I recently applied Apollo to estimate the HCM model. Since there are many latent variables, I processed the latent variables into a normal distribution. However, in the final estimation, the model rho square is "not applicable" and LL(0) is NA. Although the final likelihood value of the selection model is obtained, it is not much different from the MNL model.
I would be very grateful if you can answer my doubts.
The following is the code
Code: Select all
# ################################################################# #
#### LOAD LIBRARY AND DEFINE CORE SETTINGS ####
# ################################################################# #
### Clear memory
rm(list = ls())
library(apollo)
apollo_initialise()
apollo_control = list(
modelName = "HCM model",
modelDescr = "",
indivID = "ID",
nCores = 4,
outputDirectory = "HCMoutput"
)
database <- read.csv("C:/Users/chen1/Desktop/3.18/data v0.csv")
database['workplace1'] <- 0
database['workplace2'] <- 0
database['workplace3'] <- 0
database['workplace4'] <- 0
database$workplace1[which(database$workplace == 1)] <- 1
database$workplace2[which(database$workplace == 2)] <- 1
database$workplace3[which(database$workplace == 3)] <- 1
database$workplace4[which(database$workplace == 4)] <- 1
database['age2'] <- 0
database['age3'] <- 0
database['age4'] <- 0
database['age5'] <- 0
database$age2[which(database$age == 2)] <- 1
database$age3[which(database$age == 3)] <- 1
database$age4[which(database$age == 4)] <- 1
database$age5[which(database$age == 5)] <- 1
### Vector of parameters, including any that are kept fixed in estimation
apollo_beta = c(asc_bus = 0,
asc_subway = 0,
asc_car = 0,
asc_noncar = 0,
age_bus = 0,
# age_bus2 = 0,
# age_bus3 = 0,
# age_bus4 = 0,
# age_bus5 = 0,
gender_bus = 0,
marriage_bus = 0,
education_bus = 0,
# workplace_bus = 0,
workplace1_bus = 0,
workplace2_bus = 0,
workplace3_bus = 0,
workplace4_bus = 0,
domicile_bus = 0,
# occupation_bus = 0,
pincome_bus = 0,
fincome_bus = 0,
Numvehicles_bus = 0,
time_bus = 0,
cost_bus = 0,
# subwaystations_bus = 0,
busstops_bus = 0,
parkinglots_bus = 0,
age_noncar = 0,
# age_noncar2 = 0,
# age_noncar3 = 0,
# age_noncar4 = 0,
# age_noncar5 = 0,
gender_noncar = 0,
marriage_noncar = 0,
education_noncar = 0,
# workplace_subway = 0,
workplace1_noncar = 0,
workplace2_noncar = 0,
workplace3_noncar = 0,
workplace4_noncar = 0,
domicile_noncar = 0,
# occupation_noncar = 0,
pincome_noncar = 0,
fincome_noncar = 0,
Numvehicles_noncar = 0,
time_noncar = 0,
cost_noncar = 0,
# subwaystations_noncar = 0,
busstops_noncar = 0,
parkinglots_noncar = 0,
age_car = 0,
# age_car2 = 0,
# age_car3 = 0,
# age_car4 = 0,
# age_car5 = 0,
gender_car = 0,
marriage_car = 0,
education_car = 0,
# workplace_car = 0,
workplace1_car = 0,
workplace2_car = 0,
workplace3_car = 0,
workplace4_car = 0,
domicile_car = 0,
# occupation_car = 0,
pincome_car = 0,
fincome_car = 0,
Numvehicles_car = 0,
time_car = 0,
cost_car = 0,
# subwaystations_car = 0,
busstops_car = 0,
parkinglots_car = 0,
zeta_LA1 = 1,
zeta_LA2 = 1,
zeta_LA3 = 1,
zeta_AR1 = 1,
zeta_AR2 = 1,
zeta_AR3 = 1,
zeta_SN1 = 1,
zeta_SN2 = 1,
zeta_SN3 = 1,
zeta_AT1 = 1,
zeta_AT2 = 1,
zeta_AT3 = 1,
zeta_TH1 = 1,
zeta_TH2 = 1,
zeta_TH3 = 1,
zeta_PS1 = 1,
zeta_PS2 = 1,
zeta_PS3 = 1,
zeta_CIPI1 = 1,
zeta_CIPI2 = 1,
zeta_CIPI3 = 1,
zeta_BI1 = 1,
sigma_LA1 = 1,
sigma_LA2 = 1,
sigma_LA3 = 1,
sigma_AR1 = 1,
sigma_AR2 = 1,
sigma_AR3 = 1,
sigma_SN1 = 1,
sigma_SN2 = 1,
sigma_SN3 = 1,
sigma_AT1 = 1,
sigma_AT2 = 1,
sigma_AT3 = 1,
sigma_TH1 = 1,
sigma_TH2 = 1,
sigma_TH3 = 1,
sigma_PS1 = 1,
sigma_PS2 = 1,
sigma_PS3 = 1,
sigma_CIPI1 = 1,
sigma_CIPI2 = 1,
sigma_CIPI3 = 1,
sigma_BI1 = 1,
age_LA = 0,
gender_LA = 0,
marriage_LA = 0,
education_LA = 0,
workplace_LA = 0,
domicile_LA = 0,
pincome_LA = 0,
fincome_LA = 0,
Numvehicles_LA = 0,
age_AR = 0,
gender_AR = 0,
marriage_AR = 0,
education_AR = 0,
workplace_AR = 0,
domicile_AR = 0,
pincome_AR = 0,
fincome_AR = 0,
Numvehicles_AR = 0,
age_SN = 0,
gender_SN = 0,
marriage_SN = 0,
education_SN = 0,
workplace_SN = 0,
domicile_SN = 0,
pincome_SN = 0,
fincome_SN = 0,
Numvehicles_SN = 0,
age_AT = 0,
gender_AT = 0,
marriage_AT = 0,
education_AT = 0,
workplace_AT = 0,
domicile_AT = 0,
pincome_AT = 0,
fincome_AT = 0,
Numvehicles_AT = 0,
age_TH = 0,
gender_TH = 0,
marriage_TH = 0,
education_TH = 0,
workplace_TH = 0,
domicile_TH = 0,
pincome_TH = 0,
fincome_TH = 0,
Numvehicles_TH = 0,
age_PS = 0,
gender_PS = 0,
marriage_PS = 0,
education_PS = 0,
workplace_PS = 0,
domicile_PS = 0,
pincome_PS = 0,
fincome_PS = 0,
Numvehicles_PS = 0,
age_CIPI = 0,
gender_CIPI = 0,
marriage_CIPI = 0,
education_CIPI = 0,
workplace_CIPI = 0,
domicile_CIPI = 0,
pincome_CIPI = 0,
fincome_CIPI = 0,
Numvehicles_CIPI = 0,
age_BI = 0,
gender_BI = 0,
marriage_BI = 0,
education_BI = 0,
workplace_BI = 0,
domicile_BI = 0,
pincome_BI = 0,
fincome_BI = 0,
Numvehicles_BI = 0,
b_LA_bus = 1,
b_AR_bus = 1,
b_SN_bus = 1,
b_AT_bus = 1,
b_TH_bus = 1,
b_PS_bus = 1,
b_CIPI_bus = 1,
b_BI_bus = 1,
b_LA_noncar = 1,
b_AR_noncar = 1,
b_SN_noncar = 1,
b_AT_noncar = 1,
b_TH_noncar = 1,
b_PS_noncar = 1,
b_CIPI_noncar = 1,
b_BI_noncar = 1,
b_LA_car = 1,
b_AR_car = 1,
b_SN_car = 1,
b_AT_car = 1,
b_TH_car = 1,
b_PS_car = 1,
b_CIPI_car = 1,
b_BI_car = 1
)
### 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('asc_subway', "zeta_BI1")
### Set parameters for generating draws
apollo_draws = list(
interDrawsType="halton",
interNDraws=100,
interUnifDraws=c(),
interNormDraws=c("eta1",'eta2','eta3','eta4','eta5','eta6','eta7','eta8'),
intraDrawsType="",
intraNDraws=0,
intraUnifDraws=c(),
intraNormDraws=c()
)
### Create random parameters
apollo_randCoeff=function(apollo_beta, apollo_inputs){
randcoeff = list()
randcoeff[["LA"]] = age_LA * age +
gender_LA * gender +
marriage_LA * marriage +
education_LA * education +
workplace_LA * workplace +
domicile_LA * domicile +
pincome_LA * pincome +
fincome_LA * fincome +
Numvehicles_LA * Numvehicles +
eta1
randcoeff[["AR"]] = age_AR * age +
gender_AR * gender +
marriage_AR * marriage +
education_AR * education +
workplace_AR * workplace +
domicile_AR * domicile +
pincome_AR * pincome +
fincome_AR * fincome +
Numvehicles_AR * Numvehicles +
eta2
randcoeff[["SN"]] = age_SN * age +
gender_SN * gender +
marriage_SN * marriage +
education_SN * education +
workplace_SN * workplace +
domicile_SN * domicile +
pincome_SN * pincome +
fincome_SN * fincome +
Numvehicles_SN * Numvehicles +
eta3
randcoeff[["AT"]] = age_AT * age +
gender_AT * gender +
marriage_AT * marriage +
education_AT * education +
workplace_AT * workplace +
domicile_AT * domicile +
pincome_AT * pincome +
fincome_AT * fincome +
Numvehicles_AT * Numvehicles +
eta4
randcoeff[["TH"]] = age_TH * age +
gender_TH * gender +
marriage_TH * marriage +
education_TH * education +
workplace_TH * workplace +
domicile_TH * domicile +
pincome_TH * pincome +
fincome_TH * fincome +
Numvehicles_TH * Numvehicles +
eta5
randcoeff[["PS"]] = age_PS * age +
gender_PS * gender +
marriage_PS * marriage +
education_PS * education +
workplace_PS * workplace +
domicile_PS * domicile +
pincome_PS * pincome +
fincome_PS * fincome +
Numvehicles_PS * Numvehicles +
eta6
randcoeff[["CIPI"]] = age_CIPI * age +
gender_CIPI * gender +
marriage_CIPI * marriage +
education_CIPI * education +
workplace_CIPI * workplace +
domicile_CIPI * domicile +
pincome_CIPI * pincome +
fincome_CIPI * fincome +
Numvehicles_CIPI * Numvehicles +
eta7
randcoeff[["BI"]] = age_BI * age +
gender_BI * gender +
marriage_BI * marriage +
education_BI * education +
workplace_BI * workplace +
domicile_BI * domicile +
pincome_BI * pincome +
fincome_BI * fincome +
Numvehicles_BI * Numvehicles +
eta8
return(randcoeff)
}
apollo_inputs = apollo_validateInputs()
apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){
apollo_attach(apollo_beta, apollo_inputs)
on.exit(apollo_detach(apollo_beta, apollo_inputs))
P = list()
V = list()
### Likelihood of indicators
normalDensity_settings1 = list(outcomeNormal = LA1,
xNormal = zeta_LA1*LA,
mu = 3,
sigma = sigma_LA1,
# rows = (task==1),
componentName = "indic_LA1")
normalDensity_settings2 = list(outcomeNormal = LA2,
xNormal = zeta_LA2*LA,
mu = 3,
sigma = sigma_LA2,
# rows = (task==1),
componentName = "indic_LA2")
normalDensity_settings3 = list(outcomeNormal = LA3,
xNormal = zeta_LA3*LA,
mu = 3,
sigma = sigma_LA3,
# rows = (task==1),
componentName = "indic_LA3")
normalDensity_settings4 = list(outcomeNormal = AR1,
xNormal = zeta_AR1*AR,
mu = 3,
sigma = sigma_AR1,
# rows = (task==1),
componentName = "indic_AR1")
normalDensity_settings5 = list(outcomeNormal = AR2,
xNormal = zeta_AR2*AR,
mu = 3,
sigma = sigma_AR2,
# rows = (task==1),
componentName = "indic_AR2")
normalDensity_settings6 = list(outcomeNormal = AR3,
xNormal = zeta_AR3*AR,
mu = 3,
sigma = sigma_AR3,
# rows = (task==1),
componentName = "indic_AR3")
normalDensity_settings7 = list(outcomeNormal = SN1,
xNormal = zeta_SN1*SN,
mu = 3,
sigma = sigma_SN1,
# rows = (task==1),
componentName = "indic_SN1")
normalDensity_settings8 = list(outcomeNormal = SN2,
xNormal = zeta_SN2*SN,
mu = 3,
sigma = sigma_SN2,
# rows = (task==1),
componentName = "indic_SN2")
normalDensity_settings9 = list(outcomeNormal = SN3,
xNormal = zeta_SN3*SN,
mu = 3,
sigma = sigma_SN3,
# rows = (task==1),
componentName = "indic_SN3")
normalDensity_settings10 = list(outcomeNormal = AT1,
xNormal = zeta_AT1*AT,
mu = 3,
sigma = sigma_AT1,
# rows = (task==1),
componentName = "indic_AT1")
normalDensity_settings11 = list(outcomeNormal = AT2,
xNormal = zeta_AT2*AT,
mu = 3,
sigma = sigma_AT2,
# rows = (task==1),
componentName = "indic_AT2")
normalDensity_settings12 = list(outcomeNormal = AT3,
xNormal = zeta_AT3*AT,
mu = 3,
sigma = sigma_AT3,
# rows = (task==1),
componentName = "indic_AT3")
normalDensity_settings13 = list(outcomeNormal = TH1,
xNormal = zeta_TH1*TH,
mu = 3,
sigma = sigma_TH1,
# rows = (task==1),
componentName = "indic_TH1")
normalDensity_settings14 = list(outcomeNormal = TH2,
xNormal = zeta_TH2*TH,
mu = 3,
sigma = sigma_TH2,
# rows = (task==1),
componentName = "indic_TH2")
normalDensity_settings15 = list(outcomeNormal = TH3,
xNormal = zeta_TH3*TH,
mu = 3,
sigma = sigma_TH3,
# rows = (task==1),
componentName = "indic_TH3")
normalDensity_settings16 = list(outcomeNormal = PS1,
xNormal = zeta_PS1*PS,
mu = 3,
sigma = sigma_PS1,
# rows = (task==1),
componentName = "indic_PS1")
normalDensity_settings17 = list(outcomeNormal = PS2,
xNormal = zeta_PS2*PS,
mu = 3,
sigma = sigma_PS2,
# rows = (task==1),
componentName = "indic_PS2")
normalDensity_settings18 = list(outcomeNormal = PS3,
xNormal = zeta_PS3*PS,
mu = 3,
sigma = sigma_PS3,
# rows = (task==1),
componentName = "indic_PS3")
normalDensity_settings19 = list(outcomeNormal = CIPI1,
xNormal = zeta_CIPI1*CIPI,
mu = 3,
sigma = sigma_CIPI1,
# rows = (task==1),
componentName = "indic_CIPI1")
normalDensity_settings20 = list(outcomeNormal = CIPI2,
xNormal = zeta_CIPI2*CIPI,
mu = 3,
sigma = sigma_CIPI2,
# rows = (task==1),
componentName = "indic_CIPI2")
normalDensity_settings21 = list(outcomeNormal = CIPI3,
xNormal = zeta_CIPI3*CIPI,
mu = 3,
sigma = sigma_CIPI3,
# rows = (task==1),
componentName = "indic_CIPI3")
normalDensity_settings22 = list(outcomeNormal = BI1,
xNormal = zeta_BI1*BI,
mu = 3,
sigma = sigma_BI1,
# rows = (task==1),
componentName = "indic_BI1")
P[["indic_LA1"]] = apollo_normalDensity(normalDensity_settings1, functionality)
P[["indic_LA2"]] = apollo_normalDensity(normalDensity_settings2, functionality)
P[["indic_LA3"]] = apollo_normalDensity(normalDensity_settings3, functionality)
P[["indic_AR1"]] = apollo_normalDensity(normalDensity_settings4, functionality)
P[["indic_AR2"]] = apollo_normalDensity(normalDensity_settings5, functionality)
P[["indic_AR3"]] = apollo_normalDensity(normalDensity_settings6, functionality)
P[["indic_SN1"]] = apollo_normalDensity(normalDensity_settings7, functionality)
P[["indic_SN2"]] = apollo_normalDensity(normalDensity_settings8, functionality)
P[["indic_SN3"]] = apollo_normalDensity(normalDensity_settings9, functionality)
P[["indic_AT1"]] = apollo_normalDensity(normalDensity_settings10, functionality)
P[["indic_AT2"]] = apollo_normalDensity(normalDensity_settings11, functionality)
P[["indic_AT3"]] = apollo_normalDensity(normalDensity_settings12, functionality)
P[["indic_TH1"]] = apollo_normalDensity(normalDensity_settings13, functionality)
P[["indic_TH2"]] = apollo_normalDensity(normalDensity_settings14, functionality)
P[["indic_TH3"]] = apollo_normalDensity(normalDensity_settings15, functionality)
P[["indic_PS1"]] = apollo_normalDensity(normalDensity_settings16, functionality)
P[["indic_PS2"]] = apollo_normalDensity(normalDensity_settings17, functionality)
P[["indic_PS3"]] = apollo_normalDensity(normalDensity_settings18, functionality)
P[["indic_CIPI1"]] = apollo_normalDensity(normalDensity_settings19, functionality)
P[["indic_CIPI2"]] = apollo_normalDensity(normalDensity_settings20, functionality)
P[["indic_CIPI3"]] = apollo_normalDensity(normalDensity_settings21, functionality)
P[["indic_BI1"]] = apollo_normalDensity(normalDensity_settings22, functionality)
### Likelihood of choices
V[["noncar"]] = asc_noncar +
age_noncar * age +
# age_noncar2 * age2 +
# age_noncar3 * age3 +
# age_noncar4 * age4 +
# age_noncar5 * age5 +
gender_noncar * gender +
marriage_noncar * marriage +
education_noncar * education +
# workplace_noncar * workplace +
workplace1_noncar * workplace1 +
workplace2_noncar * workplace2 +
workplace3_noncar * workplace3 +
workplace4_noncar * workplace4 +
domicile_noncar * domicile +
# occupation_noncar * occupation +
pincome_noncar * pincome +
fincome_noncar * fincome +
Numvehicles_noncar * Numvehicles +
time_noncar * time +
cost_noncar * cost +
# subwaystations_noncar * subwaystations +
busstops_noncar * busstops +
parkinglots_noncar * parkinglots +
b_LA_noncar * LA +
b_AR_noncar * AR +
b_SN_noncar * SN +
b_AT_noncar * AT +
b_TH_noncar * TH +
b_PS_noncar * PS +
b_CIPI_noncar * CIPI +
b_BI_noncar * BI
V[["bus"]] = asc_bus +
age_bus * age +
# age_bus2 * age2 +
# age_bus3 * age3 +
# age_bus4 * age4 +
# age_bus5 * age5 +
gender_bus * gender +
marriage_bus * marriage +
education_bus * education +
# workplace_bus * workplace +
workplace1_bus * workplace1 +
workplace2_bus * workplace2 +
workplace3_bus * workplace3 +
workplace4_bus * workplace4 +
domicile_bus * domicile +
# occupation_bus * occupation +
pincome_bus * pincome +
fincome_bus * fincome +
Numvehicles_bus * Numvehicles +
time_bus * time +
cost_bus * cost +
# subwaystations_bus * subwaystations +
busstops_bus * busstops +
parkinglots_bus * parkinglots +
b_LA_bus * LA +
b_AR_bus * AR +
b_SN_bus * SN +
b_AT_bus * AT +
b_TH_bus * TH +
b_PS_bus * PS +
b_CIPI_bus * CIPI +
b_BI_bus * BI
V[["subway"]] = asc_subway
V[["car"]] = asc_car +
age_car * age +
# age_car2 * age2 +
# age_car3 * age3 +
# age_car4 * age4 +
# age_car5 * age5 +
gender_car * gender +
marriage_car * marriage +
education_car * education +
# workplace_car * workplace +
workplace1_car * workplace1 +
workplace2_car * workplace2 +
workplace3_car * workplace3 +
workplace4_car * workplace4 +
domicile_car * domicile +
# occupation_car * occupation +
pincome_car * pincome +
fincome_car * fincome +
Numvehicles_car * Numvehicles +
time_car * time +
cost_car * cost +
# subwaystations_car * subwaystations +
busstops_car * busstops +
parkinglots_car * parkinglots +
b_LA_car * LA +
b_AR_car * AR +
b_SN_car * SN +
b_AT_car * AT +
b_TH_car * TH +
b_PS_car * PS +
b_CIPI_car * CIPI +
b_BI_car * BI
### Define settings for MNL model component
mnl_settings <- list(
alternatives = c(noncar = 'noncar', bus = 'bus', subway = 'subway', car = 'car'),
choiceVar = choice,
utilities = V,
componentName = "choice"
)
### Compute probabilities for MNL model component
P[["choice"]] = apollo_mnl(mnl_settings, functionality)
### Likelihood of the whole model
P = apollo_combineModels(P, apollo_inputs, functionality)
### Average across inter-individual draws
P = apollo_avgInterDraws(P, apollo_inputs, functionality)
### Prepare and return outputs of function
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}
model <- apollo_estimate(apollo_beta, apollo_fixed, apollo_probabilities, apollo_inputs,
estimate_settings = list(estimationRoutine = "bfgs",
hessianRoutine = 'analytic',
maxIterations = 1000
))
apollo_modelOutput(model)
apollo_saveOutput(model)
Code: Select all
Model run by chen1 using Apollo 0.3.5 on R 4.3.3 for Windows.
Please acknowledge the use of Apollo by citing Hess & Palma (2019)
DOI 10.1016/j.jocm.2019.100170
www.ApolloChoiceModelling.com
Model name : HCM model
Model description :
Model run at : 2025-03-21 16:14:16.357367
Estimation method : bfgs
Model diagnosis : successful convergence
Optimisation diagnosis : Maximum found
hessian properties : Negative definite
maximum eigenvalue : -0.560043
reciprocal of condition number : 2.22631e-07
Number of individuals : 861
Number of rows in database : 861
Number of modelled outcomes : 19803
indic_LA1 : 861
indic_LA2 : 861
indic_LA3 : 861
indic_AR1 : 861
indic_AR2 : 861
indic_AR3 : 861
indic_SN1 : 861
indic_SN2 : 861
indic_SN3 : 861
indic_AT1 : 861
indic_AT2 : 861
indic_AT3 : 861
indic_TH1 : 861
indic_TH2 : 861
indic_TH3 : 861
indic_PS1 : 861
indic_PS2 : 861
indic_PS3 : 861
indic_CIPI1 : 861
indic_CIPI2 : 861
indic_CIPI3 : 861
indic_BI1 : 861
choice : 861
Number of cores used : 4
Number of inter-individual draws : 100 (halton)
WARNING: Inter-individual draws were used
without a panel data structure.
LL(start) : -34970.24
LL (whole model) at equal shares, LL(0) : NA
LL (whole model) at observed shares, LL(C) : NA
LL(final, whole model) : -31396.26
Rho-squared vs equal shares : Not applicable
Adj.Rho-squared vs equal shares : Not applicable
Rho-squared vs observed shares : Not applicable
Adj.Rho-squared vs observed shares : Not applicable
AIC : 63172.53
BIC : 64076.56
LL(0,indic_LA1) : Not applicable
LL(final,indic_LA1) : -1440.92
LL(0,indic_LA2) : Not applicable
LL(final,indic_LA2) : -1427.63
LL(0,indic_LA3) : Not applicable
LL(final,indic_LA3) : -1362.91
LL(0,indic_AR1) : Not applicable
LL(final,indic_AR1) : -1433.98
LL(0,indic_AR2) : Not applicable
LL(final,indic_AR2) : -1497.45
LL(0,indic_AR3) : Not applicable
LL(final,indic_AR3) : -1457.21
LL(0,indic_SN1) : Not applicable
LL(final,indic_SN1) : -1523.4
LL(0,indic_SN2) : Not applicable
LL(final,indic_SN2) : -1543.31
LL(0,indic_SN3) : Not applicable
LL(final,indic_SN3) : -1554.48
LL(0,indic_AT1) : Not applicable
LL(final,indic_AT1) : -1550.09
LL(0,indic_AT2) : Not applicable
LL(final,indic_AT2) : -1553.13
LL(0,indic_AT3) : Not applicable
LL(final,indic_AT3) : -1520.15
LL(0,indic_TH1) : Not applicable
LL(final,indic_TH1) : -1664.08
LL(0,indic_TH2) : Not applicable
LL(final,indic_TH2) : -1671.58
LL(0,indic_TH3) : Not applicable
LL(final,indic_TH3) : -1640.25
LL(0,indic_PS1) : Not applicable
LL(final,indic_PS1) : -1347.68
LL(0,indic_PS2) : Not applicable
LL(final,indic_PS2) : -1439.63
LL(0,indic_PS3) : Not applicable
LL(final,indic_PS3) : -1462.77
LL(0,indic_CIPI1) : Not applicable
LL(final,indic_CIPI1) : -1541.65
LL(0,indic_CIPI2) : Not applicable
LL(final,indic_CIPI2) : -1383.75
LL(0,indic_CIPI3) : Not applicable
LL(final,indic_CIPI3) : -1506.2
LL(0,indic_BI1) : Not applicable
LL(final,indic_BI1) : -1406.99
LL(0,choice) : -1193.6
LL(final,choice) : -837.93
Estimated parameters : 190
Time taken (hh:mm:ss) : 02:27:0.64
pre-estimation : 00:00:32.34
estimation : 00:23:23.77
post-estimation : 02:03:4.53
Iterations : 206
Unconstrained optimisation.
Estimates:
Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0)
asc_bus -1.240274 1.165594 -1.064071 1.162322 -1.067066
asc_subway 0.000000 NA NA NA NA
asc_car -1.576290 0.813604 -1.937416 0.817365 -1.928501
asc_noncar 3.745601 0.816100 4.589635 0.787492 4.756367
age_bus 0.221859 0.204861 1.082972 0.198567 1.117297
gender_bus -0.027355 0.327781 -0.083455 0.316366 -0.086466
marriage_bus 0.108957 0.418119 0.260589 0.372152 0.292777
education_bus 0.376751 0.196847 1.913929 0.193380 1.948239
workplace1_bus -0.909601 0.639526 -1.422305 0.682272 -1.333194
workplace2_bus -0.327924 0.475919 -0.689032 0.479738 -0.683546
workplace3_bus -0.817313 0.728153 -1.122447 0.694588 -1.176687
workplace4_bus -0.348258 0.393139 -0.885840 0.398093 -0.874816
domicile_bus -0.020547 0.341461 -0.060173 0.354001 -0.058041
pincome_bus -0.026131 0.173782 -0.150366 0.171920 -0.151995
fincome_bus -0.123389 0.152758 -0.807744 0.159548 -0.773367
Numvehicles_bus -0.265667 0.222919 -1.191766 0.207809 -1.278415
time_bus -0.035694 0.162542 -0.219599 0.144915 -0.246311
cost_bus -0.508761 0.216470 -2.350260 0.233491 -2.178927
busstops_bus 0.019172 0.009086 2.110180 0.009027 2.123842
parkinglots_bus -0.002211 0.004627 -0.477823 0.004640 -0.476512
age_noncar -0.018196 0.150501 -0.120904 0.162577 -0.111924
gender_noncar -0.342311 0.228923 -1.495316 0.228252 -1.499711
marriage_noncar 0.425102 0.302618 1.404745 0.312883 1.358661
education_noncar -0.046327 0.136293 -0.339906 0.132422 -0.349841
workplace1_noncar 0.039811 0.407621 0.097666 0.412541 0.096501
workplace2_noncar 0.060822 0.341925 0.177881 0.358616 0.169602
workplace3_noncar -0.742958 0.509846 -1.457223 0.520519 -1.427342
workplace4_noncar -0.208506 0.282432 -0.738254 0.290446 -0.717883
domicile_noncar 0.084262 0.244719 0.344322 0.245919 0.342641
pincome_noncar -0.085268 0.119711 -0.712280 0.119928 -0.710990
fincome_noncar -0.080936 0.107968 -0.749628 0.107228 -0.754804
Numvehicles_noncar -0.411240 0.147730 -2.783723 0.152658 -2.693863
time_noncar -1.577250 0.150682 -10.467415 0.154737 -10.193099
cost_noncar -0.130385 0.131762 -0.989551 0.137207 -0.950282
busstops_noncar 0.010630 0.007094 1.498381 0.006490 1.637835
parkinglots_noncar 0.004189 0.003360 1.246769 0.003059 1.369246
age_car -0.048807 0.143721 -0.339592 0.144198 -0.338469
gender_car -0.112477 0.222601 -0.505286 0.225579 -0.498615
marriage_car -0.135654 0.280212 -0.484112 0.272194 -0.498373
education_car 0.213527 0.132527 1.611197 0.133480 1.599688
workplace1_car -0.784429 0.419605 -1.869444 0.426672 -1.838484
workplace2_car -0.527900 0.342388 -1.541821 0.357475 -1.476746
workplace3_car -0.170881 0.418597 -0.408223 0.418126 -0.408682
workplace4_car -0.088372 0.275436 -0.320843 0.283562 -0.311648
domicile_car -0.020204 0.233786 -0.086422 0.236907 -0.085283
pincome_car 0.252343 0.120132 2.100544 0.123747 2.039187
fincome_car -0.179754 0.108032 -1.663893 0.113253 -1.587190
Numvehicles_car -0.017618 0.142222 -0.123877 0.138184 -0.127497
time_car 0.285781 0.107753 2.652188 0.101239 2.822840
cost_car 0.109561 0.111002 0.987019 0.109064 1.004564
busstops_car 0.011495 0.007057 1.628892 0.006612 1.738476
parkinglots_car 0.005673 0.003345 1.696063 0.003218 1.763145
zeta_LA1 0.846522 0.056882 14.881969 0.178684 4.737547
zeta_LA2 0.752628 0.055332 13.602085 0.175925 4.278131
zeta_LA3 0.643719 0.048754 13.203331 0.152681 4.216102
zeta_AR1 0.875217 0.043203 20.258370 0.085501 10.236282
zeta_AR2 0.851183 0.045398 18.749337 0.082450 10.323663
zeta_AR3 0.779553 0.042745 18.237441 0.078025 9.991093
zeta_SN1 1.062733 0.041713 25.476998 0.084196 12.622058
zeta_SN2 1.124246 0.042873 26.222744 0.098461 11.418149
zeta_SN3 1.117781 0.045196 24.731679 0.105809 10.564133
zeta_AT1 0.999017 0.045626 21.895919 0.086129 11.599054
zeta_AT2 0.985438 0.044805 21.994116 0.084007 11.730428
zeta_AT3 0.973085 0.043036 22.610734 0.078613 12.378219
zeta_TH1 1.357267 0.047292 28.699783 0.066367 20.450845
zeta_TH2 1.375590 0.045747 30.069307 0.059274 23.207509
zeta_TH3 1.305645 0.048291 27.036970 0.072223 18.077948
zeta_PS1 0.599787 0.057415 10.446492 0.183659 3.265759
zeta_PS2 0.542041 0.055278 9.805752 0.174649 3.103592
zeta_PS3 0.545486 0.055959 9.747945 0.176263 3.094727
zeta_CIPI1 0.950685 0.042730 22.248809 0.075043 12.668461
zeta_CIPI2 0.902273 0.034940 25.823402 0.055732 16.189514
zeta_CIPI3 0.960854 0.040173 23.918123 0.063520 15.126879
zeta_BI1 1.000000 NA NA NA NA
sigma_LA1 1.057623 0.036413 29.045087 0.077871 13.581702
sigma_LA2 1.019757 0.037519 27.179702 0.091944 11.091043
sigma_LA3 0.982391 0.032850 29.904956 0.072979 13.461241
sigma_AR1 0.983432 0.032974 29.824636 0.057707 17.041815
sigma_AR2 1.098805 0.033954 32.361689 0.049411 22.238197
sigma_AR3 1.078547 0.032068 33.633242 0.045994 23.449748
sigma_SN1 1.002193 0.031637 31.678048 0.055204 18.154291
sigma_SN2 0.899233 0.033932 26.501376 0.074202 12.118670
sigma_SN3 0.952210 0.035783 26.610744 0.084167 11.313357
sigma_AT1 1.066784 0.037264 28.628044 0.066395 16.067232
sigma_AT2 1.071233 0.035524 30.155256 0.063492 16.872010
sigma_AT3 1.063983 0.034487 30.851707 0.057200 18.600959
sigma_TH1 1.018403 0.032208 31.619716 0.040609 25.078261
sigma_TH2 1.006797 0.032326 31.145499 0.040702 24.735617
sigma_TH3 1.025303 0.033789 30.344588 0.048004 21.358703
sigma_PS1 1.038986 0.035375 29.370295 0.086702 11.983445
sigma_PS2 1.147927 0.036575 31.385711 0.084544 13.577903
sigma_PS3 1.188359 0.037138 31.998858 0.083105 14.299571
sigma_CIPI1 1.047348 0.034870 30.035855 0.058475 17.911024
sigma_CIPI2 0.905638 0.028977 31.254041 0.044902 20.169272
sigma_CIPI3 1.019343 0.031904 31.949978 0.043444 23.463312
sigma_BI1 1.227480 0.037669 32.586315 0.045871 26.759569
age_LA 0.281043 0.049899 5.632267 0.097359 2.886680
gender_LA 0.024683 0.075215 0.328160 0.126821 0.194626
marriage_LA -0.387568 0.102063 -3.797335 0.173210 -2.237563
education_LA 0.282857 0.037635 7.515769 0.087658 3.226834
workplace_LA 0.145164 0.023408 6.201386 0.042328 3.429487
domicile_LA -0.188992 0.078790 -2.398665 0.123794 -1.526661
pincome_LA -0.147813 0.039899 -3.704678 0.068452 -2.159373
fincome_LA 0.019204 0.038937 0.493202 0.071849 0.267280
Numvehicles_LA -0.043329 0.054355 -0.797156 0.109630 -0.395234
age_AR 0.090693 0.040488 2.239994 0.075493 1.201334
gender_AR 0.096190 0.071490 1.345492 0.121737 0.790146
marriage_AR -0.045334 0.091585 -0.494994 0.160917 -0.281722
education_AR 0.098899 0.030961 3.194274 0.053885 1.835370
workplace_AR 0.026783 0.021061 1.271675 0.035155 0.761860
domicile_AR 0.087073 0.076457 1.138855 0.144375 0.603101
pincome_AR 0.021313 0.038615 0.551930 0.067720 0.314717
fincome_AR 0.054058 0.036022 1.500719 0.062904 0.859382
Numvehicles_AR -0.071301 0.049551 -1.438931 0.091901 -0.775841
age_SN 0.179193 0.038571 4.645742 0.092691 1.933229
gender_SN 0.090124 0.064629 1.394487 0.144566 0.623406
marriage_SN -0.228929 0.087180 -2.625945 0.205280 -1.115203
education_SN 0.010335 0.029937 0.345242 0.074863 0.138058
workplace_SN 0.070388 0.019018 3.701093 0.041839 1.682362
domicile_SN -0.188394 0.068515 -2.749667 0.152209 -1.237738
pincome_SN 0.131502 0.035846 3.668573 0.087795 1.497824
fincome_SN -0.074884 0.030226 -2.477415 0.064567 -1.159784
Numvehicles_SN 0.065493 0.045661 1.434324 0.111793 0.585838
age_AT 0.081127 0.038435 2.110730 0.068144 1.190527
gender_AT 0.047893 0.065520 0.730976 0.116354 0.411617
marriage_AT 0.109589 0.085150 1.287011 0.159515 0.687017
education_AT 0.125975 0.028597 4.405186 0.053389 2.359581
workplace_AT 0.052111 0.019136 2.723208 0.033068 1.575896
domicile_AT -0.275584 0.068902 -3.999677 0.122913 -2.242113
pincome_AT -0.075836 0.035700 -2.124249 0.072390 -1.047604
fincome_AT 0.069294 0.031682 2.187145 0.061032 1.135373
Numvehicles_AT 0.033309 0.043842 0.759750 0.082775 0.402408
age_TH -0.018347 0.031497 -0.582518 0.059591 -0.307887
gender_TH 0.198359 0.055353 3.583488 0.097428 2.035945
marriage_TH -0.077053 0.071841 -1.072556 0.130889 -0.588690
education_TH -0.004962 0.023908 -0.207564 0.046671 -0.106326
workplace_TH -0.008958 0.016442 -0.544840 0.030847 -0.290412
domicile_TH 0.112589 0.061300 1.836695 0.121905 0.923575
pincome_TH 0.040386 0.028932 1.395884 0.056361 0.716558
fincome_TH 0.050200 0.027415 1.831086 0.054949 0.913575
Numvehicles_TH -0.165829 0.039087 -4.242560 0.079805 -2.077927
age_PS 0.143112 0.054323 2.634448 0.078642 1.819781
gender_PS 0.136555 0.093904 1.454195 0.149807 0.911539
marriage_PS -0.032442 0.122363 -0.265130 0.181892 -0.178359
education_PS 0.171962 0.044608 3.854928 0.089541 1.920491
workplace_PS 0.188308 0.031766 5.928055 0.069186 2.721747
domicile_PS 0.205237 0.096240 2.132558 0.139697 1.469158
pincome_PS 0.133068 0.050265 2.647338 0.078489 1.695376
fincome_PS -0.022893 0.045618 -0.501847 0.072078 -0.317619
Numvehicles_PS 0.129476 0.062954 2.056687 0.095644 1.353734
age_CIPI -0.161916 0.035483 -4.563249 0.063580 -2.546627
gender_CIPI 0.097108 0.062243 1.560146 0.110092 0.882064
marriage_CIPI 0.249329 0.085911 2.902185 0.156900 1.589094
education_CIPI 0.162688 0.027470 5.922279 0.049273 3.301778
workplace_CIPI 0.097790 0.019134 5.110814 0.038491 2.540603
domicile_CIPI 0.064304 0.067418 0.953818 0.133101 0.483124
pincome_CIPI -0.035856 0.034353 -1.043737 0.060954 -0.588239
fincome_CIPI 0.095322 0.031753 3.001962 0.058361 1.633329
Numvehicles_CIPI -0.058082 0.047741 -1.216618 0.108117 -0.537219
age_BI -0.002592 0.058583 -0.044237 0.066685 -0.038862
gender_BI -0.129825 0.098631 -1.316265 0.104755 -1.239318
marriage_BI 0.133084 0.127935 1.040246 0.135714 0.980623
education_BI 0.093443 0.043579 2.144252 0.051978 1.797760
workplace_BI 0.114023 0.028759 3.964769 0.032935 3.462057
domicile_BI 0.021279 0.102021 0.208574 0.113288 0.187829
pincome_BI 0.048812 0.051952 0.939553 0.052424 0.931098
fincome_BI 0.023842 0.047499 0.501948 0.048805 0.488516
Numvehicles_BI -1.7006e-04 0.065250 -0.002606 0.073601 -0.002311
b_LA_bus 0.002372 0.203033 0.011684 0.214346 0.011067
b_AR_bus -0.184875 0.203281 -0.909456 0.250778 -0.737204
b_SN_bus -0.011009 0.180454 -0.061006 0.167265 -0.065817
b_AT_bus -0.263078 0.176472 -1.490763 0.190973 -1.377566
b_TH_bus 0.425801 0.185509 2.295309 0.185686 2.293126
b_PS_bus -0.010953 0.205372 -0.053332 0.238698 -0.045886
b_CIPI_bus 0.284312 0.193157 1.471920 0.216118 1.315542
b_BI_bus -0.027194 0.256236 -0.106128 0.301337 -0.090244
b_LA_noncar 0.121098 0.145819 0.830471 0.161834 0.748289
b_AR_noncar -0.042746 0.143065 -0.298784 0.150325 -0.284355
b_SN_noncar 0.101069 0.128482 0.786641 0.140246 0.720655
b_AT_noncar -0.137401 0.126830 -1.083348 0.143155 -0.959807
b_TH_noncar 0.110251 0.124578 0.884995 0.136500 0.807701
b_PS_noncar 0.183015 0.145399 1.258709 0.169731 1.078265
b_CIPI_noncar 0.088205 0.128484 0.686504 0.137334 0.642267
b_BI_noncar -0.085065 0.160210 -0.530959 0.170799 -0.498040
b_LA_car 0.043122 0.136760 0.315316 0.152890 0.282049
b_AR_car -0.316738 0.134836 -2.349064 0.134944 -2.347171
b_SN_car 0.021990 0.120155 0.183012 0.134294 0.163744
b_AT_car -0.116481 0.123426 -0.943729 0.137727 -0.845734
b_TH_car 0.245223 0.118595 2.067731 0.122731 1.998055
b_PS_car -0.036933 0.140525 -0.262820 0.174691 -0.211417
b_CIPI_car 0.049678 0.124879 0.397807 0.130131 0.381750
b_BI_car -0.102071 0.159494 -0.639970 0.185248 -0.550998