pacman::p_load(tmap, sf, sp, DT,
performance, reshape2,
ggpubr, tidyverse)In-class_Ex3
Overview
Getting Started
The code chunk below load the following packages:
- tmap: for thematic mapping
- sf for geospatial data handling
- sp for efficiency of computation of spatial data frame
- reshape2 for pivoting long/fat and to handle matrix
- tidyverse for non-spatial data handling.
- knitr for creating html table
Computing Distance Matrix
In spatial interaction, a distance matrix is a table that shows the distance between pairs of locations. For example, in the table below we can see an Euclidean distance of 3926.0025 between MESZ01 and RVSZ05, of 3939.1079 between MESZ01 and SRSZ01, and so on. By definition, an location’s distance from itself, which is shown in the main diagonal of the table, is 0.
Import mpsz for distance matrix, which is a sf tibble dataframe object class as follows.
mpsz <- st_read(dsn = "data/geospatial",
layer = "MPSZ-2019") %>%
st_transform(crs = 3414)Reading layer `MPSZ-2019' from data source
`C:\jayexx\ISSS624\In-class_Exercises\In-class_Ex3\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS: WGS 84Converting from sf data.table to SpatialPolygonsDataFrame
At least two ways to compute the required distance matrix. 1. Based on sf 2. Based on sp. From past experience, computing distance matrix by using sf function takes relatively longer than sp method especially if data set is large. In view of this, sp method is used as follows.
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 Computing the distance matrix
Use spDists() of sp package to compute the Euclidean distance between the centroids of the planning subzones as follows.
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 0.000Q&A
Do you know why the distance is calculated between two centroids of a pair of spatial polygons?
Labelling column and row heanders of a distance matrix
create a list sorted according to the the distance matrix by planning sub-zone code
sz_names <- mpsz$SUBZONE_Cattach SUBZONE_C to row and column for distance matrix matching ahead
colnames(dist) <- paste0(sz_names)
rownames(dist) <- paste0(sz_names)Pivoting distance value by SUBZONE_C
Pivot the distance matrix into a long table by using the row and column subzone codes as show in the code chunk below.
distPair <- melt(dist) %>%
rename(dist = value)
head(distPair, 10) Var1 Var2 dist
1 MESZ01 MESZ01 0.000
2 RVSZ05 MESZ01 3926.003
3 SRSZ01 MESZ01 3939.108
4 WISZ01 MESZ01 20252.964
5 MUSZ02 MESZ01 2989.984
6 MPSZ05 MESZ01 1431.330
7 WISZ03 MESZ01 19211.836
8 WISZ02 MESZ01 14960.942
9 SISZ02 MESZ01 7515.256
10 SISZ01 MESZ01 6391.342Notice that the same-zone distance is 0
Updating intra-zonal distances
Append a constant value to replace the intra-zonal distance of 0.
First, we will select and find out the minimum value of the distance by using summary().
distPair %>%
filter(dist > 0) %>%
summary() Var1 Var2 dist
MESZ01 : 331 MESZ01 : 331 Min. : 173.8
RVSZ05 : 331 RVSZ05 : 331 1st Qu.: 7149.5
SRSZ01 : 331 SRSZ01 : 331 Median :11890.0
WISZ01 : 331 WISZ01 : 331 Mean :12229.4
MUSZ02 : 331 MUSZ02 : 331 3rd Qu.:16401.7
MPSZ05 : 331 MPSZ05 : 331 Max. :49894.4
(Other):107906 (Other):107906 constant distance value of 50m is added into intra-zones distance
distPair$dist <- ifelse(distPair$dist == 0,
50, distPair$dist)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 rename the origin and destination fields
distPair <- distPair %>%
rename(orig = Var1,
dest = Var2)save the dataframe for future use
write_rds(distPair, "data/rds/distPair.rds") Flow Data
import od_data
od_data <- read_rds("data/rds/od_data.rds")compute the total passenger trip between and within planning subzones by using the code chunk below. The output is all flow_data
flow_data <- od_data %>%
group_by(ORIGIN_SZ, DESTIN_SZ) %>%
summarize(TRIPS = sum(MORNING_PEAK)) `summarise()` has grouped output by 'ORIGIN_SZ'. You can override using the
`.groups` argument.display 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
Code chunk below is used to add three new fields in 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$DESTIN_SZ,
0.000001, 1)Combining passenger volume data with distance value
Before we can join flow_data and distPair, we need to convert data value type of ORIGIN_SZ and DESTIN_SZ fields of flow_data dataframe into factor data type.
flow_data$ORIGIN_SZ <- as.factor(flow_data$ORIGIN_SZ)
flow_data$DESTIN_SZ <- as.factor(flow_data$DESTIN_SZ)left_join() of dplyr will be used to flow_data dataframe and distPair dataframe. The output is called flow_data1.
flow_data1 <- flow_data %>%
left_join (distPair,
by = c("ORIGIN_SZ" = "orig",
"DESTIN_SZ" = "dest"))Preparing OD data
Importing population data
pop <- read_csv("data/aspatial/pop.csv", show_col_types = FALSE)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))Label the output data file SIM_data. it is in rds data file format.
write_rds(flow_data1, "data/rds/SIM_data")Calibrating Spatial Interaction Models
In this section, you will learn how to calibrate Spatial Interaction Models by using Poisson Regression method.
Importing the modelling data
Firstly, let us import the modelling data by using the code chunk below.
SIM_data <- read_rds("data/rds/SIM_data.rds")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.
ggplot(data = SIM_data,
aes(x = TRIPS)) +
geom_histogram()`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
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.
ggplot(data = SIM_data,
aes(x = dist,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)`geom_smooth()` using formula = 'y ~ x'
Notice that their relationship hardly resemble linear relationship.
On the other hand, if we plot the scatter plot by using the log transformed version of both variables, we can see that their relationship is more resemble linear relationship.
ggplot(data = SIM_data,
aes(x = log(dist),
y = log(TRIPS))) +
geom_point() +
geom_smooth(method = lm)`geom_smooth()` using formula = 'y ~ x'
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.
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 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.
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 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 general formula of Unconstrained Spatial Interaction Model:
lambda_ij = exp(k + mu ln V_i + alpha ln W_j - Beta ln d_ij)
The code chunk used to calibrate to model is shown below:
SIM_data$ORIGIN_AGE25_64 <- ifelse(SIM_data$ORIGIN_AGE25_64 == 0,
0.0000001, SIM_data$ORIGIN_AGE25_64)
SIM_data$DESTIN_AGE25_64 <- ifelse(SIM_data$DESTIN_AGE25_64 == 0,
0.0000001, SIM_data$DESTIN_AGE25_64)
uncSIM <- glm(formula = TRIPS ~
log(ORIGIN_AGE25_64) +
log(DESTIN_AGE25_64) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
uncSIM
Call: glm(formula = TRIPS ~ log(ORIGIN_AGE25_64) + log(DESTIN_AGE25_64) +
log(dist), family = poisson(link = "log"), data = SIM_data,
na.action = na.exclude)
Coefficients:
(Intercept) log(ORIGIN_AGE25_64) log(DESTIN_AGE25_64)
18.375357 0.048510 -0.003123
log(dist)
-1.495664
Degrees of Freedom: 14273 Total (i.e. Null); 14270 Residual
Null Deviance: 36120000
Residual Deviance: 21150000 AIC: 21230000R-squared function
In order to measure how much variation of the trips can be accounted by the model we will write a function to calculate R-Squared value as shown below.
CalcRSquared <- function(observed,estimated){
r <- cor(observed,estimated)
R2 <- r^2
R2
}Next, we will compute the R-squared of the unconstrained SIM by using the code chunk below.
CalcRSquared(uncSIM$data$TRIPS, uncSIM$fitted.values)[1] 0.1249537r2_mcfadden(uncSIM)# R2 for Generalized Linear Regression
R2: 0.414
adj. R2: 0.414Origin (Production) constrained SIM
In this section, we will fit an origin constrained SIM by using the code3 chunk below.
The general formula of Origin Constrained Spatial Interaction Model
lambda_ij = exp(k + mu + alpha ln W_j - Beta ln d_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)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.014e+01 5.326e-03 3781.553 < 2e-16 ***
ORIGIN_SZAMSZ02 6.756e-01 5.269e-03 128.237 < 2e-16 ***
ORIGIN_SZAMSZ03 3.609e-01 5.488e-03 65.762 < 2e-16 ***
ORIGIN_SZAMSZ04 -1.114e-01 6.003e-03 -18.563 < 2e-16 ***
ORIGIN_SZAMSZ05 -3.168e-01 6.800e-03 -46.583 < 2e-16 ***
ORIGIN_SZAMSZ06 5.709e-02 6.026e-03 9.474 < 2e-16 ***
ORIGIN_SZAMSZ07 -1.135e+00 1.103e-02 -102.892 < 2e-16 ***
ORIGIN_SZAMSZ08 -6.438e-01 1.029e-02 -62.537 < 2e-16 ***
ORIGIN_SZAMSZ09 9.370e-02 6.345e-03 14.769 < 2e-16 ***
ORIGIN_SZAMSZ10 4.968e-01 5.389e-03 92.188 < 2e-16 ***
ORIGIN_SZAMSZ11 -1.331e+00 1.449e-02 -91.881 < 2e-16 ***
ORIGIN_SZAMSZ12 -1.514e+00 1.275e-02 -118.789 < 2e-16 ***
ORIGIN_SZBDSZ01 1.368e+00 5.143e-03 266.065 < 2e-16 ***
ORIGIN_SZBDSZ02 9.655e-01 5.966e-03 161.847 < 2e-16 ***
ORIGIN_SZBDSZ03 1.159e+00 5.428e-03 213.611 < 2e-16 ***
ORIGIN_SZBDSZ04 2.017e+00 4.635e-03 435.159 < 2e-16 ***
ORIGIN_SZBDSZ05 1.068e+00 5.398e-03 197.895 < 2e-16 ***
ORIGIN_SZBDSZ06 1.277e+00 5.477e-03 233.109 < 2e-16 ***
ORIGIN_SZBDSZ07 -4.996e-01 1.116e-02 -44.788 < 2e-16 ***
ORIGIN_SZBDSZ08 -3.418e-01 1.029e-02 -33.199 < 2e-16 ***
ORIGIN_SZBKSZ01 -3.552e-01 7.547e-03 -47.067 < 2e-16 ***
ORIGIN_SZBKSZ02 1.334e-01 6.139e-03 21.732 < 2e-16 ***
ORIGIN_SZBKSZ03 4.097e-01 5.898e-03 69.461 < 2e-16 ***
ORIGIN_SZBKSZ04 -3.377e-01 7.076e-03 -47.721 < 2e-16 ***
ORIGIN_SZBKSZ05 -3.028e-01 7.407e-03 -40.875 < 2e-16 ***
ORIGIN_SZBKSZ06 -2.627e-01 6.874e-03 -38.213 < 2e-16 ***
ORIGIN_SZBKSZ07 5.470e-01 5.148e-03 106.257 < 2e-16 ***
ORIGIN_SZBKSZ08 -5.322e-02 6.146e-03 -8.659 < 2e-16 ***
ORIGIN_SZBKSZ09 -1.653e-01 6.730e-03 -24.556 < 2e-16 ***
ORIGIN_SZBLSZ01 -1.787e+00 1.766e-02 -101.197 < 2e-16 ***
ORIGIN_SZBLSZ02 -1.989e+00 2.139e-02 -92.981 < 2e-16 ***
ORIGIN_SZBLSZ03 -2.955e+00 5.358e-02 -55.156 < 2e-16 ***
ORIGIN_SZBLSZ04 -1.518e+00 2.547e-02 -59.604 < 2e-16 ***
ORIGIN_SZBMSZ01 1.656e-01 6.056e-03 27.341 < 2e-16 ***
ORIGIN_SZBMSZ02 -1.417e+00 7.824e-03 -181.074 < 2e-16 ***
ORIGIN_SZBMSZ03 -6.150e-01 6.381e-03 -96.391 < 2e-16 ***
ORIGIN_SZBMSZ04 -5.629e-01 5.906e-03 -95.321 < 2e-16 ***
ORIGIN_SZBMSZ05 -3.121e+00 1.881e-02 -165.912 < 2e-16 ***
ORIGIN_SZBMSZ06 -3.040e+00 1.943e-02 -156.427 < 2e-16 ***
ORIGIN_SZBMSZ07 -7.571e-01 6.686e-03 -113.233 < 2e-16 ***
ORIGIN_SZBMSZ08 -9.476e-01 6.719e-03 -141.045 < 2e-16 ***
ORIGIN_SZBMSZ09 -1.422e+00 1.011e-02 -140.664 < 2e-16 ***
ORIGIN_SZBMSZ10 -1.723e+00 1.016e-02 -169.658 < 2e-16 ***
ORIGIN_SZBMSZ11 -1.259e+00 7.679e-03 -163.980 < 2e-16 ***
ORIGIN_SZBMSZ12 -1.393e+00 1.098e-02 -126.887 < 2e-16 ***
ORIGIN_SZBMSZ13 -4.550e-01 6.933e-03 -65.631 < 2e-16 ***
ORIGIN_SZBMSZ14 -1.016e+00 7.630e-03 -133.192 < 2e-16 ***
ORIGIN_SZBMSZ15 -6.720e-01 6.896e-03 -97.450 < 2e-16 ***
ORIGIN_SZBMSZ16 -1.544e+00 1.053e-02 -146.623 < 2e-16 ***
ORIGIN_SZBMSZ17 -1.671e+00 1.807e-02 -92.489 < 2e-16 ***
ORIGIN_SZBPSZ01 1.567e-01 6.473e-03 24.204 < 2e-16 ***
ORIGIN_SZBPSZ02 -3.516e-01 7.390e-03 -47.580 < 2e-16 ***
ORIGIN_SZBPSZ03 -1.487e-01 7.223e-03 -20.586 < 2e-16 ***
ORIGIN_SZBPSZ04 4.529e-01 5.842e-03 77.525 < 2e-16 ***
ORIGIN_SZBPSZ05 5.035e-01 5.368e-03 93.798 < 2e-16 ***
ORIGIN_SZBPSZ06 -1.009e+00 1.056e-02 -95.539 < 2e-16 ***
ORIGIN_SZBPSZ07 -3.919e-01 9.856e-03 -39.757 < 2e-16 ***
ORIGIN_SZBSSZ01 1.427e-01 6.550e-03 21.784 < 2e-16 ***
ORIGIN_SZBSSZ02 4.272e-01 5.589e-03 76.432 < 2e-16 ***
ORIGIN_SZBSSZ03 -2.457e-01 6.202e-03 -39.616 < 2e-16 ***
ORIGIN_SZBTSZ01 1.946e-01 6.667e-03 29.188 < 2e-16 ***
ORIGIN_SZBTSZ02 -4.649e-01 9.078e-03 -51.214 < 2e-16 ***
ORIGIN_SZBTSZ03 -2.809e-01 7.794e-03 -36.039 < 2e-16 ***
ORIGIN_SZBTSZ04 -1.118e+00 1.152e-02 -97.035 < 2e-16 ***
ORIGIN_SZBTSZ05 -1.016e+00 1.326e-02 -76.661 < 2e-16 ***
ORIGIN_SZBTSZ06 -1.097e+00 1.022e-02 -107.309 < 2e-16 ***
ORIGIN_SZBTSZ07 -2.326e+00 1.585e-02 -146.776 < 2e-16 ***
ORIGIN_SZBTSZ08 -1.173e+00 1.212e-02 -96.810 < 2e-16 ***
ORIGIN_SZCBSZ01 -1.104e+00 5.778e-02 -19.107 < 2e-16 ***
ORIGIN_SZCCSZ01 -8.153e-01 1.526e-02 -53.416 < 2e-16 ***
ORIGIN_SZCHSZ01 3.810e-02 1.332e-02 2.860 0.004242 **
ORIGIN_SZCHSZ02 -6.439e-01 9.639e-03 -66.804 < 2e-16 ***
ORIGIN_SZCHSZ03 1.676e+00 6.956e-03 240.919 < 2e-16 ***
ORIGIN_SZCKSZ01 8.808e-02 5.993e-03 14.695 < 2e-16 ***
ORIGIN_SZCKSZ02 4.422e-01 6.229e-03 70.999 < 2e-16 ***
ORIGIN_SZCKSZ03 8.014e-01 5.189e-03 154.436 < 2e-16 ***
ORIGIN_SZCKSZ04 1.276e+00 5.317e-03 239.971 < 2e-16 ***
ORIGIN_SZCKSZ05 9.428e-01 6.180e-03 152.546 < 2e-16 ***
ORIGIN_SZCKSZ06 4.034e-01 8.564e-03 47.106 < 2e-16 ***
ORIGIN_SZCLSZ01 -7.581e-01 9.466e-03 -80.088 < 2e-16 ***
ORIGIN_SZCLSZ02 -1.392e+00 1.533e-02 -90.838 < 2e-16 ***
ORIGIN_SZCLSZ03 -8.043e-01 9.101e-03 -88.372 < 2e-16 ***
ORIGIN_SZCLSZ04 8.306e-01 5.125e-03 162.063 < 2e-16 ***
ORIGIN_SZCLSZ05 -1.665e+00 1.661e-02 -100.234 < 2e-16 ***
ORIGIN_SZCLSZ06 9.334e-01 4.818e-03 193.746 < 2e-16 ***
ORIGIN_SZCLSZ07 -2.697e-01 6.462e-03 -41.740 < 2e-16 ***
ORIGIN_SZCLSZ08 1.239e-01 6.929e-03 17.887 < 2e-16 ***
ORIGIN_SZCLSZ09 -1.394e+00 1.927e-02 -72.305 < 2e-16 ***
ORIGIN_SZDTSZ02 -3.786e+00 8.713e-02 -43.454 < 2e-16 ***
ORIGIN_SZDTSZ03 -3.861e+00 8.402e-02 -45.957 < 2e-16 ***
ORIGIN_SZDTSZ13 -3.000e+00 3.492e-02 -85.912 < 2e-16 ***
ORIGIN_SZGLSZ01 -1.517e+00 1.101e-02 -137.752 < 2e-16 ***
ORIGIN_SZGLSZ02 2.352e-01 5.874e-03 40.033 < 2e-16 ***
ORIGIN_SZGLSZ03 1.927e-01 6.199e-03 31.082 < 2e-16 ***
ORIGIN_SZGLSZ04 1.021e+00 4.903e-03 208.246 < 2e-16 ***
ORIGIN_SZGLSZ05 9.840e-01 5.090e-03 193.324 < 2e-16 ***
ORIGIN_SZHGSZ01 3.135e-01 5.431e-03 57.729 < 2e-16 ***
ORIGIN_SZHGSZ02 3.752e-01 5.456e-03 68.763 < 2e-16 ***
ORIGIN_SZHGSZ03 2.425e-01 5.924e-03 40.942 < 2e-16 ***
ORIGIN_SZHGSZ04 8.772e-01 4.964e-03 176.718 < 2e-16 ***
ORIGIN_SZHGSZ05 1.176e+00 4.947e-03 237.769 < 2e-16 ***
ORIGIN_SZHGSZ06 -4.019e-02 6.380e-03 -6.298 3.01e-10 ***
ORIGIN_SZHGSZ07 4.473e-01 5.514e-03 81.117 < 2e-16 ***
ORIGIN_SZHGSZ08 2.200e-01 6.128e-03 35.903 < 2e-16 ***
ORIGIN_SZHGSZ09 -1.683e+00 8.447e-03 -199.258 < 2e-16 ***
ORIGIN_SZHGSZ10 -3.025e+00 5.010e-02 -60.370 < 2e-16 ***
ORIGIN_SZJESZ01 3.834e-01 5.627e-03 68.136 < 2e-16 ***
ORIGIN_SZJESZ02 1.093e-01 5.686e-03 19.225 < 2e-16 ***
ORIGIN_SZJESZ03 1.542e-03 6.101e-03 0.253 0.800529
ORIGIN_SZJESZ04 -1.369e+00 1.172e-02 -116.825 < 2e-16 ***
ORIGIN_SZJESZ05 -2.090e+00 1.571e-02 -133.036 < 2e-16 ***
ORIGIN_SZJESZ06 1.385e-01 5.524e-03 25.073 < 2e-16 ***
ORIGIN_SZJESZ07 -1.781e+00 1.332e-02 -133.724 < 2e-16 ***
ORIGIN_SZJESZ08 -9.407e-01 1.382e-02 -68.066 < 2e-16 ***
ORIGIN_SZJESZ09 5.856e-01 6.037e-03 96.995 < 2e-16 ***
ORIGIN_SZJESZ10 -1.221e+00 2.332e-02 -52.336 < 2e-16 ***
ORIGIN_SZJESZ11 -1.432e+00 2.209e-02 -64.820 < 2e-16 ***
ORIGIN_SZJWSZ01 5.911e-01 7.774e-03 76.041 < 2e-16 ***
ORIGIN_SZJWSZ02 9.712e-01 5.303e-03 183.139 < 2e-16 ***
ORIGIN_SZJWSZ03 1.314e+00 4.907e-03 267.710 < 2e-16 ***
ORIGIN_SZJWSZ04 5.342e-01 5.782e-03 92.398 < 2e-16 ***
ORIGIN_SZJWSZ05 -1.580e+00 1.469e-02 -107.539 < 2e-16 ***
ORIGIN_SZJWSZ06 -9.191e-01 1.269e-02 -72.413 < 2e-16 ***
ORIGIN_SZJWSZ07 -2.314e+00 3.578e-02 -64.677 < 2e-16 ***
ORIGIN_SZJWSZ08 1.999e+00 4.798e-03 416.564 < 2e-16 ***
ORIGIN_SZJWSZ09 1.893e+00 4.527e-03 418.059 < 2e-16 ***
ORIGIN_SZKLSZ01 2.651e-01 5.691e-03 46.584 < 2e-16 ***
ORIGIN_SZKLSZ02 -6.551e-01 7.452e-03 -87.913 < 2e-16 ***
ORIGIN_SZKLSZ03 -4.120e-01 6.721e-03 -61.295 < 2e-16 ***
ORIGIN_SZKLSZ04 -2.154e+00 1.384e-02 -155.628 < 2e-16 ***
ORIGIN_SZKLSZ05 -1.117e+00 1.215e-02 -91.947 < 2e-16 ***
ORIGIN_SZKLSZ06 -5.679e+00 1.857e-01 -30.575 < 2e-16 ***
ORIGIN_SZKLSZ07 -1.204e+00 9.683e-03 -124.389 < 2e-16 ***
ORIGIN_SZKLSZ08 -1.709e+00 1.143e-02 -149.493 < 2e-16 ***
ORIGIN_SZLKSZ01 -1.690e+00 4.464e-02 -37.864 < 2e-16 ***
ORIGIN_SZMDSZ01 -1.155e+00 3.188e-02 -36.226 < 2e-16 ***
ORIGIN_SZMDSZ02 -5.117e-01 1.166e-02 -43.866 < 2e-16 ***
ORIGIN_SZMDSZ03 -1.910e+00 1.983e-02 -96.312 < 2e-16 ***
ORIGIN_SZMPSZ01 -5.297e-01 9.420e-03 -56.234 < 2e-16 ***
ORIGIN_SZMPSZ02 -2.862e-01 7.797e-03 -36.701 < 2e-16 ***
ORIGIN_SZMPSZ03 3.316e-01 6.372e-03 52.039 < 2e-16 ***
ORIGIN_SZMUSZ02 -3.834e+00 1.105e-01 -34.691 < 2e-16 ***
ORIGIN_SZNTSZ01 -2.994e+00 3.970e-02 -75.418 < 2e-16 ***
ORIGIN_SZNTSZ02 -3.225e+00 2.495e-02 -129.268 < 2e-16 ***
ORIGIN_SZNTSZ03 -1.005e+00 8.542e-03 -117.664 < 2e-16 ***
ORIGIN_SZNTSZ05 -4.286e+00 5.797e-02 -73.933 < 2e-16 ***
ORIGIN_SZNTSZ06 -4.639e+00 5.835e-02 -79.508 < 2e-16 ***
ORIGIN_SZNVSZ01 3.075e-01 5.294e-03 58.073 < 2e-16 ***
ORIGIN_SZNVSZ02 -5.582e-01 7.374e-03 -75.697 < 2e-16 ***
ORIGIN_SZNVSZ03 -1.010e+00 9.056e-03 -111.478 < 2e-16 ***
ORIGIN_SZNVSZ04 -8.440e-01 9.959e-03 -84.750 < 2e-16 ***
ORIGIN_SZNVSZ05 -2.148e+00 1.824e-02 -117.754 < 2e-16 ***
ORIGIN_SZPGSZ01 -5.425e-01 1.515e-02 -35.803 < 2e-16 ***
ORIGIN_SZPGSZ02 -3.894e-01 8.513e-03 -45.738 < 2e-16 ***
ORIGIN_SZPGSZ03 7.077e-01 5.553e-03 127.437 < 2e-16 ***
ORIGIN_SZPGSZ04 1.234e+00 5.107e-03 241.546 < 2e-16 ***
ORIGIN_SZPGSZ05 4.080e-01 6.984e-03 58.410 < 2e-16 ***
ORIGIN_SZPLSZ01 -5.507e-01 1.345e-02 -40.952 < 2e-16 ***
ORIGIN_SZPLSZ02 -1.002e+00 1.723e-02 -58.153 < 2e-16 ***
ORIGIN_SZPLSZ03 -1.726e+00 4.726e-02 -36.524 < 2e-16 ***
ORIGIN_SZPLSZ04 -2.205e+00 3.736e-02 -59.024 < 2e-16 ***
ORIGIN_SZPLSZ05 -1.710e+00 2.609e-02 -65.537 < 2e-16 ***
ORIGIN_SZPNSZ01 1.489e+00 5.515e-03 270.096 < 2e-16 ***
ORIGIN_SZPNSZ02 6.893e-01 1.278e-02 53.923 < 2e-16 ***
ORIGIN_SZPNSZ03 -1.416e+00 2.162e-02 -65.496 < 2e-16 ***
ORIGIN_SZPNSZ04 -2.060e+00 3.607e-02 -57.104 < 2e-16 ***
ORIGIN_SZPNSZ05 -9.722e-01 3.210e-02 -30.289 < 2e-16 ***
ORIGIN_SZPRSZ01 6.116e-02 1.391e-02 4.396 1.10e-05 ***
ORIGIN_SZPRSZ02 1.305e+00 5.381e-03 242.598 < 2e-16 ***
ORIGIN_SZPRSZ03 1.002e+00 5.429e-03 184.636 < 2e-16 ***
ORIGIN_SZPRSZ04 -2.500e-02 8.801e-03 -2.840 0.004511 **
ORIGIN_SZPRSZ05 1.685e+00 5.084e-03 331.530 < 2e-16 ***
ORIGIN_SZPRSZ06 -8.502e-01 1.313e-02 -64.756 < 2e-16 ***
ORIGIN_SZPRSZ07 -2.199e+00 1.774e-02 -123.982 < 2e-16 ***
ORIGIN_SZPRSZ08 4.520e-01 7.261e-03 62.252 < 2e-16 ***
ORIGIN_SZQTSZ01 -3.688e-01 7.877e-03 -46.819 < 2e-16 ***
ORIGIN_SZQTSZ02 -8.373e-01 7.154e-03 -117.032 < 2e-16 ***
ORIGIN_SZQTSZ03 -2.607e-01 6.556e-03 -39.763 < 2e-16 ***
ORIGIN_SZQTSZ04 -1.240e+00 8.405e-03 -147.512 < 2e-16 ***
ORIGIN_SZQTSZ05 -7.392e-01 7.236e-03 -102.161 < 2e-16 ***
ORIGIN_SZQTSZ06 -6.805e-01 7.666e-03 -88.773 < 2e-16 ***
ORIGIN_SZQTSZ07 -1.461e+00 1.094e-02 -133.600 < 2e-16 ***
ORIGIN_SZQTSZ08 -3.004e-01 7.019e-03 -42.805 < 2e-16 ***
ORIGIN_SZQTSZ09 -6.296e-01 7.874e-03 -79.959 < 2e-16 ***
ORIGIN_SZQTSZ10 -3.463e-01 7.545e-03 -45.897 < 2e-16 ***
ORIGIN_SZQTSZ11 -1.983e+00 1.512e-02 -131.141 < 2e-16 ***
ORIGIN_SZQTSZ12 -2.683e+00 2.059e-02 -130.356 < 2e-16 ***
ORIGIN_SZQTSZ13 -4.182e-01 8.841e-03 -47.306 < 2e-16 ***
ORIGIN_SZQTSZ14 -1.683e+00 1.344e-02 -125.226 < 2e-16 ***
ORIGIN_SZQTSZ15 -3.718e-01 1.319e-02 -28.177 < 2e-16 ***
ORIGIN_SZRCSZ01 -1.720e+00 1.412e-02 -121.849 < 2e-16 ***
ORIGIN_SZRCSZ06 -1.165e+00 9.489e-03 -122.735 < 2e-16 ***
ORIGIN_SZRVSZ01 -3.053e+00 3.397e-02 -89.862 < 2e-16 ***
ORIGIN_SZRVSZ02 -3.631e+00 2.976e-02 -121.982 < 2e-16 ***
ORIGIN_SZRVSZ03 -3.261e+00 2.591e-02 -125.820 < 2e-16 ***
ORIGIN_SZRVSZ04 -3.764e+00 5.759e-02 -65.350 < 2e-16 ***
ORIGIN_SZRVSZ05 -2.977e+00 1.786e-02 -166.704 < 2e-16 ***
ORIGIN_SZSBSZ01 2.817e-02 7.856e-03 3.586 0.000336 ***
ORIGIN_SZSBSZ02 -5.725e-01 9.305e-03 -61.526 < 2e-16 ***
ORIGIN_SZSBSZ03 8.912e-01 5.459e-03 163.267 < 2e-16 ***
ORIGIN_SZSBSZ04 8.291e-01 6.190e-03 133.936 < 2e-16 ***
ORIGIN_SZSBSZ05 -1.657e-01 7.834e-03 -21.149 < 2e-16 ***
ORIGIN_SZSBSZ06 -1.142e+00 1.964e-02 -58.132 < 2e-16 ***
ORIGIN_SZSBSZ07 -8.886e-01 1.607e-02 -55.289 < 2e-16 ***
ORIGIN_SZSBSZ08 -1.137e+00 1.746e-02 -65.107 < 2e-16 ***
ORIGIN_SZSBSZ09 -5.911e-01 1.020e-02 -57.971 < 2e-16 ***
ORIGIN_SZSESZ02 1.130e+00 5.094e-03 221.775 < 2e-16 ***
ORIGIN_SZSESZ03 1.119e+00 4.902e-03 228.273 < 2e-16 ***
ORIGIN_SZSESZ04 7.530e-01 5.695e-03 132.233 < 2e-16 ***
ORIGIN_SZSESZ05 -2.681e-01 6.959e-03 -38.530 < 2e-16 ***
ORIGIN_SZSESZ06 8.151e-01 5.580e-03 146.077 < 2e-16 ***
ORIGIN_SZSESZ07 -2.285e+00 2.312e-02 -98.840 < 2e-16 ***
ORIGIN_SZSGSZ01 -7.290e-01 9.896e-03 -73.669 < 2e-16 ***
ORIGIN_SZSGSZ02 -1.111e+00 1.109e-02 -100.124 < 2e-16 ***
ORIGIN_SZSGSZ03 1.781e-01 6.051e-03 29.441 < 2e-16 ***
ORIGIN_SZSGSZ04 3.793e-01 5.617e-03 67.533 < 2e-16 ***
ORIGIN_SZSGSZ05 -1.718e+00 1.189e-02 -144.416 < 2e-16 ***
ORIGIN_SZSGSZ06 4.625e-01 5.289e-03 87.452 < 2e-16 ***
ORIGIN_SZSGSZ07 -7.111e-01 7.313e-03 -97.240 < 2e-16 ***
ORIGIN_SZSKSZ01 1.757e-01 1.007e-02 17.443 < 2e-16 ***
ORIGIN_SZSKSZ02 1.237e+00 6.351e-03 194.744 < 2e-16 ***
ORIGIN_SZSKSZ03 -3.102e-01 9.679e-03 -32.053 < 2e-16 ***
ORIGIN_SZSKSZ04 -1.826e+00 3.592e-02 -50.819 < 2e-16 ***
ORIGIN_SZSKSZ05 -4.231e-01 1.767e-02 -23.943 < 2e-16 ***
ORIGIN_SZSLSZ01 -2.596e+00 3.480e-02 -74.596 < 2e-16 ***
ORIGIN_SZSLSZ04 -2.146e-01 8.852e-03 -24.249 < 2e-16 ***
ORIGIN_SZSRSZ01 -2.981e+00 1.736e-02 -171.687 < 2e-16 ***
ORIGIN_SZTHSZ01 -1.978e+00 5.703e-02 -34.689 < 2e-16 ***
ORIGIN_SZTHSZ03 -1.750e+00 2.728e-02 -64.141 < 2e-16 ***
ORIGIN_SZTHSZ04 -2.769e+00 3.432e-02 -80.678 < 2e-16 ***
ORIGIN_SZTHSZ06 -2.184e+00 2.055e-02 -106.298 < 2e-16 ***
ORIGIN_SZTMSZ01 8.343e-01 6.682e-03 124.847 < 2e-16 ***
ORIGIN_SZTMSZ02 2.321e+00 4.498e-03 515.896 < 2e-16 ***
ORIGIN_SZTMSZ03 1.709e+00 4.862e-03 351.580 < 2e-16 ***
ORIGIN_SZTMSZ04 1.248e+00 5.839e-03 213.680 < 2e-16 ***
ORIGIN_SZTMSZ05 -8.754e-02 1.241e-02 -7.055 1.72e-12 ***
ORIGIN_SZTNSZ01 -2.059e+00 1.396e-02 -147.516 < 2e-16 ***
ORIGIN_SZTNSZ02 -1.892e+00 1.079e-02 -175.317 < 2e-16 ***
ORIGIN_SZTNSZ03 -2.184e+00 1.468e-02 -148.846 < 2e-16 ***
ORIGIN_SZTNSZ04 -5.183e-01 8.150e-03 -63.595 < 2e-16 ***
ORIGIN_SZTPSZ01 -6.802e-01 7.561e-03 -89.963 < 2e-16 ***
ORIGIN_SZTPSZ02 4.469e-01 5.019e-03 89.042 < 2e-16 ***
ORIGIN_SZTPSZ03 -7.869e-01 7.225e-03 -108.911 < 2e-16 ***
ORIGIN_SZTPSZ04 -7.108e-01 6.646e-03 -106.946 < 2e-16 ***
ORIGIN_SZTPSZ05 -5.636e-01 7.037e-03 -80.084 < 2e-16 ***
ORIGIN_SZTPSZ06 -4.351e-01 6.871e-03 -63.322 < 2e-16 ***
ORIGIN_SZTPSZ07 -2.877e-01 7.103e-03 -40.510 < 2e-16 ***
ORIGIN_SZTPSZ08 -1.091e+00 1.100e-02 -99.143 < 2e-16 ***
ORIGIN_SZTPSZ09 -8.156e-01 7.916e-03 -103.027 < 2e-16 ***
ORIGIN_SZTPSZ10 -9.365e-01 8.681e-03 -107.877 < 2e-16 ***
ORIGIN_SZTPSZ11 -5.242e-02 6.434e-03 -8.147 3.72e-16 ***
ORIGIN_SZTPSZ12 -6.372e-01 7.832e-03 -81.353 < 2e-16 ***
ORIGIN_SZTSSZ01 -1.821e+00 5.174e-02 -35.203 < 2e-16 ***
ORIGIN_SZTSSZ02 1.121e+00 9.420e-03 119.037 < 2e-16 ***
ORIGIN_SZTSSZ03 6.082e-01 9.592e-03 63.403 < 2e-16 ***
ORIGIN_SZTSSZ04 8.172e-01 1.050e-02 77.844 < 2e-16 ***
ORIGIN_SZTSSZ05 4.000e-02 1.787e-02 2.238 0.025209 *
ORIGIN_SZTSSZ06 1.705e+00 2.068e-02 82.420 < 2e-16 ***
ORIGIN_SZWCSZ01 8.029e-01 1.056e-02 76.008 < 2e-16 ***
ORIGIN_SZWCSZ02 -1.991e+00 3.457e-02 -57.589 < 2e-16 ***
ORIGIN_SZWCSZ03 -5.068e+00 1.475e-01 -34.359 < 2e-16 ***
ORIGIN_SZWDSZ01 1.492e+00 4.722e-03 316.015 < 2e-16 ***
ORIGIN_SZWDSZ02 9.860e-01 5.577e-03 176.779 < 2e-16 ***
ORIGIN_SZWDSZ03 1.588e+00 5.219e-03 304.180 < 2e-16 ***
ORIGIN_SZWDSZ04 1.382e+00 6.052e-03 228.327 < 2e-16 ***
ORIGIN_SZWDSZ05 6.605e-01 6.229e-03 106.026 < 2e-16 ***
ORIGIN_SZWDSZ06 7.977e-01 6.096e-03 130.865 < 2e-16 ***
ORIGIN_SZWDSZ07 -6.617e-01 9.357e-03 -70.722 < 2e-16 ***
ORIGIN_SZWDSZ08 -3.747e-01 9.645e-03 -38.852 < 2e-16 ***
ORIGIN_SZWDSZ09 1.418e+00 5.231e-03 271.027 < 2e-16 ***
ORIGIN_SZYSSZ01 -1.927e-01 6.955e-03 -27.704 < 2e-16 ***
ORIGIN_SZYSSZ02 8.767e-01 5.896e-03 148.707 < 2e-16 ***
ORIGIN_SZYSSZ03 1.832e+00 5.038e-03 363.581 < 2e-16 ***
ORIGIN_SZYSSZ04 1.075e+00 5.296e-03 202.917 < 2e-16 ***
ORIGIN_SZYSSZ05 3.194e-01 6.970e-03 45.820 < 2e-16 ***
ORIGIN_SZYSSZ06 -4.514e-01 1.249e-02 -36.148 < 2e-16 ***
ORIGIN_SZYSSZ07 -1.039e+00 1.558e-02 -66.651 < 2e-16 ***
ORIGIN_SZYSSZ08 1.825e-01 7.094e-03 25.733 < 2e-16 ***
ORIGIN_SZYSSZ09 1.066e+00 5.045e-03 211.299 < 2e-16 ***
log(DESTIN_AGE25_64) 8.299e-03 3.958e-05 209.686 < 2e-16 ***
log(dist) -1.705e+00 4.626e-04 -3686.082 < 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: 13020597 on 13993 degrees of freedom
AIC: 13105714
Number of Fisher Scoring iterations: 6We can examine how the constraints hold for destinations this time.
CalcRSquared(orcSIM$data$TRIPS, orcSIM$fitted.values)[1] 0.3983045Destination constrained
In this section, we will fit a destination constrained SIM by using the code chunk below.
The general formula of Destination Constrained Spatial Interaction Model
lambda_ij = exp(k + mu ln V_i + alpha_i - Beta ln d_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)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.078e+01 4.880e-03 4257.201 < 2e-16 ***
DESTIN_SZAMSZ02 1.015e-01 4.974e-03 20.401 < 2e-16 ***
DESTIN_SZAMSZ03 5.837e-02 4.986e-03 11.707 < 2e-16 ***
DESTIN_SZAMSZ04 -1.167e+00 7.425e-03 -157.154 < 2e-16 ***
DESTIN_SZAMSZ05 -1.274e+00 7.585e-03 -167.972 < 2e-16 ***
DESTIN_SZAMSZ06 -1.186e+00 7.347e-03 -161.383 < 2e-16 ***
DESTIN_SZAMSZ07 -1.582e+00 1.095e-02 -144.515 < 2e-16 ***
DESTIN_SZAMSZ08 -4.466e-01 7.415e-03 -60.231 < 2e-16 ***
DESTIN_SZAMSZ09 -1.059e+00 7.680e-03 -137.875 < 2e-16 ***
DESTIN_SZAMSZ10 -1.808e-02 5.176e-03 -3.494 0.000476 ***
DESTIN_SZAMSZ11 -4.071e-01 9.487e-03 -42.914 < 2e-16 ***
DESTIN_SZAMSZ12 5.159e-01 5.324e-03 96.888 < 2e-16 ***
DESTIN_SZBDSZ01 1.066e+00 4.423e-03 241.113 < 2e-16 ***
DESTIN_SZBDSZ02 2.891e-01 5.956e-03 48.533 < 2e-16 ***
DESTIN_SZBDSZ03 3.695e-01 5.372e-03 68.784 < 2e-16 ***
DESTIN_SZBDSZ04 1.291e+00 4.311e-03 299.410 < 2e-16 ***
DESTIN_SZBDSZ05 8.675e-01 4.636e-03 187.137 < 2e-16 ***
DESTIN_SZBDSZ06 5.439e-01 5.373e-03 101.231 < 2e-16 ***
DESTIN_SZBDSZ07 -5.201e-01 1.105e-02 -47.080 < 2e-16 ***
DESTIN_SZBDSZ08 -1.180e+00 1.286e-02 -91.708 < 2e-16 ***
DESTIN_SZBKSZ01 -1.036e+00 7.777e-03 -133.177 < 2e-16 ***
DESTIN_SZBKSZ02 -3.960e-01 6.671e-03 -59.363 < 2e-16 ***
DESTIN_SZBKSZ03 -6.872e-01 6.651e-03 -103.317 < 2e-16 ***
DESTIN_SZBKSZ04 -3.992e-01 5.831e-03 -68.466 < 2e-16 ***
DESTIN_SZBKSZ05 -9.217e-01 7.387e-03 -124.783 < 2e-16 ***
DESTIN_SZBKSZ06 -9.486e-01 6.863e-03 -138.225 < 2e-16 ***
DESTIN_SZBKSZ07 -3.611e-02 4.841e-03 -7.459 8.70e-14 ***
DESTIN_SZBKSZ08 -1.276e+00 7.918e-03 -161.203 < 2e-16 ***
DESTIN_SZBKSZ09 -7.783e-02 5.428e-03 -14.338 < 2e-16 ***
DESTIN_SZBLSZ01 -3.399e-01 8.203e-03 -41.433 < 2e-16 ***
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DESTIN_SZWDSZ09 1.286e+00 5.047e-03 254.752 < 2e-16 ***
DESTIN_SZYSSZ01 8.410e-01 4.413e-03 190.577 < 2e-16 ***
DESTIN_SZYSSZ02 3.055e-01 5.824e-03 52.464 < 2e-16 ***
DESTIN_SZYSSZ03 -6.562e-02 6.834e-03 -9.602 < 2e-16 ***
DESTIN_SZYSSZ04 -9.208e-02 6.083e-03 -15.137 < 2e-16 ***
DESTIN_SZYSSZ05 -9.496e-01 1.218e-02 -77.946 < 2e-16 ***
DESTIN_SZYSSZ06 -1.434e+00 1.257e-02 -114.040 < 2e-16 ***
DESTIN_SZYSSZ07 -7.694e-01 1.653e-02 -46.549 < 2e-16 ***
DESTIN_SZYSSZ08 9.602e-01 4.589e-03 209.266 < 2e-16 ***
DESTIN_SZYSSZ09 3.229e-01 4.797e-03 67.314 < 2e-16 ***
log(ORIGIN_AGE25_64) 5.796e-02 6.135e-05 944.718 < 2e-16 ***
log(dist) -1.790e+00 4.774e-04 -3749.675 < 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: 13004479 on 13992 degrees of freedom
AIC: 13089597
Number of Fisher Scoring iterations: 7We can examine how the constraints hold for destinations this time.
CalcRSquared(decSIM$data$TRIPS, decSIM$fitted.values)[1] 0.4524005Doubly constrained
In this section, we will fit a doubly constrained SIM by using the code chunk below.
The general formula of Doubly Constrained Spatial Interaction Model
lambda_ij = exp(k + mu_i + alpha_i - Beta ln d_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)
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 ***
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ORIGIN_SZTPSZ04 -0.8537831 0.0069792 -122.332 < 2e-16 ***
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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 ***
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ORIGIN_SZTSSZ02 0.1682588 0.0119965 14.026 < 2e-16 ***
ORIGIN_SZTSSZ03 0.2587653 0.0123809 20.900 < 2e-16 ***
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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 ***
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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 ***
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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 ***
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DESTIN_SZBLSZ02 0.1362723 0.0082167 16.585 < 2e-16 ***
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DESTIN_SZBLSZ04 -0.9316219 0.0178080 -52.315 < 2e-16 ***
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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 ***
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DESTIN_SZBPSZ03 -1.6944911 0.0098520 -171.995 < 2e-16 ***
DESTIN_SZBPSZ04 -0.7664610 0.0074458 -102.939 < 2e-16 ***
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DESTIN_SZBPSZ07 -0.1666192 0.0094969 -17.545 < 2e-16 ***
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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 ***
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DESTIN_SZCLSZ08 -0.3219670 0.0075615 -42.580 < 2e-16 ***
DESTIN_SZCLSZ09 0.0564166 0.0080703 6.991 2.74e-12 ***
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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 ***
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DESTIN_SZHGSZ06 -0.9054730 0.0067581 -133.983 < 2e-16 ***
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DESTIN_SZJWSZ08 -0.4253502 0.0066584 -63.881 < 2e-16 ***
DESTIN_SZJWSZ09 0.9428005 0.0053190 177.251 < 2e-16 ***
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DESTIN_SZQTSZ13 0.5199663 0.0071928 72.290 < 2e-16 ***
DESTIN_SZQTSZ14 0.6086332 0.0078537 77.496 < 2e-16 ***
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DESTIN_SZSBSZ07 -0.7471529 0.0238628 -31.310 < 2e-16 ***
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DESTIN_SZSGSZ05 -2.0309074 0.0114993 -176.611 < 2e-16 ***
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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: 7We can examine how the constraints hold for destinations this time.
CalcRSquared(dbcSIM$data$TRIPS, dbcSIM$fitted.values)[1] 0.6883675Model comparison
Another useful model performance measure for continuous dependent variable is Root Mean Squared Error. In this sub-section, you will learn how to use compare_performance() of performance package
First of all, let us create a list called model_list by using the code chun below.
model_list <- list(unconstrained=uncSIM,
originConstrained=orcSIM,
destinationConstrained=decSIM,
doublyConstrained=dbcSIM)Next, we will compute the RMSE of all the models in model_list file by using the code chunk below.
compare_performance(model_list,
metrics = "RMSE")# Comparison of Model Performance Indices
Name | Model | RMSE
-----------------------------------------
unconstrained | glm | 2503.010
originConstrained | glm | 2065.575
destinationConstrained | glm | 1971.310
doublyConstrained | glm | 1487.111print above reveals that doubly constrained SIM is the best model among all the four SIMs because it has the smallest RMSE value of 1487.111.
Visualising fitted
In this section, you will learn how to visualise the observed values and the fitted values.
Firstly we will extract the fitted values from each model by using the code chunk below.
df <- as.data.frame(uncSIM$fitted.values) %>%
round(digits = 0)Next, we will join the values to SIM_data data frame.
SIM_data <- SIM_data %>%
cbind(df) %>%
rename(uncTRIPS = "uncSIM$fitted.values")Repeat the same step by for Origin Constrained SIM (i.e. orcSIM)
df <- as.data.frame(orcSIM$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")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)`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'