I'm estimating individuals' mode choice using LCNL (Latent Class Nested Logit) model. The model is made-up of 4 choice sets (bus, railway, highway and airline), each of which contains 4 continuous variables (cost, access time, journey time and frequency) with 3 levels and 1 dummy variable (seat comfort) with 3 levels. However, when estimating the model I run into the following warning message:
(b_seatAm= seat_comfort_average*male
b_seatGm= seat_comfort_good*male)
Warning message:
In sqrt(diag(varcov)) : NaNs produced
I am using the following code to estimate the model:
Code: Select all
### Clear memory
rm(list = ls())
### Load Apollo library
library(apollo)
### Initialise code
apollo_initialise()
apollo_control = list(
modelName ="Apollo_example_20_LC-NL-SCY",
modelDescr ="LC model with class allocation model",
indivID ="ID",
nCores = 6
)
database = read.csv("D:\\QDU\\zhoudao\\Apollo\\mode choice-Apollo\\Apollo-mode choice-SCY.csv",header = TRUE)
database = subset(database,database$SP==1)
## scaled variables
apollo_beta = c(asc_bus_c1 = 0,
asc_train_c1 = 0,
asc_high_c1 = 0,
asc_air_c1 = 0,
b_cost_c1 = 0,
b_acct_c1 = 0,
b_jourt_c1 = 0,
b_freq_c1 = 0,
b_seat_P_c1 = 0,
b_seat_A_c1 = 0,
b_seat_G_c1 = 0,
lambda_A_c1 = 1,
lambda_B_c1 = 0.5,
lambda_C_c1 = 1,
delta_c1 = 0,
asc_bus_c2 = 0,
asc_train_c2 = 0,
asc_high_c2 = 0,
asc_air_c2 = 0,
b_cost_c2 = 0,
b_acct_c2 = 0,
b_jourt_c2 = 0,
b_freq_c2 = 0,
b_seat_P_c2 = 0,
b_seat_A_c2 = 0,
b_seat_G_c2 = 0,
lambda_A_c2 = 1,
lambda_B_c2 = 0.5,
lambda_C_c2 = 1,
delta_c2 = 0,
b_seatAm_c1 = 0,
b_seatGm_c1 = 0,
b_seatAm_c2 = 0,
b_seatGm_c2 = 0
)
apollo_fixed = c("asc_bus_c1","asc_bus_c2","delta_c2","lambda_A_c1","lambda_A_c2","lambda_C_c1","lambda_C_c2","b_seat_P_c1","b_seat_P_c2")
## Define latent class components
apollo_lcPars = function(apollo_beta, apollo_inputs){
lcpars = list()
lcpars[["b_cost"]] = list(b_cost_c1,b_cost_c2)
lcpars[["b_acct"]] = list(b_acct_c1,b_acct_c2)
lcpars[["b_jourt"]] = list(b_jourt_c1,b_jourt_c2)
lcpars[["b_freq"]] = list(b_freq_c1, b_freq_c2)
lcpars[["b_seat_P"]] = list(b_seat_P_c1,b_seat_P_c2)
lcpars[["b_seat_A"]] = list(b_seat_A_c1,b_seat_A_c2)
lcpars[["b_seat_G"]] = list(b_seat_G_c1,b_seat_G_c2)
lcpars[["asc_train"]] = list(asc_train_c1,asc_train_c2)
lcpars[["asc_high"]] = list(asc_high_c1,asc_high_c2)
lcpars[["asc_air"]] = list(asc_air_c1,asc_air_c2)
lcpars[["b_seatAm"]] = list (b_seatAm_c1,b_seatAm_c2)
lcpars[["b_seatGm"]] = list(b_seatGm_c1,b_seatGm_c2)
#Utilities of class allocation model
V = list()
V[["class_1"]] = delta_c1
V[["class_2"]] = delta_c2
classAlloc_settings = list(
classes = c(class_1=1, class_2=2),
utilities = V
)
lcpars[["pi_values"]] = apollo_classAlloc(classAlloc_settings)
return(lcpars)
}
### Group and validate inputs
apollo_inputs = apollo_validateInputs()
### 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()
### Specify nests for NL model
nlNests = list()
nlNests[[1]] = list(root=1, A_c1=lambda_A_c1, B_c1 = lambda_B_c1, C_c1 = lambda_C_c1)
nlNests[[2]] = list(root=1,A_c2=lambda_A_c2, B_c2 = lambda_B_c2, C_c2 = lambda_C_c2)
nlStructure = list()
nlStructure[[1]] = list()
nlStructure[[2]] = list()
nlStructure[[1]][["root"]] = c("A_c1","B_c1","C_c1")
nlStructure[[2]][["root"]] = c("A_c2","B_c2","C_c2")
nlStructure[[1]][["A_c1"]] = c("bus")
nlStructure[[1]][["B_c1"]] = c("train","high")
nlStructure[[1]][["C_c1"]] = c("air")
nlStructure[[2]][["A_c2"]] = c("bus")
nlStructure[[2]][["B_c2"]] = c("train","high")
nlStructure[[2]][["C_c2"]] = c("air")
nl_settings <- list(
alternatives = c(bus=1, train=2, high=3, air=4),
avail = list(bus=av_bus, train=av_train, high=av_high, air=av_air),
choiceVar = choice,
nlNests = nlNests,
nlStructure = nlStructure
)
### Loop over classes
s=1
while(s<=2){
### Compute class-specific utilities
V=list()
V[['bus']] = b_cost[[s]] * cost_bus + b_acct[[s]] * acct_bus + b_jourt[[s]] * jourt_bus + b_freq[[s]] * freq_bus + b_seat_P[[s]] * (seat_bus==1) + b_seat_A[[s]] * (seat_bus==2) + b_seat_G[[s]] * (seat_bus==3) + b_seatAm[[s]]*((seat_bus==2)*male) + b_seatGm[[s]]*((seat_bus==3)*male)
V[['train']] = asc_train[[s]] + b_cost[[s]] * cost_train + b_acct[[s]] * acct_train + b_jourt[[s]] * jourt_train + b_freq[[s]] * freq_train + b_seat_P[[s]] * (seat_train==1) + b_seat_A[[s]] * (seat_train==2) + b_seat_G[[s]] * (seat_train==3)+ b_seatAm[[s]]*((seat_train==2)*male)+b_seatGm[[s]]*((seat_train==3)*male)
V[['high']] = asc_high[[s]] + b_cost[[s]] * cost_high + b_acct[[s]] * acct_high + b_jourt[[s]] * jourt_high + b_freq[[s]] * freq_high + b_seat_P[[s]] * (seat_high==1) + b_seat_A[[s]] * (seat_high==2) + b_seat_G[[s]] * (seat_high==3) + b_seatAm[[s]]*((seat_high==2)*male)+ b_seatGm[[s]]*((seat_high==3)*male)
V[['air']] = asc_air[[s]] + b_cost[[s]] * cost_air + b_acct[[s]] * acct_air + b_jourt[[s]] * jourt_air + b_freq[[s]] * freq_air + b_seat_P[[s]] * (seat_air==1) + b_seat_A[[s]] * (seat_air==2) + b_seat_G[[s]] * (seat_air==3) + b_seatAm[[s]]*((seat_air==2)*male)+ b_seatGm[[s]]*((seat_air==3)*male)
nl_settings$V = V
nl_settings$nlNests = nlNests[[s]]
nl_settings$nlStructure = nlStructure[[s]]
P[[s]] = apollo_nl(nl_settings, functionality)
P[[s]] = apollo_panelProd(P[[s]],apollo_inputs,functionality)
s=s+1
}
lc_settings = list(inClassProb = P, classProb=pi_values)
P[["model"]] = apollo_lc(lc_settings,apollo_inputs,functionality)
P = apollo_prepareProb(P,apollo_inputs,functionality)
}
#apollo_control$worklnLogs=TRUE
model = apollo_estimate(apollo_beta, apollo_fixed, apollo_probabilities,apollo_inputs)
apollo_modelOutput(model,modelOutput_settings = list(printPVal=TRUE))Code: Select all
Warning message:
In sqrt(diag(varcov)) : NaNs produced
> apollo_modelOutput(model,modelOutput_settings = list(printPVal=TRUE))
Model run by lenovo using Apollo 0.2.7 on R 4.2.1 for Windows.
www.ApolloChoiceModelling.com
Model name : Apollo_example_20_LC-NL-SCY
Model description : LC model with class allocation model
Model run at : 2023-05-06 16:04:02
Estimation method : bfgs
Model diagnosis : successful convergence
Number of individuals : 439
Number of rows in database : 2634
Number of modelled outcomes : 7902
1 : 2634
2 : 2634
model : 2634
Number of cores used : 6
Model without mixing
LL(start) : -3936.22
LL(0, whole model) : -3651.5
LL(C, whole model) : -3028.74
LL(final, whole model) : -2629.62
Rho-square (0) : 0.2799
Adj.Rho-square (0) : 0.273
Rho-square (C) : 0.1318
Adj.Rho-square (C) : 0.1235
AIC : 5309.25
BIC : 5483.62
LL(0,component_1) : -3651.5
LL(final,component_1) : -Inf Likelihood equal to zero for at least
one individual in this component.
LL(0,component_2) : -3651.5
LL(final,component_2) : -Inf Likelihood equal to zero for at least
one individual in this component.
Estimated parameters : 25
Time taken (hh:mm:ss) : 00:02:9.77
pre-estimation : 00:00:9.32
estimation : 00:01:23.39
post-estimation : 00:00:37.06
Iterations : 129
Min abs eigenvalue of Hessian : 1431139
Some eigenvalues of Hessian are positive, indicating potential problems!
Unconstrained optimisation.
Estimates:
Estimate s.e. t.rat.(0) p(1-sided) Rob.s.e. Rob.t.rat.(0) p(1-sided)
asc_bus_c1 0.000000 NA NA NA NA NA NA
asc_train_c1 3.248857 NaN NaN NaN 0.001106 2938.38622 0.00000
asc_high_c1 3.096513 NaN NaN NaN 0.001508 2053.82939 0.00000
asc_air_c1 1.846577 0.065261 28.29523 0.000000 0.123262 14.98096 0.00000
b_cost_c1 -0.001809 NaN NaN NaN 7.643e-06 -236.62763 0.00000
b_acct_c1 -0.150757 NaN NaN NaN 0.026421 -5.70598 5.784e-09
b_jourt_c1 -0.197729 NaN NaN NaN 1.5580e-04 -1269.09841 0.00000
b_freq_c1 0.014161 NaN NaN NaN 7.9082e-04 17.90612 0.00000
b_seat_P_c1 0.000000 NA NA NA NA NA NA
b_seat_A_c1 0.167447 0.008071 20.74793 0.000000 0.002400 69.78094 0.00000
b_seat_G_c1 -0.040720 NaN NaN NaN 0.002171 -18.75382 0.00000
lambda_A_c1 1.000000 NA NA NA NA NA NA
lambda_B_c1 0.007403 NaN NaN NaN 0.001313 5.63643 8.681e-09
lambda_C_c1 1.000000 NA NA NA NA NA NA
delta_c1 0.162121 0.099651 1.62689 0.051880 0.104840 1.54638 0.06101
asc_bus_c2 0.000000 NA NA NA NA NA NA
asc_train_c2 0.872793 0.131832 6.62049 1.790e-11 0.161702 5.39753 3.378e-08
asc_high_c2 0.946578 0.150436 6.29221 1.565e-10 0.144131 6.56750 2.558e-11
asc_air_c2 -0.013408 0.228424 -0.05870 0.476597 0.247061 -0.05427 0.47836
b_cost_c2 -0.003953 6.1395e-04 -6.43865 6.027e-11 6.7848e-04 -5.82625 2.834e-09
b_acct_c2 -0.255237 0.099688 -2.56035 0.005228 0.079069 -3.22804 6.2322e-04
b_jourt_c2 -0.038368 0.014965 -2.56384 0.005176 0.012041 -3.18652 7.1997e-04
b_freq_c2 0.002302 0.005912 0.38938 0.348499 0.004756 0.48400 0.31419
b_seat_P_c2 0.000000 NA NA NA NA NA NA
b_seat_A_c2 0.577226 0.112626 5.12518 1.486e-07 0.115537 4.99603 2.926e-07
b_seat_G_c2 0.767851 0.110701 6.93629 2.013e-12 0.130821 5.86947 2.186e-09
lambda_A_c2 1.000000 NA NA NA NA NA NA
lambda_B_c2 0.659898 0.148464 4.44483 4.398e-06 0.134554 4.90435 4.687e-07
lambda_C_c2 1.000000 NA NA NA NA NA NA
delta_c2 0.000000 NA NA NA NA NA NA
b_seatAm_c1 0.007009 0.004399 1.59340 0.055535 0.004567 1.53484 0.06241
b_seatGm_c1 0.005471 0.003246 1.68586 0.045912 0.004424 1.23663 0.10811
b_seatAm_c2 -0.586488 0.147873 -3.96618 3.652e-05 0.172829 -3.39347 3.4507e-04
b_seatGm_c2 -0.639784 0.159948 -3.99994 3.168e-05 0.188321 -3.39731 3.4026e-04
Nesting structure for NL model component 1:
Nest: root (1)
|-Nest: A_c1 (1)
| '-Alternative: bus
|-Nest: B_c1 (0.0074)
| |-Alternative: train
| '-Alternative: high
'-Nest: C_c1 (1)
'-Alternative: air
Nesting structure for NL model component 2:
Nest: root (1)
|-Nest: A_c2 (1)
| '-Alternative: bus
|-Nest: B_c2 (0.6599)
| |-Alternative: train
| '-Alternative: high
'-Nest: C_c2 (1)
'-Alternative: air
Summary of class allocation for LC model component :
Mean prob.
Class_1 0.7317
Class_2 0.2683
Do you have any idea what is happening and is there any way to resolve this issue?
Best regards, Chunyu Song