Latent Class model estimation ( Failed to converge properly)
Posted: 30 Apr 2025, 19:47
Dear Professor Hess and Apollo team, 
I'm currently conducting a LC MMNL model for a unlabelled design dataset.
Here is the code for three classes estimation, there are five attributes associated with alternatives, where I defined price with negative values, and the rest positive, because those attributes are expected to be more preferrable than without.
This provided me with a converged results based on 500 halton draws, overall results seems reasonable
despite some discrepancies in parameter value
Then I tries to use this as baseline to estimate four classes models, the apollo warned that the data did not converged properly , the results is as follow
the results seems to suggests that there does not exists a fourth group, but I cannot fully sure about this, and parameter value report suggests a huge differences
I also tried LC MNL with four classes , which also failed to converge. I tried, LC MNL with 2,3 classes, and same LC MMNL with 2 classes, with LC MMNL 3 classes has the lowest AIC and BIC.
Based on given results and code, would it suggests that there is no fourth latent group in the data, and LC MMNL 3 class is an appropriate model?
What other method would you suggest me to try out to further diagnose this ?
I'm currently conducting a LC MMNL model for a unlabelled design dataset.
Here is the code for three classes estimation, there are five attributes associated with alternatives, where I defined price with negative values, and the rest positive, because those attributes are expected to be more preferrable than without.
Code: Select all
# ---------------------------------------------------- #
#### CLEAN WORKSPACE AND LOAD LIBRARY ####
# ---------------------------------------------------- #
rm(list = ls())
gc()
library(apollo)
apollo_initialise()
# ---------------------------------------------------- #
#### CORE SETTINGS ####
# ---------------------------------------------------- #
apollo_control = list(
modelName = "LCMIXL_DriedApple_3Class",
modelDescr = "3-class LC Mixed Logit model for dried apple",
indivID = "respID",
nCores = 16,
outputDirectory = "output",
mixing = TRUE
)
# ---------------------------------------------------- #
#### LOAD DATA ####
# ---------------------------------------------------- #
database <- read.csv("dataset_apple_wide.csv")
# ---------------------------------------------------- #
#### DEFINE MODEL PARAMETERS ####
# ---------------------------------------------------- #
apollo_beta = c(
# Means
asc_opt_1 = 0,
mu_b_price_1 = -1,
mu_b_process_1 = 0.2,
mu_b_carbon_1 = 0.2,
mu_b_fibre_1 = 0.2,
mu_b_crispy_1 = 0.2,
asc_opt_2 = 0,
mu_b_price_2 = -1.1,
mu_b_process_2 = 0.4,
mu_b_carbon_2 = 0.1,
mu_b_fibre_2 = 0.1,
mu_b_crispy_2 = 0.3,
asc_opt_3 = 0,
mu_b_price_3 = -0.9,
mu_b_process_3 = 0.1,
mu_b_carbon_3 = 0.3,
mu_b_fibre_3 = 0.2,
mu_b_crispy_3 = 0.2,
# Standard deviations
sigma_price_1 = 0.3,
sigma_process_1 = 0.3,
sigma_carbon_1 = 0.3,
sigma_fibre_1 = 0.3,
sigma_crispy_1 = 0.3,
sigma_price_2 = 0.2,
sigma_process_2 = 0.2,
sigma_carbon_2 = 0.2,
sigma_fibre_2 = 0.2,
sigma_crispy_2 = 0.2,
sigma_price_3 = 0.1,
sigma_process_3 = 0.1,
sigma_carbon_3 = 0.1,
sigma_fibre_3 = 0.1,
sigma_crispy_3 = 0.1,
# Class allocation
theta1 = 0,
theta2 = 0
)
apollo_fixed = c("asc_opt_1", "asc_opt_2", "asc_opt_3")
# ---------------------------------------------------- #
#### DRAW SETTINGS ####
# ---------------------------------------------------- #
apollo_draws = list(
interDrawsType = "halton",
interNDraws = 500,
interNormDraws = c("draws_price", "draws_process", "draws_carbon", "draws_fibre", "draws_crispy")
)
# ---------------------------------------------------- #
#### DEFINE RANDOM COEFFICIENTS ####
# ---------------------------------------------------- #
apollo_randCoeff = function(apollo_beta, apollo_inputs){
randcoeff = list()
for (i in 1:3) {
randcoeff[[paste0("b_price_", i)]] = get(paste0("mu_b_price_", i)) + get(paste0("sigma_price_", i)) * draws_price
randcoeff[[paste0("b_process_", i)]] = get(paste0("mu_b_process_", i)) + get(paste0("sigma_process_", i)) * draws_process
randcoeff[[paste0("b_carbon_", i)]] = get(paste0("mu_b_carbon_", i)) + get(paste0("sigma_carbon_", i)) * draws_carbon
randcoeff[[paste0("b_fibre_", i)]] = get(paste0("mu_b_fibre_", i)) + get(paste0("sigma_fibre_", i)) * draws_fibre
randcoeff[[paste0("b_crispy_", i)]] = get(paste0("mu_b_crispy_", i)) + get(paste0("sigma_crispy_", i)) * draws_crispy
}
return(randcoeff)
}
# ---------------------------------------------------- #
#### CLASS ALLOCATION ####
# ---------------------------------------------------- #
apollo_lcPars = function(apollo_beta, apollo_inputs){
lcpars = list()
for (i in 1:3) {
lcpars[["b_price"]][[i]] = get(paste0("b_price_", i))
lcpars[["b_process"]][[i]] = get(paste0("b_process_", i))
lcpars[["b_carbon"]][[i]] = get(paste0("b_carbon_", i))
lcpars[["b_fibre"]][[i]] = get(paste0("b_fibre_", i))
lcpars[["b_crispy"]][[i]] = get(paste0("b_crispy_", i))
lcpars[["asc_opt"]][[i]] = get(paste0("asc_opt_", i))
}
V = list(class1 = 0, class2 = theta1, class3 = theta2)
lcpars[["pi_values"]] = apollo_classAlloc(list(classes = c(class1=1, class2=2, class3=3), utilities = V))
return(lcpars)
}
# ---------------------------------------------------- #
#### VALIDATE INPUTS ####
# ---------------------------------------------------- #
apollo_inputs = apollo_validateInputs()
# ---------------------------------------------------- #
#### DEFINE PROBABILITIES ####
# ---------------------------------------------------- #
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()
for (s in 1:3) {
V = list()
V[["alt1"]] = b_price[[s]] * price_1 + b_process[[s]] * process_1 + b_carbon[[s]] * carbon_1 + b_fibre[[s]] * fibre_1 + b_crispy[[s]] * crispy_1
V[["alt2"]] = b_price[[s]] * price_2 + b_process[[s]] * process_2 + b_carbon[[s]] * carbon_2 + b_fibre[[s]] * fibre_2 + b_crispy[[s]] * crispy_2
V[["alt3"]] = asc_opt[[s]] + b_price[[s]] * price_3 + b_process[[s]] * process_3 + b_carbon[[s]] * carbon_3 + b_fibre[[s]] * fibre_3 + b_crispy[[s]] * crispy_3
mnl_settings = list(
alternatives = c(alt1=1, alt2=2, alt3=3),
choiceVar = choice_new,
V = V
)
P[[paste0("class", s)]] = apollo_mnl(mnl_settings, functionality)
P[[paste0("class", s)]] = apollo_panelProd(P[[paste0("class", s)]], apollo_inputs, functionality)
P[[paste0("class", s)]] = apollo_avgInterDraws(P[[paste0("class", s)]], apollo_inputs, functionality)
}
lc_settings = list(inClassProb = P, classProb = pi_values)
P[["model"]] = apollo_lc(lc_settings, apollo_inputs, functionality)
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}
# ---------------------------------------------------- #
#### ESTIMATE MODEL ####
# ---------------------------------------------------- #
model = apollo_estimate(apollo_beta, apollo_fixed, apollo_probabilities, apollo_inputs)
apollo_modelOutput(model)
apollo_saveOutput(model)
# Create an empty list to store WTPs
mWTP = list()
# Attributes for each class
attributes1 = c("mu_b_process_1", "mu_b_carbon_1", "mu_b_fibre_1", "mu_b_crispy_1")
attributes2 = c("mu_b_process_2", "mu_b_carbon_2", "mu_b_fibre_2", "mu_b_crispy_2")
attributes3 = c("mu_b_process_3", "mu_b_carbon_3", "mu_b_fibre_3", "mu_b_crispy_3")
# Loop for Class 1
for (attr in attributes1) {
deltaMethod_settings = list(
operation = "ratio",
parName1 = attr,
parName2 = "mu_b_price_1",
multPar1 = -1
)
mWTP[[attr]] <- apollo_deltaMethod(model, deltaMethod_settings)
}
# Loop for Class 2
for (attr in attributes2) {
deltaMethod_settings = list(
operation = "ratio",
parName1 = attr,
parName2 = "mu_b_price_2",
multPar1 = -1
)
mWTP[[attr]] <- apollo_deltaMethod(model, deltaMethod_settings)
}
# Loop for Class 3
for (attr in attributes3) {
deltaMethod_settings = list(
operation = "ratio",
parName1 = attr,
parName2 = "mu_b_price_3",
multPar1 = -1
)
mWTP[[attr]] <- apollo_deltaMethod(model, deltaMethod_settings)
}
# Output results
cat("\nEstimated Willingness-to-Pay (WTP) values for all classes:\n")
print(mWTP)
Code: Select all
Model name : LCMIXL_DriedApple_3Class
Model description : 3-class LC Mixed Logit model for dried apple
Model run at : 2025-04-30 18:57:27.926488
Estimation method : bgw
Model diagnosis : Relative function convergence
Optimisation diagnosis : Maximum found
hessian properties : Negative definite
maximum eigenvalue : -0.270401
reciprocal of condition number : 0.000221373
Number of individuals : 337
Number of rows in database : 3370
Number of modelled outcomes : 3370
Number of cores used : 4
Number of inter-individual draws : 500 (halton)
LL(start) : -3952.55
LL (whole model) at equal shares, LL(0) : -3702.32
LL (whole model) at observed shares, LL(C) : -3578.9
LL(final, whole model) : -2584.83
Rho-squared vs equal shares : 0.3018
Adj.Rho-squared vs equal shares : 0.2932
Rho-squared vs observed shares : 0.2778
Adj.Rho-squared vs observed shares : 0.2705
AIC : 5233.66
BIC : 5429.58
LL(0,class1) : -3702.32
LL(final,class1) : -3697.5
LL(0,class2) : -3702.32
LL(final,class2) : -3579.05
LL(0,class3) : -3702.32
LL(final,class3) : -3057.11
Estimated parameters : 32
Time taken (hh:mm:ss) : 00:09:9.83
pre-estimation : 00:00:26.14
estimation : 00:01:33.19
post-estimation : 00:07:10.5
Iterations : 34
Unconstrained optimisation.
Estimates:
Estimate s.e. t.rat.(0) Rob.s.e.
asc_opt_1 0.000000 NA NA NA
mu_b_price_1 -1.152593 0.09724 -11.852845 0.154686
mu_b_process_1 1.014236 0.11802 8.593455 0.103312
mu_b_carbon_1 1.504771 0.13841 10.871456 0.150597
mu_b_fibre_1 1.368967 0.13027 10.508684 0.129252
mu_b_crispy_1 1.989127 0.23652 8.409805 0.391446
asc_opt_2 0.000000 NA NA NA
mu_b_price_2 -0.739687 0.24919 -2.968360 0.539437
mu_b_process_2 -4.428926 1.42061 -3.117631 3.120268
mu_b_carbon_2 0.206159 0.51374 0.401292 0.479176
mu_b_fibre_2 0.646197 0.34237 1.887444 0.360466
mu_b_crispy_2 0.560655 0.32649 1.717219 0.329188
asc_opt_3 0.000000 NA NA NA
mu_b_price_3 -0.113794 0.04716 -2.412901 0.052260
mu_b_process_3 0.796775 0.34539 2.306877 0.863318
mu_b_carbon_3 0.215023 0.13752 1.563532 0.170829
mu_b_fibre_3 0.862340 0.12090 7.132776 0.137223
mu_b_crispy_3 0.081946 0.16591 0.493914 0.243494
sigma_price_1 0.216065 0.05026 4.299239 0.050293
sigma_process_1 -0.006563 0.20727 -0.031667 0.012554
sigma_carbon_1 -0.020148 0.22079 -0.091252 0.022279
sigma_fibre_1 -8.0485e-04 0.14449 -0.005570 0.005112
sigma_crispy_1 0.966497 0.20697 4.669792 0.317935
sigma_price_2 0.783916 0.24381 3.215227 0.567616
sigma_process_2 -2.232379 0.83008 -2.689355 1.758403
sigma_carbon_2 -3.473860 1.03235 -3.365017 2.332288
sigma_fibre_2 -1.035261 0.53145 -1.947993 0.841735
sigma_crispy_2 -0.749543 0.46979 -1.595486 0.506811
sigma_price_3 -0.183003 0.05999 -3.050390 0.114276
sigma_process_3 1.197187 0.40343 2.967534 1.013020
sigma_carbon_3 -0.367009 0.26000 -1.411564 0.454346
sigma_fibre_3 -0.530327 0.15573 -3.405380 0.215532
sigma_crispy_3 0.960287 0.18554 5.175685 0.270616
theta1 -0.810224 0.27787 -2.915821 0.631373
theta2 -0.392524 0.21241 -1.847924 0.297783
Rob.t.rat.(0)
asc_opt_1 NA
mu_b_price_1 -7.4512
mu_b_process_1 9.8172
mu_b_carbon_1 9.9920
mu_b_fibre_1 10.5915
mu_b_crispy_1 5.0815
asc_opt_2 NA
mu_b_price_2 -1.3712
mu_b_process_2 -1.4194
mu_b_carbon_2 0.4302
mu_b_fibre_2 1.7927
mu_b_crispy_2 1.7031
asc_opt_3 NA
mu_b_price_3 -2.1774
mu_b_process_3 0.9229
mu_b_carbon_3 1.2587
mu_b_fibre_3 6.2842
mu_b_crispy_3 0.3365
sigma_price_1 4.2961
sigma_process_1 -0.5228
sigma_carbon_1 -0.9043
sigma_fibre_1 -0.1574
sigma_crispy_1 3.0399
sigma_price_2 1.3811
sigma_process_2 -1.2695
sigma_carbon_2 -1.4895
sigma_fibre_2 -1.2299
sigma_crispy_2 -1.4789
sigma_price_3 -1.6014
sigma_process_3 1.1818
sigma_carbon_3 -0.8078
sigma_fibre_3 -2.4605
sigma_crispy_3 3.5485
theta1 -1.2833
theta2 -1.3182
Summary of class allocation for model component :
Mean prob.
class1 0.4717
class2 0.2098
class3 0.3185Code: Select all
Changes in parameter estimates from starting values:
Initial Estimate Difference
asc_opt_1 0.0000 0.000000 0.00000
mu_b_price_1 -1.0000 -1.152593 -0.15259
mu_b_process_1 0.2000 1.014236 0.81424
mu_b_carbon_1 0.2000 1.504771 1.30477
mu_b_fibre_1 0.2000 1.368967 1.16897
mu_b_crispy_1 0.2000 1.989127 1.78913
asc_opt_2 0.0000 0.000000 0.00000
mu_b_price_2 -1.1000 -0.739687 0.36031
mu_b_process_2 0.4000 -4.428926 -4.82893
mu_b_carbon_2 0.1000 0.206159 0.10616
mu_b_fibre_2 0.1000 0.646197 0.54620
mu_b_crispy_2 0.3000 0.560655 0.26065
asc_opt_3 0.0000 0.000000 0.00000
mu_b_price_3 -0.9000 -0.113794 0.78621
mu_b_process_3 0.1000 0.796775 0.69677
mu_b_carbon_3 0.3000 0.215023 -0.08498
mu_b_fibre_3 0.2000 0.862340 0.66234
mu_b_crispy_3 0.2000 0.081946 -0.11805
sigma_price_1 0.3000 0.216065 -0.08393
sigma_process_1 0.3000 -0.006563 -0.30656
sigma_carbon_1 0.3000 -0.020148 -0.32015
sigma_fibre_1 0.3000 -8.0485e-04 -0.30080
sigma_crispy_1 0.3000 0.966497 0.66650
sigma_price_2 0.2000 0.783916 0.58392
sigma_process_2 0.2000 -2.232379 -2.43238
sigma_carbon_2 0.2000 -3.473860 -3.67386
sigma_fibre_2 0.2000 -1.035261 -1.23526
sigma_crispy_2 0.2000 -0.749543 -0.94954
sigma_price_3 0.1000 -0.183003 -0.28300
sigma_process_3 0.1000 1.197187 1.09719
sigma_carbon_3 0.1000 -0.367009 -0.46701
sigma_fibre_3 0.1000 -0.530327 -0.63033
sigma_crispy_3 0.1000 0.960287 0.86029
theta1 0.0000 -0.810224 -0.81022
theta2 0.0000 -0.392524 -0.39252Code: Select all
# ---------------------------------------------------- #
#### CLEAN WORKSPACE AND LOAD LIBRARY ####
# ---------------------------------------------------- #
rm(list = ls())
gc()
library(apollo)
apollo_initialise()
# ---------------------------------------------------- #
#### CORE SETTINGS ####
# ---------------------------------------------------- #
apollo_control = list(
modelName = "LCMIXL_DriedApple_3Class",
modelDescr = "4-class LC Mixed Logit model for dried apple",
indivID = "respID",
nCores = 16,
outputDirectory = "output",
mixing = TRUE
)
# ---------------------------------------------------- #
#### LOAD DATA ####
# ---------------------------------------------------- #
database <- read.csv("dataset_apple_wide.csv")
# ---------------------------------------------------- #
#### DEFINE MODEL PARAMETERS ####
# ---------------------------------------------------- #
apollo_beta = c(
# Means
asc_opt_1 = 0,
mu_b_price_1 = -1,
mu_b_process_1 = 0.2,
mu_b_carbon_1 = 0.2,
mu_b_fibre_1 = 0.2,
mu_b_crispy_1 = 0.2,
asc_opt_2 = 0,
mu_b_price_2 = -1.1,
mu_b_process_2 = 0.4,
mu_b_carbon_2 = 0.1,
mu_b_fibre_2 = 0.1,
mu_b_crispy_2 = 0.3,
asc_opt_3 = 0,
mu_b_price_3 = -0.9,
mu_b_process_3 = 0.1,
mu_b_carbon_3 = 0.3,
mu_b_fibre_3 = 0.2,
mu_b_crispy_3 = 0.2,
asc_opt_4 = 0,
mu_b_price_4 = -1.2,
mu_b_process_4 = 0.3,
mu_b_carbon_4 = 0.3,
mu_b_fibre_4 = 0.3,
mu_b_crispy_4 = 0.3,
# Standard deviations
sigma_price_1 = 0.3,
sigma_process_1 = 0.3,
sigma_carbon_1 = 0.3,
sigma_fibre_1 = 0.3,
sigma_crispy_1 = 0.3,
sigma_price_2 = 0.2,
sigma_process_2 = 0.2,
sigma_carbon_2 = 0.2,
sigma_fibre_2 = 0.2,
sigma_crispy_2 = 0.2,
sigma_price_3 = 0.1,
sigma_process_3 = 0.1,
sigma_carbon_3 = 0.1,
sigma_fibre_3 = 0.1,
sigma_crispy_3 = 0.1,
sigma_price_4 = 0.2,
sigma_process_4 = 0.2,
sigma_carbon_4 = 0.2,
sigma_fibre_4 = 0.2,
sigma_crispy_4 = 0.2,
# Class allocation
theta1 = 0,
theta2 = 0,
theta3 = 0
)
apollo_fixed = c("asc_opt_1", "asc_opt_2", "asc_opt_3","asc_opt_4")
# ---------------------------------------------------- #
#### DRAW SETTINGS ####
# ---------------------------------------------------- #
apollo_draws = list(
interDrawsType = "halton",
interNDraws = 500,
interNormDraws = c("draws_price", "draws_process", "draws_carbon", "draws_fibre", "draws_crispy")
)
# ---------------------------------------------------- #
#### DEFINE RANDOM COEFFICIENTS ####
# ---------------------------------------------------- #
apollo_randCoeff = function(apollo_beta, apollo_inputs){
randcoeff = list()
for (i in 1:4) {
randcoeff[[paste0("b_price_", i)]] = get(paste0("mu_b_price_", i)) + get(paste0("sigma_price_", i)) * draws_price
randcoeff[[paste0("b_process_", i)]] = get(paste0("mu_b_process_", i)) + get(paste0("sigma_process_", i)) * draws_process
randcoeff[[paste0("b_carbon_", i)]] = get(paste0("mu_b_carbon_", i)) + get(paste0("sigma_carbon_", i)) * draws_carbon
randcoeff[[paste0("b_fibre_", i)]] = get(paste0("mu_b_fibre_", i)) + get(paste0("sigma_fibre_", i)) * draws_fibre
randcoeff[[paste0("b_crispy_", i)]] = get(paste0("mu_b_crispy_", i)) + get(paste0("sigma_crispy_", i)) * draws_crispy
}
return(randcoeff)
}
# ---------------------------------------------------- #
#### CLASS ALLOCATION ####
# ---------------------------------------------------- #
apollo_lcPars = function(apollo_beta, apollo_inputs){
lcpars = list()
for (i in 1:4) {
lcpars[["b_price"]][[i]] = get(paste0("b_price_", i))
lcpars[["b_process"]][[i]] = get(paste0("b_process_", i))
lcpars[["b_carbon"]][[i]] = get(paste0("b_carbon_", i))
lcpars[["b_fibre"]][[i]] = get(paste0("b_fibre_", i))
lcpars[["b_crispy"]][[i]] = get(paste0("b_crispy_", i))
lcpars[["asc_opt"]][[i]] = get(paste0("asc_opt_", i))
}
V = list(class1 = 0, class2 = theta1, class3 = theta2, class4 = theta3)
lcpars[["pi_values"]] = apollo_classAlloc(list(classes = c(class1=1, class2=2, class3=3, class4=4), utilities = V))
return(lcpars)
}
# ---------------------------------------------------- #
#### VALIDATE INPUTS ####
# ---------------------------------------------------- #
apollo_inputs = apollo_validateInputs()
# ---------------------------------------------------- #
#### DEFINE PROBABILITIES ####
# ---------------------------------------------------- #
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()
for (s in 1:4) {
V = list()
V[["alt1"]] = b_price[[s]] * price_1 + b_process[[s]] * process_1 + b_carbon[[s]] * carbon_1 + b_fibre[[s]] * fibre_1 + b_crispy[[s]] * crispy_1
V[["alt2"]] = b_price[[s]] * price_2 + b_process[[s]] * process_2 + b_carbon[[s]] * carbon_2 + b_fibre[[s]] * fibre_2 + b_crispy[[s]] * crispy_2
V[["alt3"]] = asc_opt[[s]] + b_price[[s]] * price_3 + b_process[[s]] * process_3 + b_carbon[[s]] * carbon_3 + b_fibre[[s]] * fibre_3 + b_crispy[[s]] * crispy_3
mnl_settings = list(
alternatives = c(alt1=1, alt2=2, alt3=3),
choiceVar = choice_new,
V = V
)
P[[paste0("class", s)]] = apollo_mnl(mnl_settings, functionality)
P[[paste0("class", s)]] = apollo_panelProd(P[[paste0("class", s)]], apollo_inputs, functionality)
P[[paste0("class", s)]] = apollo_avgInterDraws(P[[paste0("class", s)]], apollo_inputs, functionality)
}
lc_settings = list(inClassProb = P, classProb = pi_values)
P[["model"]] = apollo_lc(lc_settings, apollo_inputs, functionality)
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}
# ---------------------------------------------------- #
#### ESTIMATE MODEL ####
# ---------------------------------------------------- #
model = apollo_estimate(apollo_beta, apollo_fixed, apollo_probabilities, apollo_inputs)
apollo_modelOutput(model)
apollo_saveOutput(model)
Code: Select all
Model name : LCMIXL_DriedApple_3Class
Model description : 4-class LC Mixed Logit model for dried apple
Model run at : 2025-04-30 19:18:07.58613
Estimation method : bgw
Model diagnosis : Function evaluation limit
Number of individuals : 337
Number of rows in database : 3370
Number of modelled outcomes : 3370
Number of cores used : 16
Number of inter-individual draws : 500 (halton)
LL(start) : -4006.56
LL (whole model) at equal shares, LL(0) : -3702.32
LL (whole model) at observed shares, LL(C) : -3578.9
LL(final, whole model) : -2583.95
Rho-squared vs equal shares : 0.3021
Adj.Rho-squared vs equal shares : 0.2905
Rho-squared vs observed shares : 0.278
Adj.Rho-squared vs observed shares : 0.2682
AIC : 5253.9
BIC : 5517.17
LL(0,class1) : -3702.32
LL(final,class1) : -2921.61
LL(0,class2) : -3702.32
LL(final,class2) : -66614.52
LL(0,class3) : -3702.32
LL(final,class3) : -Inf Likelihood equal to zero for at least
one individual in this component.
LL(0,class4) : -3702.32
LL(final,class4) : -3634.59
Estimated parameters : 43
Time taken (hh:mm:ss) : 00:06:15.46
pre-estimation : 00:00:51.66
estimation : 00:05:20.05
post-estimation : 00:00:3.74
Iterations : 88 (Function evaluation limit)
Unconstrained optimisation.
Estimates:
Estimate s.e. t.rat.(0) Rob.s.e.
asc_opt_1 0.000000 NA NA NA
mu_b_price_1 -0.171451 NA NA NA
mu_b_process_1 -0.255591 NA NA NA
mu_b_carbon_1 0.321396 NA NA NA
mu_b_fibre_1 0.875223 NA NA NA
mu_b_crispy_1 0.208823 NA NA NA
asc_opt_2 0.000000 NA NA NA
mu_b_price_2 -22.751562 NA NA NA
mu_b_process_2 -36.295984 NA NA NA
mu_b_carbon_2 -811.346441 NA NA NA
mu_b_fibre_2 -18.064016 NA NA NA
mu_b_crispy_2 -17.006011 NA NA NA
asc_opt_3 0.000000 NA NA NA
mu_b_price_3 1.156e+04 NA NA NA
mu_b_process_3 3.179e+04 NA NA NA
mu_b_carbon_3 1773.110131 NA NA NA
mu_b_fibre_3 -2564.768215 NA NA NA
mu_b_crispy_3 3.722e+04 NA NA NA
asc_opt_4 0.000000 NA NA NA
mu_b_price_4 -1.110255 NA NA NA
mu_b_process_4 1.040486 NA NA NA
mu_b_carbon_4 1.471342 NA NA NA
mu_b_fibre_4 1.337368 NA NA NA
mu_b_crispy_4 1.904001 NA NA NA
sigma_price_1 0.303276 NA NA NA
sigma_process_1 2.124713 NA NA NA
sigma_carbon_1 -0.734768 NA NA NA
sigma_fibre_1 0.612134 NA NA NA
sigma_crispy_1 0.993179 NA NA NA
sigma_price_2 10.959878 NA NA NA
sigma_process_2 25.858891 NA NA NA
sigma_carbon_2 -1278.895842 NA NA NA
sigma_fibre_2 19.404407 NA NA NA
sigma_crispy_2 8.465367 NA NA NA
sigma_price_3 658.012072 NA NA NA
sigma_process_3 4028.540016 NA NA NA
sigma_carbon_3 -558.139016 NA NA NA
sigma_fibre_3 917.603379 NA NA NA
sigma_crispy_3 1.085e+04 NA NA NA
sigma_price_4 0.224516 NA NA NA
sigma_process_4 0.002376 NA NA NA
sigma_carbon_4 -0.011173 NA NA NA
sigma_fibre_4 -0.002029 NA NA NA
sigma_crispy_4 -0.881905 NA NA NA
theta1 -1.945271 NA NA NA
theta2 -667.495140 NA NA NA
theta3 0.034525 NA NA NA
Rob.t.rat.(0)
asc_opt_1 NA
mu_b_price_1 NA
mu_b_process_1 NA
mu_b_carbon_1 NA
mu_b_fibre_1 NA
mu_b_crispy_1 NA
asc_opt_2 NA
mu_b_price_2 NA
mu_b_process_2 NA
mu_b_carbon_2 NA
mu_b_fibre_2 NA
mu_b_crispy_2 NA
asc_opt_3 NA
mu_b_price_3 NA
mu_b_process_3 NA
mu_b_carbon_3 NA
mu_b_fibre_3 NA
mu_b_crispy_3 NA
asc_opt_4 NA
mu_b_price_4 NA
mu_b_process_4 NA
mu_b_carbon_4 NA
mu_b_fibre_4 NA
mu_b_crispy_4 NA
sigma_price_1 NA
sigma_process_1 NA
sigma_carbon_1 NA
sigma_fibre_1 NA
sigma_crispy_1 NA
sigma_price_2 NA
sigma_process_2 NA
sigma_carbon_2 NA
sigma_fibre_2 NA
sigma_crispy_2 NA
sigma_price_3 NA
sigma_process_3 NA
sigma_carbon_3 NA
sigma_fibre_3 NA
sigma_crispy_3 NA
sigma_price_4 NA
sigma_process_4 NA
sigma_carbon_4 NA
sigma_fibre_4 NA
sigma_crispy_4 NA
theta1 NA
theta2 NA
theta3 NA
Your model did not converge properly, and some of your parameter
values are tending to +/- infinity. This could point to an
identification issue. If you want to retain these parameters in
the model, you may wish to set their value(s) in apollo_beta to
the estimated value(s), include the parameter name(s) in
apollo_fixed, and re-estimate the model.
Summary of class allocation for model component :
Mean prob.
class1 0.45912
class2 0.06563
class3 5.922e-291
class4 0.47525
Code: Select all
Changes in parameter estimates from starting values:
Initial Estimate Difference
asc_opt_1 0.0000 0.000000 0.000000
mu_b_price_1 -1.0000 -0.171451 0.828549
mu_b_process_1 0.2000 -0.255591 -0.455591
mu_b_carbon_1 0.2000 0.321396 0.121396
mu_b_fibre_1 0.2000 0.875223 0.675223
mu_b_crispy_1 0.2000 0.208823 0.008823
asc_opt_2 0.0000 0.000000 0.000000
mu_b_price_2 -1.1000 -22.751562 -21.651562
mu_b_process_2 0.4000 -36.295984 -36.695984
mu_b_carbon_2 0.1000 -811.346441 -811.446441
mu_b_fibre_2 0.1000 -18.064016 -18.164016
mu_b_crispy_2 0.3000 -17.006011 -17.306011
asc_opt_3 0.0000 0.000000 0.000000
mu_b_price_3 -0.9000 1.156e+04 1.156e+04
mu_b_process_3 0.1000 3.179e+04 3.179e+04
mu_b_carbon_3 0.3000 1773.110131 1772.810131
mu_b_fibre_3 0.2000 -2564.768215 -2564.968215
mu_b_crispy_3 0.2000 3.722e+04 3.722e+04
asc_opt_4 0.0000 0.000000 0.000000
mu_b_price_4 -1.2000 -1.110255 0.089745
mu_b_process_4 0.3000 1.040486 0.740486
mu_b_carbon_4 0.3000 1.471342 1.171342
mu_b_fibre_4 0.3000 1.337368 1.037368
mu_b_crispy_4 0.3000 1.904001 1.604001
sigma_price_1 0.3000 0.303276 0.003276
sigma_process_1 0.3000 2.124713 1.824713
sigma_carbon_1 0.3000 -0.734768 -1.034768
sigma_fibre_1 0.3000 0.612134 0.312134
sigma_crispy_1 0.3000 0.993179 0.693179
sigma_price_2 0.2000 10.959878 10.759878
sigma_process_2 0.2000 25.858891 25.658891
sigma_carbon_2 0.2000 -1278.895842 -1279.095842
sigma_fibre_2 0.2000 19.404407 19.204407
sigma_crispy_2 0.2000 8.465367 8.265367
sigma_price_3 0.1000 658.012072 657.912072
sigma_process_3 0.1000 4028.540016 4028.440016
sigma_carbon_3 0.1000 -558.139016 -558.239016
sigma_fibre_3 0.1000 917.603379 917.503379
sigma_crispy_3 0.1000 1.085e+04 1.084e+04
sigma_price_4 0.2000 0.224516 0.024516
sigma_process_4 0.2000 0.002376 -0.197624
sigma_carbon_4 0.2000 -0.011173 -0.211173
sigma_fibre_4 0.2000 -0.002029 -0.202029
sigma_crispy_4 0.2000 -0.881905 -1.081905
theta1 0.0000 -1.945271 -1.945271
theta2 0.0000 -667.495140 -667.495140
theta3 0.0000 0.034525 0.034525
Based on given results and code, would it suggests that there is no fourth latent group in the data, and LC MMNL 3 class is an appropriate model?
What other method would you suggest me to try out to further diagnose this ?