -64.517 < 2e-16 ***
ORIGIN_SZBTSZ06 -1.1383111 0.0106421 -106.963 < 2e-16 ***
ORIGIN_SZBTSZ07 -2.3477669 0.0160858 -145.953 < 2e-16 ***
ORIGIN_SZBTSZ08 -1.2918779 0.0124862 -103.464 < 2e-16 ***
ORIGIN_SZCBSZ01 -3.3713588 0.0578683 -58.259 < 2e-16 ***
ORIGIN_SZCCSZ01 -0.6029242 0.0153385 -39.308 < 2e-16 ***
ORIGIN_SZCHSZ01 -0.7641380 0.0135100 -56.561 < 2e-16 ***
ORIGIN_SZCHSZ02 -0.8400736 0.0101951 -82.400 < 2e-16 ***
ORIGIN_SZCHSZ03 1.2753127 0.0072576 175.720 < 2e-16 ***
ORIGIN_SZCKSZ01 0.2470943 0.0067135 36.806 < 2e-16 ***
ORIGIN_SZCKSZ02 0.5793581 0.0070498 82.181 < 2e-16 ***
ORIGIN_SZCKSZ03 1.0795767 0.0060642 178.025 < 2e-16 ***
ORIGIN_SZCKSZ04 1.4947920 0.0063122 236.808 < 2e-16 ***
ORIGIN_SZCKSZ05 0.7457580 0.0074071 100.681 < 2e-16 ***
ORIGIN_SZCKSZ06 0.5760952 0.0094861 60.730 < 2e-16 ***
ORIGIN_SZCLSZ01 -0.9061335 0.0098617 -91.884 < 2e-16 ***
ORIGIN_SZCLSZ02 -1.7609479 0.0156124 -112.791 < 2e-16 ***
ORIGIN_SZCLSZ03 -1.0081325 0.0095171 -105.929 < 2e-16 ***
ORIGIN_SZCLSZ04 0.6181200 0.0057953 106.659 < 2e-16 ***
ORIGIN_SZCLSZ05 -2.0462335 0.0168934 -121.127 < 2e-16 ***
ORIGIN_SZCLSZ06 0.7902389 0.0055680 141.924 < 2e-16 ***
ORIGIN_SZCLSZ07 -0.5472929 0.0071001 -77.082 < 2e-16 ***
ORIGIN_SZCLSZ08 -0.2197650 0.0077460 -28.372 < 2e-16 ***
ORIGIN_SZCLSZ09 -1.8175782 0.0195989 -92.739 < 2e-16 ***
ORIGIN_SZDTSZ02 -3.7618796 0.0872098 -43.136 < 2e-16 ***
ORIGIN_SZDTSZ03 -3.4514766 0.0840812 -41.049 < 2e-16 ***
ORIGIN_SZDTSZ13 -3.0627578 0.0352485 -86.891 < 2e-16 ***
ORIGIN_SZGLSZ01 -1.8055929 0.0111938 -161.303 < 2e-16 ***
ORIGIN_SZGLSZ02 -0.1588829 0.0061413 -25.871 < 2e-16 ***
ORIGIN_SZGLSZ03 -0.2508524 0.0064276 -39.027 < 2e-16 ***
ORIGIN_SZGLSZ04 0.8819358 0.0051993 169.627 < 2e-16 ***
ORIGIN_SZGLSZ05 0.6062778 0.0053735 112.828 < 2e-16 ***
ORIGIN_SZHGSZ01 0.3841503 0.0056776 67.660 < 2e-16 ***
ORIGIN_SZHGSZ02 0.3962330 0.0057579 68.815 < 2e-16 ***
ORIGIN_SZHGSZ03 0.2159531 0.0061671 35.017 < 2e-16 ***
ORIGIN_SZHGSZ04 0.7831941 0.0052216 149.992 < 2e-16 ***
ORIGIN_SZHGSZ05 1.1741558 0.0051799 226.677 < 2e-16 ***
ORIGIN_SZHGSZ06 -0.1891403 0.0065556 -28.852 < 2e-16 ***
ORIGIN_SZHGSZ07 0.3105421 0.0057186 54.304 < 2e-16 ***
ORIGIN_SZHGSZ08 -0.0766364 0.0063474 -12.074 < 2e-16 ***
ORIGIN_SZHGSZ09 -1.2211107 0.0101434 -120.384 < 2e-16 ***
ORIGIN_SZHGSZ10 -3.4844709 0.0504793 -69.028 < 2e-16 ***
ORIGIN_SZJESZ01 0.4916496 0.0063444 77.493 < 2e-16 ***
ORIGIN_SZJESZ02 0.1343893 0.0063762 21.077 < 2e-16 ***
ORIGIN_SZJESZ03 -0.2761723 0.0068085 -40.563 < 2e-16 ***
ORIGIN_SZJESZ04 -1.5932744 0.0121402 -131.240 < 2e-16 ***
ORIGIN_SZJESZ05 -2.3041311 0.0160245 -143.788 < 2e-16 ***
ORIGIN_SZJESZ06 0.2811076 0.0062495 44.981 < 2e-16 ***
ORIGIN_SZJESZ07 -1.9413956 0.0136276 -142.461 < 2e-16 ***
ORIGIN_SZJESZ08 -1.3315645 0.0143168 -93.007 < 2e-16 ***
ORIGIN_SZJESZ09 0.4418314 0.0069208 63.841 < 2e-16 ***
ORIGIN_SZJESZ10 -1.5551555 0.0236523 -65.751 < 2e-16 ***
ORIGIN_SZJESZ11 -1.8888230 0.0224630 -84.086 < 2e-16 ***
ORIGIN_SZJWSZ01 0.2564586 0.0084699 30.279 < 2e-16 ***
ORIGIN_SZJWSZ02 0.6899398 0.0061751 111.729 < 2e-16 ***
ORIGIN_SZJWSZ03 1.4761229 0.0057392 257.198 < 2e-16 ***
ORIGIN_SZJWSZ04 0.5701272 0.0065749 86.713 < 2e-16 ***
ORIGIN_SZJWSZ05 -2.1253657 0.0150769 -140.968 < 2e-16 ***
ORIGIN_SZJWSZ06 -1.5307265 0.0131906 -116.047 < 2e-16 ***
ORIGIN_SZJWSZ07 -2.8801618 0.0360772 -79.833 < 2e-16 ***
ORIGIN_SZJWSZ08 1.4428820 0.0059638 241.938 < 2e-16 ***
ORIGIN_SZJWSZ09 1.8968475 0.0055649 340.860 < 2e-16 ***
ORIGIN_SZKLSZ01 0.1116580 0.0059844 18.658 < 2e-16 ***
ORIGIN_SZKLSZ02 -0.9618787 0.0077344 -124.364 < 2e-16 ***
ORIGIN_SZKLSZ03 -0.7070626 0.0070275 -100.613 < 2e-16 ***
ORIGIN_SZKLSZ04 -2.2742765 0.0139991 -162.459 < 2e-16 ***
ORIGIN_SZKLSZ05 -1.1907262 0.0123719 -96.244 < 2e-16 ***
ORIGIN_SZKLSZ06 -5.9774897 0.1857994 -32.172 < 2e-16 ***
ORIGIN_SZKLSZ07 -1.4258369 0.0103083 -138.320 < 2e-16 ***
ORIGIN_SZKLSZ08 -1.7625888 0.0116107 -151.808 < 2e-16 ***
ORIGIN_SZLKSZ01 -2.0541388 0.0448216 -45.829 < 2e-16 ***
ORIGIN_SZMDSZ01 -0.8571117 0.0321054 -26.697 < 2e-16 ***
ORIGIN_SZMDSZ02 -0.6034597 0.0120724 -49.987 < 2e-16 ***
ORIGIN_SZMDSZ03 -2.1681163 0.0201078 -107.825 < 2e-16 ***
ORIGIN_SZMPSZ01 -0.9331562 0.0096218 -96.984 < 2e-16 ***
ORIGIN_SZMPSZ02 -1.0268229 0.0081379 -126.178 < 2e-16 ***
ORIGIN_SZMPSZ03 0.0054001 0.0066875 0.807 0.419385
ORIGIN_SZMUSZ02 -3.6269863 0.1105492 -32.809 < 2e-16 ***
ORIGIN_SZNTSZ01 -3.0593717 0.0399843 -76.514 < 2e-16 ***
ORIGIN_SZNTSZ02 -3.3331415 0.0251754 -132.397 < 2e-16 ***
ORIGIN_SZNTSZ03 -0.8351522 0.0090372 -92.413 < 2e-16 ***
ORIGIN_SZNTSZ05 -4.2082472 0.0583343 -72.140 < 2e-16 ***
ORIGIN_SZNTSZ06 -3.8549296 0.0593793 -64.920 < 2e-16 ***
ORIGIN_SZNVSZ01 0.2789069 0.0056024 49.784 < 2e-16 ***
ORIGIN_SZNVSZ02 -0.6036857 0.0077126 -78.273 < 2e-16 ***
ORIGIN_SZNVSZ03 -1.0072683 0.0092678 -108.685 < 2e-16 ***
ORIGIN_SZNVSZ04 -0.8723996 0.0101399 -86.037 < 2e-16 ***
ORIGIN_SZNVSZ05 -2.1552928 0.0183064 -117.734 < 2e-16 ***
ORIGIN_SZPGSZ01 0.0520607 0.0157846 3.298 0.000973 ***
ORIGIN_SZPGSZ02 -0.3481687 0.0089328 -38.976 < 2e-16 ***
ORIGIN_SZPGSZ03 0.9095292 0.0058835 154.590 < 2e-16 ***
ORIGIN_SZPGSZ04 1.3653717 0.0054727 249.489 < 2e-16 ***
ORIGIN_SZPGSZ05 0.3762720 0.0073841 50.957 < 2e-16 ***
ORIGIN_SZPLSZ01 -0.9142754 0.0136552 -66.954 < 2e-16 ***
ORIGIN_SZPLSZ02 -1.0987582 0.0175891 -62.468 < 2e-16 ***
ORIGIN_SZPLSZ03 -2.3427113 0.0474176 -49.406 < 2e-16 ***
ORIGIN_SZPLSZ04 -2.9140779 0.0374458 -77.821 < 2e-16 ***
ORIGIN_SZPLSZ05 -2.2381965 0.0261572 -85.567 < 2e-16 ***
ORIGIN_SZPNSZ01 0.9659006 0.0075177 128.484 < 2e-16 ***
ORIGIN_SZPNSZ02 -0.0158348 0.0143869 -1.101 0.271053
ORIGIN_SZPNSZ03 -2.1837321 0.0224396 -97.316 < 2e-16 ***
ORIGIN_SZPNSZ04 -3.2481509 0.0370762 -87.608 < 2e-16 ***
ORIGIN_SZPNSZ05 -2.0450679 0.0328165 -62.318 < 2e-16 ***
ORIGIN_SZPRSZ01 -0.6701245 0.0141567 -47.336 < 2e-16 ***
ORIGIN_SZPRSZ02 0.7931907 0.0058079 136.570 < 2e-16 ***
ORIGIN_SZPRSZ03 0.4249094 0.0058610 72.498 < 2e-16 ***
ORIGIN_SZPRSZ04 -0.8529967 0.0090997 -93.739 < 2e-16 ***
ORIGIN_SZPRSZ05 0.7865479 0.0055282 142.278 < 2e-16 ***
ORIGIN_SZPRSZ06 -1.3303664 0.0134512 -98.903 < 2e-16 ***
ORIGIN_SZPRSZ07 -3.0458370 0.0181514 -167.802 < 2e-16 ***
ORIGIN_SZPRSZ08 -0.5342399 0.0075966 -70.327 < 2e-16 ***
ORIGIN_SZQTSZ01 -0.2548930 0.0086485 -29.473 < 2e-16 ***
ORIGIN_SZQTSZ02 -0.8662439 0.0076549 -113.162 < 2e-16 ***
ORIGIN_SZQTSZ03 -0.0890168 0.0072455 -12.286 < 2e-16 ***
ORIGIN_SZQTSZ04 -1.4634370 0.0089384 -163.724 < 2e-16 ***
ORIGIN_SZQTSZ05 -0.6535669 0.0077612 -84.210 < 2e-16 ***
ORIGIN_SZQTSZ06 -0.8275765 0.0081835 -101.128 < 2e-16 ***
ORIGIN_SZQTSZ07 -1.5369800 0.0112808 -136.248 < 2e-16 ***
ORIGIN_SZQTSZ08 -0.4437979 0.0075302 -58.936 < 2e-16 ***
ORIGIN_SZQTSZ09 -0.8184934 0.0083589 -97.918 < 2e-16 ***
ORIGIN_SZQTSZ10 -0.6906597 0.0080980 -85.288 < 2e-16 ***
ORIGIN_SZQTSZ11 -2.3251162 0.0154191 -150.795 < 2e-16 ***
ORIGIN_SZQTSZ12 -3.0442790 0.0208985 -145.670 < 2e-16 ***
ORIGIN_SZQTSZ13 -0.7241013 0.0093441 -77.493 < 2e-16 ***
ORIGIN_SZQTSZ14 -1.8225351 0.0138207 -131.870 < 2e-16 ***
ORIGIN_SZQTSZ15 -0.8720806 0.0138589 -62.926 < 2e-16 ***
ORIGIN_SZRCSZ01 -1.8063415 0.0144295 -125.184 < 2e-16 ***
ORIGIN_SZRCSZ06 -0.5370905 0.0101573 -52.877 < 2e-16 ***
ORIGIN_SZRVSZ01 -2.7426167 0.0341386 -80.338 < 2e-16 ***
ORIGIN_SZRVSZ02 -3.0827269 0.0302299 -101.976 < 2e-16 ***
ORIGIN_SZRVSZ03 -2.9133853 0.0262543 -110.968 < 2e-16 ***
ORIGIN_SZRVSZ04 -3.4220022 0.0582209 -58.776 < 2e-16 ***
ORIGIN_SZRVSZ05 -2.6206257 0.0197470 -132.710 < 2e-16 ***
ORIGIN_SZSBSZ01 0.1010337 0.0085117 11.870 < 2e-16 ***
ORIGIN_SZSBSZ02 -0.8810456 0.0098244 -89.680 < 2e-16 ***
ORIGIN_SZSBSZ03 0.8303668 0.0063009 131.785 < 2e-16 ***
ORIGIN_SZSBSZ04 0.3489128 0.0071456 48.829 < 2e-16 ***
ORIGIN_SZSBSZ05 -0.3182914 0.0085560 -37.201 < 2e-16 ***
ORIGIN_SZSBSZ06 -0.9074308 0.0200035 -45.364 < 2e-16 ***
ORIGIN_SZSBSZ07 -0.2217124 0.0167188 -13.261 < 2e-16 ***
ORIGIN_SZSBSZ08 -1.3007367 0.0178771 -72.760 < 2e-16 ***
ORIGIN_SZSBSZ09 -0.9813703 0.0107885 -90.965 < 2e-16 ***
ORIGIN_SZSESZ02 1.1283424 0.0054209 208.146 < 2e-16 ***
ORIGIN_SZSESZ03 1.2389996 0.0051926 238.610 < 2e-16 ***
ORIGIN_SZSESZ04 0.7535119 0.0060371 124.814 < 2e-16 ***
ORIGIN_SZSESZ05 -0.2347978 0.0071482 -32.847 < 2e-16 ***
ORIGIN_SZSESZ06 0.9520620 0.0057572 165.368 < 2e-16 ***
ORIGIN_SZSESZ07 -2.4296685 0.0231677 -104.873 < 2e-16 ***
ORIGIN_SZSGSZ01 -0.6995899 0.0099969 -69.980 < 2e-16 ***
ORIGIN_SZSGSZ02 -1.2602157 0.0111471 -113.053 < 2e-16 ***
ORIGIN_SZSGSZ03 0.0725860 0.0061970 11.713 < 2e-16 ***
ORIGIN_SZSGSZ04 0.2738315 0.0057524 47.603 < 2e-16 ***
ORIGIN_SZSGSZ05 -2.0207710 0.0119838 -168.625 < 2e-16 ***
ORIGIN_SZSGSZ06 0.4885608 0.0054646 89.404 < 2e-16 ***
ORIGIN_SZSGSZ07 -0.8892155 0.0075074 -118.445 < 2e-16 ***
ORIGIN_SZSKSZ01 -0.3682754 0.0108025 -34.092 < 2e-16 ***
ORIGIN_SZSKSZ02 1.1826086 0.0071388 165.659 < 2e-16 ***
ORIGIN_SZSKSZ03 -0.3230177 0.0101683 -31.767 < 2e-16 ***
ORIGIN_SZSKSZ04 -1.8504236 0.0362400 -51.060 < 2e-16 ***
ORIGIN_SZSKSZ05 -0.2759035 0.0185157 -14.901 < 2e-16 ***
ORIGIN_SZSLSZ01 -2.2757902 0.0348766 -65.253 < 2e-16 ***
ORIGIN_SZSLSZ04 -0.0899820 0.0090356 -9.959 < 2e-16 ***
ORIGIN_SZSRSZ01 -2.1460151 0.0187871 -114.228 < 2e-16 ***
ORIGIN_SZTHSZ01 -2.6851549 0.0571841 -46.956 < 2e-16 ***
ORIGIN_SZTHSZ03 -1.0121495 0.0275551 -36.732 < 2e-16 ***
ORIGIN_SZTHSZ04 -2.6129645 0.0345167 -75.701 < 2e-16 ***
ORIGIN_SZTHSZ06 -1.7229100 0.0208134 -82.779 < 2e-16 ***
ORIGIN_SZTMSZ01 -0.2254986 0.0070312 -32.071 < 2e-16 ***
ORIGIN_SZTMSZ02 1.7271575 0.0049219 350.914 < 2e-16 ***
ORIGIN_SZTMSZ03 0.9891319 0.0052266 189.250 < 2e-16 ***
ORIGIN_SZTMSZ04 0.2018090 0.0062114 32.490 < 2e-16 ***
ORIGIN_SZTMSZ05 -1.1882870 0.0125842 -94.427 < 2e-16 ***
ORIGIN_SZTNSZ01 -1.6122620 0.0141911 -113.611 < 2e-16 ***
ORIGIN_SZTNSZ02 -1.5630967 0.0112227 -139.280 < 2e-16 ***
ORIGIN_SZTNSZ03 -2.0739538 0.0149298 -138.914 < 2e-16 ***
ORIGIN_SZTNSZ04 -0.2816960 0.0085295 -33.026 < 2e-16 ***
ORIGIN_SZTPSZ01 -0.7822239 0.0077901 -100.412 < 2e-16 ***
ORIGIN_SZTPSZ02 0.5735478 0.0053042 108.131 < 2e-16 ***
ORIGIN_SZTPSZ03 -0.8748650 0.0074202 -117.903 < 2e-16 ***
ORIGIN_SZTPSZ04 -0.8537831 0.0069792 -122.332 < 2e-16 ***
ORIGIN_SZTPSZ05 -0.5581114 0.0077012 -72.471 < 2e-16 ***
ORIGIN_SZTPSZ06 0.0262001 0.0075241 3.482 0.000497 ***
ORIGIN_SZTPSZ07 -0.5969952 0.0074272 -80.380 < 2e-16 ***
ORIGIN_SZTPSZ08 -1.0537959 0.0111297 -94.683 < 2e-16 ***
ORIGIN_SZTPSZ09 -0.9588508 0.0081314 -117.920 < 2e-16 ***
ORIGIN_SZTPSZ10 -1.1177249 0.0089403 -125.021 < 2e-16 ***
ORIGIN_SZTPSZ11 -0.2799677 0.0067135 -41.702 < 2e-16 ***
ORIGIN_SZTPSZ12 -0.8898871 0.0080215 -110.938 < 2e-16 ***
ORIGIN_SZTSSZ01 -2.6146463 0.0521606 -50.127 < 2e-16 ***
ORIGIN_SZTSSZ02 0.1682588 0.0119965 14.026 < 2e-16 ***
ORIGIN_SZTSSZ03 0.2587653 0.0123809 20.900 < 2e-16 ***
ORIGIN_SZTSSZ04 -0.5473825 0.0135215 -40.482 < 2e-16 ***
ORIGIN_SZTSSZ05 -0.9967379 0.0206068 -48.369 < 2e-16 ***
ORIGIN_SZTSSZ06 0.4933147 0.0229597 21.486 < 2e-16 ***
ORIGIN_SZWCSZ01 1.2524706 0.0111133 112.700 < 2e-16 ***
ORIGIN_SZWCSZ02 -2.8544820 0.0347805 -82.071 < 2e-16 ***
ORIGIN_SZWCSZ03 -5.1277334 0.1475585 -34.751 < 2e-16 ***
ORIGIN_SZWDSZ01 1.4725308 0.0056496 260.645 < 2e-16 ***
ORIGIN_SZWDSZ02 0.1571680 0.0064909 24.214 < 2e-16 ***
ORIGIN_SZWDSZ03 1.2584097 0.0061471 204.717 < 2e-16 ***
ORIGIN_SZWDSZ04 0.8578765 0.0069277 123.833 < 2e-16 ***
ORIGIN_SZWDSZ05 0.1702728 0.0069687 24.434 < 2e-16 ***
ORIGIN_SZWDSZ06 0.1736910 0.0069507 24.989 < 2e-16 ***
ORIGIN_SZWDSZ07 -1.5610176 0.0100803 -154.859 < 2e-16 ***
ORIGIN_SZWDSZ08 -0.9490906 0.0102047 -93.005 < 2e-16 ***
ORIGIN_SZWDSZ09 1.2107011 0.0062294 194.354 < 2e-16 ***
ORIGIN_SZYSSZ01 -0.3324158 0.0074537 -44.598 < 2e-16 ***
ORIGIN_SZYSSZ02 0.8177113 0.0066108 123.693 < 2e-16 ***
ORIGIN_SZYSSZ03 1.6751777 0.0058470 286.503 < 2e-16 ***
ORIGIN_SZYSSZ04 0.8130044 0.0059025 137.738 < 2e-16 ***
ORIGIN_SZYSSZ05 0.3678420 0.0072431 50.785 < 2e-16 ***
ORIGIN_SZYSSZ06 -0.6024384 0.0126722 -47.540 < 2e-16 ***
ORIGIN_SZYSSZ07 -0.7631918 0.0158478 -48.157 < 2e-16 ***
ORIGIN_SZYSSZ08 0.2141930 0.0076154 28.126 < 2e-16 ***
ORIGIN_SZYSSZ09 1.0809368 0.0057973 186.457 < 2e-16 ***
DESTIN_SZAMSZ02 0.0761304 0.0051207 14.867 < 2e-16 ***
DESTIN_SZAMSZ03 0.0143394 0.0050755 2.825 0.004724 **
DESTIN_SZAMSZ04 -1.2516780 0.0074947 -167.008 < 2e-16 ***
DESTIN_SZAMSZ05 -1.2312375 0.0076598 -160.741 < 2e-16 ***
DESTIN_SZAMSZ06 -1.0333412 0.0075283 -137.261 < 2e-16 ***
DESTIN_SZAMSZ07 -1.5338249 0.0110036 -139.392 < 2e-16 ***
DESTIN_SZAMSZ08 -0.3751665 0.0075358 -49.784 < 2e-16 ***
DESTIN_SZAMSZ09 -1.1633493 0.0077556 -150.001 < 2e-16 ***
DESTIN_SZAMSZ10 0.1017717 0.0053151 19.148 < 2e-16 ***
DESTIN_SZAMSZ11 -0.8840362 0.0097007 -91.131 < 2e-16 ***
DESTIN_SZAMSZ12 0.1628123 0.0055220 29.484 < 2e-16 ***
DESTIN_SZBDSZ01 1.0040794 0.0047922 209.523 < 2e-16 ***
DESTIN_SZBDSZ02 -0.2478149 0.0063085 -39.283 < 2e-16 ***
DESTIN_SZBDSZ03 0.1016088 0.0057420 17.696 < 2e-16 ***
DESTIN_SZBDSZ04 1.1082928 0.0047747 232.116 < 2e-16 ***
DESTIN_SZBDSZ05 0.8737933 0.0050593 172.712 < 2e-16 ***
DESTIN_SZBDSZ06 0.2897032 0.0058244 49.740 < 2e-16 ***
DESTIN_SZBDSZ07 -0.9026193 0.0113656 -79.416 < 2e-16 ***
DESTIN_SZBDSZ08 -1.7063577 0.0131234 -130.024 < 2e-16 ***
DESTIN_SZBKSZ01 -1.3892839 0.0083307 -166.767 < 2e-16 ***
DESTIN_SZBKSZ02 -0.6661120 0.0073464 -90.672 < 2e-16 ***
DESTIN_SZBKSZ03 -0.9536826 0.0073196 -130.292 < 2e-16 ***
DESTIN_SZBKSZ04 -0.6655610 0.0065868 -101.044 < 2e-16 ***
DESTIN_SZBKSZ05 -0.9053119 0.0079264 -114.215 < 2e-16 ***
DESTIN_SZBKSZ06 -1.2622159 0.0075079 -168.119 < 2e-16 ***
DESTIN_SZBKSZ07 -0.0423370 0.0056686 -7.469 8.10e-14 ***
DESTIN_SZBKSZ08 -1.3811240 0.0084985 -162.515 < 2e-16 ***
DESTIN_SZBKSZ09 -0.0797012 0.0061428 -12.975 < 2e-16 ***
DESTIN_SZBLSZ01 -0.8859670 0.0088108 -100.555 < 2e-16 ***
DESTIN_SZBLSZ02 0.1362723 0.0082167 16.585 < 2e-16 ***
DESTIN_SZBLSZ03 1.2037396 0.0093508 128.732 < 2e-16 ***
DESTIN_SZBLSZ04 -0.9316219 0.0178080 -52.315 < 2e-16 ***
DESTIN_SZBMSZ01 0.7188470 0.0061160 117.536 < 2e-16 ***
DESTIN_SZBMSZ02 -0.0597895 0.0061206 -9.769 < 2e-16 ***
DESTIN_SZBMSZ03 -0.2427075 0.0069937 -34.704 < 2e-16 ***
DESTIN_SZBMSZ04 -0.0622494 0.0065569 -9.494 < 2e-16 ***
DESTIN_SZBMSZ05 -0.2857019 0.0086450 -33.048 < 2e-16 ***
DESTIN_SZBMSZ06 -1.3486558 0.0158904 -84.872 < 2e-16 ***
DESTIN_SZBMSZ07 0.4549687 0.0058315 78.020 < 2e-16 ***
DESTIN_SZBMSZ08 -0.8730268 0.0077814 -112.195 < 2e-16 ***
DESTIN_SZBMSZ09 -2.0319890 0.0163038 -124.633 < 2e-16 ***
DESTIN_SZBMSZ10 -1.4319101 0.0102616 -139.541 < 2e-16 ***
DESTIN_SZBMSZ11 -1.2429176 0.0092250 -134.733 < 2e-16 ***
DESTIN_SZBMSZ12 -0.8526549 0.0096009 -88.810 < 2e-16 ***
DESTIN_SZBMSZ13 0.1399907 0.0066885 20.930 < 2e-16 ***
DESTIN_SZBMSZ14 -1.0103155 0.0091377 -110.566 < 2e-16 ***
DESTIN_SZBMSZ15 -0.6819769 0.0086179 -79.135 < 2e-16 ***
DESTIN_SZBMSZ16 -1.4468308 0.0134051 -107.931 < 2e-16 ***
DESTIN_SZBMSZ17 -1.5312175 0.0186843 -81.952 < 2e-16 ***
DESTIN_SZBPSZ01 -1.1726725 0.0073257 -160.077 < 2e-16 ***
DESTIN_SZBPSZ02 -2.1072012 0.0103320 -203.949 < 2e-16 ***
DESTIN_SZBPSZ03 -1.6944911 0.0098520 -171.995 < 2e-16 ***
DESTIN_SZBPSZ04 -0.7664610 0.0074458 -102.939 < 2e-16 ***
DESTIN_SZBPSZ05 0.1358370 0.0056258 24.145 < 2e-16 ***
DESTIN_SZBPSZ06 -1.2425471 0.0096942 -128.175 < 2e-16 ***
DESTIN_SZBPSZ07 -0.1666192 0.0094969 -17.545 < 2e-16 ***
DESTIN_SZBSSZ01 0.3857894 0.0057261 67.374 < 2e-16 ***
DESTIN_SZBSSZ02 -0.5293265 0.0064886 -81.578 < 2e-16 ***
DESTIN_SZBSSZ03 0.3909966 0.0048540 80.551 < 2e-16 ***
DESTIN_SZBTSZ01 0.7114965 0.0054528 130.482 < 2e-16 ***
DESTIN_SZBTSZ02 -0.0487084 0.0082474 -5.906 3.51e-09 ***
DESTIN_SZBTSZ03 0.5539032 0.0064423 85.979 < 2e-16 ***
DESTIN_SZBTSZ04 -0.7120734 0.0128676 -55.339 < 2e-16 ***
DESTIN_SZBTSZ05 0.2176097 0.0086791 25.073 < 2e-16 ***
DESTIN_SZBTSZ06 -0.2167084 0.0084925 -25.518 < 2e-16 ***
DESTIN_SZBTSZ07 -1.4045618 0.0124363 -112.940 < 2e-16 ***
DESTIN_SZBTSZ08 -0.8213918 0.0120793 -68.000 < 2e-16 ***
DESTIN_SZCBSZ01 -5.7340877 0.3333916 -17.199 < 2e-16 ***
DESTIN_SZCCSZ01 -0.0304192 0.0095920 -3.171 0.001518 **
DESTIN_SZCHSZ01 -0.2598507 0.0115311 -22.535 < 2e-16 ***
DESTIN_SZCHSZ02 0.3497750 0.0068334 51.186 < 2e-16 ***
DESTIN_SZCHSZ03 2.4550172 0.0050883 482.481 < 2e-16 ***
DESTIN_SZCKSZ01 -0.4691744 0.0063130 -74.319 < 2e-16 ***
DESTIN_SZCKSZ02 -0.9557084 0.0069331 -137.847 < 2e-16 ***
DESTIN_SZCKSZ03 0.0442112 0.0057117 7.740 9.91e-15 ***
DESTIN_SZCKSZ04 -0.8592063 0.0081238 -105.764 < 2e-16 ***
DESTIN_SZCKSZ05 -1.1745333 0.0087305 -134.532 < 2e-16 ***
DESTIN_SZCKSZ06 -0.4982877 0.0085514 -58.269 < 2e-16 ***
DESTIN_SZCLSZ01 0.2665065 0.0059712 44.632 < 2e-16 ***
DESTIN_SZCLSZ02 -1.9758876 0.0150823 -131.007 < 2e-16 ***
DESTIN_SZCLSZ03 -0.9051310 0.0091479 -98.944 < 2e-16 ***
DESTIN_SZCLSZ04 -0.0828732 0.0061559 -13.462 < 2e-16 ***
DESTIN_SZCLSZ05 -1.1414780 0.0100760 -113.287 < 2e-16 ***
DESTIN_SZCLSZ06 0.3229402 0.0056269 57.392 < 2e-16 ***
DESTIN_SZCLSZ07 -0.4833612 0.0069777 -69.272 < 2e-16 ***
DESTIN_SZCLSZ08 -0.3219670 0.0075615 -42.580 < 2e-16 ***
DESTIN_SZCLSZ09 0.0564166 0.0080703 6.991 2.74e-12 ***
DESTIN_SZDTSZ02 -1.6384236 0.0374725 -43.723 < 2e-16 ***
DESTIN_SZDTSZ03 -0.4021571 0.0152716 -26.334 < 2e-16 ***
DESTIN_SZDTSZ13 -1.2799441 0.0177095 -72.274 < 2e-16 ***
DESTIN_SZGLSZ01 -0.0190303 0.0060665 -3.137 0.001707 **
DESTIN_SZGLSZ02 -0.0308469 0.0058724 -5.253 1.50e-07 ***
DESTIN_SZGLSZ03 0.6927638 0.0048456 142.969 < 2e-16 ***
DESTIN_SZGLSZ04 0.9325848 0.0049183 189.616 < 2e-16 ***
DESTIN_SZGLSZ05 0.8480056 0.0048801 173.768 < 2e-16 ***
DESTIN_SZHGSZ01 0.0652969 0.0047795 13.662 < 2e-16 ***
DESTIN_SZHGSZ02 -0.9498251 0.0066577 -142.667 < 2e-16 ***
DESTIN_SZHGSZ03 -1.4372499 0.0076387 -188.154 < 2e-16 ***
DESTIN_SZHGSZ04 -0.5236292 0.0055353 -94.599 < 2e-16 ***
DESTIN_SZHGSZ05 -0.5420295 0.0058099 -93.295 < 2e-16 ***
DESTIN_SZHGSZ06 -0.9054730 0.0067581 -133.983 < 2e-16 ***
DESTIN_SZHGSZ07 0.0215109 0.0054019 3.982 6.83e-05 ***
DESTIN_SZHGSZ08 -0.0490979 0.0059206 -8.293 < 2e-16 ***
DESTIN_SZHGSZ09 -0.0711560 0.0062875 -11.317 < 2e-16 ***
DESTIN_SZHGSZ10 -3.5807154 0.0290642 -123.200 < 2e-16 ***
DESTIN_SZJESZ01 -0.4023638 0.0065057 -61.848 < 2e-16 ***
DESTIN_SZJESZ02 -0.7654353 0.0067096 -114.081 < 2e-16 ***
DESTIN_SZJESZ03 -0.8778812 0.0071238 -123.232 < 2e-16 ***
DESTIN_SZJESZ04 -1.1998075 0.0088733 -135.215 < 2e-16 ***
DESTIN_SZJESZ05 -1.5623652 0.0116898 -133.652 < 2e-16 ***
DESTIN_SZJESZ06 0.2311474 0.0055595 41.577 < 2e-16 ***
DESTIN_SZJESZ07 -1.2753348 0.0094838 -134.475 < 2e-16 ***
DESTIN_SZJESZ08 -0.7654533 0.0099306 -77.081 < 2e-16 ***
DESTIN_SZJESZ09 0.1637628 0.0074164 22.081 < 2e-16 ***
DESTIN_SZJESZ10 0.7394958 0.0091249 81.041 < 2e-16 ***
DESTIN_SZJESZ11 0.5157364 0.0086546 59.591 < 2e-16 ***
DESTIN_SZJWSZ01 -1.0165204 0.0083025 -122.435 < 2e-16 ***
DESTIN_SZJWSZ02 -0.8530646 0.0067851 -125.727 < 2e-16 ***
DESTIN_SZJWSZ03 0.5176135 0.0056449 91.695 < 2e-16 ***
DESTIN_SZJWSZ04 0.3427105 0.0058499 58.584 < 2e-16 ***
DESTIN_SZJWSZ05 -1.1695940 0.0080069 -146.073 < 2e-16 ***
DESTIN_SZJWSZ06 -0.7466462 0.0070240 -106.299 < 2e-16 ***
DESTIN_SZJWSZ07 -3.0124535 0.0333481 -90.334 < 2e-16 ***
DESTIN_SZJWSZ08 -0.4253502 0.0066584 -63.881 < 2e-16 ***
DESTIN_SZJWSZ09 0.9428005 0.0053190 177.251 < 2e-16 ***
DESTIN_SZKLSZ01 -0.2965013 0.0066422 -44.639 < 2e-16 ***
DESTIN_SZKLSZ02 -0.4921137 0.0067689 -72.702 < 2e-16 ***
DESTIN_SZKLSZ03 -0.8489213 0.0078294 -108.427 < 2e-16 ***
DESTIN_SZKLSZ04 -1.2656342 0.0099918 -126.667 < 2e-16 ***
DESTIN_SZKLSZ05 -0.3570126 0.0096300 -37.073 < 2e-16 ***
DESTIN_SZKLSZ06 -2.4764906 0.0390868 -63.359 < 2e-16 ***
DESTIN_SZKLSZ07 -0.7316189 0.0080994 -90.330 < 2e-16 ***
DESTIN_SZKLSZ08 -0.1115398 0.0061168 -18.235 < 2e-16 ***
DESTIN_SZLKSZ01 -1.4940710 0.0271518 -55.027 < 2e-16 ***
DESTIN_SZMDSZ01 -1.6101440 0.0231238 -69.631 < 2e-16 ***
DESTIN_SZMDSZ02 -0.9339318 0.0126277 -73.959 < 2e-16 ***
DESTIN_SZMDSZ03 -3.4868547 0.0303657 -114.829 < 2e-16 ***
DESTIN_SZMPSZ01 -0.4518483 0.0089869 -50.279 < 2e-16 ***
DESTIN_SZMPSZ02 -0.5868264 0.0073193 -80.176 < 2e-16 ***
DESTIN_SZMPSZ03 0.4805365 0.0059041 81.391 < 2e-16 ***
DESTIN_SZMUSZ02 -1.3837581 0.0218713 -63.268 < 2e-16 ***
DESTIN_SZNTSZ01 -3.0694691 0.0533346 -57.551 < 2e-16 ***
DESTIN_SZNTSZ02 -1.4992973 0.0130358 -115.014 < 2e-16 ***
DESTIN_SZNTSZ03 -0.5221236 0.0089923 -58.064 < 2e-16 ***
DESTIN_SZNTSZ05 -1.9751162 0.0282369 -69.948 < 2e-16 ***
DESTIN_SZNTSZ06 -3.9959411 0.0511214 -78.166 < 2e-16 ***
DESTIN_SZNVSZ01 -0.1126966 0.0057077 -19.745 < 2e-16 ***
DESTIN_SZNVSZ02 -0.0259250 0.0064427 -4.024 5.72e-05 ***
DESTIN_SZNVSZ03 -0.0123214 0.0067692 -1.820 0.068725 .
DESTIN_SZNVSZ04 -1.3371298 0.0130261 -102.650 < 2e-16 ***
DESTIN_SZNVSZ05 -0.9686333 0.0101539 -95.395 < 2e-16 ***
DESTIN_SZPGSZ01 -1.1798309 0.0180543 -65.349 < 2e-16 ***
DESTIN_SZPGSZ02 -1.3289737 0.0085335 -155.736 < 2e-16 ***
DESTIN_SZPGSZ03 -0.1661373 0.0055166 -30.116 < 2e-16 ***
DESTIN_SZPGSZ04 -0.3046408 0.0058469 -52.103 < 2e-16 ***
DESTIN_SZPGSZ05 -1.5412612 0.0093261 -165.264 < 2e-16 ***
DESTIN_SZPLSZ01 -0.3439667 0.0083504 -41.192 < 2e-16 ***
DESTIN_SZPLSZ02 -1.7574919 0.0154244 -113.942 < 2e-16 ***
DESTIN_SZPLSZ03 -0.3455776 0.0112089 -30.831 < 2e-16 ***
DESTIN_SZPLSZ04 -2.0749385 0.0141153 -146.999 < 2e-16 ***
DESTIN_SZPLSZ05 -0.4855216 0.0134069 -36.214 < 2e-16 ***
DESTIN_SZPNSZ01 0.0117816 0.0083558 1.410 0.158543
DESTIN_SZPNSZ02 0.7389858 0.0089823 82.272 < 2e-16 ***
DESTIN_SZPNSZ03 -0.4708719 0.0098588 -47.761 < 2e-16 ***
DESTIN_SZPNSZ04 1.3156771 0.0111200 118.316 < 2e-16 ***
DESTIN_SZPNSZ05 0.9881886 0.0153169 64.516 < 2e-16 ***
DESTIN_SZPRSZ01 -1.0678999 0.0098295 -108.642 < 2e-16 ***
DESTIN_SZPRSZ02 0.0650279 0.0063927 10.172 < 2e-16 ***
DESTIN_SZPRSZ03 0.6348138 0.0050147 126.592 < 2e-16 ***
DESTIN_SZPRSZ04 -0.3640286 0.0097572 -37.309 < 2e-16 ***
DESTIN_SZPRSZ05 0.0380410 0.0062577 6.079 1.21e-09 ***
DESTIN_SZPRSZ06 0.3153712 0.0068742 45.877 < 2e-16 ***
DESTIN_SZPRSZ07 -1.6669973 0.0145573 -114.513 < 2e-16 ***
DESTIN_SZPRSZ08 -0.6170648 0.0078424 -78.683 < 2e-16 ***
DESTIN_SZQTSZ01 -0.5496582 0.0098285 -55.925 < 2e-16 ***
DESTIN_SZQTSZ02 -0.7318114 0.0086807 -84.303 < 2e-16 ***
DESTIN_SZQTSZ03 -0.5893064 0.0084789 -69.503 < 2e-16 ***
DESTIN_SZQTSZ04 -0.7103906 0.0085341 -83.242 < 2e-16 ***
DESTIN_SZQTSZ05 -0.4721472 0.0078164 -60.405 < 2e-16 ***
DESTIN_SZQTSZ06 -0.6591466 0.0080069 -82.322 < 2e-16 ***
DESTIN_SZQTSZ07 -0.9540454 0.0126807 -75.236 < 2e-16 ***
DESTIN_SZQTSZ08 0.4508867 0.0064870 69.507 < 2e-16 ***
DESTIN_SZQTSZ09 -0.4061810 0.0075485 -53.810 < 2e-16 ***
DESTIN_SZQTSZ10 0.1351889 0.0068202 19.822 < 2e-16 ***
DESTIN_SZQTSZ11 0.3181553 0.0067958 46.816 < 2e-16 ***
DESTIN_SZQTSZ12 -0.1055766 0.0095576 -11.046 < 2e-16 ***
DESTIN_SZQTSZ13 0.5199663 0.0071928 72.290 < 2e-16 ***
DESTIN_SZQTSZ14 0.6086332 0.0078537 77.496 < 2e-16 ***
DESTIN_SZQTSZ15 1.3906866 0.0092250 150.753 < 2e-16 ***
DESTIN_SZRCSZ01 -0.0862091 0.0085363 -10.099 < 2e-16 ***
DESTIN_SZRCSZ06 -1.0186282 0.0211113 -48.250 < 2e-16 ***
DESTIN_SZRVSZ01 -1.5294454 0.0179337 -85.283 < 2e-16 ***
DESTIN_SZRVSZ02 -2.3607754 0.0355628 -66.383 < 2e-16 ***
DESTIN_SZRVSZ03 -1.5266254 0.0156276 -97.688 < 2e-16 ***
DESTIN_SZRVSZ04 -1.0986565 0.0168695 -65.127 < 2e-16 ***
DESTIN_SZRVSZ05 -2.4004418 0.0320917 -74.799 < 2e-16 ***
DESTIN_SZSBSZ01 -1.4023966 0.0109496 -128.078 < 2e-16 ***
DESTIN_SZSBSZ02 -1.3899893 0.0090891 -152.929 < 2e-16 ***
DESTIN_SZSBSZ03 0.4509008 0.0059864 75.321 < 2e-16 ***
DESTIN_SZSBSZ04 0.1796309 0.0070142 25.610 < 2e-16 ***
DESTIN_SZSBSZ05 -1.3159699 0.0096485 -136.391 < 2e-16 ***
DESTIN_SZSBSZ06 -1.7705263 0.0253064 -69.964 < 2e-16 ***
DESTIN_SZSBSZ07 -0.7471529 0.0238628 -31.310 < 2e-16 ***
DESTIN_SZSBSZ08 0.7884520 0.0069638 113.221 < 2e-16 ***
DESTIN_SZSBSZ09 0.0131702 0.0066350 1.985 0.047150 *
DESTIN_SZSESZ02 -0.7247347 0.0060626 -119.541 < 2e-16 ***
DESTIN_SZSESZ03 0.1032728 0.0048330 21.368 < 2e-16 ***
DESTIN_SZSESZ04 -1.0992420 0.0068328 -160.878 < 2e-16 ***
DESTIN_SZSESZ05 -0.8374712 0.0058155 -144.006 < 2e-16 ***
DESTIN_SZSESZ06 -0.5531619 0.0074766 -73.985 < 2e-16 ***
DESTIN_SZSESZ07 -3.0328672 0.0246371 -123.101 < 2e-16 ***
DESTIN_SZSGSZ01 -0.1933777 0.0068235 -28.340 < 2e-16 ***
DESTIN_SZSGSZ02 -0.3000845 0.0060284 -49.779 < 2e-16 ***
DESTIN_SZSGSZ03 -0.4322879 0.0057308 -75.433 < 2e-16 ***
DESTIN_SZSGSZ04 -0.1214792 0.0056548 -21.482 < 2e-16 ***
DESTIN_SZSGSZ05 -2.0309074 0.0114993 -176.611 < 2e-16 ***
DESTIN_SZSGSZ06 0.6592095 0.0046364 142.182 < 2e-16 ***
DESTIN_SZSGSZ07 -0.4618538 0.0062027 -74.460 < 2e-16 ***
DESTIN_SZSISZ01 -0.5227257 0.0293399 -17.816 < 2e-16 ***
DESTIN_SZSKSZ01 -0.4797341 0.0091087 -52.668 < 2e-16 ***
DESTIN_SZSKSZ02 0.8477357 0.0067821 124.996 < 2e-16 ***
DESTIN_SZSKSZ03 -0.2477566 0.0074817 -33.115 < 2e-16 ***
DESTIN_SZSKSZ04 -1.3315992 0.0167055 -79.710 < 2e-16 ***
DESTIN_SZSKSZ05 -0.3519096 0.0131326 -26.797 < 2e-16 ***
DESTIN_SZSLSZ01 -0.8570431 0.0102100 -83.941 < 2e-16 ***
DESTIN_SZSLSZ04 -0.9949105 0.0088280 -112.699 < 2e-16 ***
DESTIN_SZSRSZ01 -1.0260696 0.0154393 -66.458 < 2e-16 ***
DESTIN_SZTHSZ01 -4.2040410 0.0404795 -103.856 < 2e-16 ***
DESTIN_SZTHSZ03 -2.4907000 0.0264056 -94.325 < 2e-16 ***
DESTIN_SZTHSZ04 -3.0701470 0.0244975 -125.325 < 2e-16 ***
DESTIN_SZTHSZ06 -2.5308161 0.0169699 -149.135 < 2e-16 ***
DESTIN_SZTMSZ01 -0.2354889 0.0067201 -35.042 < 2e-16 ***
DESTIN_SZTMSZ02 1.7379292 0.0044573 389.906 < 2e-16 ***
DESTIN_SZTMSZ03 0.9112458 0.0048718 187.043 < 2e-16 ***
DESTIN_SZTMSZ04 1.0731075 0.0048626 220.685 < 2e-16 ***
DESTIN_SZTMSZ05 0.6398583 0.0067321 95.046 < 2e-16 ***
DESTIN_SZTNSZ01 -0.3500456 0.0083835 -41.754 < 2e-16 ***
DESTIN_SZTNSZ02 -1.0573515 0.0112412 -94.060 < 2e-16 ***
DESTIN_SZTNSZ03 -1.4069979 0.0132733 -106.002 < 2e-16 ***
DESTIN_SZTNSZ04 -0.3616604 0.0085207 -42.445 < 2e-16 ***
DESTIN_SZTPSZ01 -0.5919243 0.0071153 -83.190 < 2e-16 ***
DESTIN_SZTPSZ02 0.7083350 0.0046540 152.198 < 2e-16 ***
DESTIN_SZTPSZ03 -0.5746433 0.0069625 -82.534 < 2e-16 ***
DESTIN_SZTPSZ04 -1.5821259 0.0084517 -187.196 < 2e-16 ***
DESTIN_SZTPSZ05 -1.1796256 0.0073039 -161.505 < 2e-16 ***
DESTIN_SZTPSZ06 -0.3968272 0.0077295 -51.339 < 2e-16 ***
DESTIN_SZTPSZ07 -2.1796617 0.0135199 -161.219 < 2e-16 ***
DESTIN_SZTPSZ08 -1.2568483 0.0107267 -117.170 < 2e-16 ***
DESTIN_SZTPSZ09 -0.2446623 0.0080840 -30.265 < 2e-16 ***
DESTIN_SZTPSZ10 -1.2542191 0.0102049 -122.904 < 2e-16 ***
DESTIN_SZTPSZ11 -0.0886883 0.0062888 -14.102 < 2e-16 ***
DESTIN_SZTPSZ12 -0.7211823 0.0075086 -96.048 < 2e-16 ***
DESTIN_SZTSSZ01 -1.6271921 0.0238498 -68.227 < 2e-16 ***
DESTIN_SZTSSZ02 -0.3340439 0.0169137 -19.750 < 2e-16 ***
DESTIN_SZTSSZ03 0.3924580 0.0111060 35.338 < 2e-16 ***
DESTIN_SZTSSZ04 0.4169932 0.0114926 36.283 < 2e-16 ***
DESTIN_SZTSSZ05 1.3206287 0.0120381 109.704 < 2e-16 ***
DESTIN_SZTSSZ06 2.4023725 0.0192840 124.579 < 2e-16 ***
DESTIN_SZWCSZ01 2.0697378 0.0061379 337.206 < 2e-16 ***
DESTIN_SZWCSZ02 -2.0934025 0.0134782 -155.318 < 2e-16 ***
DESTIN_SZWCSZ03 -3.0670149 0.0349748 -87.692 < 2e-16 ***
DESTIN_SZWDSZ01 1.0113215 0.0051461 196.522 < 2e-16 ***
DESTIN_SZWDSZ02 -1.3383793 0.0076482 -174.993 < 2e-16 ***
DESTIN_SZWDSZ03 0.3394361 0.0060396 56.202 < 2e-16 ***
DESTIN_SZWDSZ04 -0.8324928 0.0086019 -96.780 < 2e-16 ***
DESTIN_SZWDSZ05 -0.8279090 0.0083251 -99.447 < 2e-16 ***
DESTIN_SZWDSZ06 -0.2252899 0.0061074 -36.888 < 2e-16 ***
DESTIN_SZWDSZ07 -1.3638599 0.0077990 -174.877 < 2e-16 ***
DESTIN_SZWDSZ08 -0.4350176 0.0077566 -56.083 < 2e-16 ***
DESTIN_SZWDSZ09 0.5461048 0.0060745 89.901 < 2e-16 ***
DESTIN_SZYSSZ01 0.0243093 0.0053476 4.546 5.47e-06 ***
DESTIN_SZYSSZ02 -0.3398962 0.0065947 -51.540 < 2e-16 ***
DESTIN_SZYSSZ03 -0.3694187 0.0074032 -49.900 < 2e-16 ***
DESTIN_SZYSSZ04 -0.5222848 0.0067396 -77.495 < 2e-16 ***
DESTIN_SZYSSZ05 -1.5460539 0.0124899 -123.784 < 2e-16 ***
DESTIN_SZYSSZ06 -1.5556892 0.0127640 -121.881 < 2e-16 ***
DESTIN_SZYSSZ07 -0.8673403 0.0167723 -51.713 < 2e-16 ***
DESTIN_SZYSSZ08 0.5389364 0.0052540 102.577 < 2e-16 ***
DESTIN_SZYSSZ09 0.1199483 0.0055235 21.716 < 2e-16 ***
log(dist) -1.8906989 0.0005319 -3554.786 < 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: 36117615 on 14273 degrees of freedom
Residual deviance: 8091747 on 13715 degrees of freedom
AIC: 8177420
Number of Fisher Scoring iterations: 7Examine how the constraints hold for destinations this time.
CalcRSquared(dbcSIM$data$TRIPS, dbcSIM$fitted.values)[1] 0.6883675Notice that there is a relatively greater improvement in the R^2 value.
Model comparison
Another useful model performance measure for continuous dependent variable is Root Mean Squared Error, which can be done using the compare_performance() of the performance package.
First, create a list called model_list using the code chunk below.
model_list <- list(unconstrained=uncSIM,
originConstrained=orcSIM,
destinationConstrained=decSIM,
doublyConstrained=dbcSIM)Next, compute the RMSE of all the models in model_list using the code chunk below.
compare_performance(model_list, metrics = "RMSE")# Comparison of Model Performance Indices
Name | Model | RMSE
-----------------------------------------
unconstrained | glm | 2429.978
originConstrained | glm | 2057.579
destinationConstrained | glm | 1891.724
doublyConstrained | glm | 1487.111The print above reveals that doubly constrained SIM is the best model among all the four SIMs because it has the smallest RMSE value of 1487.111.
Visualising Fitted Values
Next, to visualise the observed values and the fitted values, first extract the fitted values from each model by using the code chunk below.
df <- as.data.frame(uncSIM$fitted.values) %>%
round(digits = 0)Next, join the values to SIM_data data frame.
SIM_data <- SIM_data %>%
cbind(df) %>%
rename(uncTRIPS = "uncSIM$fitted.values")Repeat the same steps for Origin Constrained SIM (i.e. orcSIM).
df <- as.data.frame(orcSIM$fitted.values) %>%
round(digits = 0)SIM_data <- SIM_data %>%
cbind(df) %>%
rename(orcTRIPS = "orcSIM$fitted.values")Repeat the same step by for Destination Constrained SIM (i.e. decSIM).
df <- as.data.frame(decSIM$fitted.values) %>%
round(digits = 0)SIM_data <- SIM_data %>%
cbind(df) %>%
rename(decTRIPS = "decSIM$fitted.values")Repeat the same step by for Doubly Constrained SIM (i.e. dbcSIM).
df <- as.data.frame(dbcSIM$fitted.values) %>%
round(digits = 0)SIM_data <- SIM_data %>%
cbind(df) %>%
rename(dbcTRIPS = "dbcSIM$fitted.values")Finally, plot the fitted values for all four SIM.
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)
ggarrange(unc_p, orc_p, dec_p, dbc_p,
ncol = 2,
nrow = 2)