I am doing model estimation on travel-related SP data and have encountered some unexpected results.
Specifically, I have two types of choice experiments in my SP survey: economy class design and upper class design. The designs, attributes, and levels are the same for both classes, except for a 60% increase in the cost attribute for the upper class design. Respondents are assigned to one of the two designs based on their answers to previous questions before participating in the choice experiment.
After collecting the data, I found that 58% of the respondents did the upper class design, while the others did the economy class design. I estimated a MNL model using all the data and obtained a value of time of 145.1 (h/currency). When I segmented the data into economy and upper class and estimated separate MNL models. However, I found that the value of time for the economy class segment was 179 (h/currency), which is higher than the pooled data value of time. The value of time for the upper class segment was 797 (h/currency).
I am wondering if it is possible for the value of time for the economy class to be higher than the pooled data value of time. I would have expected the order to be VTT_economyclass < VTT_pooleddata < VTT_upperclass. Could there be something wrong with the design or estimation?
I have attached the code and results for the three MNL models below.
CODE: The code I'm presenting here is for the pooled data. The code for the two segments is identical except for the data subset.
Code: Select all
# ################################################################# #
#### LOAD LIBRARY AND DEFINE CORE SETTINGS ####
# ################################################################# #
#install.packages("apollo")
### Clear memory
rm(list = ls())
dirname(rstudioapi::getActiveDocumentContext()$path) #checking path
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
getwd() #checking active path
### Load Apollo library
library("apollo")
### Initialise code
apollo_initialise()
### Set core controls
apollo_control = list(
modelName = "MNL_data_FINAL_nofilter_ASC",
modelDescr = "MNL model on main data 6min no filter WITH ASC",
indivID = "ID",
outputDirectory = "output"
)
# ################################################################# #
#### LOAD DATA AND APPLY ANY TRANSFORMATIONS ####
# ################################################################# #
### Loading data from package
### if data is to be loaded from a file (e.g. called data.csv),
### the code would be: database = read.csv("data.csv",header=TRUE)
database = read.csv("Processed_FINAL_6min_NOFILTER.csv",header=TRUE)
#####for economy class#####
database<- subset (database, UPP_Block==0)
#####for upper class#####
database<- subset (database, ECO_Block==0)
# ################################################################# #
#### DEFINE MODEL PARAMETERS ####
# ################################################################# #
### Vector of parameters, including any that are kept fixed in estimation
apollo_beta = c(ASC1 = 0,
ASC2 = 0,
ASC3 = 0,
b_fare = 0,
b_time = 0,
b_type1 = 0,
b_type2 = 0,
b_type3 = 0,
b_type0 = 0,
b_emission_reduction = 0)
### 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_fixed = c("b_type0","ASC3")
# ################################################################# #
#### GROUP AND VALIDATE INPUTS ####
# ################################################################# #
apollo_inputs = apollo_validateInputs()
# ################################################################# #
#### DEFINE MODEL AND LIKELIHOOD FUNCTION ####
# ################################################################# #
apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){
### Function initialisation: do not change the following three commands
### 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[["alt1"]] = ASC1 + b_fare * alt1.fare + b_time * alt1.time + b_type1 * (alt1.type ==1) + b_type2 * (alt1.type ==2) + b_type3 * (alt1.type ==3)+ b_type0* (alt1.type ==0) + b_emission_reduction * alt1.emission
V[["alt2"]] = ASC2 + b_fare * alt2.fare + b_time * alt2.time + b_type1 * (alt2.type ==1) + b_type2 * (alt2.type ==2) + b_type3 * (alt2.type ==3)+
b_type0 * (alt2.type ==0) + b_emission_reduction * alt2.emission
V[["alt3"]] = ASC3 + b_fare * alt3.fare + b_time * alt3.time + b_type1 * (alt3.type ==1) + b_type2 * (alt3.type ==2) + b_type3* (alt3.type ==3)+
b_type0* (alt3.type ==0) + b_emission_reduction * alt3.emission
### Define settings for MNL model component
mnl_settings = list(
alternatives = c(alt1=1, alt2=2, alt3=3),
#avail = list(alt1=1, alt2=1, alt3=1),
choiceVar = choice,
utilities = V
)
### Compute probabilities using MNL model
P[["model"]] = apollo_mnl(mnl_settings, functionality)
### Take product across observation for same individual
P = apollo_panelProd(P, apollo_inputs, functionality)
### Prepare and return outputs of function
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}
# ################################################################# #
#### MODEL ESTIMATION ####
# ################################################################# #
model = apollo_estimate(apollo_beta, apollo_fixed,
apollo_probabilities, apollo_inputs)
# ################################################################# #
#### MODEL OUTPUTS ####
# ################################################################# #
# ----------------------------------------------------------------- #
#---- FORMATTED OUTPUT (TO SCREEN) ----
# ----------------------------------------------------------------- #
apollo_modelOutput(model)
# ----------------------------------------------------------------- #
#---- FORMATTED OUTPUT (TO FILE, using model name) ----
# ----------------------------------------------------------------- #
apollo_saveOutput(model)
# ----------------------------------------------------------------- #
#---- FUNCTIONS OF MODEL PARAMETERS ----
# ----------------------------------------------------------------- #
#deltaMethod_settings=list(operation="ratio", parName1="b_time", parName2="b_fare", multPar1 = 60)
#apollo_deltaMethod(model, deltaMethod_settings)
apollo_deltaMethod(model,deltaMethod_settings = list(operation="ratio",
parName1="b_time",
parName2="b_fare",
multPar1=60))
Code: Select all
Model name : MNL_data_FINAL_nofilter_ASC
Model description : MNL model on main data 6min no filter WITH ASC
Model run at : 2023-05-03 14:59:35
Estimation method : bfgs
Model diagnosis : successful convergence
Number of individuals : 3188
Number of rows in database : 28692
Number of modelled outcomes : 28692
Number of cores used : 1
Model without mixing
LL(start) : -31521.38
LL at equal shares, LL(0) : -31521.38
LL at observed shares, LL(C) : -30988.81
LL(final) : -27690.19
Rho-squared vs equal shares : 0.1215
Adj.Rho-squared vs equal shares : 0.1213
Rho-squared vs observed shares : 0.1064
Adj.Rho-squared vs observed shares : 0.1062
AIC : 55396.37
BIC : 55462.49
Estimated parameters : 8
Time taken (hh:mm:ss) : 00:00:7.76
pre-estimation : 00:00:2.26
estimation : 00:00:2.55
post-estimation : 00:00:2.96
Iterations : 16
Min abs eigenvalue of Hessian : 170.649
Unconstrained optimisation.
These outputs have had the scaling used in estimation applied to them.
Estimates:
Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0)
ASC1 0.172113 0.01663 10.352 0.01605 10.727
ASC2 0.138729 0.01665 8.332 0.01639 8.464
ASC3 0.000000 NA NA NA NA
b_fare -0.001340 3.318e-05 -40.389 4.114e-05 -32.574
b_time -0.003241 6.6913e-04 -4.844 7.5585e-04 -4.288
b_type1 0.402288 0.03202 12.565 0.03626 11.094
b_type2 0.809267 0.05778 14.005 0.06104 13.257
b_type3 0.575849 0.04962 11.605 0.05525 10.423
b_type0 0.000000 NA NA NA NA
b_emission_reduction 0.005278 4.3509e-04 12.130 4.6338e-04 11.390
Overview of choices for MNL model component :
alt1 alt2 alt3
Times available 28692.00 28692.00 28692.00
Times chosen 9523.00 11833.00 7336.00
Percentage chosen overall 33.19 41.24 25.57
Percentage chosen when available 33.19 41.24 25.57
Classical covariance matrix:
ASC1 ASC2 b_fare b_flighttime
ASC1 2.7645e-04 1.5238e-04 3.246e-08 8.430e-07
ASC2 1.5238e-04 2.7721e-04 1.983e-08 -7.225e-07
b_fare 3.246e-08 1.983e-08 1.101e-09 1.437e-08
b_time 8.430e-07 -7.225e-07 1.437e-08 4.477e-07
b_b_type1 -2.241e-05 -8.294e-05 -3.323e-07 -1.556e-06
b_b_type2 -6.950e-05 -6.552e-05 -3.962e-07 -1.318e-05
b_b_type3 -5.890e-05 -6.721e-05 -4.059e-07 -1.190e-05
b_emission_reduction 1.894e-07 -3.624e-08 -5.789e-10 -8.596e-09
b_SAF b_EA b_HA b_emission_reduction
ASC1 -2.241e-05 -6.950e-05 -5.890e-05 1.894e-07
ASC2 -8.294e-05 -6.552e-05 -6.721e-05 -3.624e-08
b_fare -3.323e-07 -3.962e-07 -4.059e-07 -5.789e-10
b_time -1.556e-06 -1.318e-05 -1.190e-05 -8.596e-09
b_type1 0.001025 0.001232 0.001233 -1.053e-05
b_type2 0.001232 0.003339 0.002290 -1.808e-05
b_type3 0.001233 0.002290 0.002462 -1.814e-05
b_emission_reduction -1.053e-05 -1.808e-05 -1.814e-05 1.893e-07
Robust covariance matrix:
ASC1 ASC2 b_fare b_flighttime
ASC1 2.5745e-04 1.4009e-04 8.650e-08 1.965e-06
ASC2 1.4009e-04 2.6866e-04 8.254e-09 -2.439e-07
b_fare 8.650e-08 8.254e-09 1.693e-09 1.645e-08
b_time 1.965e-06 -2.439e-07 1.645e-08 5.713e-07
b_type1 2.551e-05 -6.169e-05 -2.137e-07 -4.055e-06
b_type2 -5.694e-05 -5.486e-05 -4.522e-07 -1.611e-05
b_type3 -1.799e-05 -5.481e-05 -3.423e-07 -1.625e-05
b_emission_reduction -2.446e-07 -1.341e-07 -1.855e-09 -9.764e-09
b_SAF b_EA b_HA b_emission_reduction
ASC1 2.551e-05 -5.694e-05 -1.799e-05 -2.446e-07
ASC2 -6.169e-05 -5.486e-05 -5.481e-05 -1.341e-07
b_fare -2.137e-07 -4.522e-07 -3.423e-07 -1.855e-09
b_time -4.055e-06 -1.611e-05 -1.625e-05 -9.764e-09
b_type1 0.001315 0.001558 0.001614 -1.058e-05
b_type2 0.001558 0.003726 0.002821 -1.953e-05
b_type3 0.001614 0.002821 0.003052 -1.950e-05
b_emission_reduction -1.058e-05 -1.953e-05 -1.950e-05 2.147e-07
Classical correlation matrix:
ASC1 ASC2 b_fare b_flighttime
ASC1 1.00000 0.550432 0.05884 0.07577
ASC2 0.55043 1.000000 0.03589 -0.06485
b_fare 0.05884 0.035893 1.00000 0.64741
b_time 0.07577 -0.064849 0.64741 1.00000
b_type1 -0.04209 -0.155598 -0.31284 -0.07265
b_type2 -0.07234 -0.068104 -0.20667 -0.34090
b_type3 -0.07139 -0.081352 -0.24653 -0.35829
b_emission_reduction 0.02618 -0.005002 -0.04010 -0.02953
b_SAF b_EA b_HA b_emission_reduction
ASC1 -0.04209 -0.07234 -0.07139 0.026178
ASC2 -0.15560 -0.06810 -0.08135 -0.005002
b_fare -0.31284 -0.20667 -0.24653 -0.040099
b_time -0.07265 -0.34090 -0.35829 -0.029526
b_type1 1.00000 0.66586 0.77612 -0.756082
b_type2 0.66586 1.00000 0.79856 -0.719240
b_type3 0.77612 0.79856 1.00000 -0.840282
b_emission_reduction -0.75608 -0.71924 -0.84028 1.000000
Robust correlation matrix:
ASC1 ASC2 b_fare b_flighttime
ASC1 1.00000 0.53265 0.13104 0.16202
ASC2 0.53265 1.00000 0.01224 -0.01969
b_fare 0.13104 0.01224 1.00000 0.52884
b_time 0.16202 -0.01969 0.52884 1.00000
b_type1 0.04384 -0.10379 -0.14322 -0.14794
b_type2 -0.05813 -0.05483 -0.18005 -0.34906
b_type3 -0.02029 -0.06052 -0.15058 -0.38906
b_emission_reduction -0.03290 -0.01765 -0.09731 -0.02788
b_SAF b_EA b_HA b_emission_reduction
ASC1 0.04384 -0.05813 -0.02029 -0.03290
ASC2 -0.10379 -0.05483 -0.06052 -0.01765
b_fare -0.14322 -0.18005 -0.15058 -0.09731
b_time -0.14794 -0.34906 -0.38906 -0.02788
b_type1 1.00000 0.70379 0.80568 -0.62984
b_type2 0.70379 1.00000 0.83637 -0.69058
b_type3 0.80568 0.83637 1.00000 -0.76155
b_emission_reduction -0.62984 -0.69058 -0.76155 1.00000
20 worst outliers in terms of lowest average per choice prediction:
ID Avg prob per choice
1378 0.1568203
875 0.1654853
61 0.1669630
2142 0.1682588
2075 0.1696047
156 0.1728958
248 0.1728958
255 0.1728958
2512 0.1739157
134 0.1742798
225 0.1757682
173 0.1765429
1893 0.1774203
2117 0.1805586
2128 0.1812739
2988 0.1828989
1087 0.1841452
911 0.1859834
2476 0.1868619
885 0.1883451
Changes in parameter estimates from starting values:
Initial Estimate Difference
ASC1 0.000 0.172113 0.172113
ASC2 0.000 0.138729 0.138729
ASC3 0.000 0.000000 0.000000
b_fare 0.000 -0.001340 -0.001340
b_time 0.000 -0.003241 -0.003241
b_type1 0.000 0.402288 0.402288
b_type2 0.000 0.809267 0.809267
b_type3 0.000 0.575849 0.575849
b_type0 0.000 0.000000 0.000000
b_emission_reduction 0.000 0.005278 0.005278
Settings and functions used in model definition:
apollo_control
--------------
Value
modelName "MNL_data_FINAL_nofilter_ASC"
modelDescr "MNL model on main data 6min no filter WITH ASC"
indivID "ID"
outputDirectory "output/"
debug "FALSE"
nCores "1"
workInLogs "FALSE"
seed "13"
mixing "FALSE"
HB "FALSE"
noValidation "FALSE"
noDiagnostics "FALSE"
calculateLLC "TRUE"
panelData "TRUE"
analyticGrad "TRUE"
analyticGrad_manualSet "FALSE"
Hessian routines attempted
--------------
numerical jacobian of LL analytical gradient
Scaling in estimation
--------------
Value
ASC1 0.172113166
ASC2 0.138729148
b_fare 0.001340111
b_time 0.003240962
b_type1 0.402283217
b_type2 0.809269652
b_type3 0.575853885
b_emission_reduction 0.005277718
Scaling used in computing Hessian
--------------
Value
ASC1 0.172113275
ASC2 0.138729435
b_fare 0.001340110
b_time 0.003240961
b_type1 0.402287777
b_type2 0.809266541
b_type3 0.575848824
b_emission_reduction 0.005277772
Running Delta method computations
Value Robust s.e. Rob t-ratio (0)
Ratio of b_time (multiplied by 60) and b_fare: 145.1 31.71 4.576
Code: Select all
Model name : MNL_data_6min_ECO_ASC
Model description : MNL model on main data 6min no filter WITH ASC ECONOMY CLASS
Model run at : 2023-05-03 15:47:30
Estimation method : bfgs
Model diagnosis : successful convergence
Number of individuals : 1325
Number of rows in database : 11925
Number of modelled outcomes : 11925
Number of cores used : 1
Model without mixing
LL(start) : -13100.95
LL at equal shares, LL(0) : -13100.95
LL at observed shares, LL(C) : -12949.48
LL(final) : -9866.76
Rho-squared vs equal shares : 0.2469
Adj.Rho-squared vs equal shares : 0.2463
Rho-squared vs observed shares : 0.2381
Adj.Rho-squared vs observed shares : 0.2374
AIC : 19749.52
BIC : 19808.61
Estimated parameters : 8
Time taken (hh:mm:ss) : 00:00:7.37
pre-estimation : 00:00:1.78
estimation : 00:00:2.18
post-estimation : 00:00:3.41
Iterations : 20
Min abs eigenvalue of Hessian : 57.03027
Unconstrained optimisation.
These outputs have had the scaling used in estimation applied to them.
Estimates:
Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0)
ASC1 0.050441 0.029074 1.735 0.027721 1.820
ASC2 0.177005 0.027309 6.482 0.026521 6.674
ASC3 0.000000 NA NA NA NA
b_fare -0.004243 8.993e-05 -47.175 1.1908e-04 -35.627
b_time -0.012658 0.001069 -11.844 0.001091 -11.606
b_type1 0.211077 0.056914 3.709 0.062077 3.400
b_type2 0.874358 0.098243 8.900 0.094061 9.296
b_type3 0.416190 0.087601 4.751 0.087694 4.746
b_type0 0.000000 NA NA NA NA
b_emission_reduction 0.008422 7.5953e-04 11.089 7.7564e-04 10.858
Overview of choices for MNL model component :
alt1 alt2 alt3
Times available 11925.00 11925.00 11925.00
Times chosen 3409.00 4874.00 3642.00
Percentage chosen overall 28.59 40.87 30.54
Percentage chosen when available 28.59 40.87 30.54
Classical covariance matrix:
ASC1 ASC2 b_fare b_flighttime b_SAF
ASC1 8.4530e-04 2.8867e-04 8.612e-08 6.410e-06 2.0328e-04
ASC2 2.8867e-04 7.4579e-04 7.665e-08 -1.548e-06 -2.6109e-04
b_fare 8.612e-08 7.665e-08 8.088e-09 6.118e-08 -1.638e-06
b_time 6.410e-06 -1.548e-06 6.118e-08 1.142e-06 -4.718e-06
b_type1 2.0328e-04 -2.6109e-04 -1.638e-06 -4.718e-06 0.003239
b_type2 6.102e-05 -2.2868e-04 -1.252e-06 -3.026e-05 0.003750
b_type3 -1.8371e-04 -2.8726e-04 -1.717e-06 -3.205e-05 0.003781
b_emission_reduction 1.191e-06 5.585e-07 -6.302e-09 -1.465e-08 -3.108e-05
b_EA b_HA b_emission_reduction
ASC1 6.102e-05 -1.8371e-04 1.191e-06
ASC2 -2.2868e-04 -2.8726e-04 5.585e-07
b_fare -1.252e-06 -1.717e-06 -6.302e-09
b_time -3.026e-05 -3.205e-05 -1.465e-08
b_type1 0.003750 0.003781 -3.108e-05
b_type2 0.009652 0.006813 -5.506e-05
b_type3 0.006813 0.007674 -5.632e-05
b_emission_reduction -5.506e-05 -5.632e-05 5.769e-07
Robust covariance matrix:
ASC1 ASC2 b_fare b_flighttime b_SAF
ASC1 7.6843e-04 2.7410e-04 4.031e-07 1.018e-05 7.003e-05
ASC2 2.7410e-04 7.0336e-04 1.158e-07 4.000e-07 -2.5901e-04
b_fare 4.031e-07 1.158e-07 1.418e-08 6.574e-08 -1.374e-06
b_time 1.018e-05 4.000e-07 6.574e-08 1.189e-06 -6.493e-06
b_type1 7.003e-05 -2.5901e-04 -1.374e-06 -6.493e-06 0.003854
b_type2 -2.3689e-04 -2.8245e-04 -1.276e-06 -2.896e-05 0.004000
b_type3 -4.4810e-04 -3.4229e-04 -1.517e-06 -3.172e-05 0.004127
b_emission_reduction 2.538e-06 9.365e-07 -1.240e-08 -1.334e-08 -2.831e-05
b_EA b_HA b_emission_reduction
ASC1 -2.3689e-04 -4.4810e-04 2.538e-06
ASC2 -2.8245e-04 -3.4229e-04 9.365e-07
b_fare -1.276e-06 -1.517e-06 -1.240e-08
b_time -2.896e-05 -3.172e-05 -1.334e-08
b_type1 0.004000 0.004127 -2.831e-05
b_type2 0.008847 0.006580 -4.741e-05
b_type3 0.006580 0.007690 -5.231e-05
b_emission_reduction -4.741e-05 -5.231e-05 6.016e-07
Classical correlation matrix:
ASC1 ASC2 b_fare b_flighttime b_SAF
ASC1 1.00000 0.36357 0.03294 0.20631 0.12285
ASC2 0.36357 1.00000 0.03121 -0.05303 -0.16798
b_fare 0.03294 0.03121 1.00000 0.63658 -0.32006
b_time 0.20631 -0.05303 0.63658 1.00000 -0.07757
b_type1 0.12285 -0.16798 -0.32006 -0.07757 1.00000
b_type2 0.02136 -0.08523 -0.14168 -0.28819 0.67071
b_type3 -0.07213 -0.12008 -0.21800 -0.34230 0.75843
b_emission_reduction 0.05394 0.02693 -0.09226 -0.01805 -0.71897
b_EA b_HA b_emission_reduction
ASC1 0.02136 -0.07213 0.05394
ASC2 -0.08523 -0.12008 0.02693
b_fare -0.14168 -0.21800 -0.09226
b_time -0.28819 -0.34230 -0.01805
b_type1 0.67071 0.75843 -0.71897
b_type2 1.00000 0.79167 -0.73787
b_type3 0.79167 1.00000 -0.84650
b_emission_reduction -0.73787 -0.84650 1.00000
Robust correlation matrix:
ASC1 ASC2 b_fare b_flighttime b_SAF
ASC1 1.00000 0.37283 0.12212 0.33666 0.04070
ASC2 0.37283 1.00000 0.03666 0.01383 -0.15732
b_fare 0.12212 0.03666 1.00000 0.50620 -0.18592
b_time 0.33666 0.01383 0.50620 1.00000 -0.09591
b_type1 0.04070 -0.15732 -0.18592 -0.09591 1.00000
b_type2 -0.09085 -0.11322 -0.11392 -0.28229 0.68508
b_type3 -0.18433 -0.14717 -0.14527 -0.33161 0.75815
b_emission_reduction 0.11805 0.04553 -0.13429 -0.01577 -0.58788
b_EA b_HA b_emission_reduction
ASC1 -0.09085 -0.1843 0.11805
ASC2 -0.11322 -0.1472 0.04553
b_fare -0.11392 -0.1453 -0.13429
b_time -0.28229 -0.3316 -0.01577
b_type1 0.68508 0.7582 -0.58788
b_type2 1.00000 0.7977 -0.64990
b_type3 0.79766 1.0000 -0.76912
b_emission_reduction -0.64990 -0.7691 1.00000
20 worst outliers in terms of lowest average per choice prediction:
ID Avg prob per choice
173 0.1085297
2619 0.1167428
906 0.1273156
1684 0.1298964
106 0.1415237
1241 0.1430520
1221 0.1464643
315 0.1524352
2530 0.1588139
1208 0.1594307
2179 0.1606433
1964 0.1633451
2324 0.1654127
53 0.1658439
126 0.1660460
2666 0.1667559
844 0.1669666
798 0.1724656
1029 0.1728904
3052 0.1736867
Changes in parameter estimates from starting values:
Initial Estimate Difference
ASC1 0.000 0.050441 0.050441
ASC2 0.000 0.177005 0.177005
ASC3 0.000 0.000000 0.000000
b_fare 0.000 -0.004243 -0.004243
b_time 0.000 -0.012658 -0.012658
b_type1 0.000 0.211077 0.211077
b_type2 0.000 0.874358 0.874358
b_type3 0.000 0.416190 0.416190
b_type0 0.000 0.000000 0.000000
b_emission_reduction 0.000 0.008422 0.008422
Settings and functions used in model definition:
apollo_control
--------------
Value
modelName "MNL_data_6min_ECO_ASC"
modelDescr "MNL model on main data 6min no filter WITH ASC ECONOMY CLASS"
indivID "ID"
outputDirectory "output/"
debug "FALSE"
nCores "1"
workInLogs "FALSE"
seed "13"
mixing "FALSE"
HB "FALSE"
noValidation "FALSE"
noDiagnostics "FALSE"
calculateLLC "TRUE"
panelData "TRUE"
analyticGrad "TRUE"
analyticGrad_manualSet "FALSE"
Hessian routines attempted
--------------
numerical jacobian of LL analytical gradient
Scaling in estimation
--------------
Value
ASC1 0.050440637
ASC2 0.177005289
b_fare 0.004242533
b_time 0.012657870
b_type1 0.211076794
b_type2 0.874359201
b_type3 0.416187921
b_emission_reduction 0.008422139
Scaling used in computing Hessian
--------------
Value
ASC1 0.050440702
ASC2 0.177004777
b_fare 0.004242531
b_flighttime 0.012657788
b_type1 0.211076555
b_type2 0.874357977
b_type3 0.416189508
b_emission_reduction 0.008422197
Running Delta method computations
Value Robust s.e. Rob t-ratio (0)
Ratio of b_time (multiplied by 60) and b_fare: 179 13.59 13.17
Code: Select all
Model name : MNL_data_6min_UPP_ASC
Model description : MNL model on main data 6min no filter WITH ASC for Upper class
Model run at : 2023-05-03 15:43:41
Estimation method : bfgs
Model diagnosis : successful convergence
Number of individuals : 1863
Number of rows in database : 16767
Number of modelled outcomes : 16767
Number of cores used : 1
Model without mixing
LL(start) : -18420.43
LL at equal shares, LL(0) : -18420.43
LL at observed shares, LL(C) : -17875.5
LL(final) : -15858.61
Rho-squared vs equal shares : 0.1391
Adj.Rho-squared vs equal shares : 0.1386
Rho-squared vs observed shares : 0.1128
Adj.Rho-squared vs observed shares : 0.1124
AIC : 31733.22
BIC : 31795.03
Estimated parameters : 8
Time taken (hh:mm:ss) : 00:00:4.22
pre-estimation : 00:00:0.97
estimation : 00:00:1.79
post-estimation : 00:00:1.47
Iterations : 17
Min abs eigenvalue of Hessian : 97.41227
Unconstrained optimisation.
These outputs have had the scaling used in estimation applied to
them.
Estimates:
Estimate s.e. t.rat.(0) Rob.s.e.
ASC1 0.164729 0.023226 7.092 0.021371
ASC2 0.117621 0.023549 4.995 0.024336
ASC3 0.000000 NA NA NA
b_fare -0.001491 4.322e-05 -34.488 4.785e-05
b_time -0.019791 0.001089 -18.182 0.001208
b_type1 0.826075 0.042013 19.662 0.045773
b_type2 1.108554 0.077002 14.396 0.082995
b_type3 1.140216 0.064496 17.679 0.072445
b_type0 0.000000 NA NA NA
b_emission_reduction 0.006725 5.5229e-04 12.176 5.7952e-04
Rob.t.rat.(0)
ASC1 7.708
ASC2 4.833
ASC3 NA
b_fare -31.154
b_time -16.387
b_type1 18.047
b_type2 13.357
b_type3 15.739
b_type0 NA
b_emission_reduction 11.604
Overview of choices for MNL model component :
alt1 alt2 alt3
Times available 16767.00 16767.0 16767.00
Times chosen 6114.00 6959.0 3694.00
Percentage chosen overall 36.46 41.5 22.03
Percentage chosen when available 36.46 41.5 22.03
Classical covariance matrix:
ASC1 ASC2
ASC1 5.3945e-04 3.5920e-04
ASC2 3.5920e-04 5.5456e-04
b_fare 1.008e-07 7.686e-08
b_time 4.505e-07 -1.303e-06
b_type1 -1.6353e-04 -2.0882e-04
b_type2 -2.2397e-04 -1.7022e-04
b_type3 -1.3298e-04 -1.2679e-04
b_emission_reduction 4.692e-08 -2.921e-07
b_fare b_flighttime
ASC1 1.008e-07 4.505e-07
ASC2 7.686e-08 -1.303e-06
b_fare 1.868e-09 3.493e-08
b_time 3.493e-08 1.185e-06
b_type1 -7.536e-07 -8.484e-06
b_type2 -1.088e-06 -3.560e-05
b_type3 -9.961e-07 -3.111e-05
b_emission_reduction -7.045e-10 -2.721e-08
b_SAF b_EA
ASC1 -1.6353e-04 -2.2397e-04
ASC2 -2.0882e-04 -1.7022e-04
b_fare -7.536e-07 -1.088e-06
b_time -8.484e-06 -3.560e-05
b_type1 0.001765 0.002197
b_type2 0.002197 0.005929
b_type3 0.002108 0.004022
b_emission_reduction -1.643e-05 -2.827e-05
b_HA b_emission_reduction
ASC1 -1.3298e-04 4.692e-08
ASC2 -1.2679e-04 -2.921e-07
b_fare -9.961e-07 -7.045e-10
b_time -3.111e-05 -2.721e-08
b_type1 0.002108 -1.643e-05
b_type2 0.004022 -2.827e-05
b_type3 0.004160 -2.790e-05
b_emission_reduction -2.790e-05 3.050e-07
Robust covariance matrix:
ASC1 ASC2
ASC1 4.5673e-04 3.4310e-04
ASC2 3.4310e-04 5.9226e-04
b_fare 4.013e-08 -7.586e-09
b_time -7.386e-07 -3.136e-06
b_type1 -1.682e-05 -1.5396e-04
b_type2 9.146e-06 -3.962e-06
b_type3 4.883e-05 -1.829e-05
b_emission_reduction -1.033e-06 -8.736e-07
b_fare b_flighttime
ASC1 4.013e-08 -7.386e-07
ASC2 -7.586e-09 -3.136e-06
b_fare 2.289e-09 3.861e-08
b_time 3.861e-08 1.459e-06
b_type1 -7.297e-07 -1.306e-05
b_type2 -1.301e-06 -4.761e-05
b_type3 -1.105e-06 -4.243e-05
b_emission_reduction -1.065e-09 1.208e-08
b_SAF b_EA
ASC1 -1.682e-05 9.146e-06
ASC2 -1.5396e-04 -3.962e-06
b_fare -7.297e-07 -1.301e-06
b_time -1.306e-05 -4.761e-05
b_type1 0.002095 0.002735
b_type2 0.002735 0.006888
b_type3 0.002666 0.005125
b_emission_reduction -1.522e-05 -3.016e-05
b_HA b_emission_reduction
ASC1 4.883e-05 -1.033e-06
ASC2 -1.829e-05 -8.736e-07
b_fare -1.105e-06 -1.065e-09
b_time -4.243e-05 1.208e-08
b_type1 0.002666 -1.522e-05
b_type2 0.005125 -3.016e-05
b_type3 0.005248 -2.902e-05
b_emission_reduction -2.902e-05 3.358e-07
Classical correlation matrix:
ASC1 ASC2
ASC1 1.000000 0.65673
ASC2 0.656725 1.00000
b_fare 0.100457 0.07551
b_time 0.017820 -0.05083
b_type1 -0.167587 -0.21106
b_type2 -0.125233 -0.09387
b_type3 -0.088773 -0.08348
b_emission_reduction 0.003657 -0.02246
b_fare b_flighttime
ASC1 0.10046 0.01782
ASC2 0.07551 -0.05083
b_fare 1.00000 0.74243
b_time 0.74243 1.00000
b_type1 -0.41500 -0.18552
b_type2 -0.32683 -0.42476
b_type3 -0.35732 -0.44319
b_emission_reduction -0.02951 -0.04527
b_SAF b_EA
ASC1 -0.1676 -0.12523
ASC2 -0.2111 -0.09387
b_fare -0.4150 -0.32683
b_time -0.1855 -0.42476
b_type1 1.0000 0.67912
b_type2 0.6791 1.00000
b_type3 0.7778 0.80986
b_emission_reduction -0.7083 -0.66472
b_HA b_emission_reduction
ASC1 -0.08877 0.003657
ASC2 -0.08348 -0.022459
b_fare -0.35732 -0.029513
b_time -0.44319 -0.045268
b_type1 0.77780 -0.708280
b_type2 0.80986 -0.664722
b_type3 1.00000 -0.783257
b_emission_reduction -0.78326 1.000000
Robust correlation matrix:
ASC1 ASC2
ASC1 1.000000 0.659681
ASC2 0.659681 1.000000
b_fare 0.039250 -0.006515
b_time -0.028617 -0.106698
b_type1 -0.017192 -0.138207
b_type2 0.005156 -0.001962
b_type3 0.031542 -0.010375
b_emission_reduction -0.083412 -0.061944
b_fare b_flighttime
ASC1 0.039250 -0.02862
ASC2 -0.006515 -0.10670
b_fare 1.000000 0.66809
b_time 0.668090 1.00000
b_type1 -0.333165 -0.23622
b_type2 -0.327611 -0.47495
b_type3 -0.318792 -0.48491
b_emission_reduction -0.038410 0.01726
b_SAF b_EA
ASC1 -0.01719 0.005156
ASC2 -0.13821 -0.001962
b_fare -0.33317 -0.327611
b_time -0.23622 -0.474951
b_type1 1.00000 0.719853
b_type2 0.71985 1.000000
b_type3 0.80393 0.852413
b_emission_reduction -0.57358 -0.627158
b_HA b_emission_reduction
ASC1 0.03154 -0.08341
ASC2 -0.01037 -0.06194
b_fare -0.31879 -0.03841
b_time -0.48491 0.01726
b_type1 0.80393 -0.57358
b_type2 0.85241 -0.62716
b_type3 1.00000 -0.69132
b_emission_reduction -0.69132 1.00000
20 worst outliers in terms of lowest average per choice prediction:
ID Avg prob per choice
1378 0.1441980
875 0.1580217
156 0.1596559
248 0.1596559
255 0.1596559
1811 0.1614643
2512 0.1620763
329 0.1623155
2117 0.1624230
3134 0.1644534
225 0.1682671
885 0.1747638
739 0.1748051
2075 0.1771145
2356 0.1775844
61 0.1818256
1670 0.1832686
2507 0.1840305
3026 0.1844901
2734 0.1854417
Changes in parameter estimates from starting values:
Initial Estimate Difference
ASC1 0.000 0.164729 0.164729
ASC2 0.000 0.117621 0.117621
ASC3 0.000 0.000000 0.000000
b_fare 0.000 -0.001491 -0.001491
b_time 0.000 -0.019791 -0.019791
b_type1 0.000 0.826075 0.826075
b_type2 0.000 1.108554 1.108554
b_type3 0.000 1.140216 1.140216
b_type4 0.000 0.000000 0.000000
b_emission_reduction 0.000 0.006725 0.006725
Settings and functions used in model definition:
apollo_control
--------------
Value
modelName "MNL_data_6min_UPP_ASC"
modelDescr "MNL model on main data 6min no filter WITH ASC for upper class"
indivID "ID"
outputDirectory "output/"
debug "FALSE"
nCores "1"
workInLogs "FALSE"
seed "13"
mixing "FALSE"
HB "FALSE"
noValidation "FALSE"
noDiagnostics "FALSE"
calculateLLC "TRUE"
panelData "TRUE"
analyticGrad "TRUE"
analyticGrad_manualSet "FALSE"
Hessian routines attempted
--------------
numerical jacobian of LL analytical gradient
Scaling in estimation
--------------
Value
ASC1 0.164728891
ASC2 0.117620487
b_fare 0.001490599
b_time 0.019791498
b_type1 0.826076410
b_type2 1.108553072
b_type3 1.140214886
b_emission_reduction 0.006724660
Scaling used in computing Hessian
--------------
Value
ASC1 0.164728842
ASC2 0.117620504
b_fare 0.001490603
b_time 0.019791406
b_type1 0.826075059
b_type2 1.108553812
b_type3 1.140215530
b_emission_reduction 0.006724657
Running Delta method computations
Value Robust s.e.
Ratio of b_time (multiplied by 60) and b_fare: 796.6 36.83
Rob t-ratio (0)
Ratio of b_time (multiplied by 60) and b_fare: 21.63
Many thanks,
Peggy