R is a programming language for statistical computing and graphics. To install R, required installation files can be found in the following link:
Apollo Choice Modeling framework has been employed in running the mode choice model component. We prepared the R notebooks for all models included in the guidebook.
rm(list = ls())In first step of data processing in R, we need to call required package
library(apollo)## Apollo 0.2.8
## http://www.ApolloChoiceModelling.com
## See url for a detailed manual, examples and a user forum.
## Sign up to the user forum to receive updates on new releases.
##
## Your version of Apollo is more than six months old.
## Using the latest version will ensure you have all
## current functionality and bug fixes.
## You can update to the latest version by typing:
## install.packages("apollo")apollo_initialise()
apollo_control = list(
modelName = "MNL_Mode Choice Model_Base",
modelDescr = "Simple MNL model on base mode choice data",
indivID = "id",
outputDirectory = "output",
panelData = FALSE
)database = read.csv("D:/Projects/20-102/Project Task/Task 4/R code/Mode choice data_base.csv",header=TRUE)
summary(database)## id Choice Drive Passenger
## Min. : 1 Min. :1.000 Min. :0.0000 Min. :0.0000
## 1st Qu.:1251 1st Qu.:2.000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :2500 Median :2.000 Median :1.0000 Median :0.0000
## Mean :2500 Mean :2.825 Mean :0.6468 Mean :0.0548
## 3rd Qu.:3750 3rd Qu.:4.000 3rd Qu.:1.0000 3rd Qu.:0.0000
## Max. :5000 Max. :7.000 Max. :1.0000 Max. :1.0000
## Transit Bike Walk PRKR
## Min. :0.0000 Min. :0.0000 Min. :0.000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.0000 Median :0.0000 Median :0.000 Median :0.000
## Mean :0.1968 Mean :0.0132 Mean :0.052 Mean :0.034
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.000 3rd Qu.:0.000
## Max. :1.0000 Max. :1.0000 Max. :1.000 Max. :1.000
## Other av_Drive av_Passenger av_Transit
## Min. :0.0000 Min. :0.000 Min. :1 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:1.000 1st Qu.:1 1st Qu.:1.000
## Median :0.0000 Median :1.000 Median :1 Median :1.000
## Mean :0.0024 Mean :0.865 Mean :1 Mean :0.992
## 3rd Qu.:0.0000 3rd Qu.:1.000 3rd Qu.:1 3rd Qu.:1.000
## Max. :1.0000 Max. :1.000 Max. :1 Max. :1.000
## av_Bike av_Walk av_Other av_PRKR time_Drive
## Min. :0.0000 Min. :0.0000 Min. :1 Min. :1 Min. : 0.01667
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:1 1st Qu.:1 1st Qu.: 9.84583
## Median :1.0000 Median :0.0000 Median :1 Median :1 Median :16.60833
## Mean :0.5688 Mean :0.1916 Mean :1 Mean :1 Mean :18.10670
## 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:1 3rd Qu.:1 3rd Qu.:24.39167
## Max. :1.0000 Max. :1.0000 Max. :1 Max. :1 Max. :78.28333
## time_Transit time_PRKR time_Bike time_Walk
## Min. : 0.0 Min. : 10.0 Min. : 0.10 Min. : 0.3167
## 1st Qu.: 14.0 1st Qu.: 24.0 1st Qu.: 22.54 1st Qu.: 60.7750
## Median : 29.0 Median : 39.0 Median : 50.33 Median : 134.2083
## Mean : 34.2 Mean : 44.2 Mean : 65.56 Mean : 171.9537
## 3rd Qu.: 48.0 3rd Qu.: 58.0 3rd Qu.: 93.91 3rd Qu.: 245.9250
## Max. :202.7 Max. :212.7 Max. :380.65 Max. :1451.8333
## time_Other cost_Drive cost_Transit cost_PRKR
## Min. : 0.02167 Min. : 1.335 Min. :1.280 Min. : 1.428
## 1st Qu.: 12.79958 1st Qu.: 2.266 1st Qu.:3.250 1st Qu.: 3.410
## Median : 21.59083 Median : 3.465 Median :3.250 Median : 3.953
## Mean : 23.53870 Mean : 4.095 Mean :4.468 Mean : 4.878
## 3rd Qu.: 31.70917 3rd Qu.: 5.289 3rd Qu.:6.750 3rd Qu.: 6.977
## Max. :101.76833 Max. :19.818 Max. :9.750 Max. :10.204
## cost_Other OCBD DCBD Male
## Min. : 1.934 Min. : 0.2863 Min. : 0.1264 Min. :0.0000
## 1st Qu.: 3.987 1st Qu.: 8.2237 1st Qu.: 3.4522 1st Qu.:0.0000
## Median : 5.864 Median :14.3008 Median : 9.6320 Median :1.0000
## Mean : 5.994 Mean :18.0263 Mean :12.7275 Mean :0.5278
## 3rd Qu.: 7.441 3rd Qu.:25.3998 3rd Qu.:17.1038 3rd Qu.:1.0000
## Max. :18.598 Max. :76.6941 Max. :68.9812 Max. :1.0000
## Age20 Age2140 HH_1pers HH_0car
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.0342 Mean :0.3782 Mean :0.1028 Mean :0.0836
## 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## HH_2cars MOR_PIK
## Min. :0.0000 Min. :0.00
## 1st Qu.:0.0000 1st Qu.:0.00
## Median :0.0000 Median :1.00
## Mean :0.4278 Mean :0.68
## 3rd Qu.:1.0000 3rd Qu.:1.00
## Max. :1.0000 Max. :1.00table(database$Choice)##
## 1 2 3 4 5 6 7
## 12 3234 274 984 260 66 170Here, Choice = Mode alternatives, Drive = Drive mode, Passenger = Passenger mode, Transit = Transit mode, Walk = Walk mode, Bike = Bike mode, PRKR = Park and Ride mode, Other = Other mode, TNC = TNC mode, Micro = Shared-micromobility mode, av_Drive = Availability of drive mode, av_Passenger = Availability of Passenger mode, av_Transit = Availability of Transit mode, av_Walk = Availability of Walk mode, av_Bike = Availability of Bike mode, av_PRKR = Availability of Park and Ride mode, av_TNC = Availability of TNC mode, av_Micro = Availability of Shared-micromobility mode, av_Other = Availability of Other mode, time_Other = Travel time of Other mode, time_Drive = Travel time of Drive mode, time_Transit = Travel time of Transit mode, time_PRKR = Travel time of Park and Ride mode, time_Bike = Travel time of Bike mode, time_Walk = Travel time of Walk mode, time_TNC = Travel time of TNC mode, time_Micro = Travel time of Shared-micromobility mode, cost_Drive = Travel cost of Drive mode, cost_Transit = Travel cost of Transit mode, cost_PRKR = Travel cost of Park and Ride mode, cost_Other = Travel cost of Other mode, cost_TNC = Travel cost of TNC mode, cost_Micro = Travel cost of Shared-micromobility mode, OCBD = Origin distance from CBD, DCBD = Destination distance from CBD, Male = Male, Age 20 = Age <= 20, Age2140 = Age 21-40, HH_1pers = One person HH, HH_0car = Zero car HH, HH_2cars = HH with two cars, MOR_PIK = Morning peak
Include fixed parameters in estimation process. Vector with names (in quotes) of parameters to be kept fixed at their starting value in apollo_beta, use apollo_beta_fixed = c() if none
apollo_beta=c(asc_Other = 0,
asc_Drive = 0,
asc_Passenger = 0,
asc_Transit = 0,
asc_Walk = 0,
asc_Bike = 0,
asc_PRKR = 0,
b_tt = 0,
b_cost = 0,
b_OCBD_PRKR = 0,
b_DCBD_Drive = 0,
b_DCBD_Passenger= 0,
b_male_Passenger = 0,
b_male = 0,
b_Age20 = 0,
b_Age2140_Transit = 0,
b_HH1pers_Passenger = 0,
b_HH0car = 0,
b_HH2cars_Drive = 0,
b_Morpik_Transit = 0,
b_Morpik_PRKR = 0)
apollo_fixed = c("asc_Other")
apollo_inputs = apollo_validateInputs()## All checks on apollo_control completed.
## All checks on database completed.# Define model and likelihood function
apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){
# Attach inputs and detach after function exit
apollo_attach(apollo_beta, apollo_inputs)
on.exit(apollo_detach(apollo_beta, apollo_inputs))
# Create list of probabilities P
P = list()
# List of utilities: these must use the same names as in mnl_settings, order is irrelevant
V = list()
V[["Other"]] = asc_Other + b_tt * time_Other + b_cost * cost_Other
V[["Drive"]] = asc_Drive + b_tt * time_Drive + b_cost * cost_Drive + b_DCBD_Drive * DCBD + b_HH2cars_Drive * HH_2cars
V[["Passenger"]] = asc_Passenger + b_tt * time_Drive + b_DCBD_Passenger * DCBD + b_male_Passenger * Male + b_Age20 * Age20 + b_HH1pers_Passenger * HH_1pers
V[["Transit"]] = asc_Transit + b_tt * time_Transit + b_cost * cost_Transit + b_male * Male + b_Age20 * Age20 + b_Age2140_Transit * Age2140 + b_HH0car * HH_0car + b_Morpik_Transit * MOR_PIK
V[["Walk"]] = asc_Walk + b_tt * time_Walk + b_male * Male + b_HH0car * HH_0car
V[["Bike"]] = asc_Bike + b_tt * time_Bike + b_Age20 * Age20 + b_HH0car * HH_0car
V[["PRKR"]] = asc_PRKR + b_tt * time_PRKR + b_cost * cost_PRKR + b_OCBD_PRKR * OCBD + b_male * Male + b_Morpik_PRKR * MOR_PIK
# Define settings for MNL model component
mnl_settings = list(alternatives = c(Other=1, Drive=2, Passenger=3, Transit=4,Walk=5, Bike=6, PRKR=7),
avail = list(Other=av_Other, Drive=av_Drive, Passenger=av_Passenger, Transit=av_Transit, Walk=av_Walk, Bike=av_Bike, PRKR=av_PRKR),
choiceVar = Choice,
utilities = V
)
# Compute probabilities using MNL model
P[["model"]] = apollo_mnl(mnl_settings, functionality)
# Prepare and return outputs of function
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
nrow(p)
}model = apollo_estimate(apollo_beta, apollo_fixed, apollo_probabilities, apollo_inputs)## Preparing user-defined functions.
##
## Testing likelihood function...
##
## Overview of choices for MNL model component :
## Other Drive Passenger Transit Walk
## Times available 5000.00 4325.00 5000.00 4960.00 958.00
## Times chosen 12.00 3234.00 274.00 984.00 260.00
## Percentage chosen overall 0.24 64.68 5.48 19.68 5.20
## Percentage chosen when available 0.24 74.77 5.48 19.84 27.14
## Bike PRKR
## Times available 2844.00 5000.0
## Times chosen 66.00 170.0
## Percentage chosen overall 1.32 3.4
## Percentage chosen when available 2.32 3.4
##
## Pre-processing likelihood function...
##
## Testing influence of parameters
## Starting main estimation
## Initial function value: -8584.2
## Initial gradient value:
## asc_Drive asc_Passenger asc_Transit asc_Walk
## 2460.74048 -632.22619 86.72381 117.32381
## asc_Bike asc_PRKR b_tt b_cost
## -402.10952 -736.22619 -38033.93695 -150.22688
## b_OCBD_PRKR b_DCBD_Drive b_DCBD_Passenger b_male_Passenger
## -12968.84476 41359.96703 -7990.23703 -394.76667
## b_male b_Age20 b_Age2140_Transit b_HH1pers_Passenger
## -376.15000 -16.30476 91.75714 -84.34286
## b_HH0car b_HH2cars_Drive b_Morpik_Transit b_Morpik_PRKR
## 213.62619 1378.11667 103.90000 -472.65000
## initial value 8584.199774
## iter 2 value 5790.374284
## iter 3 value 5129.513130
## iter 4 value 5021.011772
## iter 5 value 4737.526476
## iter 6 value 4184.796678
## iter 7 value 3987.561533
## iter 8 value 3616.890087
## iter 9 value 3500.816661
## iter 10 value 3454.496394
## iter 11 value 3428.048370
## iter 12 value 3427.739581
## iter 13 value 3425.719540
## iter 14 value 3419.304027
## iter 15 value 3398.563290
## iter 16 value 3379.135393
## iter 17 value 3373.656452
## iter 18 value 3363.711461
## iter 19 value 3343.540335
## iter 20 value 3332.866488
## iter 21 value 3327.187416
## iter 22 value 3310.865493
## iter 23 value 3307.039842
## iter 24 value 3300.175629
## iter 25 value 3296.198586
## iter 26 value 3294.474197
## iter 27 value 3293.799964
## iter 28 value 3293.390589
## iter 29 value 3293.143748
## iter 30 value 3293.036674
## iter 31 value 3293.006856
## iter 32 value 3293.000534
## iter 33 value 3292.999934
## iter 33 value 3292.999902
## iter 33 value 3292.999901
## final value 3292.999901
## converged
## Additional convergence test using scaled estimation. Parameters will be
## scaled by their current estimates and additional iterations will be
## performed.
## initial value 3292.999901
## iter 1 value 3292.999901
## final value 3292.999901
## converged
## Estimated parameters:
## Estimate
## asc_Other 0.00000
## asc_Drive 3.62365
## asc_Passenger 0.76950
## asc_Transit 3.66729
## asc_Walk 4.57696
## asc_Bike 1.18742
## asc_PRKR 1.04307
## b_tt -0.05247
## b_cost -0.34554
## b_OCBD_PRKR 0.08008
## b_DCBD_Drive 0.11435
## b_DCBD_Passenger 0.07263
## b_male_Passenger -1.36442
## b_male -0.29545
## b_Age20 0.57697
## b_Age2140_Transit 0.27045
## b_HH1pers_Passenger -1.37528
## b_HH0car 1.10681
## b_HH2cars_Drive 0.96670
## b_Morpik_Transit 0.34726
## b_Morpik_PRKR 1.09273
##
## Final LL: -3292.9999
##
## Calculating log-likelihood at equal shares (LL(0)) for applicable
## models...
## Calculating log-likelihood at observed shares from estimation data
## (LL(c)) for applicable models...
## Calculating LL of each model component...
## Calculating other model fit measures
## Computing covariance matrix using analytical gradient.
## 0%....25%....50%....75%..100%
## Negative definite Hessian with maximum eigenvalue: -1.846626
## Computing score matrix...apollo_modelOutput(model)## Model run by Surface using Apollo 0.2.8 on R 4.1.3 for Windows.
## www.ApolloChoiceModelling.com
##
## Model name : MNL_Mode Choice Model_Base
## Model description : Simple MNL model on base mode choice data
## Model run at : 2023-11-20 12:42:52
## Estimation method : bfgs
## Model diagnosis : successful convergence
## Number of individuals : 5000
## Number of rows in database : 5000
## Number of modelled outcomes : 5000
##
## Number of cores used : 1
## Model without mixing
##
## LL(start) : -8584.2
## LL at equal shares, LL(0) : -8584.2
## LL at observed shares, LL(C) : -4243.58
## LL(final) : -3293
## Rho-squared vs equal shares : 0.6164
## Adj.Rho-squared vs equal shares : 0.6141
## Rho-squared vs observed shares : 0.224
## Adj.Rho-squared vs observed shares : 0.2193
## AIC : 6626
## BIC : 6756.34
##
## Estimated parameters : 20
## Time taken (hh:mm:ss) : 00:00:7.14
## pre-estimation : 00:00:1.89
## estimation : 00:00:1.6
## post-estimation : 00:00:3.66
## Iterations : 37
## Min abs eigenvalue of Hessian : 1.846626
##
## Unconstrained optimisation.
##
## These outputs have had the scaling used in estimation applied to them.
## Estimates:
## Estimate s.e. t.rat.(0) Rob.s.e.
## asc_Other 0.00000 NA NA NA
## asc_Drive 3.62365 0.297517 12.180 0.290690
## asc_Passenger 0.76950 0.327189 2.352 0.337169
## asc_Transit 3.66729 0.309269 11.858 0.305553
## asc_Walk 4.57696 0.314072 14.573 0.325422
## asc_Bike 1.18742 0.325348 3.650 0.329857
## asc_PRKR 1.04307 0.386642 2.698 0.378206
## b_tt -0.05247 0.003225 -16.272 0.006129
## b_cost -0.34554 0.018197 -18.989 0.019922
## b_OCBD_PRKR 0.08008 0.006760 11.846 0.007112
## b_DCBD_Drive 0.11435 0.006523 17.531 0.008583
## b_DCBD_Passenger 0.07263 0.008123 8.942 0.009909
## b_male_Passenger -1.36442 0.147991 -9.220 0.161200
## b_male -0.29545 0.087859 -3.363 0.082639
## b_Age20 0.57697 0.226425 2.548 0.230349
## b_Age2140_Transit 0.27045 0.092055 2.938 0.083892
## b_HH1pers_Passenger -1.37528 0.354065 -3.884 0.342276
## b_HH0car 1.10681 0.218646 5.062 0.196778
## b_HH2cars_Drive 0.96670 0.086522 11.173 0.084132
## b_Morpik_Transit 0.34726 0.103280 3.362 0.093022
## b_Morpik_PRKR 1.09273 0.229737 4.756 0.228538
## Rob.t.rat.(0)
## asc_Other NA
## asc_Drive 12.466
## asc_Passenger 2.282
## asc_Transit 12.002
## asc_Walk 14.065
## asc_Bike 3.600
## asc_PRKR 2.758
## b_tt -8.561
## b_cost -17.345
## b_OCBD_PRKR 11.260
## b_DCBD_Drive 13.324
## b_DCBD_Passenger 7.330
## b_male_Passenger -8.464
## b_male -3.575
## b_Age20 2.505
## b_Age2140_Transit 3.224
## b_HH1pers_Passenger -4.018
## b_HH0car 5.625
## b_HH2cars_Drive 11.490
## b_Morpik_Transit 3.733
## b_Morpik_PRKR 4.781Here, asc_Other = Alternative specific constant for Other mode, asc_Drive = Alternative specific constant for Drive mode, asc_Passenger = Alternative specific constant Passenger mode, asc_Transit = Alternative specific constant for Transit mode, asc_Walk = Alternative specific constant for Wlak mode, asc_Bike = Alternative specific constant for Bike mode, asc_PRKR = Alternative specific constant for Park and Ride mode, asc_TNC = Alternative specific constant for TNC mode, asc_Micro = Alternative specific constant for Shared-micromobility mode, b_tt = Coefficient for travel time, b_cost = Coefficient for travel cost (Drive, Transit and Park & Ride mode), b_OCBD_Drive = Coefficient for destination distance from CBD (Park and Ride mode), b_DCBD_Drive = Coefficient for destination distance from CBD (Drive mode), b_DCBD_Passenger = Coefficient for destination distance from CBD (Passenger mode), b_male_Passenger = Coefficient for male (Passenger mode), b_male = Coefficient for male (Transit, Walk and Park & Ride mode), b_Age20 = Coefficient for Age <= 20 (Passenger, Transit and Bike mode), b_Age2140_Transit = Coefficient for Age 21-40 (Transit mode), b_HH1pers_Passenger = Coefficient for HH with 1 person (Passenger mode), b_HH0car = Coefficient for HH with zero car (transit, Walk and Bike mode), b_HH2cars_Drive = Coefficient for HH with two cars (Drive mode), b_Morpik_Transit = Coefficient for Morning peak (Transit mode) b_Morpik_PRKR = Coefficient for Morning peak (Park and Ride mode)