Latent Class Choice Model: NaNs produced
Posted: 04 Nov 2025, 10:59
Dear Dr. Stephane and the Apollo Choice Modelling Community,
I am trying to configure a 3-class LCCM model incorporating a Latent variable and running into an error of convergence to a saddle point (NaNs produced).
Fundamentally, the choice-specific model consists of 5 alternatives (including an opt-out-like alternative, without any specific alternative attributes). No covariates are considered at this stage. I am sharing the code and the output as follows:
1. The code
2. The output
I am also sharing the output of the simpler model without the Latent variable for your reference.
I am looking forward to receiving your support.
I am trying to configure a 3-class LCCM model incorporating a Latent variable and running into an error of convergence to a saddle point (NaNs produced).
Fundamentally, the choice-specific model consists of 5 alternatives (including an opt-out-like alternative, without any specific alternative attributes). No covariates are considered at this stage. I am sharing the code and the output as follows:
1. The code
Code: Select all
library(apollo)
### Initialise code
apollo_initialise()
### Set core controls
apollo_control = list(
modelName = "MNL",
modelDescr = "Simple MNL model MaaS bundle SP x LCCM 3C x LV",
indivID = "ID",
nCores = 16,
panelData = TRUE,
noValidation = FALSE,
analyticGrad = FALSE,
outputDirectory = "output"
)
# ####################################################### #
#### 2. Data loading ####
# ####################################################### #
maas <- read.csv("HCM_Data_R_working.csv")
database = maas
rm(maas)
# ################################################################# #
#### DEFINE MODEL PARAMETERS ####
# ################################################################# #
### Vector of parameters, including any that are kept fixed
### during estimation
apollo_beta=c(asc_B1_a = 1.3, asc_B1_b = -0.91, asc_B1_c = 0.35,
asc_B2_a = 2.0, asc_B2_b = -1.65, asc_B2_c = 2.0,
asc_B3_a = 1.9, asc_B3_b = 1.17, asc_B3_c = 1.89,
asc_B4_a = 1.06, asc_B4_b = 2.15, asc_B4_c = 1.61,
asc_PAYG = 0,
# sigma_eta = 1,
# Class allocation parameters
delta_a = 0.37, delta_b = -0.23, delta_c = 0,
lambda_LV_a = -0.11, lambda_LV_b = -0.1, lambda_LV_c = 0,
# Alternative-specific variables
b_MCH_a = 0.03, b_MCH_b = -0.5, b_MCH_c = 0.2,
b_CAH_a = 0.3, b_CAH_b = -1.6, b_CAH_c = 0.2,
b_EM_a = -0.6, b_EM_b = -0.3, b_EM_c = -0.2,
b_PR_a = -0.4, b_PR_b = -0.3, b_PR_c = -0.1,
#Measurement equation parameters
zeta_CD1 = 1, zeta_CD2 = 1,
zeta_CD4 = 1, zeta_CD5 = 1,
zeta_CD6 = 1, zeta_CD7 = 1,
zeta_CD8 = 1, zeta_CD9 = 1,
tau_CD1_1 = -3, tau_CD2_1 = -3,
tau_CD1_2 = -2, tau_CD2_2 = -2,
tau_CD1_3 = -1, tau_CD2_3 = -1,
tau_CD1_4 = 1, tau_CD2_4 = 1,
tau_CD1_5 = 2, tau_CD2_5 = 2,
tau_CD1_6 = 3, tau_CD2_6 = 3,
tau_CD4_1 = -3, tau_CD5_1 = -3,
tau_CD4_2 = -2, tau_CD5_2 = -2,
tau_CD4_3 = -1, tau_CD5_3 = -1,
tau_CD4_4 = 1, tau_CD5_4 = 1,
tau_CD4_5 = 2, tau_CD5_5 = 2,
tau_CD4_6 = 3, tau_CD5_6 = 3,
tau_CD6_1 = -3, tau_CD7_1 = -3,
tau_CD6_2 = -2, tau_CD7_2 = -2,
tau_CD6_3 = -1, tau_CD7_3 = -1,
tau_CD6_4 = 1, tau_CD7_4 = 1,
tau_CD6_5 = 2, tau_CD7_5 = 2,
tau_CD6_6 = 3, tau_CD7_6 = 3,
tau_CD8_1 = -3, tau_CD9_1 = -3,
tau_CD8_2 = -2, tau_CD9_2 = -2,
tau_CD8_3 = -1, tau_CD9_3 = -1,
tau_CD8_4 = 1, tau_CD9_4 = 1,
tau_CD8_5 = 2, tau_CD9_5 = 2,
tau_CD8_6 = 3, tau_CD9_6 = 3
)
### 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_PAYG", "delta_c", "lambda_LV_c")
# ################################################################# #
#### DEFINE RANDOM COMPONENTS ####
# ################################################################# #
### Set parameters for generating draws
apollo_draws = list(
interDrawsType = "MLHS",
interNDraws = 500,
interNormDraws = c("eta_LV")
)
### Create random parameters
apollo_randCoeff=function(apollo_beta, apollo_inputs){
randcoeff = list()
randcoeff[["LV"]] = eta_LV
return(randcoeff)
}
### Read in starting values for at least some parameters from existing model output file
#apollo_beta = apollo_readBeta(apollo_beta, apollo_fixed, "MNL_SP", overwriteFixed=FALSE)
# ################################################################# #
#### DEFINE LATENT CLASS COMPONENTS ####
# ################################################################# #
apollo_lcPars=function(apollo_beta, apollo_inputs){
lcpars = list()
lcpars[["asc_B1"]] = list(asc_B1_a, asc_B1_b, asc_B1_c)
lcpars[["asc_B2"]] = list(asc_B2_a, asc_B2_b, asc_B2_c)
lcpars[["asc_B3"]] = list(asc_B3_a, asc_B3_b, asc_B3_c)
lcpars[["asc_B4"]] = list(asc_B4_a, asc_B4_b, asc_B4_c)
lcpars[["b_MCH"]] = list(b_MCH_a, b_MCH_b, b_MCH_c)
lcpars[["b_CAH"]] = list(b_CAH_a, b_CAH_b, b_CAH_c)
lcpars[["b_EM"]] = list(b_EM_a, b_EM_b, b_EM_c)
lcpars[["b_PR"]] = list(b_PR_a, b_PR_b, b_PR_c)
### Utilities of class allocation model
V=list()
V[["class_a"]] = delta_a + lambda_LV_a*LV
V[["class_b"]] = delta_b + lambda_LV_b*LV
V[["class_c"]] = delta_c + lambda_LV_c*LV
### Settings for class allocation models
classAlloc_settings = list(
classes = c(class_a=1, class_b=2, class_c=3),
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()
### Likelihood of indicators
ol_settings_CD1 = list(outcomeOrdered = CD1, #the column (variable) inside the database
utility = zeta_CD1*LV, #A numeric vector contains the explanatory var used in the OL
tau = list(tau_CD1_1, tau_CD1_2, tau_CD1_3, tau_CD1_4, tau_CD1_5, tau_CD1_6), #A vector contains the threshold parameters (should have 1 element less than the Scale)
coding = -3:3,
rows = (choiceid==1),
componentName = "indic_CD1")
ol_settings_CD2 = list(outcomeOrdered = CD2,
utility = zeta_CD2*LV,
tau = list(tau_CD2_1, tau_CD2_2, tau_CD2_3, tau_CD2_4, tau_CD2_5, tau_CD2_6),
coding = -3:3,
rows = (choiceid==1),
componentName = "indic_CD2")
ol_settings_CD4 = list(outcomeOrdered = CD4,
utility = zeta_CD4*LV,
tau = list(tau_CD4_1, tau_CD4_2, tau_CD4_3, tau_CD4_4, tau_CD4_5, tau_CD4_6),
coding = -3:3,
rows = (choiceid==1),
componentName = "indic_CD4")
ol_settings_CD5 = list(outcomeOrdered = CD5,
utility = zeta_CD5*LV,
tau = list(tau_CD5_1, tau_CD5_2, tau_CD5_3, tau_CD5_4, tau_CD5_5, tau_CD5_6),
coding = -3:3,
rows = (choiceid==1),
componentName = "indic_CD5")
ol_settings_CD6 = list(outcomeOrdered = CD6,
utility = zeta_CD6*LV,
tau = list(tau_CD6_1, tau_CD6_2, tau_CD6_3, tau_CD6_4, tau_CD6_5, tau_CD6_6),
coding = -3:3,
rows = (choiceid==1),
componentName = "indic_CD6")
ol_settings_CD7 = list(outcomeOrdered = CD7,
utility = zeta_CD7*LV,
tau = list(tau_CD7_1, tau_CD7_2, tau_CD7_3, tau_CD7_4, tau_CD7_5, tau_CD7_6),
coding = -3:3,
rows = (choiceid==1),
componentName = "indic_CD7")
ol_settings_CD8 = list(outcomeOrdered = CD8,
utility = zeta_CD8*LV,
tau = list(tau_CD8_1, tau_CD8_2, tau_CD8_3, tau_CD8_4, tau_CD8_5, tau_CD8_6),
coding = -3:3,
rows = (choiceid==1),
componentName = "indic_CD8")
ol_settings_CD9 = list(outcomeOrdered = CD9,
utility = zeta_CD9*LV,
tau = list(tau_CD9_1, tau_CD9_2, tau_CD9_3, tau_CD9_4, tau_CD9_5, tau_CD9_6),
coding = -3:3,
rows = (choiceid==1),
componentName = "indic_CD9")
P[["indic_CD1"]] = apollo_ol(ol_settings_CD1, functionality)
P[["indic_CD2"]] = apollo_ol(ol_settings_CD2, functionality)
P[["indic_CD4"]] = apollo_ol(ol_settings_CD4, functionality)
P[["indic_CD5"]] = apollo_ol(ol_settings_CD5, functionality)
P[["indic_CD6"]] = apollo_ol(ol_settings_CD6, functionality)
P[["indic_CD7"]] = apollo_ol(ol_settings_CD7, functionality)
P[["indic_CD8"]] = apollo_ol(ol_settings_CD8, functionality)
P[["indic_CD9"]] = apollo_ol(ol_settings_CD9, functionality)
### Combine Model
P = apollo_combineModels(P, apollo_inputs, functionality)
### Take product across observation for same individual
P = apollo_panelProd(P, apollo_inputs, functionality)
### Rename model
names(P)[which(names(P)=="model")] <- "Measurement_model"
################################################################################################################################################
### Likelihood of choices inside each class
P_within<-list()
### Loop over classes
S = 3
for(s in 1:S){
### Compute class-specific utilities
### Utilities for alternatives
V = list()
V[['PAYG']] = asc_PAYG
V[['B1']] = asc_B1[[s]] +
b_MCH[[s]]*MCH_B1 +
b_CAH[[s]]*CAH_B1 +
b_EM[[s]]*EM_B1 +
b_PR[[s]]*PR_B1
V[['B2']] = asc_B2[[s]] +
b_MCH[[s]]*MCH_B2 +
b_CAH[[s]]*CAH_B2 +
b_EM[[s]]*EM_B2 +
b_PR[[s]]*PR_B2
V[['B3']] = asc_B3[[s]] +
b_MCH[[s]]*MCH_B3 +
b_CAH[[s]]*CAH_B3 +
b_EM[[s]]*EM_B3 +
b_PR[[s]]*PR_B3
V[['B4']] = asc_B4[[s]] +
b_MCH[[s]]*MCH_B4 +
b_CAH[[s]]*CAH_B4 +
b_EM[[s]]*EM_B4 +
b_PR[[s]]*PR_B4
### Define settings for MNL model component
mnl_settings = list(
alternatives = c(B1=1, B2=2, B3=3, B4=4, PAYG=5),
avail = list(B1=1, B2=1, B3=1, B4=1, PAYG=1),
choiceVar = choice,
utilities = V
)
### Compute within-class choice probabilities using MNL model
P_within[[paste0("Class_",s)]] = apollo_mnl(mnl_settings, functionality)
### Take product across observation for same individual
P_within[[paste0("Class_",s)]] = apollo_panelProd(P_within[[paste0("Class_",s)]], apollo_inputs ,functionality)
}
### Compute latent class model probabilities
lc_settings = list(inClassProb = P_within, classProb=pi_values)
P[["LC_model"]] = apollo_lc(lc_settings, apollo_inputs, functionality)
### Comment out as necessary
P = apollo_combineModels(P, apollo_inputs, functionality)
P = apollo_avgInterDraws(P, apollo_inputs, functionality)
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}
# ################################################################# #
#### CALCULATE LL AT STARTING VALUES ####
# ################################################################# #
apollo_llCalc(apollo_beta, apollo_probabilities, apollo_inputs)
# ################################################################# #
#### MODEL ESTIMATION ####
# ################################################################# #
### Optional starting values search
# apollo_beta=apollo_searchStart(apollo_beta, apollo_fixed,apollo_probabilities, apollo_inputs)
estimate_settings = list(estimationRoutine = "bfgs", maxIterations = 300)
model = apollo_estimate(apollo_beta,
apollo_fixed,
apollo_probabilities,
apollo_inputs,
estimate_settings=estimate_settings)
# ################################################################# #
#### MODEL OUTPUTS ####
# ################################################################# #
# ----------------------------------------------------------------- #
#---- FORMATTED OUTPUT (TO SCREEN) ----
# ----------------------------------------------------------------- #
apollo_modelOutput(model)
Code: Select all
Preparing user-defined functions.
Testing likelihood function...
Apollo found a model component of type classAlloc without a componentName. The name was set to "classAlloc" by default.
INFORMATION: Setting "avail" is missing, so full availability is assumed.
Overview of choices for OL model component indic_CD1:
1 2 3 4 5 6 7
Times chosen 25.00 4.00 31.00 134.00 129.00 77.00 88.00
Percentage chosen overall 5.12 0.82 6.35 27.46 26.43 15.78 18.03
Overview of choices for OL model component indic_CD2:
1 2 3 4 5 6 7
Times chosen 36.00 16.00 58.00 150.00 87.00 68.00 73.00
Percentage chosen overall 7.38 3.28 11.89 30.74 17.83 13.93 14.96
Overview of choices for OL model component indic_CD4:
1 2 3 4 5 6 7
Times chosen 57.00 21.0 91.00 168.00 55.00 42.00 54.00
Percentage chosen overall 11.68 4.3 18.65 34.43 11.27 8.61 11.07
Overview of choices for OL model component indic_CD5:
1 2 3 4 5 6 7
Times chosen 35.00 18.00 42.00 199.00 79.00 53.00 62.0
Percentage chosen overall 7.17 3.69 8.61 40.78 16.19 10.86 12.7
Overview of choices for OL model component indic_CD6:
1 2 3 4 5 6 7
Times chosen 46.00 18.00 48.00 182.0 78.00 54.00 62.0
Percentage chosen overall 9.43 3.69 9.84 37.3 15.98 11.07 12.7
Overview of choices for OL model component indic_CD7:
1 2 3 4 5 6 7
Times chosen 33.00 15.00 31.00 131.00 122 64.00 92.00
Percentage chosen overall 6.76 3.07 6.35 26.84 25 13.11 18.85
Overview of choices for OL model component indic_CD8:
1 2 3 4 5 6 7
Times chosen 64.00 20.0 75.00 169.00 59.00 44.00 57.00
Percentage chosen overall 13.11 4.1 15.37 34.63 12.09 9.02 11.68
Overview of choices for OL model component indic_CD9:
1 2 3 4 5 6 7
Times chosen 52.00 29.00 72.00 155.00 67.00 46.00 67.00
Percentage chosen overall 10.66 5.94 14.75 31.76 13.73 9.43 13.73
Apollo found a model component of type MNL without a componentName. The name was set to "Class_1" by default.
Overview of choices for MNL model component Class_1:
B1 B2 B3 B4 PAYG
Times available 2440.00 2440.00 2440.00 2440.00 2440.00
Times chosen 1013.00 403.00 279.00 181.00 564.00
Percentage chosen overall 41.52 16.52 11.43 7.42 23.11
Percentage chosen when available 41.52 16.52 11.43 7.42 23.11
Apollo found a model component of type MNL without a componentName. The name was set to "Class_2" by default.
Overview of choices for MNL model component Class_2:
B1 B2 B3 B4 PAYG
Times available 2440.00 2440.00 2440.00 2440.00 2440.00
Times chosen 1013.00 403.00 279.00 181.00 564.00
Percentage chosen overall 41.52 16.52 11.43 7.42 23.11
Percentage chosen when available 41.52 16.52 11.43 7.42 23.11
Apollo found a model component of type MNL without a componentName. The name was set to "Class_3" by default.
Overview of choices for MNL model component Class_3:
B1 B2 B3 B4 PAYG
Times available 2440.00 2440.00 2440.00 2440.00 2440.00
Times chosen 1013.00 403.00 279.00 181.00 564.00
Percentage chosen overall 41.52 16.52 11.43 7.42 23.11
Percentage chosen when available 41.52 16.52 11.43 7.42 23.11
Apollo found a model component of type LC without a componentName. The name was set to "LC_model" by default.
Summary of class allocation for model component LC_model:
Mean prob.
Class_1 0.4463
Class_2 0.2448
Class_3 0.3089
The class allocation probabilities for model component "LC_model" are calculated at the observation level in 'apollo_lcPars', but are used in 'apollo_probabilities' to multiply within class probabilities
that are at the individual level. Apollo will average the class allocation probabilities across observations for the same individual level before using them to multiply the within-class probabilities.
If your class allocation probabilities are constant across choice situations for the same individual, then this is of no concern. If your class allocation probabilities however vary across choice
tasks, then you should change your model specification in 'apollo_probabilities' to only call 'apollo_panelProd' after calling 'apollo_lc'.
Pre-processing likelihood function...
Creating cluster...
Preparing workers for multithreading...
Testing influence of parameters....................................................................................
Starting main estimation
Initial function value: -9304.484
Initial gradient value:
asc_B1_a asc_B1_b asc_B1_c asc_B2_a asc_B2_b asc_B2_c asc_B3_a asc_B3_b asc_B3_c asc_B4_a asc_B4_b asc_B4_c delta_a delta_b lambda_LV_a lambda_LV_b b_MCH_a b_MCH_b
619.253042 -8.012079 -13.117649 -186.906333 -10.777510 -58.457545 -225.532720 -14.284142 53.826554 -81.379951 -12.333778 25.793286 57.847063 3.834919 -44.698363 15.364139 -673.057417 -76.050374
b_MCH_c b_CAH_a b_CAH_b b_CAH_c b_EM_a b_EM_b b_EM_c b_PR_a b_PR_b b_PR_c zeta_CD1 zeta_CD2 zeta_CD4 zeta_CD5 zeta_CD6 zeta_CD7 zeta_CD8 zeta_CD9
141.089464 -471.063244 -43.142509 107.682175 93.581417 -23.833712 16.197255 -873.984638 -112.057753 239.968611 58.403859 106.289019 100.445859 110.788113 99.066008 110.699777 89.400626 131.526987
tau_CD1_1 tau_CD2_1 tau_CD1_2 tau_CD2_2 tau_CD1_3 tau_CD2_3 tau_CD1_4 tau_CD2_4 tau_CD1_5 tau_CD2_5 tau_CD1_6 tau_CD2_6 tau_CD4_1 tau_CD5_1 tau_CD4_2 tau_CD5_2 tau_CD4_3 tau_CD5_3
13.133116 14.061223 -20.717149 -25.483745 -30.109915 -2.838584 -97.673592 -35.333846 6.206948 -11.144011 -3.333438 6.444154 27.495607 9.823127 -41.116353 -11.570677 42.758658 -40.123730
tau_CD4_4 tau_CD5_4 tau_CD4_5 tau_CD5_5 tau_CD4_6 tau_CD5_6 tau_CD6_1 tau_CD7_1 tau_CD6_2 tau_CD7_2 tau_CD6_3 tau_CD7_3 tau_CD6_4 tau_CD7_4 tau_CD6_5 tau_CD7_5 tau_CD6_6 tau_CD7_6
22.330265 -1.070166 2.345656 2.784178 4.853262 6.731696 20.718624 10.447771 -14.987252 -7.385996 -25.984911 -25.017847 -8.243174 -90.087457 3.219968 16.834647 7.124427 -14.018746
tau_CD8_1 tau_CD9_1 tau_CD8_2 tau_CD9_2 tau_CD8_3 tau_CD9_3 tau_CD8_4 tau_CD9_4 tau_CD8_5 tau_CD9_5 tau_CD8_6 tau_CD9_6
35.486290 17.125129 -29.959341 -15.694015 19.605523 22.185395 13.596882 -1.686622 1.282722 4.178024 3.909245 -3.368930
initial value 9304.484190
iter 2 value 8882.770889
iter 3 value 8256.357190
iter 4 value 8186.283191
iter 5 value 8016.243014
iter 6 value 7984.542712
iter 7 value 7913.618042
iter 8 value 7859.011997
iter 9 value 7812.047903
iter 10 value 7780.736819
iter 11 value 7736.691833
iter 12 value 7723.543087
iter 13 value 7712.871024
iter 14 value 7712.257706
iter 15 value 7699.591249
iter 16 value 7691.405840
iter 17 value 7680.866695
iter 18 value 7664.983329
iter 19 value 7651.417342
iter 20 value 7645.510078
iter 21 value 7636.885790
iter 22 value 7633.290422
iter 23 value 7629.007889
iter 24 value 7617.871190
iter 25 value 7611.425090
iter 26 value 7608.638876
iter 27 value 7603.326255
iter 28 value 7596.227317
iter 29 value 7586.068682
iter 30 value 7585.590213
iter 31 value 7584.352660
iter 32 value 7582.498257
iter 33 value 7579.471819
iter 34 value 7577.185032
iter 35 value 7574.739476
iter 36 value 7573.725708
iter 37 value 7572.470534
iter 38 value 7571.699454
iter 39 value 7570.854239
iter 40 value 7569.882826
iter 41 value 7569.516835
iter 42 value 7568.942007
iter 43 value 7568.463047
iter 44 value 7568.175006
iter 45 value 7567.767827
iter 46 value 7567.424527
iter 47 value 7567.223027
iter 48 value 7567.084437
iter 49 value 7566.882967
iter 50 value 7566.582124
iter 51 value 7566.518164
iter 52 value 7566.304149
iter 53 value 7566.071606
iter 54 value 7565.867347
iter 55 value 7565.611287
iter 56 value 7565.322904
iter 57 value 7565.156804
iter 58 value 7564.984536
iter 59 value 7564.778372
iter 60 value 7564.520533
iter 61 value 7564.185701
iter 62 value 7563.942224
iter 63 value 7563.802477
iter 64 value 7563.714958
iter 65 value 7563.640029
iter 66 value 7563.520927
iter 67 value 7563.377238
iter 68 value 7563.249434
iter 69 value 7563.163451
iter 70 value 7563.064432
iter 71 value 7562.968334
iter 72 value 7562.871095
iter 73 value 7562.820491
iter 74 value 7562.724303
iter 75 value 7562.635137
iter 76 value 7562.516082
iter 77 value 7562.431776
iter 78 value 7562.326540
iter 79 value 7562.236680
iter 80 value 7562.194514
iter 81 value 7562.113868
iter 82 value 7561.929829
iter 83 value 7561.792045
iter 84 value 7561.615635
iter 85 value 7561.568363
iter 86 value 7561.541420
iter 87 value 7561.493766
iter 88 value 7561.479203
iter 89 value 7561.444246
iter 90 value 7561.423128
iter 91 value 7561.416977
iter 92 value 7561.415191
iter 93 value 7561.412879
iter 94 value 7561.412720
iter 94 value 7561.412658
iter 94 value 7561.412656
final value 7561.412656
converged
Estimated parameters with approximate standard errors from BHHH matrix:
Estimate BHHH se BHH t-ratio (0)
asc_B1_a 5.60443 0.54299 10.3215
asc_B1_b -0.91316 0.46736 -1.9539
asc_B1_c 0.35246 0.28270 1.2468
asc_B2_a 3.91355 0.56891 6.8791
asc_B2_b -1.65458 0.81347 -2.0340
asc_B2_c 2.41741 0.20625 11.7205
asc_B3_a 2.02469 0.82184 2.4636
asc_B3_b 1.18095 1.79620 0.6575
asc_B3_c 2.18018 0.29319 7.4360
asc_B4_a 1.07005 1.24818 0.8573
asc_B4_b 2.60384 2.37347 1.0971
asc_B4_c 1.61577 0.36656 4.4079
asc_PAYG 0.00000 NA NA
delta_a 0.42021 0.13676 3.0726
delta_b -0.13113 0.14606 -0.8978
delta_c 0.00000 NA NA
lambda_LV_a -0.78729 0.13964 -5.6381
lambda_LV_b -0.42306 0.17148 -2.4672
lambda_LV_c 0.00000 NA NA
b_MCH_a 0.03296 0.24049 0.1371
b_MCH_b -0.73826 0.61230 -1.2057
b_MCH_c 0.12785 0.09856 1.2972
b_CAH_a 0.24401 0.71344 0.3420
b_CAH_b -2.53679 1.94914 -1.3015
b_CAH_c 0.14874 0.16491 0.9019
b_EM_a -0.37514 0.12334 -3.0415
b_EM_b -0.62732 0.32762 -1.9148
b_EM_c -0.15226 0.10040 -1.5166
b_PR_a -0.44137 0.36023 -1.2252
b_PR_b -0.43282 1.00329 -0.4314
b_PR_c -0.02598 0.09474 -0.2743
zeta_CD1 1.73521 0.16621 10.4398
zeta_CD2 2.71063 0.24262 11.1723
zeta_CD4 4.02563 0.29291 13.7434
zeta_CD5 4.45080 0.33454 13.3043
zeta_CD6 3.37225 0.26283 12.8305
zeta_CD7 2.28034 0.20470 11.1399
zeta_CD8 3.03796 0.23142 13.1276
zeta_CD9 3.73711 0.29985 12.4631
tau_CD1_1 -3.82554 0.45097 -8.4830
tau_CD2_1 -4.21309 0.45834 -9.1921
tau_CD1_2 -3.61678 0.39429 -9.1729
tau_CD2_2 -3.59625 0.35573 -10.1094
tau_CD1_3 -2.60596 0.23272 -11.1981
tau_CD2_3 -2.27057 0.25613 -8.8648
tau_CD1_4 -0.58073 0.16934 -3.4294
tau_CD2_4 0.03925 0.22257 0.1763
tau_CD1_5 0.97796 0.18127 5.3951
tau_CD2_5 1.57724 0.25253 6.2458
tau_CD1_6 2.25044 0.21779 10.3330
tau_CD2_6 3.36239 0.31461 10.6875
tau_CD4_1 -4.63144 0.40368 -11.4731
tau_CD5_1 -6.17810 0.55894 -11.0533
tau_CD4_2 -3.88816 0.37140 -10.4689
tau_CD5_2 -5.10061 0.51292 -9.9443
tau_CD4_3 -1.87276 0.29973 -6.2481
tau_CD5_3 -3.61908 0.38591 -9.3781
tau_CD4_4 1.42150 0.34622 4.1058
tau_CD5_4 0.51628 0.35316 1.4619
tau_CD4_5 3.31428 0.38480 8.6130
tau_CD5_5 2.78717 0.37108 7.5110
tau_CD4_6 5.60829 0.53533 10.4763
tau_CD5_6 5.51474 0.50693 10.8788
tau_CD6_1 -4.48758 0.38863 -11.5473
tau_CD7_1 -4.04256 0.36352 -11.1207
tau_CD6_2 -3.82043 0.35832 -10.6620
tau_CD7_2 -3.40600 0.32646 -10.4333
tau_CD6_3 -2.64323 0.28486 -9.2790
tau_CD7_3 -2.53423 0.25466 -9.9516
tau_CD6_4 0.46556 0.27178 1.7130
tau_CD7_4 -0.51553 0.20370 -2.5309
tau_CD6_5 2.37568 0.30524 7.7829
tau_CD7_5 1.20880 0.21168 5.7106
tau_CD6_6 4.45780 0.37423 11.9120
tau_CD7_6 2.47954 0.24694 10.0409
tau_CD8_1 -3.55840 0.35509 -10.0211
tau_CD9_1 -4.57605 0.44083 -10.3806
tau_CD8_2 -3.02587 0.32696 -9.2544
tau_CD9_2 -3.53322 0.36081 -9.7926
tau_CD8_3 -1.67057 0.26208 -6.3744
tau_CD9_3 -1.98351 0.29375 -6.7523
tau_CD8_4 1.00452 0.26754 3.7546
tau_CD9_4 0.82893 0.29193 2.8395
tau_CD8_5 2.52434 0.29321 8.6093
tau_CD9_5 2.65529 0.33193 7.9995
tau_CD8_6 4.34079 0.39952 10.8651
tau_CD9_6 4.49737 0.38483 11.6867
Final LL: -7561.4127
Summary of class allocation for model component LC_model:
Mean prob.
Class_1 0.4474
Class_2 0.2454
Class_3 0.3073
Calculating log-likelihood at equal shares (LL(0)) for applicable models...
Calculating log-likelihood at observed shares from estimation data (LL(c)) for applicable models...
Calculating LL of each model component...
Calculating other model fit measures
INFORMATION: Your model took more than 10 minutes to estimate, so it was saved to file output/MNL_model.rds before calculating its covariance matrix. If calculation of the covariance matrix fails or is stopped before
finishing, you can load the model up to this point using apollo_loadModel. You may also want to inspect the approximate BHHH standard errors shown above to determine whether you wish to continue this
process.
Computing covariance matrix using numerical methods (numDeriv).
0%....25%....50%....75%....100% (332 NA values)
Computing covariance matrix using numerical methods (maxLik). This may take a while, no progress bar displayed.
WARNING: Some eigenvalues of the Hessian are positive, indicating convergence to a saddle point!
Please acknowledge the use of Apollo by citing Hess & Palma (2019) - doi.org/10.1016/j.jocm.2019.100170
Warning message:
In sqrt(diag(varcov)) : NaNs produced
>
> # model = apollo_estimate(apollo_beta, apollo_fixed, apollo_probabilities, apollo_inputs)
>
> # ################################################################# #
> #### MODEL OUTPUTS ####
> # ################################################################# #
>
> # ----------------------------------------------------------------- #
> #---- FORMATTED OUTPUT (TO SCREEN) ----
> # ----------------------------------------------------------------- #
>
> apollo_modelOutput(model)
Model run by Viet Hong Cung using Apollo 0.3.5 on R 4.3.2 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 : MNL
Model description : Simple MNL model MaaS bundle SP x LCCM 3C x LV
Model run at : 2025-11-04 17:07:10.861362
Estimation method : bfgs
Model diagnosis : successful convergence
Optimisation diagnosis : Saddle point found
hessian properties : Some eigenvalues are positive and others negative
maximum eigenvalue : 1393.792594
reciprocal of condition number : not calculated (Hessian is not negative definite)
Number of individuals : 488
Number of rows in database : 2440
Number of modelled outcomes : 6344
indic_CD1 : 488
indic_CD2 : 488
indic_CD4 : 488
indic_CD5 : 488
indic_CD6 : 488
indic_CD7 : 488
indic_CD8 : 488
indic_CD9 : 488
LC_model : 2440
Number of cores used : 16
Number of inter-individual draws : 500 (MLHS)
LL(start) : -9304.48
LL (whole model) at equal shares, LL(0) : -19120.69
LL (whole model) at observed shares, LL(C) : -17175.4
LL(final, whole model) : -7561.41
Rho-squared vs equal shares : 0.6045
Adj.Rho-squared vs equal shares : 0.6001
Rho-squared vs observed shares : 0.5598
Adj.Rho-squared vs observed shares : 0.5577
AIC : 15290.83
BIC : 15642.81
LL(0,indic_CD1) : -949.6
LL(final,indic_CD1) : -817.96
LL(0,indic_CD2) : -949.6
LL(final,indic_CD2) : -876.15
LL(0,indic_CD4) : -949.6
LL(final,indic_CD4) : -874.19
LL(0,indic_CD5) : -949.6
LL(final,indic_CD5) : -834.87
LL(0,indic_CD6) : -949.6
LL(final,indic_CD6) : -857.13
LL(0,indic_CD7) : -949.6
LL(final,indic_CD7) : -853.86
LL(0,indic_CD8) : -949.6
LL(final,indic_CD8) : -876.01
LL(0,indic_CD9) : -949.6
LL(final,indic_CD9) : -896.65
LL(0,Measurement_model) : -7596.83
LL(final,Measurement_model) : -5353.24
LL(0,LC_model) : -3927.03
LL(final,LC_model) : -2229.41
Estimated parameters : 84
Time taken (hh:mm:ss) : 01:56:50.98
pre-estimation : 00:00:45.24
estimation : 00:30:47.21
post-estimation : 01:25:18.52
Iterations : 95
Unconstrained optimisation.
Estimates:
Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0)
asc_B1_a 5.60443 0.96918 5.7826 2.71776 2.0622
asc_B1_b -0.91316 NaN NaN 0.60239 -1.5159
asc_B1_c 0.35246 0.39398 0.8946 0.96480 0.3653
asc_B2_a 3.91355 1.07472 3.6415 3.07004 1.2748
asc_B2_b -1.65458 0.43014 -3.8466 1.63106 -1.0144
asc_B2_c 2.41741 0.29856 8.0969 0.65601 3.6850
asc_B3_a 2.02469 1.60529 1.2613 4.72546 0.4285
asc_B3_b 1.18095 0.43210 2.7330 2.52718 0.4673
asc_B3_c 2.18018 0.42529 5.1264 0.89089 2.4472
asc_B4_a 1.07005 2.08729 0.5126 6.03586 0.1773
asc_B4_b 2.60384 2.16542 1.2025 6.72301 0.3873
asc_B4_c 1.61577 0.51387 3.1443 1.03433 1.5621
asc_PAYG 0.00000 NA NA NA NA
delta_a 0.42021 0.12735 3.2998 0.16817 2.4987
delta_b -0.13113 0.12413 -1.0564 0.18012 -0.7280
delta_c 0.00000 NA NA NA NA
lambda_LV_a -0.78729 0.13120 -6.0006 0.14852 -5.3008
lambda_LV_b -0.42306 0.13479 -3.1386 0.13103 -3.2288
lambda_LV_c 0.00000 NA NA NA NA
b_MCH_a 0.03296 NaN NaN 0.04434 0.7434
b_MCH_b -0.73826 0.66394 -1.1119 1.84104 -0.4010
b_MCH_c 0.12785 0.05115 2.4993 0.09033 1.4154
b_CAH_a 0.24401 0.12246 1.9927 0.34840 0.7004
b_CAH_b -2.53679 1.22832 -2.0652 2.66789 -0.9509
b_CAH_c 0.14874 0.10777 1.3802 0.16174 0.9196
b_EM_a -0.37514 0.14418 -2.6018 0.27793 -1.3498
b_EM_b -0.62732 0.30463 -2.0593 0.61422 -1.0213
b_EM_c -0.15226 0.09103 -1.6727 0.11531 -1.3205
b_PR_a -0.44137 0.22404 -1.9700 0.63499 -0.6951
b_PR_b -0.43282 0.22798 -1.8985 1.35005 -0.3206
b_PR_c -0.02598 NaN NaN 0.10752 -0.2417
zeta_CD1 1.73521 0.14055 12.3456 0.16997 10.2088
zeta_CD2 2.71063 0.19939 13.5943 0.23784 11.3967
zeta_CD4 4.02563 0.30216 13.3230 0.41153 9.7820
zeta_CD5 4.45080 0.35187 12.6488 0.46206 9.6325
zeta_CD6 3.37225 0.24800 13.5980 0.32978 10.2258
zeta_CD7 2.28034 0.17485 13.0419 0.21536 10.5885
zeta_CD8 3.03796 0.22660 13.4067 0.30947 9.8167
zeta_CD9 3.73711 0.28196 13.2540 0.35507 10.5249
tau_CD1_1 -3.82554 0.24719 -15.4763 0.22220 -17.2170
tau_CD2_1 -4.21309 0.25660 -16.4187 0.24648 -17.0929
tau_CD1_2 -3.61678 0.23064 -15.6812 0.20662 -17.5044
tau_CD2_2 -3.59625 0.21876 -16.4393 0.22719 -15.8294
tau_CD1_3 -2.60596 0.17118 -15.2233 0.17931 -14.5335
tau_CD2_3 -2.27057 0.15938 -14.2467 0.17152 -13.2376
tau_CD1_4 -0.58073 0.11889 -4.8844 0.13636 -4.2587
tau_CD2_4 0.03925 NaN NaN 0.08826 0.4447
tau_CD1_5 0.97796 0.13094 7.4688 0.18807 5.2001
tau_CD2_5 1.57724 0.14606 10.7986 0.17622 8.9506
tau_CD1_6 2.25044 0.17139 13.1303 0.24023 9.3680
tau_CD2_6 3.36239 0.24053 13.9793 0.30734 10.9404
tau_CD4_1 -4.63144 0.31897 -14.5198 0.41246 -11.2289
tau_CD5_1 -6.17810 0.44136 -13.9980 0.51492 -11.9981
tau_CD4_2 -3.88816 0.28183 -13.7960 0.37378 -10.4022
tau_CD5_2 -5.10061 0.36773 -13.8704 0.42101 -12.1152
tau_CD4_3 -1.87276 0.20831 -8.9905 0.29423 -6.3650
tau_CD5_3 -3.61908 0.29082 -12.4444 0.37192 -9.7309
tau_CD4_4 1.42150 0.21325 6.6659 0.30820 4.6122
tau_CD5_4 0.51628 0.18391 2.8072 0.27012 1.9113
tau_CD4_5 3.31428 0.28309 11.7073 0.39059 8.4853
tau_CD5_5 2.78717 0.27349 10.1910 0.40797 6.8319
tau_CD4_6 5.60829 0.42598 13.1655 0.58995 9.5064
tau_CD5_6 5.51474 0.44392 12.4229 0.60252 9.1528
tau_CD6_1 -4.48758 0.29648 -15.1363 0.39337 -11.4080
tau_CD7_1 -4.04256 0.27337 -14.7881 0.35949 -11.2452
tau_CD6_2 -3.82043 0.26146 -14.6118 0.34386 -11.1104
tau_CD7_2 -3.40600 0.23624 -14.4175 0.34417 -9.8962
tau_CD6_3 -2.64323 0.21349 -12.3813 0.29896 -8.8416
tau_CD7_3 -2.53423 0.19354 -13.0942 0.30428 -8.3288
tau_CD6_4 0.46556 0.16076 2.8960 0.21060 2.2106
tau_CD7_4 -0.51553 0.15331 -3.3626 0.32628 -1.5800
tau_CD6_5 2.37568 0.21581 11.0084 0.28491 8.3382
tau_CD7_5 1.20880 0.14786 8.1751 0.21905 5.5185
tau_CD6_6 4.45780 0.32374 13.7698 0.45579 9.7804
tau_CD7_6 2.47954 0.18675 13.2776 0.25318 9.7937
tau_CD8_1 -3.55840 0.24159 -14.7292 0.34242 -10.3919
tau_CD9_1 -4.57605 0.31373 -14.5860 0.36975 -12.3760
tau_CD8_2 -3.02587 0.21671 -13.9626 0.30473 -9.9298
tau_CD9_2 -3.53322 0.25893 -13.6457 0.31956 -11.0566
tau_CD8_3 -1.67057 0.17532 -9.5286 0.27001 -6.1870
tau_CD9_3 -1.98351 0.20436 -9.7058 0.28455 -6.9706
tau_CD8_4 1.00452 0.16976 5.9171 0.24176 4.1549
tau_CD9_4 0.82893 0.19804 4.1856 0.34023 2.4364
tau_CD8_5 2.52434 0.21465 11.7600 0.28289 8.9234
tau_CD9_5 2.65529 0.24170 10.9858 0.34687 7.6550
tau_CD8_6 4.34079 0.31664 13.7090 0.40637 10.6819
tau_CD9_6 4.49737 0.33850 13.2862 0.49667 9.0550
Summary of class allocation for model component LC_model:
Mean prob.
Class_1 0.4474
Class_2 0.2454
Class_3 0.3073
Code: Select all
Model run by Viet Hong Cung using Apollo 0.3.5 on R 4.3.2 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 : MNL
Model description : Simple MNL model MaaS bundle SP x LCCM 3C x LV
Model run at : 2025-11-04 17:07:10.861362
Estimation method : bfgs
Model diagnosis : successful convergence
Optimisation diagnosis : Saddle point found
hessian properties : Some eigenvalues are positive and others negative
maximum eigenvalue : 1393.792594
reciprocal of condition number : not calculated (Hessian is not negative definite)
Number of individuals : 488
Number of rows in database : 2440
Number of modelled outcomes : 6344
indic_CD1 : 488
indic_CD2 : 488
indic_CD4 : 488
indic_CD5 : 488
indic_CD6 : 488
indic_CD7 : 488
indic_CD8 : 488
indic_CD9 : 488
LC_model : 2440
Number of cores used : 16
Number of inter-individual draws : 500 (MLHS)
LL(start) : -9304.48
LL (whole model) at equal shares, LL(0) : -19120.69
LL (whole model) at observed shares, LL(C) : -17175.4
LL(final, whole model) : -7561.41
Rho-squared vs equal shares : 0.6045
Adj.Rho-squared vs equal shares : 0.6001
Rho-squared vs observed shares : 0.5598
Adj.Rho-squared vs observed shares : 0.5577
AIC : 15290.83
BIC : 15642.81
LL(0,indic_CD1) : -949.6
LL(final,indic_CD1) : -817.96
LL(0,indic_CD2) : -949.6
LL(final,indic_CD2) : -876.15
LL(0,indic_CD4) : -949.6
LL(final,indic_CD4) : -874.19
LL(0,indic_CD5) : -949.6
LL(final,indic_CD5) : -834.87
LL(0,indic_CD6) : -949.6
LL(final,indic_CD6) : -857.13
LL(0,indic_CD7) : -949.6
LL(final,indic_CD7) : -853.86
LL(0,indic_CD8) : -949.6
LL(final,indic_CD8) : -876.01
LL(0,indic_CD9) : -949.6
LL(final,indic_CD9) : -896.65
LL(0,Measurement_model) : -7596.83
LL(final,Measurement_model) : -5353.24
LL(0,LC_model) : -3927.03
LL(final,LC_model) : -2229.41
Estimated parameters : 84
Time taken (hh:mm:ss) : 01:56:50.98
pre-estimation : 00:00:45.24
estimation : 00:30:47.21
post-estimation : 01:25:18.52
Iterations : 95
Unconstrained optimisation.
Estimates:
Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0)
asc_B1_a 5.60443 0.96918 5.7826 2.71776 2.0622
asc_B1_b -0.91316 NaN NaN 0.60239 -1.5159
asc_B1_c 0.35246 0.39398 0.8946 0.96480 0.3653
asc_B2_a 3.91355 1.07472 3.6415 3.07004 1.2748
asc_B2_b -1.65458 0.43014 -3.8466 1.63106 -1.0144
asc_B2_c 2.41741 0.29856 8.0969 0.65601 3.6850
asc_B3_a 2.02469 1.60529 1.2613 4.72546 0.4285
asc_B3_b 1.18095 0.43210 2.7330 2.52718 0.4673
asc_B3_c 2.18018 0.42529 5.1264 0.89089 2.4472
asc_B4_a 1.07005 2.08729 0.5126 6.03586 0.1773
asc_B4_b 2.60384 2.16542 1.2025 6.72301 0.3873
asc_B4_c 1.61577 0.51387 3.1443 1.03433 1.5621
asc_PAYG 0.00000 NA NA NA NA
delta_a 0.42021 0.12735 3.2998 0.16817 2.4987
delta_b -0.13113 0.12413 -1.0564 0.18012 -0.7280
delta_c 0.00000 NA NA NA NA
lambda_LV_a -0.78729 0.13120 -6.0006 0.14852 -5.3008
lambda_LV_b -0.42306 0.13479 -3.1386 0.13103 -3.2288
lambda_LV_c 0.00000 NA NA NA NA
b_MCH_a 0.03296 NaN NaN 0.04434 0.7434
b_MCH_b -0.73826 0.66394 -1.1119 1.84104 -0.4010
b_MCH_c 0.12785 0.05115 2.4993 0.09033 1.4154
b_CAH_a 0.24401 0.12246 1.9927 0.34840 0.7004
b_CAH_b -2.53679 1.22832 -2.0652 2.66789 -0.9509
b_CAH_c 0.14874 0.10777 1.3802 0.16174 0.9196
b_EM_a -0.37514 0.14418 -2.6018 0.27793 -1.3498
b_EM_b -0.62732 0.30463 -2.0593 0.61422 -1.0213
b_EM_c -0.15226 0.09103 -1.6727 0.11531 -1.3205
b_PR_a -0.44137 0.22404 -1.9700 0.63499 -0.6951
b_PR_b -0.43282 0.22798 -1.8985 1.35005 -0.3206
b_PR_c -0.02598 NaN NaN 0.10752 -0.2417
zeta_CD1 1.73521 0.14055 12.3456 0.16997 10.2088
zeta_CD2 2.71063 0.19939 13.5943 0.23784 11.3967
zeta_CD4 4.02563 0.30216 13.3230 0.41153 9.7820
zeta_CD5 4.45080 0.35187 12.6488 0.46206 9.6325
zeta_CD6 3.37225 0.24800 13.5980 0.32978 10.2258
zeta_CD7 2.28034 0.17485 13.0419 0.21536 10.5885
zeta_CD8 3.03796 0.22660 13.4067 0.30947 9.8167
zeta_CD9 3.73711 0.28196 13.2540 0.35507 10.5249
tau_CD1_1 -3.82554 0.24719 -15.4763 0.22220 -17.2170
tau_CD2_1 -4.21309 0.25660 -16.4187 0.24648 -17.0929
tau_CD1_2 -3.61678 0.23064 -15.6812 0.20662 -17.5044
tau_CD2_2 -3.59625 0.21876 -16.4393 0.22719 -15.8294
tau_CD1_3 -2.60596 0.17118 -15.2233 0.17931 -14.5335
tau_CD2_3 -2.27057 0.15938 -14.2467 0.17152 -13.2376
tau_CD1_4 -0.58073 0.11889 -4.8844 0.13636 -4.2587
tau_CD2_4 0.03925 NaN NaN 0.08826 0.4447
tau_CD1_5 0.97796 0.13094 7.4688 0.18807 5.2001
tau_CD2_5 1.57724 0.14606 10.7986 0.17622 8.9506
tau_CD1_6 2.25044 0.17139 13.1303 0.24023 9.3680
tau_CD2_6 3.36239 0.24053 13.9793 0.30734 10.9404
tau_CD4_1 -4.63144 0.31897 -14.5198 0.41246 -11.2289
tau_CD5_1 -6.17810 0.44136 -13.9980 0.51492 -11.9981
tau_CD4_2 -3.88816 0.28183 -13.7960 0.37378 -10.4022
tau_CD5_2 -5.10061 0.36773 -13.8704 0.42101 -12.1152
tau_CD4_3 -1.87276 0.20831 -8.9905 0.29423 -6.3650
tau_CD5_3 -3.61908 0.29082 -12.4444 0.37192 -9.7309
tau_CD4_4 1.42150 0.21325 6.6659 0.30820 4.6122
tau_CD5_4 0.51628 0.18391 2.8072 0.27012 1.9113
tau_CD4_5 3.31428 0.28309 11.7073 0.39059 8.4853
tau_CD5_5 2.78717 0.27349 10.1910 0.40797 6.8319
tau_CD4_6 5.60829 0.42598 13.1655 0.58995 9.5064
tau_CD5_6 5.51474 0.44392 12.4229 0.60252 9.1528
tau_CD6_1 -4.48758 0.29648 -15.1363 0.39337 -11.4080
tau_CD7_1 -4.04256 0.27337 -14.7881 0.35949 -11.2452
tau_CD6_2 -3.82043 0.26146 -14.6118 0.34386 -11.1104
tau_CD7_2 -3.40600 0.23624 -14.4175 0.34417 -9.8962
tau_CD6_3 -2.64323 0.21349 -12.3813 0.29896 -8.8416
tau_CD7_3 -2.53423 0.19354 -13.0942 0.30428 -8.3288
tau_CD6_4 0.46556 0.16076 2.8960 0.21060 2.2106
tau_CD7_4 -0.51553 0.15331 -3.3626 0.32628 -1.5800
tau_CD6_5 2.37568 0.21581 11.0084 0.28491 8.3382
tau_CD7_5 1.20880 0.14786 8.1751 0.21905 5.5185
tau_CD6_6 4.45780 0.32374 13.7698 0.45579 9.7804
tau_CD7_6 2.47954 0.18675 13.2776 0.25318 9.7937
tau_CD8_1 -3.55840 0.24159 -14.7292 0.34242 -10.3919
tau_CD9_1 -4.57605 0.31373 -14.5860 0.36975 -12.3760
tau_CD8_2 -3.02587 0.21671 -13.9626 0.30473 -9.9298
tau_CD9_2 -3.53322 0.25893 -13.6457 0.31956 -11.0566
tau_CD8_3 -1.67057 0.17532 -9.5286 0.27001 -6.1870
tau_CD9_3 -1.98351 0.20436 -9.7058 0.28455 -6.9706
tau_CD8_4 1.00452 0.16976 5.9171 0.24176 4.1549
tau_CD9_4 0.82893 0.19804 4.1856 0.34023 2.4364
tau_CD8_5 2.52434 0.21465 11.7600 0.28289 8.9234
tau_CD9_5 2.65529 0.24170 10.9858 0.34687 7.6550
tau_CD8_6 4.34079 0.31664 13.7090 0.40637 10.6819
tau_CD9_6 4.49737 0.33850 13.2862 0.49667 9.0550
Summary of class allocation for model component LC_model:
Mean prob.
Class_1 0.4474
Class_2 0.2454
Class_3 0.3073