Hands-on Exercise 10b: Calibrating Spatial Interaction Models with R

Author

Ho Zi Jun

Published

October 31, 2024

Modified

October 31, 2024

1 Overview

Spatial Interaction Models (SIMs), developed by Alan Wilson in the late 1960s and early 1970s, are mathematical models designed to estimate flows between spatial entities. Since their inception, these models have been widely applied and refined, especially for transport modelling (Boyce and Williams, 2015).

There are four primary types of traditional SIMs (Wilson, 1971):

Unconstrained
Production-constrained
Attraction-constrained
Doubly-constrained

Ordinary Least Squares (OLS), log-normal, Poisson, and negative binomial (NB) regression methods are commonly used to calibrate Origin-Destination (OD) flow models by treating flow data as different types of dependent variables. This chapter provides hands-on practice with these methods using relevant R packages to calibrate Spatial Interaction Models (SIMs).

Note

Calibration involves adjusting model parameters to align estimated results with observed data as closely as possible. This iterative process, ideal for computers, uses goodness-of-fit statistics to identify an optimal solution. Historically, calibration required researchers to code algorithms that iteratively adjusted each parameter, assessed the fit, and repeated until the best fit was achieved (Adam Dennett, 2018).

2 The Case Study and Data

In this exercise, we will calibrate a Spatial Interaction Model (SIM) to identify key factors influencing public bus passenger flows during the morning peak hours in Singapore.

3 Getting Started

For the purpose of this exercise, four r packages will be used. They are:

sf for importing, integrating, processing and transforming geospatial data.
tidyverse for importing, integrating, wrangling and visualising data.
tmap for creating thematic maps.

pacman::p_load(tmap, sf, sp,
               performance, reshape2,
               ggpubr, tidyverse)

4 The Data

This exercise is a continuation of Hands-on Ex10a: Processing and Visualising Flow Data and the following data will be used:

od_data.rds, weekday morning peak passenger flows at planning subzone level.
mpsz.rds, URA Master Plan 2019 Planning Subzone boundary in simple feature tibble data frame format.

Beside these two data sets, an additional attribute data file called pop.csv will be provided. It

5 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.

In this section, we’ll learn how to compute a distance matrix using the URA Master Plan 2019 Planning Subzone boundaries, saved as an RDS file named mpsz.

To begin, import mpsz.rds into the R environment with the code chunk below.

mpsz <- read_rds("data/rds/mpsz.rds")
mpsz

Simple 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.

5.1 Converting from sf data.table to SpatialPolygonsDataFrame

There are two main methods for computing the distance matrix: one using sf and the other using sp. Based on past experience, the sf method tends to be slower, especially for large datasets. Therefore, the sp method is used in the code chunks below for greater efficiency.

First as.Spatial() will be 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_sp

class       : 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

5.2 Computing the distance matrix

Next, spDists() of sp package will be used to compute the Euclidean distance between the centroids of the planning subzones.

Q&A

Do you know why the distance is calculated between two centroids of a pair of spatial polygons?

5.3 Ans

The distance between centroids of spatial polygons is often calculated to represent the average distance between two areas in a simplified, computationally efficient way. Centroids provide a single reference point per polygon, allowing for straightforward distance comparisons without the complexity of measuring every possible point-to-point distance within the polygons. This approach is particularly useful in models and analyses where approximate distances are sufficient, such as in origin-destination or spatial interaction matrices.

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     0.000

Notice from the output dist is a matrix object class of R. The column headers and row headers are not labelled with the planning subzone codes as well.

5.4 Labelling column and row heanders of a distance matrix

First, to create a list sorted according to the the distance matrix by planning sub-zone code.

sz_names <- mpsz$SUBZONE_C

Next to attach SUBZONE_C to row and column for distance matrix matching ahead with the code chunk below:

colnames(dist) <- paste0(sz_names)
rownames(dist) <- paste0(sz_names)

5.5 Pivoting distance value by SUBZONE_C

The next step is to pivot the distance matrix into a long table format, using the subzone codes from the rows and columns as identifiers, as demonstrated 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  6391.342

Notice that the within zone distance is 0.

5.6 Updating intra-zonal distances

In this section, a constant value will be added to replace intra-zonal distances of 0. First, the minimum distance value will be identified using the summary() function.

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 50metres 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 of the 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")

distPair <- read_rds("data/rds/distPair.rds")

6 Preparing flow data

The code chunk below is used to import od_data which was saved in hands-on exercise 10a into R environment.

od_data_fii <- read_rds("data/rds/od_data_fii.rds")

Next, the total passenger trips between and within planning subzones will be calculated using the code chunk below, producing the output dataset flow_data.

flow_data <- od_data_fii %>%
  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.

Using the code chunk below to 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     1998
 2 AMSZ01    AMSZ02     8289
 3 AMSZ01    AMSZ03     8971
 4 AMSZ01    AMSZ04     2252
 5 AMSZ01    AMSZ05     6136
 6 AMSZ01    AMSZ06     2148
 7 AMSZ01    AMSZ07     1620
 8 AMSZ01    AMSZ08     1925
 9 AMSZ01    AMSZ09     1773
10 AMSZ01    AMSZ10       63

6.1 Separating 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)

6.2 Combining passenger volume data with distance value

Before joining flow_data and distPair, the data types of the ORIGIN_SZ and DESTIN_SZ fields in the flow_data dataframe must be converted to factors.

flow_data$ORIGIN_SZ <- as.factor(flow_data$ORIGIN_SZ)
flow_data$DESTIN_SZ <- as.factor(flow_data$DESTIN_SZ)

The left_join() function from dplyr will be applied to merge the flow_data dataframe with the distPair dataframe, creating the output dataframe flow_data1.

flow_data1 <- flow_data %>%
  left_join (distPair,
             by = c("ORIGIN_SZ" = "orig",
                    "DESTIN_SZ" = "dest"))

7 Preparing Origin and Destination Attributes

7.1 Importing population data

pop <- read_csv("data/aspatial/pop.csv")

Rows: 332 Columns: 5
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (2): PA, SZ
dbl (3): AGE7_12, AGE13_24, AGE25_64

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

7.2 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)

7.3 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))

7.4 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))

We will call the output data file as SIM_data. it is in rds data file format.

write_rds(flow_data1, "data/rds/SIM_data.rds")

8 Calibrating Spatial Interaction Models

This section covers the calibration of Spatial Interaction Models using the Poisson Regression method.

8.1 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")

8.2 Visualising the dependent variable

First, the distribution of the dependent variable (i.e., TRIPS) will be visualized using a histogram, as shown in the code chunk below.

ggplot(data = SIM_data,
       aes(x = TRIPS)) +
  geom_histogram()

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

The distribution of the dependent variable, TRIPS, is highly skewed and does not follow a normal (bell-shaped) distribution. Next, the relationship between the dependent variable and a key independent variable in Spatial Interaction Models—distance—will be visualized.

ggplot(data = SIM_data,
       aes(x = dist,
           y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm)

`geom_smooth()` using formula = 'y ~ x'

The relationship between the two variables does not appear linear in the original scatter plot. However, when both variables are log-transformed, their relationship more closely resembles a linear pattern.

ggplot(data = SIM_data,
       aes(x = log(dist),
           y = log(TRIPS))) +
  geom_point() +
  geom_smooth(method = lm)

`geom_smooth()` using formula = 'y ~ x'

8.3 Checking for variables with zero values

Since Poisson Regression operates on log-transformed values and log(0) is undefined, it is essential to ensure no 0 values are present in the explanatory variables. In the code chunk below, the summary() function from Base R is used to compute summary statistics for all variables in the SIM_data dataframe.

summary(SIM_data)

  ORIGIN_SZ          DESTIN_SZ             TRIPS         FlowNoIntra      
 Length:14734       Length:14734       Min.   :     1   Min.   :     0.0  
 Class :character   Class :character   1st Qu.:    14   1st Qu.:    13.0  
 Mode  :character   Mode  :character   Median :    76   Median :    70.0  
                                       Mean   :  1021   Mean   :   839.9  
                                       3rd Qu.:   426   3rd Qu.:   379.0  
                                       Max.   :232187   Max.   :148274.0  
     offset              dist       ORIGIN_AGE7_12 ORIGIN_AGE13_24
 Min.   :0.000001   Min.   :   50   Min.   :   0   Min.   :    0  
 1st Qu.:1.000000   1st Qu.: 3346   1st Qu.: 240   1st Qu.:  440  
 Median :1.000000   Median : 6067   Median : 700   Median : 1350  
 Mean   :0.982150   Mean   : 6880   Mean   :1032   Mean   : 2269  
 3rd Qu.:1.000000   3rd Qu.: 9729   3rd Qu.:1480   3rd Qu.: 3260  
 Max.   :1.000000   Max.   :26136   Max.   :6340   Max.   :16380  
 ORIGIN_AGE25_64 DESTIN_AGE7_12 DESTIN_AGE13_24 DESTIN_AGE25_64
 Min.   :    0   Min.   :   0   Min.   :    0   Min.   :    0  
 1st Qu.: 2200   1st Qu.: 240   1st Qu.:  460   1st Qu.: 2200  
 Median : 6810   Median : 720   Median : 1420   Median : 7030  
 Mean   :10487   Mean   :1033   Mean   : 2290   Mean   :10574  
 3rd Qu.:15770   3rd Qu.:1500   3rd Qu.: 3260   3rd Qu.:15830  
 Max.   :74610   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 consist of 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)

Re-run the summary() again.

summary(SIM_data)

  ORIGIN_SZ          DESTIN_SZ             TRIPS         FlowNoIntra      
 Length:14734       Length:14734       Min.   :     1   Min.   :     0.0  
 Class :character   Class :character   1st Qu.:    14   1st Qu.:    13.0  
 Mode  :character   Mode  :character   Median :    76   Median :    70.0  
                                       Mean   :  1021   Mean   :   839.9  
                                       3rd Qu.:   426   3rd Qu.:   379.0  
                                       Max.   :232187   Max.   :148274.0  
     offset              dist       ORIGIN_AGE7_12    ORIGIN_AGE13_24   
 Min.   :0.000001   Min.   :   50   Min.   :   0.99   Min.   :    0.99  
 1st Qu.:1.000000   1st Qu.: 3346   1st Qu.: 240.00   1st Qu.:  440.00  
 Median :1.000000   Median : 6067   Median : 700.00   Median : 1350.00  
 Mean   :0.982150   Mean   : 6880   Mean   :1031.86   Mean   : 2268.84  
 3rd Qu.:1.000000   3rd Qu.: 9729   3rd Qu.:1480.00   3rd Qu.: 3260.00  
 Max.   :1.000000   Max.   :26136   Max.   :6340.00   Max.   :16380.00  
 ORIGIN_AGE25_64    DESTIN_AGE7_12    DESTIN_AGE13_24    DESTIN_AGE25_64   
 Min.   :    0.99   Min.   :   0.99   Min.   :    0.99   Min.   :    0.99  
 1st Qu.: 2200.00   1st Qu.: 240.00   1st Qu.:  460.00   1st Qu.: 2200.00  
 Median : 6810.00   Median : 720.00   Median : 1420.00   Median : 7030.00  
 Mean   :10487.62   Mean   :1033.40   Mean   : 2290.35   Mean   :10574.46  
 3rd Qu.:15770.00   3rd Qu.:1500.00   3rd Qu.: 3260.00   3rd Qu.:15830.00  
 Max.   :74610.00   Max.   :6340.00   Max.   :16380.00   Max.   :74610.00

Notice that all the 0 values have been replaced by 0.99.

8.4 Unconstrained Spatial Interaction Model

In this section, the process of calibrating an unconstrained spatial interaction model using glm() from Base R’s Stats package is demonstrated. The explanatory variables include the origin population by age cohort, the destination population by age cohort (e.g., ORIGIN_AGE25_64), and the distance between origin and destination in kilometers (e.g., dist).

The general formula for an Unconstrained Spatial Interaction Model is outlined below.

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)  
           10.407308              0.244859              0.009562  
           log(dist)  
           -0.705896  

Degrees of Freedom: 14733 Total (i.e. Null);  14730 Residual
Null Deviance:      60800000 
Residual Deviance: 36430000     AIC: 36520000

8.5 R-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, the R-squared of the unconstrained SIM is used by using the code chunk below.

CalcRSquared(uncSIM$data$TRIPS, uncSIM$fitted.values)

[1] 0.1892576

r2_mcfadden(uncSIM)

# R2 for Generalized Linear Regression
       R2: 0.400
  adj. R2: 0.400

8.6 Origin (Production) constrained SIM

This section demonstrates fitting an origin-constrained Spatial Interaction Model (SIM) using the code chunk provided below.

The general formula for an Origin-Constrained Spatial Interaction Model is outlined below.

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)           1.211e+01  3.785e-03  3199.012  < 2e-16 ***
ORIGIN_SZAMSZ02       1.008e+00  4.450e-03   226.401  < 2e-16 ***
ORIGIN_SZAMSZ03       5.474e-01  4.563e-03   119.959  < 2e-16 ***
ORIGIN_SZAMSZ04      -7.494e-02  5.187e-03   -14.448  < 2e-16 ***
ORIGIN_SZAMSZ05      -2.006e-01  5.790e-03   -34.650  < 2e-16 ***
ORIGIN_SZAMSZ06       4.193e-01  5.130e-03    81.736  < 2e-16 ***
ORIGIN_SZAMSZ07      -1.372e+00  9.683e-03  -141.686  < 2e-16 ***
ORIGIN_SZAMSZ08      -1.022e+00  8.956e-03  -114.087  < 2e-16 ***
ORIGIN_SZAMSZ09       2.239e-01  5.408e-03    41.396  < 2e-16 ***
ORIGIN_SZAMSZ10       5.061e-01  4.716e-03   107.311  < 2e-16 ***
ORIGIN_SZAMSZ11      -1.856e+00  1.285e-02  -144.414  < 2e-16 ***
ORIGIN_SZAMSZ12      -1.580e+00  1.076e-02  -146.883  < 2e-16 ***
ORIGIN_SZBDSZ01       1.072e+00  4.345e-03   246.734  < 2e-16 ***
ORIGIN_SZBDSZ02       5.198e-01  5.079e-03   102.340  < 2e-16 ***
ORIGIN_SZBDSZ03       9.865e-01  4.490e-03   219.724  < 2e-16 ***
ORIGIN_SZBDSZ04       1.767e+00  3.894e-03   453.646  < 2e-16 ***
ORIGIN_SZBDSZ05       6.395e-01  4.546e-03   140.691  < 2e-16 ***
ORIGIN_SZBDSZ06       9.363e-01  4.543e-03   206.094  < 2e-16 ***
ORIGIN_SZBDSZ07      -1.281e+00  9.558e-03  -133.991  < 2e-16 ***
ORIGIN_SZBDSZ08      -1.167e+00  9.032e-03  -129.194  < 2e-16 ***
ORIGIN_SZBKSZ01      -4.540e-01  6.538e-03   -69.437  < 2e-16 ***
ORIGIN_SZBKSZ02       3.736e-01  5.115e-03    73.050  < 2e-16 ***
ORIGIN_SZBKSZ03       5.841e-01  4.934e-03   118.375  < 2e-16 ***
ORIGIN_SZBKSZ04      -1.177e-01  5.914e-03   -19.895  < 2e-16 ***
ORIGIN_SZBKSZ05      -2.164e-01  5.832e-03   -37.115  < 2e-16 ***
ORIGIN_SZBKSZ06       3.684e-03  5.873e-03     0.627  0.53048    
ORIGIN_SZBKSZ07       7.456e-01  4.426e-03   168.439  < 2e-16 ***
ORIGIN_SZBKSZ08      -2.279e-02  5.348e-03    -4.261 2.04e-05 ***
ORIGIN_SZBKSZ09      -9.572e-02  5.721e-03   -16.733  < 2e-16 ***
ORIGIN_SZBLSZ01      -1.688e+00  1.482e-02  -113.887  < 2e-16 ***
ORIGIN_SZBLSZ02      -2.154e+00  1.924e-02  -111.980  < 2e-16 ***
ORIGIN_SZBLSZ03      -3.249e+00  3.930e-02   -82.662  < 2e-16 ***
ORIGIN_SZBLSZ04      -2.203e+00  2.306e-02   -95.557  < 2e-16 ***
ORIGIN_SZBMSZ01      -1.267e-01  5.222e-03   -24.266  < 2e-16 ***
ORIGIN_SZBMSZ02      -1.075e+00  6.742e-03  -159.386  < 2e-16 ***
ORIGIN_SZBMSZ03      -4.386e-01  5.794e-03   -75.707  < 2e-16 ***
ORIGIN_SZBMSZ04      -6.333e-02  5.157e-03   -12.280  < 2e-16 ***
ORIGIN_SZBMSZ05      -2.256e+00  1.247e-02  -180.957  < 2e-16 ***
ORIGIN_SZBMSZ06      -2.378e+00  1.618e-02  -147.029  < 2e-16 ***
ORIGIN_SZBMSZ07      -4.769e-01  5.653e-03   -84.362  < 2e-16 ***
ORIGIN_SZBMSZ08      -5.652e-01  5.811e-03   -97.259  < 2e-16 ***
ORIGIN_SZBMSZ09      -1.232e+00  8.688e-03  -141.760  < 2e-16 ***
ORIGIN_SZBMSZ10      -1.471e+00  9.130e-03  -161.131  < 2e-16 ***
ORIGIN_SZBMSZ11      -7.866e-01  6.595e-03  -119.263  < 2e-16 ***
ORIGIN_SZBMSZ12      -1.072e+00  9.149e-03  -117.206  < 2e-16 ***
ORIGIN_SZBMSZ13      -1.207e-01  5.691e-03   -21.218  < 2e-16 ***
ORIGIN_SZBMSZ14      -5.376e-01  6.629e-03   -81.098  < 2e-16 ***
ORIGIN_SZBMSZ15      -3.253e-01  6.054e-03   -53.740  < 2e-16 ***
ORIGIN_SZBMSZ16      -1.548e+00  9.144e-03  -169.303  < 2e-16 ***
ORIGIN_SZBMSZ17      -2.169e+00  1.576e-02  -137.622  < 2e-16 ***
ORIGIN_SZBPSZ01       1.369e-01  5.553e-03    24.660  < 2e-16 ***
ORIGIN_SZBPSZ02      -3.292e-02  6.462e-03    -5.094 3.50e-07 ***
ORIGIN_SZBPSZ03       1.491e-01  6.149e-03    24.241  < 2e-16 ***
ORIGIN_SZBPSZ04       3.544e-01  5.084e-03    69.711  < 2e-16 ***
ORIGIN_SZBPSZ05       5.454e-01  4.554e-03   119.764  < 2e-16 ***
ORIGIN_SZBPSZ06      -1.406e+00  9.311e-03  -151.045  < 2e-16 ***
ORIGIN_SZBPSZ07      -1.004e+00  8.575e-03  -117.068  < 2e-16 ***
ORIGIN_SZBSSZ01      -1.625e-02  5.276e-03    -3.080  0.00207 ** 
ORIGIN_SZBSSZ02       3.088e-01  4.787e-03    64.495  < 2e-16 ***
ORIGIN_SZBSSZ03       2.555e-01  4.689e-03    54.487  < 2e-16 ***
ORIGIN_SZBTSZ01      -6.646e-02  5.385e-03   -12.340  < 2e-16 ***
ORIGIN_SZBTSZ02      -1.078e+00  7.797e-03  -138.225  < 2e-16 ***
ORIGIN_SZBTSZ03      -2.284e-01  5.727e-03   -39.876  < 2e-16 ***
ORIGIN_SZBTSZ04      -1.053e+00  1.019e-02  -103.339  < 2e-16 ***
ORIGIN_SZBTSZ05      -1.647e+00  1.100e-02  -149.690  < 2e-16 ***
ORIGIN_SZBTSZ06      -7.804e-01  7.181e-03  -108.682  < 2e-16 ***
ORIGIN_SZBTSZ07      -2.298e+00  1.321e-02  -173.921  < 2e-16 ***
ORIGIN_SZBTSZ08      -1.283e+00  9.394e-03  -136.560  < 2e-16 ***
ORIGIN_SZCBSZ01      -1.911e+00  5.483e-02   -34.844  < 2e-16 ***
ORIGIN_SZCCSZ01      -1.758e+00  1.331e-02  -132.099  < 2e-16 ***
ORIGIN_SZCHSZ01      -1.236e+00  1.178e-02  -104.954  < 2e-16 ***
ORIGIN_SZCHSZ02      -5.424e-01  7.940e-03   -68.307  < 2e-16 ***
ORIGIN_SZCHSZ03       4.332e-01  5.841e-03    74.153  < 2e-16 ***
ORIGIN_SZCKSZ01       1.843e-01  5.117e-03    36.007  < 2e-16 ***
ORIGIN_SZCKSZ02       6.800e-01  5.087e-03   133.672  < 2e-16 ***
ORIGIN_SZCKSZ03       8.030e-01  4.522e-03   177.574  < 2e-16 ***
ORIGIN_SZCKSZ04       1.298e+00  4.562e-03   284.446  < 2e-16 ***
ORIGIN_SZCKSZ05       1.011e+00  5.305e-03   190.602  < 2e-16 ***
ORIGIN_SZCKSZ06       1.262e+00  5.042e-03   250.262  < 2e-16 ***
ORIGIN_SZCLSZ01      -6.805e-01  7.661e-03   -88.836  < 2e-16 ***
ORIGIN_SZCLSZ02      -1.837e+00  1.364e-02  -134.665  < 2e-16 ***
ORIGIN_SZCLSZ03      -1.001e+00  7.949e-03  -125.969  < 2e-16 ***
ORIGIN_SZCLSZ04       6.966e-01  4.460e-03   156.204  < 2e-16 ***
ORIGIN_SZCLSZ05      -1.974e+00  1.474e-02  -133.906  < 2e-16 ***
ORIGIN_SZCLSZ06       8.585e-01  4.204e-03   204.230  < 2e-16 ***
ORIGIN_SZCLSZ07      -2.974e-01  5.575e-03   -53.346  < 2e-16 ***
ORIGIN_SZCLSZ08       3.231e-01  5.802e-03    55.688  < 2e-16 ***
ORIGIN_SZCLSZ09      -1.697e+00  1.555e-02  -109.106  < 2e-16 ***
ORIGIN_SZDTSZ02      -4.061e+00  8.341e-02   -48.693  < 2e-16 ***
ORIGIN_SZDTSZ03      -4.031e+00  7.381e-02   -54.618  < 2e-16 ***
ORIGIN_SZDTSZ13      -3.000e+00  3.129e-02   -95.889  < 2e-16 ***
ORIGIN_SZGLSZ01      -1.405e+00  9.192e-03  -152.876  < 2e-16 ***
ORIGIN_SZGLSZ02       2.536e-01  4.889e-03    51.880  < 2e-16 ***
ORIGIN_SZGLSZ03       2.411e-01  4.855e-03    49.649  < 2e-16 ***
ORIGIN_SZGLSZ04       8.350e-01  4.200e-03   198.826  < 2e-16 ***
ORIGIN_SZGLSZ05       6.207e-01  4.375e-03   141.857  < 2e-16 ***
ORIGIN_SZHGSZ01       2.806e-01  4.746e-03    59.121  < 2e-16 ***
ORIGIN_SZHGSZ02       4.917e-01  4.712e-03   104.351  < 2e-16 ***
ORIGIN_SZHGSZ03       2.452e-01  5.113e-03    47.952  < 2e-16 ***
ORIGIN_SZHGSZ04       9.052e-01  4.303e-03   210.358  < 2e-16 ***
ORIGIN_SZHGSZ05       1.170e+00  4.253e-03   275.033  < 2e-16 ***
ORIGIN_SZHGSZ06      -1.016e-01  5.413e-03   -18.773  < 2e-16 ***
ORIGIN_SZHGSZ07       6.984e-01  4.455e-03   156.757  < 2e-16 ***
ORIGIN_SZHGSZ08       1.005e-01  5.354e-03    18.781  < 2e-16 ***
ORIGIN_SZHGSZ09      -5.390e-01  6.962e-03   -77.417  < 2e-16 ***
ORIGIN_SZHGSZ10      -3.512e+00  4.211e-02   -83.388  < 2e-16 ***
ORIGIN_SZJESZ01       4.022e-01  4.869e-03    82.601  < 2e-16 ***
ORIGIN_SZJESZ02       2.273e-01  4.924e-03    46.158  < 2e-16 ***
ORIGIN_SZJESZ03       1.829e-01  5.286e-03    34.598  < 2e-16 ***
ORIGIN_SZJESZ04      -1.177e+00  9.142e-03  -128.767  < 2e-16 ***
ORIGIN_SZJESZ05      -2.065e+00  1.382e-02  -149.494  < 2e-16 ***
ORIGIN_SZJESZ06       2.301e-01  4.853e-03    47.410  < 2e-16 ***
ORIGIN_SZJESZ07      -1.889e+00  1.183e-02  -159.599  < 2e-16 ***
ORIGIN_SZJESZ08      -1.062e+00  1.147e-02   -92.551  < 2e-16 ***
ORIGIN_SZJESZ09       5.237e-01  4.959e-03   105.612  < 2e-16 ***
ORIGIN_SZJESZ10      -1.829e+00  1.800e-02  -101.616  < 2e-16 ***
ORIGIN_SZJESZ11      -2.023e+00  1.931e-02  -104.738  < 2e-16 ***
ORIGIN_SZJWSZ01       2.125e-01  6.405e-03    33.183  < 2e-16 ***
ORIGIN_SZJWSZ02       8.858e-01  4.521e-03   195.929  < 2e-16 ***
ORIGIN_SZJWSZ03       1.269e+00  4.188e-03   302.922  < 2e-16 ***
ORIGIN_SZJWSZ04       1.284e+00  4.280e-03   300.017  < 2e-16 ***
ORIGIN_SZJWSZ05      -1.393e+00  1.252e-02  -111.339  < 2e-16 ***
ORIGIN_SZJWSZ06      -1.015e+00  1.067e-02   -95.109  < 2e-16 ***
ORIGIN_SZJWSZ07      -2.694e+00  2.751e-02   -97.911  < 2e-16 ***
ORIGIN_SZJWSZ08       1.950e+00  4.110e-03   474.430  < 2e-16 ***
ORIGIN_SZJWSZ09       1.831e+00  3.899e-03   469.595  < 2e-16 ***
ORIGIN_SZKLSZ01       1.636e-01  4.902e-03    33.374  < 2e-16 ***
ORIGIN_SZKLSZ02      -5.156e-01  6.321e-03   -81.570  < 2e-16 ***
ORIGIN_SZKLSZ03      -4.145e-01  5.949e-03   -69.666  < 2e-16 ***
ORIGIN_SZKLSZ04      -2.283e+00  1.187e-02  -192.327  < 2e-16 ***
ORIGIN_SZKLSZ05      -8.593e-01  8.272e-03  -103.882  < 2e-16 ***
ORIGIN_SZKLSZ06      -4.709e+00  1.857e-01   -25.352  < 2e-16 ***
ORIGIN_SZKLSZ07      -1.123e+00  8.408e-03  -133.615  < 2e-16 ***
ORIGIN_SZKLSZ08      -1.476e+00  9.152e-03  -161.321  < 2e-16 ***
ORIGIN_SZLKSZ01      -3.273e+00  3.875e-02   -84.465  < 2e-16 ***
ORIGIN_SZMDSZ01      -2.615e+00  2.802e-02   -93.303  < 2e-16 ***
ORIGIN_SZMDSZ02      -8.945e-01  1.035e-02   -86.389  < 2e-16 ***
ORIGIN_SZMDSZ03      -1.998e+00  1.703e-02  -117.297  < 2e-16 ***
ORIGIN_SZMPSZ01      -1.093e+00  8.367e-03  -130.656  < 2e-16 ***
ORIGIN_SZMPSZ02      -5.975e-01  6.898e-03   -86.616  < 2e-16 ***
ORIGIN_SZMPSZ03      -9.706e-03  5.319e-03    -1.825  0.06804 .  
ORIGIN_SZMUSZ02      -3.923e+00  1.038e-01   -37.806  < 2e-16 ***
ORIGIN_SZNTSZ01      -2.829e+00  3.529e-02   -80.157  < 2e-16 ***
ORIGIN_SZNTSZ02      -3.256e+00  2.323e-02  -140.180  < 2e-16 ***
ORIGIN_SZNTSZ03      -9.865e-01  7.777e-03  -126.848  < 2e-16 ***
ORIGIN_SZNTSZ05      -3.353e+00  4.964e-02   -67.546  < 2e-16 ***
ORIGIN_SZNTSZ06      -3.818e+00  5.576e-02   -68.483  < 2e-16 ***
ORIGIN_SZNVSZ01       4.449e-01  4.482e-03    99.269  < 2e-16 ***
ORIGIN_SZNVSZ02      -6.279e-01  6.470e-03   -97.044  < 2e-16 ***
ORIGIN_SZNVSZ03      -1.212e+00  7.788e-03  -155.644  < 2e-16 ***
ORIGIN_SZNVSZ04      -1.469e+00  9.091e-03  -161.543  < 2e-16 ***
ORIGIN_SZNVSZ05      -2.628e+00  1.579e-02  -166.466  < 2e-16 ***
ORIGIN_SZPGSZ01      -9.541e-01  1.223e-02   -78.035  < 2e-16 ***
ORIGIN_SZPGSZ02      -5.353e-01  7.233e-03   -74.009  < 2e-16 ***
ORIGIN_SZPGSZ03       9.574e-01  4.437e-03   215.779  < 2e-16 ***
ORIGIN_SZPGSZ04       1.110e+00  4.417e-03   251.169  < 2e-16 ***
ORIGIN_SZPGSZ05       2.658e-01  5.758e-03    46.156  < 2e-16 ***
ORIGIN_SZPLSZ01      -8.153e-01  1.044e-02   -78.119  < 2e-16 ***
ORIGIN_SZPLSZ02      -1.675e+00  1.478e-02  -113.340  < 2e-16 ***
ORIGIN_SZPLSZ03      -2.963e+00  3.672e-02   -80.686  < 2e-16 ***
ORIGIN_SZPLSZ04      -3.279e+00  3.684e-02   -89.012  < 2e-16 ***
ORIGIN_SZPLSZ05      -2.466e+00  2.245e-02  -109.864  < 2e-16 ***
ORIGIN_SZPNSZ01       1.411e+00  4.584e-03   307.690  < 2e-16 ***
ORIGIN_SZPNSZ02      -5.043e-01  1.108e-02   -45.503  < 2e-16 ***
ORIGIN_SZPNSZ03      -1.878e+00  1.940e-02   -96.796  < 2e-16 ***
ORIGIN_SZPNSZ04      -2.761e+00  3.112e-02   -88.706  < 2e-16 ***
ORIGIN_SZPNSZ05      -2.277e+00  2.628e-02   -86.662  < 2e-16 ***
ORIGIN_SZPRSZ01      -7.934e-01  1.142e-02   -69.499  < 2e-16 ***
ORIGIN_SZPRSZ02       9.414e-01  4.615e-03   203.981  < 2e-16 ***
ORIGIN_SZPRSZ03       7.674e-01  4.626e-03   165.881  < 2e-16 ***
ORIGIN_SZPRSZ04      -3.771e-01  7.516e-03   -50.168  < 2e-16 ***
ORIGIN_SZPRSZ05       1.327e+00  4.325e-03   306.737  < 2e-16 ***
ORIGIN_SZPRSZ06      -4.081e-01  8.651e-03   -47.172  < 2e-16 ***
ORIGIN_SZPRSZ07      -2.151e+00  1.610e-02  -133.558  < 2e-16 ***
ORIGIN_SZPRSZ08       5.293e-04  6.383e-03     0.083  0.93391    
ORIGIN_SZQTSZ01      -4.144e-01  6.846e-03   -60.539  < 2e-16 ***
ORIGIN_SZQTSZ02      -7.967e-01  6.327e-03  -125.933  < 2e-16 ***
ORIGIN_SZQTSZ03      -2.415e-01  5.681e-03   -42.509  < 2e-16 ***
ORIGIN_SZQTSZ04      -1.013e+00  7.129e-03  -142.123  < 2e-16 ***
ORIGIN_SZQTSZ05      -3.923e-01  5.994e-03   -65.446  < 2e-16 ***
ORIGIN_SZQTSZ06      -5.662e-01  6.481e-03   -87.359  < 2e-16 ***
ORIGIN_SZQTSZ07      -1.558e+00  9.635e-03  -161.662  < 2e-16 ***
ORIGIN_SZQTSZ08      -1.577e-01  5.699e-03   -27.665  < 2e-16 ***
ORIGIN_SZQTSZ09      -6.189e-01  6.633e-03   -93.312  < 2e-16 ***
ORIGIN_SZQTSZ10      -4.511e-01  6.512e-03   -69.271  < 2e-16 ***
ORIGIN_SZQTSZ11      -1.455e+00  9.800e-03  -148.421  < 2e-16 ***
ORIGIN_SZQTSZ12      -1.475e+00  1.044e-02  -141.309  < 2e-16 ***
ORIGIN_SZQTSZ13      -3.529e-01  6.413e-03   -55.038  < 2e-16 ***
ORIGIN_SZQTSZ14      -1.591e+00  9.847e-03  -161.565  < 2e-16 ***
ORIGIN_SZQTSZ15      -8.955e-01  1.027e-02   -87.184  < 2e-16 ***
ORIGIN_SZRCSZ01      -1.375e+00  1.265e-02  -108.704  < 2e-16 ***
ORIGIN_SZRCSZ06      -6.196e-01  8.475e-03   -73.116  < 2e-16 ***
ORIGIN_SZRVSZ01      -3.523e+00  3.237e-02  -108.818  < 2e-16 ***
ORIGIN_SZRVSZ02      -2.912e+00  2.776e-02  -104.868  < 2e-16 ***
ORIGIN_SZRVSZ03      -3.145e+00  2.379e-02  -132.232  < 2e-16 ***
ORIGIN_SZRVSZ04      -3.357e+00  5.567e-02   -60.309  < 2e-16 ***
ORIGIN_SZRVSZ05      -2.438e+00  1.644e-02  -148.272  < 2e-16 ***
ORIGIN_SZSBSZ01       5.890e-01  5.529e-03   106.520  < 2e-16 ***
ORIGIN_SZSBSZ02      -7.098e-01  8.213e-03   -86.432  < 2e-16 ***
ORIGIN_SZSBSZ03       9.634e-01  4.611e-03   208.943  < 2e-16 ***
ORIGIN_SZSBSZ04       7.729e-01  5.289e-03   146.136  < 2e-16 ***
ORIGIN_SZSBSZ05      -9.966e-02  6.543e-03   -15.231  < 2e-16 ***
ORIGIN_SZSBSZ06      -1.778e+00  1.719e-02  -103.427  < 2e-16 ***
ORIGIN_SZSBSZ07      -1.161e+00  1.256e-02   -92.436  < 2e-16 ***
ORIGIN_SZSBSZ08      -1.212e+00  1.222e-02   -99.227  < 2e-16 ***
ORIGIN_SZSBSZ09      -5.783e-01  8.579e-03   -67.412  < 2e-16 ***
ORIGIN_SZSESZ02       9.999e-01  4.409e-03   226.798  < 2e-16 ***
ORIGIN_SZSESZ03       1.214e+00  4.164e-03   291.675  < 2e-16 ***
ORIGIN_SZSESZ04       8.141e-01  4.868e-03   167.238  < 2e-16 ***
ORIGIN_SZSESZ05      -2.186e-01  5.915e-03   -36.961  < 2e-16 ***
ORIGIN_SZSESZ06       7.298e-01  4.689e-03   155.641  < 2e-16 ***
ORIGIN_SZSESZ07      -2.543e+00  1.961e-02  -129.689  < 2e-16 ***
ORIGIN_SZSGSZ01      -1.016e+00  8.550e-03  -118.869  < 2e-16 ***
ORIGIN_SZSGSZ02      -1.120e+00  9.589e-03  -116.799  < 2e-16 ***
ORIGIN_SZSGSZ03       2.169e-01  5.167e-03    41.970  < 2e-16 ***
ORIGIN_SZSGSZ04       2.672e-01  4.792e-03    55.757  < 2e-16 ***
ORIGIN_SZSGSZ05      -1.785e+00  1.060e-02  -168.456  < 2e-16 ***
ORIGIN_SZSGSZ06       4.017e-01  4.541e-03    88.470  < 2e-16 ***
ORIGIN_SZSGSZ07      -6.303e-01  6.235e-03  -101.098  < 2e-16 ***
ORIGIN_SZSKSZ01      -1.928e-01  7.765e-03   -24.826  < 2e-16 ***
ORIGIN_SZSKSZ02       3.870e-01  5.689e-03    68.026  < 2e-16 ***
ORIGIN_SZSKSZ03      -6.815e-01  7.983e-03   -85.369  < 2e-16 ***
ORIGIN_SZSKSZ04      -2.528e+00  2.702e-02   -93.548  < 2e-16 ***
ORIGIN_SZSKSZ05      -1.370e+00  1.552e-02   -88.311  < 2e-16 ***
ORIGIN_SZSLSZ01      -3.218e+00  3.058e-02  -105.238  < 2e-16 ***
ORIGIN_SZSLSZ04      -6.800e-01  7.683e-03   -88.497  < 2e-16 ***
ORIGIN_SZSRSZ01      -2.389e+00  1.583e-02  -150.989  < 2e-16 ***
ORIGIN_SZTHSZ01      -2.183e+00  4.887e-02   -44.666  < 2e-16 ***
ORIGIN_SZTHSZ03      -2.243e+00  2.243e-02  -100.025  < 2e-16 ***
ORIGIN_SZTHSZ04      -2.005e+00  2.869e-02   -69.879  < 2e-16 ***
ORIGIN_SZTHSZ06      -2.276e+00  1.784e-02  -127.557  < 2e-16 ***
ORIGIN_SZTMSZ01       4.015e-01  5.814e-03    69.048  < 2e-16 ***
ORIGIN_SZTMSZ02       2.222e+00  3.795e-03   585.568  < 2e-16 ***
ORIGIN_SZTMSZ03       1.412e+00  4.108e-03   343.608  < 2e-16 ***
ORIGIN_SZTMSZ04       9.106e-01  4.742e-03   192.036  < 2e-16 ***
ORIGIN_SZTMSZ05      -3.259e-01  7.534e-03   -43.253  < 2e-16 ***
ORIGIN_SZTNSZ01      -1.806e+00  1.038e-02  -174.076  < 2e-16 ***
ORIGIN_SZTNSZ02      -1.741e+00  9.778e-03  -178.108  < 2e-16 ***
ORIGIN_SZTNSZ03      -2.277e+00  1.338e-02  -170.199  < 2e-16 ***
ORIGIN_SZTNSZ04      -7.703e-01  7.197e-03  -107.032  < 2e-16 ***
ORIGIN_SZTPSZ01      -6.466e-01  6.287e-03  -102.841  < 2e-16 ***
ORIGIN_SZTPSZ02       4.633e-01  4.347e-03   106.578  < 2e-16 ***
ORIGIN_SZTPSZ03      -5.186e-01  6.085e-03   -85.234  < 2e-16 ***
ORIGIN_SZTPSZ04      -2.900e-01  5.779e-03   -50.190  < 2e-16 ***
ORIGIN_SZTPSZ05      -2.169e-01  6.072e-03   -35.720  < 2e-16 ***
ORIGIN_SZTPSZ06       3.357e-01  5.942e-03    56.486  < 2e-16 ***
ORIGIN_SZTPSZ07      -2.517e-01  6.317e-03   -39.846  < 2e-16 ***
ORIGIN_SZTPSZ08      -1.075e+00  9.109e-03  -118.034  < 2e-16 ***
ORIGIN_SZTPSZ09      -3.708e-01  6.189e-03   -59.903  < 2e-16 ***
ORIGIN_SZTPSZ10      -6.889e-01  7.634e-03   -90.229  < 2e-16 ***
ORIGIN_SZTPSZ11       7.661e-02  5.459e-03    14.033  < 2e-16 ***
ORIGIN_SZTPSZ12      -5.971e-01  6.522e-03   -91.552  < 2e-16 ***
ORIGIN_SZTSSZ01      -3.517e+00  4.739e-02   -74.210  < 2e-16 ***
ORIGIN_SZTSSZ02       3.022e-01  7.334e-03    41.203  < 2e-16 ***
ORIGIN_SZTSSZ03       3.730e-01  7.073e-03    52.733  < 2e-16 ***
ORIGIN_SZTSSZ04       3.610e-01  7.463e-03    48.372  < 2e-16 ***
ORIGIN_SZTSSZ05      -1.103e+00  1.404e-02   -78.566  < 2e-16 ***
ORIGIN_SZTSSZ06      -1.310e+00  1.718e-02   -76.286  < 2e-16 ***
ORIGIN_SZWCSZ01      -1.233e-01  7.861e-03   -15.690  < 2e-16 ***
ORIGIN_SZWCSZ02      -2.872e+00  3.159e-02   -90.911  < 2e-16 ***
ORIGIN_SZWCSZ03      -4.138e+00  1.241e-01   -33.349  < 2e-16 ***
ORIGIN_SZWDSZ01       1.370e+00  4.146e-03   330.448  < 2e-16 ***
ORIGIN_SZWDSZ02       1.041e+00  4.747e-03   219.219  < 2e-16 ***
ORIGIN_SZWDSZ03       2.189e+00  4.035e-03   542.344  < 2e-16 ***
ORIGIN_SZWDSZ04       1.142e+00  4.963e-03   230.074  < 2e-16 ***
ORIGIN_SZWDSZ05       5.160e-01  4.998e-03   103.230  < 2e-16 ***
ORIGIN_SZWDSZ06       1.208e+00  4.611e-03   262.019  < 2e-16 ***
ORIGIN_SZWDSZ07      -3.805e-01  8.034e-03   -47.365  < 2e-16 ***
ORIGIN_SZWDSZ08      -4.839e-01  7.878e-03   -61.426  < 2e-16 ***
ORIGIN_SZWDSZ09       1.475e+00  4.401e-03   335.097  < 2e-16 ***
ORIGIN_SZYSSZ01      -1.552e-01  5.643e-03   -27.496  < 2e-16 ***
ORIGIN_SZYSSZ02       8.958e-01  4.973e-03   180.144  < 2e-16 ***
ORIGIN_SZYSSZ03       1.757e+00  4.275e-03   411.050  < 2e-16 ***
ORIGIN_SZYSSZ04       8.439e-01  4.538e-03   185.955  < 2e-16 ***
ORIGIN_SZYSSZ05      -9.995e-02  5.920e-03   -16.884  < 2e-16 ***
ORIGIN_SZYSSZ06      -1.175e+00  1.079e-02  -108.835  < 2e-16 ***
ORIGIN_SZYSSZ07      -1.202e+00  1.127e-02  -106.642  < 2e-16 ***
ORIGIN_SZYSSZ08       1.244e-02  6.104e-03     2.039  0.04148 *  
ORIGIN_SZYSSZ09       1.385e+00  4.239e-03   326.757  < 2e-16 ***
log(DESTIN_AGE25_64)  2.298e-02  8.832e-05   260.146  < 2e-16 ***
log(dist)            -6.947e-01  1.295e-04 -5363.438  < 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: 60796037  on 14733  degrees of freedom
Residual deviance: 26726668  on 14453  degrees of freedom
AIC: 26818857

Number of Fisher Scoring iterations: 7

Examining how the constraints hold for destinations this time.

CalcRSquared(orcSIM$data$TRIPS, orcSIM$fitted.values)

[1] 0.4165837

8.7 Destination constrained

This section demonstrates fitting a destination-constrained Spatial Interaction Model (SIM) using the code chunk provided below.

The general formula for a Destination-Constrained Spatial Interaction Model is outlined below.

decSIM <- glm(formula = TRIPS ~ 
                DESTIN_SZ + 
                log(ORIGIN_AGE25_64) + 
                log(dist),
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
summary(decSIM)


Call:
glm(formula = TRIPS ~ DESTIN_SZ + log(ORIGIN_AGE25_64) + log(dist), 
    family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)

Coefficients:
                       Estimate Std. Error   z value Pr(>|z|)    
(Intercept)          10.8110189  0.0033476  3229.499  < 2e-16 ***
DESTIN_SZAMSZ02       0.1775885  0.0041530    42.761  < 2e-16 ***
DESTIN_SZAMSZ03       0.2064091  0.0040888    50.482  < 2e-16 ***
DESTIN_SZAMSZ04      -0.9406455  0.0060637  -155.127  < 2e-16 ***
DESTIN_SZAMSZ05      -1.1578100  0.0061804  -187.337  < 2e-16 ***
DESTIN_SZAMSZ06      -0.8861493  0.0059241  -149.584  < 2e-16 ***
DESTIN_SZAMSZ07      -1.7712447  0.0096070  -184.370  < 2e-16 ***
DESTIN_SZAMSZ08      -1.0707197  0.0067763  -158.009  < 2e-16 ***
DESTIN_SZAMSZ09      -0.9682250  0.0060435  -160.210  < 2e-16 ***
DESTIN_SZAMSZ10       0.2612773  0.0043738    59.737  < 2e-16 ***
DESTIN_SZAMSZ11      -0.3714704  0.0086200   -43.094  < 2e-16 ***
DESTIN_SZAMSZ12       0.0250455  0.0049850     5.024 5.06e-07 ***
DESTIN_SZBDSZ01       0.5154763  0.0037827   136.271  < 2e-16 ***
DESTIN_SZBDSZ02      -0.2843120  0.0049517   -57.417  < 2e-16 ***
DESTIN_SZBDSZ03      -0.0134646  0.0042692    -3.154  0.00161 ** 
DESTIN_SZBDSZ04       1.0014441  0.0034463   290.582  < 2e-16 ***
DESTIN_SZBDSZ05       0.3721573  0.0038992    95.445  < 2e-16 ***
DESTIN_SZBDSZ06       0.2013935  0.0042182    47.744  < 2e-16 ***
DESTIN_SZBDSZ07      -1.0642612  0.0092942  -114.508  < 2e-16 ***
DESTIN_SZBDSZ08      -1.7769370  0.0105721  -168.077  < 2e-16 ***
DESTIN_SZBKSZ01      -1.1944766  0.0065580  -182.141  < 2e-16 ***
DESTIN_SZBKSZ02      -0.2604946  0.0052044   -50.053  < 2e-16 ***
DESTIN_SZBKSZ03      -0.5905775  0.0055618  -106.184  < 2e-16 ***
DESTIN_SZBKSZ04      -0.0521573  0.0048274   -10.804  < 2e-16 ***
DESTIN_SZBKSZ05      -0.8258599  0.0057094  -144.650  < 2e-16 ***
DESTIN_SZBKSZ06      -0.8696763  0.0060934  -142.725  < 2e-16 ***
DESTIN_SZBKSZ07       0.2216292  0.0040334    54.949  < 2e-16 ***
DESTIN_SZBKSZ08      -1.1179375  0.0068749  -162.612  < 2e-16 ***
DESTIN_SZBKSZ09      -0.2888733  0.0049056   -58.886  < 2e-16 ***
DESTIN_SZBLSZ01      -0.4487061  0.0070226   -63.894  < 2e-16 ***
DESTIN_SZBLSZ02       0.6343096  0.0065174    97.326  < 2e-16 ***
DESTIN_SZBLSZ03       1.3492337  0.0074135   181.997  < 2e-16 ***
DESTIN_SZBLSZ04      -0.0339193  0.0131568    -2.578  0.00993 ** 
DESTIN_SZBMSZ01      -0.3497912  0.0046910   -74.567  < 2e-16 ***
DESTIN_SZBMSZ02      -0.5995634  0.0048828  -122.792  < 2e-16 ***
DESTIN_SZBMSZ03      -0.8726401  0.0056851  -153.495  < 2e-16 ***
DESTIN_SZBMSZ04      -0.5350402  0.0048888  -109.442  < 2e-16 ***
DESTIN_SZBMSZ05      -0.4981814  0.0065971   -75.515  < 2e-16 ***
DESTIN_SZBMSZ06      -2.0640198  0.0123050  -167.739  < 2e-16 ***
DESTIN_SZBMSZ07      -0.3100988  0.0045283   -68.480  < 2e-16 ***
DESTIN_SZBMSZ08      -1.2748152  0.0062622  -203.573  < 2e-16 ***
DESTIN_SZBMSZ09      -2.8056325  0.0143532  -195.471  < 2e-16 ***
DESTIN_SZBMSZ10      -1.9166407  0.0089273  -214.693  < 2e-16 ***
DESTIN_SZBMSZ11      -1.7261160  0.0079281  -217.722  < 2e-16 ***
DESTIN_SZBMSZ12      -1.1495908  0.0077721  -147.912  < 2e-16 ***
DESTIN_SZBMSZ13      -0.5428008  0.0050824  -106.799  < 2e-16 ***
DESTIN_SZBMSZ14      -1.1422302  0.0076325  -149.653  < 2e-16 ***
DESTIN_SZBMSZ15      -1.2217517  0.0068685  -177.878  < 2e-16 ***
DESTIN_SZBMSZ16      -2.4074288  0.0107900  -223.116  < 2e-16 ***
DESTIN_SZBMSZ17      -2.6985491  0.0164771  -163.776  < 2e-16 ***
DESTIN_SZBPSZ01      -0.6183085  0.0054605  -113.233  < 2e-16 ***
DESTIN_SZBPSZ02      -1.4579175  0.0083271  -175.080  < 2e-16 ***
DESTIN_SZBPSZ03      -1.0775392  0.0075109  -143.463  < 2e-16 ***
DESTIN_SZBPSZ04      -0.6645303  0.0058070  -114.436  < 2e-16 ***
DESTIN_SZBPSZ05       0.3449386  0.0039504    87.318  < 2e-16 ***
DESTIN_SZBPSZ06      -0.9360064  0.0077394  -120.941  < 2e-16 ***
DESTIN_SZBPSZ07      -0.6850065  0.0077761   -88.091  < 2e-16 ***
DESTIN_SZBSSZ01      -0.3144210  0.0045803   -68.647  < 2e-16 ***
DESTIN_SZBSSZ02      -0.7531935  0.0051075  -147.469  < 2e-16 ***
DESTIN_SZBSSZ03       0.1964072  0.0038255    51.342  < 2e-16 ***
DESTIN_SZBTSZ01       0.0749897  0.0041584    18.033  < 2e-16 ***
DESTIN_SZBTSZ02      -0.8214254  0.0065659  -125.105  < 2e-16 ***
DESTIN_SZBTSZ03      -0.1672596  0.0047942   -34.888  < 2e-16 ***
DESTIN_SZBTSZ04      -1.7727273  0.0103706  -170.938  < 2e-16 ***
DESTIN_SZBTSZ05      -0.8162630  0.0067401  -121.105  < 2e-16 ***
DESTIN_SZBTSZ06      -0.8159130  0.0059754  -136.546  < 2e-16 ***
DESTIN_SZBTSZ07      -2.1139258  0.0105602  -200.178  < 2e-16 ***
DESTIN_SZBTSZ08      -1.3565179  0.0086828  -156.231  < 2e-16 ***
DESTIN_SZCBSZ01      -4.6643129  0.3162417   -14.749  < 2e-16 ***
DESTIN_SZCCSZ01      -1.0088833  0.0080155  -125.866  < 2e-16 ***
DESTIN_SZCHSZ01      -1.1909317  0.0095262  -125.017  < 2e-16 ***
DESTIN_SZCHSZ02       0.0890035  0.0052277    17.025  < 2e-16 ***
DESTIN_SZCHSZ03       1.4883985  0.0039094   380.724  < 2e-16 ***
DESTIN_SZCKSZ01      -0.1684738  0.0047561   -35.422  < 2e-16 ***
DESTIN_SZCKSZ02      -0.4314614  0.0051537   -83.720  < 2e-16 ***
DESTIN_SZCKSZ03       0.6413457  0.0038639   165.983  < 2e-16 ***
DESTIN_SZCKSZ04      -0.6370791  0.0059869  -106.412  < 2e-16 ***
DESTIN_SZCKSZ05      -0.4185112  0.0065348   -64.044  < 2e-16 ***
DESTIN_SZCKSZ06       0.7003888  0.0045139   155.163  < 2e-16 ***
DESTIN_SZCLSZ01       0.3751343  0.0047400    79.143  < 2e-16 ***
DESTIN_SZCLSZ02      -2.2913668  0.0133371  -171.804  < 2e-16 ***
DESTIN_SZCLSZ03      -1.0498490  0.0076548  -137.149  < 2e-16 ***
DESTIN_SZCLSZ04      -0.1118915  0.0044886   -24.928  < 2e-16 ***
DESTIN_SZCLSZ05      -1.3113032  0.0084067  -155.983  < 2e-16 ***
DESTIN_SZCLSZ06       0.1661786  0.0040203    41.334  < 2e-16 ***
DESTIN_SZCLSZ07      -0.6429895  0.0052617  -122.202  < 2e-16 ***
DESTIN_SZCLSZ08      -0.4271702  0.0057208   -74.670  < 2e-16 ***
DESTIN_SZCLSZ09       0.3882136  0.0063758    60.888  < 2e-16 ***
DESTIN_SZDTSZ02      -3.0106480  0.0348374   -86.420  < 2e-16 ***
DESTIN_SZDTSZ03      -1.4195712  0.0144110   -98.506  < 2e-16 ***
DESTIN_SZDTSZ13      -2.2368573  0.0161427  -138.567  < 2e-16 ***
DESTIN_SZGLSZ01       0.0013721  0.0051224     0.268  0.78881    
DESTIN_SZGLSZ02      -0.3376674  0.0046195   -73.097  < 2e-16 ***
DESTIN_SZGLSZ03       0.3659900  0.0038384    95.350  < 2e-16 ***
DESTIN_SZGLSZ04       0.2969928  0.0038026    78.103  < 2e-16 ***
DESTIN_SZGLSZ05       0.1786445  0.0038853    45.980  < 2e-16 ***
DESTIN_SZHGSZ01       0.2979206  0.0038825    76.735  < 2e-16 ***
DESTIN_SZHGSZ02      -0.5701034  0.0051182  -111.388  < 2e-16 ***
DESTIN_SZHGSZ03      -1.0387610  0.0061020  -170.233  < 2e-16 ***
DESTIN_SZHGSZ04      -0.2264881  0.0043617   -51.926  < 2e-16 ***
DESTIN_SZHGSZ05      -0.2287090  0.0044851   -50.993  < 2e-16 ***
DESTIN_SZHGSZ06      -0.7896437  0.0054081  -146.010  < 2e-16 ***
DESTIN_SZHGSZ07       0.2268880  0.0040336    56.249  < 2e-16 ***
DESTIN_SZHGSZ08      -0.4260784  0.0048967   -87.013  < 2e-16 ***
DESTIN_SZHGSZ09       0.1027784  0.0051341    20.019  < 2e-16 ***
DESTIN_SZHGSZ10      -2.8571803  0.0262064  -109.026  < 2e-16 ***
DESTIN_SZJESZ01      -0.0843635  0.0048222   -17.495  < 2e-16 ***
DESTIN_SZJESZ02      -0.5197682  0.0051511  -100.904  < 2e-16 ***
DESTIN_SZJESZ03      -0.6250311  0.0056619  -110.392  < 2e-16 ***
DESTIN_SZJESZ04      -0.3937360  0.0065536   -60.080  < 2e-16 ***
DESTIN_SZJESZ05      -0.9748291  0.0097665   -99.814  < 2e-16 ***
DESTIN_SZJESZ06       0.3642736  0.0040600    89.722  < 2e-16 ***
DESTIN_SZJESZ07      -1.1571882  0.0081557  -141.887  < 2e-16 ***
DESTIN_SZJESZ08      -0.5955747  0.0078071   -76.286  < 2e-16 ***
DESTIN_SZJESZ09      -0.3629500  0.0053966   -67.256  < 2e-16 ***
DESTIN_SZJESZ10       0.7691552  0.0069348   110.912  < 2e-16 ***
DESTIN_SZJESZ11       0.9365743  0.0065801   142.335  < 2e-16 ***
DESTIN_SZJWSZ01      -0.4568805  0.0064536   -70.795  < 2e-16 ***
DESTIN_SZJWSZ02      -0.2880426  0.0051632   -55.788  < 2e-16 ***
DESTIN_SZJWSZ03       0.6680404  0.0039264   170.142  < 2e-16 ***
DESTIN_SZJWSZ04       0.9492158  0.0037186   255.262  < 2e-16 ***
DESTIN_SZJWSZ05      -0.1938053  0.0060810   -31.871  < 2e-16 ***
DESTIN_SZJWSZ06       0.3813164  0.0054551    69.900  < 2e-16 ***
DESTIN_SZJWSZ07      -1.2676010  0.0280038   -45.265  < 2e-16 ***
DESTIN_SZJWSZ08       0.5013149  0.0044573   112.471  < 2e-16 ***
DESTIN_SZJWSZ09       1.4161404  0.0033937   417.291  < 2e-16 ***
DESTIN_SZKLSZ01      -0.6909444  0.0051540  -134.059  < 2e-16 ***
DESTIN_SZKLSZ02      -0.8146023  0.0057129  -142.589  < 2e-16 ***
DESTIN_SZKLSZ03      -1.3956114  0.0065167  -214.161  < 2e-16 ***
DESTIN_SZKLSZ04      -1.9070281  0.0087370  -218.270  < 2e-16 ***
DESTIN_SZKLSZ05      -0.9293576  0.0071070  -130.766  < 2e-16 ***
DESTIN_SZKLSZ06      -2.5402234  0.0362062   -70.160  < 2e-16 ***
DESTIN_SZKLSZ07      -1.2017213  0.0065751  -182.769  < 2e-16 ***
DESTIN_SZKLSZ08      -0.6083433  0.0050916  -119.480  < 2e-16 ***
DESTIN_SZLKSZ01      -1.5186810  0.0204155   -74.389  < 2e-16 ***
DESTIN_SZMDSZ01      -1.4601772  0.0198347   -73.617  < 2e-16 ***
DESTIN_SZMDSZ02      -1.1554609  0.0111345  -103.773  < 2e-16 ***
DESTIN_SZMDSZ03      -2.9919337  0.0250838  -119.277  < 2e-16 ***
DESTIN_SZMPSZ01      -1.1705809  0.0077128  -151.771  < 2e-16 ***
DESTIN_SZMPSZ02      -0.9380957  0.0060321  -155.517  < 2e-16 ***
DESTIN_SZMPSZ03      -0.1761013  0.0046389   -37.962  < 2e-16 ***
DESTIN_SZMUSZ02      -2.4525115  0.0199630  -122.853  < 2e-16 ***
DESTIN_SZNTSZ01      -3.6605524  0.0447752   -81.754  < 2e-16 ***
DESTIN_SZNTSZ02      -2.0082021  0.0108736  -184.686  < 2e-16 ***
DESTIN_SZNTSZ03      -1.2387489  0.0076141  -162.691  < 2e-16 ***
DESTIN_SZNTSZ05      -1.8054361  0.0249540   -72.351  < 2e-16 ***
DESTIN_SZNTSZ06      -2.9500517  0.0428601   -68.830  < 2e-16 ***
DESTIN_SZNVSZ01      -0.4089022  0.0044288   -92.327  < 2e-16 ***
DESTIN_SZNVSZ02      -0.6865452  0.0052770  -130.102  < 2e-16 ***
DESTIN_SZNVSZ03      -0.7333670  0.0054243  -135.199  < 2e-16 ***
DESTIN_SZNVSZ04      -2.2095097  0.0106997  -206.503  < 2e-16 ***
DESTIN_SZNVSZ05      -1.8721104  0.0089058  -210.212  < 2e-16 ***
DESTIN_SZPGSZ01      -1.8756618  0.0153008  -122.586  < 2e-16 ***
DESTIN_SZPGSZ02      -0.9435337  0.0067224  -140.356  < 2e-16 ***
DESTIN_SZPGSZ03       0.3458476  0.0040152    86.134  < 2e-16 ***
DESTIN_SZPGSZ04      -0.0271485  0.0044805    -6.059 1.37e-09 ***
DESTIN_SZPGSZ05      -0.8920273  0.0070730  -126.117  < 2e-16 ***
DESTIN_SZPLSZ01      -0.2153087  0.0068270   -31.538  < 2e-16 ***
DESTIN_SZPLSZ02      -1.3646116  0.0131155  -104.046  < 2e-16 ***
DESTIN_SZPLSZ03      -0.0869245  0.0095838    -9.070  < 2e-16 ***
DESTIN_SZPLSZ04      -0.2574560  0.0093336   -27.584  < 2e-16 ***
DESTIN_SZPLSZ05      -0.7186364  0.0116835   -61.509  < 2e-16 ***
DESTIN_SZPNSZ01       1.1326963  0.0049977   226.643  < 2e-16 ***
DESTIN_SZPNSZ02       1.6516855  0.0064492   256.106  < 2e-16 ***
DESTIN_SZPNSZ03       0.8504093  0.0077034   110.394  < 2e-16 ***
DESTIN_SZPNSZ04       1.6891381  0.0075802   222.836  < 2e-16 ***
DESTIN_SZPNSZ05       0.7402750  0.0115948    63.845  < 2e-16 ***
DESTIN_SZPRSZ01      -1.0257636  0.0084652  -121.175  < 2e-16 ***
DESTIN_SZPRSZ02      -0.2028503  0.0049839   -40.701  < 2e-16 ***
DESTIN_SZPRSZ03       0.5560483  0.0038496   144.442  < 2e-16 ***
DESTIN_SZPRSZ04      -0.6824142  0.0079047   -86.330  < 2e-16 ***
DESTIN_SZPRSZ05       0.0316117  0.0044946     7.033 2.02e-12 ***
DESTIN_SZPRSZ06       0.3706283  0.0052006    71.267  < 2e-16 ***
DESTIN_SZPRSZ07      -1.4740460  0.0117304  -125.661  < 2e-16 ***
DESTIN_SZPRSZ08      -0.7869180  0.0064862  -121.321  < 2e-16 ***
DESTIN_SZQTSZ01      -1.2790095  0.0085392  -149.781  < 2e-16 ***
DESTIN_SZQTSZ02      -1.4989188  0.0073423  -204.149  < 2e-16 ***
DESTIN_SZQTSZ03      -0.9334132  0.0064035  -145.765  < 2e-16 ***
DESTIN_SZQTSZ04      -1.0506142  0.0065335  -160.805  < 2e-16 ***
DESTIN_SZQTSZ05      -0.9765013  0.0058471  -167.006  < 2e-16 ***
DESTIN_SZQTSZ06      -1.2206088  0.0063560  -192.042  < 2e-16 ***
DESTIN_SZQTSZ07      -1.6794007  0.0108727  -154.460  < 2e-16 ***
DESTIN_SZQTSZ08      -0.1214413  0.0047980   -25.311  < 2e-16 ***
DESTIN_SZQTSZ09      -0.5252607  0.0057371   -91.555  < 2e-16 ***
DESTIN_SZQTSZ10      -0.5981644  0.0054192  -110.378  < 2e-16 ***
DESTIN_SZQTSZ11      -0.0766021  0.0053446   -14.333  < 2e-16 ***
DESTIN_SZQTSZ12      -0.6153017  0.0070680   -87.054  < 2e-16 ***
DESTIN_SZQTSZ13      -0.1690535  0.0051315   -32.944  < 2e-16 ***
DESTIN_SZQTSZ14      -0.5398362  0.0062233   -86.744  < 2e-16 ***
DESTIN_SZQTSZ15      -0.1873015  0.0073132   -25.611  < 2e-16 ***
DESTIN_SZRCSZ01      -0.5875494  0.0071798   -81.833  < 2e-16 ***
DESTIN_SZRCSZ06      -2.0856090  0.0188789  -110.473  < 2e-16 ***
DESTIN_SZRVSZ01      -2.6183708  0.0162319  -161.310  < 2e-16 ***
DESTIN_SZRVSZ02      -3.1882190  0.0326141   -97.756  < 2e-16 ***
DESTIN_SZRVSZ03      -2.5981974  0.0135074  -192.353  < 2e-16 ***
DESTIN_SZRVSZ04      -1.9741504  0.0154961  -127.396  < 2e-16 ***
DESTIN_SZRVSZ05      -3.1547734  0.0256310  -123.084  < 2e-16 ***
DESTIN_SZSBSZ01      -0.3097949  0.0060601   -51.121  < 2e-16 ***
DESTIN_SZSBSZ02      -1.1229132  0.0076338  -147.097  < 2e-16 ***
DESTIN_SZSBSZ03       0.6289715  0.0041400   151.926  < 2e-16 ***
DESTIN_SZSBSZ04       0.1419430  0.0051357    27.638  < 2e-16 ***
DESTIN_SZSBSZ05      -0.9256413  0.0071963  -128.628  < 2e-16 ***
DESTIN_SZSBSZ06      -2.3487368  0.0221611  -105.984  < 2e-16 ***
DESTIN_SZSBSZ07      -0.7864630  0.0181706   -43.282  < 2e-16 ***
DESTIN_SZSBSZ08       1.3240051  0.0051598   256.599  < 2e-16 ***
DESTIN_SZSBSZ09       0.8431156  0.0048330   174.449  < 2e-16 ***
DESTIN_SZSESZ02      -0.2385874  0.0046618   -51.180  < 2e-16 ***
DESTIN_SZSESZ03       0.5439188  0.0036932   147.276  < 2e-16 ***
DESTIN_SZSESZ04      -0.6715716  0.0054222  -123.856  < 2e-16 ***
DESTIN_SZSESZ05      -0.3601932  0.0047508   -75.818  < 2e-16 ***
DESTIN_SZSESZ06      -0.6088413  0.0057017  -106.782  < 2e-16 ***
DESTIN_SZSESZ07      -2.9477507  0.0226797  -129.973  < 2e-16 ***
DESTIN_SZSGSZ01      -0.5100640  0.0058280   -87.519  < 2e-16 ***
DESTIN_SZSGSZ02      -0.0439941  0.0051633    -8.520  < 2e-16 ***
DESTIN_SZSGSZ03      -0.3700648  0.0047152   -78.483  < 2e-16 ***
DESTIN_SZSGSZ04      -0.3021335  0.0046865   -64.468  < 2e-16 ***
DESTIN_SZSGSZ05      -2.2253287  0.0097908  -227.288  < 2e-16 ***
DESTIN_SZSGSZ06       0.2963602  0.0037948    78.097  < 2e-16 ***
DESTIN_SZSGSZ07      -0.5940373  0.0051371  -115.637  < 2e-16 ***
DESTIN_SZSISZ01      -1.4528976  0.0257790   -56.360  < 2e-16 ***
DESTIN_SZSKSZ01      -0.0374952  0.0066885    -5.606 2.07e-08 ***
DESTIN_SZSKSZ02       0.7271418  0.0050281   144.617  < 2e-16 ***
DESTIN_SZSKSZ03      -0.0640794  0.0059146   -10.834  < 2e-16 ***
DESTIN_SZSKSZ04      -0.5610767  0.0139676   -40.170  < 2e-16 ***
DESTIN_SZSKSZ05       0.1510974  0.0104871    14.408  < 2e-16 ***
DESTIN_SZSLSZ01      -0.5823031  0.0083356   -69.858  < 2e-16 ***
DESTIN_SZSLSZ04      -0.8166665  0.0070329  -116.122  < 2e-16 ***
DESTIN_SZSRSZ01      -2.3241796  0.0127215  -182.696  < 2e-16 ***
DESTIN_SZTHSZ01      -2.8157635  0.0366840   -76.757  < 2e-16 ***
DESTIN_SZTHSZ03      -2.1005978  0.0250842   -83.742  < 2e-16 ***
DESTIN_SZTHSZ04      -2.1246250  0.0213690   -99.425  < 2e-16 ***
DESTIN_SZTHSZ06      -1.4571092  0.0150031   -97.121  < 2e-16 ***
DESTIN_SZTMSZ01      -0.1234559  0.0055152   -22.385  < 2e-16 ***
DESTIN_SZTMSZ02       1.5961628  0.0032599   489.635  < 2e-16 ***
DESTIN_SZTMSZ03       0.6977233  0.0037138   187.875  < 2e-16 ***
DESTIN_SZTMSZ04       0.8606606  0.0037592   228.947  < 2e-16 ***
DESTIN_SZTMSZ05       0.3750655  0.0051281    73.140  < 2e-16 ***
DESTIN_SZTNSZ01      -1.2624562  0.0066979  -188.485  < 2e-16 ***
DESTIN_SZTNSZ02      -2.0761581  0.0096538  -215.062  < 2e-16 ***
DESTIN_SZTNSZ03      -2.1128125  0.0115717  -182.584  < 2e-16 ***
DESTIN_SZTNSZ04      -1.2417494  0.0068502  -181.271  < 2e-16 ***
DESTIN_SZTPSZ01      -0.7094356  0.0055768  -127.211  < 2e-16 ***
DESTIN_SZTPSZ02       0.1491604  0.0037260    40.032  < 2e-16 ***
DESTIN_SZTPSZ03      -0.4973355  0.0054878   -90.626  < 2e-16 ***
DESTIN_SZTPSZ04      -1.5160395  0.0071592  -211.761  < 2e-16 ***
DESTIN_SZTPSZ05      -0.9196565  0.0056750  -162.054  < 2e-16 ***
DESTIN_SZTPSZ06      -0.2710649  0.0062637   -43.276  < 2e-16 ***
DESTIN_SZTPSZ07      -2.0198681  0.0116556  -173.296  < 2e-16 ***
DESTIN_SZTPSZ08      -1.4881412  0.0085532  -173.987  < 2e-16 ***
DESTIN_SZTPSZ09      -0.5901273  0.0059394   -99.358  < 2e-16 ***
DESTIN_SZTPSZ10      -1.1215711  0.0084488  -132.749  < 2e-16 ***
DESTIN_SZTPSZ11      -0.4837089  0.0050905   -95.022  < 2e-16 ***
DESTIN_SZTPSZ12      -0.8653927  0.0061326  -141.113  < 2e-16 ***
DESTIN_SZTSSZ01      -0.5515103  0.0208541   -26.446  < 2e-16 ***
DESTIN_SZTSSZ02       0.8373778  0.0093757    89.314  < 2e-16 ***
DESTIN_SZTSSZ03       1.7021888  0.0064394   264.340  < 2e-16 ***
DESTIN_SZTSSZ04       1.5355016  0.0067855   226.292  < 2e-16 ***
DESTIN_SZTSSZ05       1.6932319  0.0073725   229.668  < 2e-16 ***
DESTIN_SZTSSZ06       0.4567808  0.0137927    33.118  < 2e-16 ***
DESTIN_SZWCSZ01       1.3967640  0.0045392   307.711  < 2e-16 ***
DESTIN_SZWCSZ02      -0.4560229  0.0122949   -37.090  < 2e-16 ***
DESTIN_SZWCSZ03      -2.0710051  0.0325121   -63.699  < 2e-16 ***
DESTIN_SZWDSZ01       1.5137342  0.0034774   435.310  < 2e-16 ***
DESTIN_SZWDSZ02      -0.3005475  0.0055149   -54.497  < 2e-16 ***
DESTIN_SZWDSZ03       1.2514543  0.0036112   346.550  < 2e-16 ***
DESTIN_SZWDSZ04      -0.1702528  0.0058295   -29.205  < 2e-16 ***
DESTIN_SZWDSZ05      -0.0005419  0.0053911    -0.101  0.91994    
DESTIN_SZWDSZ06       0.5203361  0.0040318   129.058  < 2e-16 ***
DESTIN_SZWDSZ07       0.6006472  0.0061745    97.279  < 2e-16 ***
DESTIN_SZWDSZ08       0.6650867  0.0060867   109.268  < 2e-16 ***
DESTIN_SZWDSZ09       0.6237312  0.0044830   139.132  < 2e-16 ***
DESTIN_SZYSSZ01       1.0471638  0.0038255   273.732  < 2e-16 ***
DESTIN_SZYSSZ02       0.2341114  0.0048213    48.558  < 2e-16 ***
DESTIN_SZYSSZ03      -0.0916446  0.0051335   -17.852  < 2e-16 ***
DESTIN_SZYSSZ04      -0.0085536  0.0048684    -1.757  0.07892 .  
DESTIN_SZYSSZ05      -1.5775071  0.0100297  -157.283  < 2e-16 ***
DESTIN_SZYSSZ06      -1.8130307  0.0098617  -183.846  < 2e-16 ***
DESTIN_SZYSSZ07      -1.1703963  0.0111525  -104.945  < 2e-16 ***
DESTIN_SZYSSZ08       0.5253514  0.0039556   132.813  < 2e-16 ***
DESTIN_SZYSSZ09       0.4353435  0.0038890   111.943  < 2e-16 ***
log(ORIGIN_AGE25_64)  0.2249135  0.0001404  1602.353  < 2e-16 ***
log(dist)            -0.6989356  0.0001287 -5431.279  < 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: 60796037  on 14733  degrees of freedom
Residual deviance: 26208384  on 14452  degrees of freedom
AIC: 26300575

Number of Fisher Scoring iterations: 7

Now to examine how the constraints hold for destinations this time.

CalcRSquared(decSIM$data$TRIPS, decSIM$fitted.values)

[1] 0.4972985

8.8 Doubly constrained

This section demonstrates fitting a doubly constrained Spatial Interaction Model (SIM) using the code chunk below.

The general formula for a Doubly Constrained Spatial Interaction Model is outlined below.

dbcSIM <- glm(formula = TRIPS ~ 
                ORIGIN_SZ + 
                DESTIN_SZ + 
                log(dist),
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
summary(dbcSIM)


Call:
glm(formula = TRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(dist), family = poisson(link = "log"), 
    data = SIM_data, na.action = na.exclude)

Coefficients:
                  Estimate Std. Error   z value Pr(>|z|)    
(Intercept)     12.4165310  0.0043949  2825.242  < 2e-16 ***
ORIGIN_SZAMSZ02  0.9496891  0.0045740   207.630  < 2e-16 ***
ORIGIN_SZAMSZ03  0.5519174  0.0046672   118.253  < 2e-16 ***
ORIGIN_SZAMSZ04  0.1028140  0.0052468    19.596  < 2e-16 ***
ORIGIN_SZAMSZ05  0.0822549  0.0058663    14.022  < 2e-16 ***
ORIGIN_SZAMSZ06  0.6617809  0.0052580   125.861  < 2e-16 ***
ORIGIN_SZAMSZ07 -0.9508298  0.0097681   -97.340  < 2e-16 ***
ORIGIN_SZAMSZ08 -0.7271779  0.0090946   -79.958  < 2e-16 ***
ORIGIN_SZAMSZ09  0.4896781  0.0055203    88.704  < 2e-16 ***
ORIGIN_SZAMSZ10  0.4819428  0.0048175   100.040  < 2e-16 ***
ORIGIN_SZAMSZ11 -1.7719841  0.0130695  -135.582  < 2e-16 ***
ORIGIN_SZAMSZ12 -1.7679107  0.0108777  -162.526  < 2e-16 ***
ORIGIN_SZBDSZ01  0.8314812  0.0045187   184.010  < 2e-16 ***
ORIGIN_SZBDSZ02  0.4305836  0.0052535    81.961  < 2e-16 ***
ORIGIN_SZBDSZ03  0.8009370  0.0046384   172.676  < 2e-16 ***
ORIGIN_SZBDSZ04  1.4562985  0.0040456   359.971  < 2e-16 ***
ORIGIN_SZBDSZ05  0.4501939  0.0046960    95.867  < 2e-16 ***
ORIGIN_SZBDSZ06  0.7745026  0.0047424   163.314  < 2e-16 ***
ORIGIN_SZBDSZ07 -1.1784123  0.0098105  -120.117  < 2e-16 ***
ORIGIN_SZBDSZ08 -0.9830996  0.0091135  -107.873  < 2e-16 ***
ORIGIN_SZBKSZ01 -0.3042966  0.0067086   -45.359  < 2e-16 ***
ORIGIN_SZBKSZ02  0.4801541  0.0054160    88.655  < 2e-16 ***
ORIGIN_SZBKSZ03  0.7823931  0.0052007   150.440  < 2e-16 ***
ORIGIN_SZBKSZ04 -0.1292545  0.0061735   -20.937  < 2e-16 ***
ORIGIN_SZBKSZ05 -0.0258584  0.0060192    -4.296 1.74e-05 ***
ORIGIN_SZBKSZ06  0.1994719  0.0061206    32.590  < 2e-16 ***
ORIGIN_SZBKSZ07  0.7434860  0.0046598   159.553  < 2e-16 ***
ORIGIN_SZBKSZ08  0.1625007  0.0055219    29.428  < 2e-16 ***
ORIGIN_SZBKSZ09 -0.0864293  0.0059533   -14.518  < 2e-16 ***
ORIGIN_SZBLSZ01 -2.1022485  0.0150316  -139.855  < 2e-16 ***
ORIGIN_SZBLSZ02 -2.9460181  0.0195760  -150.491  < 2e-16 ***
ORIGIN_SZBLSZ03 -4.9412872  0.0398540  -123.985  < 2e-16 ***
ORIGIN_SZBLSZ04 -2.8143593  0.0239209  -117.653  < 2e-16 ***
ORIGIN_SZBMSZ01 -0.0264561  0.0053639    -4.932 8.13e-07 ***
ORIGIN_SZBMSZ02 -0.8656513  0.0068511  -126.353  < 2e-16 ***
ORIGIN_SZBMSZ03 -0.1723467  0.0059613   -28.911  < 2e-16 ***
ORIGIN_SZBMSZ04  0.2169844  0.0053578    40.499  < 2e-16 ***
ORIGIN_SZBMSZ05 -2.0252956  0.0126107  -160.602  < 2e-16 ***
ORIGIN_SZBMSZ06 -1.7642018  0.0163931  -107.619  < 2e-16 ***
ORIGIN_SZBMSZ07 -0.3271629  0.0058137   -56.274  < 2e-16 ***
ORIGIN_SZBMSZ08 -0.2533255  0.0059335   -42.694  < 2e-16 ***
ORIGIN_SZBMSZ09 -0.7712635  0.0087939   -87.704  < 2e-16 ***
ORIGIN_SZBMSZ10 -1.0098048  0.0092519  -109.145  < 2e-16 ***
ORIGIN_SZBMSZ11 -0.3816187  0.0067302   -56.702  < 2e-16 ***
ORIGIN_SZBMSZ12 -0.6666616  0.0095680   -69.676  < 2e-16 ***
ORIGIN_SZBMSZ13 -0.0076108  0.0059040    -1.289  0.19737    
ORIGIN_SZBMSZ14 -0.1682476  0.0069391   -24.246  < 2e-16 ***
ORIGIN_SZBMSZ15  0.0904585  0.0062822    14.399  < 2e-16 ***
ORIGIN_SZBMSZ16 -1.1808741  0.0092258  -127.997  < 2e-16 ***
ORIGIN_SZBMSZ17 -1.7189127  0.0158408  -108.512  < 2e-16 ***
ORIGIN_SZBPSZ01  0.4294645  0.0058051    73.980  < 2e-16 ***
ORIGIN_SZBPSZ02  0.5028906  0.0068169    73.771  < 2e-16 ***
ORIGIN_SZBPSZ03  0.6656178  0.0066126   100.658  < 2e-16 ***
ORIGIN_SZBPSZ04  0.5203612  0.0053224    97.769  < 2e-16 ***
ORIGIN_SZBPSZ05  0.5377769  0.0047907   112.256  < 2e-16 ***
ORIGIN_SZBPSZ06 -1.2327809  0.0094950  -129.835  < 2e-16 ***
ORIGIN_SZBPSZ07 -0.9035255  0.0088739  -101.818  < 2e-16 ***
ORIGIN_SZBSSZ01  0.1210027  0.0053990    22.412  < 2e-16 ***
ORIGIN_SZBSSZ02  0.4618449  0.0048641    94.951  < 2e-16 ***
ORIGIN_SZBSSZ03  0.2160739  0.0047835    45.170  < 2e-16 ***
ORIGIN_SZBTSZ01 -0.1108042  0.0055599   -19.929  < 2e-16 ***
ORIGIN_SZBTSZ02 -0.8911221  0.0079213  -112.498  < 2e-16 ***
ORIGIN_SZBTSZ03 -0.2203980  0.0059325   -37.151  < 2e-16 ***
ORIGIN_SZBTSZ04 -0.6427946  0.0105438   -60.964  < 2e-16 ***
ORIGIN_SZBTSZ05 -1.4662312  0.0111784  -131.166  < 2e-16 ***
ORIGIN_SZBTSZ06 -0.6105884  0.0073456   -83.123  < 2e-16 ***
ORIGIN_SZBTSZ07 -1.9041317  0.0132781  -143.404  < 2e-16 ***
ORIGIN_SZBTSZ08 -1.0627939  0.0095982  -110.728  < 2e-16 ***
ORIGIN_SZCBSZ01 -2.9365941  0.0548632   -53.526  < 2e-16 ***
ORIGIN_SZCCSZ01 -1.5313555  0.0134599  -113.772  < 2e-16 ***
ORIGIN_SZCHSZ01 -1.2034494  0.0119468  -100.734  < 2e-16 ***
ORIGIN_SZCHSZ02 -0.8299415  0.0081984  -101.232  < 2e-16 ***
ORIGIN_SZCHSZ03 -0.5143946  0.0061944   -83.042  < 2e-16 ***
ORIGIN_SZCKSZ01  0.2372583  0.0053612    44.255  < 2e-16 ***
ORIGIN_SZCKSZ02  0.9124836  0.0054472   167.515  < 2e-16 ***
ORIGIN_SZCKSZ03  0.7237808  0.0048401   149.539  < 2e-16 ***
ORIGIN_SZCKSZ04  1.6884022  0.0050169   336.540  < 2e-16 ***
ORIGIN_SZCKSZ05  1.3932005  0.0062346   223.464  < 2e-16 ***
ORIGIN_SZCKSZ06  1.0670053  0.0066112   161.394  < 2e-16 ***
ORIGIN_SZCLSZ01 -0.8602837  0.0079240  -108.567  < 2e-16 ***
ORIGIN_SZCLSZ02 -1.3853421  0.0137444  -100.793  < 2e-16 ***
ORIGIN_SZCLSZ03 -0.8582608  0.0081177  -105.727  < 2e-16 ***
ORIGIN_SZCLSZ04  0.7836027  0.0046427   168.782  < 2e-16 ***
ORIGIN_SZCLSZ05 -1.8121756  0.0148960  -121.655  < 2e-16 ***
ORIGIN_SZCLSZ06  0.8296870  0.0043909   188.955  < 2e-16 ***
ORIGIN_SZCLSZ07 -0.2325219  0.0057432   -40.487  < 2e-16 ***
ORIGIN_SZCLSZ08  0.2714336  0.0062625    43.342  < 2e-16 ***
ORIGIN_SZCLSZ09 -2.2223744  0.0160946  -138.082  < 2e-16 ***
ORIGIN_SZDTSZ02 -4.0704970  0.0834192   -48.796  < 2e-16 ***
ORIGIN_SZDTSZ03 -3.4529031  0.0738295   -46.769  < 2e-16 ***
ORIGIN_SZDTSZ13 -2.8301983  0.0313085   -90.397  < 2e-16 ***
ORIGIN_SZGLSZ01 -1.4674986  0.0093137  -157.563  < 2e-16 ***
ORIGIN_SZGLSZ02  0.2749369  0.0050051    54.931  < 2e-16 ***
ORIGIN_SZGLSZ03  0.0781954  0.0049748    15.718  < 2e-16 ***
ORIGIN_SZGLSZ04  0.8167797  0.0043260   188.808  < 2e-16 ***
ORIGIN_SZGLSZ05  0.5277509  0.0044879   117.595  < 2e-16 ***
ORIGIN_SZHGSZ01  0.2323885  0.0048555    47.861  < 2e-16 ***
ORIGIN_SZHGSZ02  0.5707182  0.0048256   118.268  < 2e-16 ***
ORIGIN_SZHGSZ03  0.4231170  0.0052149    81.136  < 2e-16 ***
ORIGIN_SZHGSZ04  0.9341168  0.0044128   211.681  < 2e-16 ***
ORIGIN_SZHGSZ05  1.2192790  0.0043790   278.437  < 2e-16 ***
ORIGIN_SZHGSZ06  0.0490041  0.0054961     8.916  < 2e-16 ***
ORIGIN_SZHGSZ07  0.6337041  0.0045735   138.559  < 2e-16 ***
ORIGIN_SZHGSZ08  0.0312612  0.0054684     5.717 1.09e-08 ***
ORIGIN_SZHGSZ09 -0.6985397  0.0071800   -97.289  < 2e-16 ***
ORIGIN_SZHGSZ10 -2.9958967  0.0422303   -70.942  < 2e-16 ***
ORIGIN_SZJESZ01  0.4363431  0.0051329    85.010  < 2e-16 ***
ORIGIN_SZJESZ02  0.3460900  0.0051372    67.370  < 2e-16 ***
ORIGIN_SZJESZ03  0.2928005  0.0055108    53.132  < 2e-16 ***
ORIGIN_SZJESZ04 -1.1924298  0.0093540  -127.478  < 2e-16 ***
ORIGIN_SZJESZ05 -2.0178136  0.0139479  -144.668  < 2e-16 ***
ORIGIN_SZJESZ06  0.1637633  0.0050685    32.310  < 2e-16 ***
ORIGIN_SZJESZ07 -1.8227460  0.0119383  -152.680  < 2e-16 ***
ORIGIN_SZJESZ08 -1.1556281  0.0117870   -98.043  < 2e-16 ***
ORIGIN_SZJESZ09  0.4766229  0.0052813    90.248  < 2e-16 ***
ORIGIN_SZJESZ10 -2.6868992  0.0186864  -143.789  < 2e-16 ***
ORIGIN_SZJESZ11 -3.0618150  0.0199755  -153.278  < 2e-16 ***
ORIGIN_SZJWSZ01  0.4417418  0.0068611    64.383  < 2e-16 ***
ORIGIN_SZJWSZ02  0.9738087  0.0047905   203.281  < 2e-16 ***
ORIGIN_SZJWSZ03  1.1548028  0.0045180   255.599  < 2e-16 ***
ORIGIN_SZJWSZ04  0.9078417  0.0046668   194.532  < 2e-16 ***
ORIGIN_SZJWSZ05 -1.7092500  0.0127422  -134.141  < 2e-16 ***
ORIGIN_SZJWSZ06 -1.3284287  0.0109785  -121.002  < 2e-16 ***
ORIGIN_SZJWSZ07 -2.3231549  0.0281427   -82.549  < 2e-16 ***
ORIGIN_SZJWSZ08  1.9386127  0.0046041   421.059  < 2e-16 ***
ORIGIN_SZJWSZ09  1.3987549  0.0042610   328.266  < 2e-16 ***
ORIGIN_SZKLSZ01  0.2617735  0.0050089    52.261  < 2e-16 ***
ORIGIN_SZKLSZ02 -0.4325093  0.0064279   -67.286  < 2e-16 ***
ORIGIN_SZKLSZ03 -0.2787173  0.0060380   -46.161  < 2e-16 ***
ORIGIN_SZKLSZ04 -1.9432693  0.0119163  -163.076  < 2e-16 ***
ORIGIN_SZKLSZ05 -0.5420067  0.0085529   -63.371  < 2e-16 ***
ORIGIN_SZKLSZ06 -4.2949009  0.1857686   -23.120  < 2e-16 ***
ORIGIN_SZKLSZ07 -0.8576946  0.0085178  -100.694  < 2e-16 ***
ORIGIN_SZKLSZ08 -1.3840925  0.0092323  -149.918  < 2e-16 ***
ORIGIN_SZLKSZ01 -2.8108510  0.0392356   -71.640  < 2e-16 ***
ORIGIN_SZMDSZ01 -1.6745388  0.0296543   -56.469  < 2e-16 ***
ORIGIN_SZMDSZ02 -0.8193738  0.0106631   -76.842  < 2e-16 ***
ORIGIN_SZMDSZ03 -1.5088267  0.0172032   -87.706  < 2e-16 ***
ORIGIN_SZMPSZ01 -0.9860154  0.0085053  -115.929  < 2e-16 ***
ORIGIN_SZMPSZ02 -0.5958875  0.0070097   -85.008  < 2e-16 ***
ORIGIN_SZMPSZ03 -0.0490122  0.0054582    -8.980  < 2e-16 ***
ORIGIN_SZMUSZ02 -3.5233367  0.1037749   -33.952  < 2e-16 ***
ORIGIN_SZNTSZ01 -2.6451541  0.0353125   -74.907  < 2e-16 ***
ORIGIN_SZNTSZ02 -2.7710546  0.0232841  -119.011  < 2e-16 ***
ORIGIN_SZNTSZ03 -0.6123404  0.0079083   -77.430  < 2e-16 ***
ORIGIN_SZNTSZ05 -2.9257445  0.0496704   -58.903  < 2e-16 ***
ORIGIN_SZNTSZ06 -3.3260031  0.0557966   -59.609  < 2e-16 ***
ORIGIN_SZNVSZ01  0.6421306  0.0046037   139.482  < 2e-16 ***
ORIGIN_SZNVSZ02 -0.4251550  0.0065890   -64.525  < 2e-16 ***
ORIGIN_SZNVSZ03 -1.0765622  0.0078766  -136.679  < 2e-16 ***
ORIGIN_SZNVSZ04 -1.2289504  0.0091468  -134.358  < 2e-16 ***
ORIGIN_SZNVSZ05 -2.3551389  0.0158219  -148.853  < 2e-16 ***
ORIGIN_SZPGSZ01  0.1518212  0.0154825     9.806  < 2e-16 ***
ORIGIN_SZPGSZ02 -0.4062609  0.0073780   -55.064  < 2e-16 ***
ORIGIN_SZPGSZ03  0.8976913  0.0046122   194.636  < 2e-16 ***
ORIGIN_SZPGSZ04  1.1161685  0.0045850   243.437  < 2e-16 ***
ORIGIN_SZPGSZ05  0.4794249  0.0060213    79.621  < 2e-16 ***
ORIGIN_SZPLSZ01 -0.8322377  0.0107898   -77.132  < 2e-16 ***
ORIGIN_SZPLSZ02 -1.2968937  0.0149841   -86.551  < 2e-16 ***
ORIGIN_SZPLSZ03 -3.2744991  0.0374541   -87.427  < 2e-16 ***
ORIGIN_SZPLSZ04 -3.5423615  0.0372570   -95.079  < 2e-16 ***
ORIGIN_SZPLSZ05 -2.4343705  0.0227807  -106.861  < 2e-16 ***
ORIGIN_SZPNSZ01  0.8052461  0.0056124   143.476  < 2e-16 ***
ORIGIN_SZPNSZ02 -1.8042362  0.0128222  -140.712  < 2e-16 ***
ORIGIN_SZPNSZ03 -2.6363996  0.0200058  -131.782  < 2e-16 ***
ORIGIN_SZPNSZ04 -4.8427070  0.0320126  -151.275  < 2e-16 ***
ORIGIN_SZPNSZ05 -3.6613775  0.0285686  -128.161  < 2e-16 ***
ORIGIN_SZPRSZ01 -0.5645384  0.0117126   -48.199  < 2e-16 ***
ORIGIN_SZPRSZ02  0.9145886  0.0048137   189.998  < 2e-16 ***
ORIGIN_SZPRSZ03  0.4478971  0.0048102    93.113  < 2e-16 ***
ORIGIN_SZPRSZ04 -0.5312444  0.0079019   -67.230  < 2e-16 ***
ORIGIN_SZPRSZ05  1.1462662  0.0045250   253.318  < 2e-16 ***
ORIGIN_SZPRSZ06 -0.7392744  0.0090347   -81.826  < 2e-16 ***
ORIGIN_SZPRSZ07 -2.1667862  0.0162528  -133.318  < 2e-16 ***
ORIGIN_SZPRSZ08 -0.1327079  0.0065712   -20.195  < 2e-16 ***
ORIGIN_SZQTSZ01  0.1062151  0.0071538    14.847  < 2e-16 ***
ORIGIN_SZQTSZ02 -0.4993990  0.0064382   -77.568  < 2e-16 ***
ORIGIN_SZQTSZ03  0.1161844  0.0058822    19.752  < 2e-16 ***
ORIGIN_SZQTSZ04 -0.8102612  0.0072742  -111.389  < 2e-16 ***
ORIGIN_SZQTSZ05 -0.0417272  0.0061917    -6.739 1.59e-11 ***
ORIGIN_SZQTSZ06 -0.2521417  0.0066449   -37.945  < 2e-16 ***
ORIGIN_SZQTSZ07 -1.2395975  0.0097496  -127.143  < 2e-16 ***
ORIGIN_SZQTSZ08 -0.1105467  0.0059364   -18.622  < 2e-16 ***
ORIGIN_SZQTSZ09 -0.5078461  0.0067895   -74.798  < 2e-16 ***
ORIGIN_SZQTSZ10 -0.3866593  0.0066995   -57.714  < 2e-16 ***
ORIGIN_SZQTSZ11 -1.5264609  0.0099770  -152.998  < 2e-16 ***
ORIGIN_SZQTSZ12 -1.3866518  0.0106887  -129.730  < 2e-16 ***
ORIGIN_SZQTSZ13 -0.3764286  0.0066707   -56.430  < 2e-16 ***
ORIGIN_SZQTSZ14 -1.4907399  0.0100120  -148.896  < 2e-16 ***
ORIGIN_SZQTSZ15 -1.0552239  0.0108792   -96.994  < 2e-16 ***
ORIGIN_SZRCSZ01 -1.3136074  0.0126986  -103.445  < 2e-16 ***
ORIGIN_SZRCSZ06 -0.2418276  0.0085509   -28.281  < 2e-16 ***
ORIGIN_SZRVSZ01 -2.9263747  0.0324968   -90.051  < 2e-16 ***
ORIGIN_SZRVSZ02 -2.2980940  0.0278202   -82.605  < 2e-16 ***
ORIGIN_SZRVSZ03 -2.4663765  0.0238674  -103.336  < 2e-16 ***
ORIGIN_SZRVSZ04 -3.1853677  0.0556939   -57.194  < 2e-16 ***
ORIGIN_SZRVSZ05 -1.5695490  0.0166684   -94.163  < 2e-16 ***
ORIGIN_SZSBSZ01  0.7674590  0.0061811   124.163  < 2e-16 ***
ORIGIN_SZSBSZ02 -0.7307279  0.0084105   -86.883  < 2e-16 ***
ORIGIN_SZSBSZ03  0.5920074  0.0050167   118.008  < 2e-16 ***
ORIGIN_SZSBSZ04  0.3684857  0.0058575    62.908  < 2e-16 ***
ORIGIN_SZSBSZ05 -0.0036863  0.0068459    -0.538  0.59026    
ORIGIN_SZSBSZ06 -1.1939284  0.0181541   -65.766  < 2e-16 ***
ORIGIN_SZSBSZ07 -0.4896579  0.0135618   -36.106  < 2e-16 ***
ORIGIN_SZSBSZ08 -2.1221691  0.0127258  -166.762  < 2e-16 ***
ORIGIN_SZSBSZ09 -1.2032410  0.0089611  -134.273  < 2e-16 ***
ORIGIN_SZSESZ02  1.0721820  0.0045336   236.498  < 2e-16 ***
ORIGIN_SZSESZ03  1.0808012  0.0042923   251.801  < 2e-16 ***
ORIGIN_SZSESZ04  1.0137448  0.0050668   200.076  < 2e-16 ***
ORIGIN_SZSESZ05 -0.1678679  0.0060206   -27.882  < 2e-16 ***
ORIGIN_SZSESZ06  0.9165834  0.0048323   189.677  < 2e-16 ***
ORIGIN_SZSESZ07 -2.2499789  0.0196327  -114.603  < 2e-16 ***
ORIGIN_SZSGSZ01 -0.9369800  0.0087282  -107.351  < 2e-16 ***
ORIGIN_SZSGSZ02 -1.1690716  0.0097131  -120.360  < 2e-16 ***
ORIGIN_SZSGSZ03  0.2604352  0.0052709    49.410  < 2e-16 ***
ORIGIN_SZSGSZ04  0.3468823  0.0048897    70.942  < 2e-16 ***
ORIGIN_SZSGSZ05 -1.5927797  0.0106308  -149.827  < 2e-16 ***
ORIGIN_SZSGSZ06  0.3605651  0.0046361    77.774  < 2e-16 ***
ORIGIN_SZSGSZ07 -0.5333873  0.0063119   -84.504  < 2e-16 ***
ORIGIN_SZSKSZ01 -0.2706750  0.0082836   -32.676  < 2e-16 ***
ORIGIN_SZSKSZ02  0.0970953  0.0063378    15.320  < 2e-16 ***
ORIGIN_SZSKSZ03 -0.6954342  0.0082538   -84.256  < 2e-16 ***
ORIGIN_SZSKSZ04 -2.3863580  0.0284607   -83.847  < 2e-16 ***
ORIGIN_SZSKSZ05 -1.5443140  0.0179059   -86.246  < 2e-16 ***
ORIGIN_SZSLSZ01 -2.9450656  0.0307283   -95.842  < 2e-16 ***
ORIGIN_SZSLSZ04 -0.5739349  0.0077851   -73.722  < 2e-16 ***
ORIGIN_SZSRSZ01 -1.6136735  0.0160199  -100.729  < 2e-16 ***
ORIGIN_SZTHSZ01 -2.6034976  0.0489378   -53.200  < 2e-16 ***
ORIGIN_SZTHSZ03 -1.2770601  0.0229815   -55.569  < 2e-16 ***
ORIGIN_SZTHSZ04 -2.0110399  0.0287527   -69.943  < 2e-16 ***
ORIGIN_SZTHSZ06 -1.7720116  0.0180394   -98.230  < 2e-16 ***
ORIGIN_SZTMSZ01  0.1254729  0.0060924    20.595  < 2e-16 ***
ORIGIN_SZTMSZ02  1.6667504  0.0039836   418.403  < 2e-16 ***
ORIGIN_SZTMSZ03  1.0941176  0.0042911   254.976  < 2e-16 ***
ORIGIN_SZTMSZ04  0.3209520  0.0050349    63.746  < 2e-16 ***
ORIGIN_SZTMSZ05 -0.8155124  0.0079342  -102.785  < 2e-16 ***
ORIGIN_SZTNSZ01 -1.4237298  0.0104636  -136.064  < 2e-16 ***
ORIGIN_SZTNSZ02 -1.2718890  0.0098660  -128.916  < 2e-16 ***
ORIGIN_SZTNSZ03 -1.7960517  0.0134675  -133.362  < 2e-16 ***
ORIGIN_SZTNSZ04 -0.3508142  0.0073556   -47.694  < 2e-16 ***
ORIGIN_SZTPSZ01 -0.3841699  0.0064137   -59.898  < 2e-16 ***
ORIGIN_SZTPSZ02  0.5315265  0.0044497   119.451  < 2e-16 ***
ORIGIN_SZTPSZ03 -0.4669723  0.0062160   -75.124  < 2e-16 ***
ORIGIN_SZTPSZ04 -0.0617169  0.0058830   -10.491  < 2e-16 ***
ORIGIN_SZTPSZ05  0.0713309  0.0062133    11.480  < 2e-16 ***
ORIGIN_SZTPSZ06  0.6800356  0.0069456    97.909  < 2e-16 ***
ORIGIN_SZTPSZ07 -0.0432782  0.0064382    -6.722 1.79e-11 ***
ORIGIN_SZTPSZ08 -0.6976429  0.0092416   -75.490  < 2e-16 ***
ORIGIN_SZTPSZ09 -0.3708833  0.0063548   -58.363  < 2e-16 ***
ORIGIN_SZTPSZ10 -0.4063575  0.0077803   -52.229  < 2e-16 ***
ORIGIN_SZTPSZ11  0.1040282  0.0056115    18.538  < 2e-16 ***
ORIGIN_SZTPSZ12 -0.5104672  0.0066261   -77.039  < 2e-16 ***
ORIGIN_SZTSSZ01 -3.5036830  0.0487290   -71.901  < 2e-16 ***
ORIGIN_SZTSSZ02 -0.0386819  0.0094886    -4.077 4.57e-05 ***
ORIGIN_SZTSSZ03 -0.3862387  0.0095139   -40.597  < 2e-16 ***
ORIGIN_SZTSSZ04 -0.6380676  0.0099905   -63.867  < 2e-16 ***
ORIGIN_SZTSSZ05 -2.7354613  0.0162414  -168.425  < 2e-16 ***
ORIGIN_SZTSSZ06 -2.6310865  0.0255772  -102.868  < 2e-16 ***
ORIGIN_SZWCSZ01 -1.1561047  0.0087394  -132.286  < 2e-16 ***
ORIGIN_SZWCSZ02 -2.6956217  0.0319117   -84.471  < 2e-16 ***
ORIGIN_SZWCSZ03 -4.3526889  0.1241082   -35.072  < 2e-16 ***
ORIGIN_SZWDSZ01  0.8712417  0.0043720   199.277  < 2e-16 ***
ORIGIN_SZWDSZ02  0.9119539  0.0050326   181.210  < 2e-16 ***
ORIGIN_SZWDSZ03  1.6205678  0.0045250   358.136  < 2e-16 ***
ORIGIN_SZWDSZ04  1.2081941  0.0054272   222.618  < 2e-16 ***
ORIGIN_SZWDSZ05  0.4284783  0.0052752    81.224  < 2e-16 ***
ORIGIN_SZWDSZ06  0.9018716  0.0049820   181.028  < 2e-16 ***
ORIGIN_SZWDSZ07 -0.6444820  0.0084731   -76.062  < 2e-16 ***
ORIGIN_SZWDSZ08 -0.8764983  0.0082622  -106.085  < 2e-16 ***
ORIGIN_SZWDSZ09  1.3292589  0.0048663   273.158  < 2e-16 ***
ORIGIN_SZYSSZ01 -0.4780462  0.0058489   -81.733  < 2e-16 ***
ORIGIN_SZYSSZ02  0.9323419  0.0054402   171.380  < 2e-16 ***
ORIGIN_SZYSSZ03  2.0577240  0.0046737   440.274  < 2e-16 ***
ORIGIN_SZYSSZ04  0.8697472  0.0047269   184.000  < 2e-16 ***
ORIGIN_SZYSSZ05  0.1662764  0.0060376    27.540  < 2e-16 ***
ORIGIN_SZYSSZ06 -0.8115617  0.0109084   -74.398  < 2e-16 ***
ORIGIN_SZYSSZ07 -0.8971248  0.0119220   -75.250  < 2e-16 ***
ORIGIN_SZYSSZ08 -0.2738680  0.0063553   -43.093  < 2e-16 ***
ORIGIN_SZYSSZ09  1.2274518  0.0044951   273.066  < 2e-16 ***
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DESTIN_SZAMSZ03  0.0801823  0.0041904    19.135  < 2e-16 ***
DESTIN_SZAMSZ04 -0.9282211  0.0061322  -151.368  < 2e-16 ***
DESTIN_SZAMSZ05 -1.0794168  0.0062543  -172.588  < 2e-16 ***
DESTIN_SZAMSZ06 -0.8839603  0.0060851  -145.267  < 2e-16 ***
DESTIN_SZAMSZ07 -1.5835093  0.0096846  -163.508  < 2e-16 ***
DESTIN_SZAMSZ08 -0.9756903  0.0068829  -141.756  < 2e-16 ***
DESTIN_SZAMSZ09 -1.0362692  0.0061651  -168.087  < 2e-16 ***
DESTIN_SZAMSZ10 -0.1227646  0.0044788   -27.410  < 2e-16 ***
DESTIN_SZAMSZ11 -0.4802374  0.0088108   -54.506  < 2e-16 ***
DESTIN_SZAMSZ12  0.2142621  0.0050653    42.300  < 2e-16 ***
DESTIN_SZBDSZ01  0.3582789  0.0039578    90.524  < 2e-16 ***
DESTIN_SZBDSZ02 -0.4368229  0.0051384   -85.012  < 2e-16 ***
DESTIN_SZBDSZ03 -0.1568727  0.0044329   -35.388  < 2e-16 ***
DESTIN_SZBDSZ04  0.6731669  0.0036215   185.882  < 2e-16 ***
DESTIN_SZBDSZ05  0.3647198  0.0040496    90.062  < 2e-16 ***
DESTIN_SZBDSZ06  0.0589240  0.0044352    13.286  < 2e-16 ***
DESTIN_SZBDSZ07 -0.6648168  0.0095742   -69.438  < 2e-16 ***
DESTIN_SZBDSZ08 -1.7214136  0.0106600  -161.483  < 2e-16 ***
DESTIN_SZBKSZ01 -1.2688264  0.0067263  -188.637  < 2e-16 ***
DESTIN_SZBKSZ02 -0.3912129  0.0055446   -70.558  < 2e-16 ***
DESTIN_SZBKSZ03 -0.8663392  0.0058693  -147.605  < 2e-16 ***
DESTIN_SZBKSZ04 -0.1247273  0.0051254   -24.335  < 2e-16 ***
DESTIN_SZBKSZ05 -0.7407774  0.0059120  -125.300  < 2e-16 ***
DESTIN_SZBKSZ06 -0.9934643  0.0063345  -156.834  < 2e-16 ***
DESTIN_SZBKSZ07  0.0882230  0.0042928    20.551  < 2e-16 ***
DESTIN_SZBKSZ08 -1.1134447  0.0070752  -157.372  < 2e-16 ***
DESTIN_SZBKSZ09 -0.1788171  0.0051327   -34.839  < 2e-16 ***
DESTIN_SZBLSZ01 -0.7696433  0.0071898  -107.047  < 2e-16 ***
DESTIN_SZBLSZ02  0.4076650  0.0068001    59.950  < 2e-16 ***
DESTIN_SZBLSZ03  1.5398488  0.0078230   196.836  < 2e-16 ***
DESTIN_SZBLSZ04 -0.3499486  0.0136985   -25.546  < 2e-16 ***
DESTIN_SZBMSZ01 -0.2114705  0.0048311   -43.773  < 2e-16 ***
DESTIN_SZBMSZ02 -0.3316806  0.0049958   -66.391  < 2e-16 ***
DESTIN_SZBMSZ03 -0.5134774  0.0058534   -87.723  < 2e-16 ***
DESTIN_SZBMSZ04 -0.2205274  0.0051028   -43.217  < 2e-16 ***
DESTIN_SZBMSZ05 -0.2101165  0.0067710   -31.032  < 2e-16 ***
DESTIN_SZBMSZ06 -1.3832385  0.0124821  -110.818  < 2e-16 ***
DESTIN_SZBMSZ07 -0.0133462  0.0046787    -2.853  0.00434 ** 
DESTIN_SZBMSZ08 -0.9056756  0.0063868  -141.805  < 2e-16 ***
DESTIN_SZBMSZ09 -2.3175407  0.0144523  -160.358  < 2e-16 ***
DESTIN_SZBMSZ10 -1.3973725  0.0090463  -154.470  < 2e-16 ***
DESTIN_SZBMSZ11 -1.3950206  0.0080459  -173.383  < 2e-16 ***
DESTIN_SZBMSZ12 -0.6882789  0.0081539   -84.411  < 2e-16 ***
DESTIN_SZBMSZ13 -0.2729120  0.0052969   -51.523  < 2e-16 ***
DESTIN_SZBMSZ14 -0.7581980  0.0080215   -94.521  < 2e-16 ***
DESTIN_SZBMSZ15 -0.9323237  0.0071093  -131.142  < 2e-16 ***
DESTIN_SZBMSZ16 -2.0655530  0.0108490  -190.391  < 2e-16 ***
DESTIN_SZBMSZ17 -2.5124893  0.0165366  -151.935  < 2e-16 ***
DESTIN_SZBPSZ01 -0.8203274  0.0057682  -142.216  < 2e-16 ***
DESTIN_SZBPSZ02 -1.5284265  0.0087447  -174.783  < 2e-16 ***
DESTIN_SZBPSZ03 -1.2434382  0.0080852  -153.792  < 2e-16 ***
DESTIN_SZBPSZ04 -0.7778558  0.0060900  -127.727  < 2e-16 ***
DESTIN_SZBPSZ05  0.1782204  0.0042331    42.101  < 2e-16 ***
DESTIN_SZBPSZ06 -0.6758807  0.0079728   -84.773  < 2e-16 ***
DESTIN_SZBPSZ07 -0.5029450  0.0081151   -61.976  < 2e-16 ***
DESTIN_SZBSSZ01 -0.1269916  0.0046949   -27.049  < 2e-16 ***
DESTIN_SZBSSZ02 -0.7536917  0.0051895  -145.233  < 2e-16 ***
DESTIN_SZBSSZ03  0.2747969  0.0039115    70.254  < 2e-16 ***
DESTIN_SZBTSZ01  0.1708577  0.0043381    39.385  < 2e-16 ***
DESTIN_SZBTSZ02 -0.6820190  0.0067243  -101.427  < 2e-16 ***
DESTIN_SZBTSZ03  0.0610599  0.0049825    12.255  < 2e-16 ***
DESTIN_SZBTSZ04 -1.3199639  0.0107063  -123.288  < 2e-16 ***
DESTIN_SZBTSZ05 -0.4174991  0.0069221   -60.314  < 2e-16 ***
DESTIN_SZBTSZ06 -0.5260242  0.0061145   -86.029  < 2e-16 ***
DESTIN_SZBTSZ07 -1.6678047  0.0106335  -156.844  < 2e-16 ***
DESTIN_SZBTSZ08 -0.7999935  0.0089175   -89.711  < 2e-16 ***
DESTIN_SZCBSZ01 -5.6321332  0.3162476   -17.809  < 2e-16 ***
DESTIN_SZCCSZ01 -0.9342781  0.0081409  -114.763  < 2e-16 ***
DESTIN_SZCHSZ01 -1.2808546  0.0096774  -132.355  < 2e-16 ***
DESTIN_SZCHSZ02  0.0067332  0.0054322     1.239  0.21516    
DESTIN_SZCHSZ03  1.0988838  0.0041378   265.570  < 2e-16 ***
DESTIN_SZCKSZ01 -0.3192235  0.0050632   -63.048  < 2e-16 ***
DESTIN_SZCKSZ02 -0.7776453  0.0055279  -140.676  < 2e-16 ***
DESTIN_SZCKSZ03  0.2772358  0.0042541    65.170  < 2e-16 ***
DESTIN_SZCKSZ04 -1.3842048  0.0065159  -212.436  < 2e-16 ***
DESTIN_SZCKSZ05 -1.2051808  0.0076814  -156.897  < 2e-16 ***
DESTIN_SZCKSZ06  0.1321955  0.0061568    21.472  < 2e-16 ***
DESTIN_SZCLSZ01  0.1942449  0.0049977    38.867  < 2e-16 ***
DESTIN_SZCLSZ02 -2.0828648  0.0134597  -154.749  < 2e-16 ***
DESTIN_SZCLSZ03 -0.8823728  0.0078307  -112.681  < 2e-16 ***
DESTIN_SZCLSZ04 -0.2311432  0.0047194   -48.977  < 2e-16 ***
DESTIN_SZCLSZ05 -1.0113430  0.0085536  -118.237  < 2e-16 ***
DESTIN_SZCLSZ06  0.0694682  0.0042166    16.475  < 2e-16 ***
DESTIN_SZCLSZ07 -0.4953961  0.0054184   -91.429  < 2e-16 ***
DESTIN_SZCLSZ08 -0.3849563  0.0061404   -62.693  < 2e-16 ***
DESTIN_SZCLSZ09  0.4201808  0.0067112    62.609  < 2e-16 ***
DESTIN_SZDTSZ02 -2.6513032  0.0348725   -76.029  < 2e-16 ***
DESTIN_SZDTSZ03 -1.5192228  0.0144477  -105.153  < 2e-16 ***
DESTIN_SZDTSZ13 -2.2041951  0.0161726  -136.292  < 2e-16 ***
DESTIN_SZGLSZ01 -0.0139744  0.0052464    -2.664  0.00773 ** 
DESTIN_SZGLSZ02 -0.2850816  0.0047467   -60.059  < 2e-16 ***
DESTIN_SZGLSZ03  0.3511872  0.0039473    88.969  < 2e-16 ***
DESTIN_SZGLSZ04  0.2909117  0.0039436    73.769  < 2e-16 ***
DESTIN_SZGLSZ05  0.1845361  0.0040011    46.121  < 2e-16 ***
DESTIN_SZHGSZ01  0.1418382  0.0039875    35.571  < 2e-16 ***
DESTIN_SZHGSZ02 -0.7233151  0.0052374  -138.105  < 2e-16 ***
DESTIN_SZHGSZ03 -1.1918463  0.0062129  -191.834  < 2e-16 ***
DESTIN_SZHGSZ04 -0.4380360  0.0044839   -97.691  < 2e-16 ***
DESTIN_SZHGSZ05 -0.5671024  0.0046427  -122.149  < 2e-16 ***
DESTIN_SZHGSZ06 -0.8271411  0.0054935  -150.566  < 2e-16 ***
DESTIN_SZHGSZ07  0.0721800  0.0041589    17.356  < 2e-16 ***
DESTIN_SZHGSZ08 -0.4297429  0.0050021   -85.913  < 2e-16 ***
DESTIN_SZHGSZ09 -0.2085461  0.0052544   -39.690  < 2e-16 ***
DESTIN_SZHGSZ10 -2.9169699  0.0262698  -111.039  < 2e-16 ***
DESTIN_SZJESZ01 -0.2822473  0.0051166   -55.163  < 2e-16 ***
DESTIN_SZJESZ02 -0.6761389  0.0053635  -126.063  < 2e-16 ***
DESTIN_SZJESZ03 -0.7371756  0.0058983  -124.980  < 2e-16 ***
DESTIN_SZJESZ04 -0.4593491  0.0067970   -67.581  < 2e-16 ***
DESTIN_SZJESZ05 -1.1418012  0.0099049  -115.277  < 2e-16 ***
DESTIN_SZJESZ06  0.1759680  0.0042791    41.123  < 2e-16 ***
DESTIN_SZJESZ07 -1.2260587  0.0082714  -148.229  < 2e-16 ***
DESTIN_SZJESZ08 -0.8547001  0.0080417  -106.283  < 2e-16 ***
DESTIN_SZJESZ09 -0.4306353  0.0057006   -75.542  < 2e-16 ***
DESTIN_SZJESZ10  0.6584971  0.0073664    89.392  < 2e-16 ***
DESTIN_SZJESZ11  0.9661208  0.0070491   137.056  < 2e-16 ***
DESTIN_SZJWSZ01 -0.9128436  0.0069529  -131.290  < 2e-16 ***
DESTIN_SZJWSZ02 -0.7285851  0.0054839  -132.859  < 2e-16 ***
DESTIN_SZJWSZ03  0.2601455  0.0043215    60.198  < 2e-16 ***
DESTIN_SZJWSZ04  0.6860274  0.0041135   166.775  < 2e-16 ***
DESTIN_SZJWSZ05 -0.4684576  0.0062875   -74.506  < 2e-16 ***
DESTIN_SZJWSZ06 -0.2459774  0.0057575   -42.723  < 2e-16 ***
DESTIN_SZJWSZ07 -1.8854234  0.0287721   -65.529  < 2e-16 ***
DESTIN_SZJWSZ08 -0.5523308  0.0051054  -108.186  < 2e-16 ***
DESTIN_SZJWSZ09  0.8818747  0.0037800   233.301  < 2e-16 ***
DESTIN_SZKLSZ01 -0.5814386  0.0052711  -110.308  < 2e-16 ***
DESTIN_SZKLSZ02 -0.7090577  0.0058161  -121.914  < 2e-16 ***
DESTIN_SZKLSZ03 -1.2191910  0.0065984  -184.772  < 2e-16 ***
DESTIN_SZKLSZ04 -1.6961428  0.0087866  -193.038  < 2e-16 ***
DESTIN_SZKLSZ05 -0.6927144  0.0073574   -94.153  < 2e-16 ***
DESTIN_SZKLSZ06 -2.2967464  0.0362605   -63.340  < 2e-16 ***
DESTIN_SZKLSZ07 -0.9536980  0.0066777  -142.819  < 2e-16 ***
DESTIN_SZKLSZ08 -0.4565596  0.0051736   -88.249  < 2e-16 ***
DESTIN_SZLKSZ01 -1.7277135  0.0207336   -83.329  < 2e-16 ***
DESTIN_SZMDSZ01 -1.7155417  0.0210080   -81.661  < 2e-16 ***
DESTIN_SZMDSZ02 -1.3694928  0.0114174  -119.948  < 2e-16 ***
DESTIN_SZMDSZ03 -2.7183729  0.0252678  -107.582  < 2e-16 ***
DESTIN_SZMPSZ01 -0.8051991  0.0078564  -102.490  < 2e-16 ***
DESTIN_SZMPSZ02 -0.7627000  0.0061386  -124.246  < 2e-16 ***
DESTIN_SZMPSZ03 -0.0649484  0.0047787   -13.591  < 2e-16 ***
DESTIN_SZMUSZ02 -1.9549128  0.0200160   -97.667  < 2e-16 ***
DESTIN_SZNTSZ01 -3.3048398  0.0448053   -73.760  < 2e-16 ***
DESTIN_SZNTSZ02 -1.6454847  0.0109337  -150.497  < 2e-16 ***
DESTIN_SZNTSZ03 -1.1389723  0.0077396  -147.161  < 2e-16 ***
DESTIN_SZNTSZ05 -2.0264109  0.0250226   -80.983  < 2e-16 ***
DESTIN_SZNTSZ06 -3.3496282  0.0428989   -78.082  < 2e-16 ***
DESTIN_SZNVSZ01 -0.3407614  0.0045493   -74.905  < 2e-16 ***
DESTIN_SZNVSZ02 -0.4987695  0.0053942   -92.465  < 2e-16 ***
DESTIN_SZNVSZ03 -0.4936107  0.0055158   -89.491  < 2e-16 ***
DESTIN_SZNVSZ04 -1.9141281  0.0107557  -177.964  < 2e-16 ***
DESTIN_SZNVSZ05 -1.5378263  0.0089577  -171.677  < 2e-16 ***
DESTIN_SZPGSZ01 -1.7744485  0.0194346   -91.304  < 2e-16 ***
DESTIN_SZPGSZ02 -0.9282918  0.0069006  -134.523  < 2e-16 ***
DESTIN_SZPGSZ03  0.0885025  0.0042145    21.000  < 2e-16 ***
DESTIN_SZPGSZ04 -0.3879375  0.0046862   -82.784  < 2e-16 ***
DESTIN_SZPGSZ05 -0.9649873  0.0074625  -129.311  < 2e-16 ***
DESTIN_SZPLSZ01 -0.6159175  0.0070845   -86.939  < 2e-16 ***
DESTIN_SZPLSZ02 -1.7551386  0.0133081  -131.885  < 2e-16 ***
DESTIN_SZPLSZ03 -0.1378379  0.0098704   -13.965  < 2e-16 ***
DESTIN_SZPLSZ04 -0.1411200  0.0096446   -14.632  < 2e-16 ***
DESTIN_SZPLSZ05 -0.8483196  0.0119048   -71.259  < 2e-16 ***
DESTIN_SZPNSZ01 -0.1579087  0.0057330   -27.544  < 2e-16 ***
DESTIN_SZPNSZ02  1.0243480  0.0076680   133.587  < 2e-16 ***
DESTIN_SZPNSZ03  0.0451598  0.0081444     5.545 2.94e-08 ***
DESTIN_SZPNSZ04  1.8941928  0.0087479   216.530  < 2e-16 ***
DESTIN_SZPNSZ05  1.0341581  0.0130830    79.046  < 2e-16 ***
DESTIN_SZPRSZ01 -1.4038513  0.0086911  -161.527  < 2e-16 ***
DESTIN_SZPRSZ02 -0.4942539  0.0052403   -94.319  < 2e-16 ***
DESTIN_SZPRSZ03  0.4219510  0.0040281   104.751  < 2e-16 ***
DESTIN_SZPRSZ04 -0.4841099  0.0083498   -57.979  < 2e-16 ***
DESTIN_SZPRSZ05 -0.2988481  0.0047512   -62.899  < 2e-16 ***
DESTIN_SZPRSZ06  0.0012333  0.0054530     0.226  0.82108    
DESTIN_SZPRSZ07 -1.1417482  0.0118845   -96.070  < 2e-16 ***
DESTIN_SZPRSZ08 -0.8259249  0.0066757  -123.720  < 2e-16 ***
DESTIN_SZQTSZ01 -1.2134330  0.0089222  -136.002  < 2e-16 ***
DESTIN_SZQTSZ02 -1.2397956  0.0074512  -166.388  < 2e-16 ***
DESTIN_SZQTSZ03 -0.7448659  0.0066511  -111.992  < 2e-16 ***
DESTIN_SZQTSZ04 -0.6243112  0.0066812   -93.443  < 2e-16 ***
DESTIN_SZQTSZ05 -0.6102589  0.0060458  -100.940  < 2e-16 ***
DESTIN_SZQTSZ06 -0.9164592  0.0065095  -140.788  < 2e-16 ***
DESTIN_SZQTSZ07 -1.4600643  0.0109976  -132.762  < 2e-16 ***
DESTIN_SZQTSZ08  0.0004582  0.0050178     0.091  0.92724    
DESTIN_SZQTSZ09 -0.5226213  0.0058901   -88.728  < 2e-16 ***
DESTIN_SZQTSZ10 -0.3867082  0.0055876   -69.208  < 2e-16 ***
DESTIN_SZQTSZ11  0.0260589  0.0055065     4.732 2.22e-06 ***
DESTIN_SZQTSZ12 -0.3387634  0.0072779   -46.547  < 2e-16 ***
DESTIN_SZQTSZ13 -0.0512118  0.0053664    -9.543  < 2e-16 ***
DESTIN_SZQTSZ14 -0.2555346  0.0063792   -40.057  < 2e-16 ***
DESTIN_SZQTSZ15 -0.1820651  0.0077537   -23.481  < 2e-16 ***
DESTIN_SZRCSZ01 -0.4641196  0.0072515   -64.003  < 2e-16 ***
DESTIN_SZRCSZ06 -2.0929548  0.0189106  -110.676  < 2e-16 ***
DESTIN_SZRVSZ01 -1.7885682  0.0163492  -109.398  < 2e-16 ***
DESTIN_SZRVSZ02 -3.1669721  0.0326320   -97.051  < 2e-16 ***
DESTIN_SZRVSZ03 -2.0306835  0.0135749  -149.591  < 2e-16 ***
DESTIN_SZRVSZ04 -1.5113470  0.0155637   -97.107  < 2e-16 ***
DESTIN_SZRVSZ05 -2.3683855  0.0259334   -91.326  < 2e-16 ***
DESTIN_SZSBSZ01 -0.5841063  0.0068588   -85.162  < 2e-16 ***
DESTIN_SZSBSZ02 -1.0777704  0.0078288  -137.667  < 2e-16 ***
DESTIN_SZSBSZ03  0.4734371  0.0045880   103.190  < 2e-16 ***
DESTIN_SZSBSZ04  0.0546094  0.0057517     9.494  < 2e-16 ***
DESTIN_SZSBSZ05 -0.9588198  0.0075242  -127.431  < 2e-16 ***
DESTIN_SZSBSZ06 -1.8528944  0.0234040   -79.170  < 2e-16 ***
DESTIN_SZSBSZ07 -1.8403768  0.0195878   -93.955  < 2e-16 ***
DESTIN_SZSBSZ08  0.9205969  0.0055698   165.285  < 2e-16 ***
DESTIN_SZSBSZ09  0.5166486  0.0051939    99.472  < 2e-16 ***
DESTIN_SZSESZ02 -0.5728211  0.0048270  -118.669  < 2e-16 ***
DESTIN_SZSESZ03  0.2554787  0.0038335    66.645  < 2e-16 ***
DESTIN_SZSESZ04 -0.8982794  0.0056698  -158.432  < 2e-16 ***
DESTIN_SZSESZ05 -0.4661655  0.0048578   -95.962  < 2e-16 ***
DESTIN_SZSESZ06 -0.8392849  0.0059198  -141.777  < 2e-16 ***
DESTIN_SZSESZ07 -3.2182325  0.0227089  -141.717  < 2e-16 ***
DESTIN_SZSGSZ01 -0.2751206  0.0059581   -46.176  < 2e-16 ***
DESTIN_SZSGSZ02 -0.2951806  0.0052515   -56.209  < 2e-16 ***
DESTIN_SZSGSZ03 -0.4469508  0.0048181   -92.766  < 2e-16 ***
DESTIN_SZSGSZ04 -0.2842809  0.0047961   -59.274  < 2e-16 ***
DESTIN_SZSGSZ05 -2.0643753  0.0098252  -210.109  < 2e-16 ***
DESTIN_SZSGSZ06  0.2501247  0.0038873    64.343  < 2e-16 ***
DESTIN_SZSGSZ07 -0.5743750  0.0052184  -110.067  < 2e-16 ***
DESTIN_SZSISZ01 -1.1030669  0.0259113   -42.571  < 2e-16 ***
DESTIN_SZSKSZ01 -0.5462538  0.0071443   -76.460  < 2e-16 ***
DESTIN_SZSKSZ02  0.2965180  0.0056707    52.290  < 2e-16 ***
DESTIN_SZSKSZ03 -0.4521490  0.0062177   -72.719  < 2e-16 ***
DESTIN_SZSKSZ04 -0.6665145  0.0148252   -44.958  < 2e-16 ***
DESTIN_SZSKSZ05 -0.1474142  0.0121958   -12.087  < 2e-16 ***
DESTIN_SZSLSZ01 -0.8855715  0.0084587  -104.693  < 2e-16 ***
DESTIN_SZSLSZ04 -1.1787840  0.0071355  -165.200  < 2e-16 ***
DESTIN_SZSRSZ01 -1.6435064  0.0128822  -127.580  < 2e-16 ***
DESTIN_SZTHSZ01 -3.4388625  0.0367651   -93.536  < 2e-16 ***
DESTIN_SZTHSZ03 -2.5809435  0.0256853  -100.483  < 2e-16 ***
DESTIN_SZTHSZ04 -2.4887189  0.0214441  -116.056  < 2e-16 ***
DESTIN_SZTHSZ06 -1.7965101  0.0152160  -118.067  < 2e-16 ***
DESTIN_SZTMSZ01 -0.3251891  0.0058067   -56.002  < 2e-16 ***
DESTIN_SZTMSZ02  1.1558743  0.0034703   333.080  < 2e-16 ***
DESTIN_SZTMSZ03  0.4525619  0.0039244   115.319  < 2e-16 ***
DESTIN_SZTMSZ04  0.8223271  0.0040060   205.274  < 2e-16 ***
DESTIN_SZTMSZ05  0.3880619  0.0054308    71.456  < 2e-16 ***
DESTIN_SZTNSZ01 -0.9533112  0.0067853  -140.496  < 2e-16 ***
DESTIN_SZTNSZ02 -1.5909451  0.0097396  -163.348  < 2e-16 ***
DESTIN_SZTNSZ03 -1.6470771  0.0116598  -141.261  < 2e-16 ***
DESTIN_SZTNSZ04 -1.0686173  0.0069848  -152.993  < 2e-16 ***
DESTIN_SZTPSZ01 -0.5180183  0.0056886   -91.063  < 2e-16 ***
DESTIN_SZTPSZ02  0.2160781  0.0038283    56.443  < 2e-16 ***
DESTIN_SZTPSZ03 -0.2479956  0.0056651   -43.776  < 2e-16 ***
DESTIN_SZTPSZ04 -1.5015463  0.0072444  -207.271  < 2e-16 ***
DESTIN_SZTPSZ05 -0.9551144  0.0057981  -164.729  < 2e-16 ***
DESTIN_SZTPSZ06 -0.4846634  0.0074621   -64.950  < 2e-16 ***
DESTIN_SZTPSZ07 -1.9753440  0.0118295  -166.984  < 2e-16 ***
DESTIN_SZTPSZ08 -1.3455063  0.0086909  -154.817  < 2e-16 ***
DESTIN_SZTPSZ09 -0.3556620  0.0061296   -58.024  < 2e-16 ***
DESTIN_SZTPSZ10 -1.3213501  0.0085951  -153.733  < 2e-16 ***
DESTIN_SZTPSZ11 -0.3877006  0.0052409   -73.977  < 2e-16 ***
DESTIN_SZTPSZ12 -0.7064020  0.0062472  -113.075  < 2e-16 ***
DESTIN_SZTSSZ01 -0.8827157  0.0218327   -40.431  < 2e-16 ***
DESTIN_SZTSSZ02 -0.6067055  0.0115514   -52.522  < 2e-16 ***
DESTIN_SZTSSZ03  0.4380259  0.0086774    50.479  < 2e-16 ***
DESTIN_SZTSSZ04  0.4902124  0.0089922    54.515  < 2e-16 ***
DESTIN_SZTSSZ05  1.4336278  0.0093410   153.477  < 2e-16 ***
DESTIN_SZTSSZ06  0.9223573  0.0209024    44.127  < 2e-16 ***
DESTIN_SZWCSZ01  1.1559309  0.0051787   223.208  < 2e-16 ***
DESTIN_SZWCSZ02 -1.2664455  0.0126131  -100.407  < 2e-16 ***
DESTIN_SZWCSZ03 -2.7360882  0.0325753   -83.993  < 2e-16 ***
DESTIN_SZWDSZ01  0.8193492  0.0037301   219.657  < 2e-16 ***
DESTIN_SZWDSZ02 -0.7852474  0.0058655  -133.875  < 2e-16 ***
DESTIN_SZWDSZ03  0.5742422  0.0041884   137.104  < 2e-16 ***
DESTIN_SZWDSZ04 -0.8391525  0.0065075  -128.951  < 2e-16 ***
DESTIN_SZWDSZ05 -0.3510692  0.0057253   -61.319  < 2e-16 ***
DESTIN_SZWDSZ06  0.1358804  0.0043968    30.905  < 2e-16 ***
DESTIN_SZWDSZ07 -0.2207379  0.0066369   -33.259  < 2e-16 ***
DESTIN_SZWDSZ08 -0.0264655  0.0065065    -4.068 4.75e-05 ***
DESTIN_SZWDSZ09 -0.2065828  0.0050524   -40.888  < 2e-16 ***
DESTIN_SZYSSZ01  0.7467996  0.0040979   182.238  < 2e-16 ***
DESTIN_SZYSSZ02 -0.3002718  0.0053434   -56.195  < 2e-16 ***
DESTIN_SZYSSZ03 -1.1087686  0.0057219  -193.778  < 2e-16 ***
DESTIN_SZYSSZ04 -0.3748076  0.0051481   -72.805  < 2e-16 ***
DESTIN_SZYSSZ05 -1.7909654  0.0102064  -175.475  < 2e-16 ***
DESTIN_SZYSSZ06 -1.8519179  0.0099601  -185.933  < 2e-16 ***
DESTIN_SZYSSZ07 -0.9246626  0.0118101   -78.294  < 2e-16 ***
DESTIN_SZYSSZ08  0.4403129  0.0041268   106.697  < 2e-16 ***
DESTIN_SZYSSZ09  0.0267012  0.0041393     6.451 1.11e-10 ***
log(dist)       -0.6721961  0.0001353 -4969.566  < 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: 60796037  on 14733  degrees of freedom
Residual deviance: 20988409  on 14175  degrees of freedom
AIC: 21081154

Number of Fisher Scoring iterations: 7

Similarly to examine how the constraints hold for destinations this time.

CalcRSquared(dbcSIM$data$TRIPS, dbcSIM$fitted.values)

[1] 0.5739638

Notice that there is a relatively greater improvement in the R^2 value.

8.9 Model comparison

Another useful model performance measure for continuous dependent variable is Root Mean Squared Error. In this sub-section, you will learn how to use compare_performance() of performance package

First, a list named model_list will be created using the code chunk below.

model_list <- list(unconstrained=uncSIM,
                   originConstrained=orcSIM,
                   destinationConstrained=decSIM,
                   doublyConstrained=dbcSIM)

Next, to 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 | 4288.012
originConstrained      |   glm | 3659.954
destinationConstrained |   glm | 3389.556
doublyConstrained      |   glm | 3252.297

The 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.

8.10 Visualising fitted values

This section covers visualizing observed versus fitted values. First, fitted values will be extracted from each model using the code chunk below.

df <- as.data.frame(uncSIM$fitted.values) %>%
  round(digits = 0)

Next, to 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")

Once again, 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")

Finally 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)

Now, to put all the graphs into a single visual for better comparison by using the code chunk below.

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'