Show the code chunk
pacman::p_load(tmap, sf, performance, knitr,
ggpubr, tidyverse)In-class Exercise 4: Calibrating Spatial Interaction Models with R
Overview
This in-class exercise is a continuation of Hands-on Exercise 3, In-class Exercise 3 and In-class Exercise 4: Preparing Spatial Interaction Modelling Variables. We will continue our journey of calibrating Spatial Interaction Models by using propulsiveness and attractiveness variables prepared in earlier in-class exercise.
Getting Started
For the purpose of this exercise, five 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 plotting cartographicquality thematic maps.
- performance for computing model comparison matrices such as rmse.
- ggpubr for creating publication quality statistical graphics.
Do it yourself
Using the steps you learned in previous exercises, load the above packages onto R environment.
The Data
This exercise is a continuation of Hands-on Exercise 3 and In-class Exercise 4: Preparing Spatial Interaction Modelling Variables. The following data will be used:
- flow_data_tidy.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.
flow_data <- read_rds("data/rds/flow_data_tidy.rds")glimpse(flow_data)Rows: 14,734
Columns: 13
$ ORIGIN_SZ <chr> "AMSZ01", "AMSZ01", "AMSZ01", "AMSZ01", "AMSZ01", "AMS…
$ DESTIN_SZ <chr> "AMSZ01", "AMSZ02", "AMSZ03", "AMSZ04", "AMSZ05", "AMS…
$ TRIPS <dbl> 1998, 8289, 8971, 2252, 6136, 2148, 1620, 1925, 1773, …
$ DIST <dbl> 50.0000, 810.4491, 1360.9294, 840.4432, 1076.7916, 805…
$ ORIGIN_AGE7_12 <dbl> 310, 310, 310, 310, 310, 310, 310, 310, 310, 310, 310,…
$ ORIGIN_AGE13_24 <dbl> 710, 710, 710, 710, 710, 710, 710, 710, 710, 710, 710,…
$ ORIGIN_AGE25_64 <dbl> 2780, 2780, 2780, 2780, 2780, 2780, 2780, 2780, 2780, …
$ DESTIN_AGE7_12 <dbl> 310.00, 1140.00, 1010.00, 980.00, 810.00, 1050.00, 420…
$ DESTIN_AGE13_24 <dbl> 710.00, 2770.00, 2650.00, 2000.00, 1920.00, 2390.00, 1…
$ DESTIN_AGE25_64 <dbl> 2780.00, 15700.00, 14240.00, 11320.00, 9650.00, 12460.…
$ SCHOOL_COUNT <dbl> 0.99, 2.00, 2.00, 1.00, 3.00, 2.00, 0.99, 0.99, 3.00, …
$ BUSINESS_COUNT <dbl> 1.00, 0.99, 6.00, 0.99, 0.99, 0.99, 1.00, 117.00, 0.99…
$ geometry <LINESTRING [m]> LINESTRING (29501.77 39419...., LINESTRING …Notice that this sf tibble data.frame includes two additional fields namely: SCHOOL_COUNT and BUSINESS_COUNT. Both of them will be used as attractiveness variables when calibrating origin constrained SIM.
The code chunk below is used to display the first five columns and rows of flow_data.
kable(head(flow_data[, 1:5], n = 5))| ORIGIN_SZ | DESTIN_SZ | TRIPS | DIST | ORIGIN_AGE7_12 | geometry |
|---|---|---|---|---|---|
| AMSZ01 | AMSZ01 | 1998 | 50.0000 | 310 | LINESTRING (29501.77 39419…. |
| AMSZ01 | AMSZ02 | 8289 | 810.4491 | 310 | LINESTRING (29501.77 39419…. |
| AMSZ01 | AMSZ03 | 8971 | 1360.9294 | 310 | LINESTRING (29501.77 39419…. |
| AMSZ01 | AMSZ04 | 2252 | 840.4432 | 310 | LINESTRING (29501.77 39419…. |
| AMSZ01 | AMSZ05 | 6136 | 1076.7916 | 310 | LINESTRING (29501.77 39419…. |
Important
Notice that this data.frame include intra-zonal flow.
Preparing inter-zonal flow data
In general, we will calibrate separate Spatial Interaction Models for inter- and intra-zonal flows. In this hands-on exercise, we will focus our attention on inter-zonal flow. Hence, we need to exclude the intra-zonal flow from flow_data.
First, two new columns called FlowNoIntra and offset will be created by using the code chunk below.
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)According to the syntax used to derive values in FlowNoIntra field, all intra-zonal flow will be given a value of 0 or else the original flow values will be inserted.
Next, inter-zonal flow will be selected from flow_data and save into a new output data.frame called inter_zonal_flow by using the code chunk below.
inter_zonal_flow <- flow_data %>%
filter(FlowNoIntra > 0)You are ready to calibrate the Spatial Interaction Models now.
Calibrating Spatial Interaction Models
In this section, we will focus on calibrating an origin constrained SIM and a doubly constrained by using flow_data prepared. They complement what you have learned in Hands-on Exercise 3.
Note
Students are encouraged to revise the lesson slides as well as Sub-section 2.2 of Kingsley E. Haynes and A. Stewart Fotheringham (2020) Gravity and Spatial Interaction Models.
Origin- (Production-) constrained Model
Figure below shows the general formula of the origin-constrained model.
Code chunk below shows the calibration of the model by using glm() of R and flow_data.
orcSIM_Poisson <- glm(formula = TRIPS ~
ORIGIN_SZ +
log(SCHOOL_COUNT) +
log(BUSINESS_COUNT) +
log(DIST) - 1,
family = poisson(link = "log"),
data = inter_zonal_flow,
na.action = na.exclude)
summary(orcSIM_Poisson)
Things to learning from the conde chunk
- For origin-constrained model, only explanatory variables representing the attractiveness at the destinations will be used.
- All the explanatory variables including distance will be log transformed.
- ORIGIN_SZ is used to model 𝜇𝑖 . It must be in categorical data type.
- It is important to note that -1 is added in the equation after the distance variable. The -1 serves the purpose of removing the intercept that by default, glm will insert into the model.
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + log(SCHOOL_COUNT) + log(BUSINESS_COUNT) +
log(DIST) - 1, family = poisson(link = "log"), data = inter_zonal_flow,
na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
ORIGIN_SZAMSZ01 19.8739840 0.0047627 4172.84 <2e-16 ***
ORIGIN_SZAMSZ02 20.5902203 0.0042786 4812.33 <2e-16 ***
ORIGIN_SZAMSZ03 20.2327026 0.0045531 4443.70 <2e-16 ***
ORIGIN_SZAMSZ04 19.7744438 0.0049837 3967.79 <2e-16 ***
ORIGIN_SZAMSZ05 19.6574529 0.0056396 3485.61 <2e-16 ***
ORIGIN_SZAMSZ06 19.9659115 0.0048946 4079.16 <2e-16 ***
ORIGIN_SZAMSZ07 18.6746164 0.0096316 1938.90 <2e-16 ***
ORIGIN_SZAMSZ08 19.2701601 0.0090776 2122.82 <2e-16 ***
ORIGIN_SZAMSZ09 19.9889467 0.0052858 3781.64 <2e-16 ***
ORIGIN_SZAMSZ10 20.3422035 0.0045778 4443.62 <2e-16 ***
ORIGIN_SZAMSZ11 18.3944113 0.0129212 1423.58 <2e-16 ***
ORIGIN_SZAMSZ12 18.3484209 0.0109652 1673.33 <2e-16 ***
ORIGIN_SZBDSZ01 20.9668587 0.0043388 4832.36 <2e-16 ***
ORIGIN_SZBDSZ02 20.4059518 0.0050601 4032.75 <2e-16 ***
ORIGIN_SZBDSZ03 20.6725514 0.0045276 4565.93 <2e-16 ***
ORIGIN_SZBDSZ04 21.6703853 0.0038930 5566.44 <2e-16 ***
ORIGIN_SZBDSZ05 20.7497445 0.0046085 4502.46 <2e-16 ***
ORIGIN_SZBDSZ06 20.9119361 0.0046432 4503.77 <2e-16 ***
ORIGIN_SZBDSZ07 18.9749815 0.0097896 1938.28 <2e-16 ***
ORIGIN_SZBDSZ08 19.1933901 0.0091312 2101.95 <2e-16 ***
ORIGIN_SZBKSZ01 19.5422606 0.0064732 3018.96 <2e-16 ***
ORIGIN_SZBKSZ02 20.1748913 0.0050076 4028.89 <2e-16 ***
ORIGIN_SZBKSZ03 20.3984624 0.0047226 4319.35 <2e-16 ***
ORIGIN_SZBKSZ04 19.6182212 0.0059652 3288.76 <2e-16 ***
ORIGIN_SZBKSZ05 19.6033818 0.0063181 3102.74 <2e-16 ***
ORIGIN_SZBKSZ06 19.7145224 0.0056372 3497.20 <2e-16 ***
ORIGIN_SZBKSZ07 20.4237448 0.0041912 4873.03 <2e-16 ***
ORIGIN_SZBKSZ08 19.7992538 0.0050405 3928.02 <2e-16 ***
ORIGIN_SZBKSZ09 19.7821586 0.0055558 3560.66 <2e-16 ***
ORIGIN_SZBLSZ01 17.7977276 0.0149058 1194.01 <2e-16 ***
ORIGIN_SZBLSZ02 17.4287491 0.0192364 906.03 <2e-16 ***
ORIGIN_SZBLSZ03 16.5884288 0.0459848 360.74 <2e-16 ***
ORIGIN_SZBLSZ04 17.7851626 0.0232823 763.89 <2e-16 ***
ORIGIN_SZBMSZ01 20.0751840 0.0052887 3795.89 <2e-16 ***
ORIGIN_SZBMSZ02 18.6956140 0.0066656 2804.80 <2e-16 ***
ORIGIN_SZBMSZ03 19.3204425 0.0054755 3528.56 <2e-16 ***
ORIGIN_SZBMSZ04 19.4724220 0.0049390 3942.59 <2e-16 ***
ORIGIN_SZBMSZ05 16.9581801 0.0168804 1004.61 <2e-16 ***
ORIGIN_SZBMSZ06 16.9898638 0.0181852 934.27 <2e-16 ***
ORIGIN_SZBMSZ07 19.2868403 0.0056231 3429.91 <2e-16 ***
ORIGIN_SZBMSZ08 19.1477543 0.0055918 3424.28 <2e-16 ***
ORIGIN_SZBMSZ09 18.7564539 0.0086298 2173.46 <2e-16 ***
ORIGIN_SZBMSZ10 18.3617854 0.0089250 2057.35 <2e-16 ***
ORIGIN_SZBMSZ11 18.9167941 0.0063340 2986.54 <2e-16 ***
ORIGIN_SZBMSZ12 18.7874661 0.0093024 2019.63 <2e-16 ***
ORIGIN_SZBMSZ13 19.5654046 0.0057517 3401.70 <2e-16 ***
ORIGIN_SZBMSZ14 19.0685619 0.0063346 3010.24 <2e-16 ***
ORIGIN_SZBMSZ15 19.4403124 0.0058147 3343.30 <2e-16 ***
ORIGIN_SZBMSZ16 18.4469203 0.0092638 1991.28 <2e-16 ***
ORIGIN_SZBMSZ17 18.3430175 0.0157692 1163.22 <2e-16 ***
ORIGIN_SZBPSZ01 20.1806714 0.0053660 3760.81 <2e-16 ***
ORIGIN_SZBPSZ02 19.8116707 0.0061485 3222.19 <2e-16 ***
ORIGIN_SZBPSZ03 19.8467602 0.0059769 3320.57 <2e-16 ***
ORIGIN_SZBPSZ04 20.4613200 0.0048398 4227.72 <2e-16 ***
ORIGIN_SZBPSZ05 20.5379711 0.0043769 4692.39 <2e-16 ***
ORIGIN_SZBPSZ06 18.8948034 0.0093668 2017.21 <2e-16 ***
ORIGIN_SZBPSZ07 19.4104568 0.0087961 2206.70 <2e-16 ***
ORIGIN_SZBSSZ01 20.0139503 0.0056561 3538.45 <2e-16 ***
ORIGIN_SZBSSZ02 20.2543885 0.0047198 4291.38 <2e-16 ***
ORIGIN_SZBSSZ03 19.5428803 0.0052713 3707.41 <2e-16 ***
ORIGIN_SZBTSZ01 20.0198045 0.0058541 3419.77 <2e-16 ***
ORIGIN_SZBTSZ02 19.3618525 0.0081472 2376.51 <2e-16 ***
ORIGIN_SZBTSZ03 19.5883853 0.0068935 2841.59 <2e-16 ***
ORIGIN_SZBTSZ04 18.7720238 0.0103909 1806.58 <2e-16 ***
ORIGIN_SZBTSZ05 18.8069026 0.0120628 1559.08 <2e-16 ***
ORIGIN_SZBTSZ06 18.7068633 0.0094575 1978.00 <2e-16 ***
ORIGIN_SZBTSZ07 17.6292257 0.0141551 1245.43 <2e-16 ***
ORIGIN_SZBTSZ08 18.6989374 0.0109610 1705.94 <2e-16 ***
ORIGIN_SZCBSZ01 18.2189868 0.0548317 332.27 <2e-16 ***
ORIGIN_SZCCSZ01 18.9734563 0.0139450 1360.59 <2e-16 ***
ORIGIN_SZCHSZ01 19.5955119 0.0121035 1619.00 <2e-16 ***
ORIGIN_SZCHSZ02 19.3320960 0.0081620 2368.55 <2e-16 ***
ORIGIN_SZCHSZ03 21.2164518 0.0063552 3338.43 <2e-16 ***
ORIGIN_SZCKSZ01 20.1046845 0.0049333 4075.29 <2e-16 ***
ORIGIN_SZCKSZ02 20.5371946 0.0050256 4086.53 <2e-16 ***
ORIGIN_SZCKSZ03 20.7210560 0.0042184 4912.07 <2e-16 ***
ORIGIN_SZCKSZ04 21.4013886 0.0042524 5032.80 <2e-16 ***
ORIGIN_SZCKSZ05 20.9413146 0.0049434 4236.18 <2e-16 ***
ORIGIN_SZCKSZ06 20.2557727 0.0071832 2819.88 <2e-16 ***
ORIGIN_SZCLSZ01 19.3383703 0.0076634 2523.46 <2e-16 ***
ORIGIN_SZCLSZ02 18.5226956 0.0135522 1366.77 <2e-16 ***
ORIGIN_SZCLSZ03 19.0225512 0.0080145 2373.51 <2e-16 ***
ORIGIN_SZCLSZ04 20.7981505 0.0042400 4905.22 <2e-16 ***
ORIGIN_SZCLSZ05 18.3015625 0.0146815 1246.58 <2e-16 ***
ORIGIN_SZCLSZ06 20.8207386 0.0039567 5262.09 <2e-16 ***
ORIGIN_SZCLSZ07 19.6728958 0.0054199 3629.76 <2e-16 ***
ORIGIN_SZCLSZ08 20.0851929 0.0056956 3526.43 <2e-16 ***
ORIGIN_SZCLSZ09 18.5749589 0.0165415 1122.93 <2e-16 ***
ORIGIN_SZDTSZ02 15.8276209 0.0833992 189.78 <2e-16 ***
ORIGIN_SZDTSZ03 16.2512838 0.0737972 220.22 <2e-16 ***
ORIGIN_SZDTSZ13 16.7744385 0.0312450 536.87 <2e-16 ***
ORIGIN_SZGLSZ01 18.2368248 0.0096104 1897.62 <2e-16 ***
ORIGIN_SZGLSZ02 19.8705255 0.0049014 4054.06 <2e-16 ***
ORIGIN_SZGLSZ03 19.8249435 0.0053109 3732.85 <2e-16 ***
ORIGIN_SZGLSZ04 20.7800335 0.0041261 5036.20 <2e-16 ***
ORIGIN_SZGLSZ05 20.6040494 0.0043049 4786.23 <2e-16 ***
ORIGIN_SZHGSZ01 20.0273475 0.0044824 4468.04 <2e-16 ***
ORIGIN_SZHGSZ02 20.2480656 0.0044575 4542.47 <2e-16 ***
ORIGIN_SZHGSZ03 20.0756442 0.0049003 4096.81 <2e-16 ***
ORIGIN_SZHGSZ04 20.7577748 0.0040465 5129.84 <2e-16 ***
ORIGIN_SZHGSZ05 20.9779992 0.0040123 5228.42 <2e-16 ***
ORIGIN_SZHGSZ06 19.7403058 0.0054229 3640.20 <2e-16 ***
ORIGIN_SZHGSZ07 20.1896268 0.0046051 4384.22 <2e-16 ***
ORIGIN_SZHGSZ08 19.8646492 0.0052403 3790.72 <2e-16 ***
ORIGIN_SZHGSZ09 18.3647736 0.0069196 2654.04 <2e-16 ***
ORIGIN_SZHGSZ10 16.8720475 0.0421046 400.72 <2e-16 ***
ORIGIN_SZJESZ01 20.2673794 0.0046723 4337.79 <2e-16 ***
ORIGIN_SZJESZ02 20.0595982 0.0046503 4313.61 <2e-16 ***
ORIGIN_SZJESZ03 19.9128778 0.0049848 3994.75 <2e-16 ***
ORIGIN_SZJESZ04 18.5053667 0.0099227 1864.94 <2e-16 ***
ORIGIN_SZJESZ05 17.8172930 0.0138840 1283.29 <2e-16 ***
ORIGIN_SZJESZ06 20.0124157 0.0045009 4446.36 <2e-16 ***
ORIGIN_SZJESZ07 18.1821423 0.0117267 1550.49 <2e-16 ***
ORIGIN_SZJESZ08 18.8713046 0.0116456 1620.46 <2e-16 ***
ORIGIN_SZJESZ09 20.5535527 0.0048456 4241.72 <2e-16 ***
ORIGIN_SZJESZ10 18.4922322 0.0191243 966.95 <2e-16 ***
ORIGIN_SZJESZ11 18.2891211 0.0197114 927.85 <2e-16 ***
ORIGIN_SZJWSZ01 20.4912737 0.0063102 3247.35 <2e-16 ***
ORIGIN_SZJWSZ02 20.8236694 0.0042249 4928.82 <2e-16 ***
ORIGIN_SZJWSZ03 21.2587613 0.0039733 5350.40 <2e-16 ***
ORIGIN_SZJWSZ04 20.3816464 0.0046199 4411.67 <2e-16 ***
ORIGIN_SZJWSZ05 18.0607448 0.0128857 1401.61 <2e-16 ***
ORIGIN_SZJWSZ06 18.7015202 0.0107614 1737.83 <2e-16 ***
ORIGIN_SZJWSZ07 17.3991822 0.0277096 627.91 <2e-16 ***
ORIGIN_SZJWSZ08 21.8044465 0.0037356 5836.95 <2e-16 ***
ORIGIN_SZJWSZ09 21.5414930 0.0036033 5978.19 <2e-16 ***
ORIGIN_SZKLSZ01 20.0307712 0.0047868 4184.59 <2e-16 ***
ORIGIN_SZKLSZ02 19.0634769 0.0062318 3059.05 <2e-16 ***
ORIGIN_SZKLSZ03 19.2685700 0.0057172 3370.25 <2e-16 ***
ORIGIN_SZKLSZ04 17.7085067 0.0119809 1478.06 <2e-16 ***
ORIGIN_SZKLSZ05 18.6384471 0.0107596 1732.26 <2e-16 ***
ORIGIN_SZKLSZ06 13.7280296 0.1857160 73.92 <2e-16 ***
ORIGIN_SZKLSZ07 18.6425146 0.0084952 2194.47 <2e-16 ***
ORIGIN_SZKLSZ08 18.0928506 0.0101567 1781.37 <2e-16 ***
ORIGIN_SZLKSZ01 17.8907138 0.0397083 450.55 <2e-16 ***
ORIGIN_SZMDSZ01 18.7605188 0.0285455 657.22 <2e-16 ***
ORIGIN_SZMDSZ02 19.1533927 0.0102815 1862.90 <2e-16 ***
ORIGIN_SZMDSZ03 17.8404982 0.0169690 1051.36 <2e-16 ***
ORIGIN_SZMPSZ01 19.0765941 0.0083937 2272.74 <2e-16 ***
ORIGIN_SZMPSZ02 19.2162527 0.0068331 2812.24 <2e-16 ***
ORIGIN_SZMPSZ03 19.9965344 0.0054569 3664.44 <2e-16 ***
ORIGIN_SZMUSZ02 15.9130765 0.1037472 153.38 <2e-16 ***
ORIGIN_SZNTSZ01 17.0840999 0.0352513 484.64 <2e-16 ***
ORIGIN_SZNTSZ02 16.5792122 0.0233186 710.99 <2e-16 ***
ORIGIN_SZNTSZ03 18.9506415 0.0075957 2494.93 <2e-16 ***
ORIGIN_SZNTSZ05 15.8770261 0.0495825 320.21 <2e-16 ***
ORIGIN_SZNTSZ06 15.3997415 0.0557029 276.46 <2e-16 ***
ORIGIN_SZNVSZ01 20.2241694 0.0043487 4650.65 <2e-16 ***
ORIGIN_SZNVSZ02 19.1897826 0.0065383 2934.97 <2e-16 ***
ORIGIN_SZNVSZ03 18.8854268 0.0080459 2347.22 <2e-16 ***
ORIGIN_SZNVSZ04 18.8940191 0.0090985 2076.61 <2e-16 ***
ORIGIN_SZNVSZ05 17.6278585 0.0168107 1048.61 <2e-16 ***
ORIGIN_SZPGSZ01 19.4825220 0.0122960 1584.46 <2e-16 ***
ORIGIN_SZPGSZ02 19.4726761 0.0073116 2663.25 <2e-16 ***
ORIGIN_SZPGSZ03 20.5515713 0.0045631 4503.86 <2e-16 ***
ORIGIN_SZPGSZ04 21.0527131 0.0041500 5072.89 <2e-16 ***
ORIGIN_SZPGSZ05 20.1436604 0.0057267 3517.48 <2e-16 ***
ORIGIN_SZPLSZ01 19.1832002 0.0120006 1598.53 <2e-16 ***
ORIGIN_SZPLSZ02 18.8752206 0.0149740 1260.53 <2e-16 ***
ORIGIN_SZPLSZ03 18.1000818 0.0371769 486.86 <2e-16 ***
ORIGIN_SZPLSZ04 17.1730559 0.0370280 463.79 <2e-16 ***
ORIGIN_SZPLSZ05 17.9084439 0.0225031 795.82 <2e-16 ***
ORIGIN_SZPNSZ01 21.0804425 0.0044829 4702.41 <2e-16 ***
ORIGIN_SZPNSZ02 19.8822123 0.0111507 1783.05 <2e-16 ***
ORIGIN_SZPNSZ03 17.9293289 0.0193571 926.24 <2e-16 ***
ORIGIN_SZPNSZ04 17.1039594 0.0334954 510.64 <2e-16 ***
ORIGIN_SZPNSZ05 18.2543864 0.0275554 662.46 <2e-16 ***
ORIGIN_SZPRSZ01 19.8777935 0.0117586 1690.49 <2e-16 ***
ORIGIN_SZPRSZ02 21.0751780 0.0044832 4700.88 <2e-16 ***
ORIGIN_SZPRSZ03 20.6717019 0.0045577 4535.55 <2e-16 ***
ORIGIN_SZPRSZ04 19.6365125 0.0074923 2620.90 <2e-16 ***
ORIGIN_SZPRSZ05 21.3132151 0.0042119 5060.24 <2e-16 ***
ORIGIN_SZPRSZ06 18.9314574 0.0117278 1614.24 <2e-16 ***
ORIGIN_SZPRSZ07 17.2822918 0.0162430 1063.98 <2e-16 ***
ORIGIN_SZPRSZ08 19.9267642 0.0062298 3198.62 <2e-16 ***
ORIGIN_SZQTSZ01 19.7357175 0.0066359 2974.08 <2e-16 ***
ORIGIN_SZQTSZ02 19.2082141 0.0061402 3128.26 <2e-16 ***
ORIGIN_SZQTSZ03 19.7771883 0.0056220 3517.83 <2e-16 ***
ORIGIN_SZQTSZ04 18.7114421 0.0072842 2568.76 <2e-16 ***
ORIGIN_SZQTSZ05 19.3049324 0.0062401 3093.69 <2e-16 ***
ORIGIN_SZQTSZ06 19.2643228 0.0065590 2937.09 <2e-16 ***
ORIGIN_SZQTSZ07 18.5697347 0.0095373 1947.06 <2e-16 ***
ORIGIN_SZQTSZ08 19.6147001 0.0061330 3198.21 <2e-16 ***
ORIGIN_SZQTSZ09 19.2550793 0.0069947 2752.82 <2e-16 ***
ORIGIN_SZQTSZ10 19.5801866 0.0064513 3035.07 <2e-16 ***
ORIGIN_SZQTSZ11 17.7398366 0.0143648 1234.95 <2e-16 ***
ORIGIN_SZQTSZ12 17.2420354 0.0186736 923.34 <2e-16 ***
ORIGIN_SZQTSZ13 19.3857418 0.0078878 2457.69 <2e-16 ***
ORIGIN_SZQTSZ14 18.1300753 0.0122096 1484.90 <2e-16 ***
ORIGIN_SZQTSZ15 19.4222283 0.0120871 1606.86 <2e-16 ***
ORIGIN_SZRCSZ01 18.1549045 0.0125108 1451.13 <2e-16 ***
ORIGIN_SZRCSZ06 18.8836400 0.0082161 2298.38 <2e-16 ***
ORIGIN_SZRVSZ01 16.7864438 0.0323796 518.43 <2e-16 ***
ORIGIN_SZRVSZ02 16.4203244 0.0276836 593.14 <2e-16 ***
ORIGIN_SZRVSZ03 16.6453738 0.0244992 679.42 <2e-16 ***
ORIGIN_SZRVSZ04 15.9559213 0.0556344 286.80 <2e-16 ***
ORIGIN_SZRVSZ05 17.0476331 0.0164122 1038.71 <2e-16 ***
ORIGIN_SZSBSZ01 20.0417968 0.0062488 3207.29 <2e-16 ***
ORIGIN_SZSBSZ02 19.1869565 0.0081051 2367.26 <2e-16 ***
ORIGIN_SZSBSZ03 20.5769861 0.0045108 4561.70 <2e-16 ***
ORIGIN_SZSBSZ04 20.5154199 0.0050548 4058.57 <2e-16 ***
ORIGIN_SZSBSZ05 19.6250669 0.0065562 2993.35 <2e-16 ***
ORIGIN_SZSBSZ06 18.8419757 0.0171135 1101.00 <2e-16 ***
ORIGIN_SZSBSZ07 19.4897259 0.0124528 1565.09 <2e-16 ***
ORIGIN_SZSBSZ08 18.7027917 0.0140545 1330.73 <2e-16 ***
ORIGIN_SZSBSZ09 18.8893480 0.0088571 2132.67 <2e-16 ***
ORIGIN_SZSESZ02 20.8962192 0.0041665 5015.34 <2e-16 ***
ORIGIN_SZSESZ03 20.9452771 0.0039737 5270.94 <2e-16 ***
ORIGIN_SZSESZ04 20.6576142 0.0046364 4455.55 <2e-16 ***
ORIGIN_SZSESZ05 19.5170732 0.0058912 3312.92 <2e-16 ***
ORIGIN_SZSESZ06 20.7595824 0.0045747 4537.89 <2e-16 ***
ORIGIN_SZSESZ07 17.6888256 0.0195787 903.47 <2e-16 ***
ORIGIN_SZSGSZ01 19.1359250 0.0085781 2230.79 <2e-16 ***
ORIGIN_SZSGSZ02 18.5614369 0.0102037 1819.10 <2e-16 ***
ORIGIN_SZSGSZ03 19.9933176 0.0050434 3964.23 <2e-16 ***
ORIGIN_SZSGSZ04 20.2426871 0.0047211 4287.71 <2e-16 ***
ORIGIN_SZSGSZ05 18.0114965 0.0107743 1671.70 <2e-16 ***
ORIGIN_SZSGSZ06 20.2593194 0.0044538 4548.76 <2e-16 ***
ORIGIN_SZSGSZ07 19.0763664 0.0062968 3029.54 <2e-16 ***
ORIGIN_SZSKSZ01 19.9222451 0.0085136 2340.04 <2e-16 ***
ORIGIN_SZSKSZ02 20.8633383 0.0055248 3776.33 <2e-16 ***
ORIGIN_SZSKSZ03 19.6528148 0.0080534 2440.33 <2e-16 ***
ORIGIN_SZSKSZ04 18.0754470 0.0275771 655.45 <2e-16 ***
ORIGIN_SZSKSZ05 19.1192521 0.0155579 1228.91 <2e-16 ***
ORIGIN_SZSLSZ01 17.1501034 0.0329384 520.67 <2e-16 ***
ORIGIN_SZSLSZ04 19.5949774 0.0076753 2552.98 <2e-16 ***
ORIGIN_SZSRSZ01 16.9761403 0.0162020 1047.78 <2e-16 ***
ORIGIN_SZTHSZ01 17.9695687 0.0488559 367.81 <2e-16 ***
ORIGIN_SZTHSZ03 18.5427522 0.0223617 829.22 <2e-16 ***
ORIGIN_SZTHSZ04 17.4760374 0.0286247 610.52 <2e-16 ***
ORIGIN_SZTHSZ06 17.8401186 0.0183322 973.16 <2e-16 ***
ORIGIN_SZTMSZ01 20.3406361 0.0056607 3593.33 <2e-16 ***
ORIGIN_SZTMSZ02 22.0307026 0.0037386 5892.85 <2e-16 ***
ORIGIN_SZTMSZ03 21.3451920 0.0040606 5256.65 <2e-16 ***
ORIGIN_SZTMSZ04 20.6611593 0.0049896 4140.87 <2e-16 ***
ORIGIN_SZTMSZ05 19.3323133 0.0112868 1712.82 <2e-16 ***
ORIGIN_SZTNSZ01 17.9513571 0.0128266 1399.54 <2e-16 ***
ORIGIN_SZTNSZ02 18.0267387 0.0098372 1832.51 <2e-16 ***
ORIGIN_SZTNSZ03 17.7253700 0.0134668 1316.23 <2e-16 ***
ORIGIN_SZTNSZ04 19.4474075 0.0073760 2636.59 <2e-16 ***
ORIGIN_SZTPSZ01 19.1078631 0.0065635 2911.25 <2e-16 ***
ORIGIN_SZTPSZ02 20.2837634 0.0041411 4898.18 <2e-16 ***
ORIGIN_SZTPSZ03 19.1838238 0.0059552 3221.37 <2e-16 ***
ORIGIN_SZTPSZ04 19.1805388 0.0054778 3501.53 <2e-16 ***
ORIGIN_SZTPSZ05 19.3718076 0.0058610 3305.18 <2e-16 ***
ORIGIN_SZTPSZ06 19.6605723 0.0054968 3576.70 <2e-16 ***
ORIGIN_SZTPSZ07 19.4499807 0.0060491 3215.36 <2e-16 ***
ORIGIN_SZTPSZ08 18.7996538 0.0095757 1963.28 <2e-16 ***
ORIGIN_SZTPSZ09 19.0025110 0.0067068 2833.31 <2e-16 ***
ORIGIN_SZTPSZ10 18.8899657 0.0076094 2482.46 <2e-16 ***
ORIGIN_SZTPSZ11 19.6277780 0.0053983 3635.93 <2e-16 ***
ORIGIN_SZTPSZ12 19.1471104 0.0065742 2912.45 <2e-16 ***
ORIGIN_SZTSSZ01 17.4901113 0.0478954 365.17 <2e-16 ***
ORIGIN_SZTSSZ02 20.4997466 0.0081850 2504.55 <2e-16 ***
ORIGIN_SZTSSZ03 20.1076553 0.0084728 2373.19 <2e-16 ***
ORIGIN_SZTSSZ04 20.0646610 0.0089008 2254.26 <2e-16 ***
ORIGIN_SZTSSZ05 19.3962067 0.0151392 1281.19 <2e-16 ***
ORIGIN_SZTSSZ06 20.9235857 0.0178278 1173.65 <2e-16 ***
ORIGIN_SZWCSZ01 20.8411600 0.0086519 2408.86 <2e-16 ***
ORIGIN_SZWCSZ02 17.7355404 0.0328889 539.26 <2e-16 ***
ORIGIN_SZWCSZ03 14.9380886 0.1240699 120.40 <2e-16 ***
ORIGIN_SZWDSZ01 21.1969012 0.0037830 5603.23 <2e-16 ***
ORIGIN_SZWDSZ02 20.5930001 0.0044572 4620.13 <2e-16 ***
ORIGIN_SZWDSZ03 21.2521867 0.0041672 5099.85 <2e-16 ***
ORIGIN_SZWDSZ04 21.0702687 0.0048648 4331.13 <2e-16 ***
ORIGIN_SZWDSZ05 20.4008998 0.0051801 3938.35 <2e-16 ***
ORIGIN_SZWDSZ06 20.6669176 0.0049280 4193.78 <2e-16 ***
ORIGIN_SZWDSZ07 19.0500370 0.0082729 2302.71 <2e-16 ***
ORIGIN_SZWDSZ08 19.0816252 0.0080667 2365.49 <2e-16 ***
ORIGIN_SZWDSZ09 21.4182096 0.0040391 5302.73 <2e-16 ***
ORIGIN_SZYSSZ01 19.5355157 0.0057540 3395.14 <2e-16 ***
ORIGIN_SZYSSZ02 20.8737972 0.0048278 4323.64 <2e-16 ***
ORIGIN_SZYSSZ03 21.6614437 0.0040011 5413.81 <2e-16 ***
ORIGIN_SZYSSZ04 20.9305289 0.0043595 4801.10 <2e-16 ***
ORIGIN_SZYSSZ05 20.1727678 0.0058466 3450.34 <2e-16 ***
ORIGIN_SZYSSZ06 19.1481507 0.0116724 1640.47 <2e-16 ***
ORIGIN_SZYSSZ07 18.7919074 0.0141636 1326.78 <2e-16 ***
ORIGIN_SZYSSZ08 19.9733515 0.0061229 3262.07 <2e-16 ***
ORIGIN_SZYSSZ09 20.9366181 0.0040347 5189.15 <2e-16 ***
log(SCHOOL_COUNT) 0.4755516 0.0004701 1011.55 <2e-16 ***
log(BUSINESS_COUNT) 0.1796905 0.0001856 968.12 <2e-16 ***
log(DIST) -1.6929522 0.0004093 -4136.01 <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: 189463537 on 14471 degrees of freedom
Residual deviance: 15526121 on 14189 degrees of freedom
AIC: 15615824
Number of Fisher Scoring iterations: 6
What can we learn from the report above?
the ⍺1 and ⍺2 of SCHOOL_COUNT and BUSINESS_COUNT are 0.4755516 and 0.1796905 respectively.
𝛽, the distance decay parameter is -1.6929522
there are a series of parameters which are the vector of 𝜇𝑖 values associated with the origin constraints.
Goodness of fit
In statistical modelling, the next question we would like to answer is how well the proportion of variance in the dependent variable (i.e. TRIPS) that can be explained by the explanatory variables.
In order to provide answer to this question, R-squared statistics will be used. However, R-squared is not an output of glm(). Hence we will write a function called CalcRSquared by using the code chunk below.
CalcRSquared <- function(observed, estimated){
r <- cor(observed, estimated)
R2 <- r^2
R2
}NOw, we can examine how the constraints hold for destinations this time.
CalcRSquared(orcSIM_Poisson$data$TRIPS, orcSIM_Poisson$fitted.values)[1] 0.4362208With reference to the R-Squared above, we can conclude that the model accounts for about 44% of the variation of flows in the systems. Not bad, but not brilliant either.
Doubly constrained model
In this section, we will fit a doubly constrained SIM by using the general formula shown below:
and the code chunk used is shown below.
dbcSIM_Poisson <- glm(formula = TRIPS ~
ORIGIN_SZ +
DESTIN_SZ +
log(DIST),
family = poisson(link = "log"),
data = inter_zonal_flow,
na.action = na.exclude)
summary(dbcSIM_Poisson)
Important
It is important to note that there is a slight change of the code chunk. I have removed the -1 which means that an intercept will appear in the model again. This is not because I want an intercept as it makes the origin and destination coefficients harder to interpret, rather the -1 cheat for removing the intercept only works with one factor level but in double-constrained model we have two factor levels, namely: origins and destinations.
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(DIST), family = poisson(link = "log"),
data = inter_zonal_flow, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 21.8312374 0.0059160 3690.190 < 2e-16 ***
ORIGIN_SZAMSZ02 0.5263502 0.0048031 109.585 < 2e-16 ***
ORIGIN_SZAMSZ03 0.3139982 0.0049254 63.751 < 2e-16 ***
ORIGIN_SZAMSZ04 -0.2146257 0.0053639 -40.013 < 2e-16 ***
ORIGIN_SZAMSZ05 -0.1890446 0.0060386 -31.306 < 2e-16 ***
ORIGIN_SZAMSZ06 0.1539201 0.0054401 28.294 < 2e-16 ***
ORIGIN_SZAMSZ07 -0.9826565 0.0098676 -99.584 < 2e-16 ***
ORIGIN_SZAMSZ08 -0.4488417 0.0093070 -48.226 < 2e-16 ***
ORIGIN_SZAMSZ09 0.0713474 0.0057402 12.429 < 2e-16 ***
ORIGIN_SZAMSZ10 0.4313742 0.0050370 85.641 < 2e-16 ***
ORIGIN_SZAMSZ11 -1.4712226 0.0131178 -112.154 < 2e-16 ***
ORIGIN_SZAMSZ12 -1.7250733 0.0111603 -154.573 < 2e-16 ***
ORIGIN_SZBDSZ01 0.8810576 0.0048168 182.914 < 2e-16 ***
ORIGIN_SZBDSZ02 0.1100240 0.0055529 19.814 < 2e-16 ***
ORIGIN_SZBDSZ03 0.3606166 0.0050672 71.167 < 2e-16 ***
ORIGIN_SZBDSZ04 1.4624347 0.0044212 330.781 < 2e-16 ***
ORIGIN_SZBDSZ05 0.6207557 0.0050843 122.092 < 2e-16 ***
ORIGIN_SZBDSZ06 0.6712973 0.0051953 129.214 < 2e-16 ***
ORIGIN_SZBDSZ07 -1.2338669 0.0100775 -122.437 < 2e-16 ***
ORIGIN_SZBDSZ08 -1.0444562 0.0094555 -110.460 < 2e-16 ***
ORIGIN_SZBKSZ01 -0.2838426 0.0071354 -39.780 < 2e-16 ***
ORIGIN_SZBKSZ02 0.5550522 0.0059014 94.054 < 2e-16 ***
ORIGIN_SZBKSZ03 0.7396640 0.0056796 130.231 < 2e-16 ***
ORIGIN_SZBKSZ04 -0.2242451 0.0067482 -33.230 < 2e-16 ***
ORIGIN_SZBKSZ05 -0.2371614 0.0069386 -34.180 < 2e-16 ***
ORIGIN_SZBKSZ06 -0.1413812 0.0065035 -21.739 < 2e-16 ***
ORIGIN_SZBKSZ07 0.7089989 0.0051843 136.758 < 2e-16 ***
ORIGIN_SZBKSZ08 -0.0907065 0.0059157 -15.333 < 2e-16 ***
ORIGIN_SZBKSZ09 -0.1775146 0.0063302 -28.042 < 2e-16 ***
ORIGIN_SZBLSZ01 -2.3684539 0.0154280 -153.516 < 2e-16 ***
ORIGIN_SZBLSZ02 -2.8078475 0.0197839 -141.926 < 2e-16 ***
ORIGIN_SZBLSZ03 -3.3122763 0.0466091 -71.065 < 2e-16 ***
ORIGIN_SZBLSZ04 -2.6770542 0.0241793 -110.717 < 2e-16 ***
ORIGIN_SZBMSZ01 0.0618035 0.0059400 10.405 < 2e-16 ***
ORIGIN_SZBMSZ02 -1.3535767 0.0073741 -183.557 < 2e-16 ***
ORIGIN_SZBMSZ03 -0.7569095 0.0063187 -119.790 < 2e-16 ***
ORIGIN_SZBMSZ04 -0.2949304 0.0059603 -49.483 < 2e-16 ***
ORIGIN_SZBMSZ05 -2.6131992 0.0172376 -151.599 < 2e-16 ***
ORIGIN_SZBMSZ06 -3.0315024 0.0185502 -163.422 < 2e-16 ***
ORIGIN_SZBMSZ07 -0.6962524 0.0064068 -108.674 < 2e-16 ***
ORIGIN_SZBMSZ08 -0.9310730 0.0064541 -144.261 < 2e-16 ***
ORIGIN_SZBMSZ09 -1.2911253 0.0092047 -140.268 < 2e-16 ***
ORIGIN_SZBMSZ10 -1.6687004 0.0095708 -174.353 < 2e-16 ***
ORIGIN_SZBMSZ11 -1.1152794 0.0072027 -154.841 < 2e-16 ***
ORIGIN_SZBMSZ12 -1.5323954 0.0099932 -153.344 < 2e-16 ***
ORIGIN_SZBMSZ13 -0.6267376 0.0065863 -95.158 < 2e-16 ***
ORIGIN_SZBMSZ14 -1.0475467 0.0072472 -144.544 < 2e-16 ***
ORIGIN_SZBMSZ15 -0.5049444 0.0067390 -74.929 < 2e-16 ***
ORIGIN_SZBMSZ16 -1.5282897 0.0099545 -153.527 < 2e-16 ***
ORIGIN_SZBMSZ17 -1.5722349 0.0161533 -97.332 < 2e-16 ***
ORIGIN_SZBPSZ01 0.5814175 0.0062904 92.429 < 2e-16 ***
ORIGIN_SZBPSZ02 0.0875442 0.0072190 12.127 < 2e-16 ***
ORIGIN_SZBPSZ03 0.3358227 0.0070460 47.662 < 2e-16 ***
ORIGIN_SZBPSZ04 0.6507586 0.0057726 112.733 < 2e-16 ***
ORIGIN_SZBPSZ05 0.9502124 0.0052971 179.384 < 2e-16 ***
ORIGIN_SZBPSZ06 -1.0480314 0.0098191 -106.734 < 2e-16 ***
ORIGIN_SZBPSZ07 -0.5467931 0.0091676 -59.644 < 2e-16 ***
ORIGIN_SZBSSZ01 0.2998334 0.0059193 50.654 < 2e-16 ***
ORIGIN_SZBSSZ02 0.2841036 0.0050863 55.856 < 2e-16 ***
ORIGIN_SZBSSZ03 -0.2331505 0.0056565 -41.218 < 2e-16 ***
ORIGIN_SZBTSZ01 0.0987284 0.0063715 15.495 < 2e-16 ***
ORIGIN_SZBTSZ02 -0.6261229 0.0084604 -74.006 < 2e-16 ***
ORIGIN_SZBTSZ03 -0.4326963 0.0073452 -58.909 < 2e-16 ***
ORIGIN_SZBTSZ04 -1.4998668 0.0110013 -136.336 < 2e-16 ***
ORIGIN_SZBTSZ05 -0.9564768 0.0122202 -78.270 < 2e-16 ***
ORIGIN_SZBTSZ06 -1.2853131 0.0099328 -129.401 < 2e-16 ***
ORIGIN_SZBTSZ07 -2.3870991 0.0144589 -165.096 < 2e-16 ***
ORIGIN_SZBTSZ08 -1.3715855 0.0113825 -120.499 < 2e-16 ***
ORIGIN_SZCBSZ01 -3.5940232 0.0548979 -65.467 < 2e-16 ***
ORIGIN_SZCCSZ01 -0.7008220 0.0140373 -49.926 < 2e-16 ***
ORIGIN_SZCHSZ01 -0.9109524 0.0122869 -74.140 < 2e-16 ***
ORIGIN_SZCHSZ02 -0.8566547 0.0088749 -96.526 < 2e-16 ***
ORIGIN_SZCHSZ03 1.1153731 0.0066136 168.650 < 2e-16 ***
ORIGIN_SZCKSZ01 0.3001815 0.0058548 51.271 < 2e-16 ***
ORIGIN_SZCKSZ02 0.7185711 0.0060595 118.585 < 2e-16 ***
ORIGIN_SZCKSZ03 1.1389824 0.0053179 214.178 < 2e-16 ***
ORIGIN_SZCKSZ04 1.6281772 0.0054761 297.324 < 2e-16 ***
ORIGIN_SZCKSZ05 0.8338470 0.0064178 129.927 < 2e-16 ***
ORIGIN_SZCKSZ06 0.6528993 0.0082375 79.259 < 2e-16 ***
ORIGIN_SZCLSZ01 -0.7174758 0.0082123 -87.366 < 2e-16 ***
ORIGIN_SZCLSZ02 -1.7513100 0.0139062 -125.938 < 2e-16 ***
ORIGIN_SZCLSZ03 -1.0362873 0.0085485 -121.224 < 2e-16 ***
ORIGIN_SZCLSZ04 0.6160017 0.0051276 120.136 < 2e-16 ***
ORIGIN_SZCLSZ05 -2.1005122 0.0150228 -139.821 < 2e-16 ***
ORIGIN_SZCLSZ06 0.7252108 0.0049447 146.665 < 2e-16 ***
ORIGIN_SZCLSZ07 -0.5343482 0.0062500 -85.496 < 2e-16 ***
ORIGIN_SZCLSZ08 -0.2153408 0.0067571 -31.869 < 2e-16 ***
ORIGIN_SZCLSZ09 -1.8019961 0.0169078 -106.578 < 2e-16 ***
ORIGIN_SZDTSZ02 -3.9057711 0.0834668 -46.794 < 2e-16 ***
ORIGIN_SZDTSZ03 -3.4152419 0.0738650 -46.236 < 2e-16 ***
ORIGIN_SZDTSZ13 -3.0183438 0.0315257 -95.742 < 2e-16 ***
ORIGIN_SZGLSZ01 -1.7812384 0.0099367 -179.258 < 2e-16 ***
ORIGIN_SZGLSZ02 -0.1074991 0.0054325 -19.788 < 2e-16 ***
ORIGIN_SZGLSZ03 -0.2461106 0.0057176 -43.045 < 2e-16 ***
ORIGIN_SZGLSZ04 0.8657186 0.0046413 186.524 < 2e-16 ***
ORIGIN_SZGLSZ05 0.5871393 0.0047939 122.477 < 2e-16 ***
ORIGIN_SZHGSZ01 0.3543819 0.0050461 70.229 < 2e-16 ***
ORIGIN_SZHGSZ02 0.4218178 0.0050820 83.003 < 2e-16 ***
ORIGIN_SZHGSZ03 0.2411309 0.0054241 44.456 < 2e-16 ***
ORIGIN_SZHGSZ04 0.8180622 0.0046153 177.252 < 2e-16 ***
ORIGIN_SZHGSZ05 1.2173687 0.0045655 266.647 < 2e-16 ***
ORIGIN_SZHGSZ06 -0.1826300 0.0058214 -31.372 < 2e-16 ***
ORIGIN_SZHGSZ07 0.3172839 0.0050733 62.540 < 2e-16 ***
ORIGIN_SZHGSZ08 -0.1151369 0.0057067 -20.176 < 2e-16 ***
ORIGIN_SZHGSZ09 -1.2873441 0.0091690 -140.401 < 2e-16 ***
ORIGIN_SZHGSZ10 -3.3783178 0.0424682 -79.549 < 2e-16 ***
ORIGIN_SZJESZ01 0.4859234 0.0055927 86.885 < 2e-16 ***
ORIGIN_SZJESZ02 0.1766088 0.0055800 31.650 < 2e-16 ***
ORIGIN_SZJESZ03 -0.2177441 0.0059535 -36.574 < 2e-16 ***
ORIGIN_SZJESZ04 -1.5532182 0.0104526 -148.597 < 2e-16 ***
ORIGIN_SZJESZ05 -2.3332926 0.0142701 -163.509 < 2e-16 ***
ORIGIN_SZJESZ06 0.3007382 0.0055019 54.661 < 2e-16 ***
ORIGIN_SZJESZ07 -1.9687994 0.0121092 -162.587 < 2e-16 ***
ORIGIN_SZJESZ08 -1.3032070 0.0122024 -106.800 < 2e-16 ***
ORIGIN_SZJESZ09 0.5762635 0.0058766 98.061 < 2e-16 ***
ORIGIN_SZJESZ10 -1.4423113 0.0194773 -74.051 < 2e-16 ***
ORIGIN_SZJESZ11 -1.9720897 0.0200811 -98.206 < 2e-16 ***
ORIGIN_SZJWSZ01 0.3808627 0.0071357 53.374 < 2e-16 ***
ORIGIN_SZJWSZ02 0.7963999 0.0053150 149.840 < 2e-16 ***
ORIGIN_SZJWSZ03 1.5429636 0.0049961 308.834 < 2e-16 ***
ORIGIN_SZJWSZ04 0.6410760 0.0056711 113.042 < 2e-16 ***
ORIGIN_SZJWSZ05 -2.1571049 0.0133584 -161.479 < 2e-16 ***
ORIGIN_SZJWSZ06 -1.5174532 0.0113384 -133.833 < 2e-16 ***
ORIGIN_SZJWSZ07 -2.7089963 0.0280439 -96.598 < 2e-16 ***
ORIGIN_SZJWSZ08 1.5343415 0.0051711 296.713 < 2e-16 ***
ORIGIN_SZJWSZ09 1.8837410 0.0048845 385.656 < 2e-16 ***
ORIGIN_SZKLSZ01 0.1081286 0.0053307 20.284 < 2e-16 ***
ORIGIN_SZKLSZ02 -0.8844695 0.0067728 -130.591 < 2e-16 ***
ORIGIN_SZKLSZ03 -0.6872640 0.0062857 -109.337 < 2e-16 ***
ORIGIN_SZKLSZ04 -2.2090319 0.0122440 -180.418 < 2e-16 ***
ORIGIN_SZKLSZ05 -1.1728726 0.0110765 -105.888 < 2e-16 ***
ORIGIN_SZKLSZ06 -6.1162315 0.1857789 -32.922 < 2e-16 ***
ORIGIN_SZKLSZ07 -1.4082749 0.0092299 -152.578 < 2e-16 ***
ORIGIN_SZKLSZ08 -1.7781551 0.0104682 -169.862 < 2e-16 ***
ORIGIN_SZLKSZ01 -2.0531568 0.0398803 -51.483 < 2e-16 ***
ORIGIN_SZMDSZ01 -0.8825639 0.0287621 -30.685 < 2e-16 ***
ORIGIN_SZMDSZ02 -0.6219993 0.0107388 -57.921 < 2e-16 ***
ORIGIN_SZMDSZ03 -2.0840156 0.0173117 -120.382 < 2e-16 ***
ORIGIN_SZMPSZ01 -0.9659093 0.0086972 -111.060 < 2e-16 ***
ORIGIN_SZMPSZ02 -1.0411153 0.0073403 -141.836 < 2e-16 ***
ORIGIN_SZMPSZ03 0.0001659 0.0059401 0.028 0.977719
ORIGIN_SZMUSZ02 -3.7599031 0.1037937 -36.225 < 2e-16 ***
ORIGIN_SZNTSZ01 -3.0388366 0.0355325 -85.523 < 2e-16 ***
ORIGIN_SZNTSZ02 -3.4230640 0.0235902 -145.106 < 2e-16 ***
ORIGIN_SZNTSZ03 -0.9094796 0.0082551 -110.172 < 2e-16 ***
ORIGIN_SZNTSZ05 -4.0861681 0.0499630 -81.784 < 2e-16 ***
ORIGIN_SZNTSZ06 -3.9497128 0.0565388 -69.858 < 2e-16 ***
ORIGIN_SZNVSZ01 0.3235636 0.0049439 65.447 < 2e-16 ***
ORIGIN_SZNVSZ02 -0.6946748 0.0070536 -98.485 < 2e-16 ***
ORIGIN_SZNVSZ03 -1.0540196 0.0083781 -125.806 < 2e-16 ***
ORIGIN_SZNVSZ04 -0.9897977 0.0093463 -105.903 < 2e-16 ***
ORIGIN_SZNVSZ05 -2.2578432 0.0169180 -133.458 < 2e-16 ***
ORIGIN_SZPGSZ01 0.2399827 0.0130436 18.398 < 2e-16 ***
ORIGIN_SZPGSZ02 -0.3352342 0.0078451 -42.732 < 2e-16 ***
ORIGIN_SZPGSZ03 0.9515148 0.0051376 185.207 < 2e-16 ***
ORIGIN_SZPGSZ04 1.3998952 0.0047991 291.697 < 2e-16 ***
ORIGIN_SZPGSZ05 0.4451629 0.0063423 70.189 < 2e-16 ***
ORIGIN_SZPLSZ01 -0.9705918 0.0122781 -79.050 < 2e-16 ***
ORIGIN_SZPLSZ02 -1.0670151 0.0153358 -69.577 < 2e-16 ***
ORIGIN_SZPLSZ03 -2.1229124 0.0373527 -56.834 < 2e-16 ***
ORIGIN_SZPLSZ04 -3.0911932 0.0371296 -83.254 < 2e-16 ***
ORIGIN_SZPLSZ05 -2.1705708 0.0226085 -96.007 < 2e-16 ***
ORIGIN_SZPNSZ01 0.9052637 0.0065952 137.262 < 2e-16 ***
ORIGIN_SZPNSZ02 -0.1720425 0.0125658 -13.691 < 2e-16 ***
ORIGIN_SZPNSZ03 -2.3973459 0.0201408 -119.029 < 2e-16 ***
ORIGIN_SZPNSZ04 -3.4483689 0.0343741 -100.319 < 2e-16 ***
ORIGIN_SZPNSZ05 -2.0588530 0.0282328 -72.924 < 2e-16 ***
ORIGIN_SZPRSZ01 -0.6399015 0.0120470 -53.117 < 2e-16 ***
ORIGIN_SZPRSZ02 0.8122270 0.0050886 159.617 < 2e-16 ***
ORIGIN_SZPRSZ03 0.3990960 0.0051810 77.031 < 2e-16 ***
ORIGIN_SZPRSZ04 -0.8485348 0.0079236 -107.089 < 2e-16 ***
ORIGIN_SZPRSZ05 0.8008791 0.0048532 165.021 < 2e-16 ***
ORIGIN_SZPRSZ06 -1.4498806 0.0121422 -119.408 < 2e-16 ***
ORIGIN_SZPRSZ07 -3.2025045 0.0167118 -191.631 < 2e-16 ***
ORIGIN_SZPRSZ08 -0.5862269 0.0067255 -87.165 < 2e-16 ***
ORIGIN_SZQTSZ01 -0.1859270 0.0075531 -24.616 < 2e-16 ***
ORIGIN_SZQTSZ02 -0.8715122 0.0068124 -127.929 < 2e-16 ***
ORIGIN_SZQTSZ03 -0.1259816 0.0064796 -19.443 < 2e-16 ***
ORIGIN_SZQTSZ04 -1.4620032 0.0079848 -183.098 < 2e-16 ***
ORIGIN_SZQTSZ05 -0.6675643 0.0069616 -95.892 < 2e-16 ***
ORIGIN_SZQTSZ06 -0.8190026 0.0072713 -112.634 < 2e-16 ***
ORIGIN_SZQTSZ07 -1.5189403 0.0099864 -152.101 < 2e-16 ***
ORIGIN_SZQTSZ08 -0.4976238 0.0067874 -73.316 < 2e-16 ***
ORIGIN_SZQTSZ09 -0.9006162 0.0075978 -118.536 < 2e-16 ***
ORIGIN_SZQTSZ10 -0.6690184 0.0071574 -93.473 < 2e-16 ***
ORIGIN_SZQTSZ11 -2.5203437 0.0147000 -171.452 < 2e-16 ***
ORIGIN_SZQTSZ12 -3.0461675 0.0190193 -160.162 < 2e-16 ***
ORIGIN_SZQTSZ13 -0.7501068 0.0084481 -88.791 < 2e-16 ***
ORIGIN_SZQTSZ14 -1.9321849 0.0126114 -153.209 < 2e-16 ***
ORIGIN_SZQTSZ15 -0.9576828 0.0127157 -75.315 < 2e-16 ***
ORIGIN_SZRCSZ01 -1.8167951 0.0129234 -140.582 < 2e-16 ***
ORIGIN_SZRCSZ06 -0.5560563 0.0090507 -61.438 < 2e-16 ***
ORIGIN_SZRVSZ01 -2.8862570 0.0325532 -88.663 < 2e-16 ***
ORIGIN_SZRVSZ02 -3.1555662 0.0281279 -112.186 < 2e-16 ***
ORIGIN_SZRVSZ03 -2.9836089 0.0248449 -120.089 < 2e-16 ***
ORIGIN_SZRVSZ04 -3.5520422 0.0561371 -63.274 < 2e-16 ***
ORIGIN_SZRVSZ05 -2.5866584 0.0180382 -143.399 < 2e-16 ***
ORIGIN_SZSBSZ01 0.2867444 0.0071098 40.331 < 2e-16 ***
ORIGIN_SZSBSZ02 -0.9012334 0.0087262 -103.278 < 2e-16 ***
ORIGIN_SZSBSZ03 0.8311038 0.0055422 149.958 < 2e-16 ***
ORIGIN_SZSBSZ04 0.4044170 0.0062047 65.179 < 2e-16 ***
ORIGIN_SZSBSZ05 -0.2661845 0.0074162 -35.892 < 2e-16 ***
ORIGIN_SZSBSZ06 -0.9023075 0.0175046 -51.547 < 2e-16 ***
ORIGIN_SZSBSZ07 0.0505870 0.0131317 3.852 0.000117 ***
ORIGIN_SZSBSZ08 -1.1158011 0.0145416 -76.732 < 2e-16 ***
ORIGIN_SZSBSZ09 -0.9682835 0.0095396 -101.501 < 2e-16 ***
ORIGIN_SZSESZ02 1.1452735 0.0047810 239.548 < 2e-16 ***
ORIGIN_SZSESZ03 1.2815277 0.0045677 280.564 < 2e-16 ***
ORIGIN_SZSESZ04 0.8085857 0.0052756 153.269 < 2e-16 ***
ORIGIN_SZSESZ05 -0.2329413 0.0063113 -36.909 < 2e-16 ***
ORIGIN_SZSESZ06 1.0576879 0.0049909 211.925 < 2e-16 ***
ORIGIN_SZSESZ07 -2.3165908 0.0196831 -117.695 < 2e-16 ***
ORIGIN_SZSGSZ01 -0.6606350 0.0088079 -75.005 < 2e-16 ***
ORIGIN_SZSGSZ02 -1.3638984 0.0104040 -131.094 < 2e-16 ***
ORIGIN_SZSGSZ03 0.1152591 0.0054649 21.091 < 2e-16 ***
ORIGIN_SZSGSZ04 0.2954067 0.0050865 58.077 < 2e-16 ***
ORIGIN_SZSGSZ05 -2.0792678 0.0109882 -189.227 < 2e-16 ***
ORIGIN_SZSGSZ06 0.4563227 0.0048880 93.356 < 2e-16 ***
ORIGIN_SZSGSZ07 -0.8955254 0.0067100 -133.461 < 2e-16 ***
ORIGIN_SZSKSZ01 -0.3184402 0.0093032 -34.229 < 2e-16 ***
ORIGIN_SZSKSZ02 1.1160484 0.0063851 174.790 < 2e-16 ***
ORIGIN_SZSKSZ03 -0.2566692 0.0086021 -29.838 < 2e-16 ***
ORIGIN_SZSKSZ04 -1.5781827 0.0279394 -56.486 < 2e-16 ***
ORIGIN_SZSKSZ05 -0.2724361 0.0163597 -16.653 < 2e-16 ***
ORIGIN_SZSLSZ01 -2.4458625 0.0330301 -74.050 < 2e-16 ***
ORIGIN_SZSLSZ04 -0.0987076 0.0079626 -12.396 < 2e-16 ***
ORIGIN_SZSRSZ01 -2.2584977 0.0176647 -127.854 < 2e-16 ***
ORIGIN_SZTHSZ01 -2.5878524 0.0489998 -52.814 < 2e-16 ***
ORIGIN_SZTHSZ03 -0.8101746 0.0226814 -35.720 < 2e-16 ***
ORIGIN_SZTHSZ04 -2.4186655 0.0288663 -83.789 < 2e-16 ***
ORIGIN_SZTHSZ06 -1.7080541 0.0186353 -91.657 < 2e-16 ***
ORIGIN_SZTMSZ01 -0.2193476 0.0061823 -35.480 < 2e-16 ***
ORIGIN_SZTMSZ02 1.7772464 0.0043394 409.558 < 2e-16 ***
ORIGIN_SZTMSZ03 1.0051343 0.0046055 218.249 < 2e-16 ***
ORIGIN_SZTMSZ04 0.1642370 0.0055078 29.819 < 2e-16 ***
ORIGIN_SZTMSZ05 -1.2878706 0.0114828 -112.157 < 2e-16 ***
ORIGIN_SZTNSZ01 -1.7163504 0.0131268 -130.751 < 2e-16 ***
ORIGIN_SZTNSZ02 -1.6508988 0.0103851 -158.968 < 2e-16 ***
ORIGIN_SZTNSZ03 -2.1545577 0.0137947 -156.187 < 2e-16 ***
ORIGIN_SZTNSZ04 -0.3949120 0.0078496 -50.310 < 2e-16 ***
ORIGIN_SZTPSZ01 -0.8058100 0.0069916 -115.253 < 2e-16 ***
ORIGIN_SZTPSZ02 0.5369060 0.0047272 113.577 < 2e-16 ***
ORIGIN_SZTPSZ03 -0.7779333 0.0064278 -121.027 < 2e-16 ***
ORIGIN_SZTPSZ04 -0.8153581 0.0061387 -132.823 < 2e-16 ***
ORIGIN_SZTPSZ05 -0.5073676 0.0067771 -74.865 < 2e-16 ***
ORIGIN_SZTPSZ06 0.0847301 0.0065717 12.893 < 2e-16 ***
ORIGIN_SZTPSZ07 -0.5839519 0.0066148 -88.280 < 2e-16 ***
ORIGIN_SZTPSZ08 -1.0577941 0.0098480 -107.412 < 2e-16 ***
ORIGIN_SZTPSZ09 -0.9067707 0.0071367 -127.057 < 2e-16 ***
ORIGIN_SZTPSZ10 -1.1362091 0.0080905 -140.438 < 2e-16 ***
ORIGIN_SZTPSZ11 -0.2374621 0.0059472 -39.928 < 2e-16 ***
ORIGIN_SZTPSZ12 -0.8028874 0.0069663 -115.253 < 2e-16 ***
ORIGIN_SZTSSZ01 -2.7809271 0.0482843 -57.595 < 2e-16 ***
ORIGIN_SZTSSZ02 0.0425804 0.0105088 4.052 5.08e-05 ***
ORIGIN_SZTSSZ03 0.1142369 0.0109412 10.441 < 2e-16 ***
ORIGIN_SZTSSZ04 -0.6186261 0.0116324 -53.181 < 2e-16 ***
ORIGIN_SZTSSZ05 -1.0846732 0.0173555 -62.497 < 2e-16 ***
ORIGIN_SZTSSZ06 0.3980173 0.0198100 20.092 < 2e-16 ***
ORIGIN_SZWCSZ01 1.3545143 0.0092002 147.227 < 2e-16 ***
ORIGIN_SZWCSZ02 -2.9863278 0.0330906 -90.247 < 2e-16 ***
ORIGIN_SZWCSZ03 -5.0504916 0.1241385 -40.684 < 2e-16 ***
ORIGIN_SZWDSZ01 1.5238429 0.0049404 308.448 < 2e-16 ***
ORIGIN_SZWDSZ02 0.2832576 0.0056218 50.386 < 2e-16 ***
ORIGIN_SZWDSZ03 1.3702524 0.0053266 257.245 < 2e-16 ***
ORIGIN_SZWDSZ04 1.0248225 0.0059272 172.903 < 2e-16 ***
ORIGIN_SZWDSZ05 0.2356778 0.0060587 38.899 < 2e-16 ***
ORIGIN_SZWDSZ06 0.3146925 0.0059919 52.520 < 2e-16 ***
ORIGIN_SZWDSZ07 -1.4971897 0.0091243 -164.088 < 2e-16 ***
ORIGIN_SZWDSZ08 -0.8894079 0.0087414 -101.747 < 2e-16 ***
ORIGIN_SZWDSZ09 1.4437633 0.0053160 271.590 < 2e-16 ***
ORIGIN_SZYSSZ01 -0.2519398 0.0064443 -39.095 < 2e-16 ***
ORIGIN_SZYSSZ02 0.8726785 0.0057658 151.354 < 2e-16 ***
ORIGIN_SZYSSZ03 1.7868139 0.0050674 352.611 < 2e-16 ***
ORIGIN_SZYSSZ04 0.8418040 0.0051738 162.704 < 2e-16 ***
ORIGIN_SZYSSZ05 0.4292096 0.0062520 68.652 < 2e-16 ***
ORIGIN_SZYSSZ06 -0.7459961 0.0119123 -62.624 < 2e-16 ***
ORIGIN_SZYSSZ07 -0.8422281 0.0144559 -58.262 < 2e-16 ***
ORIGIN_SZYSSZ08 0.1829428 0.0067885 26.949 < 2e-16 ***
ORIGIN_SZYSSZ09 1.1159712 0.0050760 219.853 < 2e-16 ***
DESTIN_SZAMSZ02 0.0694567 0.0045966 15.111 < 2e-16 ***
DESTIN_SZAMSZ03 0.0760100 0.0044639 17.028 < 2e-16 ***
DESTIN_SZAMSZ04 -1.1306391 0.0064373 -175.639 < 2e-16 ***
DESTIN_SZAMSZ05 -1.0751133 0.0065164 -164.985 < 2e-16 ***
DESTIN_SZAMSZ06 -0.9624298 0.0065937 -145.962 < 2e-16 ***
DESTIN_SZAMSZ07 -1.5060319 0.0097616 -154.281 < 2e-16 ***
DESTIN_SZAMSZ08 -0.4813202 0.0069794 -68.963 < 2e-16 ***
DESTIN_SZAMSZ09 -1.0220675 0.0066313 -154.129 < 2e-16 ***
DESTIN_SZAMSZ10 0.1235142 0.0047044 26.255 < 2e-16 ***
DESTIN_SZAMSZ11 -0.8917993 0.0088519 -100.746 < 2e-16 ***
DESTIN_SZAMSZ12 0.0195208 0.0051704 3.775 0.000160 ***
DESTIN_SZBDSZ01 0.9736349 0.0042757 227.713 < 2e-16 ***
DESTIN_SZBDSZ02 -0.1969470 0.0055284 -35.625 < 2e-16 ***
DESTIN_SZBDSZ03 0.1266471 0.0050786 24.938 < 2e-16 ***
DESTIN_SZBDSZ04 1.1608485 0.0041956 276.684 < 2e-16 ***
DESTIN_SZBDSZ05 0.9293840 0.0044412 209.265 < 2e-16 ***
DESTIN_SZBDSZ06 0.4090567 0.0050300 81.323 < 2e-16 ***
DESTIN_SZBDSZ07 -0.8171478 0.0098945 -82.586 < 2e-16 ***
DESTIN_SZBDSZ08 -1.5895287 0.0111632 -142.391 < 2e-16 ***
DESTIN_SZBKSZ01 -1.3793311 0.0072145 -191.189 < 2e-16 ***
DESTIN_SZBKSZ02 -0.5253670 0.0061879 -84.903 < 2e-16 ***
DESTIN_SZBKSZ03 -1.0095362 0.0065426 -154.301 < 2e-16 ***
DESTIN_SZBKSZ04 -0.5662858 0.0056453 -100.311 < 2e-16 ***
DESTIN_SZBKSZ05 -0.9406607 0.0070597 -133.244 < 2e-16 ***
DESTIN_SZBKSZ06 -1.3129276 0.0067414 -194.755 < 2e-16 ***
DESTIN_SZBKSZ07 0.0120605 0.0049284 2.447 0.014400 *
DESTIN_SZBKSZ08 -1.3658471 0.0075109 -181.849 < 2e-16 ***
DESTIN_SZBKSZ09 -0.1771310 0.0055645 -31.832 < 2e-16 ***
DESTIN_SZBLSZ01 -0.8175223 0.0075645 -108.074 < 2e-16 ***
DESTIN_SZBLSZ02 0.1631280 0.0071753 22.735 < 2e-16 ***
DESTIN_SZBLSZ03 1.2598494 0.0081706 154.194 < 2e-16 ***
DESTIN_SZBLSZ04 -0.5642975 0.0137827 -40.943 < 2e-16 ***
DESTIN_SZBMSZ01 0.6921844 0.0054211 127.684 < 2e-16 ***
DESTIN_SZBMSZ02 -0.1209392 0.0055362 -21.845 < 2e-16 ***
DESTIN_SZBMSZ03 -0.2373881 0.0062427 -38.027 < 2e-16 ***
DESTIN_SZBMSZ04 -0.0407117 0.0058001 -7.019 2.23e-12 ***
DESTIN_SZBMSZ05 -0.2363309 0.0075967 -31.110 < 2e-16 ***
DESTIN_SZBMSZ06 -1.1930710 0.0134761 -88.532 < 2e-16 ***
DESTIN_SZBMSZ07 0.4625103 0.0051864 89.178 < 2e-16 ***
DESTIN_SZBMSZ08 -0.8604731 0.0069899 -123.102 < 2e-16 ***
DESTIN_SZBMSZ09 -2.1290239 0.0154841 -137.498 < 2e-16 ***
DESTIN_SZBMSZ10 -1.4617153 0.0094014 -155.478 < 2e-16 ***
DESTIN_SZBMSZ11 -1.3234050 0.0085506 -154.773 < 2e-16 ***
DESTIN_SZBMSZ12 -0.8399230 0.0085361 -98.397 < 2e-16 ***
DESTIN_SZBMSZ13 0.1366529 0.0059697 22.891 < 2e-16 ***
DESTIN_SZBMSZ14 -1.0491968 0.0083021 -126.378 < 2e-16 ***
DESTIN_SZBMSZ15 -0.6726684 0.0076276 -88.189 < 2e-16 ***
DESTIN_SZBMSZ16 -1.4011734 0.0116569 -120.201 < 2e-16 ***
DESTIN_SZBMSZ17 -1.5682752 0.0167333 -93.722 < 2e-16 ***
DESTIN_SZBPSZ01 -1.1120017 0.0063197 -175.959 < 2e-16 ***
DESTIN_SZBPSZ02 -2.0833466 0.0091139 -228.590 < 2e-16 ***
DESTIN_SZBPSZ03 -1.6937265 0.0087437 -193.709 < 2e-16 ***
DESTIN_SZBPSZ04 -0.7964999 0.0066129 -120.447 < 2e-16 ***
DESTIN_SZBPSZ05 0.2109118 0.0048815 43.206 < 2e-16 ***
DESTIN_SZBPSZ06 -1.1808365 0.0083657 -141.152 < 2e-16 ***
DESTIN_SZBPSZ07 -0.2077428 0.0084543 -24.572 < 2e-16 ***
DESTIN_SZBSSZ01 0.3164175 0.0050682 62.431 < 2e-16 ***
DESTIN_SZBSSZ02 -0.4852688 0.0057001 -85.134 < 2e-16 ***
DESTIN_SZBSSZ03 0.4130432 0.0043061 95.921 < 2e-16 ***
DESTIN_SZBTSZ01 0.6215095 0.0048914 127.061 < 2e-16 ***
DESTIN_SZBTSZ02 -0.0145076 0.0071799 -2.021 0.043324 *
DESTIN_SZBTSZ03 0.4919981 0.0058498 84.105 < 2e-16 ***
DESTIN_SZBTSZ04 -0.6957555 0.0114078 -60.989 < 2e-16 ***
DESTIN_SZBTSZ05 0.3329814 0.0073568 45.262 < 2e-16 ***
DESTIN_SZBTSZ06 -0.1333295 0.0073965 -18.026 < 2e-16 ***
DESTIN_SZBTSZ07 -1.4449581 0.0113186 -127.663 < 2e-16 ***
DESTIN_SZBTSZ08 -0.7079056 0.0103797 -68.201 < 2e-16 ***
DESTIN_SZCBSZ01 -5.7344725 0.3162767 -18.131 < 2e-16 ***
DESTIN_SZCCSZ01 -0.0009541 0.0083381 -0.114 0.908900
DESTIN_SZCHSZ01 -0.2083016 0.0099054 -21.029 < 2e-16 ***
DESTIN_SZCHSZ02 0.5369606 0.0057531 93.334 < 2e-16 ***
DESTIN_SZCHSZ03 2.5530638 0.0043945 580.971 < 2e-16 ***
DESTIN_SZCKSZ01 -0.5725975 0.0056507 -101.333 < 2e-16 ***
DESTIN_SZCKSZ02 -1.1181852 0.0063287 -176.685 < 2e-16 ***
DESTIN_SZCKSZ03 0.1156680 0.0049440 23.396 < 2e-16 ***
DESTIN_SZCKSZ04 -0.8647725 0.0071003 -121.794 < 2e-16 ***
DESTIN_SZCKSZ05 -1.1641791 0.0076248 -152.684 < 2e-16 ***
DESTIN_SZCKSZ06 -0.4397612 0.0073040 -60.208 < 2e-16 ***
DESTIN_SZCLSZ01 0.1930552 0.0053752 35.916 < 2e-16 ***
DESTIN_SZCLSZ02 -2.0436501 0.0136039 -150.225 < 2e-16 ***
DESTIN_SZCLSZ03 -0.9338571 0.0082908 -112.638 < 2e-16 ***
DESTIN_SZCLSZ04 0.0532041 0.0053276 9.987 < 2e-16 ***
DESTIN_SZCLSZ05 -1.0782781 0.0088184 -122.276 < 2e-16 ***
DESTIN_SZCLSZ06 0.4068171 0.0049068 82.910 < 2e-16 ***
DESTIN_SZCLSZ07 -0.3579507 0.0060289 -59.373 < 2e-16 ***
DESTIN_SZCLSZ08 -0.2487993 0.0066588 -37.364 < 2e-16 ***
DESTIN_SZCLSZ09 0.1611080 0.0071178 22.635 < 2e-16 ***
DESTIN_SZDTSZ02 -1.7308348 0.0349466 -49.528 < 2e-16 ***
DESTIN_SZDTSZ03 -0.5994253 0.0146230 -40.992 < 2e-16 ***
DESTIN_SZDTSZ13 -1.3685031 0.0162803 -84.059 < 2e-16 ***
DESTIN_SZGLSZ01 -0.0910001 0.0055275 -16.463 < 2e-16 ***
DESTIN_SZGLSZ02 -0.0692224 0.0052840 -13.100 < 2e-16 ***
DESTIN_SZGLSZ03 0.6493421 0.0043446 149.459 < 2e-16 ***
DESTIN_SZGLSZ04 0.9327947 0.0043674 213.583 < 2e-16 ***
DESTIN_SZGLSZ05 0.8161728 0.0043625 187.087 < 2e-16 ***
DESTIN_SZHGSZ01 0.0658625 0.0042516 15.491 < 2e-16 ***
DESTIN_SZHGSZ02 -0.8134329 0.0056721 -143.409 < 2e-16 ***
DESTIN_SZHGSZ03 -1.3546132 0.0066257 -204.448 < 2e-16 ***
DESTIN_SZHGSZ04 -0.4500588 0.0048448 -92.895 < 2e-16 ***
DESTIN_SZHGSZ05 -0.5026431 0.0050996 -98.566 < 2e-16 ***
DESTIN_SZHGSZ06 -0.8673686 0.0059530 -145.704 < 2e-16 ***
DESTIN_SZHGSZ07 0.0560490 0.0047702 11.750 < 2e-16 ***
DESTIN_SZHGSZ08 -0.0443189 0.0052599 -8.426 < 2e-16 ***
DESTIN_SZHGSZ09 -0.0126355 0.0054966 -2.299 0.021518 *
DESTIN_SZHGSZ10 -3.5821793 0.0263281 -136.059 < 2e-16 ***
DESTIN_SZJESZ01 -0.3704281 0.0056684 -65.350 < 2e-16 ***
DESTIN_SZJESZ02 -0.7369159 0.0058686 -125.570 < 2e-16 ***
DESTIN_SZJESZ03 -0.8985484 0.0063627 -141.222 < 2e-16 ***
DESTIN_SZJESZ04 -1.0511995 0.0073996 -142.061 < 2e-16 ***
DESTIN_SZJESZ05 -1.5324974 0.0102612 -149.349 < 2e-16 ***
DESTIN_SZJESZ06 0.3105267 0.0048241 64.370 < 2e-16 ***
DESTIN_SZJESZ07 -1.3234483 0.0085497 -154.795 < 2e-16 ***
DESTIN_SZJESZ08 -0.6559742 0.0083174 -78.867 < 2e-16 ***
DESTIN_SZJESZ09 0.2663752 0.0063370 42.035 < 2e-16 ***
DESTIN_SZJESZ10 0.8529026 0.0076067 112.126 < 2e-16 ***
DESTIN_SZJESZ11 0.5559641 0.0074629 74.497 < 2e-16 ***
DESTIN_SZJWSZ01 -0.9790971 0.0071830 -136.308 < 2e-16 ***
DESTIN_SZJWSZ02 -0.8746590 0.0060179 -145.342 < 2e-16 ***
DESTIN_SZJWSZ03 0.5689062 0.0049105 115.855 < 2e-16 ***
DESTIN_SZJWSZ04 0.4520963 0.0050302 89.876 < 2e-16 ***
DESTIN_SZJWSZ05 -1.0249671 0.0067371 -152.137 < 2e-16 ***
DESTIN_SZJWSZ06 -0.7451483 0.0062189 -119.819 < 2e-16 ***
DESTIN_SZJWSZ07 -2.8453099 0.0287335 -99.024 < 2e-16 ***
DESTIN_SZJWSZ08 -0.3372309 0.0058003 -58.141 < 2e-16 ***
DESTIN_SZJWSZ09 1.0505330 0.0045908 228.832 < 2e-16 ***
DESTIN_SZKLSZ01 -0.2334836 0.0057970 -40.277 < 2e-16 ***
DESTIN_SZKLSZ02 -0.5416148 0.0061432 -88.164 < 2e-16 ***
DESTIN_SZKLSZ03 -0.8026495 0.0068745 -116.757 < 2e-16 ***
DESTIN_SZKLSZ04 -1.2918594 0.0090197 -143.227 < 2e-16 ***
DESTIN_SZKLSZ05 -0.4069101 0.0087812 -46.339 < 2e-16 ***
DESTIN_SZKLSZ06 -2.5333101 0.0363215 -69.747 < 2e-16 ***
DESTIN_SZKLSZ07 -0.6623343 0.0070761 -93.601 < 2e-16 ***
DESTIN_SZKLSZ08 -0.1408205 0.0054965 -25.620 < 2e-16 ***
DESTIN_SZLKSZ01 -1.2639235 0.0208254 -60.691 < 2e-16 ***
DESTIN_SZMDSZ01 -1.5655800 0.0202787 -77.203 < 2e-16 ***
DESTIN_SZMDSZ02 -0.9767682 0.0114687 -85.168 < 2e-16 ***
DESTIN_SZMDSZ03 -3.3328109 0.0254294 -131.061 < 2e-16 ***
DESTIN_SZMPSZ01 -0.4552859 0.0080666 -56.441 < 2e-16 ***
DESTIN_SZMPSZ02 -0.5386560 0.0064620 -83.358 < 2e-16 ***
DESTIN_SZMPSZ03 0.4952000 0.0052295 94.694 < 2e-16 ***
DESTIN_SZMUSZ02 -1.4434175 0.0202509 -71.277 < 2e-16 ***
DESTIN_SZNTSZ01 -2.9194067 0.0449654 -64.926 < 2e-16 ***
DESTIN_SZNTSZ02 -1.3780179 0.0112867 -122.092 < 2e-16 ***
DESTIN_SZNTSZ03 -0.5044699 0.0080449 -62.707 < 2e-16 ***
DESTIN_SZNTSZ05 -2.0017134 0.0258750 -77.361 < 2e-16 ***
DESTIN_SZNTSZ06 -3.8120537 0.0434271 -87.781 < 2e-16 ***
DESTIN_SZNVSZ01 -0.1071506 0.0051026 -20.999 < 2e-16 ***
DESTIN_SZNVSZ02 -0.0274710 0.0057611 -4.768 1.86e-06 ***
DESTIN_SZNVSZ03 0.1076352 0.0057909 18.587 < 2e-16 ***
DESTIN_SZNVSZ04 -1.2087250 0.0110438 -109.448 < 2e-16 ***
DESTIN_SZNVSZ05 -1.0058290 0.0092167 -109.131 < 2e-16 ***
DESTIN_SZPGSZ01 -1.2029931 0.0163170 -73.726 < 2e-16 ***
DESTIN_SZPGSZ02 -1.2878671 0.0074139 -173.709 < 2e-16 ***
DESTIN_SZPGSZ03 -0.1520894 0.0048629 -31.275 < 2e-16 ***
DESTIN_SZPGSZ04 -0.1985959 0.0050374 -39.424 < 2e-16 ***
DESTIN_SZPGSZ05 -1.5290983 0.0082617 -185.083 < 2e-16 ***
DESTIN_SZPLSZ01 -0.3567934 0.0074298 -48.022 < 2e-16 ***
DESTIN_SZPLSZ02 -1.7114351 0.0134462 -127.280 < 2e-16 ***
DESTIN_SZPLSZ03 -0.3241427 0.0098895 -32.776 < 2e-16 ***
DESTIN_SZPLSZ04 -1.7117196 0.0119003 -143.838 < 2e-16 ***
DESTIN_SZPLSZ05 -0.5086379 0.0120051 -42.368 < 2e-16 ***
DESTIN_SZPNSZ01 0.2026781 0.0068977 29.383 < 2e-16 ***
DESTIN_SZPNSZ02 0.8313754 0.0078544 105.848 < 2e-16 ***
DESTIN_SZPNSZ03 -0.4041254 0.0086586 -46.673 < 2e-16 ***
DESTIN_SZPNSZ04 1.5814539 0.0093641 168.885 < 2e-16 ***
DESTIN_SZPNSZ05 1.1823430 0.0129843 91.059 < 2e-16 ***
DESTIN_SZPRSZ01 -1.1057553 0.0088197 -125.374 < 2e-16 ***
DESTIN_SZPRSZ02 0.0895099 0.0056308 15.897 < 2e-16 ***
DESTIN_SZPRSZ03 0.6921925 0.0043977 157.397 < 2e-16 ***
DESTIN_SZPRSZ04 -0.2848336 0.0084725 -33.619 < 2e-16 ***
DESTIN_SZPRSZ05 0.1744480 0.0053553 32.575 < 2e-16 ***
DESTIN_SZPRSZ06 0.4279206 0.0058735 72.856 < 2e-16 ***
DESTIN_SZPRSZ07 -1.5123108 0.0124303 -121.664 < 2e-16 ***
DESTIN_SZPRSZ08 -0.5650226 0.0068530 -82.449 < 2e-16 ***
DESTIN_SZQTSZ01 -0.5952360 0.0090505 -65.769 < 2e-16 ***
DESTIN_SZQTSZ02 -0.7728170 0.0078910 -97.937 < 2e-16 ***
DESTIN_SZQTSZ03 -0.5066812 0.0073996 -68.474 < 2e-16 ***
DESTIN_SZQTSZ04 -0.6398414 0.0075411 -84.847 < 2e-16 ***
DESTIN_SZQTSZ05 -0.4354527 0.0069345 -62.795 < 2e-16 ***
DESTIN_SZQTSZ06 -0.6597391 0.0071919 -91.733 < 2e-16 ***
DESTIN_SZQTSZ07 -0.9392696 0.0112518 -83.477 < 2e-16 ***
DESTIN_SZQTSZ08 0.4617774 0.0057011 80.998 < 2e-16 ***
DESTIN_SZQTSZ09 -0.3174497 0.0065890 -48.178 < 2e-16 ***
DESTIN_SZQTSZ10 0.1993449 0.0059923 33.267 < 2e-16 ***
DESTIN_SZQTSZ11 0.2551535 0.0061885 41.230 < 2e-16 ***
DESTIN_SZQTSZ12 -0.1662603 0.0086701 -19.176 < 2e-16 ***
DESTIN_SZQTSZ13 0.5500978 0.0063091 87.192 < 2e-16 ***
DESTIN_SZQTSZ14 0.5364435 0.0070157 76.463 < 2e-16 ***
DESTIN_SZQTSZ15 1.3611043 0.0081643 166.715 < 2e-16 ***
DESTIN_SZRCSZ01 -0.1034049 0.0076769 -13.470 < 2e-16 ***
DESTIN_SZRCSZ06 -1.0633902 0.0189846 -56.013 < 2e-16 ***
DESTIN_SZRVSZ01 -1.5486221 0.0165272 -93.701 < 2e-16 ***
DESTIN_SZRVSZ02 -2.4092611 0.0326906 -73.699 < 2e-16 ***
DESTIN_SZRVSZ03 -1.5172079 0.0139258 -108.950 < 2e-16 ***
DESTIN_SZRVSZ04 -1.1663615 0.0157430 -74.088 < 2e-16 ***
DESTIN_SZRVSZ05 -2.2404292 0.0281339 -79.634 < 2e-16 ***
DESTIN_SZSBSZ01 -1.3783780 0.0096022 -143.549 < 2e-16 ***
DESTIN_SZSBSZ02 -1.4445213 0.0081630 -176.959 < 2e-16 ***
DESTIN_SZSBSZ03 0.5149906 0.0051663 99.683 < 2e-16 ***
DESTIN_SZSBSZ04 0.2389086 0.0060765 39.317 < 2e-16 ***
DESTIN_SZSBSZ05 -1.2737442 0.0082818 -153.801 < 2e-16 ***
DESTIN_SZSBSZ06 -1.8683520 0.0227277 -82.206 < 2e-16 ***
DESTIN_SZSBSZ07 -0.5993154 0.0184895 -32.414 < 2e-16 ***
DESTIN_SZSBSZ08 0.8156302 0.0059840 136.302 < 2e-16 ***
DESTIN_SZSBSZ09 0.0900611 0.0057054 15.785 < 2e-16 ***
DESTIN_SZSESZ02 -0.6397704 0.0052491 -121.882 < 2e-16 ***
DESTIN_SZSESZ03 0.1714103 0.0042357 40.468 < 2e-16 ***
DESTIN_SZSESZ04 -1.0596175 0.0059865 -177.002 < 2e-16 ***
DESTIN_SZSESZ05 -0.8071891 0.0051229 -157.566 < 2e-16 ***
DESTIN_SZSESZ06 -0.5580934 0.0066216 -84.284 < 2e-16 ***
DESTIN_SZSESZ07 -3.1448863 0.0227788 -138.062 < 2e-16 ***
DESTIN_SZSGSZ01 -0.1795225 0.0060127 -29.857 < 2e-16 ***
DESTIN_SZSGSZ02 -0.2986570 0.0053561 -55.760 < 2e-16 ***
DESTIN_SZSGSZ03 -0.4074671 0.0050609 -80.513 < 2e-16 ***
DESTIN_SZSGSZ04 -0.1505164 0.0050931 -29.553 < 2e-16 ***
DESTIN_SZSGSZ05 -1.9908372 0.0101448 -196.242 < 2e-16 ***
DESTIN_SZSGSZ06 0.6715268 0.0041161 163.148 < 2e-16 ***
DESTIN_SZSGSZ07 -0.4494757 0.0055319 -81.252 < 2e-16 ***
DESTIN_SZSISZ01 -0.5517983 0.0261860 -21.072 < 2e-16 ***
DESTIN_SZSKSZ01 -0.4749154 0.0079257 -59.921 < 2e-16 ***
DESTIN_SZSKSZ02 0.9400302 0.0057218 164.290 < 2e-16 ***
DESTIN_SZSKSZ03 -0.2800377 0.0066081 -42.378 < 2e-16 ***
DESTIN_SZSKSZ04 -1.2570212 0.0145351 -86.482 < 2e-16 ***
DESTIN_SZSKSZ05 -0.2600474 0.0112800 -23.054 < 2e-16 ***
DESTIN_SZSLSZ01 -0.7775604 0.0085818 -90.606 < 2e-16 ***
DESTIN_SZSLSZ04 -0.8586515 0.0073142 -117.396 < 2e-16 ***
DESTIN_SZSRSZ01 -1.1370887 0.0142148 -79.993 < 2e-16 ***
DESTIN_SZTHSZ01 -4.3259988 0.0368554 -117.378 < 2e-16 ***
DESTIN_SZTHSZ03 -2.6632914 0.0252720 -105.385 < 2e-16 ***
DESTIN_SZTHSZ04 -3.1000906 0.0216372 -143.276 < 2e-16 ***
DESTIN_SZTHSZ06 -2.5952642 0.0156340 -166.001 < 2e-16 ***
DESTIN_SZTMSZ01 -0.2092828 0.0059257 -35.318 < 2e-16 ***
DESTIN_SZTMSZ02 1.8238139 0.0039155 465.798 < 2e-16 ***
DESTIN_SZTMSZ03 0.8518259 0.0043636 195.210 < 2e-16 ***
DESTIN_SZTMSZ04 1.0222812 0.0043466 235.191 < 2e-16 ***
DESTIN_SZTMSZ05 0.6323777 0.0060058 105.294 < 2e-16 ***
DESTIN_SZTNSZ01 -0.3336078 0.0074388 -44.847 < 2e-16 ***
DESTIN_SZTNSZ02 -1.0820469 0.0101689 -106.408 < 2e-16 ***
DESTIN_SZTNSZ03 -1.4186505 0.0119906 -118.313 < 2e-16 ***
DESTIN_SZTNSZ04 -0.3058199 0.0074743 -40.916 < 2e-16 ***
DESTIN_SZTPSZ01 -0.4872299 0.0061571 -79.133 < 2e-16 ***
DESTIN_SZTPSZ02 0.7158441 0.0041312 173.278 < 2e-16 ***
DESTIN_SZTPSZ03 -0.4314229 0.0059917 -72.004 < 2e-16 ***
DESTIN_SZTPSZ04 -1.5898245 0.0076083 -208.959 < 2e-16 ***
DESTIN_SZTPSZ05 -1.0445550 0.0062363 -167.497 < 2e-16 ***
DESTIN_SZTPSZ06 -0.4319582 0.0070100 -61.621 < 2e-16 ***
DESTIN_SZTPSZ07 -2.1602303 0.0120352 -179.493 < 2e-16 ***
DESTIN_SZTPSZ08 -1.1920493 0.0093083 -128.063 < 2e-16 ***
DESTIN_SZTPSZ09 -0.2022481 0.0071137 -28.431 < 2e-16 ***
DESTIN_SZTPSZ10 -1.2464793 0.0090124 -138.308 < 2e-16 ***
DESTIN_SZTPSZ11 -0.0808445 0.0056019 -14.432 < 2e-16 ***
DESTIN_SZTPSZ12 -0.6784376 0.0066340 -102.267 < 2e-16 ***
DESTIN_SZTSSZ01 -1.5845062 0.0222086 -71.346 < 2e-16 ***
DESTIN_SZTSSZ02 -0.1886010 0.0146338 -12.888 < 2e-16 ***
DESTIN_SZTSSZ03 0.6525526 0.0092450 70.585 < 2e-16 ***
DESTIN_SZTSSZ04 0.5285464 0.0100182 52.759 < 2e-16 ***
DESTIN_SZTSSZ05 1.4670106 0.0104357 140.577 < 2e-16 ***
DESTIN_SZTSSZ06 2.5043588 0.0167444 149.564 < 2e-16 ***
DESTIN_SZWCSZ01 1.9787931 0.0054306 364.375 < 2e-16 ***
DESTIN_SZWCSZ02 -2.2593108 0.0127916 -176.624 < 2e-16 ***
DESTIN_SZWCSZ03 -3.1897655 0.0326927 -97.568 < 2e-16 ***
DESTIN_SZWDSZ01 1.0476108 0.0044629 234.738 < 2e-16 ***
DESTIN_SZWDSZ02 -1.3176990 0.0065894 -199.973 < 2e-16 ***
DESTIN_SZWDSZ03 0.3432057 0.0052496 65.377 < 2e-16 ***
DESTIN_SZWDSZ04 -0.7895927 0.0073392 -107.586 < 2e-16 ***
DESTIN_SZWDSZ05 -0.8751665 0.0072946 -119.975 < 2e-16 ***
DESTIN_SZWDSZ06 -0.2106221 0.0053027 -39.720 < 2e-16 ***
DESTIN_SZWDSZ07 -1.6050834 0.0071754 -223.692 < 2e-16 ***
DESTIN_SZWDSZ08 -0.5124717 0.0069223 -74.032 < 2e-16 ***
DESTIN_SZWDSZ09 0.3813542 0.0054697 69.721 < 2e-16 ***
DESTIN_SZYSSZ01 0.0853753 0.0046572 18.332 < 2e-16 ***
DESTIN_SZYSSZ02 -0.3227172 0.0057351 -56.271 < 2e-16 ***
DESTIN_SZYSSZ03 -0.4151283 0.0066299 -62.615 < 2e-16 ***
DESTIN_SZYSSZ04 -0.4637327 0.0058206 -79.671 < 2e-16 ***
DESTIN_SZYSSZ05 -1.5888242 0.0111001 -143.136 < 2e-16 ***
DESTIN_SZYSSZ06 -1.4606209 0.0107759 -135.545 < 2e-16 ***
DESTIN_SZYSSZ07 -0.7839065 0.0144357 -54.304 < 2e-16 ***
DESTIN_SZYSSZ08 0.6265412 0.0045504 137.691 < 2e-16 ***
DESTIN_SZYSSZ09 0.1520067 0.0048092 31.607 < 2e-16 ***
log(DIST) -1.8468315 0.0004608 -4008.033 < 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: 47094011 on 14470 degrees of freedom
Residual deviance: 10420261 on 13912 degrees of freedom
AIC: 10510518
Number of Fisher Scoring iterations: 7
Do it yourself
What statistical conclusion you can draw from the report above?
Next, let us examine how well the proportion of variance in the dependent variable (i.e. TRIPS) that can be explained by the explanatory variables.
Do it yourself
Using the R-Squared function written earlier, compute the R-Squared of the Doubly-constrined Model.
Show the code chunk
CalcRSquared(dbcSIM_Poisson$data$TRIPS,
dbcSIM_Poisson$fitted.values)[1] 0.7001882Notice that there is a relatively greater improvement in the R-Squared value.
Model comparison
Statistical measures
Another useful model performance measure for continuous dependent variable is Root Mean Squared Error. In this sub-section, you will learn how to use compare_performance() of performance package
First of all, let us create a list called model_list by using the code chunk below.
model_list <- list(
Origin_Constrained = orcSIM_Poisson,
Doubly_Constrained = dbcSIM_Poisson)Next, we will compute the RMSE of all the models in model_list file by using the code chunk below.
compare_performance(model_list,
metrics = "RMSE")# Comparison of Model Performance Indices
Name | Model | RMSE
-------------------------------------
Origin_Constrained | glm | 2613.236
Doubly_Constrained | glm | 1906.694The print above reveals that doubly constrained SIM is the best model among the two SIMs because it has the smallest RMSE value of 1906.694.
Visualising fitted values
In this section, you will learn how to visualise the observed values and the fitted values.
Firstly we will extract the fitted values from Origin-constrained Model by using the code chunk below.
df <- as.data.frame(orcSIM_Poisson$fitted.values) %>%
round(digits = 0)Next, we will append the fitted values into inter_zonal_flow data frame by using the code chunk below.
inter_zonal_flow <- inter_zonal_flow %>%
cbind(df) %>%
rename(orcTRIPS = "orcSIM_Poisson.fitted.values")
Tip
Notice that rename() is used to rename the field name and the $ in the original field name has been replaced with an .. This is because R replaced $ with . during the cbind().
Do it yourself
Repeat the same step for Doubly Constrained Model (i.e. dbcSIM_Poisson)
Show the code chunk
df <- as.data.frame(dbcSIM_Poisson$fitted.values) %>%
round(digits = 0)Show the code chunk
inter_zonal_flow <- inter_zonal_flow %>%
cbind(df) %>%
rename(dbcTRIPS = "dbcSIM_Poisson.fitted.values")Next, two scatterplots will be created by using geom_point() and other appropriate functions of ggplot2 package.
orc_p <- ggplot(data = inter_zonal_flow,
aes(x = orcTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm) +
coord_cartesian(xlim=c(0,150000),
ylim=c(0,150000))
dbc_p <- ggplot(data = inter_zonal_flow,
aes(x = dbcTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm) +
coord_cartesian(xlim=c(0,150000),
ylim=c(0,150000))Now, we will put all the graphs into a single visual for better comparison by using the code chunk below.
ggarrange(orc_p, dbc_p,
ncol = 2,
nrow = 1)
Quiz
What observation can you draw from the figure above and what follow-up action will you take?